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タイトル Microstructure and Chemical Properties of Cement Treated Soft Bangladesh Clays
著者 "Md. Mokhlesur Rahman, Abu Siddique, MD. Kamal Uddin"
出版 Soils and Foundations Vol.50 No.1
ページ 1〜7 発行 2010/02/15 文書ID 64337
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タイトル Effects on Reliquefaction Resistance Produced by Changes in Anisotropy during Liquefaction
著者 "Shotaro Yamada, Tomoko Takamori, Kenichi Sato"
出版 Soils and Foundations Vol.50 No.1
ページ 9〜25 発行 2010/02/15 文書ID 64338
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タイトル Experimental Study on the Behavior of Unsaturated Compacted Silt under Triaxial Compression
著者 "Fusao Oka, Takeshi Kodaka, Hirotaka Suzuki, Y. S. Kim, Norisuke Nishimatsu, Sayuri Kimoto"
出版 Soils and Foundations Vol.50 No.1
ページ 27〜44 発行 2010/02/15 文書ID 64339
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タイトル Stress-strain Relationships and Nonlinear Mohr Strength Criteria of Frozen Sandy Clay
著者 "L. Yuanming, G. Zhihua, Z. Shujuan, C. Xiaoxiao"
出版 Soils and Foundations Vol.50 No.1
ページ 45〜53 発行 2010/02/15 文書ID 64340
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タイトル Characterization of the Fouled Ballast Layer in the Substructure of a 19th Century Railway Track under Renewal
著者 "E. Fortunato, A. Pinelo, M. M. Fernandes"
出版 Soils and Foundations Vol.50 No.1
ページ 55〜62 発行 2010/02/15 文書ID 64341
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タイトル Load Tests of Piled Raft Models with Different Pile Head Connection Conditions and Their Analyses
著者 "Tatsunori Matsumoto, Hisashi Nemoto, Hiroshi Mikami, Kou Yaegashi, Toshiaki Arai, P. Kitiyodom"
出版 Soils and Foundations Vol.50 No.1
ページ 63〜81 発行 2010/02/15 文書ID 64342
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タイトル Stability Analysis of Slope with Water Flow by Strength Reduction Method
著者 "W. B. Wei, Y. M. Cheng"
出版 Soils and Foundations Vol.50 No.1
ページ 83〜92 発行 2010/02/15 文書ID 64343
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タイトル Effects of Sampling Tube Geometry on Soft Clayey Sample Quality Evaluated by Nondestructive Methods
著者 "V. Horng, Hiroyuki Tanaka, Takashi Obara"
出版 Soils and Foundations Vol.50 No.1
ページ 93〜107 発行 2010/02/15 文書ID 64344
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タイトル Proposal of a Simple Method for Assessing the Susceptibility of Naturally Deposited Clay Grounds to Large Long-term Settlement due to Embankment Loading
著者 "Motohiro Inagaki, Masaki Nakano, Toshihiro Noda, Mutsumi Tashiro, Akira Asaoka"
出版 Soils and Foundations Vol.50 No.1
ページ 109〜122 発行 2010/02/15 文書ID 64345
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タイトル Estimation of the Air Permeability Coefficient and the Radius of Vacuum Influence for Contaminated Soil and Groundwater Remediation
著者 "Yoshihiko Hibi, Kenji Jinno, Kentaro Masuoka, Junichi Kawabata"
出版 Soils and Foundations Vol.50 No.1
ページ 123〜142 発行 2010/02/15 文書ID 64347
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タイトル Investigation for Necessity of Dispersivity and Tortuosity in the Dusty Gas Model for a Binary Gas System in Soil
著者 "Yoshihiko Hibi, Katsuyuki Fujinawa, Seiji Nishizaki, Kazuo Okamura, Masaharu Tasaki"
出版 Soils and Foundations Vol.50 No.1
ページ 143〜159 発行 2010/02/15 文書ID 64348
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タイトル Effects of Dry Density and Grain Size Distribution on Soil-Water Characteristic Curves of Sandy Soils
著者 "C. P. K. Gallage, Taro Uchimura"
出版 Soils and Foundations Vol.50 No.1
ページ 161〜172 発行 2010/02/15 文書ID 64349
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タイトル The Effect of Fines on Critical State and Liquefaction Resistance Characteristics of Non-Plastic Silty Sands
著者 C. A. Stamatopoulos
出版 Soils and Foundations Vol.50 No.1
ページ 173〜176 発行 2010/02/15 文書ID 64350
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タイトル The Effect of Fines on Critical State and Liquefaction Resistance Characteristics of Non-Plastic Silty Sands (closure)
著者 "A. Papadopoulou, T. Tika"
出版 Soils and Foundations Vol.50 No.1
ページ 176〜176 発行 2010/02/15 文書ID 64351
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  • Soils and Foundations Vol.50 No.1
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  • Microstructure and Chemical Properties of Cement Treated Soft Bangladesh Clays
  • 著者
  • "Md. Mokhlesur Rahman, Abu Siddique, MD. Kamal Uddin"
  • 出版
  • Soils and Foundations Vol.50 No.1
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  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 1–7, Feb. 2010MICROSTRUCTURE AND CHEMICAL PROPERTIES OFCEMENT TREATED SOFT BANGLADESH CLAYSMD. MOKHLESUR RAHMANi), ABU SIDDIQUEii) and MD. KAMAL UDDINiii)ABSTRACTThis paper examines the relationship between the microstructure and chemical properties of soft Bangladesh claysdue to cementation. The microstructure was investigated using X-ray diŠraction, scanning electron microscopy, pHmeasurement, speciˆc surface area and soil chemical tests. The results indicate that a multitude of changes occurred inthe properties and behavior of cement-treated clays that can be explained by the interaction between four underlyingmicrostructural mechanisms. That is, it is suggested that the hydrated lime is formed by hydration, which causes the‰occulation of the little clay particles, by the preferential attack of the calcium ions on kaolinite rather than on illiteand monmorillinite in the pozzolanic reaction, by surface deposition and shallow inˆlling by cementitious productssuch as calcium silicate hydrate and calcium alumino silicate hydrate (CSH and CASH) on clay clusters, and ˆnally, bythe presence of water trapped within the clay clusters. The chemical properties of the cement-treated clays were foundto depend on the plasticity of soil.Key words: cement treated clay, cementation bond, clay clusters, clay-water/cement ratio, fabric, high water content,microscopy, microstructure, mineralogy, soil chemical test (IGC: F2)improvement process. Even so, the engineering behaviorof cemented soil outlined above appears to indicate thatapart from an increase in strength a new type of structureis established.The microstructure of lime-treated clays has been studied by Locat et al. (1990) among others. However, the absence of the primary hydration reaction in lime treatmentmay lead to a diŠerent microstructure than that producedby cement treatment (Chew et al., 2002). In regions wherelime is not available cheaply, cement may be preferred asan additive due to the faster strength development thatresults from the hydration reaction. However, therelationship between the observed microstructures in improved soil has not been completely clariˆed to date.This paper examines the development of the microstructure of cement-treated soft clay and its relation tothe change in chemical properties. The soft clay used inthis study is Bangladesh soft clays with high water content in low land areas, which are inorganic clays of various plasticity, including high plastic (HP), medium plastic (MP) and low plastic (LP) clays. The mineralogy andmicrostructure of cement-treated soft Bangladesh clayshave been examined for the ˆrst time using X-ray diŠraction and a scanning electron microscope. The grain sizesof the cement-treated soil matrix were then examined by aspeciˆc surface area test. Finally, the changes in theINTRODUCTIONThe improvement of the properties of cement-treatedsoil has been attributed to the soil-cement reaction, whichproduces primary and secondary cementitious materialsin the soil-cement matrix (Chew et al., 2002; Kamruzzaman et al., 2002). The primary cementitious materials areformed by a hydration reaction and are comprised ofhydrated calcium silicates (C2SH4, C3S3H4), calciumaluminates (C3AH4, C4AH4), and hydrated lime,Ca(OH)2. A secondary pozzolanic reaction between thehydrated lime, the silica and alumina from the clayminerals leads to the formation of additional calcium silicate hydrates and calcium aluminate hydrates. This soilcement reaction provides a clear basis on which the improvement in strength of stabilized soil can be explained.Another property that can aŠect the addition of cementto soil is its permeability (Chew et al., 2004). While thechemical properties are known (Head, 1990; Bigham,1996; SRDI, 2002; Mokhlesur, 2008), it remains unclearwhat type of structure is induced in the soil-cement mixby the changing chemical properties. Many processes ofintroducing cement into soft ground, such as jet groutingand deep cement mixing, involve a large amount of mixing and remolding of in situ soil. Hence, the in-situ structure of the soil is likely to be destroyed at the end of thei)ii)iii)Associate Professor, Department of Civil Engineering, Dhaka University of Engineering and Technology, Gazipur, Bangladesh (mokhlesur_2005@yahoo.com).Professor, Department of Civil Engineering, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.Professor, Institute of Appropriate Technology, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh.The manuscript for this paper was received for review on July 2, 2007; approved on December 2, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.1 RAHMAN ET AL.2chemical properties of the cement-treated soil were investigated and clariˆed in terms of the soil-cement reactionand induced microstructure.EXPERIMENTAL INVESTIGATIONSoil SampleClays were collected in various districts of Bangladesh:HP clay was taken from Gazipur, MP clay was takenfrom Gopalgonj and LP clay was taken from Khulna.The soils were collected from a depth of 2–3 m from existing ground level in both disturbed and undisturbedstates. Their basic physical properties are listed in Table1. Type I Portland cement was used in this study. Samples were prepared from these clays and cement slurries.Table 1. Characteristics value of the basic physical properties of theuntreated claysPropertiesCharacteristics ValuesType of SoilMP clayLP clayHP clay(LLÀ50z) (LL=35–50z) (LLº35z)Liquid limit, LL (z)784733Plastic limit, PL (z)312520Plasticity index, PI (z)472213Natural water content, wn (z)493627Clay (z), Size rangeº0.002 mm734132Silt (z), Size range0.002–0.075 mm235158Sand (z), Size range0.075–1.0 mm4810The chemical properties for untreated and treated claysare presented in Table 2.Methodology for Reconstituted Soil Sample PreparationThe clay paste was passed through a 2-mm sieve for theremoval of shell pieces and other bigger size particles.The intentional increase in water content is designed tosimulate the increase inwater content that takes place inthe wet method of dispensing cement admixture in deepsoil mixing. Cement quantities of 4z, 8z, 12z, 16z,30z and 60z were thoroughly mixed so as to ensureuniform dispersion of the cementing agent. The initialcontent of the mixing water used was 120z. The cementcontent was in the ratio of the mass of cement to the massof soil solid. The mixing time was arbitrarily ˆxed at 10minutes. Samples of the uniform paste of this mixturewere transferred to cylindrical split moulds of 50 mm indiameter×100 mm in height connected with 50 mmheight top collars and a bottom ended cap to prevent anyair entrapment. After 24 hours the cylindrical sampleswere dismantled. All the cylindrical samples werewrapped in thick polythene bags and these were stored ina room of constant temperature (25±29C) until the lapseof the desired planned curing times.RESULTS AND DISCUSSIONX-Ray DiŠraction AnalysisX-ray diŠraction (XRD) analysis of untreated andcement treated Bangladesh clays was carried out using aPhilips PW 3040 X'Pert-PRO X-ray difractometer. XRDpatterns were obtained using a Cu Ka (l=1.54178 Å)X-ray tube with input voltage of 40 kV and current of 30mA. A continuous scan mode and a scan rate of 2-degreeTable 2. Characteristics values of the basic chemical properties of the untreated (cement=0%) and treated clays at 4 week curing (water=120%and cement=8% and 16%)PropertiesCharacteristics ValuesTypes of clayHP clay8zMP clay0z8z12.56.69.610.019.234.563.062.173.943.332.544.431.442.613.041.132.212.940.931.86Organic carbon (z)2.560.831.861.760.651.281.700.541.08EC (ds/m)0.235.217.560.923.234.490.784.165.56Nitrogen (z)0.0370.0720.1020.0270.0680.0970.0240.0410.093P (mg/g)4.629.68Cement0zpH value8.310.5Loss on ignition (z)11.39Organic matter (z)CEC (meq/100 g)Ca2+Mg2+12.286.2316z11.911.5614.130z7.87.748z10.216z12.413.2318.8225.533.646.017.526.736.623.130.742.3(meq/100 g)16.727.232.010.723.224.012.124.826.6(meq/100 g)5.84.83.63.33.02.74.53.82.90.210.410.620.350.570.670.260.460.660.270.570.850.450.690.880.330.610.76+Na (meq/100 g)+16zLP clayK (meq/100 g)Note: EC=Electrical conductivity, P=Phosphorus and CEC=Cation exchange capacity. CEMENT TREATED SOFT BANGLADESH CLAYTable 3.3Semi-quantitative proportions of clay minerals cementitious compounds (wi=120%, Particle Size º63 mm and Curing=4 w)Normalized mass ofmineral (z)Untreated claysTreated 16z cement claysTreated 30z cement claysTreated 60z cement claysLP clayHP clayLP clayHP clayLP clayHP clayLP clayHP clayTotal mass (z)100100116116130130160160Illite (z)2119918615410Smectite (z)91231189108Quartz (z)6461605765586864Kaolinite (z)68000000CSH +CASH (z)00303850527582Fig. 1. X-Ray diffraction patterns of untreated clays (a) LP clay and(b) HP clayFig. 2. X-Ray diŠraction patterns of 16% cement treated clays (a) LPclay and (b) HP clayper minute were selected. The air-dried powdered samples (particle size less than 63 mm) of treated and untreated soil samples were used. A u-2u scan was taken from 69to 609to get the possible fundamental peaks of the minerals present in the sample with a sampling pitch of 0.029and the time for each step data collection was 0.6 sec. Thesamples were maintained in an Al-sample holder withdimensions of 15×10×2 mm3. The samples were nottreated for ion-saturation prior to scanning. The clayminerals contained in the cohesive soil demonstrate thatphysicochemical interactions with hardening agents aŠectthe properties of the treated soil, so it is necessary to investigate the mineral compositions and the relationshipsbetween the minerals in these soils. The basic mineralogical properties of the treated and untreated clays are summarized in Table 3. The clay mineral constituents of theuntreated clays were identiˆed as illite, smectite, quartzand kaolinite using the selected peaks. A silt fraction wasalso identiˆed in the base clay. The mineral quantiˆcations were calculated from the respective peaks, as shown Fig. 3. X-Ray diŠraction patterns of 30% cement treated clays (a) LPclay and (b) HP clayin Figs. 1 to 4. By multiplying the average height (keps),and average width (degree) of peaks, the unit volume/ 4RAHMAN ET AL.Fig. 6.SEM typical image of untreated reconstituted HP clayFig. 4. X-Ray diŠraction patterns of 60% cement treated clays (a) LPclay and (b) HP clayFig. 5. Relationship between cement content and cementitiousproducts (CSH+CASH) of treated clays (wi=120% and curing=4weeks)unit mass of mineral was found. By adding the unit massof minerals and proportionate illite, smectite, quartz andCSH+CASH, the total masses (100z, 116z, 130z and160z) were shown to be distributed according to proportionate values for ˆnding normalized mass in percentages. The silt fraction was found to contain mainlyquartz and a smaller fraction of feldspar. Other cementitious products, such as calcium silicate hydrate (CSH)and calcium alumino silicate hydrate (CASH) were foundto be present in the 16z, 30z and 60z cement treatedclays, as shown in Figs. 2, 3 and 4, respectively.In Fig. 5, the mass of CSH and CASH was normalizedby the mass of the treated soil solid and this quantity istermed as the cementitious product content and theseproducts increase non linearly at low amounts of cementcontent (0–30z) and increase linearly when the cementcontent is higher (30–60z). This suggests that when thecement content is up to 15z, the rate of increase in CSHand CASH content is higher. The change in compositionof the treated clay can be seen from Table 3, whereFig. 7. SEM typical image of cement-treated HP clay (wi=120% andcuring=12 weeks) (a) 16% cement, (b) 30% cement and (c) 60%cementkaolinite appears to have vanished in all six of thecement-treated soil specimens. This suggests thatkaolinite is rapidly exhausted by the pozzolanic reaction,which is consistent with the rapid increase in cementitiousproduct content. Similar ˆndings were also reported byChew et al. (2004).Scanning Electron Microscope AnalysisScanning electron microscope (SEM) analyses of treated and untreated clay were carried out using Philips 4100,model XL–30 in order to understand the bridging(cementation) eŠect and indicate the microstructure ofthe weak failure zone in the cement-treated clay matrix.Figure 6 shows typical SEM images of untreated HP clay CEMENT TREATED SOFT BANGLADESH CLAYof an open type of microstructure with the ‰at clay particles assembled in a dispersed arrangement. However, themicrographs of 16z, 30z and 60z cement treated clayafter 12 weeks of curing time exhibit some sign of reticulation, as is shown in Fig. 7. As the cement content increases, the ‰occulated nature of the structure becomesmore evident with clay particle clusters being interspersedwith large openings. As the curing time increases from 1to 12 weeks, the ‰occulated nature of the structurebecomes more and more evident with the formation ofclay-cement clusters. At the same time, areas of ‰atnessin the structure become less evident and the degree ofreticulation appears to increase. The increase in thedegree of reticulation and formation of clay cementclusters is considered to be due to the formation ofcementitious products (CSH+CASH). This ˆnding wasalso reported by Chew et al. (2002).Chemical PropertiesThe chemical tests were conducted with the referenceBS 1377 (BS, 1990) from the soil suspensions of untreatedand cement treated clays. The chemical properties of theuntreated and treated clays (curing time=4 and 12 weeks,mixing water content=120z and cement content=8z,16z, 30z and 60z) were compared and are partlypresented in Table 2. The loss of ignition for treated clayswas lower than those of untreated clays because the increased ignition resistance due to cementation. The lossof ignition was determined by the percentage of weightdiŠerence between the following conditions: 110±59Ctemperatures during 24 hours, and 445±109C temperatures during 6 hours. The reduction in organic matter andorganic carbon in the treated clays was due to the cementtreatment. In soil samples without CaCO3, the total carbon content was determined with the LECO C-200Analyzer as being equal to the organic carbon content.The z organic carbon was equal to the z total carbon-0.12×z CaCO3 and the z organic matter was equalto z organic carbon×1.724.The salinity of clay was measured by the electrical conductivity (EC) test. The amount of salt dissolved in thepore water is responsible for the amount of soluble cations. The EC was measured by the Metrohm 644 ECmeter for the preparation of 1:5 soil-water extract. TheEC values for treated clays are found to increase 33, 5and 7 times for HP, MP and LP clays, respectively, dueto cementation of up to 16z. The phenomenon of thereplacement of cations is referred to as the cation exchange capacity (CEC). The CEC values for 16z cementtreated clays were found to increase 1.80, 1.44 and 1.66times for HP, MP and LP clays respectively after chemical reactions after 4 weeks of curing. The exchangeablecations, Ca2+, Mg2+, K+ and Na+ were identiˆed and estimated for untreated and treated clays. The Ca2+ andMg2+ were determined by atomic absorption spectrometer and K+ and Na+ were determined by ‰ame photometer from soil extraction. The cations, Ca2+, K+ and Na+were found to increase while Mg2+ decreased due tocementation for each type of clay. The engineering prop-5erties of treated clays are governed by the chemical properties due to cementation. The total nitrogen (N) was determined by the Kjeldahl method involving 3 steps, namely digestion, distillation and titration. The amount of Pfrom the soil solution extract was measured spectrophotometrically. The amount of nitrogen and phosphorus in the soil has no role in the strength or deformationfunction but has a remarkable role in the soil fertilizationfunction. The eŠects of cement stabilization on the environment of treated soils was explained here by theamounts of nitrogen and phosphorus.Grain Size Distribution and Surface Area DistributionThe grain size and speciˆc surface area of soil were determined by hydrometer apparatus and by the Flowsorb2300 model apparatus, respectively. The percent of clay,silt and sand is shown in Table 1. The grain size is indicated in Fig. 8. The changes in grain size distribution due tocement treatment were rather di‹cult to determine accurately (Kamaluddin et al., 1997). The usual hydrometermethod did not render a true picture for the cementationof soil, so rather than discuss the grain size distribution,the focus was shifted to one of the speciˆc surface areadistribution. The surface area of the soil sample was calculated by the BET method. Secondary cementitiousproducts appear to be deposited on or near the speciˆcsurfaces of the clay clusters. This gives rise to a reductionFig. 8.Comparison of grain size distribution curve for three claysFig. 9. EŠect of type of clay, cement content and curing time onspeciˆc surface area for untreated and treated clays (wi=120%) 6RAHMAN ET AL.in entrance pore diameter but an increase in particle size.This, in turn, leads to a reduction in permeability. TheeŠect depending on the type of clay and the amount of cement on speciˆc surface area is shown in Fig. 9. It may beconcluded that the surface area and pore size of changedsoil changed according to the cement content, curing timeand plasticity of soil. The more the cement content usedfor ˆnal product, the larger the grain size/surface areaand the increase in pore size of the soil during chemicalstabilizations. As the curing time increased, the speciˆcsurface area and pore size were found to decrease. Therefore, it would be wrong to assume that the particle sizedecreases by noting the larger pore size. Thus, cementstabilization especially with high water content clay slurrydoes not necessarily make the soil less porous. In fact, insuch a case, the porosity signiˆcantly increases.Water Content and pH ValueFigure 10 shows the variation of ˆnal water content forthe cement treated clays after periods of immediate mixing and 4 weeks curing. The immediate reduction of thewater content from that of the slurry clay is due to the addition of dry cement; therefore, it should be regarded asthe initial water content. For less reduction of water, soilswith higher plasticity were observed because of their highwater holding capacity. This is not surprising since wateris absorbed and transformed into hydrated CSH andCASH during the hydration and pozzolanic reactions. Athigher cement content, the exhaustion of the kaolinitefurther inhibits the pozzolanic reaction leaving only thehydration reaction. Thus, the increase in water used wasmoderated at higher cement content due to the rapidhydration reaction compared to the pozzolanic reactionat short curing times. In the case of longer curing times,the water lost was consumed largely by the pozzolanicreaction. With the help of the Metrohm 691 pH meter,the pH was determined for 1:2.5 soil-water extract fromuntreated and treated clays. The pH values of the baseclays were found to be 8.3, 6.6 and 7.8 for HP clay, MPclay and LP clay, respectively. The pH value, the electrical conductivity, the number of exchangeable cations andˆnally the amount of cementitious products for MP clay(PI=22z) may explain why the HP clay and LP clay arealkaline in nature while MP clay, which has exchangeableH+ ion, is acidic. It is said that MP clays have a largereserve of potential acidity or buŠering capacity, which isdeˆned as the capacity of the soil to release exchangeableH+ ion into the soil solution to restore the equilibriumpH. It should be noted that no soil reaction takes placewith cement until the reserve H+ ion is exhausted. Figure11 shows the pH value of the treated soil at various cement contents with 4 and 12 weeks curing for various softBangladesh clays. It can be seen that the pH value risesrapidly at lower cement content but the rate of the risewas moderate at higher cement content. The pH valuedecreases with increasing curing time and increases withincreasing strength of soil. At very high cement content,the pH value approaches 12.5, corresponding to that ofCa(OH)2. The increase of pH with increased cement con-Fig. 10. EŠect of type of clay, curing time and cement content on ˆnalwater contentFig. 11. Variation of pH value with cement contents of treated clays atvarious curing (wi=120%)tent is due to crowding of the Ca+2 ion concentration onthe clay surface leading to changes in the fabric of thecement-treated clay (i.e., the formation of a ‰occulatedclay-cement matrix), as explained earlier. A similar eŠectof pH on the fabric changes of such clay-water-electrolytesystem was reported by Chew et al. (2004).CONCLUSIONSOur investigation revealed the various facets of the behavior of soft clay due to cementation, which have beenexplained by the interplay of a few underlying chemicaland micro-structural mechanisms. The mixing of cementslurry into soft Bangladesh clays leads to an immediateincrease in the water content due to the additional waterin the slurry. The hydration reaction of the cement follows shortly, leading to a decrease in water content andthe formation of primary cementitious products as wellas hydrated lime. The calcium ions released by thehydrated lime give rise to a ‰occulated clay structurecomprising of clay clusters separated by large intracluster voids. The ‰occulation of the clay particles alsocauses water to be trapped within the cluster and a changeto take place in the microstructure.The rapid hydration reaction is accompanied by themuch slower pozzolanic reaction over time. The ˆndingsof this study indicate that in the pozzolanic reaction,kaolinite is preferentially attacked in comparison to illiteand smectite. For cement content above 15z, this leadsto the complete disappearance of the kaolinite. The sec- CEMENT TREATED SOFT BANGLADESH CLAYondary cementitious products are deposited on or nearthe speciˆc surfaces of the clay clusters. This gives rise toa reduction in the entrance pore diameter, but also an increase in particle size. The deposition of secondarycementitious products on the clay cluster, on the otherhand, leads to a decrease in surface activity of the illiteand smectite clusters. As a result, the chemical propertieschange over time and with a higher cement content.The results of this study also have showed that at a cement content of above ¿8z, the extent of pozzolanicreaction stabilizes to a limiting level. This has been supported by the changes in cementitious product, watercontent as well as chemical properties. The pH measurements show that this stabilization was not brought aboutby exhaustion of the lime but rather by the exhaustion ofthe kaolinite. This ˆnding was quite unexpected since illite is also pozzolanic. One possible explanation is thatpozzolanic reactions involving illite and smectite aremuch slower than that with kaolinite and also a muchhigher cement content is required to initiate the reactionThis would explain why kaolinite is preferentially attacked. As secondary cementitious products from thekaolinite driven pozzolanic reaction are deposited ontothe illite and smectite cluster surface, the clusters gradually become encapsulated by the cementitious products.This encapsulation protects the illite and smectite fromfurther attack by the lime and no further pozzolanic reaction occurs. Whatever the cause of the limited pozzolanicreaction, it is clear that in the case of cement, the microstructure may be a more eŠective stabilizing agent thanlime since the eŠectiveness of the latter can be hinderedby the lack of pozzolanic clay minerals. The results of this7study into the physicochemical behavior of soft Bangladesh clays at high water content by cementation leadto the conclusion that high plastic clay shows a betterresponse to soil improvement techniques than low plasticclay, which in turn has a better response than mediumplastic clay.REFERENCES1) Bigham, J. M. (1996): Methods of Soil Analysis Part-3 ChemicalMethods, Soil Science Society of America, Inc., USA.2) Chew, S. H., Kamruzzaman, A. H. M. and Lee, F. H. (2002):Structuration and destructuration behavior of cement treated clays,Journal of Geotechnique, 173–189.3) Chew, S. H., Kamruzzaman, A. H. M. and Lee, F. H. (2004):Physicochemical and engineering behavior of cement treated clays,Journal of Geotechnical and Geoenvironmental Engg., 53–71.4) Head, K. H. (1990): Soil Chemical Tests-Manual of Soil Testing.5) Imamul-Huq, S. M. and Didar-ul-Alam, M. (2000): A Handbookfor Chemical Test on Analyses of Soil, Plant and Water, Bangladesh-Australia Centre for Environmental Research.6) Kamaluddin, M., Balasubramaniam, A. S. and Bergado, D. T.(1997): Engineering behavior of cement-treated Bangkok soft clay,Geotech Eng., 28(1), 89–119.7) Kamruzzaman, A. H. M., Chew, S. H. and Lee, F. H. (2002):Microstructure of cement treated Singapore marine clay, Soils andFoundations, 80–90.8) Locat, J., Berube, M. A. and Choquette, M. (1990): Laboratory investigations on the lime stabilization of sensitive clay: Shearstrength development, Canadian Geoteh. Journal, 77–91.9) Mokhlesur, M. R. (2008): Investigation of strength and deformation characteristics of cement and lime treated soft clays, Ph. D.Thesis, BUET, Dhaka, Bangladesh.10) SRDI (2002): Analytical Methods Soil Water Plant Material Fertilizer Soil Resources Management, Soil Resources DevelopmentInstitute (SRDI), Danida Kampsax, Dhaka, 117–137.
  • ログイン
  • タイトル
  • Effects on Reliquefaction Resistance Produced by Changes in Anisotropy during Liquefaction
  • 著者
  • "Shotaro Yamada, Tomoko Takamori, Kenichi Sato"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 9〜25
  • 発行
  • 2010/02/15
  • 文書ID
  • 64338
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 9–25, Feb. 2010EFFECTS ON RELIQUEFACTION RESISTANCE PRODUCED BYCHANGES IN ANISOTROPY DURING LIQUEFACTIONSHOTARO YAMADAi), TOMOKO TAKAMORIii) and KENICHI SATOiii)ABSTRACTA distinctive characteristic of the reliquefaction behavior of soils is that there are instances where the phenomenonof a sharp decrease in liquefaction resistance occurs in spite of increases in soil density caused by drainage of water after liquefaction. On the other hand, there have also been examples of increased liquefaction resistance occurringthroughout a soil's liquefaction history that cannot be explained merely by density increases. These facts point to theexistence of factors other than density that sway the liquefaction resistance of soils. The current paper demonstratesthat, in fact, anisotropy is an important factor in‰uencing liquefaction resistance. This is made clear through theresults of systematic triaxial shear tests, which show that the higher the level of developed anisotropy, the lower the liquefaction resistance. In the process of verifying the above, we found that continuous and orderly changes in anisotropyare repeated with dizzying rapidity during liquefaction. Furthermore, we show herein that there is no intrinsic diŠerence between the inherent anisotropy acquired by soil during its sedimentation period and the induced anisotropy produced by plastic deformation developed through its stress history, although anisotropy has often been divided intothese two types and has been considered separately in the past. We also show that what has been referred to as inherentanisotropy is nothing more than the initial state of induced anisotropy.Key words: anisotropy, liquefaction, reliquefaction, sand, triaxial test (IGC: D6)uefaction resistance becomes greater in soils that havepreviously experienced liquefaction. Although this can beinterpreted at ˆrst glance to be common knowledge, theinteresting point is that there have been cases where thelevel of increase in liquefaction resistance is so large thatit is not possible to explain the phenomenon simply by anincrease in density.Although they appear to be contradictory, both of theabove claims are in fact correct, as will be explained below. Figure 1 illustrates the results of reliquefaction experiments carried out by the authors using a triaxial sheartesting apparatus (the plots within the ˆgures indicate thepositions at which the liquefaction tests were stopped). Inthe experiments, specimens made by the air pluviationmethod were subjected to cycles of liquefaction anddrainage. The soil used for making the specimens wasToyoura sand. The experimental method was the same asthat described in the latter section of this paper. The relative density Dr after each cycle is shown in the corresponding ˆgure. As can be seen from these ˆgures, liquefaction occurred several times, and the density of thespecimens increased as the number of loading cycles increased. Along with this increase in density, the extent ofstrain per cycle during liquefaction is gradually suppressed with each successive test. However, there is noINTRODUCTIONWhen sandy soils liquefy, they inevitably become densiˆed because of the drainage of water that occurs afterliquefaction. In general, denser soil is less prone to liquefaction. This means that once liquefaction occurs, thesoil should become less prone to liquefaction because ofthe increase in density. The ˆrst researchers to raise theirvoices against this simple theory were Finn et al. (1970).Through their results of simple and triaxial shear tests,they showed that once sandy soil experiences liquefaction, it can become extremely prone to liquefactionin spite of an increase in density. That is to say, its reliquefaction resistance becomes much lower than its liquefaction resistance. This phenomenon, for which thereis no simple explanation, received widespread attentionimmediately after the paper was published and was laterconˆrmed experimentally by many other researchers.There are also reports of actual examples of reliquefaction of sandy soils being caused by earthquakes smallerthan those that had occurred previously (for example,Yasuda and Tohno, 1988; Yoshida and Wakamatsu,1990). Another interesting aspect of reliquefaction seemingly contrary to this was pointed out by Seed et al. (1977)and many other researchers. They pointed out that liqi)ii)iii)Research Associate, Department of Civil Engineering, Fukuoka University, Fukuoka, Japan (s-yamada@fukuoka-u.ac.jp).Graduate Student, ditto.Professor, ditto.The manuscript for this paper was received for review on October 30, 2008; approved on September 29, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.9 10YAMADA ET AL.consistent trend with respect to the ease of liquefactionor, to put it diŠerently, liquefaction resistance. Certainly,as can be seen in past reports, there are cases in which liquefaction resistance decreases and cases in which it increases compared with a previous test. In the presentcase, although there is a diŠerence of about 25z in therelative densities of the specimens in the 1st and 4th tests,the liquefaction resistance in the latter test is clearly lower. On the other hand, the liquefaction resistance in the3rd test is extremely high compared with the 2nd test, butFig. 1.this increase cannot be explained merely by the increase indensity. As described above, liquefaction history cancause liquefaction resistance to increase or decrease appreciably, but this attribute cannot be explained by arguments based only on the density variations of the soil.This being the case, what would be the mechanism thatproduces such increases or decreases in liquefactionresistance? Like many previous studies on reliquefaction,the main aim of the current study was to ˆnd an answer tothis question. Skipping to the conclusion ˆrst, the key-Reliquefaction test RELIQUEFACTION RESISTANCE AND ANISOTROPYword is anisotropy. Of course, several past studies onboth liquefaction and reliquefaction have shownanisotropy to be one of the factors in‰uencing liquefaction resistance. Among these, the reports of Ishihara and Okada (1978, 1982) and Towhata and Ishihara(1985) present experimental results rich in data that enable the reader to have a perception of the in‰uence ofanisotropy on reliquefaction resistance. The results of thetriaxial shear tests presented in the current study go a stepfurther and consolidate the relationship between liquefaction resistance and anisotropy. In addition, throughthe results of systematic experiments, this paper showsnot only the eŠect of the state of anisotropy after liquefaction on reliquefaction resistance, but also how thechanges in anisotropy proceed during liquefaction.Moreover, this paper contends that the increase anddecrease in liquefaction resistance, which are apparentlycon‰icting experimental facts, can be explained collectively by considering anisotropy as the key factor. Thecurrent study diŠers from all past studies concerning therelationship between reliquefaction and anisotropy in thesense that past studies have dealt only with the decrease inliquefaction resistance.Let us explain here, in the ˆnal part of this introduction, how this paper is structured to demonstrate the connection between reliquefaction resistance and anisotropy.First, using sand specimens made by the air pluviationmethod, the distinctive eŠects of initial anisotropy on themonotonic undrained shear behavior and cyclic undrained shear behavior of sand are pointed out. On thebasis of the above, we show next that continuous andorderly changes in anisotropy are repeated with dizzyingrapidity during liquefaction and that the specimens afterliquefaction can exist in various states ranging from severely anisotropic to nearly isotropic. Within the discussion of the results, we show that there is no intrinsicdiŠerence between the inherent anisotropy acquired bythe specimens when they were made and the inducedanisotropy developed through their liquefaction history.Finally, we show that the diŠerences in the level of development of anisotropy after liquefaction exert a strongin‰uence on reliquefaction behavior. Having read thispaper, the reader should come to understand that as faras liquefaction is concerned, anisotropy is a crucial factorthat surpasses even the importance of density. In Fig. 1,in addition to the diŠerences in liquefaction resistance,there are other diŠerences in soil behavior. For example,the mean eŠective stress decreases signiˆcantly dependingon whether the shear is in the triaxial compression or extension state. Furthermore, the progress of the strain produced during compression and extension diŠers. We arecertain that the reasons why the above diŠerences (shownin Fig. 1) arise will be su‹ciently understood by the reader once he or she has ˆnished reading this paper. We alsobelieve that the reader should be able to formulate ageneral idea of how soil would behave if the liquefactiontest were carried out a 5th time ( see APPENDIX A forthe behavior during liquefaction for a 5th time).Table 1.Physical properties of Toyoura sandDensity of soil perticles rs (g/cm3)Maximum void ratio emaxMinimum void ratio eminFig. 2.112.6460.9850.639Cumulative grain size distribution of Toyoura sandOUTLINE OF EXPERIMENTSMaterial Used and Method of Specimen PreparationToyoura sand was used to prepare test specimens. Thephysical properties and cumulative grain size distributionof this sand are shown in Table 1 and Fig. 2, respectively.As is well known, Toyoura sand is a siliceous sand with ahomogeneous grain size.Specimens with a diameter of 7.5 cm and a height of 15cm were prepared by the air pluviation method for thetriaxial shear tests. The targeted relative density of thespecimens, other than those mentioned in Figs. 1 and 4,was 80z. The actual relative densities Dr of the specimens in each experiment are mentioned within the corresponding ˆgures showing the experiment results. The targeted relative density was 80z because, in the case ofspecimens with low relative densities, there is a possibilityof their homogeneity being lost due to necking or similarphenomena caused by the signiˆcant strains that arisewith the onset of liquefaction. In actuality, the specimenshape remained highly homogeneous during all tests carried out in this study. Although the arguments presentedin this paper are centered on experiment results pertaining to dense sands, it can be inferred from the results illustrated in Fig. 1 that the conclusions obtained here areapplicable to at least medium dense sands with relativedensities of around 60z.Experimental ConditionsAll experiments were carried out under a conˆningpressure of 98.1 kPa and a backpressure of 294.3 kPa.The B values of the specimens were conˆrmed to be 0.96or higher. Broadly divided, the following are the four experimental patterns that form the framework of thispaper. YAMADA ET AL.12I. Monotonic undrained shear test (with no liquefaction history)II. Cyclic undrained shear test (with no liquefactionhistory)=Liquefaction testIII. Monotonic undrained shear test (with liquefactionhistory)IV. Cyclic undrained shear test (with liquefactionhistory)=Reliquefaction testBoth the monotonic and cyclic undrained shear testswere strain-controlled. The loading rate was 0.12z/minor higher. Although this loading rate is slow for liquefaction tests, phenomena such as segregation of waterand sand were not observed. The stress amplitude in theliquefaction tests was applied in such a manner that thehalf-amplitude basically became qmax=39.2 kPa. (In thetest whose results are shown in Fig. 1, qmax was set at 22.6kPa. In the case of the test whose results are shown inFigs. 14 and 15, qmax was set at 294.3 kPa.) The scheme ofapplication of reliquefaction history will be explainedlater in the appropriate sections of this paper.In the sections below, the results of the tests carried outon sand specimens (without prior liquefaction history)that had been prepared by the air pluviation method (patterns I and II above) are described ˆrst, together with explanations of the eŠects of initial anisotropy on themonotonic and cyclic undrained shear behaviors of thesand. Bearing the results of these tests in mind, the monotonic undrained shear behavior of sand subjected to liquefaction history (pattern III) is presented next, and thedevelopment of anisotropy after liquefaction is examined. Herein, in order to surmise the manner in which thechanges in anisotropy occur during liquefaction, particular attention is paid to systematically show how themonotonic undrained shear behavior after liquefactionvaries according to the conditions of halting of the liquefaction test. Finally, after subjecting the specimens toliquefaction history equivalent to pattern III, cyclic un-Fig. 3.drained shear testing is carried out again (pattern IV) inorder to show how the ease of reliquefaction is aŠected bythe state of development of anisotropy resulting fromprior liquefaction.In addition to the four above experimental patternsthat form the framework of this paper, the results for thefollowing two test patterns are also presented to supplement pattern III.III? Monotonic undrained shear test (with history ofmonotonic undrained shear)III! Monotonic undrained shear test (with history ofcyclic undrained shear up to a level at which no liquefaction occurs)Test pattern III? is a modiˆcation of pattern III, withmonotonic undrained shear history being imparted to thespecimen instead of liquefaction history. This patternwas applied to compare the changes in anisotropy thatoccur during liquefaction with those that occur duringmonotonic loading. Test pattern III! is another modiˆcation of pattern III, in which the application of the cyclicundrained shear load to cause liquefaction is stopped before liquefaction begins. This pattern was applied to determine the level of change in anisotropy before liquefaction takes place. Through the results of the abovetests, this paper attempts to obtain a deeper understanding of the anisotropy of sand.MONOTONIC UNDRAINED SHEAR BEHAVIOR OFSAND WITH NO PRIOR LIQUEFACTION HISTORY(EFFECT OF INITIAL ANISOTROPY ONMONOTONIC UNDRAINED SHEAR BEHAVIOR)The eŠect of the initial anisotropy on monotonic undrained shear behavior is explained ˆrst. The monotonicundrained shear behavior of a specimen prepared by theair pluviation method with no prior liquefaction historyis shown in Fig. 3. Since specimens prepared by the airMonotonic undrained shear behavior of sand with initial anisotropy RELIQUEFACTION RESISTANCE AND ANISOTROPYFig. 4.Fig. 5.13Monotonic compressive undrained shear behavior of sands with diŠering densitiesCyclic undrained shear behavior of sand with initial anisotropy=liquefaction behaviorpluviation method exhibit diŠerent behavior in the compression and extension states, it can be conˆrmed thatthey possess initial anisotropy, as is well known. Ofcourse, the anisotropy referred to here is mechanicalanisotropy, which is the property of a solid diŠering instiŠness in accordance with shear direction. From thedeviator stress-axial strain relationship, it can be seenthat the specimen prepared by the air pluviation methodis hard when subjected to compressive shear in the samedirection as the direction of sedimentation.The monotonic undrained shear behavior of Toyourasand specimens with diŠering densities prepared by theair pluviation method is shown in Fig. 4. Comparison ofthe eŠective stress paths in Figs. 3 and 4 shows that, inFig. 3, although the density of the specimen is almost thesame in both the compression and extension conditions,behavior more like that of loose sand appeared in the extension state rather than in the compression state. Thesame can be said with respect to the deviator stress-axialstrain relationship in Fig. 3 even though the absolutevalues of the axial strains in Figs. 3 and 4 are diŠerent. Inother words, the behavior is similar to that of dense sandin the shear direction with high rigidity, while in the sheardirection with low rigidity, the behavior resembles that ofloose sand. In the case of sand, it can be said that the``diŠerences in stiŠness'' that appear in accordance withthe direction of shear will materialize as ``diŠerences inpseudo-density.''CYCLIC UNDRAINED SHEAR BEHAVIOR OFSAND WITH NO PRIOR LIQUEFACTION HISTORY(EFFECT OF INITIAL ANISOTROPY ONLIQUEFACTION BEHAVIOR)The eŠect of initial anisotropy on liquefaction behavior is discussed next. Figure 5 illustrates the cyclic undrained shear behavior of a sand specimen without priorliquefaction history that was prepared by the air pluviation method. The broken line in the ˆgure denotes themonotonic undrained shear behavior (same as in Fig. 3)of a sand specimen with a similar status. The followingtwo distinctive features of the cyclic undrained shear behavior of specimens prepared by the air pluviationmethod are evident from this ˆgure.(1) The eŠective stress path indicates that, until commencement of the cyclic mobility trace, the meaneŠective stress decreases signiˆcantly in the extension state compared with the compression state. Inother words, the pore water pressure increases appreciably in the extension state.(2) The deviator stress-axial strain relationship showsthat strain development is biased towards that of 14YAMADA ET AL.extension during liquefaction.It is easy to comprehend that feature (2), of course,results from the in‰uence of initial anisotropy. In addition, by comparing the eŠective stress paths traced duringthe monotonic and cyclic undrained shear tests, it can beseen that feature (1) also results from the in‰uence of initial anisotropy.The two features above demonstrate that specimensprepared by the air pluviation method exhibit behaviormore similar to that of loose sand in the extension staterather than in the compression state under cyclic undrained shear as well as monotonic undrained shear. Inaddition, feature (1) indicates that as the anisotropy develops to higher levels, behavior similar to looser sandappears in a certain shear direction, and that, being dependent on this behavior, the liquefaction resistancedecreases. Many readers may have realized at this pointthat in addition to the above, the reliquefaction resistanceshould also change signiˆcantly depending on the level ofanisotropy developed in the sand specimen after liquefaction. This is demonstrated in the latter half of thispaper.MONOTONIC UNDRAINED SHEAR BEHAVIOR OFSAND WITH PRIOR LIQUEFACTION HISTORY(EFFECT OF ANISOTROPY DEVELOPED DURINGLIQUEFACTION ON MONOTONIC UNDRAINEDSHEAR BEHAVIOR)The state of anisotropy after liquefaction is examinednext by studying the monotonic undrained shear behaviorof sand that has undergone liquefaction once. Beforepresenting the experiment results, the process by whichthe test specimens are subjected to liquefaction history isexplained below with reference to Fig. 6.Step 1: First, specimens made by the air pluviationmethod are subjected to strain-controlled cyclic undrained shear loading in a manner similar to when specimens are not subjected to liquefaction history so that liquefaction occurs.Step 2: Next, after conˆrming that a diŠerence of atleast 5z has occurred in the maximum andminimum values of the axial strain, cyclic undrained shear loading is halted at variousstages (for example, point [a] in Fig. 6. In allcases, shear loading is halted when the stressstate is nearly isotropic).Step 3: The pore water is drained out by opening thedrainage cock after the state of the loadingshaft is altered from strain-controlled loadingto stress-controlled loading so as to maintainan isotropic stress state during drainage. Atthis stage, the accumulated pore water pressureis dissipated, and the eŠective stress changesisotropically to reach the same condition asthat at the time of commencing cyclic undrained shear loading (corresponding to theposition of point [s] in Fig. 6). Furthermore,axial displacement takes place simultaneouslywith the volume change during drainage. (Evenif a very small amount of deviator stress ispresent when the cyclic undrained shear loading is halted in Step 2, this small deviator stressis removed when the state of the loading shaftis altered to allow stress-controlled loading.)Step 4: After altering the state of the loading shaft toallow strain-controlled loading and closing thedrain cock, monotonic compression and extension shear tests are performed under undrainedcondition. In this step, the standard strain condition is reset with reference to the shape of thespecimen at the time of completion of waterdrainage (point [s] in Fig. 6).The eŠects of halting cyclic undrained shear loading atvarious stages in Step 2 on the state of development ofanisotropy after liquefaction are explained below.State of Development of Anisotropy Immediately afterUnloading (EŠect of Final Shear Direction)First, referring to Fig. 6, the case where cyclic undrained shear loading is halted at the instant the specimenreturns to the isotropic stress condition following unloading after the ˆnal shear under the extension condition (ata position equivalent to point [a] in Fig. 6) is examined(in Figs. 6, 8, 10 and 16, which illustrate the manner ofapplication of cyclic shear history, the ˆnal half-cycle isdenoted by a solid line). The monotonic undrained shearbehavior of the sand specimen that underwent the aboveliquefaction history is shown in Fig. 7 (the relative densities indicated within Figs. 7, 9, 11 and 17 of the sandspecimens that had been subjected to cyclic undrainedshear history are those after drainage, i.e., the relativedensities during monotonic undrained shear). In contrastto the specimen not subjected to liquefaction history (Fig.3), behavior similar to that of loose sand appeared in thecompression state, and behavior similar to that of densesand appeared in the extension state. From this, it can beunderstood that because of being subjected to liquefaction history, the anisotropy possessed by the specimen initially is lost completely and new anisotropy develops in an entirely diŠerent direction. In addition, thelevel of the developed anisotropy is higher than that ofthe initial anisotropy.Next, referring to Fig. 8, the case where cyclic undrained shear loading is halted at the instant (at a position equivalent to point [f] in Fig. 8) the specimen returnsto the isotropic stress condition following unloading afterthe ˆnal shear cycle under the compression condition isexamined. The monotonic undrained shear behavior ofthe sand specimen that underwent the above liquefactionhistory is shown in Fig. 9. It can be seen that the behaviors in the case of ˆnal shear under the extension condition (Fig. 7) and ˆnal shear under the compression condition (Fig. 9) are nearly symmetrical. In the case of ˆnalshear under the extension condition, the behavior in theextension state is similar to that of dense sand, whereas inthe case of ˆnal shear under the compression condition,the behavior in the compression state resembles that of RELIQUEFACTION RESISTANCE AND ANISOTROPY15Fig. 6. Graphical perspective of liquefaction history (in the case where cyclic undrained shear loading is halted at the instant the specimen returnsto the isotropic stress state following unloading after the ˆnal stage of shear under the extension condition)Fig. 7. Monotonic undrained shear behavior of sand subjected to liquefaction history (in the case where cyclic undrained shear loading is halted ata position equivalent to point [a] in Fig. 6)dense sand. In other words, it is clear that the state ofanisotropy changes signiˆcantly during cyclic undrainedshear and is highly developed in the same direction as thatof ˆnal shear at the instant the eŠective stress returns tothe isotropic state. This trend in the relationship betweenloading direction and direction of development ofanisotropy is a property common to elasto-plastic materials that exhibit induced anisotropy, although there is anintervening consolidation process in the present case.This fact is conˆrmed again in a later section.Up to now, it has been thought that particulate materials such as soil possess two separate types of anisotropy.The ˆrst is inherent anisotropy, which is the anisotropyacquired during sedimentation. The other is inducedanisotropy, which is the anisotropy that develops alongwith the stress history that causes plastic deformation ofsoil. As is quite evident from the word ``inherent,'' inherent anisotropy, acquired during sedimentation of soil orduring specimen preparation, has been considered an unvarying and inherent material property. However, theresults described above show that in reality, theanisotropy acquired during sedimentation is lost completely when the material is subjected to liquefactionhistory. In addition, with respect to the point that the``diŠerences in stiŠness'' that occur according to theloading direction appear as ``diŠerences in pseudo-density,'' there is no dissimilarity between the anisotropy acquired during sedimentation and that developed by thestress history with plastic deformation. The results obtained here tell us that, in the case of sand, there is no intrinsic diŠerence between the two types of anisotropy andthat what has been referred to as inherent anisotropy until now is nothing more than a form of inducedanisotropy. It is not necessary to make a distinction between the two types of anisotropy, at least in the case ofsand. Based on this point of view, this paper refers to in- 16YAMADA ET AL.Fig. 8. Graphical perspective of liquefaction history (in the case where cyclic undrained shear loading is halted at the instant the specimen returnsto the isotropic stress state following unloading after the ˆnal stage of shear under the compression condition)Fig. 9. Monotonic undrained shear behavior of sand subjected to liquefaction history (in the case where cyclic undrained shear loading is halted ata position equivalent to point [f] in Fig. 8)duced anisotropy simply as ``anisotropy.'' In addition,the anisotropy acquired at the time of specimen preparation is referred to as ``initial anisotropy,'' in the sensethat it is the initial state of induced anisotropy.Changes in Anisotropy during LiquefactionIt is evident from Figs. 7 and 9 that the anisotropychanges appreciably during the cyclic mobility trace. Inorder to examine how such changes in anisotropyprogress during the half-cycle between point [a] in Fig. 6and point [f] in Fig. 8, the liquefaction test was halted atpositions equivalent to points [a], [b], [c], [d], and [e] inFig. 10 (the axial strain ea halt at the time of halting of thetest is shown in Table 2 relative to the maximum axialstrain ea max and minimum axial strain ea min ). The experimental procedure was identical to the one carried outpreviously. The monotonic undrained shear behavior ofthe sand specimen that had been subjected to liquefactionTable 2.Approximate positions of halting of loadingHalting position[a][b][c][d][e]|ea halt-ea min||ea max-ea min|0.150.310.450.670.92history is illustrated in Fig. 11 (the letters [a] to [e] in theˆgure correspond to the respective halting positions ofthe liquefaction test). At ˆrst glance, Fig. 11 resemblesFig. 4, which illustrated the undrained shear behavior ofsand with diŠering densities. However, in the test resultsshown in Fig. 11, there is no appreciable diŠerence in therelative densities. A closer look at the ˆgure shows that asthe halting point moves from [a] to [e], the behavior under the compression condition gradually comes to resemble that of dense sand. In contrast, the behavior under theextension condition tends to gradually become similar to RELIQUEFACTION RESISTANCE AND ANISOTROPY17Fig. 10. Graphical perspective of liquefaction history (in the case where cyclic undrained shear loading is halted at various states during ``liquefaction'')Fig. 11. Monotonic undrained shear behavior of sand subjected to liquefaction history (in the case where cyclic undrained shear loading is haltedat positions equivalent to point [a] to [e] in Fig. 10)that of loose sand. Looking closely at the individual behavior patterns one by one beginning from [a], the following features can be observed. When the liquefactiontest is halted at the position equivalent to point [a], thebehavior in the extension state is similar to that of extremely dense sand, as has been seen earlier, whereas thebehavior in the compression state resembles that of extremely loose sand. Similar to point [a], when the haltingposition moves closer to point [b], the behavior in the extension state is also more similar to that of denser sandthan that in the compression state. However, the diŠerence in the behavior between the extension and compression states is smaller than what was observed when thetest was halted at point [a]. When the test is halted nearpoint [c], the diŠerence almost completely disappears.When the halting position is close to point [d], the behavior in the compression state is more like dense sand thanthat in the extension state. Finally, when the halting posi-tion nears point [e], the behavior in the compression statebecomes similar to that of extremely dense sand, whereasthe behavior in the extension state comes to resemble thatof extremely loose sand. This behavior is completely opposite to that seen when the liquefaction test was halted atthe position equivalent to point [a]. Thus, by studying thebehavior step-by-step, the changes in anisotropy becomevisible behind the pseudo-density increase under the compression condition and the pseudo-density decrease underthe extension condition. In other words, the anisotropythat was prominent in the radial direction at point [a] inFig. 10 disappears gradually, and the sand becomes temporarily isotropic near point [c]. As liquefaction continues further, the anisotropy starts to develop in the axial direction, and at point [e], it has developed to the samelevel as that seen when the liquefaction was halted atpoint [a]. Such changes in anisotropy are believed to occur repeatedly in a dizzying manner during liquefaction. 18YAMADA ET AL.Based on the results presented in Fig. 11, the authorswould like to emphasize the following 3 points.The ˆrst point is that the changes in anisotropy occur ina ``continuous'' and ``orderly'' manner during liquefaction, although this point is likely to be misunderstood. It must be stressed that the disappearance ofanisotropy is not caused by a sudden collapse of the soilskeleton structure of the specimen to a disordered condition along with the occurrence of liquefaction and thatthe specimen does not acquire anisotropy by rebuild upof the soil skeleton structure from nothing during thestage of drainage after liquefaction.The second point is that the development of anisotropynot only makes the shear rigidity high in a certain direction, but also causes the shear rigidity in another direction to become low. Furthermore, the pseudo-densitychanges produced by the development of anisotropy areprominent enough to exceed the actual density changesoccurring during drainage after liquefaction. Therefore,if the anisotropy has attained a high level, behaviorresembling that of sand much looser than sand in theisotropic state could occur. On the other hand, if the attained level of anisotropy is low, occurrence of behaviorsimilar to that of extremely loose sand cannot take place.As will be explained later, this point is extremely important with respect to resistance to reliquefaction.The third point is related to the stage of drainage afterliquefaction. In past studies of liquefaction, the expression ``resedimentation'' has been applied frequently withrespect to the phenomenon of drainage after liquefaction. This expression, ``resedimentation,'' evokesthe idea of a soil becoming anisotropic during the stage ofdrainage after liquefaction, as in the case of preparingspecimens possessing anisotropy by the water pluviationmethod. It has been stated earlier in this work that, insand that has been subjected to liquefaction history,anisotropy basically develops during liquefaction and notduring the subsequent stage of drainage. Regarding thisstatement, the following points also need to be stressed.During the stage of drainage after liquefaction in the experiments performed in the present study, the eŠectivestress increases along the isotropic stress axis (for example, the path of eŠective stress from point [a] to point [s]in Fig. 6). A specimen that has undergone such a historyof isotropic compression should gradually becomeisotropic rather than anisotropic. In spite of this, severalstates of anisotropy, not only low level states but alsohigh level ones, can be observed even after drainage inFig. 11. This suggests that the anisotropy developed during liquefaction has remained almost intact even afterisotropic compression. Therefore, here, we venture todraw your attention to the fact that, in cases of deformation where compression is prominent, dramatic changesof anisotropy like the ones occurring during liquefactiondo not take place. This is the third point that must be emphasized.Changes in Anisotropy during Monotonic UndrainedShearIf an elasto-plastic material exhibiting inducedanisotropy is subjected to a load in a certain direction andthen the load is removed, it is natural for the state ofanisotropy to be altered compared with the state beforeloading. In general, a material that has experienced shearhistory in one direction would be in a state that wouldproduce a more rigid response when sheared again in thesame direction.In order to obtain deeper understanding about theanisotropy of sand, we ascertain here how this most fundamental property of induced anisotropy is expressed inthe case of sand. For this purpose, after subjecting thesand specimens once to extension or compression shearunder undrained condition, unloading was performeduntil isotropic stress conditions were attained. Furthermore, drainage was then carried out under a condition allowing axial displacement so that the eŠective stress wasrestored to the original state isotropically. After this,monotonic compression and extension shear tests wereperformed under undrained condition. This procedure isthe same as that used for imparting liquefaction historyto the specimens, except that cyclic undrained shearinghas been replaced by monotonic undrained shearing. Asin the case of the specimens used in the other experiments, those used here were prepared by the air pluviation method. Because of this, in the initial stages, theresponse is slightly more rigid when sheared in the compression state than it is in the extension state. The loadinghistory of the specimens is not simple monotonic loadingbecause they undergo consolidation partway through theexperiments. However, if we pay attention to the factthat because of experiencing isotropic compression history, the level of anisotropy in the specimens will notbecome higher, although it may become lower, as hasbeen mentioned earlier, the problem of the loading history not being simple monotonic loading will not impedeinterpretation of the test results below.The loading patterns are shown in Table 3. The behaviors of sand subjected to prior extension and compressionshear histories are shown in Fig. 12 and Fig. 13, respectively. The behavior during the process of imparting theshear history is also shown in the ˆgures by dashed lines.The symbols within the ˆgures correspond to thoseshown in Table 3. In the process of imparting the shearhistory, the deviator stress acting under the compressioncondition was made larger than that under the extensioncondition. The reason for this is that due to the eŠect ofinitial anisotropy, a larger force is required in the compression state than in the extension state in order toproduce appreciable plastic deformation.Table 3. Loading patterns (tests for determining anisotropy variationscaused by monotonic shear history)Stage of imparting historyExtension shear (EC-1)Extension shear (EE-1)Compression shear (CC-1)Compression shear (CE-1)Stage of observing eŠects of historyªªªªCompression shear (EC-2)Extension shear (EE-2)Compression shear (CC-2)Extension shear (CE-2) RELIQUEFACTION RESISTANCE AND ANISOTROPYFig. 12.19Monotonic undrained shear behavior of sand subjected to prior monotonic undrained shear history (in the case of extension shear history)Fig. 13. Monotonic undrained shear behavior of sand subjected to prior monotonic undrained shear history (in the case of compression shearhistory)Extremely anisotropic behaviors can be observed inboth Figs. 12 and 13. Paying attention to the direction ofdevelopment of anisotropy, it can be ascertained that thestate of the sand is more rigid in the case of undergoingshear once more in the same direction as that of priorshear history compared with undergoing shear in a diŠerent direction. It can therefore be said that, basically, theinduced anisotropy exhibited by sand has the same natureas the induced anisotropy exhibited by other elasto-plastic materials. Furthermore, comparing Figs. 12 and 13with Figs. 7 and 9, which show the behavior of specimenssubjected to prior liquefaction history, it can be recognized that the respective behaviors exhibit good resemblance. Of course, the behaviors do not match each otherperfectly since they are not determined solely byanisotropy. However, points such as the relation betweenthe loading direction and the direction of anisotropy development and the ``diŠerence in stiŠness'' in accordancewith shear direction appearing as a ``diŠerence in pseudodensity'' are common to these behaviors. It can be recognized that the anisotropy developed during liquefaction isthe same as that developed during monotonic loading.Furthermore, it can also be recognized that theanisotropy has developed to a high level and that the in‰uence of initial anisotropy has become quite weak due tomonotonic loading. This indicates that occurrence of signiˆcant variation in the induced anisotropy is possibleeven if the sand does not undergo a drastic change like 20YAMADA ET AL.liquefaction.Behavior Near the Origin in Plane p?-q during ``Liquefaction''If one takes a good look at Figs. 7 and 9 after lookingat Figs. 12 and 13, one would be led to think that the development of anisotropy during cyclic undrained shearoccurs at the stage of rapid recovery of rigidity after point[e] in Fig. 10. In actuality, however, before the recoveryof rigidity, the anisotropy has already developed to aquite high level in the interval between points [a] and [e]in Fig. 10, as can be observed from Fig. 11. In this interval between points [a] and [e] in Fig. 10, shear strain continues to be generated under the condition of mean eŠective stress p?≒0 and deviator stress q≒0. It is quite appropriate to call the condition of the eŠective stress aswell as the rigidity being nearly zero as ``liquefaction.''That is to say, the change in anisotropy during cyclic undrained shear has occurred during the stage in whichthere was a loss of almost all rigidity.With respect to the above fact, many people may besurprised by the fact that anisotropy can develop to highlevels even though there is almost no in‰uence of shearstress, although they may accept that it is possible foranisotropy to disappear under the condition of the eŠective stress being zero. To clarify this, let us take a closerlook at the stress state near the origin in plane p?-q. Magnifying and studying the region near the origin of Fig. 10,however, would entail problems of accuracy. As an alternative, cyclic undrained shear testing with the conˆningpressure and amplitude being made large was carried out.The cyclic mobility obtained from this test is shown inFig. 14, and a magniˆed view of the region near the ori-Fig. 14.gin of this ˆgure is shown in Fig. 15. In both Figs. 14 and15, the solid lines indicate the last cycle from the commencement of loading at the extension state, while thedashed lines denote the other cycles. In addition, the positions that correspond to points [a] to [e] in Fig. 10 aredenoted in Fig. 15 by the same symbols. It can be recognized from Fig. 15 that the shear stress during ``liquefaction'' has not really become zero. Near the origin,hardening occurs after unloading as soon as the eŠectivestress path crosses the isotropic stress axis. After that,softening behavior is exhibited once, followed by hardening behavior again when the stress ratios become high.Comparing this behavior with that of the prior half-cycle,it can be predicted that along with the increasing numberof cycles and progress of liquefaction, although the meaneŠective stress moves closer to the origin, it would not actually become zero but would exhibit softening andhardening behavior similar to that shown in the ˆguresabove. The fact that this type of softening and hardeningbehavior does actually occur in a state where liquefactionhas progressed can be deduced from the fact that the behavior under compression shear (the compression shearbehavior in Fig. 7) after halting liquefaction history at aposition equivalent to point [a] in Fig. 10 and executingdrainage resembles the behavior after point [a] in Fig. 15.Furthermore, it can be observed that, in the intervalwhere anisotropy develops after passing the isotropicstate, i.e., the interval between [c] and [e], a high stressratio condition exists, although the magnitude of theshear stress is small. The ``continuous'' and ``orderly''changes of anisotropy that appear during liquefactiontake place under this type of stress conditions and are accompanied by marked development of shear strain.Cyclic mobility RELIQUEFACTION RESISTANCE AND ANISOTROPYConditions of Development of Anisotropy during theStage of Cyclic Undrained Shear before LiquefactionTo conclude this section, we will show that there is nosigniˆcant change in anisotropy during the stage of cyclicundrained shear before the cyclic mobility trace begins.The case of halting cyclic undrained shear loading at aposition corresponding to point [p] in Fig. 16 is examinedhere. The monotonic undrained shear behavior of a sandspecimen that has been subjected to the above loadinghistory is shown in Fig. 17. It can be observed thatalthough there is evidence of slight overconsolidation ofthe soil, there is no appreciable diŠerence in the behaviorof this specimen compared with that of the sand specimennot subjected to cyclic undrained shear history (Fig. 3).Attention should be paid particularly to the fact that, inspite of ˆnal shearing under the extension dondition, therigidity of this sand specimen in the extension state is nothigher than that in the compression state, in contrast tothat subjected to liquefaction history (Fig. 7). These observations indicate that cyclic undrained shear before theonset of liquefaction does not result in appreciablechanges in anisotropy (this fact can also be inferred fromFig. 5, where it can be seen that until the beginning of thecyclic mobility trace, the decrease in the mean eŠectivestress is always more prominent in the extension state). Itis believed that the reason for the anisotropy remainingnearly unchanged in spite of the deviator stress beinglarger than that during ``liquefaction'' lies in the fact thatthe stress ratio is low and that almost no strain is generated during the cyclic shear before occurrence of liquefaction.Fig. 15.21CYCLIC UNDRAINED SHEAR BEHAVIOR OFSAND WITH PRIOR LIQUEFACTION HISTORY(EFFECT OF ANISOTROPY DEVELOPED DURINGLIQUEFACTION ON RELIQUEFACTIONBEHAVIOR)The relationship between the state of anisotropy developed during liquefaction and the ease of occurrence ofreliquefaction is described next. In a manner similar tothe previous experiment, the liquefaction tests were halted at positions corresponding to points [a] to [e] in Fig.10. This was followed by application of cyclic undrainedshear instead of monotonic undrained shear. The behaviors of the specimens with respect to each of the abovehalting positions during the second cyclic undrainedshear tests, that is to say, the reliquefaction behaviors,are presented in Figs. 18 to 22 (the relative densities before and after drainage are denoted within the ˆgures).The broken lines in these ˆgures represent the monotonicundrained shear behaviors after halting the liquefactiontests almost at the same positions (pertinent data extracted from Fig. 11).By comparing the cyclic undrained shear behavior andmonotonic undrained shear behavior shown in eachˆgure, it can be understood quickly that the ease of liquefaction has been in‰uenced by the state of developmentof anisotropy. In addition, by comparing the cyclic undrained shear behaviors with one another, it can be easilyunderstood that the more developed the state of development of anisotropy is, the greater the ease of liquefaction. The behaviors are examined separately in detail below. When the test is halted at positions corresponding to points [a] and [b], the anisotropy is devel-Behavior near the origin of plane p?-q during ``liquefaction'' (expanded view of the vicinity of the origin of Fig. 14) 22YAMADA ET AL.Fig. 16. Graphical perspective of cyclic undrained shear (in the case where undrained shear loading is halted before commencement of cyclicmobility trace)Fig. 17. Monotonic undrained shear behavior of sand subjected to cyclic undrained shear loading history that is insu‹cient to cause liquefaction(in the case where cyclic undrained shear loading is halted at a position equivalent to point [p] in Fig. 16)oped in the radial direction. Under such conditions, sincebehavior similar to that of loose sand appears in the compression state rather than in the extension state, a largedecrease in the mean eŠective stress occurrs when shearoccurrs in the compression state. In contrast, when thetest is halted at positions corresponding to points [d] and[e], the anisotropy is developed in the axial direction.Under such conditions, since behavior similar to that ofloose sand appears in the extension state rather than inthe compression state, there is a large decrease in themean eŠective stress when shear occurrs in the extensionstate. In the case of halting the test at a position corresponding to point [c], the specimen is nearly isotropic,and there is not much diŠerence in the manner in whichthe mean eŠective stress decrease occurs in the compression and extension state. Furthermore, comparison of theresults of the above tests halted at positions corresponding to points [a] and [e] with the cyclic undrainedshear behavior of sand without prior liquefaction history(Fig. 5) shows that the resistance to liquefaction hasbecome signiˆcantly lower than that before experiencingliquefaction history, in spite of the increased density. Thereason for this is that the state of anisotropy is clearlymore highly developed than before liquefaction in thecase of halting at positions corresponding to points [a]and [e]. As you have probably already realized, thedecrease in liquefaction resistance with increasing levelsof developed anisotropy is due to the fact that the specimen can latently exhibit behavior resembling looser sand.In the same manner in which initial anisotropy aŠects cyclic undrained shear behavior, the resistance to liquefaction is swayed signiˆcantly by behavior that is similar to loose sand. It may be noticed that in Figs. 18 to 22that there is not much diŠerence in the number of cyclesrequired to produce liquefaction. This is due to the relatively large stress amplitude. In the cases of the test being RELIQUEFACTION RESISTANCE AND ANISOTROPYhalted at positions corresponding to points [a] and [e],the ˆrst loading cycle causes liquefaction to occur even ifthe stress amplitude qmax is made as small as 20 kPa. Inother cases, one can expect that as the amplitude is made23smaller, a greater number of cycles would be required forliquefaction with decreasing levels of developedanisotropy. In the actual test results described earlier(Fig. 1 in INTRODUCTION), large diŠerences arose inFig. 18. Cyclic undrained shear behavior of sand subjected to liquefaction history=reliquefaction behavior (in the case where the ˆrst cyclic undrained shear loading is halted at a position equivalent to point [a] in Fig. 10)Fig. 19. Cyclic undrained shear behavior of sand subjected to liquefaction history=reliquefaction behavior (in the case where the ˆrst cyclic undrained shear loading is halted at a position equivalent to point [b] in Fig. 10)Fig. 20. Cyclic undrained shear behavior of sand subjected to liquefaction history=reliquefaction behavior (in the case where the ˆrst cyclic undrained shear loading is halted at a position equivalent to point [c] in Fig. 10) 24YAMADA ET AL.Fig. 21. Cyclic undrained shear behavior of sand subjected to liquefaction history=reliquefaction behavior (in the case where the ˆrst cyclic undrained shear loading is halted at a position equivalent to point [d] in Fig. 10)Fig. 22. Cyclic undrained shear behavior of sand subjected to liquefaction history=reliquefaction behavior (in the case where the ˆrst cyclic undrained shear loading is halted at a position equivalent to point [e] in Fig. 10)the liquefaction resistance each time the test was performed because the stress amplitude assigned was qmax=22.6 kPa. It can be seen from the above that anisotropysurpasses even density as the factor that holds the key toliquefaction resistance.Finally, let us also discuss the deviator stress-axialstrain relationship during reliquefaction (Figs. 18 to 22).First, it can be observed that strain growth is biased in thedirection of shear, which exhibits behavior that is similarto that of relatively loose sand due to the eŠect ofanisotropy developed during liquefaction. This corresponds to the manner in which initial anisotropy aŠectscyclic undrained shear behavior (Fig. 5). However, misalignment occurs in the direction of growth mainly during the ˆrst wave where the cyclic mobility trace begins.The anisotropy of the specimen at the time of commencement of cyclic undrained shear loading does exert a slightin‰uence on strain growth after that. However, information regarding the direction and level of anisotropy at thetime of commencement of cyclic undrained shear loadingis eventually forgotten. This is evident from the fact thatduring the 2nd occurrence of liquefaction behavior, therewas absolutely no eŠect of the anisotropy (initialanisotropy) that occurred at the time of commencementof the 1st cyclic undrained shear loading (Figs. 18 to 22).What is worthy of attention in the deviator stress-axialstrain relationship is the eŠect of the density increase thatoccurs during the stage of drainage after liquefaction.Comparison of Fig. 5 with Figs. 18 to 22 shows that theamount of strain growth per cycle is smaller during the2nd liquefaction test than in the 1st liquefaction test. Inaddition, it is strongly evident in Fig. 1 that increases inthe density tend to prevent the appearance of strain. Inthe case of liquefaction resistance, anisotropy surpasseseven density as the key factor of in‰uence. On the otherhand, it can be said that density is the more importantfactor with respect to the deformation that occurs duringliquefaction.CONCLUSIONIn the current study, triaxial tests were carried out toexamine the changes in anisotropy taking place duringliquefaction and to investigate the eŠects of theanisotropy developed during liquefaction on reliquefaction behavior. The main conclusions obtained in this RELIQUEFACTION RESISTANCE AND ANISOTROPYFig. A1.25Reliquefaction test (continued from Fig. 1)study are outlined below.1) During liquefaction, continuous and orderly changesin anisotropy are repeated with dizzying rapidity. Because of this, the anisotropy exists in various states ofdevelopment when liquefaction ends. Furthermore,the developed anisotropy remains without fading oŠeven after drainage.2) As the level of developed anisotropy increases, liquefaction is facilitated because behavior resemblingthat of looser sand is exhibited when sand is subjectedto shear in a certain direction.3) In cases where, because of being subjected to liquefaction history, the anisotropy has developed to appreciably higher levels than before liquefaction, thesand exhibits behavior resembling that of extremelyloose sand in spite of increased density. As a result, itsliquefaction resistance decreases signiˆcantly. In contrast, in cases where the level of anisotropy after liquefaction becomes appreciably low compared withthat before liquefaction, behavior resembling that ofextremely loose sand will not occur in any direction ofshear. Because of this, the liquefaction resistance is increased to levels that cannot be explained by only thedensity increases occurring during drainage after liquefaction.It must be admitted that the relationship between thedirection of development of anisotropy and the sheardirection in actual soils is not simple enough to be simulated by triaxial shear tests. Nevertheless, however complicated the relationship may be, because seismic vibrations occur in various diŠerent directions, soils with highly developed levels of anisotropy can be expected tonaturally exhibit shear behavior similar to that of loosesand and liquefy easily during an earthquake. Theauthors end this paper by adding that this type of possibility has been indicated by the results of experimentscarried out under limited conditions.REFERENCES1) Finn, W. D. L., Bransby, P. L. and Pickering, D. J. (1970): EŠect ofstrain history on liquefaction of sand, J. Soil Mech. Found. Div.,ASCE, 96(6), 1917–1934.2) Ishihara, K. and Okada, S. (1978): EŠects of stress history on cyclicbehavior of sand, Soils and Foundations, 18(4), 31–45.3) Ishihara, K. and Okada, S. (1982): EŠects of large pre-shearing oncyclic behavior of sand, Soils and Foundations, 22(3), 109–125.4) Seed, H. B., Mori, K. and Chan, C. K. (1977): In‰uence of seismichistory on liquefaction of sands, J. Geotech. Engrg. Div., ASCE,103(4), 257–270.5) Towhata, I. and Ishihara, K. (1985): Undrained strength of sand undergoing cyclic rotation of principal stress axes, Soils and Foundations, 25(2), 135–147.6) Yasuda, S. and Tohno, I. (1988): Sites of reliquefaction caused bythe 1983 Nihonkai-Chubu earthquake, Soils and Foundations, 28(2),61–72.7) Yoshida, N. and Wakamatsu, K. (1990): Re-liquefaction of ˆll landa comparison between the Loma Prieta earthquake and Japaneseearthquakes, Proc. International Symposium of Safety of UrbanLife and Facilities, 3.1–3.15.APPENDIX A: BEHAVIOR DURINGRELIQUEFACTION FOR A FIFTH TIMEFigure A1 shows the behavior during reliquefactiontest shown in Fig. 1 when it was carried out for the 5thtime. The positions of halting the liquefaction test in Fig.1 correspond to the following: the ˆrst time correspondsto [f] in Fig. 8, the second time corresponds to [c] in Fig.10, the third time corresponds to [a] in Fig. 10, and thefourth time corresponds to [b] in Fig. 10.
  • ログイン
  • タイトル
  • Experimental Study on the Behavior of Unsaturated Compacted Silt under Triaxial Compression
  • 著者
  • "Fusao Oka, Takeshi Kodaka, Hirotaka Suzuki, Y. S. Kim, Norisuke Nishimatsu, Sayuri Kimoto"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 27〜44
  • 発行
  • 2010/02/15
  • 文書ID
  • 64339
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 27–44, Feb. 2010EXPERIMENTAL STUDY ON THE BEHAVIOR OF UNSATURATEDCOMPACTED SILT UNDER TRIAXIAL COMPRESSIONFUSAO OKAii), TAKESHI KODAKAii), HIROTAKA SUZUKIiii),YOUNG SEOK KIMiv), NORISUKE NISHIMATSUv) and SAYURI KIMOTOi)ABSTRACTMost of the experimental investigations conducted on unsaturated soil have been performed under a constant airpressure. Changes in air pressure during deformation are in some cases important in practice. For example, in order toexplain the stability problems of embankments during earthquakes and seepage ‰ow, and grounds containing gas associated with the dissociation of methane hydrates, it is necessary to consider the interaction between the soil and thepore ‰uids. In the present study, we carried out fully undrained tests as well as drained tests, namely, constant waterand constant air shearing tests. We performed the fully undrained tests using an air-controlled valve to measure thepore air pressure. For the stress variables of the unsaturated soil, skeleton stress values were used to describe the experimental results. From triaxial compression tests on silty soil, we found that the initial suction, the conˆning pressure, and the strain rate of unsaturated soil strongly in‰uence the stress-strain behavior of unsaturated silt.Key words: laboratory tests, silt, suction, triaxial compression tests, unsaturated soil (IGC: D6)the specimen. For simplicity, we can call this the ``fullyundrained condition''.Since neither pore water nor pore air can ‰ow out fromthe soil in the fully undrained tests, both the pore-waterpressure and the pore-air pressure have to be accuratelymeasured. In the present study, we have performed fullyundrained tests, i.e., constant pore-water content andconstant pore-air content tests, using an air pressureoperated valve located close to the cap of the cell to measure the pore-air pressure. We have used the skeletonstress, which is equivalent to the average skeleton stressoriginally adopted by Jommi (2000), instead of the netstress, to describe the results of the tests on the unsaturated soil.The outline of the present paper is as follows. Firstly,the stress variables used in this study are presented. Secondly, a method for measuring the volume changes in unsaturated soil and a method for measuring the air pressure are introduced. Then, the results of triaxial compression tests on unsaturated soil under diŠerent drainageconditions are presented. These tests have been performed in order to investigate the changes in suction andpore pressure. Finally, the eŠects of the drainage conditions, the suction, the conˆning pressure, and the strainrate on the behavior of unsaturated soil are discussed using the test results.INTRODUCTIONMany laboratory tests have been conducted on unsaturated soil under a constant air pressure. However, thedrained conditions for water and air cannot always be attained in engineering problems. For example, the airpressure in river embankments increases during theseepage process and may vary during soil compaction.Yamamura (1971) indicated that air can become trappedin parts of embankments during heavy rains or ‰ooding.In the dissociation of methane hydrates that may occurduring the development of methane gas in the ground,even subsurface sea ground (Kimoto et al., 2007) becomesunsaturated with high gas pressure. In addition, pore airand pore water cannot e‹ciently ‰ow out from the soilskeleton during earthquakes. In these cases, the air pressure changes under the partially drained conditions;hence, it is necessary to investigate the air-water-soil interaction. This means that constant water and constantair content tests are needed to accurately verify the numerical models of unsaturated soil for general boundaryconditions.For this reason, we have conducted triaxial tests on silty clay under fully undrained conditions for water and airin which both the water content and the air content areconstant; that is, the mass of water and air are constant ini)ii)iii)iv)v)Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan (foka@mbox.kudpc.kyoto-u.ac.jp).Department of Civil Engineering, Meijo University, Nagoya, Japan.Osaka Gas, Osaka, Japan (formerly Master Course Student of Kyoto University, Japan).Korean Institute of Construction Technology, Seoul, Korea (formerly Doctoral Course Student of Kyoto University, Japan).Osaka City, Osaka, Japan (formerly Master Course Student of Kyoto University, Japan).The manuscript for this paper was received for review on November 11, 2008; approved on September 29, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.27 OKA ET AL.28STRESS VARIABLESTo analyze unsaturated soil, it is necessary to chooseappropriate stress variables. Stress variables for suctionand the excess total stress over the air pressure (or the excess total stress over the water pressure) have been used todescribe the mechanical behavior of unsaturated soil(Bishop, 1960; Fredlund and Morgenstern, 1977; Alonsoet al., 1990; Wheeler and Sivakumar, 1995). Karube andKawai (2001) used a generalized Bishop's stress, whileKohgo et al. (1993) and Loret and Khalili (2000) adoptedan eŠective stress that includes constitutive parameters.Recently, the term ``eŠective stress,'' or ``average skeleton stress,'' has been used when considering the mixturetheory (Bolzon et al., 1996; Jommi, 2000; Ehlers et al.,2004). The average skeleton stress is deˆned as the diŠerence in stress between the total stress and the average porepressure composed of pore-water pressure and pore-airpressure. A mathematical formula of the average skeleton stress is equal to the eŠective stress, or the generalizedeŠective stress, for unsaturated soil (Bolzon et al., 1996;Ehlers et al., 2004; Nuth and Laloui, 2008). However, itseems that the term ``eŠective'' is not appropriate because we need suction in order to describe the behavior ofunsaturated soil with skeleton stress. In addition, it is better to refer to the average skeleton stress simply as ``skeleton stress'' to avoid confusing the average skeleton stresswith the mean skeleton stress.The stress parameters used in the description of the experimental results are introduced below. The soil suction,as quantiˆed in terms of relative humidity, is commonlycalled ``total suction.'' It has two components, namely,matric suction and solute suction. The solute suction canbe disregarded because its value is less than that of thematric suction. The total suction usually equals thematric suction in geotechnical problems (Aitchison, 1960;Coleman, 1962).The matric suction, simply referred to as the suction inthis study, is deˆned asSuctions : s = u a- u w(1)where ua is the pore-air pressure and uw is the pore-waterpressure.In order to describe the experimental results for the unsaturated soil in this study, we use the skeleton stress.Deˆnitions for the skeleton stress and the average pore‰uid pressure are given as follows:s?ij=sij-P FdijP F=Sruw+(1-Sr)ua(2)(3)where s?ij is the skeleton stress, uw and ua are the porewater pressure and the pore-gas pressure, respectively, Sris the degree of saturation, and P F is the average porepressure.The adoption of skeleton stress represents a natural extension of the mixture theory to unsaturated soil (e.g.,Kim et al., 2005; Oka et al., 2006; Oka et al., 2008).Therefore, it is possible to formulate a model for unsaturated soil starting from a model for saturated soil by sub-stituting the skeleton stress for the eŠective stress. In addition, we have incorporated the suction into the constitutive model (e.g., Oka et al., 2008). This indicates theuse of a plural number of stress variables, i.e., skeletonstress and suction. A stress variable similar to that in Eq.(2) has been used by several researchers, such as Bolzon etal. (1996), Houlsby (1997), Jommi (2000), Gallipoli et al.(2002), Gallipoli et al. (2003), Ehlers et al. (2004), Wheeler et al. (2003), and Nuth and Laloui (2008). Bolzon et al.(1996), Ehlers et al. (2004), and Nuth and Laloui (2008)called it the eŠective stress, or the generalized eŠectivestress. Wheeler, Sharma, and Buisson (2003) used thename ``Bishop's stress'' for the eŠective stress or theaverage skeleton stress. Herein, we refer to it as the skeleton stress, not the eŠective stress, because we take boththe skeleton stress and suction into account.DESCRIPTION OF THE TEST DEVICEA schematic ˆgure of the triaxial test apparatus used inthis study is shown in Fig. 1(a). We employed a lucidacrylic cell so that the behavior of the specimens duringthe tests could be observed from outside the triaxial cell.The vertical load of the soil specimens was measured bythe inner load cell set up between the loading rod and thetop cap of the triaxial cell. Cell pressure was supplied byair pressure and was measured by a pressure gauge set onthe outside of the triaxial cell. The axial displacement wasmeasured by a proximity transducer for low levels of axial strain of less than 0.1z, and by a local vertical deformation transducer (LVDT) for medium to high levels ofstrain. A diŠerential pressure transducer was used tomeasure the changes in volume of the pore water.The above-mentioned testing equipment and arrangements are commonly used for fully saturated soils. Theconventional triaxial apparatus was modiˆed, therefore,to prepare the unsaturated soil for testing. The presenceof air in the pores made the testing procedure and thetechniques more complex than for ‰uid-saturated soil.The most important and yet also the most di‹cult part oftesting the unsaturated soil was that the pore-air pressureand the pore-water pressure had to be measured and controlled independently. In addition, it was necessary tomeasure the changes in volume during the tests.The triaxial cell used in this study for testing the unsaturated soil is illustrated in Fig. 1(b). In order toseparate the routes for the measurement and the controlof the pore-air pressure and the pore-water pressure, apoly‰on ˆlter and a ceramic disc were applied. The poly‰on ˆlter was placed on the top of each specimen to cutoŠ the ‰ow of water. The pore-air pressure that passedthrough the poly‰on ˆlter was measured by a pressuregauge. The ceramic disc was installed in the lowerpedestal to cut oŠ the ‰ow of air. The pore-water pressurewas measured by a diŠerential pressure transducer at thebottom of the specimen. The air entry value (A.E.V.) ofthe ceramic disc was 200 kPa.The changes in volume of each specimen during thetriaxial tests were evaluated by measuring the lateral dis- UNSATURATED COMPACTED SILTFig. 1(a).Fig. 1(b).29Schematic ˆgure of the triaxial test apparatusSchematic ˆgure of the triaxial cellplacements of the two sides of the specimen with fourproximity transducers. Aluminum foil was used as a target for the proximity transducers. The main advantage ofthis method is that changes in volume can be obtainedwithout any contact with the specimen. The proximitytransducers used in this study can be controlled by lateralmovements from outside the triaxial cell.Fully undrained tests are special tests for unsaturatedsoil. Since it is di‹cult to control the pore-air pressure,this kind of experimental research has, to our knowledge,never been performed before. In the fully undrainedtests, no pore air or pore water are allowed to ‰ow out inthe shearing process. In other words, the drainage valvesfor pore air and pore water are kept closed during shearing. Fully undrained loading causes further developmentsof excess pore-air pressure and pore-water pressure. Thevolume of the soil specimen may not remain constantduring the shearing process; it may change due to thecompression of pore air.In particular, an accurate measurement of the pore-airpressure of the specimen is important in the tests. Therefore, we improved the system for the purpose of takingmeasurements and controlling of the pore-air pressurelevels (Suzuki et al., 2006). As mentioned above, aschematic ˆgure of the modiˆed triaxial cell used in thefully undrained tests is shown in Fig. 1(b). The pore-airpressure passing through the poly‰on ˆlter was measuredfrom the top of the specimen by a pressure gauge installed OKA ET AL.30in the triaxial cell. In addition, fully undrained conditionsduring shearing were controlled by an air-operated valveinstalled in Fig. 1(b). This valve is called a ``Diaphragmvalve with an air actuator''; it is controlled by air pressure. This means we can shut oŠ the valve by applying airpressure to the outside of the valve. In this study, in orderto close the line for controlling the air pressure of thespecimen, we applied an air pressure of 500 kPa througha tube which is connected to the top of the valve illustrated in Fig. 1(b). The amount of the space between the airpressure gauge and the top of the specimen is very small;for example, the ratio of the air volume of the abovespace to the volume to the air contained in the specimenwas 1.2z, and the volume is 0.684 cm3 when the saturation was 46.6z. As mentioned in the description of thetest device, the pore-water pressure was measured fromthe bottom of the specimen by a diŠerential pressuretransducer.Grain size accumulation curvevolume was performed using saturated soil in order to determine the appropriate positions for the proximeters(Kim, 2004; Nishimatsu, 2004).CALIBRATION PROCEDURE FOR MEASURINGTHE CHANGES IN VOLUMEThe general method for measuring the changes involume during drained triaxial tests on saturated specimens is to measure the quantity of the water expelled orabsorbed. In the case of unsaturated soil, changes involume occur due to the drainage of a mixture of air andwater. Bishop and Henkel (1962) and Matyas (1967) developed a procedure to measure the volume of both ‰uidphases using two burettes. However, this method is notthought to produce accurate measurements of thechanges in volume due to the eŠects of compressibilityand capillarity in the air bubbles. Over the years, severaltechniques have been proposed to address the shortfallsof this procedure. One of them consists of measuring theeŠect of sample volume changes on the surroundingtriaxial cell liquid by using double-walled triaxial cells(Bishop and Donald, 1961; Sivakumar, 1993). Othermethods for measuring the overall volume changes in unsaturated soil include performing direct measurements ofthe axial and the radial deformation of the specimen using the internal LVDT, Hall eŠect transducers (Claytonand Khatrush, 1986), non-contacting transducers locatedaround the specimen (Cole, 1978; Khan and Hoag, 1979),strain gauges (Lo Presti et al., 1995; Kolymbas and Wu,1989), opto-electronic sensors (Baumgartl et al., 1995),laser techniques (Romero et al., 1997), and image processing (Macari et al., 1997; Rifa'i et al., 2002).This study was carried out by placing non-contactingtransducers around the specimens, as shown in Fig. 1(a).Changes in the diameter of the specimens during the testing were measured with these four proximity transducers(proximeters). As a result, the average lateral strain wasobtained. The volumetric strain, ev, is given as follows:ev=ea+2erFig. 2.(4)where ea is the axial strain and er is the average lateralstrain measured by the proximity transducers.Before the tests, a calibration procedure for changes inPHYSICAL CHARACTERISTICS OF THE SOILTESTEDIn the present study, the soil used for the triaxial compression tests is DL clay (the commercial name). Driedand powdered DL clay consists of Kaolinite and silica.Kaolinite and silica stone are used as agricultural chemicals. DL clay is homogeneous and easy to obtain. It islarger in grain size than average clay and is composed of90z silt and 10z clay. The soil's index properties are WL=NP, Ip=NP, and Gs=2.65. The soil is classiˆed as having Mo-Low compressibility (ML) according to theJapanese Geotechnical Society (JGS). The grain size distribution of DL clay is represented by the grading curve inFig. 2, which shows that about 90z of the soil particlesare silt.PREPARATION OF THE SPECIMENS ANDTESTING PROCEDUREThe specimens used in the present study were preparedby the compaction method. Prior to performing the compaction, the dry DL clay, with a particle density (speciˆcgravity) of 2.65, was mixed well with water to make up20z of the water content. Then, the mixed wet DL claywas compacted statically in a cylindrical mold, 50 mm indiameter, to obtain the best possible standardhomogeneity; we used a single static compaction technique not used the usual multi-layer compaction methodsin sample preparation. The void ratio of the specimenswas around 1.1. All the specimens used in this experimental study were 50 mm in diameter and 100 mm in height.After compaction, the measured pore-water pressure levels were around -18 to -20 kPa for all the samples.This means that the preparation procedure was alwaysfollowed carefully in order to maintain a suction state ofapproximately 20 kPa on the compacted samples. The UNSATURATED COMPACTED SILTdry density of the specimens after the compaction wasaround 1.3 g/cm3.EXPERIMENTAL RESULTSDrainage/Water-Absorption ProcessBefore the shearing tests, the drainage/water-absorption process, which can also be called the ``equalizationstage,'' was performed by drainage or water absorptionunder cell pressure and the initial suction. The soil specimens were allowed to drain during the application of thecell pressure, and then were allowed to drain/absorbwater during the application of the initial suction. Asmentioned in the previous section, the suction measuredin each specimen after compaction was around 20 kPa.After reaching a cell pressure of 270 kPa and a pore-airpressure of 250 kPa, the measured pore-water pressurewas around 230 kPa for all the samples. The suction wasthen increased and decreased. In the ˆnal stage, the cellpressure was increased to speciˆc values. The paths in thesuction-cell pressure space during the drainage/water-absorption process are illustrated in Fig. 3.A high initial suction was applied by decreasing thepore-water pressure levels. For specimens with lower suction levels, on the other hand, the initial suction was controlled by increasing the pore-water pressure. The testconditions for all the specimens are summarized in Table1. Table 2 illustrates all the specimen data before thedrainage/water-absorption process. In the tests, wemaintained pore air pressure at a constant value of 250kPa mainly because we utilized pore water pressure ofmore than 100 kPa. From a technical point of view theauthors think that a rather high value of pore water pressure is preferable to accurately measure the positive andnegative pore water pressures. The air pressure of 250kPa is higher than the air entry value of 200 kPa of theceramic disk used in the experiment. Hence, in thepreparatory tests, we conˆrmed no air inˆltration duringthe tests. This is probably due to the net pressure (diŠerence between the air pressure and the water pressure)being less than the air entry value. If we had used a ceramic disc with a higher A.E.V., it would have taken moreFig. 3.Stress paths during the drainage/water-absorption process31time for consolidation.Figure 4 represents the drainage or the water absorption at diŠerent levels of initial suction and a cell pressureof 450 kPa. As shown in this ˆgure, similar behavior under the same initial suction is obtained. The amount ofdrained water grew larger with an increase in the initialsuction. The drainage of water occurred when the specimens were tested under initial suction levels of more than20 kPa, i.e., 20, 30, 40, 50, 100, and 150 kPa. However,water absorption occurred when the specimens were tested under the initial suction level of 20 kPa, i.e., at 0 and10 kPa. Water absorption occurred when the initial suction was lower than it was just after the compaction ofthe samples.Therefore, when the initial suction was higher than thesuction after compaction, namely, at 30, 40, 50, 100, andTable 1.Test conditions for all unsaturated soil specimensNo.D150–1 D100–1 D50–1 D50–3–1 D50–3–2Initial suction (kPa)150100505050Strain rate (z/min)0.050.050.050.050.05Cell pessure (kPa)450450450650350Pore air pressure (kPa)250250250250250Pore water pressure (kPa)100150200200200Conˆning pressure (kPa)200200200400100No.D40–1D30–1D20–1D10–1D0–1Initial suction (kPa)403020100Strain rate (z/min)0.050.050.050.050.05Cell pessure (kPa)450450450450450Pore air pressure (kPa)250250250250250Pore water pressure (kPa)210220230240250Conˆning pressure (kPa)200200200200200No.U100–1 U50–1 U50–2–1 U50–2–2 U50–3Initial suction (kPa)10050505050Strain rate (z/min)0.50.50.750.050.5Cell pessure (kPa)450450450450350Pore air pressure (kPa)250250250250250Pore water pressure (kPa)150200200200200Conˆning pressure (kPa)200200200200100No.U30–1U10–1U0–1Initial suction (kPa)30100Strain rate (z/min)0.50.50.5Cell pessure (kPa)450450450Pore air pressure (kPa)250250250Pore water pressure (kPa)220240250Conˆning pressure (kPa)200200200 OKA ET AL.32Table 2.Specimen data before the drainage/water-absorption processNo.D150–1 D100–1D50–1 D50–3–1 D50–3–2Saturation Sr (z)47.0847.2147.0146.9447.03Water content w (z)20.0120.0320.0019.9419.94Void ratio e1.131.121.131.131.12No.D40–1D30–1D20–1D10–1D0–1Saturation Sr (z)47.1147.0946.7046.9947.11Water content w (z)19.9620.0619.8119.9520.06Void ratio e1.121.131.121.121.13No.U100–1Saturation Sr (z)47.0547.3747.5447.1847.15Water content w (z)19.9720.1220.1720.0019.99Void ratio e1.131.131.121.121.12No.U30–1U10–1U0–1Saturation Sr (z)47.0847.1347.30Water content w (z)19.9820.0420.07Void ratio e1.121.131.12U50–1 U50–2–1 U50–2–2 U50–3Fig. 5. Changes in volume during the drainage/water-absorptionprocessFig. 6. Changes in void ratio during the drainage/water-absorptionprocessFig. 4. Drained water/absorbed water during the drainage/water-absorption process150 kPa, initial suction was controlled by decreasing thepore-water pressure levels. On the other hand, at lowersuction levels, initial suction was controlled by increasingthe pore-water pressure.The changes in volume during the drainage/water-absorption tests are shown in Fig. 5. As can be observedfrom this ˆgure, the volumetric strain reduced with increases in the initial suction. The results show that little orno volumetric strain occurred until the loading of the cellpressure, and that a large instantaneous decrease involume was brought about by the application of the load.Figure 6 shows the changes in void ratio against theFig. 7.Water retention curve/Soil water characteristic curvemean skeleton stress during the drainage/water-absorption process. It can be seen that the slope tends todecrease with an increase in the initial suction. A cleardecrease in compressibility is observed when the suction UNSATURATED COMPACTED SILTTable 3.33Specimen data after the drainage/water-absorption processNo.D150–1 D100–1Volumetric strain (z)D50–1 D50–3–1 D50–3–22.403.582.816.431.40Drained water (cm )31.6427.7116.1815.0513.59Saturation Sr (z)17.2721.8333.1336.8734.78Water content w (z)7.018.6313.3513.7614.36Void ratio e1.061.051.070.991.09No.D40–1D30–1D20–1D10–1D0–13.943.203.334.455.46Drained water (cm )9.786.321.53-6.45-15.48Saturation Sr (z)40.6643.6248.2658.1269.19Water content w (z)15.9417.4619.1822.6026.43Void ratio e1.041.061.051.031.01No.U100–13Volumetric strain (z)3Volumetric strain (z)U50–1 U50–2–1 U50–2–2 U50–33.542.803.673.801.42Drained water (cm )27.8916.0416.0416.6613.57Saturation Sr (z)21.5033.6134.3733.4334.93Water content w (z)8.5213.5213.5713.1514.41Void ratio e1.051.071.051.041.09No.U30–1U10–1U0–13.705.306.00Drained water (cm )6.47-6.51-15.96Saturation Sr (z)43.8959.3670.81Water content w (z)17.3222.7226.63Void ratio e1.051.011.003Volumetric strain (z)3Fig. 8. Deviator stress-axial strain relations for specimens with diŠerent levels of initial suction under drained conditionsincreases. Figure 7 shows the water retention curve obtained by the drainage/water-absorption process.It is seen that the degree of saturation obtained underthe same initial suction is similar to the value after thedrainage/water-absorption process. The degree of saturation also decreases with an increase in the initial suction. The specimen data after the drainage/water-absorption tests are summarized in Table 3. It should be notedthat the sample with zero suction was not saturated, i.e.,from Tables 1 and 3, the saturation is 70z for the specimen with zero suction (U0–1).Drained Triaxial Compression Test ResultsThe drained tests were conducted after the drainage/absorption process, with the samples sheared underdrained conditions for both the pore-air phase and thepore-water phase. During the shearing process, the specimens were compressed in the axial direction by applyingthe deviator stress, i.e., s1-s3, and by keeping thedrainage valves for both pore air and pore water open.The pore-air pressure and the pore-water pressure werecontrolled at a constant pressure. Therefore, the initialFig. 9. Deviator stress-axial strain relations for specimens with diŠerent levels of initial suction under drained conditions (in the smallstrain range)suction remained constant until failure conditions werereached, which was at 15z of the axial strain in thisstudy.In this section, the eŠects of the initial suction and theconˆning pressure under drained conditions will be described. Tests were carried out on samples D150–1,D100–1, D50–1, D40–1, D30–1, D20–1, and D10–1(Table 1). The specimen data before the shearing tests arepresented in Table 2.1) EŠect of the initial suctionThe eŠect of the initial suction on the tests underdrained conditions was investigated for CasesD150–1¿D0–1. The drained tests were carried out with aconstant stain rate of 0.05z. Figures 8–12 show comparisons among the results with initial suctions of 0,10, 20,30, 40, 50, 100, and 150 kPa under a constant conˆningpressure of 200 kPa.The stress-strain relations under diŠerent suction levelsare illustrated in Figs. 8 and 9. The results show an increase in the shear strength with an increase in the initialsuction. The deviator stress for the samples with higherlevels of initial suction is larger than that for the sampleswith lower levels of initial suction. The diŠerence among OKA ET AL.34Fig. 12.Fig. 10.Saturation-axial strain relations under drained conditionsStress paths under drained conditionsFig. 13. Deviator stress-axial strain relations for diŠerent levels ofconˆning pressure under drained conditionsFig. 11. Volumetric strain-axial strain relations and normalized-axialstrain relations under drained conditionsthe stress-strain curves becomes smaller as the strain increases in the range of an axial strain of 10–16z.As shown in the small strain range of Fig. 9, for an axial strain of about 0.05z, the initial secant modulus witha suction of 150 kPa is two times larger than that obtained with a suction of 0 kPa. On the other hand, the dependence of the initial modulus on the initial suction isnot observed in the early stages of shearing.Figure 10 illustrates stress paths in terms of the deviator stress and the mean skeleton stress. Since the meanskeleton stress is used, the slope of the stress paths is not3.0 and the initial mean stress levels are not the same.Figure 11 shows the volumetric strain and the normalizeddrained water with respect to the initial value versus axialstrain during shearing. For the volumetric strain, the soilspecimen exhibits contractancy during shearing and thevolume continuously decreases. The volume changesbecome small with an increase in the initial suction. Infact, the volume change curves are only valid up to an axial strain of 10z because of the limitations of the measurement method. It can be seen that the compressibilitydecreases when the initial suction increases.During the shearing process, water drainage occurswith initial suctions of 30–150 kPa, whereas water absorption occurs with initial suctions of 0, 10 and 20 kPawhile the volume change is compressive. As mentionedfor the drainage/water-absorption process, this behavioris due to the fact that the initial suction is less than 20kPa, namely, the suction after the compaction of thesample.Figure 12 shows the degree of saturation versus the axial strain during shearing. Suction increases slightly forthe lower levels of initial suction, 0–20 kPa, while saturation is almost constant for the higher levels of suction.2) EŠect of the conˆning pressureThe eŠect of the conˆning pressure at a constant suction is illustrated in Figs. 13–17. The ˆgures show a comparison among the results of cell pressure levels of 650,450 and 350 kPa with an initial suction of 50 kPa and astrain rate of 0.05z/min.The stress-strain relations and the stress paths underdiŠerent cell pressures are illustrated in Figs. 13 and 14.The maximum deviator stress and the initial modulus increase with an increase in cell pressure for both large andsmall strain ranges. For the stress paths shown in Fig. 15,where the horizontal axis is the mean skeleton stress, themean skeleton stress increases from its initial value. From UNSATURATED COMPACTED SILTFig. 14. Deviator stress-axial strain relations for diŠerent levels ofconˆning pressure under drained conditions (in the small strainrange)35Fig. 17. Saturation-axial strain relations for diŠerent levels of conˆning pressure under drained conditionsFig. 15, it is seen that the ˆnal points of the stress pathsall meet at a straight line with a gradient of 1.23 that passes through the origin. Figure 16 shows the volumetricstrain and the normalized drained water versus the axialstrain. The eŠect of the cell pressure is not clear for thevolume changes and drained water. Figure 17 illustratesthe changes in saturation during the tests for diŠerent levels of conˆning pressure. The trend of the changes insaturation is similar in all cases and is not signiˆcantly in‰uenced by the conˆning pressure.Fig. 15. Stress paths for diŠerent levels of conˆning pressure underdrained conditionsFig. 16. Volumetric stain-axial strain relations for diŠerent levels ofconˆning pressure under drained conditionsFully Undrained Triaxial Compression Test ResultsMany laboratory tests have been conducted on unsaturated soil under a constant air pressure. However, thedrained conditions for water and air cannot always be attained in engineering problems. For example, the airpressure in river embankments increases during theseepage process (Yamamura, 1971) and it may also varyduring soil compaction. Since, in general, the air pressurechanges under partially drained conditions, constantwater and constant-air content tests (on the constantgravimetric water and air content, e.g., Wulfsohn,Adams and Fredlund, 1998) need to be carried out in order to accurately describe the behavior of unsaturatedsoil under general boundary conditions. In the presentpaper, we have conducted triaxial tests on silty clay underfully undrained conditions for water and air.In order to conˆrm that no leakage of air has occurredthrough the measuring lines, the pore pressure was measured under fully undrained conditions with the isotropiccell pressure for the specimen with a suction of 50 kPa. Inthe tests, the cell pressure was 450 kPa, and the pore-airpressure and the pore-water pressure just before shuttingoŠ the valves were 250 kPa and 200 kPa, respectively.Figures 18 and 19 indicate the changes in volume and inthe pore-air pressure and the pore-water pressure, respectively. From these ˆgures, it is seen that the volume 36OKA ET AL.Fig. 18. Volumetric strain-time proˆle under fully undrained conditions during the application of isotropic stressFig. 20. Stress paths for specimens with diŠerent levels of initial suction under fully undrained conditionsFig. 19. Pore-air and pore-water proˆles under fully undrained conditions during the application of isotropic stresschange was almost zero, the pore-water pressure was constant, and the pore-air pressure decreased slightly, by just0.5 kPa after 15 min, and then decreased by 1.5 kPa after60 min. This is due to the dissolution of the air into thepore water and not to the leakage of air. If any leakage ofair had occured, the air pressure would have increased.This means that fully undrained conditions were successfully satisˆed. Since the strain rate was set to 0.5z/minin the following tests, and it takes 30 min for the axialstrain to reach a strain of 15z, the possible change in airpressure due to the solution was around 0.5 kPa andcould be considered negligible. From the above-mentioned data, we set the strain rate to be 0.5z/min for thefully undrained tests, and then carried out the tests atstrain rates of 0.05z/min and 0.75z/min. Due to thelimitations of the apparatus, the maximum strain ratewas 0.75z/min.In this section, the behavior of the pore pressure andthe suction during the shearing process are described.Furthermore, the eŠects of the strain rate, the initial suction, and the conˆning pressure under fully undrainedconditions will be discussed.Fig. 21. Deviator stress-axial strain relations for specimens with diŠerent levels of initial suction under fully undrained conditions1)EŠect of the initial suctionIn order to study the eŠect of the initial suction on thefully undrained tests, we carried out tests for specimenswith various levels of suction, namely, 0, 10, 30, 50 and100 kPa with a conˆning pressure of 200 kPa and a strainrate of 0.5z/min. All of the tests were conducted underfully undrained conditions and under a constant cell pressure of 450 kPa. From the stress paths shown in Fig. 20,it is seen that the decrease in the mean skeleton stress forthe same deviator stress level was smaller with higher levels of suction and that the maximum deviator stressbecame larger for specimens with higher levels of initialsuction. When the initial suction was at 0 and 10 kPa, themean skeleton stress decreased and was less than the initial stress. As seen in this ˆgure, the ˆnal points meet on astraight line with a gradient of 1.23 and an intercept of 8kPa. The stress-strain relations shown in Fig. 21 indicatethat the deviator stress at the same axial strain is largerwith higher levels of initial suction. From Fig. 22, it isseen that as the initial suction becomes higher, so does the UNSATURATED COMPACTED SILTFig. 22. Deviator stress-axial strain relations for specimens with diŠerent levels of initial suction under fully undrained conditions (in thesmall strain range)37Fig. 25. Pore-air pressure-axial strain relations for specimens withdiŠerent levels of initial suction under fully undrained conditionsFig. 26. Pore-water pressure-axial strain relations for specimens withdiŠerent levels of initial suction under fully undrained conditionsFig. 23. Volumetric strain-axial strain relations for specimens withdiŠerent levels of initial suction under fully undrained conditionsFig. 24. Suction-axial strain relations for specimens with diŠerent levels of initial suction under fully undrained conditionsinitial modulus in the axial strain range between 0.0 and0.04z. Figure 23 illustrates the volumetric strain-axialstrain relations. It is seen that at the same axial strain, ahigher suction results in a smaller volumetric strain. Inthe case of a suction of 100 kPa, the volumetric strain increases and then decreases after reaching an axial strainof 10z. This is due to incline of the target of the gap sensor for measuring the volumetric strain after the deformation of the specimen. The plot of the suction againstthe axial strain in Fig. 24 shows that suction immediatelydecreased, then increased, and ˆnally for the lower levelsof initial suction, namely, 0, 10, and 30 kPa, the suctiongradually increased to a constant value. For the higherlevels of initial suction, namely, 50 and 100 kPa,however, the suction decreased slightly and then becamealmost constant.Figures 25 and 26 show the changes in pore-air pressureand pore-water pressure, respectively, during the tests. Itis seen that the air pressure increased monotonically, butthat the water pressure increased extensively in the rangeof small strain. The extensive decrease in suction in theearly stages of straining was caused by the extensive in- 38OKA ET AL.Fig. 27. Saturation-axial strain relations for specimens with diŠerentlevels of initial suction under fully undrained conditionsFig. 28. Stress paths for saturated specimens under undrained conditionscrease in pore-water pressure. This behavior is associatedwith the great change in volume just after the start of theshearing because of the collapse of the loose structure ofthe soil specimen. From Fig. 25, it is seen that a lowersuction (greater saturation) will generate a high level ofpore-air pressure at the same level of axial strain. Thiscan be explained as follows. Since the volume of air in thespecimen is smaller for the case of higher levels of saturation and the changes in volume of the soil skeleton arealmost the same for all cases, the air is compressed largelyand the air pressure becomes high. Figure 27 indicates thesaturation-axial strain proˆle in which the saturation increases in all cases and then becomes constant.The stress conditions and the specimen data before theshearing tests are presented in Table 2; those after thetests are presented in Table 3.2) EŠect of the strain rateThe eŠect of the stain rate is well known for varioussoil materials; it is particularly signiˆcant for clayeymaterials. Before investigating the stain rate eŠect for unsaturated silt, we performed undrained tests for saturatedDL clay with diŠerent strain rates at a constant conˆningpressure of 200 kPa. Figures 28 and 29 illustrate thestress paths and stress-strain relations under undrainedsaturated conditions. The stress-strain responses are similar to those of loose sand (e.g., Ishihara, 1993). Fromthese ˆgures, the deviator stress for the case with a strainrate of 0.5z/min is larger than that for the lower strainrate of 0.05z/min in the axial strain range less than 1.37z. In contrast, in the larger strain range, the deviatorstress for the case with a lower strain rate of 0.05z/minis larger than that for the case with a higher strain rate of0.5z/min. In the very small strain range where the axialstrain is less than 0.05z, the strain rate eŠect is clear andit is similar to that of the clayey soil shown in Fig. 30. Anopposite trend of the strain rate eŠect is seen for the largestrain due to the unstable structural change in the loosegranular material and the viscoelastic nature of pore air.To investigate the strain rate eŠect, we have carried outFig. 29. Deviator stress-axial strain relations for saturated specimensunder undrained conditionsfully undrained triaxial compression tests with threediŠerent axial strain rates, i.e., 0.75z/min, 0.5z/minand 0.05z/min at a constant initial suction. Figures 31and 32 indicate the stress paths and the stress-strain relations, respectively. The deviator stress for the case withthe smallest strain rate (0.05z/min) is larger than thatfor the larger strain rates (0.5z/min and 0.75z/min),and the decrease in the mean skeleton stress at the peakstress for the smallest strain rate of 0.05z/min is smallerthan that for the other two strain rates. The stress ratio atfailure is about 1.27 which is very close to the value 1.23for both drained and fully undrained conditions shown inFigs. 15 and 20.In Fig. 33, for three diŠerent strain rates, the development of the compressive volumetric strain is similar atless than 8z of the axial strain. The diŠerence in the UNSATURATED COMPACTED SILTFig. 30. Deviator stress-axial strain relations for saturated specimensunder undrained conditions (in the small strain range)39Fig. 33. Volumetric strain-axial strain relations for specimens withdiŠerent strain rates under fully undrained conditionsFig. 34. Suction-axial strain relations for specimens with diŠerentstrain rates under fully undrained conditionsFig. 31. Stress paths for specimens with diŠerent strain rates underfully undrained conditionsFig. 32. Deviator stress-axial strain relations for specimens with diŠerent strain rates under fully undrained conditionschanges in suction for the three strain rates is not as largeas that indicated in Fig. 34, except during the early stagesof loading. The average pore pressure, which is estimatedfrom the pore-air and the pore-water responses shown inFigs. 35 and 36, respectively, indicates larger values forhigher strain rates. There are three reasons for the largeraverage pore pressure that develops in the case of largerstrain rates. The ˆrst reason is the dissolution of the poreair into the pore water; the reduction in pore-air pressureis 0.5 kPa up to an axial strain of 15z for the strain rateof 0.5z/min, as shown in Fig. 19. Accordingly, if we assume that the dissolution is proportional to the time, thereduction in air pressure for a strain rate of 0.05z can beestimated at 5 kPa up to an axial strain of 15z.However, the diŠerence in pore-air pressure between thetwo strain rates shown in Fig. 35 is more than 5 kPa. Thesecond reason is the hardening of the soil skeleton due tothe changes in the larger compressive volume during thelonger loading time for the smallest strain rate, namely,0.05z/min, indicated in Fig. 33. The third possible rea- 40OKA ET AL.Fig. 35. Pore-air pressure-axial strain relations for specimens withdiŠerent strain rates under fully undrained conditionsFig. 37. Stress paths for diŠerent levels of conˆning pressure underfully undrained conditionsFig. 36. Pore-water pressure-axial strain relations for specimens withdiŠerent strain rates under fully undrained conditionsson may be the viscosity of the pore ‰uids. It should bepointed out that the possible dissolution of the air intothe pore water leads to an increase in saturation and adecrease in suction, while Fig. 34 shows that the decreasein suction is similar for all three cases. For this type oftest on unsaturated soil, the eŠect of the strain rate ismore complex when compared to saturated soil (e.g.,Adachi and Oka, 1982); it depends on the dissolution ofthe pore air, the changes in volume, and the viscousresponse of the pore ‰uids. It is worth noting that thepeak strength envelope given by the straight line with agradient of 1.23 (M=1.23) and the intercept of 8 kPa inFig. 20 is consistent with that given in Fig. 31.3) EŠect of the conˆning pressureThe eŠect of the conˆning pressure at an initial suctionof 50 kPa was observed from the tests with cell pressurelevels of 450 kPa and 350 kPa. Figures 37–39 show comparisons of the results obtained from cell pressures levelsof 450 kPa and 350 kPa under fully undrained conditions. Since the initial air pressure was 250 kPa, the initialconˆning pressure levels were 200 kPa and 100 kPa.Fig. 38. Deviator stress-axial strain relations for diŠerent levels ofconˆning pressure under fully undrained conditionsFigure 37 shows the stress paths. For the case with aconˆning pressure of 200 kPa, the mean skeleton stressincreased monotonically with an increase in the deviatorstress. For the case with a conˆning pressure of 100 kPa,however, the mean skeleton stress increased and thendecreased after the deviator stress reached 140 kPa. It appears that the peak stress falls on the straight line with agradient of 1.23 and an intercept of 8 kPa. The stressstrain relations shown in Fig. 38 indicate that a higherconˆning pressure brings about a larger deviator stress.For the volumetric strain shown in Fig. 39, a large volumetric strain is observed at the same axial strain for thehigher conˆning pressure. With an axial strain in excessof 10z, it was conˆrmed that the measurement of thevolumetric strain is not reliable because of the inclinationof the target of the gap sensor using the volume change ofsaturated soil (Kim, 2004).The plot for the suction against the axial strain in Fig. UNSATURATED COMPACTED SILTFig. 39. Volumetric strain-axial strain and normalized drained wateraxial strain relations for diŠerent levels of conˆning pressure underfully undrained conditions41Fig. 42. Pore-water pressure–axial strain relations for diŠerent levelsof conˆning pressure under fully undrained conditions40 indicates that the magnitude of the extensive decreasein suction was larger for the lower levels of conˆningpressure. Figures 41 and 42 show the changes in pore-airpressure and pore-water pressure, respectively, againstthe axial strain. An increase in pore-air pressure was observed for higher levels of conˆning pressure. Forchanges in pore-water pressure, the extensive increase inpore-water pressure at the small strain level was larger forthe lowest level of conˆning pressure. The ˆnal porewater pressure was higher for the higher levels of conˆning pressure.DISCUSSIONSFig. 40. Suction–axial strain relations for diŠerent levels of conˆningpressure under fully undrained conditionsFig. 41. Pore-air pressure–axial strain relations for diŠerent levels ofconˆning pressure under fully undrained conditionsAs shown in Fig. 8, the stress-strain relations obtainedfrom the drained tests indicate that the deviator stress forthe higher levels of initial suction is larger than that forthe lower levels of initial suction in the early stages ofstraining, while the stress reaches almost the same valuewith an increase in strain. The stress-strain relations bythe fully undrained tests, shown in Fig. 21, produce asimilar trend, but the results are diŠerent, namely, theshear strength with the highest initial suction is quite a bitlarger than that with the smallest initial suction. TheeŠect of the initial suction on the stress-strain relation inthe fully undrained tests is more signiˆcant than that obtained from the drained tests.The stress paths obtained from the fully undrainedtests in Fig. 20 show a decrease in the mean skeletonstress for the lower levels of initial suction. This explainsthe strong dependence of the shear strength on the initialsuction in the above-mentioned fully undrained tests.Next we will discuss the development of volumetricstrain during both the drained and the fully undrainedtests. The volume change feature of the drained tests inFig. 11 is clear; a higher initial suction brings about asmaller volume change. This trend for the undrained testsis similar to the trend for the drained tests. By looking atthe details of the results in Fig. 23, however, it can beseen that the initial suction dependency of the volumetricstrain is not simple. For example, the development of 42OKA ET AL.volumetric strain in the case of an initial suction of 50kPa is larger than that for an initial suction of 30 kPa.This might be due to that the dependence of the volumechange on both the compressibility of the soil skeletonand the volume of pore air. The soil specimens withhigher levels of initial suction contain a larger volume ofpore air because of the low saturation.During the fully undrained tests in Fig. 24, the suctionimmediately drops and then increases for cases with alower initial suction or decreases for cases with a higherinitial suction, and then ˆnally reaches an almost constant value of suction. It is of interest to note that thistrend is diŠerent from that of the undrained tests, i.e.,the so-called constant water content test, in which thesuction decreases monotonically because the pore-waterpressure increases while the pore-air pressure is constant(e.g., Wulfsohn et al., 1998).The eŠect of the stain rate on the behavior of the soil isimportant not only for saturated soil, but also for unsaturated soil. However, there have been very few studies onthe eŠect of the strain rate on the behavior of soil for unsaturated soil, possibly because it is di‹cult to performfully undrained tests, i.e., water-content constant andair-content constant tests, to study the time dependencyseparately from that due to the pore-‰uid ‰ow. The stresspaths with higher strain rates indicate an opposite trend,i.e., for normally consolidated saturated clayey soil, thedecrease in the mean eŠective stress is smaller for higherstrain rates, while Fig. 31 shows that the decrease in themean skeleton stress is lower for lower strain rates. Thistype of behavior is consistent with the development of thelarger pore-water pressure and the larger pore-air pressure, i.e., a higher value for the average pore pressure.From the stress-strain relations and the volume changecharacteristics of both the drained tests and the fully undrained test results shown in Figs. 8, 10, 11, 20, 21, and23, it has been shown that the critical state concept can beapplied to the behavior of this silt considering the almostzero change in volume around the peak stress. From thestress paths by the deviator stress-mean skeleton stressplots in Figs. 10 and 15, the peak stress envelopes of thedrained tests yield a gradient of 1.23 with a zero intercept.On the other hand, the peak stress envelopes of the fullyundrained tests of Figs. 20, 31, and 37 provide a gradientof 1.23 and an intercept of 8 kPa on the deviator stressmean skeleton stress plane. The same value for thegradients along the critical state line for all cases indicatesthat the behavior of the unsaturated specimen tests in thepresent study can be described well through the use of theskeleton stress expressed by Eq. (2), although the intercepts are diŠerent between the drained and the fully undrained tests. This is consistent with the implication ofthe generalized eŠective stress by Nuth and Laluoi (2008).They showed that the generalized eŠective stress is usefulfor uniquely describing the behavior of unsaturated soil.As mentioned previously, the form of the generalizedeŠective stress is the same as that for the skeleton stressaccording to Eq. (2).CONCLUSIONSIn this paper, two types of triaxial compression testsfor unsaturated compacted silt with two diŠerentdrainage conditions were conducted. One type consistedof tests under drained conditions and the second underfully undrained conditions in which the water contentand the air content were constant. The fully undrainedtests were performed using an air-controlled valve formeasuring the pore-air pressure. The changes in volumeof the specimens during the tests were measured withnon-contacting transducers. The main conclusions obtained from the tests are as follows:1) Water content and air content constant tests were carried out using an air-controlled valve in the air pressure measuring system. This type of test is called afully undrained test. The fully undrained test resultsare useful for the modeling of unsaturated soil whichcan simulate the behavior of unsaturated soil duringrapid loading, such as during earthquakes. Themethod using the non-contacting transducers generated a good estimation of the volume measurement.2) During the isotropic drainage/water-absorption process, the gradient for the decreasing void ratio with themean skeleton stress decreased with increased suctionin the skeleton stress-void ratio plane. A clear decreasein compressibility was seen when the suction increased.3) The results by the drained tests showed that the deviator stress for the samples with the higher levels of initial suction was larger than that with the lower levelsof initial suction in the range in axial strain of 6–8z.The diŠerence between the stress-strain curves becameless as the strain increased and reached an almost constant value.4) In the fully undrained tests, the initial suction stronglyaŠected the stress-strain response. The shear strengthwas larger for samples with higher levels of suctionwhile the shear strength by the drained tests (that is,the shear stress at large levels of strain) were almostequal.5) Under the fully undrained conditions, both the excesspore-air pressure and the excess pore-water pressureincreased with increasing axial strain. The suctiondecreased extensively in the range of a small axialstrain of less than 0.5z from the initial value and thenthe suction increased for lower levels of initial suction,while the suction for higher levels of initial suction increased and then slightly decreased for higher levels ofinitial suction.6) The strain rate aŠected the stress-strain relations andthe stress paths for the fully undrained tests. The maximum deviator stress for the case with higher strainrates was lower than those with lower strain rates. Itseems that the strain rate eŠect comes from a combination of the viscoelastic property of the pore ‰uidsand the loading time.7) The stress ratio (the ratio of deviator stress over themean skeleton stress) at large strain was almost in- UNSATURATED COMPACTED SILTdependent of the initial suction, the conˆning pressure, and the shearing conditions for the present experimental results. The stress ratio at failure or largestrain obtained from all the cases, was around 1.23.This result indicates that the behavior during the unsaturated specimen tests in the present study can be described well through the use of the skeleton stressadopted in the present paper.LIST OF SYMBOLSs:u a:u w:s?ij:Sr:P F:e a:er:suctionpore-air pressurepore-water pressureskeleton stressdegree of saturationaverage pore pressureaxial strainaverage lateral strainREFERENCES1) Adachi, T. and Oka, F. (1982): Constitutive equations for normallyconsolidated clay based on elasto-viscoplasticity, Soils and Foundations, 22(4), 57–70.2) Aitchison, G. D. (1960): Relationships of moisture stress and eŠective stress functions in unsaturated soils, Proc. Conference PorePressure and Suction in Soils, London, British Nat. Soc. of ISSMFE, Butterworths, 47–52.3) Alonso, E. E., Gens, A. and Josas, A. (1990): A constitutive modelfor partially saturated soils, Geotechnique, 40(3), 405–430.4) Baumgartl, Th., Winkelmann, P., Graesle, W., Richards, B. G.and Horn, R. (1995): Measurement of the interaction of soilmechanical properties and hydraulic processes with a modiˆedtriaxial test, Proc. 1st Int. Conference on Unsaturated Soils, UNSAT '95, Paris, France (eds. by Alonso, E. E. and Delage, P.),Balkema, 433–438.5) Bishop, A. W. (1960): The measurement of pore pressure in thetriaxial test, Proc. Conf. Pore Pressure and Suction in Soils, Butterworths, London, 38–46.6) Bishop, A. W. and Donald, I. B. (1961): The experimental study ofpartly saturated soil in the triaxial apparatus, Proc. 5th ICSMFE,Paris, France, 1, 13–21.7) Bishop, A. W. and Henkel, D. J. (1962): The Measurements of SoilProperties in the Triaxial Tests, Edward Arnold Publisher, 2nd edition, London.8) Bolzon, G., Schre‰er, B. A. and Zienkiewicz, O. C. (1996):Elastoplastic soil constitutive laws generalized to partially saturatedstates, Geotechnique, 46(2), 279–289.9) Clayton, C. R. and Khatrush, S. A. (1986): A new device for measuring local strains on triaxial specimens, Geotechnique, 36(4),593–597.10) Cole, D. M. (1978): A technique for measuring radial deformationduring repeated load triaxial testing, Canadian Geotechnical Journal, 15, 426–429.11) Coleman, J. D. (1962): Stress/strain relations for partly saturatedsoil, Correspondence, Geotechnique, 12(4), 348–350.12) Ehlers, W., Graf, T. and Ammann, M. (2004): Deformation andlocalization analysis of partially saturated soil, Compt. MethodsAppl. Mech. Engrg., 193, 2885–2910.13) Fredlund, D. G. and Morgenstern, N. R. (1977): Stress state variables for unsaturated soils, J. Geotech. Engng Div. Am. Soc. Civ.Engrs., 103(GT5), 313–321.14) Gallipoli, D., Gens, A., Vaunat, J. and Romeo, E. (2002): Role ofdegree of saturation on the normally consolidated behavior of unsaturated soil, Proc. 3rd Int. Conf. Unsaturated Soils, Recife,43113–120, 2002.15) Gallipoli, D., Gens, A., Sharama, R. and Vaunat, J. (2003): Anelasto-plastic model for unsaturated soil incorporating the eŠects ofsuction and degree of saturation on mechanical behaviour,Geotechnique, 53(1), 123–135.16) Houlsby, G. T. (1997): The work input to an unsaturated granularmaterial, Geotechnique, 47(1), 193–196.17) Ishihara, K. (1993): Liquefaction and ‰ow failure during earthquakes, Geotechnique, 43(3), 351–415.18) Jommi, C. (2000): Remarks on the constitutive modelling of unsaturated soils, Experimental Evidence and Theoretical Approachesin Unsaturated Soils (eds. by Tarantio, A. and Mancuso, C.),Balkema, 139–153.19) Karube, D. and Kawai, K. (2001): The role of pore water in themechanical behavior of unsaturated soils, Geotechnical and Geological Engineering, 19, 211–241.20) Khan, A. H. and Hoag, D. L. (1979): A non-contacting transducerfor measurement of lateral strains, Canadian Geotechnical Journal,16, 409–411.21) Kim, Y.-S. (2004): Elasto-viscoplastic modeling and analysis for cohesive soil considering suction and temperature eŠects, DoctoralThesis, Kyoto University.22) Kim, Y.-S., Kimoto, S., Oka, F. and Kodaka, T. (2005): Numericalsimulation of the triaxial compression behaviour of unsaturated siltusing an elasto-viscoplastic model, Proc. 11th IACMAG, Torino,Italy, 19–24, June 2005, 1361–1368.23) Kimoto, S., Oka, F., Fujiwaki, M. and Fujita, Y. (2007): Numerical analysis of deformation of methane hydrate contained soil dueto the dissociation of gas hydrate, Bifurcations, Instabilities,Degradation in Geomechanics (eds. by George E. Exadaktylos andIoannis G. Vardoulakis), Springer, 361–380.24) Kimoto, S., Oka, F., Fushita, T. and Fujiwaki, M. (2007): Achemo-thermo-mechanically coupled numerical simulation of thesubsurface ground deformations due to methane hydrate dissociation, Computers and Geotechnics, 34(4), 216–228.25) Kohgo, Y., Nakano, M. and Miyazaki, T. (1993): Theoreticalaspects of constitutive elastoplastic model for unsaturated soils,Soils and Foundations, 33(4), 49–63.26) Kolymbas, D. and Wu, W. (1989): A device for lateral strain measurements in triaxial tests with unsaturated specimens, Geotechnical Testing Journal, 12(3), 227–229.27) Lo Presti, D. C. F., Pallara, O. and Puci, I. (1995): A modiˆedcommercial triaxial testing system for small strain measurements,preliminary results on Pisa clay, Geotechnical Testing Journal,18(1), 15–31.28) Loret, B. and Khalili, N. (2000): A three phase model for unsaturated soils, Int. J. Numer. Anal. Meth. Geomech., 24(11), 893–927.29) Macari, E. J., Parker, J. K. and Costes, N. C. (1997): Measurementof volume changes in triaxial tests using digital imaging techniques,Geotechnical Testing Journal, 20(1), 103–109.30) Matyas, E. L. (1967): Air and water permeability of compactedsoils, American Society of Testing and Materials, ASTM STP 417,160–175.31) Nishimatsu, N. (2004): Experimental study of the suction eŠect onan unsaturated compacted silt, Master's Thesis, Kyoto University,Kyoto, Japan (in Japanese).32) Nuth, M. and Laloui, L. (2008): EŠective stress concept in unsaturated soil: Clariˆcation and validation of a uniˆed framework, Int.J. Num. Anal. Meth. Geomech., 32, 771–801.33) Oka, F., Kodaka, T., Kimoto, S., Kim, Y. and Yamasaki, N.(2006): An elasto-viscoplastic model and multiphase coupled FEanalysis for unsaturated soil, Unsaturated Soils Proc. 4th Int.Conf. Unsat. Soils, Carefree Arizona, 2–6 April 2006, ASCE, (2),2039–2050.34) Oka, F., Kodaka, T., Kimoto, S., Kim, Y.-S. and Yamasaki, N.(2006): A multi-phase coupled FE analysis using an elasto-viscoplastic model for unsaturated soil, Geomechanics II, Geotechnical Special Publication, ASCE, Proc. 2nd US-Japan Workshop on Geomechanics, 124–131.35) Oka, F., Feng, H., Kimoto, S., Kodaka, T. and Suzuki, H. (2008): 4436)37)38)39)OKA ET AL.A numerical simulation of triaxial tests of unsaturated soil at constant water and air content by using an elasto-viscoplastic model,Proc. 1st European Conference on Unsaturated Soil, 735–741.Rifa'i, A., Laloui, L. and Vulliet, L. (2002): Volume measurementin unsaturated triaxial test using liquid variation and image processing, Proc. 3rd Int. Conference on Unsaturated Soils, UNSAT2002, Recife, Brazil (eds. by Juca, J. F. T., De Campos, Tacio M.P. and Marinho, Fernando A. M.), Balkema, 441–445.Romero, E., Facio, J. A., Lioret, A., Gens, A. and Alonso, E. E.(1997): A new suction and temperature controlled triaxial apparatus, Proc. 14th ICSMFE, Hamburg, Balkema, 1, 185–188.Sivakumar, V. (1993): A critical state framework for unsaturatedsoil, PhD Thesis, University of She‹eld.Suzuki, H., Kodaka, H. and Oka, F. (2006): Mechanical properties40)41)42)43)of unsaturated silt under unexhausted and pore air pressure controlled condition, Proc. 41st Annual Meeting of JGS, Kagoshima,323–324 (in Japanese).Wheeler, S. J. and Sivakumar, V. (1995): An elasto-plastic criticalstate framework for unsaturated soil, Geotechnique, 45(1), 35–53.Wheeler, S. J., Sharma, R. S. and Buisson, M. S. R. (2003):Coupling of hydraulic hysterisis and stress-strain behaviour in unsaturated soils, Geotechnique, 53(1), 41–54.Wulfsohn, D., Adams, B. A. and Fredlund, D. G. (1998): Triaxialtesting of unsaturated agricultural soils, J. Agric. Engineering.Res., 69, 317–330.Yamamura, K. (1971): Soil engineering research of river embankment, Doctoral Thesis, Kyoto University, Japan (in Japanese).
  • ログイン
  • タイトル
  • Stress-strain Relationships and Nonlinear Mohr Strength Criteria of Frozen Sandy Clay
  • 著者
  • "L. Yuanming, G. Zhihua, Z. Shujuan, C. Xiaoxiao"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 45〜53
  • 発行
  • 2010/02/15
  • 文書ID
  • 64340
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 45–53, Feb. 2010STRESS-STRAIN RELATIONSHIPS AND NONLINEAR MOHRSTRENGTH CRITERIA OF FROZEN SANDY CLAYLAI YUANMINGi), GAO ZHIHUAi), ZHANG SHUJUANi) and CHANG XIAOXIAOi)ABSTRACTA series of triaxial compressive tests were performed on frozen sandy clay at -4 and -69C under conˆning pressures from 0 to 18 MPa. The experimental results indicate that the stress-strain curves show strain softening andhardening phenomena when the conˆning pressures are below and above 3.0 MPa, respectively. Since the generallyhyperbolic model can not describe the strain hardening behavior very well and the Duncan-Chang model can not ideally describe the strain softening behavior of the frozen sandy clay, an improved Duncan-Chang model is proposed. Thismodel can describe not only the strain softening behavior but also the strain hardening behavior of the frozen sandyclay, and the calculated results are rather coincident with the corresponding experimental data. In addition, it is alsosuitable for frozen silty clay with a high precision. Due to pressure melting, the shear strength of the frozen sandy claychanges nonlinearly with increasing conˆning pressures. In order to solve the problem that the linear Mohr-Coulombcriteria can not exactly re‰ect the shear strength of the frozen sandy clay, a nonlinear Mohr criteria of the frozen sandyclay is presented. The calculated results illustrate that it has higher precision and can describe the shear strength offrozen sandy soils more accurately than the linear Mohr-Coulomb criteria does.Key words: frozen clay, improved Duncan-Chang model, nonlinear Mohr strength criteria, stress-strain relationship(IGC: D6)(2002) discussed the eŠect of the unloading stress path onthe strength of frozen soils. Arenson and Springman(2005a) conducted triaxial tests on ice-rich frozen soilsfrom the Alps in Switzerland, and found that the minimum strain rate of creep increases exponentially with increasing temperature and applied deviator stress. Theyalso provided mathematical descriptions for the behaviorof ice-rich frozen soils at temperatures close to 09C(Arenson and Springman, 2005b). According to uniaxialcompressive tests, Zhu et al. (1992) proposed a uniaxialconstitutive equation for frozen soils. Lai et al. (2008) investigated strength distributions of warm frozen clay andproposed a stochastic damage constitutive model according to the uniaxial test results of warm frozen clay. Wanget al. (2004) researched the stress-strain characteristic offrozen loess subjected to K0 consolidation under unloading conditions, and showed the relationships between theinitial conˆning pressure and temperature, and the initialtangent modulus and ultimate deviator stress. In our investigations, it was found that, when stresses are adjustedby increasing the cross-sectional area during the tests(Bardet, 1997), the stress-strain behavior of frozen sandyclay has a strain softening phenomenon for low conˆningpressures and a strain hardening phenomenon for higherconˆning pressures, respectively. The shear strength increases as the conˆning pressure increases when the con-INTRODUCTIONThere are 35.76 million km2 of permafrost, which accounts for about 24z of the world's land area (French,1996). Thus, the strength and deformation of frozen soiloften must be considered in the designing of railways,roadways, oil pipelines, airports and buildings. Braggand Andersland (1981) investigated the strain rate, temperature, and sample size eŠects with tests on the compression and tensile properties of frozen sand, and determined the tensile strength using the splitting cylinder experiments. Tsytovich et al. (1981) provided the relationship between the elastic modulus and temperature according to experiments on frozen coarse-grained soil. Aas(1981) performed tensile, bending and shearing tests onfrozen clay in Oslo, and found that there was a criticalshearing stress for clay at a given temperature. Chen et al.(1998) studied the eŠects of conˆning pressure on theshear strength of clay by the artiˆcially frozen method.Wu et al. (1994) researched the in‰uence of loading rateson the strength of frozen sandy soil. Shen (1995a) studiedthe in‰uence of temperature and loading rate on theresults of the axial splitting test, the possibility of usingaxial splitting method to indirectly determine the tensilestrength of frozen soil, and then measured the tensilestrength of frozen loess (Shen et al., 1995b). Ma et al.i)State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering Research Institute, ChineseAcademy of Sciences, China (ymlai@lzb.ac.cn).The manuscript for this paper was received for review on September 29, 2008; approved on October 2, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.45 46YUANMING ET AL.ˆning pressure is below a certain critical value. Howeverwhen the conˆning pressure is beyond that critical value,the shear strength decreases with further increase in conˆning pressure. Based on rock triaxial data, Baker (2004)presented a procedure for estimating parameters fromMohr form of Hoek and Brown empirical failure criteria.Jiang et al. (2003) investigated the eŠect of strength envelope nonlinearity on slope stability computations. Thestudies mentioned above represent a great advance in thestudy on strength envelope nonlinearity. However, due tothe particular properties of frozen soil, the present nonlinear Mohr formulae, proposed by Baker and Jiang etal. for rocks, are not suitable. Therefore, in order to better describe the mechanical properties for frozen sandyclay, an improved Duncan-Chang model and nonlinearMohr strength criteria of frozen sandy clay are presentedin this paper.When the strength and deformation of frozen soil engineering is analyzed, the stress-strain relationship andstrength criterion of frozen soil need to be ascertained.For the engineering requirement of Qinghai-Tibet railway, we spent over two years to obtain the data andpresent the model in this paper. Moreover, with the wideuse of the artiˆcial ground freezing technology in constructions, engineering activities in areas with deep alluvium, such as in mining, underground power stations, railways, tunnels, etc., are gradually able to be carried out tocompletion. In such areas, the artiˆcial freezing methodis usually used to increase the soil strength. When thedeep frozen soil is excavated and high lateral pressure isreleased, high conˆning pressures are usually encountered. For example, the stresses at the frozen wall of coal,mining 800 m under ground in Shandong province in China, can reach 17.6 MPa. Sometimes, even in excavationswithout very large depth, stress concentration may alsolead to very high stress level. The purpose of this paper isto present the strength criteria and stress-strain relationship of frozen sandy clay for a large range of stress states,with particular attention to the high stress level.Fig. 1.Fig. 2.Grain size distribution curve of sandy clayDetailed ˆgure of the pressure chamberTEST CONDITIONS AND METHODThe material used in tests was remoulded QinghaiTibetan Sandy clay. The sandy clay is mainly quartz andits main ingredients were SiO2, Al2O3, Fe2O3, MgO, K2Oand TiO2 in sequence according to their mass contents.The grain size distribution curve of this soil is shown inFig. 1. The density of the soil particles was 2.65 g/cm3.The process of preparing specimens is described as follows. Firstly, distilled water was added to air-dried soil tomake an initial water content of about 13z by weight.Then the soil was put in a cylindrical rigid mold and compacted to the desired dry density, and they were quicklyfrozen from top to bottom in a freezing cabinet. Afterfreezing, the specimens were taken out from the moldsand machined to 125.0 mm in length and 61.8 mm in diameter in a cold room (Wu et al., 1994; Lai et al., 2008).At last, the average water content and dry density of thetested specimens were 12.9z (with a saturated content ofFig. 3.MTS-810 triaxial testing machineabout 22.0z) and 1.97×103 kg/m3, respectively.The tests were conducted as follows. The specimen atthe required temperature was ˆrst placed into the triaxialpressure cell for a duration of about 3–4 h, which allowedthe specimen to reach temperature equilibrium (the tem- NONLINEAR MOHR'S CRITERIONperature was measured with three thermistors laid atdiŠerent positions close to the specimen, shown in Fig.2). The conˆning pressure was then increased over aperiod of about 30 s to the desired value, and maintainedfor a period of about 2 h for the temperature and pressure of the whole apparatus to equilibrate. The compression test was then conducted at a constant conˆning pressure. The axial deformation rate was 1.25 mm/min-1,equivalent to an axial strain rate of 1.7×10-4/s-1. Alltests were conducted using the modiˆed MTS-810 triaxialtesting machine shown in Fig. 3. The test temperatureswere -49C and -69C, respectively. The both temperatures were chosen because the soil tested was taken fromthe railway line in Qinghai-Tibetan Plateau, at which thetypical ground temperature is about -4 to -69C at thedepth of soil sampling. The test pattern was the axis-symmetry, the specimen was free to expand at the specimenplaten interface. The conˆning pressures were 0–18.0MPa. The tests were controlled by MTS test applicationsoftware.TEST RESULTS AND ANALYSESC on frozenA series of triaxial tests at -4.0 and -6.09sandy clay under conˆning pressures s3 from 0 to 18.0MPa were carried out, the corresponding test results areshown in Fig. 4. From this ˆgure, it can be seen that the47stress-strain curves show strain softening and hardeningphenomena when the conˆning pressures are below andabove 3.0 MPa, respectively (Lai et al., 2008, Zhang etal., 2007).Because the plastic-volume strain becomes larger withloading when the conˆning stress is small, the overallvolumetric strain gradually increases. In addition, thestrain softening phenomena of this soil is obvious due tothe low yielding strength of sandy clay. With the increaseof the conˆning stress the compressive strain ispredominant, and because the yielding or peak strengthbecomes larger, the stress-strain curves appear to be thestrain hardening phenomena. Generally, the hyperbolicmodel (Shen, 2005) is used to describe the strain softeningphenomenon on soft soil,s 1- s 3=ed(a+ced )( a+ b e d ) 2(1)Where (s1-s3 ) is the deviator stress, ed=e1-e3, e1 and e3are axial and radial strains, respectively. a, b and c are ˆtting parameters.When the conˆning pressures s3 are larger than 3.0MPa, the stress-strain curves of -6.09C frozen sandyclay shows a strain hardening phenomena, and is generally described by the Duncan-Chang model (Duncan et al.,1970),s1 - s 3 =e1d+ e e 1(2)Where d and e are ˆtting constants.Using ˆtting data, it is found that the generally hyperbolic model (Eq. (1)) could not describe the stress-strainsoftening behavior of frozen sandy clay when the conˆning pressures are below 3.0 MPa, and the Duncan-Changmodel (Eq. (2)) could not ideally re‰ect the situationwhen the conˆning pressures are above 3.0 MPa. Hence,an improved Duncan-Chang model is presented here, andused to describe the stress-strain relationships of frozensandy clay at -6.09C when the conˆning pressures s3 arein the range of 0 to 18.0 MPa. That is,s 1- s 3=e1m+ne1+le21(3)Where m=1/E0, n=1/(s1-s3 )m-2/(e1m E0 ), l=1/(E0e 21m ), E0 is the initial elastic modulus and determinedby lime ª0 (d(s1-s3 )/de1). The physical meanings oflimiting stress, (s1-s3 )m, and limiting strain, e1m, are illustrated in Fig. 5. m, n and l can be determined according to the formulae mentioned above and Fig. 5. Theycan also be determined by the data regression methodwhen a series data of stress and strain are obtained. Theparameter m, n and l can also be determined by the leastsquare method. i.e.,1K«V=S m+ne1i+le 21i-i= 1Fig. 4. Stress-strain curves of frozen sandy soil at -4 and -69C under various conˆning pressurese 1iqi$2Where e1i is the value of e1 at the i-th measured point andqi=(s1-s3 )i, i.e., the value of (s1-s3 ) at the i-th measured point. K is the total number of measured data. YUANMING ET AL.48Fig. 5.Physical meanings of (s1-s3 )m and e1mFig. 6. Comparisons between experimental data and modeling resultsof (a) general hyperbolic model and (b) improved Duncan-Changmodel when s3=0.3 MPa at -69CLetting&V&V=0,=0,&m&nand&V=0,&l&Ve 1i=mK+nSe1i+lSe21i-S =0&mqin=1D1m=D| |Se Se21ie21iS qiSe Se31ie31iS qiSe41i1i21i31iSee21iS qiSe31iSe S q Se41iS e 1ie31i21ii&Ve31i=mSe21i+nSe31i+lSe41i-S =0&lqie1iS qi21ii&Ve21i=mSe1i+nSe21i+lS e31i-S =0&nqiFrom the three equations above, the parameter m, n and lcan also be determined by the following formulae.| || |e 1iS q SeKwe can obtain the following equations:e 1iSe S qKl=1D1iee31iSe Se S q21i1iSe Se S q21iWhere D=31i|KSeSe1i21ii21iiiSe SeSe SeSe Se1i21i21i31i31i41i|.By investigation, it is found that with the increasinglyconˆning pressure, variations of m and n are not obvious, whereas variation of l are apparent. As such, according to the test results, m and n are taken as their averagevalues of 0.018 and 0.029 at -4.09C, and 0.012 and0.025 at -6.09C, respectively; and l=1.586×(s3/Rt+ NONLINEAR MOHR'S CRITERION49Table 1. Maximal residual errors between the results calculated andthe corresponding experimental data at diŠerent strains at -69Cwhen s3=0.3 MPaAxial strain (z)0¿5.05.0¿10.010.0¿20.0À20.0General hyperbolic model(MPa)Improved Duncan-Changmodel (MPa)-0.4830.374-0.1720.244-0.2750.233-0.1420.230Table 2. Maximal residual errors between the results calculated andthe corresponding experimental data at diŠerent strains at -69Cwhen s3=10.0 MPaFig. 7. Comparisons between experimental data and modeling resultsof (a) Duncan-Chang model and (b) improved Duncan-Changmodel when s3=10 MPa at -69C0.236)-0.833, Rt is the tensile strength of frozen sandy clay,0.53 MPa at -4.09C and 0.62 MPa at -6.09C, respectively.To investigate the precision of the models mentionedabove in describing the stress-strain relationship, thecomparisons of the results calculated by Eqs. (1), (2) and(3) with the corresponding experimental data of sandyclay at -6.09C are shown in Figs. 6 and 7 when s3=0.3=MPa and s3 10.0 MPa, respectively. Maximal residualerrors between the results calculated and the corresponding experimental data are also listed in Table 1 and2 at diŠerent strains, respectively.From Fig. 6, it can be seen that the agreement of thecalculated results using the improved Duncan-Changmodel (Eq. (3)) with the corresponding experimental datais better than that of the calculated results using thegenerally hyperbolic model (Eq. (1)) with the corresponding experimental data. Table 1 also shows that thesimulated precision of Eq. (3) is better than that of Eq.(1) when the strain softening behavior of frozen sandyclay is described by it. In particular, when the axial strainis in the range of 0¿5.0z, the calculated results of Eq.(3) are much closer to the experimental values than thoseof Eq. (1).According to Fig. 7 and Table 2, it can be seen that theagreement of the calculated results of the improved Duncan-Chang model (Eq. (3)) with the corresponding ex-Axial strain (z)0¿5.05.0¿20.0À20.0Duncan-Chang model (MPa)-0.7390.307-0.435Improved Duncan-Chang model (MPa) -0.3760.1590.164perimental data is better than that of the calculatedresults of the Duncan-Chang model (Eq. (2)) with thecorresponding experimental data. Table 2 also showsthat maximal residual error between the calculated resultsof Eq. (3) and the corresponding experimental data isabout half of the residual error between the calculatedresults of Eq. (2) and the corresponding experimentaldata in the axial strain of 0¿20.0z. However, when theaxial strain is above 20.0z, the absolute value of maximal residual error between the calculated results by theimproved Duncan-Chang model and the correspondingexperimental data is about one third of the results obtained from the Duncan-Chang model and the corresponding experimental data. Our results clearly show thatthe modeling precision of the improved Duncan-Changmodel is better than that of the Duncan-Chang modelwhen it is used to describe the strain hardening behaviorof frozen sandy clay.From Figs. 6 and 7, it is known that the generallyhyperbolic model can only describe the strain softeningbehavior of frozen sandy clay, and the Duncan-Changmodel can only describe the strain hardening behavior.On the other hand, the improved Duncan-Chang modelcan describe not only the strain softening behavior offrozen sandy clay but also the strain hardening behaviour. In order to illustrate the modeling precision of theimproved Duncan-Chang model in conˆning pressures of0¿18.0 MPa, some results from the improved model andthe corresponding experimental data are shown in Figs.8(a)–(f). From Figs. 8(a)–(f), it can be seen that the calculated results approximate well with corresponding experimental data with increasingly conˆning pressure, sothere is clearly very good agreement.NONLINEAR MOHR STRENGTH CRITERIAFrom Fig. 4, it can be seen that the maximal values of(s1-s3 ) appear in the stress-strain curves of eº15zwhen the conˆning pressure s3=0¿2 MPa. For suchcases, the peak value of (s1-s3 ) was taken as the failure 50YUANMING ET AL.Fig. 8. Comparisons between the experimental data of sandy soil and the calculated results of the improved Duncan-Chang model with diŠerentconˆning pressures at -69Cabout 12.0 MPa, for further increases in conˆning pressure, the shear strength decreases due to pressure melting.If the shear strength is determined by the Mohr-Coulombcriteria, t=c+s tan q, a linear equation, tM=1.5095+0.1166×s, should be obtained. It can be seen in Fig. 9(a)that for the shear failure of frozen sandy clay at -6.09Cthere are large errors between the Mohr-Coulomb criteriaand the corresponding experimental results, and thus, anew nonlinear failure criteria is proposed in this paper.According to the test results and data regression, therelationship between conˆning pressure, s3, and axialstress, s1, can be expressed by the following equation,Øs1=(k0 )s /P sc 1+3Fig. 9. Comparison between Mohr criteria and the corresponding experimental results at -69Cstrength of the frozen sandy clay tested in this paper.With conˆning pressures s3Æ3 MPa, no peak value existsin the stress-strain curves of the frozen sandy clay withinthe range of e1º15.0z, so, the values of (s1-s3 ) at astrain of 15.0z is taken as the failure strength of frozensandy clay in this paper.According to the experimental results, the stress circleswith various conˆning pressures at -69C are plotted inFig. 9(a), in which the dotted straight line is the linearMohr-Coulomb criteria and the solid envelope representsthe experimental results. Figure 9(a) also shows that theshear strength increases with increasing pressure untilo20as3sT»b0(4)Where sc and sT are the uni-axial compressive and tensilestrengths, respectively, and K0 and b0 are experimentalparameters. For the frozen sandy clay at -6.09C, sc=2.235 MPa, sT=0.620 MPa, K0=0.982, b0=0.791, andPa=1.0133 MPa, is normal atmospheric pressure. Forthe frozen sandy clay at -4.09C, sc=1.639 MPa, sT=0.560 MPa, K0=0.985, and b0=0.820.The equation of the Mohr circle, expressed using s3 (inour test, s2=s3 ) and s1, isØ-s»Øs1 + s 3 2s 1- s 3+ t 2=22»2(5)Where s and t are the normal and shear stresses on theelement failure plane, s1 and s3 are maximum and minimum principal stresses, respectively.From Eq. (5), we can obtain the following formulationof function f NONLINEAR MOHR'S CRITERIONØf= s -»Ø»s 1 + s3 2s 1 - s3 2+ t 2-=022(6)Utilizing a chain rule for diŠerentiating the implicit function and Eq. (6), the following expressions can be obtained,&f- s+ s 1& s1&s3=- =-- s+ s 3& s3&f&s1&s 1-1&s 3tan q=(10)&s12&s3According to Eq. (4), the following expression can be obtained by diŠerentiating for s3,3s 1- s 3(7)&s 1+1&s 3Substituting Eq. (7) into Eq. (5), the following equationis obtaineds = s 3+2(s1-s3 ) 1 1-&s1& s1+1+1&s3 & s3 s1 - s 3&s 1+1&s 3aØ+(k0 )s /P・sc 1+3a»b»s3 bb・s T s 3+ s T(11)Eqs. (7), (8), (10) and (11) are mathematic formulae ofnonlinear Mohr criteria of the frozen sandy clay. Whens3ª -sT,&s 1ª /,&s 3s = s3 ,pt=0, f= .2When s1»0, Eq. (11) can be simpliˆed as following expression according to Eq. (4)Ø»&s1 ln k0b=+・s1&s 3P a s 3+ s TFrom the formulation above, the expression of shearstress t is given byt=Ø&s1 ln k0s3=・(k0 )s /P・sc 1+&s 3 P asTFrom the equation above, the following formula can beobtainedt 2=51& s1& s3Substituting Eq. (12) into Eqs. (7) and (8), respectively,the mathematic formulae of the nonlinear Mohr criteriacan be obtained as follows,(8)(s1-s3 )Pa(s3+sT )s1(s3+sT ) ln k0+Pa(bs1+s3+sT )(13a)(s1-s3 ) Pas1(s3+sT )[(s3+sT ) ln k0+Pab]s1(s3+sT ) ln k0+Pa(bs1+s3+sT )(13b)s = s3 +According to Fig. 10, tan q is deˆned bys 1 + s3-sdt2tan q= =dstt=(9)Substituting Eqs. (7) and (8) into Eq. (9), the followingequation is obtained(12)In order to examine the precision of the nonlinear Mohrcriteria expressed by Eqs. (11)¿(13), the shear failurestress circles of the frozen sandy clay under diŠerent conˆning pressures are shown in Fig. 9(b), in which a dottedcurve is described by the nonlinear Mohr criteria, and asolid envelope curve is described by the corresponding experimental results.The envelope curve of all stress circles is ˆtted by thefollowing method. First, the ˆtting curve equation is assumed as the following expression:tE=f(s`a1, b1, c1, d1 )=a1+b1s+c1s 2+d1s 3(14)Where a1, b1, c1 and d1 are parameters without dimensionto be determined.According to Eq. (5) and Fig. 10, we can obtain thefollowing formulae:Fig. 10.si=pi-qi sin qi, ti=qi cos qis1 + s 3s1 - s 3p i=, q i=22Angle q in plane of Mohr stress circleTable 3.qi (rad)0.00.00.30.60.81.02.0(16)The variation of qi vs s1 and s3 at -69Cs1 (MPa) -0.620 2.285 3.269 4.155 4.726 5.308 7.392 9.541 11.140 11.877s3 (MPa)(15)3.04.00.591 0.527 0.496 0.465 0.445 0.423 0.331 0.252 0.17412.924 14.92417.16119.38120.79522.57124.95310.012.014.016.018.05.06.08.00.01790.0710.002 -0.040 -0.056 -0.040 -0.030 -0.020 YUANMING ET AL.52Where pi and qi are the center and radius of i-th Mohr-circle, respectively. qi is the angle between the vertical lineand the line through the circle center and a tangent pointat which the envelope is tangent with the i-th Mohr-circle.si and ti depend on pi, qi and qi. qi and the parameter a1,b1, c1 and d1 can be determined by the least squaremethod (Bardet, 1997), i.e.,KP=S [ti-(a1+b1si+c1s +d1s )]22i3ii= 1K=S sqi cos (qi )-[a1+b1( pi-qi sin qi )i= 1+c1( pi-qi sin qi )2+d1( pi-qi sin qi )3 ]t2 (17)Letting&P=0,&qi&P=0,& a1&P=0,&b 1&P=0,& c1and&P=0,& d1Table 4. Relative errors between the linear, the nonlinear MohrCoulomb criteria and the envelope equation at -69Cs (MPa)-0.3187.05718.819tE (MPa)0.4633.3153.522tM (MPa)1.4732.3323.704tNM (MPa)0.4153.1543.448dM (z )dNM (z)218.300-29.7005.200-10.300-4.900-2.100parameter a1, b1, c1, d1 and qi can be determined. Thevalues of a1, b1, c1 and d1 are: a1=0.6667, b1=0.6290, c1=-0.0423 and d1=0.0009, and the values of qi are listedin Table 3 when the sandy clay is at -69C.According to the parameter values obtained, the equation of the envelope line is given by,tE=f(s`a1, b1, c1, d1 )=0.6667+0.629s-0.0423s2+9.0×10-4s3(18)dM stands for relative error between the linear MohrCoulomb criteria, tM, and the data, tE, from Eq. (18).The relative errors between the nonlinear Mohr criteria,tNM, and the data, tE, from Eq. (18), are denoted by dNM.Their values are listed in Table 4.From Table 4, it can be seen that when s=-0.318(MPa), dM=218.3z, dNM=-10.3z; when s=7.057(MPa), dM=-29.7z, dNM=-4.9z; and when s=18.819 (MPa), dM=5.2z, dNM=-2.1z. The errors between the nonlinear Mohr criteria and the envelope equation are smaller than those between the linear MohrCoulomb criteria and the envelope equation. Therefore,the nonlinear Mohr criteria is more precise, and candescribes the shear strength of the frozen sandy clay moreaccurately than the linear Mohr-Coulomb criteria does.In addition, the improved Duncan-Chang modelproposed in this paper is also suitable for silty clay with aFig. 11. Comparisons between the experimental data of silty clay and the calculated results of the improved Duncan-Chang model with diŠerentconˆning pressures at -49C and -69C NONLINEAR MOHR'S CRITERIONhigh precision under the condition of strain rate of 1.70×10-4/s-1 at -4.09C and -6.09C (Fig. 11). Based on thepresent experimental data studied in this paper, it can befound that the scope of material, temperature, and conˆning pressure most suitable for the application of theproposed model is sandy clay and silty clay, -4–-69C,and 0–18 MPa, respectively.When the model is applied to the numerical analysis,the following tests must be done to determine theparameters: uniaxial compressive and tensile strengthtests, and a series of triaxial compressive tests underdiŠerent conˆning pressures, respectively to ascertain theexact nature of the material, the frozen temperature andthe strain rate. After the test results are obtained, a modelon frozen soil can be obtained by following the procedureprovided in this paper. Equation (3) is used to evaluatethe stress-strain behavior before the failure of foundationsoil in actual engineering issues, and Eq. (13) is mainlyused to evaluate the stress state when the foundation soilis found to be in critical condition.CONCLUSIONSAn improved Duncan-Chang model is proposed. Thismodel can describe not only the strain softening behaviorof frozen sandy soils but also the strain hardening behavior of frozen sandy soils. This model solves the problemthat the generally hyperbolic model can not describe inthe strain hardening behavior, and that the DuncanChang model can not describe in the strain softening behavior of the frozen sandy soils. Moreover, the modelingprecision of the improved Duncan-Chang model is betterthan that of Duncan-Chang model and the generallyhyperbolic model.A set of nonlinear Mohr criterion of frozen sandy soilsis presented. It has higher precision and describes theshear strength of frozen sandy soils more accurately thanthe linear Mohr-Coulomb criterion does.ACKNOWLEDGEMENTSWe would like to thank very much the two anonymousreviewers whose constructive comments are helpful forthis paper revision. This research was supported by National Natural Science Foundation of China (40730736),the National Hi-Tech Research and Development Plan(2008AA11Z103), the Western Project Program of theChinese Academy of Sciences (KZCX2-XB2-10), the Program for Innovative Research Group of Natural ScienceFoundation of China (No. 40821001), and the foundation of State Key Laboratory of Frozen Soil Engineering(SKLFSE-ZY-03).53REFERENCES1) Aas, G. (1981): Laboratory determination of strength properties offrozen salt marine clay, Engineering Geology, 18, 67–78.2) Arenson, L. U. and Springman, S. M. (2005): Triaxial constantstress and constant strain rate tests on ice-rich permafrost samples,Canadian Geotechnical Journal, 42, 412–430.3) Arenson, L. U. and Springman, S. M. (2005): Mathematicaldescriptions for the behaviour of ice-rich frozen soils at temperatures close to 09C, Canadian Geotechnical Journal, 42, 431–442.4) Baker, R. (2004): Nonlinear Mohr envelopes based on triaxial data,ASCE Journal of Geotechnical and Geoenvironmental Engineering, 130(5), 498–506.5) Bardet, J. P. (1997): Experimental Soil Mechanics, Prentice-Hall,New Jersey.6) Bragg, R. A. and Andersland, O. B. (1981): Strain rate, temperature, and sample size eŠects on compression and tensile propertiesof frozen sand, Engineering Geology, 18, 35–46.7) Chen, X. S., Wang, C. X. and Wu, C. Y. (1998): Experimentalstudy of triaxial shear strength criteria for artiˆcially frozen clay,Mine Construction Technology, 19(4), 1–7.8) Duncan, J. M. and Chang, C. Y. (1970): Nonlinear analysis ofstress and strain in soils, J. Soil Mech. Found. Div. ASCE, 96(SM5).9) French, H. M. (1996): The Periglacial Environment (2nd edition),Essex, London, p341.10) Jiang, J. C. (2003): The eŠect of strength envelope nonlinearity onslope stability computations, Canadian Geotechnical Journal, 40,308–325.11) Lai, Y. M., Li, S. Y., Qi, J. L., Gao, Z. H. and Chang, X. X.(2008): Strength distributions of warm frozen clay and its stochasticdamage constitutive model, Cold Regions Science and Technology,53(2), 200–215.12) Lai, Y. M., Jin, L. and Chang, X. X. (2008): Yield criterion andelasto-plastic damage constitutive model for frozen sandy soil, International Journal of Plasticity, doi:10.1016/j.ijplas.2008.06.010.13) Ma, W. and Chang, X. X. (2002): Analyses of strength and deformation of an artiˆcially frozen soil wall in underground engineering, Cold Regions Science and Technology, 34, 11–17.14) Shen, Z. J. (2005): Selected Works on Soil Mechanics of ShenZhujiang, Qinghua University Press, Beijing, 2005 (in Chinese).15) Shen, Z. Y., Peng, W. W., Liu, Y. Z. and Chang, X. X. (1995a):Preliminary research of axial splitting method for determining tensile strength of frozen soils, Journal of Glaciology and Geocryology, 17(1), 33–39.16) Shen, Z. Y., Peng, W. W. and Liu, Y. Z. (1995b): Experimentalstudy of tensile strength on frozen loess, Journal of Glaciology andGeocryology, 17(4), 315–321.17) Tsytovich, N. A., Kronik, Y. A., Gavrilov, A. N. and Vorobyov,E. A. (1981): Mechanical properties of frozen coarse-grained soils,Engineering Geology, 18, 47–53.18) Wang, D. Y., Ma, W. and Chang, X. X. (2004): Analyses of behavior of stress-strain of frozen Lanzhou loess subjected to K0 consolidation, Cold Regions Science and Technology, 40(1–2), 19–29.19) Wu, Z. W., Ma, W., Zhang, C. Q. and Shen, Z. Y. (1994): Strengthcharacteristic of frozen sand soil, Journal of Glaciology and Geocryology, 16(1), 15–20.20) Zhang, S. J., Lai, Y. M., Sun, Z. Z. and Gao, Z. H. (2007): Volumetric strain and strength behavior of frozen soils under conˆnement, Cold Regions Science and Technology, 47(3), 263–270.21) Zhu, Y. L., Zhang, J. Y., Peng, W. W., Shen, Z. Y. and Miao, L.N. (1992): Constitutive equation of frozen soils under uniaxial compression, Journal of Glaciology and Geocryology, 14(4), 210–217.
  • ログイン
  • タイトル
  • Characterization of the Fouled Ballast Layer in the Substructure of a 19th Century Railway Track under Renewal
  • 著者
  • "E. Fortunato, A. Pinelo, M. M. Fernandes"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 55〜62
  • 発行
  • 2010/02/15
  • 文書ID
  • 64341
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 55–62, Feb. 2010CHARACTERIZATION OF THE FOULED BALLAST LAYER IN THESUBSTRUCTURE OF A 19TH CENTURY RAILWAY TRACK UNDER RENEWALÁEDUARDO FORTUNATOi), ANTONIOPINELOii) and MANUEL MATOS FERNANDESiii)ABSTRACTThe purpose of these ˆeld and lab studies undertaken during rehabilitation work being done on an ancient railwayline was to characterize a layer of ballast fouled with soil found in the track substructure. The ˆeld studies included thecharacterization of the thickness, grain size distribution and void ratio of the fouled ballast layer, as well as a largenumber of plate load tests, both on the fouled ballast layer and on the subgrade. The resilient behaviour of the fouledballast was evaluated in the lab by cyclic triaxial tests on large size reconstituted specimens with distinct fouling indexes(diŠerent grain size distribution) and distinct humidity states (dry or wet). The results obtained were used as supportfor the decision to maintain the fouled ballast layer under the new sub-ballast in a number of stretches of the renewedline.Key words: cyclic triaxial tests, fouled ballast, plate load tests, resilient modulus, track rehabilitation (IGC:C8/D6/H6)(North) with a double track 336 km in length. The NorthSouth track (N-S track) was built between 1856 and 1864,and the South-North track (S-N track) was settled between 1861 and 1930.INTRODUCTIONMany railway lines in diŠerent countries have been inoperation for more than a hundred years. Their adaptation to modern trains requires a detailed characterizationof the existing platform, by identifying the nature of thematerials and their state and by evaluating their strengthand stiŠness.A layer of ballast fouled with soil frequently occurs inthe substructure of these lines, underlying the ballast ( seeFig. 1(a)). Various mechanisms lead to the formation ofthis layer: grain size modiˆcation in ballast particles dueto cracking, weathering and crushing; the inˆltration ofmaterials from the surface; the inˆltration of materialsfrom underlying layers; and, the weathering of the sleepers.The interest in studying fouled ballast is related withthe advantage of maintaining the layer under the newsub-ballast layer ( see Fig. 1(b)), during the renewal process, thus reducing the cost, the construction period andthe disturbance to line operation.Nevertheless, the behaviour of fouled ballast is di‹cultto characterize, since it consists of a more or less densemixture of materials—soil and ballast—in highly variableproportions and thickness. In addition, collecting undisturbed samples is not possible.This paper presents ˆeld and lab studies for the renewalof an ancient Portuguese railway line which links the twomain cities in the country—Lisbon (South) and Portoi)ii)iii)Fig. 1. Schematic representation of the rail track: (a) old railway trackand (b) renewed railway trackResearch O‹cer, Laborat áorio Nacional de Engenharia Civil-LNEC, Lisbon, Portugal (efortunato@lnec.pt).Principal Research O‹cer, ditto.Professor, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal.The manuscript for this paper was received for review on November 27, 2008; approved on December 2, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.55 56FORTUNATO ET AL.The ˆeld studies of the substructure included: i) thecharacterization of the thickness, grain size distributionand void ratio of the fouled ballast layer; ii) plate loadtests, both on the fouled ballast layer and on the subgrade. In addition, a lab characterisation was developed,with cyclic triaxial equipment appropriate for testinglarge specimens (Fortunato, 2005). The density, grain sizedistribution and rock type of the fouled ballast specimenswere established on the basis of the information from theˆeld survey. Tests were performed on dry specimens andon wet specimens.Those studies are part of a more comprehensive workthe purpose of which was to establish the conditions thatexisting materials must fulˆl in order to be maintained aspart of the track substructure at the time of renewal.IN SITU CHARACTERISATION OF THE RAILWAYSUBSTRUCTUREThickness, Fouling Index and Void Ratio of FouledBallastThe ˆeld survey consisted of 144 boreholes and 93trenches carried out over a 125 km long stretch on bothtracks.At the surface two ballast materials were identiˆed:granite and limestone. However, the rock material of thefouled ballast found under the ballast was limestone sincethis was the only type of rock used as ballast for manyyears. In some sites, signiˆcant diŠerences in the quantityof ˆne particles in the fouled ballast were observed, depending on the location of the sampling points as to railand to sleeper positions.Figure 2 shows, as an example, graphs indicating thedepth (from the base of sleepers), corresponding to thebottom limit of both ballast and fouled ballast layersalong the S-N track and the N-S track. Generally, theaverage thickness of the fouled ballast along this track isabout 3 cm to 10 cm less than the one calculated for theS-N track. Since no signiˆcant diŠerences were found between the type and condition of the foundation soils ofboth tracks, the observed diŠerence is justiˆed by the factthat the S-N track was typically used by trains transporting heavier products, such as cement, because of the concentration of plants in the south of the country.The analysis of the 114 grain size curves of fouled ballast revealed the following: i) the maximum grain sizeusually ranges from 50 to 60 mm; ii) the percentage ofgrain size below 4.75 mm ranges from 3z to 30z; iii) thepercentage of grain size below 0.075 mm ranges from 1zto 18z ( see Fig. 3). The degree of the ballast fouling wasevaluated by the fouling index, FI, deˆned as (Selig andWaters, 1994):FI=P4+P200in which P4 and P200 are the percentage of material passing the 4.75 mm and the 0.075 mm sieves, respectively.The void ratio of the fouled ballast (determined in situby the membrane method developed by Yoo et al., 1978)ranged from 0.10 to 0.45 ( see Fig. 4). In general, thelowest values occurred beneath the rails, where the in‰uence of train loads is more signiˆcant. The results ledus to conclude that, generally, the void ratio of fouledballast decreases with the increase of the FI.Subgrade Modulus from Plate Load TestsIn accordance with the UIC CODE 719R (UIC, 1994),Fig. 3.Fig. 2. Depth of the bottom limit of both ballast and contaminatedballast layers: (a) along the S-N Track and (b) along N-S track(1)Fig. 4.Grain size curves of fouled ballastVoid ratio of fouled ballast versus fouling index ( FI) CHARACTERIZATION OF FOULED BALLAST LAYERthe renewed substructure must fulˆl a number of requirements based on the deformation modulus in the secondloading cycle of a plate load test, EV2 (AFNOR, 2000).The sub-ballast layer is placed on a capping layer (EV2Æ80 MPa) and at the top of the sub-ballast layer, EV2 isrequired to be equal to or higher than 120 MPa.After removing the ballast, 138 plate load tests (600mm diameter plate) on the ancient substructure were carried out, 70 of which were performed on the fouled ballast layer, with a thickness ranging from 5 to 70 cm andan average value of 24 cm. The minimum value of EV2was higher than 40 MPa and, in 60z of the cases, valueshigher than 80 MPa were reached. When the tests wereperformed on the subgrade soil (where the fouled ballastlayer was no longer present or had already been removed), the 80 MPa value was achieved only in 45z ofthe cases.In about 75z of the cases, a rather homogeneous subgrade was found below the fouled ballast layer, i.e., onlygranular soils (less than 35z passing 0.075 mm sieve) orˆne soils (35z or more passes a 0.075 mm sieve) were observed and the water content remained fairly constant indepth. An attempt was made to relate subgrade soilparameters with EV2. As was expected, it was only possible to detect fairly weak relations. In fact, bearing inmind that the plate was 600 mm in diameter and thethickness of the fouled ballast layer ranged very oftenfrom 5 to 70 cm, the eŠect on EV2 is diŠerent in eachcase, depending on the fouled ballast and the subgradesoil.Figure 5 illustrates the two relationships describedabove: one between the percentage of ˆnes, and the otherbetween the water content of the subgrade and EV2. Thethin lines in the ˆgures indicate the analogous relationsFig. 5. Deformation modulus determined on the fouled ballast layerversus (a) P200 and (b) the water content in the subgrade soil57found for the substructure without fouled ballast between the ballast and the subgrade (the markers are notshown). The comparison of the curves reveals a favourable in‰uence of the fouled ballast layer on EV2, with anincrease of about 20 to 30 MPa observed, particularlywhen the subgrade consists of ˆne soils, or when thewater content is higher than 10z. This behaviour is dueto the modulus of fouled ballast being greater than thatof the subgrade soils, as will be explained below.RESILIENT BEHAVIOUR FROM CYCLIC LOADTRIAXIAL TESTSEquipment, Specimens and TestsThe proper evaluation of the stiŠness of materials likethe fouled ballast in the lab must respect their actual grainsize distribution, since the way a load is propagatedthroughout a particulate medium depends not only on thestructural arrangement of particles but also on their size(Kolisoja, 1997). As shown by Fig. 6, the specimens builtin the lab were 0.30 m in diameter and 0.60 m in height,including particles with diameters of up to 60 mm. Theywere subject to triaxial cyclic loads on both principaldirections through distinct stress paths. The system usedallows the axial and radial strains to be recorded with aresolution of at least 10-5 on the central part of the specimen, ensuring negligible interference with the behaviourof the material to be tested.The ˆeld characterisation showed that in many samplescollected in the zones where the railway track revealedgood performance, the fouled ballast consisted of limestone, the ˆnest fraction of which mainly resulted fromthe weathering of the coarser particles and not from othersources, such as the subgrade. It was then considered thatthese would be the more relevant cases to be studied inorder to provide the basis for support of the option ofkeeping the fouled ballast layer in place under the newsub-ballast layer in the course of renewal works.Fouled ballast specimens with diŠerent grain size distributions were built, with the purpose of representing theFig. 6.A specimen prepared for testing FORTUNATO ET AL.58coarsest (C), the medium (M) and the ˆnest (F) grain sizedistributions found in the fouled ballast layer. Figure 7shows the corresponding grain size distribution curves,the fouling index and the value of the void ratio; the pictures included in the ˆgure show the aspect of the specimens. The density obtained for the specimens C, M and Fare 2.02, 2.16, and 2.33, respectively. The results obtained for the ˆeld density, for similar values of the fouling index (samples represented by the trendline presentedin Fig. 4), were 2.11, 2.30 and 2.40, respectively.The specimens were built with 0.06 m thick layers,which were compacted by vibration for nine minutes inside a cylindrical half split steel mould lined by a 1.5 mmthick rubber membrane and by two porous discs and geotextile blankets at the top and bottom. After completionof the specimens, these were kept in an oven at a 409Ctemperature for 72 hours, so they could be subsequentlytested with similar water content values, at approximately1z.The study of the fouled ballast under repeated loadingwas performed by taking into account the EN13286-7(CEN, 2000) regarding the method of variable conˆningpressure, as follows:– the 1st phase) cyclic triaxial loading (20000 cycles at afrequency of 0.25 Hz), with a high stress level (conˆning pressure ranging from 0 to 100 kPa and deviatorstress ranging from 0 to 600 kPa) in order to stabilizethe permanent strains and to attain a resilient behaviour (the so-called conditioning phase);– the 2nd phase) study of the resilient behaviour by applying 100 load cycles, and then recording the stressand strain values from cycle number 90 to cycle number 100; loading was done through distinct stress paths,with the ratio between the cyclic deviator stress ( q=s1-s3) and the mean stress ( p=(s1+2s3)/3) rangingfrom 0 to 2.5 ( see Table 1).The stress paths obtained by simulating the loadingtypes usually observed in the platform of railway tracksare compatible with the resistance of the materials typically employed for that purpose and, therefore, there isno apparent damage to the specimens.Permanent Deformation Behaviour during the Conditioning StageThe variation of the permanent strain during the 20000cycles performed during the conditioning phase is characterised by a rapid increase during the ˆrst cycles, followedby progressive stabilisation. The maximum strain valuesobtained for the specimens C, M and F were 13.4×10-4,19.3×10-4 and 23.5×10-4, respectively.The ˆrst well known relationship describing the variaption of permanent axial deformations, e 1, with the number of load cycles, N, is that proposed by Barksdalep(1972), who found a linear increase of e 1 with thelogarithm of the number of load cycles:pe 1=a+b・log ( N )Table 2 presents the values of the parameters of thismodel calculated from the triaxial test results. The highvalue of the determination coe‹cient reveals the appropriateness of the model for the studied material. Asregards parameter b, which can be considered as an indicator of the behaviour of the material when subject torepeated loading, the conclusion is that it is low for thefouled ballast with grain size distribution M and C andreaches a fairly high value for the fouled ballast of grainsize distribution F. These values point out the leastresistance to permanent deformation of the F specimen.In the ˆrst load cycles, the permanent deformation canbe particularly conditioned both by the phenomena of thelocal arrangement of particles, particularly relevant whenmaterials with sizes similar to those under study are tested, and by the initial state of compaction of the specimens. Therefore, a few models provide the reference forthe permanent deformation associated with the numberof cycles from which the long-term behaviour of thematerial is assessed, making the latter independent fromTable 2.Parameters of the Barksdale permanent deformation modelep1 (10- 4)=a+b. log (N)SpecimenFig. 7. Grain size curves, fouling index, void ratio and an aspect oftested fouled ballastTable 1.(2)abR2S (em-ec)2F3.014.6900.9917.45M15.130.9420.9920.26C7.611.4710.9533.79em–measured permanent axial strainec–calculated permanent axial strainStress paths of cyclic triaxial loading (s3 minimum=0 and q minimum=0)q/p=0.0q/p=0.5q/p=1.5q/p=2.0q/p=2.5s3 (kPa)5010017525050100175250501001502003060100101520q (kPa)00003060105150150300450600180360600150225300 CHARACTERIZATION OF FOULED BALLAST LAYERTable 3.59Parameters of the Paute et al. permanent deformation model*Specimenep1 (100)(10- 4)ep1 (20000)(10-4)A1(10-4)F11.923.537.30.069 0.99411.6M17.119.317.30.024 0.9872.0C10.613.42.90.489 0.9982.7BR2ep1 (20000)(10- 4)Fig. 9.Fig. 8.Resilient modulus of the fouled ballastRate of change of the permanent axial strainthe permanent deformation which occurs in the ˆrst cycles. In those circumstances, another way to model thepermanent axial strain accumulated after N load cycles,phigher than 100 (e 1 ( N )) is the one proposed by Paute etal. (1994), which is represented as follows:pppe 1(N )=e 1 (100)+e 1*( N )(3)Fig. 10.Variation of resilient modulus with fouling index (q/p=2.0)done, ˆrstly, on the basis of the theory of elasticity inorder to obtain the resilient modulus ( E ) through theequation:E=withp« Ø » $e 1 *( N )=A1・ 1-N100-B(4)A1 and B being parameters obtained from tests.Table 3 includes the values of the permanent strain after the ˆrst 100 cycles and after 20000 cycles, the valuesobtained using a least squares method, for parameters A1and B of the model and the coe‹cient of determinationassociated, as well as the values of the strain estimated bythe model after 20000 cycles.It can be seen that the model makes it possible to obtain a good approximation of the behaviour of thematerials. It is interesting to note that the value of the A1parameter is very small in specimen C, which impliesgood behaviour with regard to permanent deformation.Figure 8 depicts the curves relating the evolution in therate of change of the permanent axial strain (permanentaxial strain/cycle) with the value of that strain after theˆrst 100 load cycles. The rate of change of the straindecreases rapidly with the increase in the number of cycles in the C and M specimens. For specimen F, the rateof change of the strain gradually decreased. This behaviour is what was expected given the values of the bparameter of the Barksdale model.Resilient BehaviourThe interpretation of the 2nd phase test results to estimate the resilient behaviour of the fouled ballast wass21r+s1rs3r-2s 23rs1re1r+s3re1r-2s3re3r(5)where:s1r—resilient axial stress (s1max-s1min);s3r—resilient radial stress (s3max-s3min);s1max, s1min—maximum and minimum total axial stressesin one load cycle;s3max, s3min—maximum and minimum total radial stressesin one load cycle;e1r, e3r—resilient axial and radial strains.Figure 9 presents all the E values together with thecurves which best ˆt the experimental results, as a function of the mean stress. Those curves are represented byrelations such as E=a・pb, in which a and b are constants.The resilient modulus increases with the increase in themean stress and with the decrease in FI, as shown in Fig.10, established for stress ratio q/p=2.0.The results of the tests were further treated in accordance with theoretical models usually employed torepresent the resilient behaviour of conventional aggregates (Lekarp et al., 2000). Among these models, theone that provided most satisfactory results was the Boycemodel (Boyce, 1980) modiˆed by Hornych et al. (1998) inorder to take into account anisotropy through theparameter g, and represented by the following: FORTUNATO ET AL.60ev=p 1a-n・p*n«Ø »g+ 2 n - 1q*+( g+2)・p*3・Ka 18・GaØ »$-n-= p ・p «+・K・G+ q+・G Ø p » $+eq232g- 1 q *3・ G a p *1- na2g61a*ng31a(6)118**a( g-1)・Ø »q*p*2(7)withg ・ s 1 + 2s 33(8)q*=g・s1-s3(9)p* =Behaviour of the Wet MaterialAfter characterizing the resilient behaviour of the dryspecimens, these were abundantly wetted by imposing a‰ow of water under a hydraulic head of 1 m and a conˆning pressure of 30 kPa. After stopping the ‰ow, the specimens were left to freely drain for two hours and then theresilient modulus was determined in a way similar to thesecond phase, as explained in Equipment, Specimens andTests. The values of the water content of wet specimensevaluated at the end of the tests were 2.1z, 5.5z and 4.9z for the specimens C, M and F, respectively.Figure 12 summarizes the results obtained from wetspecimens. By comparing this ˆgure with Fig. 9, it can beandwhere ev and eq are the resilient volumetric and shearstrains, s1 and s3 are the principal stresses and Ka, Ga andn are model parameters.Figure 11 compares the experimental results with thecurves calculated by the Boyce model with anisotropy fordiŠerent stress paths, q/p. In most cases, the curves obtained by the model closely ˆt the volumetric and shearstrain results.Fig. 12.Resilient modulus of the fouled ballast in wet conditionFig. 11. Volumetric strain (ev) and shear strain (eq) observed and calculated by the anisotropic Boyce model: (a) grain size F, (b) grain size M and(c) grain size C CHARACTERIZATION OF FOULED BALLAST LAYERTable 4.61Characteristic value of the resilient modulusEc (MPa)Fig. 13. Variation of resilient modulus with fouling index (q/p=2.0)-wet specimensseen that the values of the resilient modulus of wet specimens are generally smaller than those for dry specimens.Moreover, it seems that the fouling index is not as in‰uent on the resilient modulus as it was found to be in thecase of the dry specimens ( see Fig. 13).RANKING OF MATERIALS BASED ON RESULTSOF THE TESTSAccording to EN13286-7 (CEN, 2000), granularmaterials used for base layers of pavements are ranked onthe basis of two parameters: i) a characteristic value ofthe resilient modulus, Ec, deˆned as the resilient modulusdetermined for the stress values p=250 kPa and q=500kPa; ii) a characteristic permanent axial strain, ec1, whichdeˆnes the resistance of the material to permanent deformations, determined from the results of the conditioning.They were calculated as follows:ppec1=e 1 (20000)-e 1 (100)c1(10)With regard to e , the dry fouled ballast exhibited verylow values: 2.8×10-4, 2.2×10-4 and 11.6×10-4 for thespecimens C, M and F, respectively. Taking into accountthe procedure followed in this study (the specimens werewetted after characterizing the resilient behaviour) it isnot possible to calculate ec1 for wet fouled ballast, becausethere is no conditioning phase for the wet specimens.The values of Ec estimated for dry and wet specimensusing the Boyce model are presented in Table 4. Thereduction in Ec induced by wetting is about 4z, 25z and34z for F, M and C specimens, respectively. However,Ec values are quite considerable for all the specimens,even higher than typical values for conventional unboundgranular materials. Paute et al. (1994) obtained Ec valuesranging from 300 to 1000 MPa for well graded crushedaggregates, usually employed as supporting layers oftransportation infrastructures.Taking into account the classiˆcation of the unboundgranular materials based on mechanical performanceparameters Ec and ec1 (CEN, 2000), the fouled ballast isclassiˆed as a C1 material (500 MPaÃEc and ec1Ã2.5×10-3).SpecimenFMCDry material9419591261Wet material902722838CONCLUSIONSExtensive ˆeld and lab studies have been carried outduring the renewal of the main railway line in Portugal,with the purpose of characterizing the physical andmechanical properties of the existing substructure materials.The ˆeld survey revealed a layer of fouled limestoneballast (ballast with soil), with a non-regular thicknessand variable grain size distribution and void ratio.Plate load tests performed on the substructure showedthat the presence of the fouled ballast contributes to increase the deformation modulus, in comparison with thetest results from the subgrade soils only.The resilient behaviour of ballast with distinct foulingindexes (diŠerent grain size distribution) was evaluatedby employing cyclic triaxial tests. During the conditioning phase of the samples, the permanent deformation obtained after 20000 load cycles was higher in samples withgreater fouling index.The results provide evidence that the resilient modulusof the fouled ballast depends not only on the appliedstress but also on the fouling index and on the materialstate (dry or wet). When the specimens are dry, theresilient modulus obtained is higher in the coarser materials. When the specimens are wet, the resilient modulusdecreases and this seems to be less dependent on the fouling index. This assumption needs to be conˆrmed by further research.The resilient behaviour and the permanent deformation of the fouled ballast can be represented by wellknown models commonly applicable to unbound granular materials. The results obtained, namely with regard tothe characteristic resilient modulus, are similar to thosefor well graded crushed aggregates, usually employed assupporting layers of transportation infrastructures.The overall evaluation of the results obtained in theˆeld and in the lab tests provided the basis to support thedecision of maintaining the fouled ballast layer under thenew sub-ballast in a number of stretches of the renewedline.REFERENCES1) AFNOR—Association Francaise de Normalisation (2000): NF P94-117-1—Soils: investigation and testing, Formation level bearingcapacity, Part 1: plate test static deformation module (EV2).2) Barksdale, R. D. (1972): Repeated load test evaluation of basecourse materials, Ph.D. Thesis, Georgia Institute of Technology,Atlanta, USA.3) Boyce, J. R. (1980): A non-linear model for the elastic behaviour of 624)5)6)7)FORTUNATO ET AL.granular materials under repeated loading, Proc. Int. Symposiumon Soil under Cyclic and Transient Loading, Swansea, A. Balkema,285–294.CEN—European Committee for Standardization (2000): Unboundand hydraulically bound mixtures—Part 7: Cyclic load triaxial testfor unbound mixtures, Draft, prEN 13286-7, Brussels, Belgium.Fortunato, E. (2005): Renewal of railway platforms. Studies aboutbearing capacity, Ph.D. Thesis, University of Porto, Portugal (inPortuguese).Hornych, P., Kazai, A. and Piau, J. M. (1998): Study of theresilient behaviour of unbound granular materials, Proc. 5th Int.Conf. on the Bearing Capacity of Roads and Airˆelds, Trondheim,Norway, 1277–1287.Kolisoja, P. (1997): Resilient deformation characteristics of granular materials, Ph.D. Thesis, Tampere University of Technology,Finland.8) Lekarp, F., Isacsson, U. and Dawson, A. (2000): State of the art. I:Resilient response of unbound aggregates, Journal of Transportation Engineering, ASCE, 126(1), 66–75.9) Paute, J. L., Hornych, P. and Benaben, J. P. (1994): Comportement m áecanique des graves non trait áees, Bulletin de Liaison desLaboratoires des Ponts et Chauss áees, Paris, (190), 27–38.10) Selig, E. T. and Waters, J. M. (1994): Track Geotechnology andSubstructure Management, Thomas Telford Services Ltd., London.11) UIC—Union International des Chemins de Fer (1994): Ouvrages enterre et couches d'assise ferroviaires, Code UIC 719R, 2 áeme áedition.12) Yoo, T. S., Chen, H. M. and Selig, E. T. (1978): Railroad ballastdensity measurement, Geotechnical Testing Journal, 1, 41–54.
  • ログイン
  • タイトル
  • Load Tests of Piled Raft Models with Different Pile Head Connection Conditions and Their Analyses
  • 著者
  • "Tatsunori Matsumoto, Hisashi Nemoto, Hiroshi Mikami, Kou Yaegashi, Toshiaki Arai, P. Kitiyodom"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 63〜81
  • 発行
  • 2010/02/15
  • 文書ID
  • 64342
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 63–81, Feb. 2010LOAD TESTS OF PILED RAFT MODELS WITH DIFFERENTPILE HEAD CONNECTION CONDITIONS AND THEIR ANALYSESTATSUNORI MATSUMOTOi), HISASHI NEMOTOii), HIROSHI MIKAMIiii),KOU YAEGASHIiv), TOSHIAKI ARAIv) and PASTSAKORN KITIYODOMvi)ABSTRACTA series of experimental and analytical studies on the behaviours of model pile groups and model piled rafts in drysand subjected to static vertical loading and static cyclic horizontal loading were carried out in order to investigate thein‰uence of various pile head connection conditions between the raft and the piles on the behaviours of the foundations models and to examine the applicability of an simpliˆed analytical method to simulate the load tests. In the loadtests, the behaviours of the model foundations were investigated in detail, with particular focus on cyclic horizontalloading, and behaviour such as horizontal stiŠness and the rotation of the foundation, the load proportions betweenthe raft and the piles, and the bending moments and shear forces generated in the piles. A simpliˆed three-dimensionaldeformation analysis method was used to simulate the experiments.Key words: 1-g test, analysis method, dry sand, horizontal load test, load proportion, pile group, pile head connectioncondition, piled raft, vertical load test (IGC: E13/E14/K7)their experimental studies, two extreme pile head connection conditions, rigid connection and hinged connectionconditions, were modelled. These experiments showedthat the pile head connection condition is one of the keyfactors aŠecting the behaviours of piled rafts duringshaking and static horizontal loading.Hence, a series of experimental and analytical study onthe behaviours of model piled rafts and model pile groupsin dry sand subjected to static vertical loading and staticcyclic horizontal loading were carried out in this researchin order to investigate the in‰uence of various pile headconnection conditions on their behaviours. In the loadtests, the behaviours of the model foundations duringhorizontal loading in particular such as horizontal stiŠness and rotation of the foundation, load proportions between the raft and the piles, and bending moments andshear forces generated in the piles were investigated in detail.Analyses of the load tests were also conducted using asimpliˆed three-dimensional deformation analysismethod in order to discuss the test results in more detailand to explore the possibility of the use of the simpliˆedmethod for design purposes.INTRODUCTIONRecently, piled raft foundation has been considered asa possible foundation type in Japan, especially in the design of building foundations. In making designs, estimations of deformation of the piled rafts during earthquakes is required. The authors are aware that a dynamicanalysis of the foundation is essential in seismic design.This design approach is, however, complicated and maybe still di‹cult in practice. A design method in which equivalent static horizontal loads are applied to the foundation structure is still one of the most practical designtechniques used in Japan. Even when using this technique, the response of piled rafts subjected to statichorizontal loading does become fully clariˆed, becausethe response of the piled raft is controlled by the loadsharing of the vertical load between the raft and the piles,the interactions between the raft, the piles and the soil, aswell as the connection condition between the pile headand the raft.Correlation between the behaviours of model piledrafts during shaking and static horizontal loading wereinvestigated using the centrifuge model provided byHorikoshi et al. (2003a, b) and the shaking table tests at1-g ˆeld presented by Matsumoto et al. (2004a, b). Ini)ii)iii)iv)v)vi)Graduate School of Natural Science and Technology, Department of Civil Engineering, Kanazawa University, Kanazawa, Japan (matsumot@t.kanazawa-u.ac.jp).Research Center, ANDO Corporation, Tokyo, Japan.Technological Development Center, Sumitomo Mitsui Construction Co. Ltd., Nagareyama, Japan.Building Engineering Department Technical Division, Hazama Corporation, Tokyo, Japan.Technical Research Institute, Nishimatsu Construction Co. Ltd., Tokyo, Japan.Geotechnical & Foundation Engineering Co., Ltd., Thailand.The manuscript for this paper was received for review on January 28, 2009; approved on December 2, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.63 MATSUMOTO ET AL.64Fig. 1.Table 1.Illustration of test set-upPhysical properties of Toyoura sand used for model testsPropertyValueMaximum dry density, rdmaxMinimum dry density, rdminDensity of soil particle, rsMean grain size, D50Internal friction angle, q?1.621 t/m31.328 t/m32.637 t/m30.17 mm40 degreesTEST DESCRIPTIONModel Ground and Model FoundationsFigure 1 shows the test set-up including a model piledraft and the model ground. Dry Toyoura sand was usedfor the model ground throughout the tests. The physicalproperties of the Toyoura sand are summarised in Table1. The sand was prepared in a steel cubic box of 1500 mmin length. Note that base bricks were set at the bottom ofthe soil box to a level of 500 mm from the bottom. Thus,the eŠective height of the model ground was 1000 mm.Figures 2 and 3 show the model raft and the modelpiles, respectively. The square model raft was made ofstainless steel plate with a width of 400 mm and a thickness of 40 mm, and could be regarded as a `rigid' plate.Fig. 2.Model raftThe Toyoura sand was glued at the bottom base of themodel raft to increase the coe‹cient of friction betweenthe raft base and the model ground.Aluminum pipe piles with an outer diameter of 40 mm,a wall thickness of 2 mm and a length of 600 mm wereused for the model piles. The top and bottom of the pipepile were capped with an aluminum plate. The geometrical and mechanical properties of the model pile are listed PILED RAFT MODEL TESTPhoto 1.Fig. 3.Table 2.65Ball joint used in the hinged connection conditionModel piles with diŠerent pile head connection conditionsGeometrical and mechanical properties of the model pilePropertyValueOuter diameter, dWall thickness, twLength, LCross sectional area, ApYoung's modulus, EpPoisson's ratio, npLongitudinal rigidity, EpApBending rigidity, EpIp40 mm2 mm600 mm239 mm 27.0×107 kPa0.31.67×104 kN3.03 kNm 2in Table 2. The Toyoura sand was glued on the outershaft of the model piles to increase the shaft resistance.Four diŠerent pile head connection conditions weremodelled by using connection bars with a length of 5 mmbetween the top steel cap and the raft. The connectionbars had diŠerent diameters, 30.5 mm, 13.0 mm and 10.0mm, as shown in Fig. 3. The bending rigidities, EbIb, ofthese connection bars are 2.974, 0.098 and 0.034 kN・m2,respectively. A ball joint (Photo 1) was used to simulatethe hinged pile head connection condition. These pilehead connection conditions are called `rigid', `semirigid', `semi-hinged' and `hinged', respectively. Notehere that EbIb of the connection bars of the rigid, semirigid and semi-hinged models are about 1, 1/30 and 1/90of the bending rigidity of the model pile, EpIp, of 3.03kNm2.The top steel plate, the connection bar and the top steelcap was made as a unit for each of the rigid, semi-rigidand semi-hinged models. The top steel cap was stiŒypushed into the top of the model pile and welded to themodel pile.Fig. 4. Shear modulus vs conˆning pressure of the Toyoura sand,together with the ˆtting linesMechanical Properties of Toyoura SandA series of triaxial consolidated drained shear tests (CDtest) of the Toyoura sand were conducted to obtain thestress dependency of the shear modulus, G, and the internal friction angle, q?. The tests were carried out with soilspecimens of relative density Dr=80z, 100 mm in heightand 50 mm in diameter, with diŠerent conˆning pressures, p0, of 49, 98, 147 and 245 kPa. From initial linearpart of the measured deviator stress, q, versus shearstrain, g=ea-er (ea and er are axial and radial strains, respectively), for each test, the shear modulus was estimated as G=q/g, and was plotted against the conˆningpressure, p0, in Fig. 4. The measured values of G are ˆtted by the lines in Fig. 4, which are expressed asG=Gref( p0/pref)0.5(1)where pref is a reference value of conˆning pressure (=100kPa) and Gref is the value of G at p0=pref.It may be seen from Fig. 4 that the shear modulus ofthe sand is proportional to the square root of p0.Figure 5 shows the peak deviator stress versus the eŠective mean stress from the CD tests. From this relation,the internal friction angle, q?, was estimated at 40degrees. MATSUMOTO ET AL.66Table 3.Test cases and pile head connection conditionsTest nameCaseCaseCaseCaseCaseCaseCase1:2:3:4:5:6:7:RaftPG-RPG-HPR-RPR-SRPR-SHPR-HType offoundationPile headconnection conditionRaft alonePile GroupPile GroupPiled RaftPiled RaftPiled RaftPiled Raft—RigidHingedRigidSemi-rigidSemi-hingedHingedPG: Pile Group, PR: Piled RaftR: Rigid connection, SR: Semi-rigid connectionH: Hinged connection, SH: Semi-hinged connectionFig. 5.Peak deviator stress versus eŠective mean stressPhoto 3.Photo 2.Model foundation with instrumentsTest Procedure and Test CasesThe method of setting-up of the model foundation inthe model ground was as follows. First, four model pileswere set in the soil box at the prescribed positions withcentre-to-centre distance of 200 mm by using speciallydesigned rigs ( see Photo 2). Second, the sand was pouredinto the soil box to have a thickness of 100 mm, and wascompacted using a vibrator until it had a relative density,Dr, of about 80z. This procedure was repeated until themodel ground was 1000 mm thick. Third, the model raftwas placed on the model piles, and the top steel plate oneach pile head was bolted to the raft.A total of 7 test cases were carried out as listed in Table3. Case 1 is the test on the raft alone, Cases 2 and 3 arethe tests on the pile groups with rigid and hinged pile headconnection conditions, and Cases 4 to 7 are the tests onthe piled rafts with the four diŠerent pile head connectionTest set-up prior to cyclic horizontal load testsconditions. Note that, in the cases of the pile groups, agap of 5 mm between the raft base and the ground surface was made prior to the start of the load test, while inthe cases of the piled rafts, the raft base was attached tothe ground surface at the start of the test.The loading process on the model foundation wasdivided into two stages, i.e., vertical loading stage and cyclic horizontal loading stage. In the vertical loading stage,the vertical load was applied by placing 9 steel plates witha weight of 0.376 kN each on the model raft one by one.Finally, a maximum vertical load of 3.384 kN was applied to the model foundation. Note that the average contact stress of the raft was 21.2 kPa for the case of raftalone. After the completion of vertical loading stage, cyclic horizontal loads were applied to the model raft bymeans of two oil jacks in the east and west directions. Thehorizontal load and horizontal displacement to the eastdirection are taken as positive in this paper.During the load test, the horizontal load, the verticaland horizontal displacements of the raft, the axial forcesand shear forces, and the bending moments of each pilewere measured. Photo 3 shows the test set-up prior to cyclic horizontal load test.The horizontal cyclic loading and measuring devicesare shown in Fig. 1(b). Two oil jacks were placed on theeast and west sides of the soil box. A steel loading bar wasconnected to each oil jack. The end of the steel loadingbar was attached with a roller that was in contact with the PILED RAFT MODEL TESTmodel raft at the mid-height of the raft (20 mm above theground surface). When the horizontal displacement in thewest direction was applied, the pushing force was appliedto the raft using the oil jack on the east side while the oiljack on the west side was released. When the horizontaldisplacement in the east direction was applied, a pushingforce was applied to the raft using an oil jack on the westside while the oil jack on the east side was released. Thehorizontal loads applied to the raft were measured bymeans of two load cells attached between the raft and thesteel loading bars.Horizontal displacement and vertical displacements ofthe raft were measured by means of laser beam displacement meters (LB in Fig. 1(b)) with a precision of 8 mmand contact displacement meters (CDP in Fig. 1(b)).From the measured vertical displacements, the averagevertical displacement and the inclination of the raft wereobtained.Axial forces and bending moments of the model pileswere estimated from the measured axial strains, andshear forces were estimated from the shear strain gauges(cross-gauges) near the pile top, based on the elastic beamtheory.67Fig. 6.Results of CPTs in the model groundsFig. 7.Vertical load - settlement relationshipTEST RESULTSResults of Cone Penetration TestsIn order to compare the test results of the 7 test caseslisted in Table 3, compatibility of the soil conditions between the test cases was conˆrmed by conducting a conepenetration test (CPT) in the model ground after thecompletion of the load test in each case. A miniature conepenetrometer with a diameter of 16.2 mm and an apexangle of 60 degrees was penetrated in the model ground ata penetration rate of 2 mm/s. The location of the CPTwas 300 mm away from the edge of the raft in order tominimise the in‰uence of soil disturbance due to the loading process of the foundation.The distributions of the cone tip resistance, qc, withdepth for the model grounds in all the test cases areshown in Fig. 6. Although some scatters are seen in qc fordepths greater than 300 mm between the test cases, it maybe said that compatibility of the model ground conditionsbetween all the test cases was achieved.Results of Vertical Load TestsFigure 7 shows the relationships of the vertical load, P,and the settlement, w, of the model foundations.Although the measured settlements were very small compared to the width of the raft (400 mm), it can be clearlyseen from the ˆgure that the settlements of the pile groups(Cases 2 and 3) were much smaller compared with the raftalone. It is also seen that the settlements of the piled rafts(Cases 4 to 7) were smaller than those of the pile groups,indicating the eŠect of the raft. It should be noted thatpile head connection condition had little in‰uence on thesettlements in both types of the foundations.Figure 8 shows the changes in the vertical load proportion carried by the raft with an increase in the verticalFig. 8.Vertical load - vertical load proportion relationship MATSUMOTO ET AL.68load. The load carried by the raft was calculated by subtracting the axial forces at the pile head of 4 piles fromthe weight applied on the raft. Of course, the proportionof the vertical load carried by the piles is 100z in the caseof the pile groups. In PR-SR (Case 5), the load proportion carried by the raft had a negative value when a vertical load of 0.38 kN was applied, which is unrealistic, anda smaller value when a vertical load of 0.76 kN was applied. It seems that these values are erroneous due to thesmall values of the vertical load. Except for these data, itFig. 9.Fig. 10.is seen from Fig. 8 that the vertical load proportion isalmost constant irrespective of the amplitude of the vertical load in all the pile raft cases. The load proportion carried by the raft is the highest in PR-R (Case 4), and that isthe lowest in PR-SR (Case 5). The load proportions carried by the raft in PR-SH (Case 6) and PR-H (Case 7) aresimilar and intermediate between PR-R and PR-SR.Hence, it may be said that the pile head connection condition has little in‰uence on the vertical load proportion.This aspect will be discussed later again in the Section ofChange in axial force distribution in pileVertical load - pile shaft resistance relationship PILED RAFT MODEL TEST``ANALYSES OF LOADING TESTS''.It is interesting to note that the vertical load proportioncarried by the raft typically ranges from 30 to 60z in theˆeld measurements of building foundations (Kakurai,2003). The results of Fig. 8 correspond to the ˆeld measurements by Kakurii (2003).Figure 9 shows the measured changes in axial force distribution in a pile within the pile groups or piled raftswith increase in the vertical load for the cases of PG-R,PG-H, PR-R and PR-H. Note here that axial strains weremeasured at three levels of the model piles due to the limitation of data recording device, although the strainFig. 11.69Table 4. Vertical load proportion carried by the raft prior to horizontal loadingTest nameCaseCaseCaseCaseCaseCaseCase1:2:3:4:5:6:7:RaftPG-RPG-HPR-RPR-SRPR-SHPR-HHorizontal loading cyclesType of foundationVertical load proportioncarried by the raft (z)Raft alonePile GroupPile GroupPiled RaftPiled RaftPiled RaftPiled Raft1000049273528 MATSUMOTO ET AL.70gauges were attached at ˆve levels of the pile model piles.As might be expected, large axial pile forces were generated in the piles in the pile groups compared with those inthe piled rafts. It is interesting to note that there is a distinct diŠerence between the axial force distributions ofthe pile group and the piled raft. The axial force decreasesalmost linearly from the pile head to the pile base in thecase of the pile group (Figs. 9(a) and (b)), whereas the axial forces from the pile head to a depth of 300 mm is relatively constant for each vertical load in the case of thepiled rafts (Figs. 9(c) and (d)), indicating interactions between the piles and the raft.The changes in shaft resistance with increase in the vertical load are shown in Fig. 10 for the pile groups and thepiled rafts, respectively. It can be said that the in‰uenceof the pile head connection condition is very small for thedevelopment of the shaft resistance in both the pilegroups and the piled rafts, and that the shaft resistancealong the lower part of the pile (depth from 300 mm to500 mm) is almost equal between the pile group and thepiled rafts.Results of Cyclic Horizontal Load TestsThe vertical load proportion carried by the raft when avertical load of 3.384 kN was applied to the raft prior tothe start of horizontal loading is listed in Table 4. In thecases of the piled rafts (Cases 4 to 7), the vertical loadproportion carried by the raft may be comparable be-Fig. 12.tween the test cases, although the vertical load proportionwas higher in Case 4.Figure 11 shows the horizontal loading cycles employed in the all test cases. A horizontal load to the Eastdirection is taken as positive. Similar horizontal loadingcycles were applied to the model foundations in all testcases.Figure 12 shows the relationship between the horizontal load, H, and the horizontal displacement, u, of theraft for all the test cases. In Case 1: Raft, the horizontalload attained its peak at a horizontal displacement of 5mm, and then gradually decreased with increasinghorizontal displacement and reached the residual load ata horizontal displacement of 10 mm. The pile head connection condition on the horizontal load versus thehorizontal displacement was found to have an in‰uencein both the pile groups and the piled rafts. In order toshow this in‰uence clearly, the horizontal load versus thehorizontal displacement at the maximum positive load ineach loading cycle is indicated in Fig. 13. It is interestingthat the horizontal stiŠness of the raft alone (Case 1) waslarger than that of PG-H (Case 3) and almost equal tothat of PG-R (Case 2) for small horizontal loads,although the horizontal resistance of PG-H and PG-R exceeded that of the raft alone for large horizontal displacements. The horizontal stiŠness of the piled rafts werelarger than those of the pile groups. The horizontal stiŠness of PR-SH (Case 6) was slightly larger than that ofHorizontal load versus horizontal displacement PILED RAFT MODEL TESTFig. 13. Horizontal load vs horizontal displacement at maximum loadin each cycle for all the test casesFig. 14.Fig. 15.71PR-H (Case 7). The horizontal stiŠness of PR-SR (Case5) and PR-R (Case 4) were almost identical, and were signiˆcantly larger than those of PR-SH and PR-H.Figure 14 shows the relationships between the inclination of the raft and the horizontal displacement. A verylarge inclination is induced at a given horizontal displacement in the pile group with the rigid pile head connection(PG-R). The inclination is largely suppressed in the pilegroup with the hinged pile head connection (PG-H). Ascan be also seen in the cases of the pile raft, the inclination of the raft decreases as the pile head connectionbecomes less rigid (i.e., the inclination of PR-HºPRSHºPR-SRºPR-R). If we compare PG-R and PR-R orPG-H and PR-H, the inclination of the piled raft issmaller than that of the corresponding pile group, indicating that the raft acts eŠectively to suppress inclination. It can be said that lower pile head connection rigidity suppresses the rotation of the foundation comparedwith higher pile head connection rigidity for a givenhorizontal displacement, although lower pile head connection rigidity results in larger horizontal displacementfor a given horizontal load.Figure 15 shows the relationships between the inclination of the raft and the horizontal load in cases of (a) pileInclination of raft versus horizontal displacementPeak horizontal load in each loading cycle versus inclination MATSUMOTO ET AL.72Fig. 16.Fig. 17.Shear force at pile head versus horizontal loadLoad carried by raft versus horizontal displacementgroups and (b) piled rafts with rigid and hinged pile headconnection conditions. It is seen that little inclination ofthe raft occurred in either the pile group or the piled raftswith hinged pile head connection condition. If we compare the pile group and piled raft with rigid pile head connection condition (PG-R and PR-R), it is seen again thatthe existence of the raft resistance eŠectively suppressedthe inclination of the raft.Figure 16 shows examples of the relationships of theshear force at pile head and the horizontal load in Case 3(PG-H) and Case 7 (PR-H). In both cases, the shearforces at the head of the front piles (P1 and P2 for positive horizontal load, or P3 and P4 for negative horizontalload) are larger than those of the rear piles. Similar behaviours were observed in the other test cases of the pilegroups and the piled rafts. If we compare the shear forcesin the piles at the same horizontal load between Case 3(PG-H) and Case 7 (PR-H), the shear forces in the piles inthe piled raft are smaller than those in the pile group, indicating that the raft base resistance makes a signiˆcantcontribution.Figure 17 shows the relationships between the horizontal load carried by the raft in the piled rafts and thehorizontal displacement. Figure 18 shows the relationships between the horizontal load carried by the piles inthe piled rafts and in the pile groups and the horizontalFig. 18.Fig. 19.Load carried by pile versus horizontal displacementLoad proportion carried by raft versus horizontal loaddisplacement. It can be seen from Fig. 17 that thehorizontal load carried by the raft at a given horizontaldisplacement becomes smaller as the pile head connectionbecomes less rigid. It can be seen from Fig. 18 that thehorizontal loads carried by the piles in the piled rafts at agiven horizontal displacement lie between PG-R and PGH. The higher load carried by the piles in the piled raftsthan in PG-H is thought to be due to the increase in thestrength and the rigidity of the soil beneath the raftcaused by the load transfer from the raft base to the soil.It can also be seen from Fig. 18 that the pile head connec- PILED RAFT MODEL TESTFig. 20.Fig. 21.73Distributions of bending moments in P1Peak horizontal load in each loading cycle versus axial load on pilestion rigidity has little in‰uence on the horizontal load carried by the piles in the piled rafts.Figure 19 shows the relationships between the horizontal load proportion carried by the raft and the horizontalload. The horizontal load proportion carried by the raftis about 80z for initial loading stages and decreases withincreasing horizontal load. This suggests that the raft actsas a `horizontal displacement reducer' for initial loadingstages, and that the horizontal resistance of the piles iseŠectively mobilised after the slippage of the raft base occurs. For large horizontal loads, the horizontal loadproportion carried by the raft is higher in the higher pilehead connection rigidity models (PR-R and PR-SR),compared to those in the lower pile head connectionrigidity models (PR-SH and PR-H).Figure 20 shows the distributions of bending momentsin pile P1 at horizontal loads of 1.92 kN and 3.84 kN, respectively. Comparing the bending moments of the pilesin the pile rafts (Cases 4 to 7) and those in the pile groups(Cases 2 and 3), the former are smaller than the latter, indicating that the piled raft has the advantage of beingable to reduce the possibility of pile failure by bending.The results from the pile groups (Cases 2 and 3) indicatethat the maximum bending moment is caused at the pilehead in PG-R (Case 2), while it is induced at a mid depthof the pile in PG-H (Case 3), although the values of the MATSUMOTO ET AL.74Fig. 22.Peak horizontal load in each loading cycle versus settlement of the raftmaximum bending moments in both cases are almost equal in these particular test conditions. Similar behaviourof pile bending moments is also found in the case of thepiled rafts. These results indicate that the reduction in thepile head connection rigidity does not necessarily reducethe maximum bending moment induced in the piles ineither the pile group or in the case of piled rafts.Figure 21 shows the relationships between the peakhorizontal load in each loading cycle and the increment ofthe axial head force of the piles from the start of horizontal loading. The `east piles' denote the average of headforces of piles 1 and 2, and the `west piles' denote that ofpiles 3 and 4. In Case 2 (the pile group with the rigid pilehead connection) shown in Fig. 21(a), compressionforces are induced in the front piles and tension forces areinduced in the rear piles, e.g., compression forces are induced in the east piles when the positive horizontal force(force in the direction to the west) is applied. The sum ofincrement of the pile head force for each pile is 0, becausethe rafts in the pile group do not support any verticalload. Similar behaviour was observed in Case 3 (the pilegroup with the hinged pile head connection) shown inFig. 21(b). However, the changes in the pile head forcesduring horizontal loading are much less in Case 3 compared to that in Case 2. In Case 2, the increment of pilehead force levelled oŠ at about 1.5 kN, suggesting thatthe pile reached geotechnical failure state. It can be concluded from the results of Figs. 21(a) and (b) that reduction of the pile head connection rigidity suppresses thechange in the axial forces in the piles during horizontalloading in case of the pile group, leading to a mitigationof geotechnical and structural pile failures in the verticaldirection due to horizontal loading.In contrast, in the case of the piled rafts (Cases 4 and7), compression pile head forces were induced in both thefront and rear piles due to horizontal loading ( see Figs.21(c) and (d)). This tendency was much clearer in Case 7(the piled raft with the hinged pile head connection) thanin Case 4 (the piled raft with the rigid pile head connection). A possible reason for this is discussed below.Figure 22 shows the relationship between the horizontal load and the increment of vertical displacement of theraft (settlement is taken as positive) in Case 2: PG-R,Case 3: PG-H, Case 4: PR-R and Case 7: PR-H. The settlement accumulated with increase in loading cycles in allthe cases. The settlement was larger in the piled rafts(Cases 4 and 7) than in the pile groups (Cases 2 and 3),contrary to the authors' expectation that the raft in thepiled raft plays a role to reduce settlement even in cyclichorizontal loading.Figure 23 shows the relationship between the horizontal load and the increment of vertical displacement of theraft alone (Case 1). See Fig. 12 for the correspondinghorizontal load versus horizontal displacement. The raftalone foundation (Case 1) settled more than the otherfoundations. It can be inferred from the comparison ofFigs. 22 and 23 that the compression of the soil beneaththe raft occurred during horizontal loading due to thenegative dilatancy of the soil caused by the shear stressesinduced by the shear resistance at the raft base. It may be PILED RAFT MODEL TEST75Fig. 23. Relationship between horizontal load and vertical displacement of the raft aloneFig. 24.reasonable to think that the negative dilatancy eŠect waslarger in the soils near the raft base, and the baseresistance of the pile was relatively large as was shown inFig. 9. In such a situation, the negative dilatancy of thesoils beneath the raft may lead to the reduction of the vertical pressure at the raft base, which in turn is compensated for by the increase in the axial forces of the piles.The test results shown in Fig. 21 suggests that piled raftwith `end-bearing' piles should be avoided if the soilsnear the ground surface are prone to compress when subjected to cyclic horizontal loading such as earthquakes.nodes and the general expression rm for the vertical soilspring, K Pz, at pile shaft nodes are estimated to include thein‰uence of ˆnite layered soils following Lee (1991).K Rz=The load tests mentioned above were analysed using asimpliˆed analysis method in order to discuss the testresults in more detail, and in order to examine theapplicability of the simpliˆed method as a design tool.Analytical MethodThe analyses of the static vertical and horizontal loadtest results of the model foundations were carried out using a computer program PRAB developed by Kitiyodomand Matsumoto (2002, 2003) which has been developedto estimate the deformation and load distribution of piledraft foundations subjected to vertical, horizontal, andmoment loads. In this program, a hybrid model is employed in which the ‰exible raft is modelled as thin plates,the piles as elastic beams, and the soil is treated as interactive springs as shown in Fig. 24. Both the vertical andhorizontal resistances of the piles as well as that of theraft base are incorporated into the model. The interactions between structural members, such as pile-soil-pile,pile-soil-raft and raft-soil-raft interactions, are taken intoaccount based on Mindlin's solutions (Mindlin, 1936) forboth vertical and horizontal forces. The considered soilproˆle may be homogeneous semi-inˆnite, arbitrarilylayered and/or underlain by a rigid bed stratum. Thenon-linear deformation of the foundations is calculatedby employing the bi-linear (elastic-perfectly plastic)response of soil springs.For soil proˆles that are arbitrarily layered and/or underlain by a rigid bed stratum, the vertical soil spring, K Rz,at raft nodes, the vertical soil spring, K Pbz , at pile base4Ga˜1×1-ns s1-exp (-h/2a)tK Pbz =K Pz=ANALYSES OF LOADING TESTSPlate-beam-spring modelling of a piled raft(2)4G b r o1×1-ns s1-exp (-h*/2ro)t2p G D Lln (rm/ro)rm=2.5(4)npS GLi= 1(3)iiGmLGmxL(1-ns) ,Gbx=1-exp (1-h/L)(5)where h is the ˆnite soil depth, h* is the distance betweenthe pile base and the rigid bed stratum, a is the equivalentradius of the raft element, ro is the pile radius, ns is thePoisson's ratio of the soil, DL and L are the pile segmentlength and the pile length. Gm is the maximum soil shearmodulus, Gb is the soil shear modulus below pile base, Giand Li are the shear modulus at and the length of pile embedded in soil layer i, and np is the total number of soillayers along the pile length. G˜ is the equivalent shearmodulus which can be determined following Fraser andWardle (1976):G˜ =E˜ s2(1+ns)n11=SDIi/DItotalE˜ s i=1 Esi(6)(7)where E˜ s is the equivalent Young's modulus, Esi is theYoung's modulus for soil layer i in the n-layered system,and I is the vertical settlement in‰uence factor which isgiven by Harr (1966). DIi=I(z itop)-I(z ibottom) where z itopand z ibottom are the depths below the surface of the top andbottom of layer i and DItotal=I(0)-I(h) where h is thedepth of the base of the bottom layer.The horizontal springs, K Rx and K Ry , at raft nodes, and MATSUMOTO ET AL.76Pbhorizontal springs, K Pbx and K y , at pile base nodes are estimated by means of Eqs. (8) and (9), and the horizontalsoil spring, K Px and K Py , at pile shaft nodes are estimatedby means of Eq. (10). As for loading in the horizontaldirection, the near surface soil layers tend to be the mostin‰uential. Therefore, the soil shear modulus Gr, which isthe shear modulus of the soil layer just beneath the raft, isemployed in the estimation of the horizontal springs atthe raft nodes.K Rx =K Ry =32(1-ns)Gra7 - 8n sPbK Pbx =K y =32(1-ns)Gbr07 - 8n sK Px =K Py =zEsDL(8)(9)(10)where z=pD/rEs in which p is the horizontal distributedforce acting along the pile element, D is the pile diameterand r is the corresponding horizontal displacement ateach pile node calculated using the integral equationmethod by Poulos and Davis (1980).When using PRAB to analyse the problem of pilegroup, the soil resistance (soil spring value) at the raftbase is set as 0.Analytical ConditionsIt has been described in Fig. 4 and Eq. (1) that theshear modulus, G, of the sand is dependent on the eŠective conˆning pressure, p0. In the analyses, the value ofGref was set at 17000 kPa throughout. In the analyses, themodel ground of 1 m in thickness was divided into 15 soillayers.The eŠective conˆning pressure, p0, at any depth wascalculated byp0=(1+2K0)s?v/3Fig. 25.(11)where s?v is the overburden pressure of the soil, and thecoe‹cient of earth pressure at rest, K0, was estimated byJ âaky's empirical formula.K0=1-sin q?(12)where q? is the soil internal friction angle and was obtained from the triaxial test results ( see Fig. 5). Note thatit was essential to carry out the triaxial tests at very lowstress level such as 5, 10 or 20 kPa, since the stresses atpile base level was 9.13 kPa. However, it was verydi‹cult to conduct such triaxial tests with the triaxial testequipment available to us.The horizontal resistance at the raft base, qh, was calculated by Eq. (13):qh=c+mbs?vb(13)where c is the cohesion between the raft base and the soil,mb is the friction coe‹cient at the raft base, and s?vb is thevertical stress at the raft base.The cohesion and the coe‹cient of friction between theraft base and the soil were set at 0 and 0.84 (=tan q?), respectively, from the results of triaxial tests of Toyourasand, because Toyoura sand was glued to the raft base.The ultimate vertical pressure at the raft base, qu, wascalculated by Eq. (14) following the speciˆcations of Architectural Institute of Japan (2001).qu=a・c・Nc+b・g1・B・h・Ng+g2・Df・Nq(14)where a=1.2, b=0.3 for a square raft with a width of B,Nc=75.3, Ng=93.7 for q?=40 degrees, h=( B/B0)-1/3,and B0= 1.0 m.The maximum shaft resistance, fmax, and limit horizontal pressure, pmax, of the piles were estimated by Eqs. (15)and (16), respectively.fmax=m・g・z・K0pmax=ap・g・z・KpComparison of calculated and measured load-settlement relationships(15)(16) PILED RAFT MODEL TESTwhere g is the unit weight of the soil, z is the depth fromthe ground surface, m is the coe‹cient of friction of thepile shaft, Kp is the Rankine passive pressure coe‹cient,and ap is an empirical coe‹cient.The value of m was set at 0.84 because Toyoura sandwas glued to the pile shaft. The value of ap was assumedas 3.0 following the proposal of Broms (1964), and Kp isgiven by Eq. (17).77through the raft base should be taken into account. In theanalyses, it was assumed that the soil just beneath the raftto a depth of 300 mm have a vertical stress equal to thevertical pressure at the raft base.The maximum pile base resistance, Rp, was estimatedby Eq. (18).Rp=qc・Ap(18)In the estimation of the shear modulus of sand and themaximum shaft resistance of the piles located justbeneath the raft, the eŠect of the increase in the verticalstress of the soil due to the vertical load transferredwhere Ap is the pile base area and qc=5000 kPa from theCPT results.Note that although cyclic horizontal loading was applied to the model foundations, analyses of monotonichorizontal loading of the model foundations were carriedout.Fig. 26. Comparison of calculated and measured proportions of vertical load carried by raftFig. 28. Comparison of calculated and measured proportions ofhorizontal load carried by raftKp=(1+sin q?)/(1-sin q?)Fig. 27.(17)Comparison of calculated and measured horizontal load-horizontal displacement relationships MATSUMOTO ET AL.78Analytical ResultsFigures 25(a) and (b) show the load-settlement behaviour of the model foundations calculated using PRABand those obtained from the model load tests, respectively. The measured behaviours were indicated again fora purpose of comparison. Although there are some diŠerences in shape of the load-settlement curves obtainedfrom the model load tests and those calculated usingPRAB, there is good agreement in the trend between themeasured values and the calculated values for all cases.At the same vertical load, pile groups settle more thanpiled rafts. The load-settlement curves are almost identical for the same type of foundation regardless of pilehead connection rigidities, i.e., the in‰uence of the rigidity of the pile head connection on the behaviour of thefoundation in the vertical loading is little.Figure 26 shows the proportions of the vertical loadFig. 29.carried by the raft in the cases of piled rafts. It is seenfrom the calculated results that the proportions of thevertical load carried by the raft are about 0.35 for alltypes of pile head connection condition. This leads to aconclusion that the rigidity of the pile head connectionhas little in‰uence on the behaviour of the foundationssubjected to vertical load.Figures 27(a) and (b) show the horizontal loaddisplacement behaviour of the model foundations calculated using PRAB and those obtained from the horizontal load tests, respectively. It can be seen from both experimental and analytical results that the initial horizontal stiŠness is higher in the case of piled raft than that ofcorresponding pile group. For the same type of foundation, the higher horizontal stiŠness and horizontalresistance can be found in the foundation that has higherrigidity of pile head connection. In the experiments, theComparison of calculated and measured distributions of axial forces in pile PILED RAFT MODEL TESTFig. 30.79Comparison of calculated and measured distributions of shear forces in pilehorizontal load continued to increase even after thehorizontal displacement exceeds 10 mm in all the cases,while the calculated results do not simulate this experimental result well. The calculation results match withthe experimental results until a horizontal displacementof 4 mm that corresponds to 10z of the pile diameter.Figure 28 shows the proportions of the horizontal loadcarried by the raft in the cases of piled raft calculated using PRAB and those obtained from the horizontal loadtests. There is reasonable agreement in the trend betweenthe calculated results and the experimental results. It isseen from the analysis results that the piles in the piledraft with the rigid pile head connection carry more of thehorizontal load than the piled rafts with less rigid pilehead connections in the initial loading stages. After thehorizontal load reaches 2.5 kN, the proportion ofhorizontal load carried by the raft for all cases is almostidentical.Figure 29 shows the calculated and measured distributions of axial forces in pile P1 (front pile in the analysis)at horizontal loads of 1.92 kN and 3.84 kN for Case 2:PG-R, Case 3: PG-H, Case 4: PR-R and Case 7: PR-H,respectively. The analyses did not simulate the experimental results well. As mentioned earlier, analyses ofmonotonic horizontal loading of the model foundationswere carried out, although cyclic horizontal loading wasapplied to the model foundations. Settlements of thefoundations occurred during cyclic horizontal loading, ashave been shown in Fig. 22. It is inferred that the axialforces of the piles were in‰uenced by the settlements ofthe foundations during cyclic horizontal loading. Sincethe simpliˆed analysis method is not capable of simulating such complicated behaviour, there was poor accordance between the calculated and measured axial forces MATSUMOTO ET AL.80Fig. 31.Comparison of calculated and measured distributions of bending moments in pilein the pile.Figure 30 shows the calculated and measured distributions of shear forces in pile P1 (front pile in the analysis)at horizontal loads of 1.92 kN and 3.84 kN for Case 2:PG-R, Case 3: PG-H, Case 4: PR-R and Case 7: PR-H,respectively. Shear force was measured only near the pilehead. The calculated shear forces at the pile head were ingood agreement with the measured values, although thecalculation underestimated the measured values at ahorizontal load of 3.84 kN in Case 3: PG-H and Case 7:PR-H.Figure 31 shows the calculated and measured proˆlesof the bending moments in the piles at horizontal loads of1.92 kN and 3.84 kN for Case 2: PG-R, Case 3: PG-H,Case 4: PR-R and Case 7: PR-H, respectively. It is seenthat although the analysis results underestimate the bending moments of the piles in the pile groups (Cases 2 and3), the analysis results simulate the measured results interms of the trend observed. It can be seen that the analysis results match the measured values for the piled rafts(Cases 4 and 7) well.CONCLUSIONSA series of experimental and analytical studies on thebehaviour of model piled rafts and model pile groups using dry sand subjected to a static vertical load and a statichorizontal load have been carried out in order to investigate the in‰uence of various pile head connection conditions on the behaviours of model piled rafts as well asmodel pile groups. In the load tests, the behaviours of themodel foundations during horizontal loading, with a particular focus on horizontal stiŠness and the rotation ofthe foundation, the load proportions between the raft PILED RAFT MODEL TESTand the piles, and the bending moments and shear forcesgenerated in the piles were investigated in detail.The main ˆndings from the load tests are as follows:From the vertical loading stage,1. The vertical settlement stiŠness of the piled raft islarger than that of the pile group and the raft alonefor smaller loads, and decreases to that of the raftalone as the vertical load increases.2. The pile head connection condition has little in‰uence on the behaviours of the pile groups and thepiled rafts subjected to vertical load alone.3. Mobilised shaft resistance along the upper part ofthe pile in piled rafts is much smaller than that in thepile group due to interaction between the raft andthe piles through the ground.The following points can be made with regard to thecyclic horizontal loading stage:4. The horizontal stiŠness of the piled rafts is largerthan that of a pile group with the same conˆguration as the piled raft, because the raft acts eŠectivelyas a `horizontal displacement reducer'.5. The bending moments of the piles in the piled raftare reduced, compared with those in the pile group.6. In the case of the piled rafts, rotation of the raftdecreases as the pile head connection rigiditybecomes lower, although the horizontal stiŠnessalso becomes lower.7. The horizontal loads carried by the piles in the piledrafts are not in‰uenced by the pile head connectionrigidity, whereas the horizontal load proportioncarried by the raft becomes lower as the pile headconnection becomes less rigid.The latter part of the paper includes a description ofthe analyses of the experiments carried out using a simpliˆed three-dimensional deformation analysis method withsoil properties estimated using well-known theoretical orempirical equations in order to examine the simpliˆedanalytical method for design. In the analyses of horizontal load tests of the model foundations, a monotonichorizontal loading was analysed, although cyclic horizontal loading was carried out in the experiments. The analyses simulated the behaviours of the model foundationsunder vertical loading well. As for horizontal loading, thecalculated results were tolerable, except for axial forces inpiles, for preliminary design. It was suggested that moresophisticated analysis methods are required to designpiled raft foundations subjected to cyclic horizontal loading.81ACKNOWLEDGEMENTSThe authors deeply thank the members of ResearchGroup on Piled Raft Foundation (2002 to 2007),Masateru Fujita (ANDO Corporation), Yoshio Takeuchi(Nishimatsu Construction), Hironori Horii (HazamaCorporation), Hideaki Hasei (Sumitomo Mitsui Construction) for their support in conducting experiments,and valuable discussions and suggestions in summarisingthe paper.REFERENCES1) Architectural Institute of Japan (2001): Recommendations for Design of Building Foundation (in Japanese).2) Broms, B. B. (1964): Lateral resistance of piles in cohesionless soils,Journal of Soil Mechanics and Foundations Division, ASCE,90(SM3), 123–156.3) Fraser, R. A. and Wardle, L. J. (1976): Numerical analysis of rectangular rafts on layered foundations, G áeotechnique, 26(4),613–630.4) Harr, M. E. (1966): Foundations of Theoretical Soil Mechanics,McGraw-Hill: New York.5) Horikoshi, K., Matsumoto, T., Hashizume, Y., Watanabe, T. andFukuyama, H. (2003a): Performance of piled raft foundations subjected to static horizontal loads, International Journal of PhysicalModelling in Geotechnics, 3(2), 37–50.6) Horikoshi, K., Matsumoto, T., Hashizume, Y. and Watanabe, T.(2003b): Performance of piled raft foundations subjected to dynamic loading, International Journal of Physical Modelling in Geotechnics, 3(2), 51–62.7) Kakurai, M. (2003): Study on vertical load transfer of piles, Dr.Thesis, Tokyo Institute of Technology, 304p (in Japanese).8) Kitiyodom, P. and Matsumoto, T. (2002): A simpliˆed analysismethod for piled raft and pile group foundations with batter piles,International Journal for Numerical and Analytical Methods inGeomechanics, 26, 1349–1369.9) Kitiyodom, P. and Matsumoto, T. (2003): A simpliˆed analysismethod for piled raft foundations in non-homogeneous soils, International Journal for Numerical and Analytical Methods in Geomechanics, 27, 85–109.10) Lee, C. Y. (1991): Discrete layer analysis of axially loaded piles andpile groups, Computers and Geotechnics, 11, 295–313.11) Matsumoto, T., Fukumura, K., Kitiyodom, P., Horikoshi, K. andOki, A. (2004a): Experimental and analytical study on behaviour ofmodel piled rafts in sand subjected to horizontal and moment loading, International Journal of Physical Modelling in Geotechnics,4(3), 1–19.12) Matsumoto, T., Fukumura, K., Horikoshi, K. and Oki, A.(2004b): Shaking table tests on model piled rafts in sand considering in‰uence of superstructures, International Journal of PhysicalModelling in Geotechnics, 4(3), 21–38.13) Mindlin, R. D. (1936): Force at a point interior of a semi-inˆnitesolid, Physics, 7, 195–202.14) Poulos, H. G. and Davis, E. H. (1980): Pile Foundation Analysisand Design, John Wiley and Sons, New York.
  • ログイン
  • タイトル
  • Stability Analysis of Slope with Water Flow by Strength Reduction Method
  • 著者
  • "W. B. Wei, Y. M. Cheng"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 83〜92
  • 発行
  • 2010/02/15
  • 文書ID
  • 64343
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 83–92, Feb. 2010STABILITY ANALYSIS OF SLOPE WITH WATER FLOW BYSTRENGTH REDUCTION METHODW. B. WEIi) and Y. M. CHENGii)ABSTRACTRainfall is one of the most critical factors with regard to slope instability. In this paper, the eŠect of seepage ‰ow onslope stability is investigated by means of a strength reduction method. It is demonstrated that the factor of safety(FOS) for a sandy soil slope is in‰uenced by seepage ‰ow more than other types of soil. If the pore pressure is generated by the use of a piezometric line, the FOS is smaller than that generated by seepage ‰ow analysis. The diŠerence issmall for clayey soil slopes but is larger and more noticeable for sandy soil slopes. The analysis also shows that the installation of retaining walls to increase the length of the seepage path is eŠective to prevent slope failure induced byseepage ‰ow. The eŠects of water ‰ow on soil nailed slopes, locally loaded slopes and pile reinforced slopes are also investigated in this study. The present study also shows that the eŠect of densely populated soil nail on the seepage ‰owcan be neglected for practical purposes.Key words: seepage ‰ow, slip surface, slope stability, strength reduction method (IGC: A1/E6)and Marquez (2007), Cheng et al. (2007, 2008), Wei et al.(2009) and others. This technique is also included inseveral well-known commercial geotechnical ˆnite element and ˆnite diŠerence programs. The SRM can alsoadopt the results from the seepage analysis easily, and themesh for the SRM and seepage analysis can actually bethe same. In the SRM, the shear strength parameters arereduced in accordance with Eq. (1)INTRODUCTIONEvery year, there are many slope failures in HongKong, and practically all the slope failures occur duringrainy times. Pore water pressure is one of the major important reasons for slope instability. In the limitequilibrium method (LEM), which is widely used in engineering practice, the most common way of deˆning thepore-water pressure is by using the piezometric line. Thevertical distance from the middle of the slice base to thepiezometric line is commonly used to evaluate the porewater pressure which is actually a hydrostatic condition.In reality, there will be seepage ‰ow so that the piezometric surface will curve downward; consequently, the assumption of a hydrostatic pore-water pressure is strictlynot correct. In some commercial software, a correctionfactor is used to account for this factor, and this is goodenough for ordinary design purposes. Furthermore, if thepore-water pressure distribution is known by the ˆniteelement or ˆnite diŠerence analysis, the LEM can also beintegrated with the pore water pressure from the seepageanalysis in the stability calculation.In recent decades, there have been various developments in the strength reduction method (SRM) for slopestability analysis. This method was used as early as 1975by Zienkiewicz et al. (1975), and has since been appliedby Naylor (1982), Donald and Giam (1988), Matsui andSan (1992), Ugai and Leshchinsky (1995), Song (1997),Dawson et al. (1999), Gri‹ths and Lane (1999), Gri‹thsi)ii)FOS=tan q c=tan qe ce(1)where c, q are the cohesive strength and the friction anglewhile ce and qe are the reduced shear strength parametersused in the calculation. The whole concept in SRM is thegeneration of the body forces on an elasto-plastic systemcontrolled by shear strength parameters ce and qe. TheFOS as shown in Eq. (1) will vary until the system cannotmaintain an equilibrium under the body forces and external loads, and the FOS will be taken as the factor of safety for the slope under consideration. Based on thetremendous amount of previous research on this point, itis commonly accepted that the factor of safety arisingfrom this analysis is very close to that from the classicallimit equilibrium or limit analysis. The advantage of theSRM for the present problem is the ease with whichseepage ‰ow can be considerd compared with other classical methods of analyses.With regard to slope stability analysis with water ‰ow,the diŠerent ways to consider the seepage forces in theResearch Student, Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hong Kong (05900931r@polyu.edu.hk).Associate Professor, ditto.The manuscript for this paper was received for review on March 30, 2009; approved on September 29, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.83 84WEI AND CHENGLEM have resulted in confusion. In the traditional LEM,the boundary water forces with the total weights are usually used and the water pressure enters into the baseforces calculation but not the interslice forces (or, consequently, the equilibrium of slice). Turnbull and Hvorslev(1967) concluded that the traditional method may yieldunreliable results for high pore-pressure, and suggestedthat the eŠective stress should be resolved in a directionnormal to the failure surface. Greenwood (1983, 1985)and King (1989) introduced some eŠective-stress methodsof slices which include the interslice water forces. Theseapproaches are, however, more complicated in the analysis and are not adopted in commercial programs. Greenwood (1983, 1985), King (1989) and Duncan and Wright(2005) have shown that there are cases where the reˆnedapproaches may have noticeable diŠerences with the classical methods. If the SRM is used, pore-pressure willaŠect the eŠective stress for which the stability analysis isbased on. The confusion about the eŠect of water in theLEM does not appear in the SRM.In this paper, the diŠerences between the use of piezometric surface and seepage ‰ow analysis on slope stabilityanalysis will be studied. Two and three-dimensionalstrength reduction analyses will be carried out to studythe eŠects of water ‰ow on slope under several cases. Thisstudy has demonstrated that besides the lowering of thefactor of safety (FOS), the failure mechanism may also beaŠected by the seepage ‰ow. Many engineers view thatdensely populated soil nails may aŠect seepage ‰ow, butit is demonstrated in this study that for practical purposes, the eŠect of soil nail on the seepage ‰ow can beneglected.STABILITY ANALYSIS FOR A SIMPLE SLOPEWITH SEEPAGE FLOWIn the present study, the eŠect of seepage has beenstudied using FLAC3D by Itasca and Phase by Rocscience. The soil is considered as an elastic-perfectly plastic material with its strength controlled by the MohrCoulomb constitutive model. Once a mesh is designed fora problem, the same mesh will be used for the seepageanalysis. The pore-pressure from the seepage analysis willbe used as the input for the stability analysis using theSRM. In this respect, the seepage analysis and the stability analysis are carried out independently. For the dilation angle of the soil, Cheng et al. (2007) have demonstrated that it is not critical for most of the problems, andthe eŠect of the dilation angle is usually less than 5z except for isolated problems. Since the main conclusionfrom the present study is highly unlikely to be aŠected bythe dilation angle, the authors have adopted a dilationangle of 0 in the present study. This method of modelingis adequate as consolidation, but is not considered in thepresent study. In the strength reduction analysis, the ultimate limit state is determined by ``failure to converge''and ``formation of a continuous yield mechanism whichcan fail''. The strain level as shown in this paper is not thetrue ``strain level''. Likewise, the displacement vector isFig. 1. Pore water pressure and ‰ow vector of a simple slope from afree-surface seepage analysis (total head=10 m for the top ‰owline, and total head diŠerence for each ‰ow line is 1 m)not the true displacement, but is simply the results of thestrength reduction analysis.In this section, a two-dimensional 6 m height slopewith 459slope angle was analyzed. A 10 m height modelwas developed in which the water was 4 m in height onthe left and 10 m in height on the right side. The porepressure and the ‰ow vector distribution for the free-surface seepage ‰ow analysis are shown in Fig. 1. In Fig. 1,the total head is 10 m for the top ‰ow line, and the totalhead diŠerence for each ‰ow line is 1 m. The density,elastic modulus and Poisson ratio of the soil were kept at20 kN/m3, 14 MPa and 0.3 respectively in the analysis.Cheng et al. (2007) have demonstrated that the uses ofthese elastic properties in SRM are not important, andthe factors of safety using diŠerent elastic properties arevirtually not aŠected by these parameters. From the SRManalyses, the regions where the shear strain concentrateare identiˆed and the failure surface can be approximately obtained by the maximum shear strain distribution, asshown in Figs. 2 to 5. As demonstrated by Cheng et al.(2007), the failure zones obtained by this approach arevery close to that based on the limit equilibrium method.For diŠerent soil properties, the FOS and slip surfaces areshown in Figs. 2 to 5, and the results were compared witha case with no water. Obviously, with the seepage ‰ow,the FOS was much smaller than the corresponding casewithout water. For sandy soil, the decrease of the FOSwith seepage ‰ow was larger than that for the clayey soil.This means that a sandy soil slope is easier to be destroyed by seepage ‰ow than a clayey slope, so more attention should be paid to preventing seepage ‰ow from destroying sandy soil slopes. Actually, Hong Kong is famousfor slope failures and there are many sandy slope failures(the soil is completely decomposed granite) during therainy season each year. On the other hand, thirty years ofobservation have shown there are much fewer slopefailures in slopes with a ˆner grain size (completelydecomposed volcanic) in Hong Kong (GEO, 1996). Thesandy and ˆner grain soils in Hong Kong are derivedfrom granitic and volcanic rock of similar chemical composition, and the main diŠerences between the two typesof soil are the grain size and the cohesive strength. It isalso found that the location of the slip surface for sandysoil is greatly in‰uenced by the water ‰ow from variousparametric studies, and the failure surface becomes shal- SLOPE ANALYSIS WITH STRENGTH REDUCTIONFig. 2.Slip surface for slope with cohesion 1 kPa and friction angle 459Fig. 3.Slip surface for slope with cohesion 2 kPa and friction angle 459Fig. 4.Slip surface for slope with cohesion 5 kPa and friction angle 359Fig. 5.Slip surface for slope with cohesion 10 kPa and friction angle 25985 WEI AND CHENG86lower and closer to the slope toe under the in‰uence ofwater seepage ‰ow. These results are also similar to theobservations of the slopes failures in Hong Kong over thelast thirty years (GEO, 1996), where many slopes failuresare initiated from toe failures under heavy rain. Withreference to Fig. 2(a), there is a relatively high hydraulicgradient around the toe of the slope, hence slope failurewill be limited to the region close to the toe of slope, whilea typical slope failure which extends to the top of theslope is obtained in Fig. 2(b) where there is no water.Such results are further supported by the tremendousnumber of slope failures during the rainy season in HongKong, with most of them initiating around the toe of theslope where there is a rapid change of the total head andhence a high hydraulic gradient. Such results are alsopredicted by the numerical analysis presented in Fig. 2.In the above analysis, the pore water pressure is generated by a seepage ‰ow analysis, which is a reasonable wayto obtain the pore pressure distribution. It is, however,possible to deˆne the pore water pressure by a water tablein the SRM similar to that in the LEM analysis. In orderto investigate the diŠerence between the two approaches,another model is developed in which the pore pressure isgenerated by the water table. The pore pressure distribution for this model is shown in Fig. 6 (the water table location is the free-surface obtained from Fig. 1). The factors of safety for the two cases are compared in Table 1.The FOS for the case where the pore pressure is generatedby the water table was smaller than the case generated bythe seepage ‰ow analysis, as the pore water pressure calculated by the water table (free-surface) was larger. Itmeans that the use of the water table (or piezometric line)is a conservative method of analysis, with a very smalldiŠerence for clayey slopes and a much larger diŠerencefor sandy soils.STABILITY ANALYSIS FOR A SIMPLE SLOPEWITH IRREGULAR PORE PRESSUREDISTRIBUTIONFig. 6. Water pressure by water table (piezometric line) assuminghydrostatic condition (total head=10 m for the top ‰ow line, andtotal head diŠerence for each ‰ow line is 1 m)Table 1.Factor of safety for diŠerent situationsCohesion and Friction angle1 kPa,4592 kPa,4595 kPa,35910 kPa,259FOS with water (pore pressuregenerated by seepage analysis)0.820.960.981.07FOS with water (pore pressuregenerated by water table)0.660.820.921.03FOS for no water1.31.441.351.37In this section, two more models are analyzed for the6 m height slope with 459slope angle discussed in theprevious section, but the pore pressure distribution is irregular due to some blocking eŠects in the slope. In theˆrst model, the soil on the left side of the slope crest andon the left side of slope toe is assigned as impermeablezone. The slip surface and the pore pressure distributionare shown in Fig. 7. In the second model, an 8 m heightthin impermeable wall near the slope crest is applied. Theslip surface and the pore pressure distribution are shownin Fig. 8. In the second model, the FOS (1.30) was muchlarger than the case with no soil blocking in Fig. 3 (0.96)and the case in Fig. 7 (1.07). With the blockage from thesoil wall, the seepage path is much longer, which greatlyreduces the pore water pressure, so the FOS becomesmuch larger. This result also shows that the installationof retaining wall to increase the seepage length is a goodmethod of preventing slope failure caused by seepage‰ow.Fig. 7. Slip surface and pore pressure with water block at upper and bottom left for slope with cohesion 2 kPa and friction angle 459(in Fig. 7(b),total head=10 m for the top ‰ow line, and total head diŠerence for each ‰ow line is 1 m) SLOPE ANALYSIS WITH STRENGTH REDUCTION87Fig. 8. Slip surface and pore pressure with water block wall for slope with cohesion 2 kPa and friction angle 459(in Fig. 8(b), total head=10 m forthe top ‰ow line, and total head diŠerence for each ‰ow line is 1 m)Table 2.Parameters of grout-soil-nail systemYoung's modulus, E [GPa]grout cohesive strength (force) per unit length, cg [kN/m]1.4135grout friction angle, qg [degree]9.23grout stiŠness per unit length, kg [MPa]grout exposed perimeter, pg [m]2Fig. 9.43.10.339cross-sectional area, A [m ]0.00785compressive yield strength (force), Fc [MN]0.238tensile yield strength (force), Ft [MN]0.238Modeling of soil nail systemSTABILITY ANALYSIS FOR SOIL NAILING SLOPEWITH SEEPAGE FLOWFor the SRM analysis of nail, if the bending eŠects arenot important, the nails can be modeled by cable elements because cable elements provide a shearingresistance (by means of grout properties) along theirlength. The shear behavior of the cable-soil interface canbe represented by the model in Fig. 9, and can be described numerically by considering the following: thegrout shear stiŠness, the grout cohesive strength, thegrout friction angle, the grout exposed perimeter (grouthole diameter) and the eŠective conˆning stress sm. Thematerial properties of the grouted nail were calculatedconsidering a combination of the stiŠness of the steel barand the cement grout, and the Young's Modulus of thegrout was determined as 45.44 GPa. At the same time, athin layer of material with a thickness of 4.0 mm surrounding the nail was used to model the shearing zone between the nail and the grout, as shown in Fig. 9. Thegrout shear stiŠness kg can be estimated as (Itasca, 2006):k g=45.442p G=43.1 MPa10 ln (1+2t/D)where G is grout shear modulus and equals to 5.28 MPa;D is grout hole diameter and is equal to 0.1 m; t is the an-nulus thickness and is equal to 0.004 m. The parametersused for the study are shown in Table 2.In this section, a 6 m height soil nailed slope with water‰ow is analyzed with a slope angle of 459. Nails were installed every 1.5 m centers horizontally and vertically.The nail length was 8 m and the inclination angle waszero. The cohesion of the soil was 2 kPa and the frictionangle was 359. A model of this slope is shown in Fig. 10.In Hong Kong where the density of soil nails is high (at aspacing of around 1 m to 1.5 m) and the diameter andlength of the soil nails are both considerable (a 32 mm or40 mm diameter bar is commonly used while a length of10 m to 20 m is also common), many engineers have wondered whether the dense population of soil nails aŠectsthe seepage pattern. To approach this problem, twomodels were developed. In the ˆrst model, the pore pressure was determined without the presence of nails. In thesecond model, the soil nails together with the grout weretreated as the impermeable zone. The pore pressure distribution for this case, shown in Fig. 11, shows that thepore pressure distribution after considering the blockageeŠect from soil nails is actually close to that of the ˆrstcase at the section where there are no soil nails. The FOSby these two models is also the same (both are 0.95 andthe slip surface as shown in Fig. 12 applies for bothcases). This means that the blockage eŠect of the soil nailcan be ignored in a soil nailed slope analysis since the diameter of the nails is small compared to the nail spacing, WEI AND CHENG88even in Hong Kong, where large diameter soil nails areused in Hong Kong. Indeed, such nails were used in theanalysis.For this soil nailed slope, the FOS was 1.71 with nowater ‰ow. If no nails were included in this slope, theFOS with and without water ‰ow is 0.72 and 1.07, respectively. It can be seen that the factor of safety for soilnailed slopes is more in‰uenced by the water ‰ow, as thepercentage decrease of the FOS is much larger when compared with slopes without nails. In this analysis, the nailsare simulated by a cable element, with its pullout strengthrelated to the conˆning pressure. When there was water,the conˆning pressure around the nail decreased due tothe pore water pressure, and two eŠects of water on a soilnailed slope were noted. Firstly, the FOS decreases due tothe seepage force, and secondly, the FOS reduces as thenail pullout strength, which is related to the eŠective conˆning pressure, is reduced. To remove the in‰uence of theconˆning pressure on the nail pullout strength, the second model was re-considered so that the nail has a constant pullout strength unaŠected by the eŠective overburden stress (only the grout cohesive strength is givenand the grout friction is zero). The results of this modelare shown in Table 3. The decrease of the FOS with thepresence of water was smaller using this model, clearly indicating that the relationship between the soil nail pulloutstrength and the eŠective overburden stress is a very critical factor in the stability of a soil nailed slope.STABILITY ANALYSIS FOR PILED SLOPE WITHSEEPAGE FLOWIn this section, our investigation of a piled slope with awater ‰ow is discussed. Like the slope taken into consideration by Won et al. (2005) and Cai and Ugai (2000),the slope we employed for this analysis was 10 m in heightwith a gradient of 1V:1.5H (Fig. 13). Two symmetric extreme boundaries were used so that the problem consistedof a row of piles with a plane of symmetry. Steel tubepiles with an outer diameter (D) of 0.8 m were used in thisstudy. The piles were treated as linear elastic solid materials and were installed in the middle of the slope with acenter-to-center spacing of 3D. The piles were embeddedFig. 12.Slip surface for the nailed slope with water ‰ow (FOS=0.95)Table 3.Factor of safety of nailed slopeCaseFig. 10.Model plot of the soil nailing slopeFig. 11.NoWithwater water ‰owWith no nail1.070.72Nail pullout strength related to conˆning pressure1.710.95Nail with constant pullout strength 5.6 kN/m1.611.01Pore pressure distribution of the soil nailing slope with water blocking eŠect SLOPE ANALYSIS WITH STRENGTH REDUCTIONand ˆxed into either the bedrock or a stable layer (inˆnitepile length assumption). In this model, the pile head wasfree. The cohesive strength, friction angle, elastic modulus, Poisson ratio and density of the soil were 10 kPa,209, 200 MPa, 0.25, and 20 kN/m3, respectively. Theelastic modulus and Poisson ratio of the piles were 60000MPa and 0.2, respectively. For slopes not reinforced withan pile, the factor of safety determined by the SRM was0.85, with a slip surface as shown in Fig. 14.Two models were developed to investigate the in‰uenceof seepage ‰ow on the failure mechanism of pile rein-Fig. 13.Model plot of the piled slopeFig. 14.Fig. 15.89forced slopes. The FOS and slip surface obtained by themodels with and without water blocking eŠect were thesame for the two cases (the FOS wass 1.29, and the resultsare shown in Figs. 15 and 16). It is clear that the blockingeŠect of the pile on the seepage can be ignored, as was thecase for soil nails.If no water is involved in this model, it was found theoptimal pile position was about at the middle of the slope(Won et al., 2005; Cai and Ugai, 2000; Wei and Cheng,2008). The slip surface is practically divided into twoparts, and obvious shear strain is mobilized in both thelower and upper parts (Wei and Cheng, 2008). Whenthere is water seepage, the slip surface is mainly located atthe lower part of the slope (Fig. 16), which is diŠerentfrom cases without seepage, which means that the upperpart of the slope is safer than the lower part. Thisphenomenon clearly arises from the eŠect of the seepageforce. Without the seepage force, there is only a minor interaction between the upper and lower parts of the failuremass (Wei and Cheng, 2008). The optimized pile positionin slopes with seepage moves towards the slope toe ratherthan the middle of the slope. It is found that the optimalpile location for this case was 2.0 m towards the slope toeas measured from the middle of the slope (Fig. 17). TheeŠect of water seepage is hence important in controllingthe failure mechanism of pile reinforced slopes.The critical slip surface of a piled slope is found to beshallower than that of a slope with no pile in this study.With the placement of a pile, the two smaller slip surfacesPore pressure and slip surface of the slope without pile (FOS=0.85)Pore pressure distribution of the piled slope with water blocking eŠect WEI AND CHENG90Fig. 16.Fig. 17.Slip surface for the piled slope with water ‰ow (FOS=1.29)Slip surface for the slope with pile installed at 2.0 m towards the slope toe as measured from the middle of slope (FOS=1.34)will control the slope failure while the original overallcritical slip surface will no longer control the failure asthere is an obstruction to the failure by the pile. Thispresent result is based on the use of maximum shearstrain in soil, and the results diŠer from those of the experiments based on a maximum point of shear force witha deep seated failure surface done by Cai and Ugai(2000). Actually, the authors found that the location forthe maximum shear force in the pile did not correspondto the location of the maximum shear strain in soil. Aspiles do not function as soil nails do, depending on skinfriction mobilization, and hence shear strain mobilization, the authors decided it was inappropriate to use themaximum shear force location as criterion in evaluatingthe critical slip surface of a piled slope problem. Based onthe tremendous number of slope failures in sandy soil inHong Kong where all failures in sandy slopes are shallowand usually less than 2 m thick (about 300 failures eachyear in Hong Kong), and numerical results showing thatthe maximum shear force location in the pile is not necessarily where the maximum shear strain is located, theauthors decided that the critical slip surface should be ashallower failure mode for a piled slope in sand. Ourstudy of the slope failures in Hong Kong revealed that thelocation of the maximum point of shear force was verydeep and far from the real critical slip surface. We con-cluded that the pile maximum shear force location is notnecessarily the location of the critical slip surface of apiled slope.STABILITY ANALYSIS FOR LOCALLY LOADEDSLOPE WITH SEEPAGE FLOWIn this section, our analysis of a 6 m height slope with a459slope angle under a rectangular shaped vertical loading is presented. It was very di‹cult to perform a modeltest with seepage ‰ow in this case, so a model test with noseepage was conducted. The width and length of the loading were 2 m and 4 m respectively, while the edge of theloading was 1 m away from the crest of the slope. The cohesion of the soil was 20 kPa and the friction angle was209. The length of the computer model was 20 m. Theresults of the analysis when the loading q was 100 kPa areshown in Fig. 18. Figure 19 illustrates the results in thecase with no water. The failure mechanism shown in Fig.19 is illustrated by the model test in sand, as shown in Fig.20(a). As the failure surface at the centre of the failuremass from the laboratory test matches well with that bynumerical modeling, the strength reduction analysis carried out in this study (Fig. 20(b)) is veriˆed by a laboratory test, as shown in Fig. 20(a). It can be seen from thismodel that the failure mechanisms for the slope with SLOPE ANALYSIS WITH STRENGTH REDUCTIONFig. 18.91Pore water pressure and slip surface for the locally loaded slope with waterFig. 19. Slip surface for the locally loaded slope with no water, FOS=1.60 (after Wei et al., 2009)water and without water were diŠerent. For a slope with atwo-dimensional seepage ‰ow, the slip surface was basically two-dimensional. On the other hand, for slopeswithout water, a nearly three-dimensional slip surfacewas mobilized around the local loading. Wei et al. (2009)investigated the failure mechanism of a locally loadedslope with no water. When the loading is small, the slipsurface is still basically two-dimensional until the loadingbecomes large enough to mobilize a three-dimensionalslip surface. For this model, the failure mechanism withand without seepage were diŠerent even though the applied loading was the same because the seepage force wasincluded in the analysis, and the ability to mobilize athree-dimensional slip surface for the local loading wasweakened by the two-dimensional seepage ‰ow.DISCUSSION AND CONCLUSIONSIn this paper, the strength reduction method is employed for a slope stability analysis with water ‰ow. Thepore water pressure was generated by seepage ‰ow analy-sis according to the boundary conditions. With seepage‰ow, the FOS was usually much smaller than corresponding cases with no water. For sandy soil slopes, thedecrease of the FOS by seepage is usually larger than thatfor clayey soil slopes. This means that sandy soil slopescan be destroyed more easily by seepage ‰ow than clayeysoil slopes, which is consistent with observations of thelarge number of slope failures in Hong Kong over the lastthirty years (with an average of about 300 slope failureseach year). The reduction of seepage ‰ow in sandy soilslopes hence deserves more attention. Furthermore, thelocation of the slip surface for sandy soil slope is moresensitive to seepage, and becomes shallower and closer tothe slope toe under the in‰uence of seepage ‰ow. Again,most of the slope failures in Hong Kong initiate aroundthe toe of slope where there is a rapid change of the totalhead and hence a high hydraulic gradient. Our numericalanalysis predicted this phenomena, as can be seen in Fig.2. If the pore pressure is generated by the use of a piezometric line, usually the FOS will be smaller than whenwhere the pore pressure is generated by seepage ‰ow analysis. It means that the water table (or piezometric line)option is a conservative method for analysis. For clayeysoil, the diŠerence between the two ways in deˆning thepore water pressure is usually small, but for sandy soil,the diŠerence is much larger.Based on the work done by Cheng et al. (2007, 2008),Wei and Cheng (2009), Saeterbo et al. (2004) and manyothers, it is generally accepted that the FOS is not sensitive to the dilation angle except for isolated problems.For some of the particular cases considered in this studybased on a zero dilation angle, the authors applied the associative ‰ow rule. The diŠerences in the FOS are usuallywithin 3–4z compared with that based on a zero dilationangle, and the failure mechanism is also virtually notaŠected by the dilation angle. It can be concluded that theˆndings of this study were not aŠected by the dilation angle in general.It has been demonstrated that the use of a retainingwall to increase the seepage path is a very eŠective in en- WEI AND CHENG92Fig. 20.Laboratory and numerical results of a model test in sandy soilhancing slope stability under seepage ‰ow. Our results ofthe seepage analysis are virtually independent of soil nailsor reinforcing piles (under practical spacing) indicatingthat engineers do not need to consider the soil nail/pile intheir seepage analyses. Water ‰ow was shown to have twoeŠects on the stability of a soil nailed slope. Firstly, theFOS decreased due to seepage force. Secondly, the FOSdecreased as the reduction of the nail pullout strengthdecreased with a reduction in the conˆning pressurearound the nail due to pore water pressure. Water ishence a major factor in controlling the stability of slope.For locally loaded slopes with water ‰ow and pile reinforced slopes, the failure mechanism can be strongly in‰uenced by the seepage force. To get a realistic failuremechanism, the pore pressure must be carefully considered in the analysis.ACKNOWLEDGEMENTThe present project is funded from Research GrantsCouncil through the project PolyU 513507E.REFERENCE1) Cai, F. and Ugai, K. (2000): Numerical analysis of the stability of aslope reinforced with piles, Soils and Foundations, 40(1), 73–84.2) Cheng, Y. M., Lansivaara, T. and Wei, W. B. (2007): Two-dimensional slope stability analysis by limit equilibrium and strengthreduction methods, Computers and Geotechnics, 34(3), 137–150.3) Cheng, Y. M., Lansivaara, T. and Wei, W. B. (2008): Reply toComments on ``Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods'', Computers and Geotechnics, 35(2), 309–311.4) Dawson, E. M., Roth, W. H. and Drescher, A. (1999): Slope stability analysis by strength reduction, Geotechnique, 49(6), 835–840.5) Donald, I. B. and Giam, S. K. (1988): Application of the nodal displacement method to slope stability analysis, Proc. 5th AustraliaNew Zealand Conference on Geomechanics, Sydney, Australia,456–460.6) Duncan, J. M. and Wright, S. G. (2005): Soil Strength and SlopeStability, John Wiley.7) FLAC 3D Version 3.1 User's Guide (2006): Itasca ConsultingGroup, Inc. Minneapolis, Minnesota, USA.8) Geotechnical Engineering O‹ce (GEO) (1996): GEO Report No.52: Investigation of Some Major Slope Failures between 1992 and1995, the HKSAR Government.9) Geotechnical Engineering O‹ce (GEO) (2000): GeotechnicalManual for Slopes, 2nd edition, Hong Kong Government.10) Greenwood, J. R. (1983): A simple approach to slope stability,Ground Engineering, 16(4), 45–48.11) Greenwood, J. R. (1985): Correspondence on stability of compacted rockˆll slopes, Charles, J. A. and Soares, M. M. (1984):Geotechnique, 35(2), 217–218.12) Gri‹ths, D. V. and Lane, P. A. (1999): Slope stability analysis byˆnite elements, Geotechnique, 49(3), 387–403.13) Gri‹ths, D. V. and Marquez, R. M. (2007): Three-dimensionalslope stability analysis by elasto-plastic ˆnite elements, Geotechnique, 57(6), 537–546.14) King, G. J. W. (1989): Revision of eŠective-stress method of slices,Geotechnique, 39(3), 497–502.15) Matsui, T. and San, K. C. (1992): Finite element slope stabilityanalysis by shear strength reduction technique, Soils and Foundations, 32(1), 59–70.16) Naylor, D. J. (1982): Finite elements and slope stability, Numer.Meth. In Geomech., Proc. NATO Advanced Study Institute, Lisbon, Portugal, 1981, 229–244.17) Saeterbo, G., M. G., Nordal, S. and Emdal, A. (2004): Slope stability evaluations using the ˆnite element method, NGM 2004, XIVNordic Geotechnical Meeting, 1, p. A49–A61.18) Song, E. (1997): Finite element analysis of safety factor for soilstructures, Chinese Journal of Geotechnical Engineering, 19(2), 1–7(in Chinese).19) Turnbull, W. J. and Hvorslev, M. J. (1967): Special problems inslope stability, Journal of the Soil Mechanics and Foundation Division, ASCE, 93(SM4), 499–528.20) Ugai, K. and Leshchinsky, D. (1995): Three-dimensional limit equilibrium and ˆnite element analysis: a comparison of results,Soils and Foundations, 35(4), 1–7.21) Wei, W. B. and Cheng, Y. M. (2008): Strength reduction analysisfor slope reinforced with one row of piles, Computers and Geotechnics, 36, 70–80.22) Wei, W. B., Cheng, Y. M. and Li, L. (2009): Three-dimensionalslope failure analysis by the strength reduction and limit equilibrium methods, Computers and Geotechnics, 36, 70–80.23) Won, J., You, K., Jeong, S. and Kim, S. (2005): Coupled eŠects instability analysis of pile-slope systems, Computers and Geotechnics, 32(4), 304–315.24) Zienkiewicz, O. C., Humpheson, C. and Lewis, R. W. (1975): Associated and non-associated visco-plasticity and plasticity in soilmechanics, Geotechnique, 25(4), 671–689.
  • ログイン
  • タイトル
  • Effects of Sampling Tube Geometry on Soft Clayey Sample Quality Evaluated by Nondestructive Methods
  • 著者
  • "V. Horng, Hiroyuki Tanaka, Takashi Obara"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 93〜107
  • 発行
  • 2010/02/15
  • 文書ID
  • 64344
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 93–107, Feb. 2010EFFECTS OF SAMPLING TUBE GEOMETRY ON SOFT CLAYEYSAMPLE QUALITY EVALUATED BY NONDESTRUCTIVE METHODSVUTHY HORNGi), HIROYUKI TANAKAii) and TAKASHI OBARAiii)ABSTRACTSample disturbance caused by diŠerence in sampling tube geometry was evaluated by two nondestructive methods:the measurement of the residual eŠective stress ( p?r ) by ceramic disc; and the use of the bender element to ascertain theshear wave velocity (Vs ), and thus the maximum shear modulus (GBE ). Samples were measured under atmosphere, i.e.,not under conˆned stress conditions. The soil samples were obtained from two sources: reconstituted Kasaoka clayprepared in the laboratory, and at the test site at Takuhoku, Hokkaido, Japan. Samplers with diŠerent geometrical designs, referring to the Japanese standard stationary piston sampler, were used for the model ground and ˆeld sampling. The geometrical eŠects of the sampling tube, for example, the thickness of the tube wall, the edge angle, and theexistence of a piston were carefully examined. The quality of the samples taken with diŠerent samplers was evaluatedby p?r and GBE, values which were normalized by the in situ vertical eŠective stress (s?vo ) and Gf measured by the seismiccone test in the ˆeld. It was found from these studies that p?r /s?vo and GBE/Gf vary considerably due to the geometry ofthe sampler, with the edge angle of sampling tubes being the most important feature in obtaining high quality samples.The wall thickness, and thus, the area ratio of the sampler is not critical to the sample quality if the edge angle is sharpenough. The existence of the piston does not signiˆcantly in‰uence the sample quality in ˆeld samples. Furthermore,the correlation between GBE and p?r was also investigated, and it was found that the two parameters are strongly dependent.Key words: clay, drilling, sample disturbance, sample quality, sampling tube, shear modulus, site investigation, suction (IGC: C6)technical Institute (SGI) have modiˆed the geometricalfeatures of their original samplers several times (for examples, see Andresen and Kolstad, 1979; Kallstenius,1958). Lefebvre and Poulin (1979) designed a new sampling method called the Sherbrooke sampler. At the sametime, La Rochelle et al. (1981) developed a new large diameter sampler called the Laval sampler. They concludedthat both the Sherbrooke and Laval sampler yield bettersample quality than conventional tube samplers. Hight etal. (1992) also studied the disturbance of the Bothkennarclay and conˆrmed that these samplers provide bettersample quality than a tube sampler. On the other hand,Tanaka (2000) reported that sample quality obtained byone of the Japanese tube samplers, the Japan standard(JPN) sampler, is equivalent to that obtained by theLaval sampler for not only the Japanese clays but also forBothkennar clay. His ˆndings indicated that the large diameter of the sampler is not always necessary to retrieve ahigh quality soil sample. However, the performance ofother tube samplers, not including the JPN sampler, wasnot as good as the Sherbrooke and the Laval samplers.Indeed, it is inferred that like the NGI and SGI, a com-INTRODUCTIONHigh quality samples are required to interpret in situsoil properties, such as permeability, compressibility, andshear strength characteristics, in order to provide designsthat are not overly conservative and decrease the cost ofconstruction. The geotechnical properties of soils are estimated either in situ or in laboratory tests. One of themost important restrictions of laboratory test results issample disturbance. Over the last few decades, a considerable eŠort has been made to improve sampling techniques, including the design of the sampling tubes so as toobtain more accurate soil parameters; for example, compressibility and shear strength particularly in poor qualitysamples (Shogaki and Kaneko, 1994; Shogaki, 1996;Mitachi et al., 2001).Sampling techniques and equipments, including sampling tubes, vary worldwide depending on the geologicalsettings, diŠerence in skills, and the aŠordability of soilinvestigations. Having realized the eŠects of the design ofthe sampling tube on the sample quality, the NorwegianGeotechnical Institute (NGI) and the Swedish Geoi)ii)iii)PhD Student, Hokkaido University, Japan.Professor, ditto (tanaka@eng.hokudai.ac.jp).Research Engineer, Kajima Corporation, Japan (formerly Graduate Student, Hokkaido University, Japan).The manuscript for this paper was received for review on May 12, 2009; approved on October 20, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.93 94HORNG ET AL.parison study must be carried out in each country orregion to establish their own standard sampler (for example, Matsumoto et al., 1968 and 1969). Those comparisons, however, included too many geometrical designfactors and mechanisms, such as diŠerent methods ofdrilling and the types of sampling involved, to specifywhich geometrical designs of sampling tube must be improved and which should be discarded. In addition, theirresults are rather inconsistent, partly due to the diŠerencein soil properties with depth in ˆeld conditions and partlydue to the considerable diŠerence in sample quality according to the location of samples within a sampler(Tanaka, 2000; Nishida et al., 2006).Traditionally, sample quality has been assessed by thefollowing values and features: i) shear strength, strain atfailure, and Young's modulus from unconˆned compression or triaxial tests; ii) the shape of the e-log p? curve,where e is the void ratio and p? is the eŠective consolidation pressure, preconsolidation pressure, or compressionindex from oedometer test; iii) volumetric strain causedby recompression to the in situ eŠective stress (Andresenand Kolstad, 1979), or the ratio De/e0, where De is thechange in void ratio during the recompression process tothe in situ eŠective stresses and e0 is the initial void ratio,which was proposed by Lunne et al. (1997). However,rather than express an absolute value, these values arestrongly dependent on the properties of the local area (forexample, see Tanaka, 2000). If sample quality is examined for every sample along the sampler, these evaluationmethods are both time consuming and costly. Themethods described above are destructive methods used todetermine sample quality, thus further laboratory testingto determine soil properties cannot be carried out afterrevealing high or low sample quality.Therefore, it is imperative that more systematic ande‹cient methods be employed to identify the main factors of geometry design and the mechanisms of the sampling tube in‰uencing the sample quality of soft clayeysoils. Edge angle and area ratio are believed to be themost important factors that aŠect sample quality. In thisstudy, one geometrical parameter was varied while theother dimensions and mechanisms of sampling procedures remained unchanged. For this purpose, commercialKasaoka clay powder was used as the model ground tosimulate laboratory sampling. Speciˆcally designed samplers were used in the laboratory model sampling to identify the geometry features that strongly in‰uence samplequality. Furthermore, the Takuhoku site was chosen as atest site due to the near-uniform ground conditions withdepth; the same driller and sampling methods were usedat this site. As a result any additional uncertainties on thesample quality, such as ground heterogeneity, diŠerentdrillers, and diŠerent sampling methods, as reported byseveral researchers (Tanaka et al., 1999 and 2001; Tsuchida, 2000) can be neglected in this study.Two nondestructive methods were used to evaluatesample quality, the measurements of suction (sometimescalled the residual eŠective stress) using a ceramic discand maximum shear modulus by a bender element (BE)test. After sample extrusion, the sample was placed on aceramic disc with a high air entry value. Following suction measurement, the sample was embedded with BEplates at the bottom and the top, and the shear wave travel time (Dt ) was measured, from which the shear wave velocity (Vs ) and maximum shear modulus (GBE ) were calculated. Tests were performed on every sample in thesampling tube, including the upper and lower parts,which are generally not used for mechanical testing sincethey are considered to be disturbed.LABORATORY TESTING METHODSSuction MeasurementWhen a soil sample is extracted from the ground to theatmosphere, some amount of the eŠective stress remainsin the soil sample in the form of negative or suction pressure. Ideally, the value of the residual eŠective stress orsuction ( p?r ) should be equal to the mean in situ eŠectiveconˆning pressure ( p?m=(s?vo+2s?ho )/3), where s?vo and s?hoare the in situ vertical and horizontal eŠective stresses, respectively. However, p?r is generally somewhat smallerthan the in situ p?m due to sample disturbance caused bythe process of sampling, transportation, storage, extrusion from the sampler, and preparation of the specimenfor laboratory testing. Thus, the residual eŠective stresscan be a soil parameter for the evaluation of sample quality to compare with the in situ p?m. However, measurement or estimation of s?ho is rather di‹cult. Therefore, inthis paper, s?vo will be normalized, as will be explained indetail. The residual eŠective stress, or loss of in situ eŠective stress, has been used to evaluate sample quality byvarious researchers (Ladd and Lambe, 1963; Okumura,1971). These researchers used the conˆning pressure in atriaxial cell to measure the residual eŠective stress, but thetest was so technically di‹cult that the measured valueswere not accurate. There are also other methods, for example, using ˆlter paper (Chandler et al., 1992; Ridley etal., 2003) or a ceramic disc. The ˆlter paper method istime consuming (7¿11 days), and has an error of at least±25z (Chandler et al., 1992). On the other hand, themeasurement of suction by a ceramic disc with high airentry value is less time consuming and more accurate thanthe other two methods above and has been used to assesssample disturbance by several researchers (Tanaka et al.,1996; Mitachi et al., 2001; Nishida et al., 2006). In thisstudy, the ceramic disc was used for measuring suction.The apparatus used for measuring suction is illustratedin Fig. 1. The air entry value of the ceramic disc was 240kPa. Before testing of p?r , the ceramic disc and the connection between the ceramic disc and transducer werecompletely de-aired and saturated. After placing thespecimen on the ceramic disc, the negative pore waterpressure gradually decreased and became constant. Theconstant absolute value of this negative pressure measured by a pressure transducer was deˆned as the suctionvalue or residual eŠective stress ( p?r ). The time durationfor a constant value of p?r in this study was approximately20 minutes. However, all specimens were placed on the SAMPLING TUBE GEOMETRYFig. 1.Suction measuring system by ceramic discFig. 2.ceramic disc for about one hour. During the suctionmeasurement, a specimen was wrapped by plastic ˆlmand covered by an acryl box to avoid loss of water content. The measurement was done under atmospheric conditions and cavity pressure (larger than 100 kPa) was notgenerated since the suction value was less than 100 kPafor all samples in this study.Bender Element TestMany researchers have tried to evaluate sample qualityby the small strain stiŠness (Tan et al., 2002; Nishida etal., 2006). Many empirical relations used to determineshear modulus are expressed in terms of soil structure,function of void ratio, and present and maximum eŠective stresses (Jamiolkowski et al., 1994; Shibuya andTanaka, 1996) as shown in the following expression;G=Af(e)[s?/(s?)r ]n[s?max/(s?)r ]m95(1)where A is a constant presenting soil structure, f(e) is afunction of void ratio, s? is the current eŠective stress,s?max is the maximum eŠective stress experienced in thepast, (s?)r is an arbitrary reference stress, and n and m areexperimental exponents. Because G was measured underunconˆned conditions in this study, s? is equal to theresidual eŠective stress in the specimen, i.e., p?r . As previously mentioned, the p?r value is smaller than the in situeŠective stress due to sample disturbance, thus the measured G should be smaller than G measured by the seismiccone in situ stress conditions. In addition, the term A,which represents soil structure, should be in‰uenced bysampling eŠects. Thus, it is inferred that the sample quality can be assessed by a comparison of G under unconˆned conditions and before sampling, i.e., in situ stressconditions. It should be noted that, since the void ratiodoes not change with sampling, f(e) has no in‰uence on Gbefore or after sampling.Among devices measuring G, the bender element (BE)Bender element equipmentstest is a simple and very fast method. The details of theBE test have been described by several researchers (Viggiani and Atkinson, 1995; Shibuya et al., 1997;Kawaguchi et al., 2001). After measuring p?r , the BE testwas performed to measure shear wave velocity (Vs ) of thesample. The test equipment and dimensions of BE are illustrated in Fig. 2. A pulse with various types of waveforms, such as sine and square over a wide range of frequency, was input by a function generator through atransmitter BE at the top of the sample. The wave propagated through the sample and was detected by the BEreceiver plate at the bottom. The shear wave travel time(Dt ) was deˆned as ``start-to-start'' between two instantsof the generated wave and the ˆrst de‰ection of thereceived wave (Kawaguchi et al., 2001). The travel distance (L) was deˆned as ``tip-to-tip'' distance between thetransmitter and the receiver of BE plates (Viggiani andAtkinson, 1995). Thus, the shear wave velocity can becalculated from Eq. (2);Vs=L/Dt(2)From the theory of shear wave propagation in an elasticbody, the shear modulus from the BE test (GBE ) can becalculated from Eq. (3);GBE=rtV 2s(3)where rt is the bulk density of soil.RECONSTITUTED MODEL GROUNDPreparation of Model GroundA cylindrical consolidation cell, 600 mm in height and250 mm in diameter, was used to create the modelground. Kasaoka clay powder with a speciˆc gravity of2.67 g/cm3, liquid limit (wL ) of 62z, and plastic limit(wP ) of 36z was used. The clay powder was mixed withdistilled water using a mixer at water content two times HORNG ET AL.96larger than wL. Vacuum pressure was applied to the cell,following which it was vibrated to eliminate air bubblesfrom the slurry. A consolidation pressure of 100 kPa wasused in this investigation. About one month was requiredfor the model ground to be fully consolidated. The heightof the model ground after full consolidation was about 30cm at a consolidation pressure of 100 kPa.Samplers and Sampling for Model GroundMain features of samplers used in the model groundare listed in Table 1. The name of the sampler, for example, 69M1.5 indicates that 69is the edge angle, the letterof ``M'' means Model (for the ˆeld sampling, the letter of``F'' was used, as shown in Table 2) and the last number``1.5'' is thickness of the sampler wall. All of the samplers are 500 mm long and are made from stainless steel.The area ratio in the table is deˆned by Hvorslev (1949)following Eq. (4);22Area ratio=(D 2o-D i )/D i(4)where Do and Di are the outside and the inside diameter,respectively. Equation (4) indicates that the area ratio isthe ratio of the volume of the displaced soil to the volumeof the sample. The area ratio of 69M1.5, for example, isabout two times larger than that of the Japanese standardsampler ( see Table 2, where the Japanese (JPN) sampleris shown as 69F1.5). Outside and inside walls are straightexcept for the cutting edge, and thus, no inside clearanceratio exists. The width at the edge angle tip is 0.20 mm.909M5 sampler has the edge angle of 909and the wallthickness of 5 mm. The last sampler of the same table,Table 1. Main features and dimensions of model samplers used forKasaoka model groundModelsamplersInsidediameter(mm)Edge angle(a) (9)Thickness(t) (mm)69M1.54061.515.6Yes69M5326572.3Yes309M1.540301.515.6Yes909M1.540901.515.6Yes909M53290572.3Yes69M1.5(O)4061.515.6NoArea ratio Piston(AR) (z)Table 2. Main features and dimensions of ˆeld samplers used in thisstudyFieldsamplersInsidediameter(mm)Edge angle(a) (9)Thickness(t) (mm)69F1.57561.58.2Yes69F107561060.4Yes909F1.575901.58.2Yes909F1075901060.4Yes69F1.5(O)7561.58.2NoArea ratio Piston(AR) (z)69M1.5(O) is the same sampler of 69M1.5 with the edgeangle of 69and wall thickness of 1.5 mm, but with nopiston in the same manner as an open drive sampler.After completing consolidation of the model ground,the piston of the cell was disassembled and sampling wasconducted. Sampling was carried out from the groundsurface without a borehole. The position of the pistonwas ˆxed at the ground surface and the sampler wassmoothly derived by an air cylinder in the same way as thehydraulic Osterberg sampler until reaching the bottom ofthe consolidation cell, where a porous metal plate wasplaced for drainage during consolidation of the ground.Therefore, when the sampler was withdrawn, no vacuumwas generated at the bottom of the sampler. It should bekept in mind that this point is diŠerent from the ˆeldsampling, and its eŠect will be discussed in more detail inthe Takuhoku sampling section.Immediately following sampling, a soil sample was extruded from the sampler with the opposite direction ofthe sampling, i.e., the sample was extruded from the cutting edge of the sampling tube. This extrusion method iswidely exercised in practice in Japan. Soil samples werecut into 50 mm pieces by a wire saw. They were wrappedby thin plastic ˆlm and coated by para‹n wax. The extruded samples were then stored in the humid and temperature controlled room until tested.Test Results of the Model GroundEŠects of sampler geometry were evaluated by comparing the normalized ratios of p?r /s?vo and GBE/Gf, where s?vois the consolidation pressure of the model ground and Gfis the maximum shear modulus obtained from BE triaxialtest for the reconsolidated Kasaoka clay sample. The tested specimen was consolidated under Ko conditions andthe vertical consolidated pressure was the same as that ofthe model ground.(1) Location of Sample Quality in SamplerFigures 3 through 7 show the test results of the modelground sampling from diŠerent sampler geometryaspects. Preliminary testing showed that the water content was somewhat diŠerent in each model ground,although the consolidation pressure was constant. Such avariety may be caused by friction between the piston andthe inside wall of the cell, as well as secondary consolidation eŠect, even though the time for consolidation wasstrictly controlled. Therefore, test results presented inthese ˆgures were obtained from the same model ground.The vertical axis in the ˆgures indicates the distance ofthe sample location for measured p?r and GBE from thebottom edge of the sampling tube. It can be seen in theseˆgures that p?r /s?vo and GBE/Gf are uniformly distributedalong the sampling tube and the diŠerence caused by thelocation is not very signiˆcant, compared with those samples obtained from the ˆeld, for example, Tanaka andTanaka (2006); Nishida et al. (2006) and Figs. 16 and 17in the present study. This diŠerence may be explained bythe sampling method adopted in the model ground. First,as the sampling was directly carried out from the groundsurface without a borehole, the upper part of samples was SAMPLING TUBE GEOMETRYFig. 3.EŠect of edge angle (model ground)Fig. 4.EŠect of edge angle (model ground)Fig. 5.Fig. 6.not disturbed as is usually the case in ˆeld samples due tothe drilling procedure. Second, as the sampler waspenetrated until the bottom of the consolidation cellwhere the porous metal plate was placed, no vacuum wasgenerated at the bottom of the sampler as the sampler waswithdrawn. Therefore, the bottom part of the samplingtube was not disturbed by the vacuum eŠect.(2) EŠect of Edge AngleFigure 3 shows in‰uence of the edge angle on the sample quality. In the upper ˆgure, 69M1.5 and 909M1.5have the same geometrical dimensions, except the edgeangles. The samples obtained from samplers with smalleredge angle (69M1.5) show larger values of p?r /s?vo andGBE/Gf than those with large edge angle (909M1.5). Asshown in the lower ˆgure, the thick wall samplers, i.e.,69M5 and 909M5, also show the same trend as the thinwall samplers.97EŠect of area ratio (model ground)Combined eŠects of edge angle and area ratio (model ground)Another consolidation cell was prepared with the sameconsolidation pressure to study eŠects of the edge angle inmore detail, using a 309sampler (309M1.5) with the samedimensions as 69M1.5 and 909M1.5. It is clear from Fig.4 that the best samples can be obtained from the samplerwith the sharpest edge angle (69M1.5), while the largestedge angle (909M1.5) provides the lowest sample quality.Sample quality from 309M1.5 is located in between.These results conˆrm that a sharp edge angle is very important in reducing disturbance for both thin and thickwall samplers.(3) EŠect of Area RatioFigure 5 shows the eŠects of the area ratio (thickness ofthe wall) at a same edge angle. The area ratios for 69M1.5M5 are 15.6z and 72.3z, respectively, a diŠerand 69 HORNG ET AL.98Fig. 7.EŠect of piston (model ground)ence of more than four. In the lower ˆgure, comparisonwas also made for 909edge angle samplers, 909M1.5 andM5. As illustrated in Fig. 5, a larger area ratio leads909to a lower sample quality for both edge angles tested,however, this diŠerence is not as signiˆcant as the eŠectof the edge angle.To examine the combined eŠects of both edge angleand area ratio from the model ground, test results in Figs.3 and 5 are replotted in Fig. 6. This ˆgure shows that69M1.5 samples have the best quality, which conˆrms theimportance of small edge angle and small area ratio.Careful observation of the same ˆgure reveals that samples retrieved by both 69edge angle samplers have highervalues of p?r /s?vo and GBE/Gf than those of 909edge angle,regardless of the sampler thickness. These results showthat the edge angle plays a more predominant role thanwall thickness for mitigating sample disturbance. Thesame ˆndings of the importance of small edge angle andthinness of a sampler to reduce sample disturbance werealso reported in other studies, for example, Clayton et al.(1998) by using ˆnite element method; Siddique et al.(2000).(4) EŠect of PistonIt is well known that the Shelby tube, an open drivesampler, has been used as a typical sampler for retrievingundisturbed samples in most countries. Reasons for thewide use of the open drive sampler may be due to its lowcost, ruggedness, and simplicity of operation. The eŠectof a piston on sample quality was investigated using themodel ground. The sampling tube, 69M1.5, was used forthis purpose, with the sampler without a piston denotedas 69M1.5(O). Comparison of the sampler with a ˆxedM1.5) and no piston sampler (69M1.5(O)) ispiston (69shown in Fig. 7. It can be recognized that the number ofmeasured points for 69M1.5(O) is small and there is nodata at location between 20 cm and 30 cm from the cutting edge. This is not because the tests were not carriedout at those depths, but samples corresponding to thesedepths could not be collected due to the low recovery.The recovery ratio of the sampler without a piston wasonly 63.5z, whereas that of the sampler with a ˆxedFig. 8.Water contents along the samplers (model ground)piston was 95.4z. Such a small recovery ratio for69M1.5(O) may be attributed to compression of themodel ground during penetration of the sample tube.To study which part of the ground was compressedwith the 69M1.5(O) sampler, a detailed distribution ofwater content (wn ) from 69M1.5(O) samples was measured and compared with that of 69M1.5 ( see Fig. 8). Therecovery ratio for 69M1.5 with a piston was nearly 100zso that its distribution of the water content presents thetrue distribution in the consolidation cell. Even thoughthe duration for consolidation of the model ground wasmore than one month, wn in the central part was somewhat larger than that at the bottom or the upper part ofthe ground. It can be seen that wn of samples collected byM1.5(O) agrees fairly well with the wn in thethe 6969M1.5 up to 8 cm from the cutting edge. However,69M1.5(O) samples further from the edge bottom show asmaller wn then 69M1.5 samples. This means that in caseof 69M1.5(O), in which the recovery ratio was low, thecentral part (between 10 and 20 cm) was deformed andmoved horizontally due to the relatively high strength atthe upper part, compared with that at the middle part. Asa result, samples in the middle part were not stored in thesampling tube. Considering this compression eŠect for69M1.5(O) sampler, the location of the samples is adjusted and replotted in Fig. 7 by symbols of (). Clear diŠerence in sample quality can be seen for the two samplers.The compressed soil samples obtained by the open drivesampler provide low sample quality compared with thesampler containing a ˆxed piston. SAMPLING TUBE GEOMETRYMain Test Results from the Model GroundIn conclusion, the laboratory simulated sampling onreconstituted Kasaoka clay has shown that edge anglesharpness and wall thickness are important parameters inobtaining high quality samples. Results have also shownthat the edge angle has a greater eŠect on the sample quality than the area ratio. The use of open drive samplinghas been shown to compress the soil sample, thus causingsample disturbance.FIELD INVESTIGATION OF TAKUHOKUModel ground sampling avoids the natural scatter insoil properties, as well as the disturbances caused by drilling and handling at the ˆeld. Additionally, laboratory experimentation is less costly than ˆeld testing. However,mechanical properties of reconstituted soils are signiˆcantly diŠerent from natural soil deposits due to thein‰uence of soil structures, which is believed to be one ofthe most important aspects in‰uencing sample quality. Inaddition, the eŠect of overburden pressure on sample disturbance cannot be considered in the model ground. It isquestionable whether the test results obtained from themodel ground can be directly applied to the ˆeld sampling. Therefore, ˆeld sampling was carried out at Takuhoku site using the samplers that correlate to those usedin the model ground testing.Characteristics of Geotechnical Properties at TakuhokuSiteThe Takuhoku site is located in Sapporo, Japan. Thefundamental properties of this site are shown in Fig. 9.The deposits consist of 5 m of ˆll and peat followed by a4.5 m silty sand deposit, overlying the clay layer investigated in this study. A sandy silt layer separates the clayFig. 9.99layer into the upper and the lower clay layers at a depth of15 to 18.5 m. Sampling using samplers with various geometrical designs was carried out at two depths: the upper(10¿15 m) and lower (20¿24 m) clay layers as indicatedin Fig. 9. The ground water table is located at 3 m belowthe ground surface. Grain size distribution shows thatboth clay layers consist of a constant clay fraction (particle smaller than 5 mm) of approximately 50z down to the32 m depth. The natural water content varies between 60and 70z and the plasticity index ( Ip ) is about 45¿53 and50¿63 for the upper and lower clay layers, respectively.Sample quality is considered to be sensitive to the in‰uence of soil structure. The soil structure expressed bythe in situ void index (Burland, 1990) is plotted in thesame ˆgure. It is seen that the soil structures of upper andlower clay layers are relatively similar. The physical properties of the soft clay in question were found to be quitehomogeneous.The yield consolidation pressure ( p?y ), which wasmeasured by CRS oedometer testing at strain rate of0.02z/min (3.3×10-6/s), is somewhat lower than theeŠective overburden pressure (s?vo ) calculated, assumingthat the pore water pressure distribution was hydrostatic,as shown in Fig. 9. However, the ˆll material at groundsurface was placed in the 1960's, thus it is believed thatthe ˆll is still undergoing consolidation. Figure 10 showsmore detailed comparison of various values measured orestimated from diŠerent tests. The dashed line in Fig. 10shows the s?vo at U=0z, where the overburden pressureof the ˆll is not considered, the dotted line on the otherhand, shows s?vo at U=100z, where consolidation of theˆll is assumed to be complete. It can be seen that p?y valueis located between the U=0z (no consolidation) and U=100z (fully consolidated) lines. Estimated s?vo valuesfrom CPT and triaxial tests are plotted on the sameTakuhoku soil profiles HORNG ET AL.100The shear wave velocity (Vf ), and thus, small strainshear modulus (Gf ) was measured by the seismic cone(SCPT) in this ˆeld. SCPT used in this investigation consisted of a shear wave generated by hammering a woodplank on the ground surface and received by two sets ofreceivers, one meter from each other. Vf was determinedby deˆning the arrival lag time of the shear wave propagation between these two receivers. The details of theSCPT test are described by Tanaka et al. (1994). Maximum shear modulus (Gf ) of the SCPT can be calculatedfrom the shear wave velocity using the relation;2Gf=rtV f(6)where rt is the bulk density of soil. The results of the Vfand Gf in the subjected clay layer are shown in Fig. 9.The ˆgure shows that both Vf and Gf linearly increasewith an increase in depth. The estimation by Tanaka et al.(1994) of Gf=50 (qt-svo ), where qt is the tip resistanceconsidering the eŠective area ratio of the cone, is alsoplotted in the ˆgure. The values of measured GBE fromBE test are normalized by these data from the seismiccone to take into account diŠerent overburden eŠectivestresses.Fig. 10.Proˆles of vertical eŠective stress of Takuhokuˆgure. It was obtained from the Ko triaxial test, whereconsolidation pressure was at the normally consolidatedstate, that the undrained stress incremental ratio ( su(triaxial)/s?v ) was 0.27, which was the average strength from thecompression and extension triaxial tests. As will be mentioned later, the in situ undrained shear strength can beobtained from CPT, assuming Nkt=11.5; this strength isdenoted as su(CPT). Combining these experimental results,the in situ eŠective burden pressure (s?vo ) has the following relation;s?vo=su(CPT)/( su(triaxial)/s?vo )(5)It can be seen that s?vo calculated by Eq. (5) is well inagreement with p?y value from the CRS test. The s?vovalues shown in Fig. 10 were used to normalize the residual eŠective stress of samples in this study for samplequality comparison.The ˆeld vane test (FVT), using a vane blade of 40 mmin diameter and 80 mm in height, and the piezocone test(CPT) were carried out to measure mechanical propertiesof the clay layer. From the CPT test, the undrained shearstrength was calculated using the relation su(CPT)=(qt-svo )/Nkt, where qt is the point resistance of the piezoconeand svo is the total overburden pressure. By equating theundrained shear strengths of CPT and FVT, the cone factor Nkt was able to be calculated. In this site Nkt is reasonably estimated to be 11.5. The undrained shear strengthsfrom the unconˆned compression test (UCT) are alsoplotted in this ˆgure, where the soil samples wereretrieved by the Japanese standard ˆxed piston sampler(69F1.5 in Table 2). The mean undrained shear strengthsfor the upper and lower sampling depths are approximately 20 kPa and 40 kPa, respectively.Sampling Tubes Used and Sampling Method in the FieldBased on the Japanese standard ˆxed piston (JPN)sampler speciˆed by the Japanese Geotechnical Society(Designation: JGS 1221–2003), and considering experimental results from the model ground, geometries ofthe sample tube for the ˆeld sampling were determined asindicated in Table 2. The JPN sampler is used in Japanfor sampling soft clay with low SPT N values, generallyless than 4. The dimensions of the sampling tube includean inside diameter of 75 mm, a length of 1 m, and theeŠective sampling length of 0.8 m. The edge angle of the. Although material of thestandard JPN sampler is 69tube is allowed to be both brass and stainless steel,nowadays it is mostly made of stainless steel. The thickness of the tube wall is 1.5 mm for stainless steel, corresponding to an area ratio of 8.2z. More details of thissampler can be referred to JGS (1998) and Tanaka et al.(1996). In this study, three additional geometricallydiŠerent sampling tubes were manufactured in additionto the JPN standard sampler. The main geometrical features of those samplers are shown in Table 2. The ˆrstsampler in the table, 69F1.5, is the standard sampler currently used in Japan. The second tube sampler, 69F10,has edge angle of 69and wall thickness of 10 mm, resulting in an area ratio of 60.4z. The last sampler,69F1.5(O), is the 69F1.5 without a piston (open drivesampler).Sampling methods are diŠerent in various countries. InScandinavian countries, the so called displacementmethod is widely adopted, in which a borehole is notnecessary. A sampler, such as NGI 54 mm is directlypushed from the ground surface to the desired samplingdepth, and then the tube is driven to obtain the soil sample. In the UK, in order to avoid the eŠects of soil disturbance at the bottom of the borehole, a sampler such as an SAMPLING TUBE GEOMETRYELE100 sampler is penetrated to a certain depth prior tosampling. Therefore, the ELE100 and NGI 54 mm samplers have a conical shape at the bottom of the piston. InJapan, however, a borehole is made to a sampling depthbefore conducting sampling (pre-borehole method). Sampling in this investigation followed the Japanese standardsampling method discussed above.A 105 mm diameter borehole was advanced using arotating drilling machine with circulating mud water.When the drilling reached the sampling depth, the bottom of the borehole was carefully cleaned so as not toleave soil cuttings. Then the drilling bit was lifted to theground surface and the sampler was descended to the bottom. In Japan, two methods are allowed for ˆxing apiston: extension rods and hydraulic (Osterberg) sampler(JGS 1221–1995). This investigation employed the extension rod method, where the piston was ˆxed through extension rods to a tripod by a turn buckle. In case of anopen sampler, a vacuum was created by a ball valve toprevent the soil sample from falling when the sampler waswithdrawn since there was no piston. Sampling was donecontinuously within the clay layers. Notice that since theeŠective depth of the penetration of the sampling tube is800 mm, the interval of each sampling was left to 200 mmto avoid sample disturbance caused by the previous sampling. The depth of the sampler penetration was recordedprecisely in order to calculate the recovery ratio. Afterstopping penetration of the sampler, the sampler waswithdrawn to the ground surface. The air vent at thepiston was released in order to avoid generation of suction between the sample and the piston when the pistonwas disassembled from the tube. The recovery ratio wasimmediately obtained by measuring the length of theretrieved sample and penetration depth of the samplerrecorded at sampling. The type of samplers and theirrecovery ratios at each sampling depth is shown in Table3. Both ends of the sampler were covered with para‹nwax of about 20 mm thickness at the site. Samples kept inthe sampling tube were placed on several layers of rubbermat in order to avoid sample disturbance and were transported to laboratory at Hokkaido University.Table 3.Depth (m)101Takuhoku samples were extruded from the samplersand cut into 100 mm long pieces by a wire saw in thelaboratory. Direction of extrusion was opposite to that ofsampling, i.e., from the edge bottom. They were wrappedby thin plastic ˆlm and coated by para‹n wax. The extruded samples were then stored in the humid and temperature controlled room until tested.Proˆles of p?r /s?vo and GBE/Gf of the Best SamplesIn order to characterize soil properties at the investigated site from a view point of sample quality, p?r and GBEwere measured on samples retrieved by the JPN standardsampler (designated as 69F1.5 in Table 2) and the location of these samples is in the middle of the samplingtube: i.e., the best quality is guaranteed, as describedlater. The variation of p?r /s?vo and GBE/Gf ratio to thedepth is presented in Fig. 11.It can be seen in this ˆgure that the normalized valuesof p?r /s?vo slightly increase with depth, and its values areabout 1/5 at the upper investigated depth and 1/3 at thelower depth. Ladd and Lambe (1963) measured p?r by theunconsolidated undrained (UU) triaxial test and foundthat for the Kawasaki clay (a Japanese marine clay), thep?r /s?p ratio ranged from 0.11 to 0.43 with an averagevalue of 0.28, where s?p is the residual eŠective stress inthe perfect sample, and they reported that the s?p was inthe range of 0.56±0.05 of s?vo. Thus, the p?r /s?vo ratio wasround 0.14, which is quite low compared with this study.Tanaka et al. (1996) studied residual eŠective stress due tosample disturbance and has shown that p?r /s?vo was in theorder of 1/5 to 1/6 for high quality samples. From thedepth of 10 to 15 m (upper clay layer), the p?r /s?vo in thisSamplers used and their recovery ratiosSampler usedRecovery ratio (z)11.00¿11.80909F1098.712.00¿12.8069F1099.413.00¿13.8069F1.599.414.00¿14.80909F1.510015.00¿15.8069F1.5(O)12020.00¿20.80909F1010021.00¿21.8069F109522.00¿22.8069F1.597.523.00¿23.80909F1.598.724.00¿24.8069F1.5(O)78.7Fig. 11. p?r /s?vo and GBE/Gf of the best quality samples along the depth(Takuhoku) 102HORNG ET AL.study is approximately 1/5 the value reported by Tanakaet al. (1996), but below 15 m the ratio linearly increasesand is larger than 1/5.In addition to the p?r /s?vo ratio, GBE/Gf is also plotted inthe same Fig. 11. Contrary to p?r /s?vo, the normalized ratio along the depth is relatively constant ranging fromaround 0.45 to 0.73 with an average of 0.57. It is interesting to compare the present results with those conductedby Landon et al. (2007). They measured BE shear wavevelocity (VBE ) in the same manner as in this study forsamples from Boston Blue Clay, retrieved by the Sherbrooke, the ˆxed piston, the free piston, and the SPTsplit spoon samplers. The VBE was normalized with Vffrom the ˆeld seismic piezocone for comparing samplequality among those samplers. But in this study sinceGBE/Gf are used to compare sample quality, the normalized VBE/Vf of Landon are converted to GBE/Gf. Theyfound that the GBE/Gf ratios were in the range of0.49¿0.64, 0.42¿0.49, 0.09¿0.25, and 0.09¿0.16 forsamples retrieved by the Sherbrooke, the ˆxed piston, thefree piston and the SPT split spoon samplers, respectively. It is revealed that the normalized ratios (GBE/Gf )obtained from this study are as high as those of Sherbrooke samples conducted by Landon et al. (2007).Test Results from the Field Sampling Using Various Samplers(1) LocationFigures 12 through 19 show a comparison of p?r /s?voand GBE/Gf ratios measured by various samplers withdiŠerent geometries. The ˆrst signiˆcant diŠerence between the ˆeld and the model samplings is the in‰uence ofsample quality locations in the sampling tube. Contraryto the model sampling (Figs. 3 through 7), the values ofp?r /s?vo and GBE/Gf for all ˆeld samplers in this study showthat the best quality sample lies in the middle part of asampler and that the lowest quality is at both its lowerand upper parts. For the actual ˆeld sampling, the disturbance at the lower edge tip may be caused by the suctioncreated by withdrawal of the sampler. The upper part ofsample in a sampling tube may suŠer from the boreholedrilling or extensive straining by removal of the overburden pressure. In addition, it is inferred that, because oflong travel distance, the upper part of sample is damagedby frictional force between the inside wall and the sampleduring both sampling and extrusion.(2) EŠect of Edge AngleFigures 12 and 13 show the eŠects of the edge angles ofthe sampler. Figure 12 shows test results from the upperclay layer using two pairs of samplers with diŠerent edgeangles: 69F1.5 and 909F1.5; 69F10 and 909F10. Thesame pairs of sampler were also used for the lower claylayer as shown in Fig. 13. The ˆrst pair of the samplers,69F1.5 and 909F1.5, have the same dimensions, with theexception of the edge angles (69and 909, respectively).From the ˆgures it can be seen that the normalized valuesof p?r /s?vo and GBE/Gf for samples retrieved by 69edge angle samplers are higher than those of 909for both claylayers. It is interesting to note from the Figs. 12 and 13Fig. 12.EŠect of edge angle (upper layer)Fig. 13.EŠect of edge angle (lower layer)that the diŠerence in p?r /s?vo and GBE/Gf for the thin wallsamplers, 69F1.5 and 909F1.5, is much smaller thanthose of the thick wall samplers, 69F10 and 909F10. Itimplies that the in‰uence of the edge angle is morepronounced on sample disturbance when the sampler hasa thicker wall.(3) EŠect of Area RatioFigures 14 and 15 show the results of the two pairs ofdiŠerent area ratio samplers, 69F1.5 and 69F10; and SAMPLING TUBE GEOMETRYFig. 14.103Fig. 16.Combined eŠects of edge angle and area ratio (upper layer)Fig. 17.Combined eŠects of edge angle and area ratio (lower layer)EŠect of area ratio (upper layer)Table 4.69F1.5SamplersArea ratio (z)8.28.2909F1060.469F1.5(O)8.20.1590.1320.0380.150(GBE/Gf)average0.4620.4190.2820.1280.417Area ratio (z)909F1.5 and 909F10. The values of p?r /s?vo and GBE/Gf ofsamples retrieved by both 69edge angle show no noticeable diŠerence between 1.5 and 10 mm thickness samplers.), sample qualityBut in the case of a larger edge angle (909obtained by the thin wall sampler (909F1.5) is signiˆcantly better than that by thick wall sampler (909F10).The magnitudes of p?r /s?vo and GBE/Gf of the above60.4909F1.50.152SamplersEŠect of area ratio (lower layer)69F10(p?r/s?vo)averageTable 5.Fig. 15.Upper clay layer of Takuhoku69F1.58.2Lower clay layer of Takuhoku69F1060.4909F1.58.2909F1060.469F1.5(O)8.2(p?r/s?vo)average0.2410.2120.1900.0800.240(GBE/Gf)average0.5070.3950.3600.1820.418four geometrically diŠerent samplers for the upper andlower clay layers of Takuhoku site are plotted together inFigs. 16 and 17, respectively. The average magnitudes ofp?r /s?vo and GBE/Gf in Figs. 16 and 17 are listed in Tables 4and 5, respectively. These ˆgures and tables show that thestandard sampler, 69F1.5, gives the best sample qualityF10)and that the thicker sampler with 909edge angle (909 104HORNG ET AL.gives the lowest sample quality. Increasing the area ratiofrom 8.2z to 60.4z or increasing the wall thicknessfrom 1.5 to 10 mm causes no signiˆcant sample disturbance for the small edge angle but profound disturbancefor the large 909edge angle. The mean values of p?r /s?voand GBE/Gf for 909F1.5 are 71z and 55z, respectively,larger than 909F10 in the upper clay layer and are 58zand 50z, respectively, in the lower clay layer.From both model and actual ˆeld samplings, the sharpedge angle of a sampling tube is the most important keyfactor to obtain good quality. In the ˆeld sampling, verylarge diŠerences in sample quality are seen between 69F10F10, compared with those of thin wall samplers,and 90969F1.5 and 909F1.5 (Figs. 12 and 13). Those diŠerencescannot be seen in the model sampling. In the model sampling, large edge angles for both thin and thick wall samplers lead to some degree of disturbance (Fig. 3).The wall thickness, and thus area ratio, has long beenconsidered to have signiˆcant in‰uence on tube samplingdisturbance since Hvorslev (1949) pointed out its importance. He realized that the penetration resistance of asampler, the possibility of entrance of excess soil, anddanger of disturbance of the sample all increase with increasing area ratio. He also suggested that ``the area ratioof sampler should be reduced to not exceed 10 to 15z foropen drive samplers, but it is possible that the allowablelimit is higher for samplers with a stationary piston, eventhough small area ratio generally causes slighter disturbance.'' The Sub-Committee on Soil Sampling of International Society for Soil Mechanics and Foundation Engineering (1981) reported that an area ratio of less than13z is generally recommendable, and up to 15z is acceptable, depending on soil conditions. The largest permissible area ratios of 11, 10, and 13z are required inJapan, United Kingdom, and United States, respectively,for their sampling standards. Matsumoto et al. (1968 and1969) reported test results from the comparative study atthe Kinkai site, using three samplers with area ratios of2.7, 5.4, and 13.7z. Dimensions and other features ofthe three samplers were identical to the JPN standardsampler. It was found that the undrained shear strengths(qu/2) and strain at failure (ef ) did not change due to thewall thicknesses of the sampling tube. In this study, in addition to the Japanese standard sampler (69F1.5), two 10mm thick wall samplers were used: 69F10 and 909F10.The area ratios of the thick wall samplers are as much as60.4z. Even though the area ratio increases more thansevenfold from 8.2z to 60.4z and far larger than thestudies of Matsumoto et al., the sample quality is not signiˆcantly aŠected. On the other hand, if the cutting edgeis not sharp, then the area ratio must be as small as possible. That is, the area ratio is dependent on the edge angleselected. The Sub-Committee on Soil Sampling of International Society for Soil Mechanics and Foundation Engineering (1965) also recognized that a large area ratiocan be compensated partly by a small edge angle, as indicated in Table 6.(4) EŠect of PistonIn this study, the eŠect of piston on sample quality wasTable 6. Relation between area ratio and cutting angle for 75 mmsamplers by the Sub-Committee on Soil Sampling of ICSMFE(1965)Cutting angle (9)Area ratio (z)1551210920540480investigated, using the sampler (69F1.5(O)), which hasthe same geometrical features as the standard Japanesesampler. It is believed that the largest advantage of thepiston sampler is considered to have high recovery ratio,because the piston can create a vacuum high enough toprevent the captured sample from falling when the sampler is withdrawn from the bottom of the borehole.The recovery ratio for each sampler, including69F1.5(O), is shown in Table 3. No remarkable diŠerenceF1.5 andcan be seen in the recovery ratio for 6969F1.5(O) in the upper clay layer. On the other hand, inthe lower clay layer, the recovery ratio of 69F1.5(O) wasas low as 79z. The high ratio in the upper clay layer mayderive from disadvantages of the open drive sampler aspointed out by Hvorslev (1949) and Osterberg and Murthy (1979): i.e., due to poor cleaning of the borehole priorto sampling, or soil shavings on the borehole wall, thesampling tube may collect soil along the wall of the borehole in the process of lowering the sampler or soil cuttingsdeposited at the bottom of the borehole. It is inferredthat even within the upper layer, the recovery ratio of69F1.5(O) would be lower than the observed value shownin Table 3, if the targeted sample was properly captured.This debris can be seen by the low p?r /s?vo and GBE/Gfvalues as shown in Fig. 18, compared with the rest ofsamples from the same sampler.The test results of p?r /s?vo and GBE/Gf for the 69F1.5(O)F1.5 in Figs. 18 and 19 forare compared with those of 69the upper and lower clay layers, respectively. It is believedthat the stationary piston is a key for collecting a highquality sample. However, a great diŠerence in p?r /s?vovalues between the stationary piston (69F1.5) and theopen drive sampler (69F1.5(O)) are not seen in both claylayers, except for the upper part of the samples, wheresome reduction in p?r /s?vo is observed. On the other hand,the GBE/Gf values of the stationary piston samplers areslightly higher than those of the open drive samplers. Theaverage values of p?r /s?vo and GBE/Gf for the two samplersfor the upper and lower clay layers are summarized inTables 4 and 5, respectively. Tanaka et al. (1996) also investigated the eŠects of piston on sample quality at theKinkai site. They showed that no diŠerence can be seenbetween the samples with and without piston from theunconˆned compression and the laboratory vane sheartests.On the other hand, as already mentioned, a piston was SAMPLING TUBE GEOMETRYeŠective in obtaining high quality samples from themodel ground. The diŠerence observed between themodel ground results and the ˆeld test results is common,and several explanations exist. A comparison of the watercontent distribution in the model ground showed that themiddle part was horizontally pushed and was not able tobe captured in the sampler. In the ˆeld testing, althoughan investigation of the detailed distribution of the watercontent could not be performed, it is believed that such ahorizontal displacement did not take place and the wholesample was recovered. This consideration is supported bythe fact that p?r /s?vo ratio for 69F1.5 and 69F1.5(O) isnearly the same until 50 cm from the bottom of the sampler, as seen in Figs. 18 and 19, in spite that the GBE/Gffor 69F1.5(O) is slightly smaller than that for 69F1.5. Thereason for no horizontal displacement for the ˆeld opensampling may be due to the eŠect of the large overburdenpressure, which prevented the horizontal displacementduring the penetration of the sampler. If this inference isvalid, then the next questions are why the recovery ratiofor 69F1.5(O) for the lower layer was so small and wherethe loss of soil sample occured. At present, the authors donot have any reasonable answer for these questions;however over-drilling can be an explanation. Since theFig. 18.EŠect of piston (upper layer)Fig. 19.EŠect of piston (lower layer)105open drive sampler does not posses a piston, the bottomof the borehole is required to be much cleaner than that inthe case of the piston sampler, as previously discussed. Itwas observed that the driller required more preparationtime of the borehole cleaning so the bottom of the borehole might be deeper than the predetermined samplingdepth. As a result, the sample length was shorter and therecovery ratio became small. In other words, low recovery ratio for 69F1.5(O) was not caused by dropping thesample during the withdrawal of the sampler.CORRELATION BETWEEN p?r AND GBEIt is anticipated from the test results of this study thatGBE increases with increase of p?r . Figure 20 shows the p?rand GBE data measured for the sample retrieved at theTakuhoku site. It can be seen that GBE is strongly relatedto p?r , although some scatter exists in this relation. According to Eq. (1), GBE is determined not only by p?r , butalso by soil structure expressed by the coe‹cient of A,void ratio (e) and the maximum past conˆning stress(s?max ). The eŠect of e does not need to be considered, as itis not changed by sampling and is nearly constant for theinvestigated layers in this study ( see the distribution of wnin Fig. 9). In order to examine the eŠects caused by adamage of soil structure, i.e., the eŠect of A, the relationmeasured for samples retrieved by 69F1.5 and 909F10 isplotted using diŠerent symbols to distinguish them fromother samplers. It should be kept in mind that 69F1.5 and909F10 samplers provided the best and the worst samplequality, respectively. If the scatter in the relation betweenp?r and GBE is created by destruction of soil structure, thenthe relation obtained from 69F1.5 should be located inthe upper part and that from 909F10 should be located inthe lower part of the band of the p?r and GBE relation inFig. 20. It can be apparently recognized that points obtained from 69F1.5 are upper 909F10, though the diŠerence is small.The eŠects of the maximum stress experienced in thepast on GBE must also be considered; in other words, theGBE for heavily disturbed sample collected at great depthsFig. 20.Correlations between p?r and GBE HORNG ET AL.106CONCLUSIONSFig. 21.Correlations between ( p?)0.6( p?max )0.2 and GBEis equivalent to a slightly disturbed sample collected fromshallow depths, provided that the measured suction is thesame. Kawaguchi and Tanaka (2008) tried to formulatethe maximum shear modulus (Gmax ) using laboratory testing for reconstituted soils and conˆrmed that this formulation is applicable to Gmax measured in the ˆeld. Theirformulation of Gmax is;Gmax=20(wL )-0.8( p?)0.6( p?max )0.2(7)where wL is the liquid limit, p? and p?max are the mean principal stress of the current and maximum stresses experienced in the past, respectively. Unlike previous formulations, they do not consider eŠects of e nor soil structure, but Gmax can be simply expressed by three terms, wL,p? and p?max. It should be noted that the eŠect of ( p?max ) israther insigniˆcant compared with p? (compare the powers of p? and p?max ). According to their formulation,eŠects of magnitude of the in situ stresses before sampling are considered in Fig. 21. The eŠect of wL is notconsidered because, as with e, it is nearly constant in thesampled layer and it is not changed by sampling disturbance. p? is the measured p?r and p?max is the mean in situeŠective stresses, (s?vo+2s?ho )/3, where s?ho is assumed tobe 0.5s?ho, i.e., Ko=0.5. Compared with Fig. 20, slightlybetter linearity in Fig. 21 is obtained, though the scatterin the relation between them cannot be eliminated. Thistendency is also applicable to test results from the modelground, although these test results are not presented inthis paper. It can be concluded that GBE is mainlygoverned by p?r and the eŠects of structure destructionand the in situ eŠective stresses before sampling are notimportant. However, this conclusion is obtained forreconstituted soil and ˆeld samples, where Ip is moderateand the sensitivity is not high. Further study is required toconˆrm whether this conclusion is valid for low plasticityand sensitive clays, such as quick clay distributed in Scandinavia and North America.This paper investigated the main geometrical featuresof samplers aŠecting sample quality. Samples were obtained from both laboratory simulated sampling formodel ground and sampling in the ˆeld. Sample qualitywas evaluated using two nondestructive methods: residual eŠective stress and maximum shear modulus. Theresults of this study show that sample quality is dependent on the geometry designs of the sampling tube, theseare, edge angle and area ratio. Comparative results ofsample quality among diŠerent samplers were obtainedfrom samples of the same location inside the samplers.Important points in this paper are summarized as follows:1) Small edge angle is very important for a samplingtube to minimize sample disturbance.2) The wall thickness, and thus, area ratio cannot bethe sole and independent geometrical factor aŠecting sample quality. A strong dependency on theedge angle is observed. If edge angle is kept smallenough, larger area ratio can be tolerated. In contrast, if edge angle is increased, the area ratio mustbe speciˆed and kept as small as possible for a welldesigned and successful sampler.3) The eŠect of a piston plays less signiˆcant role indisturbance for ˆeld sampling. Comparative resultsof samples obtained from stationary pistons andopen drive samplers show slight diŠerences in sample quality.4) Residual eŠective stress ( p?r ) and maximum shearmodulus (GBE ) are not independent parameters butare closely related.ACKNOWLEDGEMENTThe authors gratefully acknowledge Toa Corporationfor conducting site investigation and providing soil samples.REFERENCES1) Andresen, A. A. and Kolstad, P. (1979): The NGI 54 mm samplerfor undisturbed sampling of clays and representative sampling ofcoarser materials, Proc. Int. Symp. of Soil Sampling, Singapore,13–21.2) Burland, J. B. (1990): On the compressibility and shear strength ofnatural clays, Geotechnique, 40(3), 329–378.3) Chandler, R. J., Hardwood, A. H. and Skinner, P. J. (1992): Sample disturbance in London clay, Geotechnique, 42(4), 577–585.4) Clayton, C. R. I., Siddique, A. and Hopper, R. J. (1998): EŠects ofsampler design on tube sampling disturbance-numerical and analytical investigations, Geotechnique, 48(6), 847–867.5) Hight, D. W., Boese, R., Butcher, A. P., Clayton, C. R. I. andSmith, P. R. (1992): Disturbance of the Bothkennar clay prior tolaboratory testing, Geotechnique, 42(2), 199–217.6) Hvorslev, M. J. (1949): Subsurface exploration and sampling ofsoils for civil engineering purposes, U. S. Waterways ExperimentalStation, Vicksburg.7) Jamiolkowski, M., Lancellotta, R. and Lo Presti, D. C. F. (1994):Remarks on the stiŠness at small strains of six Italian clays, Proc.Prefailure Deformation of Geomaterials, 2 (eds. by Shibuya, S., SAMPLING TUBE GEOMETRYMitachi T. and Miura, S.), Balkema, 817–836.8) JGS (1998): Standard of Japanese geotechnical society for soil sampling-standards and explanations (English version), Japanese Geotechnical Society, Tokyo.9) Kallstenius, T. (1958): Mechanical disturbances in clay samplestaken with piston samplers, Proc. R. Swedish Geotech. Inst., 1–75.10) Kawaguchi, T., Mitachi, T. and Shibuya, S. (2001): Evaluation ofshear wave travel time in laboratory bender element test, Proc. 15thICSMGE, 1, 155–158.11) Kawaguchi, T. and Tanaka, H. (2008): Formulation of Gmax fromreconstituted soils and its application to Gmax measured in the ˆeld,Soils and Foundations, 48(6), 821–831.12) Ladd, C. C. and Lambe, R. W. (1963): The strength of undisturbedclay determined from undrained tests, ASTM-NRC Symp. onShear Testing Soils, Ottawa, STP 361, 342–371.13) Landon, M. M., DeGroot, D. J. and Sheahan, T. C. (2007): Nondestructive sample quality assessment of a soft clay using shearwave velocity, J. of Geotech. and Geoenv. Eng., 133(4), 424–432.14) La Rochelle, P., Sarraih J., Tavenas F., Roy M. and Leroueil, S.(1981): Causes of sample disturbance and design of a new samplerfor sensitive soils, Can. Geotech. J., 18(1), 52–66.15) Lefebvre, G. and Poulin, C. (1979): A new method of sampling insensitive clays, Can. Geotech. J., 16(1), 226–233.16) Lunne, T., Berre, T. and Standvik, S. (1997): Sample disturbanceeŠects in soft low plastic Norwegian clay, Proc. Int. Symp. on Recent Developments in Soil and Pavement Mechanics, 81–102.17) Matsumoto, K., Horie, H. and Yamamura, M. (1968): Study onboring and sampling of saturated alluvial clays (3rd report), Reportof the Port and Harbour Research Institute, 7(2), 96–113 (inJapanese).18) Matsumoto, K., Horie, H. and Yamamura, M. (1969): Study onboring and sampling of saturated alluvial clays (4th report), Reportof the Port and Harbour Research Institute, 8(2), 3–19 (inJapanese).19) Mitachi, T., Kudoh, Y. and Tsushima, M. (2001): Estimation of insitu undrained strength of soft soil deposits by use of unconˆnedcompression test with suction measurement, Soils and Foundations, 41(5), 61–71.20) Nishida, K., Tanaka, H. and Mitachi, T. (2006): In‰uence of sample quality on shear wave velocity and residual eŠective stress,Proc. 16th Int. OŠshore (Ocean) and Polar Engineering Conference, 2, 362–368.21) Okumura, T. (1971): The variation of mechanical properties of claysamples depending on its degree of disturbance, Proc. Special Session on Quality in Soil Sampling, 4th Asian Regional Conf. onSMFE, 73–81.22) Osterberg, J. O. and Murthy, W. P. (1979): State of the art of undisturbed sampling of cohesive soils, Proc. Int. Symp. of Soil Sampling, Singapore, 43–50.23) Ridley, A. M., Dineen, K., Burland, J. B. and Vaughan, P. R.24)25)26)27)28)29)30)31)32)33)34)35)36)37)38)39)107(2003): Soil matrix suction: Some examples of its measurementsand application in geotechnical engineering, Geotechnique, 52(2),1293–1322.Shibuya, S. and Tanaka, H. (1996): Estimate of elastic shear modulus in Holocene soil deposits, Soils and Foundations, 36(4), 45–55.Shibuya, S., Hwang, S. C. and Mitachi, T. (1997): Elastic shearmodulus of soft clays from shear wave velocity measurement,Geotechnique, 47(3), 593–601.Shogaki, T. and Kaneko, M. (1994): EŠects of sample disturbanceon strength and consolidation parameters of soft clay, Soils andFoundations, 34(3), 1–10.Shogaki, T. (1996): A method for correcting consolidationparameters for sample disturbance using volumetric strain, Soilsand Foundations, 36(3), 123–131.Siddique, A., Farooq, S. M. and Clayton, C. R. I. (2000): Disturbances due to tube sampling in coastal soils, J. of Geotech. and Geoenv. Eng., 126(6), 568–575.Sub-Committee on soil sampling (1965): Proc. 6th ICSMFE, Montreal, 3, 64–71.Sub-Committee on soil sampling on international society for soilmechanics and foundation engineering (1981): Tokai UniversityPress.Tan, T. S., Lee, F. H., Chong, P. T. and Tanaka, H. (2002): EŠectof sampling disturbance on properties of Singapore clay, J. of Geotech. and Geoenv. Eng., 128(11), 898–906.Tanaka, H., Tanaka, M., Iguchi, H. and Nishida, K. (1994): Shearmodulus of soft clay measured by various kinds of tests, Proc.Prefailure Deformation of Geomaterials, 1 (eds. by Shibuya, S.,Mitachi T. and Miura, S.), Balkema, 235–240.Tanaka, H., Sharma, P., Tsuchida, T. and Tanaka, M. (1996):Comparative study on sample quality using several types of samplers, Soils and Foundations, 36(2), 57–68.Tanaka, H. and Tanaka, M. (1999): Key factors governing samplequality, Proc. Int. Symp. on Characterization of Soft Marine Clays(eds. by Tsuchida, T. and Nakase, A.), Balkema, 57–81.Tanaka, H. (2000): Sample quality of cohesive soils: Lessons fromthree sites, Ariake, Bothkennar and Drammen, Soils and Foundations, 40(4), 57–74.Tanaka, H., Locat, J., Shibuya, S., Soon, T. T. and Shiwakoti, D.R. (2001): Characterization of Singapore, Bangkok, and Ariakeclays, Can. Geotech. J., 38(2), 378–400.Tanaka, H. and Tanaka, M. (2006): Main factors governing residual eŠective stress for cohesive soils sampled by tube sampling,Soils and Foundations, 46(2), 209–220.Tsuchida, T. (2000): Evaluation of undrained shear strength of softclay with consideration of sample quality, Soils and Foundations,40(3), 29–42.Viggiani, G. and Atkinson, J. H. (1995): Interpretation of benderelement tests, Geotechnique, 45(1), 149–154.
  • ログイン
  • タイトル
  • Proposal of a Simple Method for Assessing the Susceptibility of Naturally Deposited Clay Grounds to Large Long-term Settlement due to Embankment Loading
  • 著者
  • "Motohiro Inagaki, Masaki Nakano, Toshihiro Noda, Mutsumi Tashiro, Akira Asaoka"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 109〜122
  • 発行
  • 2010/02/15
  • 文書ID
  • 64345
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 109–122, Feb. 2010PROPOSAL OF A SIMPLE METHOD FOR ASSESSING THE SUSCEPTIBILITYOF NATURALLY DEPOSITED CLAY GROUNDSTO LARGE LONG-TERM SETTLEMENT DUE TO EMBANKMENT LOADINGMOTOHIRO INAGAKIi), MASAKI NAKANOii), TOSHIHIRO NODAii),MUTSUMI TASHIROiii) and AKIRA ASAOKAii)ABSTRACTA simple method that utilizes the results of laboratory tests has been proposed for determining the susceptibility ofsoft clay grounds to large residual consolidation settlement due to embankment loading. It was found that there is apossibility of large long-term settlement if the sensitivity and compression index ratios of the clay material that constitutes the ground are equal to or more than 8.0 and 1.5, respectively. The compression index ratio is deˆned in thispaper as the ratio (Cc/Ccr) of the steepest gradient of the compression curve of an undisturbed sample to that of theremolded sample. Through the SYS Cam-clay model, an elasto-plastic constitutive model that describes the actions ofthe soil skeleton structure, it was found that clays with large sensitivity and compression index ratios are characterizedby initially highly structured soils and that decay/upgradation of the structure can easily occur due to plastic deformation. In addition, by following Schmertmann's graphic method for in-situ compression curve (1953), this paper proposes a method of deducing the in-situ initial conditions from the results of laboratory consolidation tests on undisturbed samples. These investigations revealed not only that large delayed settlement is facilitated in clays, whichhave higher degrees of structure and faster rates of structural decay, but also that the De method and other simplemethods of predicting settlement may underestimate the amount of settlement.Key words: clay, (compressive index ratio), (sensitivity ratio), soil structure, (SYS Cam-clay model) (IGC: E2)the load of the embankment without failing. Once conˆrming that the ground will not fail, the deformation ofthe ground due to the load of the embankment is calculated in order to examine whether the embankment will undergo any functional disorder. This method of design isbased on the thought that the ground is at most risk at thetime of completion of embankment construction and thatonce the embankment has been constructed, the groundwill become stronger with the passage of time because itsdensity increases due to consolidation resulting from thecompression caused by the dissipation of excess porewater. This design approach, however, is well-suited forsu‹ciently remolded normal consolidation soil. As such,in the case of naturally deposited clay grounds with developed skeleton structures, one may encounter ground behavior that cannot be foreseen by this design approach.Using the soil-water coupled ˆnite deformation analysis program GEOASIA (Asaoka et al., 1994; Asaoka andNoda, 2007; Noda et al., 2008) with the SYS Cam-claymodel (Asaoka et al., 2002), which is an elasto-plasticconstitutive model capable of describing the action of thesoil skeleton structure (structure, overconsolidation andINTRODUCTIONThere are approximately 50 sites at which embankments for highways have been constructed on soft groundby the former Japan Highway Public Corporation. Inabout 20z of these sites there has been a problem with aresidual settlement of 1 m or more after the entry of service. For example, about 2 m of settlement was predictedbefore embankment construction at the Kanda site (nearthe Hitachi Minami Oota Interchange on the Joban Expressway). However, since the entry of service, more than20 years ago, it has continued gradually, resulting in asmuch as 4 m of settlement to date. Because of this, maintenance and repair work have been carried out repeatedlyfor such things as rectifying level diŠerences, expandingthe road shoulders, and repairing neighboring facilities.The accumulated cost of this work has been about 2 billion yen in the past 14 years, which works out to be asmuch as 900 million yen per meter of road.Usually, embankments for soft grounds are designed inthe following manner. First, the stability of the system isevaluated by determining whether the ground can sustaini)ii)iii)Central Nippon Expressway Company Limited, Nagoya, Japan.Professor, Department of Civil Engineering, Nagoya University, Nagoya, Japan.Research Associate, ditto (mutsumi@civil.nagoya-u.ac.jp).The manuscript for this paper was received for review on July 8, 2009; approved on November 30, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.109 110INAGAKI ET AL.anisotropy), the authors have clariˆed that large delayedand major consolidation settlements leading to largeresidual settlements similar to that mentioned at the Kanda site is caused by the decay of structure of highly structured naturally deposited clay (Asaoka et al., 2000; Nodaet al., 2005). In other words, when highly-structured clayin-situ is subjected to large stress increases greater thanthe consolidation yield stress, a large amount of compression occurs because of the signiˆcant structural degradation. Furthermore, it has also been shown that because ofthe softening that co-occurs with plastic compression, thedissipation of excess pore pressure is delayed, resulting inthe settlement being extended over a long period.The large delayed settlement described above,however, does not always occur in soft clay grounds. In80z of the sites mentioned earlier, residual settlementhas been suppressed. The computer program mentionedabove is eŠective in predicting whether or not largedelayed settlement will occur in a ground. However, sinceit is not practical to carry out such computer calculationsat all sites, a simple initial screening method is necessaryfor evaluations. This paper ˆrst sorts out the commontrends at clay ground sites that have exhibited large residual settlement. This is accomplished by taking examplesof actual highway embankments constructed on soft claygrounds and sorting out their soil proˆles, the loadingconditions, the actual amounts of settlement, and theresults of laboratory tests with respect to each site. Theprimary aim of this paper is to propose a method of judging the susceptibility of clay to large delayed settlementby focusing attention on two indices that can be determined from relatively easy laboratory tests. These two indices are the compression index and sensitivity ratios.The second aim of this study was to utilize the SYSCam-clay model to explain, in terms of elasto-plasticmechanics, the distinctive features of clays in which alarge amount of delayed settlement occurs. By paying attention to the action of the structure which governs themechanical behavior of the clay, we examined how thesettlement is aŠected by the degree of structure and themanner in which the structure changes.Furthermore, by following Schmertmann's graphicmethod (1953), this paper proposes a method for deducing the initial conditions of in-situ clay with considerationto the disturbance due to sampling and to explain themechanism of large residual settlement behavior througha comparison of the compressibilities of the in-situ claywith those of undisturbed samples in laboratory tests. Finally, a further aim is to use the soil-water coupled ˆnitedeformation analysis program GEOASIA to clarify thereason why the simple method of prediction of consolidation settlement (the De method) laid out in the formerJapan Highways Public Corporation's design manualcannot be used to predict large delayed settlement.Table 1. Outline of the sites investigated and actual residual settlement at each siteSiteHeight ofThickness of Residual(Layer) embankment soft clay layer settlement(m)(m)(cm)Measuring pointafter entry intoservice (year)〈Small residual settlement〉A5.7303020B7.7286720C7233820D6.8142920E6135520F9112610G1010310〈Large residual settlement〉H82511212I91618816J7.53112220K52220025ACTUAL RESIDUAL SETTLEMENT DUE TOEMBANKMENT LOADING OBSERVED IN THESOFT CLAY GROUNDSTable 1 shows an outline of representative soft clayground sites together with the actual conditions of settlement at each site due to embankment loading. Theground layer structures of these sites are illustrated inFig. 1 using the symbols speciˆed in JIS0051-2000,Method of Classiˆcation of Geomaterials for Engineering Purposes. The ``thickness of the soft clay layer''shown in Table 1 is the sum of the thicknesses of the cohesive soil (Cs) and the organic soil (O; grey colored layer) in Fig. 1.According to the former Japan Highways Public Corporation Design Guideline (Earthwork), grounds composed of soft layers (including loose sand layers) 15 m orthicker are classiˆed as deep layer-type (Type III)grounds, where settlement is said to extend over longperiods. The majority of sites mentioned in Table 1 belong to this deep layer type. It is evident from the valuesshown in the table that it is not possible to judge the extent of long-term residual settlement purely on the basisof the thickness of the soft clay layer.Embankment loading on soft clay grounds may alsocause stability problems in addition to settlement problems. If the soft clay layer is situated near the surface layer of the ground, stability problems occur often. Becauseof this, ground improvement measures, such as verticaldrain method, are carried out in certain cases before theconstruction of an embankment. In the sites studied here,the sand drains methods was applied at Site-F and Site-K,while Site-G used a cardboard drain. The masspermeability improvement of the ground due to thedrains promotes the consolidation settlement of the soft JUDGMENT OF DELAYED SETTLEMENTFig. 1.111Histograms of the sites studiedclay layer. In cases like Site-F and Site-G, where the softclay layer is only about 10 m thick and the drain eŠect extends over the entire soft clay layer, drains can be eŠective in signiˆcantly reducing residual settlement. At SiteK, however, the drain was placed to a depth of only 6 mfrom the ground surface despite the 22 m thick soft claylayer. As a result, the residual settlement reduction eŠectis seen to have been small.As for the problem of settlement, the basic principle inthe former Japan Highways Public Corporation DesignGuideline was not to take countermeasures before embankment construction but to execute maintenance andrepairs as necessary after the entry of service. Among thegrounds with thick deposited soft clay layers, there arecases of naturally deposited clay grounds in which disturbance has caused decreases in strength. In such grounds,and especially in the case of those similar to Site-I andSite-J, which have experienced no stability problems because of the presence of a sand layer in the upper part ofthe ground, embankment loading without any priorground treatment has produced large residual settlement.The height/weight of the embankment also needs to betaken into consideration. The open circles in Fig. 1 indicate the vertical eŠective stress (initial eŠective overburden pressure+eŠective stress increase due to embankment loading as determined from Osterberg's In‰uenceChart, 1957) within the ground after embankment loading. The ˆlled symbols denote the consolidation yieldstress determined from oedometer tests carried out on un-disturbed specimens sampled at each depth. The ˆlled circles represent the undisturbed specimens sampled beforeembankment loading from the ground directly beneaththe embankment site. The ˆlled triangles indicate thosesampled from the bare ground parts near the embankment after the entry of service, where the eŠect of embankment loading is small. Taking account of the consolidation yield stress distributions at Site-H, Site-I, andSite-J in the direction of depth, it is assumed in this paperthat the eŠect of sampling time and sampling location onthe consolidation yield stress is small. Usually, little stresshistory is experienced by alluvial clay grounds due to suchthings as ground deformation during the deposition stageand erosion. Because of this, the initial eŠective overburden pressure is almost equal to, but slightly smaller than,the consolidation yield stress (i.e., the soil is in a slightlyoverconsolidated state) in most cases. As a result, in thesites studied here, the relatively large embankment loadsdue to tall embankments of at least 5 m in height causethe stress states to exceed the consolidation yield stresseven in fairly deep locations of the soft clay layer. Apartfrom the clays in sites such as Site-F and Site-G, wherethe clay layers exist in a shallow part of the ground andthe consolidation yield stresses are small, the embankment loading results in the clays of most sites being understress levels slightly exceeding the consolidation yieldstresses. From the above, it can be understood that it isnot possible to judge the extent of residual settlementfrom only the stress levels. INAGAKI ET AL.112METHOD OF JUDGING CLAYS SUSCEPTIBLE TOLARGE RESIDUAL SETTLEMENT THROUGH THERESULTS OF CONVENTIONAL LABORATORYTESTSAs explained above, it is not possible to judge the extent of residual settlement by only the thickness of a softclay layer or by its stress level. In this section, the distinctive trends of soft clays that exhibit large residual settlement are determined by examining the results of laboratory tests commonly carried out at many sites, and criteria for assessing this type of clay are proposed. Attentionwas focused on parameters that are strongly related to thedecay of structure because the large delayed settlement atthe Kanda site on the Joban Expressway was caused bythe structural decay of highly structured clay. In thisstudy, the two parameters used for assessing the clayswere 1) the sensitivity index, which can be obtained fromunconˆned compression tests, and 2) an originalparameter deˆned in this study, called the compressionindex ratio, which can be determined from oedometertests.The gradient of the compression curve of an undisturbed sample becomes a maximum near stress levelsjust exceeding the consolidation yield stress, and largecompression occurs at this stage. The majority of the softclay sites studied here reach these stress levels due to embankment loading. For this reason, attention was paid tothe steepest gradient immediately after exceeding the consolidation yield stress in the compression curves for theundisturbed samples. This is termed the compression index Cc. In addition, attention was also paid to thegradient of the compression curve for remolded samples.This value was deˆned as Ccr. Remolded samples refersto those that are obtained from undisturbed samples bysu‹ciently kneading them without changing the watercontent or after adding the proper quantity of water.In actual practice, oedometer tests are rarely carriedout on remolded samples. For this reason, Ccr was calculated in a uniˆed manner from the liquid limit wL (z) us-Fig. 3.ing the following empirical equation proposed by Skempton (1944).Ccr=0.007 swL-10t(1)In this paper, the value of Cc/Ccr was deˆned as thecompression index ratio (Fig. 2).The sensitivity and compression index ratios of the softclays at Site-A to Site-K investigated in this paper areshown in Figs. 3(a) and (b), respectively. According toTerzaghi and Peck (1967), clays with sensitivity ratios between 4 and 8 are classiˆed as sensitive clays, whereasthose with sensitivity ratios of 8 or higher are classiˆed asextra-sensitive clays. In addition, clays with low or medium sensitivity ratios are expressed by the following equation.Cc=1-1.3Ccr=0.009 swL-10t(2)In other words, their compression index ratios are between 1 and 1.3. Furthermore, it has been shown that thecompression index ratio is even greater in clays with extremely high sensitivity ratios and that Eq. (2) above canonly estimate the lower limit of the amount of compres-Fig. 2.Deˆnition of the compression index ratioCharacteristics of the soft clays at the sites investigated JUDGMENT OF DELAYED SETTLEMENT113solidation tests should be performed on remolded specimens when designing embankments and other structuresto be constructed on soft ground.INTERPRETATION OF THE MECHANICALCHARACTERISTICS OF CLAYS SUSCEPTIBLE TOLARGE RESIDUAL SETTLEMENT THROUGH THESYS CAM-CLAY MODELFig. 4. Classiˆcation based on the sensitivity and compression indexratiossion.It can be noticed that among the clays in the sites investigated here, those in sites that exhibited large residualdeformation have large sensitivity ratios and can be classiˆed as extra-sensitive clays. At the same time, theircompression index ratios are also large. With regard tosamples whose sensitivity and compression index ratioswere both determined, Fig. 4 classiˆes the extent of settlement at the respective sites on the basis of these twoparameters. The ˆgure indicates that, generally speaking,a compression index of 1.5 or greater and sensitivity ratioof 8 or greater, can be used as criterion to judge clays thatexhibit large residual settlement. In the future, when anaturally deposited clay is encountered where the embankment load exceeds the preconsolidation stress, reference to the criterion shown in Fig. 4 will allow judgmentof whether or not long-term large settlement is likely tooccur.The data for Site-G shown in Fig. 4 is for Ariake clay,which is a well-known extra-sensitive clay. As mentionedearlier, because of the stability problem due to the softclay layer extending up to the vicinity of the ground surface, the embankment at Site-G was constructed afterground improvement by drain methods. As a result, consolidation of the soft clay layer was promoted, and settlement had mostly subsided before the entry of service.Consequently, the amount of residual settlement at thissite is small.In order to collate the test results in the manner mentioned above, it is necessary to use remolded samples toobtain test results that will become the criteria for deˆning the sensitivity and compression index ratios. Giventhat the compression curve (NCL) of remolded specimenssamples deˆnes the elasto-plastic parameters unique tothe type of soil, it can be understood that remolded samples are deˆned as those in which the soil skeleton structure has been lost completely. The authors suggest that,as a rule, distinct methods for specimen preparation andtesting on remolded samples should be speciˆed and con-As described above, clays that exhibit large residualsettlement have a tendency to have high sensitivity andcompression index ratios. The aim of this section is to explain this characteristic in the language of elasto-plasticmechanics through the use of the SYS Cam-clay model.The compressibility and strength of soils are determined by the soil type and their soil conditions. In theSYS Cam-clay model, the type indicates the elasto-plasticparameters, which are non-dependent on the soil skeletonstructure as well as the evolution parameters that determine how the soil skeleton structure changes. If the soil issaturated, the condition is deˆned by the void ratio, theamount of stress, and the degree of soil skeleton structure. Furthermore, remolded specimens and undisturbedspecimens can be considered the same type of soil, theremolded specimens being in a state of having completelylost their soil skeleton structures. Therefore, expressingthe compressibilities and strengths of remolded specimens and undisturbed specimens by the respective ratios(i.e., compression index and sensitivity ratios) can be interpreted to mean that the eŠects of the elasto-plasticparameters are eliminated, while the eŠects of the degreeof the soil skeleton structure and how it changes (i.e.,evolution parameters) are made more prominent.In previous research studies (for example, Noda et al.,2005), the authors have shown that structure dominatesthe mechanical characteristics of naturally depositedclays even within the skeleton structure and that thedelayed consolidation settlement behavior leading tolarge residual settlement is particular to clays with a highdegree of structure. In the current study, special attentionwas paid to the degree of evolution of structure in theskeleton structure of the clays and the manner in whichthe structures change in order to investigate how thesefactors aŠect the sensitivity and compression index ratios.Figures 5 and 6 show the eŠects of the initial degree ofstructure (1/R*0 ) and the structural decay rate (structuraldegradation index a) on the undrained shear behavior (assuming unconˆned compression tests) and one-dimensional compression behavior (assuming oedometer tests),which were obtained through the responses of the SYSCam-clay model in a uniform deformation ˆeld. The setof material constants shown in Table 2 for the clay ofSite-I was used in these computations as the parametersrepresenting conventional clay.It can be observed from the ˆgures that, with an increasing degree of initial structure (Fig. 5, 1/R*0 : Large)and faster structural decay rate (Fig. 6, a: Large), thepeaks of undrained shear behaviors become high and the INAGAKI ET AL.114Fig. 5.Fig. 6.Table 2.EŠect of initial degree of structure (a=0.22)EŠect of initial degree of structure (1/R0*=45.5)Material constants used in the analysis (Site-I)〈Elasto-plastic parameters〉Compressive index lÃ0.29Swelling index kã0.05Critical state constant M1.90NCL intercept N2.75Poisson's ratio n0.1steepest gradients of the compression curves becomelarge. In other words, it can be said that clays with largesensitivity and compression index ratios Cc/Ccr, whichlead to large residual settlement, have high degrees ofstructure. In addition, such structures can evolve easily(i.e., structural decay/upgradation can occur easily).In this study, the following equation is used as the evolution law that expresses structural decay/upgradation.{R_ *=JU * (1-cs)(-D p[)+cs〈Evolution parameters〉Normal consolidation index m2.0Structural degradation index a0.22〃b0.65〃cs0.2Rotational hardening index br0.001Rotational hardening limit mb1.0U *=aR*b(1-R*)D}2¿D ps¿ ,3(3)In the above equation, D p[ and ¿D ps¿ indicate the volumetric component of plastic stretching and the deviatorcomponent of the Euclidian norm, respectively. In orderto reproduce the experimental fact that structural decayin clay occurs more easily under compression than undershear, the value of cs is made small in the case of clay. In JUDGMENT OF DELAYED SETTLEMENTthe present computations, the value of cs was taken as0.2. According to the above equation, the plastic swelling(-D p[º0) caused by the loss of overconsolidation willproduce structural upgradation ( R*ª 0). Since loss ofoverconsolidation is faster than structural decay in clays,structural upgradation will occur before the peak in thecase of undrained shear and before the consolidationyield stress in the case of one-dimensional compression.Furthermore, a, which determines the structural decayrate, in‰uences not only the rate of structural degradation (decay) but also the rate of upgradation. Consequently, with increasing structural decay rates, structuredoverconsolidated clays, such as naturally deposited clay,exhibit larger sensitivity ratios (peak strengths) alongwith structural upgradation. Since the structural decayafter this stage is also rapid, the compression index ratioalso becomes large at the same time (in the case of evolution laws where only structural decay occurs, the compression index ratio becomes large at faster structuraldecay rates, but the sensitivity ratio decreases).The evolution laws of the soil skeleton structure are important enough to be referred to as the 2nd set of constitutive equations. However, with respect to structure,overconsolidation, and anisotropy that occur due to plastic deformation, evolution/loss of all three factors takesplace simultaneously. Therefore, it is not possible to formulate evolution laws for each of these factors directlyfrom the test results. However, the evolution law ofstructure shown in Eq. (3) is capable of explaining thehigh sensitivity and compression index ratio characteristics of the clays within the same framework. As such, it iseŠective as an evolution law that simulates the mechanical behavior of naturally deposited clays well.THE CONDITIONS THAT LEAD TO OCCURRENCEOF LARGE RESIDUAL SETTLEMENT BASED ONDEDUCTION OF IN-SITU INITIAL CONDITIONSAs discussed in the preceding sections, clays exhibitinglarge residual settlement are characterized by the fact thatthey can be classiˆed through laboratory tests as thosewith both high sensitivity and high compression index ratios. The SYS Cam-clay model also showed that theseclays could be described as having high levels of structureand a structure can evolve easily. This section examineswhy it is di‹cult to predict in-situ large residual settlement in such types of clays.When predicting the in-situ settlement that could occur, it is usually assumed that the undisturbed specimenssampled from the site are in the same condition as the insitu clay and that the compression characteristics of bothare the same. The method of prediction ( De method) ofconsolidation settlement laid down in the former JapanHighway Public Corporation's Design Guideline is alsoone based on the above assumption. In this method, thecompression curves of undisturbed specimens are used tocalculate the amount of settlement by determining theamount of variation in the pore ratio with respect to thestress increase within the ground due to embankment115loading. Although this simple method of prediction hasshown a fair extent of accuracy in many sites, it has beenknown to underestimate the amount of settlement attimes. In other words, although there are instances inwhich the compressibility of the in-situ clay is well reproduced by the compressibility of the undisturbed specimens determined through laboratory tests, there areother instances where the compressibility of the in-situclay is greater. Large residual settlement occurs in the latter instance.Samples used for laboratory tests experience complicated stress paths during sampling, removal from thesampling tube, specimen preparation, and setting-up onthe testing machine. Therefore, although undisturbedspecimens are the ones with little disturbance, some variation from the in-situ condition cannot be avoided. Furthermore, since disturbance is irreversible plastic deformation, it is impossible, in principle, to restore the specimens to their predisturbance condition. The soil type,however, is not changed by disturbance. Therefore, bytaking into account the changes that take place due to disturbance, that is, by considering the laboratory testresults of undisturbed specimens that were closest to theclays in-situ, the initial conditions and mechanical characteristics of the in-situ clay are deduced in this paper. Inaddition, the relative ease or di‹culty of predicting settlement through laboratory test results is examined by comparing the compressibilities of the clays in-situ with thosedetermined from laboratory tests on undisturbed specimens.The initial conditions of the clays in-situ are deducedhere by referring to Schmertmann's graphic method(1953) for the compression curves of in-situ sediments.According to this method, if the compression curve obtained for undisturbed specimens is similar to the curveKu shown in Fig. 7, the compression curve K in-situ isdeduced in the following manner. First, it is assumed thatthe undisturbed specimen was set up on the testingmachine without any change in the water content. Consequently, the pore ratio ea0 in the initial condition (pointB?) of the laboratory test will be the same as that of thein-situ clay. Therefore, point A, which is equivalent tothe overburden pressure s?v0, becomes the in-situ initialcondition. Next, by assuming that the consolidation yieldstress pc of curve Ku is equal to the consolidation yieldstress of curve K, the point denoting the initial condition(point A) and that denoting the consolidation yield stress(point D) are joined by a line with a gradient equal to thegradient Cs of the swelling line of curve Ku. The in-situcompression curve K is then obtained by joining the consolidation yield stress point (point D) and the point (pointF) that lies on curve Ku and is equivalent to 0.4 times theinitial pore ratio.The details of this graphical method are given in theoriginal publication (Schmertmann, 1953). The most important aspect of this method is point D, which indicatesthe consolidation yield stress. Regarding the consolidation yield stress of the in-situ compression curve,although Schmertmann suggested a number of methods 116INAGAKI ET AL.Table 3‚ Method for estimating initial in-situ state, considering disturbance during samplingInitial in-situ state quantitiesEstimating methodSpeciˆc volume v (=1+e)Initial value in test of``undisturbed'' sampleStressstateSkeletalstructureVertical eŠectivestress s?v0EŠective overburden pressureLateral stresscoe‹cient K0(stress ratio h0)General value K0=0.5(h0=0.75)Anisotropy z0Initial value in test of``undisturbed'' sampleStructure 1/R*0Values which satisfy both the 4conditions above and theconsolidated state stress for an``undisturbed'' sampleOverconsolidation1/R*0Fig. 7. Schmertmann's graphic method for compression curves of insitu sedimentsslow characteristics. The method of estimating each initial in-situ state is shown in Table 3.N-v0-là ln p?0 -(là -kã ) lnfor deducing it, he did not elaborate on it. In addition, hepresented experimental evidence indicating that the consolidation yield stress decreases due to disturbance.However, unless the extent of disturbance that occursfrom the sampling in-situ up to the time of commencingthe laboratory test is known accurately, it is di‹cult todetermine how much the consolidation yield stress of thein-situ clay has decreased compared with an undisturbedspecimen. For this reason, in later studies (Terzaghi andPeck, 1967, etc.), the consolidation yield stress obtainedfrom the compression curve Ku of the undisturbed specimen was applied just as it was to the compression curve Kof the in-situ clay.For the sake of simplicity, the above graphical methodwas used in this study in order to deduce the in-situ initialconditions from the compression curves of undisturbedspecimens and, from them, the compressibility characteristics. In the SYS Cam-clay model, the initial conditionsare expressed by the speciˆc volume (v0), stress state (s?v0,K0) and three soil skeleton structures ( R*0 (structure)/R0(overconsolidation)/z0 (anisotropy)). Given that point Ain Fig. 7 denotes the initial condition of the clay in-situ,the speciˆc volume v0 and vertical eŠective stress s?v0 willbe decided by it. As a general value for all clays, the lateral stress coe‹cient in-situ was assumed to be K0=0.5(stress ratio h0=0.75), referring to the in-situ test resultsfor the clays of Site-A, B, C and I shown in Table 2.With regard to the soil skeleton structures, the compression curve of the in-situ clay was ˆrst determined sothat it satisˆed the condition that the consolidation yieldstress of the undisturbed specimen and the in-situ claywas equal. The three soil skeleton structures were thenobtained from the initial conditions. Since the above initial state quantities are related through Eq. (4), itbecomes possible to determine each initial state quantitatively, in the case of clays, for example, if it is assumedthat evolution/degradation of anisotropy are extremelyØ»M2+(h0-z0)2 R0*=0M2R0(4)The compression curves Ku of the undisturbed samples(indicated by [1]) determined assuming laboratory testsand the compression curves K of the in-situ clay (indicated by [3]) deduced as described above are shown in Fig. 8with respect to clays with slow and rapid structural decayrates and those that are highly structured and less structured initially. The compression curve NCL of clay thathas lost its structure completely (indicated by [2]) is alsoshown in the same ˆgure. Assuming the amount of stressincrease in-situ due to embankment loading to be Ds?v =150 kPa (corresponding to the mid-depth of the clay layerin Fig. 11), a comparison of the amount of compressionafter the initial overburden pressure (Fig. 8(a)) showsthat, in the case of clays with high sensitivity and compression ratios (i.e., clays having highly developed structures as well as rapid structural decay rates), the in-situcompressibility is greater than that of the undisturbedsample, according to laboratory test results.The compressibility of the clay at Site-J, where largedelayed settlement occurred, is illustrated in Fig. 9(a). Initially, the compression curve of the undisturbed sampleis in a bulky (highly structured) state compared with theremolded one. This bulky state is lost rapidly (decay israpid) after the consolidation yield stress is reached. Because of this, the in-situ settlement was greater than thatdetermined through laboratory tests on the undisturbedsample. On the other hand, in the case of Site-F, whereno large delayed settlement occurred, even though thecompression curve of the undisturbed sample is in abulky (highly structured) state compared with theremolded one, loss of the bulky state does not occureasily (decay is slow) even after reaching the consolidation yield stress as illustrated in Fig. 9(b). Since the compressibilities of the undisturbed sample and the in-situclay due to embankment loading are nearly equal, theamount of settlement predicted by laboratory tests on the JUDGMENT OF DELAYED SETTLEMENTFig. 8.117Compressive behavior of ``undisturbed'' clay in-situ and in the laboratoryundisturbed sample agrees relatively well with the actualmeasured settlement. In the case of less structured claytoo, the changes in the compressibilities before and aftersampling are small because the eŠect of structural decayis primarily small. As a result, the amount of settlementpredicted from laboratory tests on the undisturbed sample can be expected to have a tendency to agree well withthe actual measured settlement.In addition to the possibility of large delayed settlement occurring in highly structured clays with rapidstructural degradation rates, there is also a possibility ofunderestimating the amount of settlement when simplemethods of prediction, such as the De method, are used.Therefore, it is necessary to perform detailed calculationsof the settlement using ˆnite element analysis methods,etc. in designs concerning the settlement of this type ofclay ground.The results of unconˆned compression tests on remolded and undisturbed samples of the clays in the two sites,described in Fig. 9(a) and (b) are presented in Fig. 10. Inthe case of highly structured clay with a rapid structuraldegradation rate such as the one in a, Site-J, the stressstrain curve of the undisturbed sample rises sharply in theinitial stages, reaches the peak value of stress early, andshows a decrease in strength after that, as is shown in Fig.10(a). On the other hand, in the case of highly structuredclay which has a slow structural degradation rate, such asthe one in b, Site-F, the stress-strain curve of the undisturbed sample rises very gradually but continuouslywithout exhibiting a clear peak, as can be seen in Fig.10(b). These characteristics also correspond well with therelationship to the structural degradation rate shown inFig. 6(a).SOIL-WATER COUPLED BEHAVIOR OF THEFOUR TYPES OF CLAY DESCRIBED ABOVEFinally, the above discussion was conˆrmed through INAGAKI ET AL.118Fig. 9.Fig. 10.Comparison of compression curvesComparison of unconˆned compression behaviorsoil-water coupled ˆnite element deformation analysisutilizing the SYS Cam-clay model. The case of a ground(similar in ground structure to Site-I) consisting of a softclay layer below a top sand layer and subject to a 10-membankment load is considered here (Fig. 11). The ˆnalamount of settlement calculated using the De method isconsidered to be the predicted value. It is compared herewith the time-settlement relationship determined by soilwater coupled ˆnite element deformation analysis, whichis considered to be the actual measured value.Table 4 shows the material constants and initial conditions used in the computations. It was assumed that theembankment was made up of very dense sand and thatthe sand layer was medium dense sand. The material constants assumed for the soft clay layer are the same asthose shown in Table 2. As in the case of Fig. 8 above,four types of clays were considered: (a) initially highlystructured clay with a rapid structural degradation rate,(b) initially less structured clay with a rapid structuraldegradation rate, (c) initially highly structured clay with aslow structural degradation rate, and (d) initially lessstructured clay with a slow structural degradation rate.To simplify the analysis, it was assumed that the speciˆcvolume, stress ratio, degree of structure, and degree ofanisotropy were uniform along the direction of depth initially in both the clay and sand layers, and the initial overconsolidation ratios were distributed according to theoverburden pressures.In the soil-water coupled ˆnite element deformationanalyses, the embankment was represented by elastoplastic ˆnite elements and by adding the ˆnite elements tothe ground as and when necessary. Since ground settlement progresses along with embankment loading, adjustments were made so that the crown of the embankmentattained the speciˆed height of 10 m at the time of completion of the embankment (120 days).In calculating the settlement using the De method, theclay layer was divided into ˆve 3-m thick layers, and theamount of settlement was calculated by hypothesizing thecompression curves of undisturbed samples at the center JUDGMENT OF DELAYED SETTLEMENTFig. 11.Table 4.Embankment(very dense)119Finite element mesh and boundary conditionsMaterial constants and initial conditions used in the computationsSand(medium dense)Soft clay(a) Highly Rapid(b) Less Rapid(c) Highly Slow(d) Less Slow0.050.052.702.3080.014.0〈Material parameters〉lÃ0.0630.29kã0.0120.050M1.4501.90N1.512.302.75n0.30.1m0.152.00a10.00b1.000.65cs1.000.2br0.3000.0010.220.65mbk (cm/sec)0.221.0×10rs (t/m 3)-51.001.0×10-51.0×10- 72.652.63〈Initial conditions〉v (=1+e)0.5661.250h00.600.601/R*01.374.00z00.7200.7202.702.300.5080.0of each layer. The curves shown earlier in Fig. 8 correspond to the compression curves of the in-situ clay andundisturbed samples of the center of the third layer(counting from the top) of the clay layer.In Fig. 12, which shows the amount of settlement directly below the center of the embankment, the dashedlines denote the predicted values (ˆnal amount of settle-14.00.900ment obtained by the De method) and the solid linesdenote the actual measured values (time-settlementrelationship determined through soil-water coupled analyses utilizing the SYS Cam-clay model). The predictedvalue of the ˆnal amount of settlement is greater than theactual measured values in three cases, (b), (c), and (d).This diŠerence can be attributed to the following three 120INAGAKI ET AL.Fig. 12. Comparison of settlements computed using the De methodand the soil-water coupled ˆnite deformation methodfactors. (1) DiŠerences in the theories: the stress increaseswithin the ground are based on elastic theory in the Demethod, whereas the soil is treated as an elasto-plasticmaterial in the SYS Cam-clay model. (2) DiŠerences inthe stress paths: the De method presumes one-dimensional compression at all times, whereas the eŠects ofsoil-water coupling, such as a partially undrained stateduring loading and multi-dimensional compression during the period of constant load, appear in the case of soilwater coupled analyses. (3) DiŠerences in the loadingconditions: the distributed load application is instantaneous in the De method. Whereas, in soil-water coupledanalyses, additional load such as overlay are applied according to the settlement. Whatever the case, the valuespredicted by the De method are on the safe side in thecases of (b), (c), and (d).In contrast, although the diŠerences in theories, stresspaths, and loading conditions are the same as in the casesof (b), (c), and (d), there is a possibility that the in-situsettlement would be greater than that predicted by the Demethod in the case of (a), which is an initially highlystructured clay with a rapid structural degradation rate.Moreover, although the conditions of permeability of theground in all four cases, (a) to (d), are the same, settlement in the case of (a) accelerates during the constantload period, but gradual settlement continues over a verylong period. This type of delayed consolidation settlement with acceleration of settlement is actually what hasbeen observed at the Kanda site mentioned at the beginning of this paper. Further details and the mechanism ofthe above phenomenon have been described in otherworks by various authors (for example, Noda, et al.,2005).CONCLUSIONSFrom the construction records for embankments onsoft ground of the former Japan Highway Public Corporation, the properties of soft clay grounds in which largelong-term settlement occurred were sorted out, and a simple method of judging clays that are susceptible to largesettlement was proposed. In addition, the characteristicsof this type of clay were theoretically discussed using theSYS Cam-clay model. The main conclusions obtainedthrough this study are as follows:(1) A simple method of judging clays susceptible to largelong-term settlement due to embankment loading wasproposed. The proposed method makes use of two indices. There is a possibility of large long-term settlement occurring if the sensitivity and compression index ratios of the clay material that constitutes theground are equal to or greater than 8.0 and 1.5, respectively. The compression index ratio is deˆned byCc/Ccr, where Cc is the steepest gradient of the compression curve of an undisturbed sample immediatelyafter reaching the consolidation yield stress and Ccr isthe gradient of the compression curve of the remolded sample. Because of the importance of these indices, the authors suggest that consolidation tests onremolded samples be performed when the design ofstructures to be constructed on soft ground is carriedout.(2) The SYS Cam-clay model, an elasto-plastic constitutive model that describes the actions of the soil skeleton structure, was used to discuss the two indices usedin the above method of judgment. It was clariˆed thatclays with high sensitivity and compression index ratios are characterized by high levels of structure initially and that further evolution of the structure canoccur easily, i.e., decay/upgradation of the structurecan occur easily.(3) Referring to Schmertmann's graphic method for thecompression curves of in-situ sediments (1953), amethod of deducing the in-situ initial conditions fromthe results of laboratory consolidation tests on undisturbed samples was proposed. Computation of thecompression curves of undisturbed samples and thoseof the in-situ clays through numerical analyses usingthe SYS Cam-clay model showed that the compressibilities of in-situ clay are only greater than those obtained assuming laboratory tests on undisturbed samples in the case of clays with both high levels of structure and rapid structural decay rates. These resultsshow not only that large delayed settlement occurredin clays that have high levels of structure and rapidstructural decay rates, but also that the De methodand other simple methods of settlement predictionmay underestimate the amount of settlement.REFERENCES1) Asaoka, A., Nakano, M. and Noda, T. (1994): Soil-water coupledbehavior of saturated clay near/at critical state, Soils and Foundations, 34(1), 91–105.2) Asaoka, A., Nakano, M., Noda, T. and Kaneda, K. (2000):Delayed compression/consolidation of natural clay due to degradation of soil structure, Soils and Foundations, 40(3), 75–85.3) Asaoka, A., Noda, T., Yamada, E., Kaneda, K. and Nakano, M.(2002): An elasto-plastic description of two distinct volume changemechanisms of soils, Soils and Foundations, 42(5), 47–57.4) Asaoka, A. and Noda, T. (2007): All soils all states all round geo- JUDGMENT OF DELAYED SETTLEMENT5)6)7)8)9)10)11)12)13)14)15)16)17)analysis integration, International Workshop on ConstitutiveModeling—Development, Implementation, Evaluation, and Application, Hong Kong, China, 11–27.Central Research Institute, Central Nippon Expressway CompanyLimited (2006): Soil Explorations Concerning the Properties ofClay Grounds (in Japanese).Japan Highway Public Corporation (1975): Report on Soil Exploration of Douou Highway ( Sapporo-Iwamizawa) between Higasinopporo and Toyohoro (in Japanese).Japan Highway Public Corporation (1976): Report on the 2nd SoilExploration of Douou Highway ( Sapporo-Iwamizawa) EbetsuArea (in Japanese).Japan Highway Public Corporation (1998): Design Guideline ( Sekkei youryou), Earthworks—Countermeasures for Soft Ground (inJapanese).Japan Highway Public Corporation (2002): Study on Rational Design and Construction of Deep Mixing Method (2) (in Japanese).Japan Highway Public Corporation (2004): Study on DynamicMechanical Characteristics of Soft Grounds (in Japanese).Japan Highway Public Corporation (2005): Study on DynamicCharacteristics and Deformation of Soft Clays (in Japanese).Noda, T., Asaoka, A., Nakano, M., Yamada, E. and Tashiro, M.(2005): Progressive consolidation settlement of naturally depositedclayey soil under embankment loading, Soils and Foundations,45(5), 39–51.Noda, T., Asaoka, A. and Nakano, M. (2008): Soil-water coupledˆnite deformation analysis based on a rate-type equation of motionincorporating the SYS Cam-clay model, Soils and Foundations,48(6), 771–790.Osterberg, J. O. (1957): In‰uences for vertical stresses in a semi-inˆnite mass due to an embankment loading, Proc. 4th ICSMFE, 1,393–394.Schmertmann, J. H. (1953): Estimating the true consolidation behavior of clay from laboratory test results, Proc. ASCE, 79(312),1–26.Skempton, A. W. (1944): Notes On The Compressibility of Clays,Quart. J. Geol. Soc., London, C, 119–135.Terzaghi, K. and B. Peck (1967): Soil Mechanics in EngineeringPractice, 2nd edition, John Wiley & Sons.APPENDIX 1: THE SUPER/SUBLOADING YIELDSURFACE (SYS) CAM-CLAY MODELThe Quantiˆed Expression of Structure, Overconsolidation, Anisotropy, and Their Respective Evolution RulesNaturally deposited soils, whether clayey or sandy,generally exist in a `structured' and overconsolidatedstate. To describe the deformation behavior of a soil inthis state, we have to start from the base of an elasto-plastic model of a de-structured soil in a state of normal consolidation. Given that a soil in this unstructured and normally consolidated state still possesses anisotropy, wetake for our `base' in this paper the corrected Cam-claymodel of Roscoe and Burland (1968) with the introducedaddition of the rotational hardening concept of Sekiguchiand Ohta (1977), which treats stress parameter h* and itsevolution rule as an expression of anisotropy. Thedegrees of structure and overconsolidation are then introduced and quantiˆed by means of the two concepts ofthe superloading surface for structure (Asaoka et al.,1998a, 2000, 2002), and the subloading surface for overconsolidation (Hashiguchi, 1978, 1989; Asaoka et al.,1997). That is to say, the degree of structure is expressedby means of a superloading surface situated on the outside of the Cam-clay normal-yield surface and similar to121Fig. A1-1.Three loading surfacesit (the center of similarity being the origin p?=q=0 andthe similarity rate being given by R* (0ºR*Ã1), whilethe overconsolidation state is expressed by means of asubloading surface situated on the inside of the superloading surface and again similar to it (center of similarity p?=q=0, similarity rate R (0ºRÃ1); reciprocal 1/Ris the overconsolidation ratio). p? here is the mean eŠective stress and q is the shear stress. Using eŠective stresstensor T? (tension: positive), we can say: p?=-tr T?/3, q= 3/2S・S.The closer R* is to 0 the higher the degree of structure,but with the loss of structure that accompanies theprogressive plastic deformation R* will approach 1 (theevolution rule for R*). Similarly, the closer R is to 0 themore overconsolidated the state of the soil, but as R increases toward 1 with plastic deformation, the state of thesoil will also approach normal consolidation (the evolution rule for R). It can thus be assumed that the loss ofstructure with progressive plastic deformation brings asimultaneous release from overconsolidation (a transitionto the normally consolidated state), resulting ˆnally inconditions that match those in the Cam-clay model. Therelative positions of the three loading surfaces, assumingconditions of axial symmetry, are as shown in Fig.(A1-1).If we start from Cam-clay Eq. (A1-1) below as ourbase, given that the current eŠective stress exists on thesubloading surface, we ˆrst need to adapt relations to thesubloading surface through the application of variouselasto-plastic principles such as the associated ‰ow ruleand Prager's consistency condition, so as to give Eq.(A1-2).The Cam-clay potential:MD lntãp?M 2+ h * 2+MD ln+ãp?0M2fJ tr D dtp0tfJ tr D dt=0=f ( ãp?, h*)+p(A1-1)0The subloading surface:tfJ tr D dt=0f ( p?, h*)+MD ln R*-MD ln R+p0(A1-2) INAGAKI ET AL.122Here, D=(là -kã )/M/(1+e0) is the dilatancy coe‹cient,and M, là , kã and e0 are the critical state constant, compression index, swelling index, and initial void ratio. J=(1+e)/(1+e0) (e is the void ratio at time t=t ). -ft0 J trD pdt (compression: positive) corresponds to the plasticvolumetric strain h*, the expression of anisotropy, is obtained using the rotational hardening variable b, from thecalculation h*= 3/2hâ ・hâ , hâ =h-b, h=S/p?, S=T?+p?I. b=0 expresses a state of no anisotropy. In thepresent paper, the evolution rules for R*, R and b aregiven by the following equations.Evolution rule for R*:R_ *=JU*scs 2/3¿D ps¿+(1-cs)(-D p[)t,U *=aR*b(1-R*)cD(A1-3)Evolution rule for R:R_ =JU¿D p¿,U=-mln RDcontribution of plastic deformation to the change of soilstructure into the deviator of the plastic stretching2/3D ps and volumetric component -D p[. The ratio between these terms is given by cs (0ÃcsÃ1).The Associated Flow Rule and the Constitutive EquationAssociated ‰ow rule:&f・T° ?&f& T?D p=l, l=À0& T?MD22J(Ms -h )p?(M2+h*2)&fConstitutive equation: T° ?=ED-LE&T ?brDØ2hâ-b¿D ps¿ ¿hâ ¿ mb¿hâ ¿3(A1-4)M2s =M2a+br»-MD(A1-5)D p here is the plastic stretching tensor, D ps is the deviatorcomponent of D p, -D p[ is the volumetric component ofD p, and ¿ ¿ represents its norms. b° in Eq. (A1-5) is theGreen and Nahdhi's (1965) rate of b. The parametergroups for the evolution rules in Eqs. (A1-3)–(A1-5) allconsists of constants, and from their respective functionswe may call a, b, c, cs the degradation indices of structure, m the degradation index of overconsolidation, brthe rotational hardening index, and mb the rotationalhardening limit constant.A new evolution rule for R* is proposed to replace Eq.(A1-3) for expressing structural upgradation, dividing the(A1-7)E here is the elastic modulus tensor, T° ? is the Green andNaghdi's (1965) rate of T?, and L is the expression ofplastic multiplier l in terms to stretching D. Further, wecan establish the relationsEvolution rule for b:b° =J(A1-6)Ø4Mh*2mbh*-M 2+ h * 2Ø UR*U2h * +*R6h *2 +3hâ ・b2»»1(M2a-h2)2 (A1-8)3andM2a=M2+z 2,z= 3/2¿b¿(A1-9)The slope Ms of the threshold between hardening andsoftening q=Ms p?, obtained under loading conditionslÀ0, varies according to structural degradation, loss ofoverconsolidation and development or loss ofanisotropy, as well as with the current stress ratio. Similarly, the slope Ma of the threshold between plastic compression and expansion q=Ma p? varies in response to thedevelopment or loss of anisotropy. For details, the readeris referred to Asaoka et al. (2002).
  • ログイン
  • タイトル
  • Estimation of the Air Permeability Coefficient and the Radius of Vacuum Influence for Contaminated Soil and Groundwater Remediation
  • 著者
  • "Yoshihiko Hibi, Kenji Jinno, Kentaro Masuoka, Junichi Kawabata"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 123〜142
  • 発行
  • 2010/02/15
  • 文書ID
  • 64347
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 123–142, Feb. 2010ESTIMATION OF THE AIR PERMEABILITY COEFFICIENTAND THE RADIUS OF VACUUM INFLUENCE FORCONTAMINATED SOIL AND GROUNDWATER REMEDIATIONYOSHIHIKO HIBIi), KENJI JINNOii), KENTARO MASUOKAiii) and JUNICHI KAWABATAiv)ABSTRACTThe air permeability coe‹cient and the radius of vacuum in‰uence are important parameters in the design of soilvapor extraction systems for removing volatile organic chemicals, but procedures for obtaining these parameters havenot yet been established. We developed procedures using previously derived analytical equations for the relationshipbetween air discharge rates from an extraction well and the air pressure head generated in the neighborhood of the extraction well in soil with a uniform degree of water saturation in order to obtain these parameters in soil with varyingdegrees of water saturation. We veriˆed that these procedures could be used to obtain these parameters by using airpermeability test data from ˆve sites. In addition, we demonstrated that these procedures could also be applied to gravel soil with fast air ‰ow.Key words: air permeability coefficient, air permeability test, contaminated soil, gas phase of soil, numerical simulation, radius of vacuum influence (IGC: C8/C9/E7)above the groundwater table, are simpler than those forsoil with variable degree of water saturation, such as thelayer of silt or sand directly above the groundwater table.These simpler analytical equations have the advantage ofcalculation e‹ciency of the air permeability coe‹cient,and they are convenient for use during air permeabilitytests on site. However, procedures for obtaining the airpermeability coe‹cient and the radius of vacuum in‰uence using analytical equations for the relationship between the distribution of the air pressure head and air discharge rates in soil with uniform degree of water saturation have not yet been established. Moreover, therelationship between the degree of air pressure head andair discharge rates obtained with the analytical equationsfor the air permeability coe‹cient in soil with uniformdegree of water saturation have not been compared withthose obtained by air permeability tests carried out in theˆeld, and the limits of those equations have not been validated. To address these problems, we carried out simulations with ˆnite-element method for air-water two-phase‰ow in soil and obtained the relationships between thedistribution of the air pressure head and air dischargerates in soil with uniform or variable degree of watersaturation. These relationships were then compared withthose gained by the analytical equations for the airINTRODUCTIONUnsaturated soils in some areas are contaminated withvolatile organic chemicals (VOCs), such as trichloroethylene,tetrachloroethylene,tetrachloromethane,dichloroethane, and trichloroethane, because of leaksfrom storage tanks or pipelines or illegal disposal. TheseVOCs are removed from soil by using a soil vapor extraction (SVE) technique involving extraction wells installedin unsaturated soil (Helmig, 1997; Gerke et al., 1999).The air permeability coe‹cient and the radius of vacuum in‰uence are important parameters in the design ofSVE systems. The locations of the extraction wells andthe air extraction rate from each extraction well are determined by using these two parameters. However, SVE systems are often designed empirically without rigorous analyses and by assuming a uniform degree of water saturation in the soil (McWhorter, 1990; Baehr and Hult, 1991;Shan et al., 1992; US Army Corps of Engineers, 2002) because the analytical equations for the air permeabilitycoe‹cient in soil with variable degree of water saturationare complex (US Army Corps of Engineers, 2002).The analytical equations for the air permeabilitycoe‹cient in soil with the uniform degree of water saturation, such as a layer of sand or gravel some distancei)ii)iii)iv)Department of Environmental Science and Technology, Faculty of Science and Technology, Meijo University, Nagoya, Aichi, Japan (hibiy@ccmfs.meijo-u.ac.jp).Department of Urban and Environment Engineering, Graduate School of Engineering, Kyushu University, Fukuoka, Japan.Geo-environment Engineering Section, Civil Engineering Research Institute, Technology Center, Taisei Corporation, Kanagawa, Japan.Geotechnical Engineering and Soil Environment Group, Kajima Technical Research Institute, Kajima Corporation, Tokyo, Japan.The manuscript for this paper was received for review on February 10, 2009; approved on September 29, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.123 HIBI ET AL.124permeability coe‹cient in soil with uniform degree ofwater saturation. Consequently, this paper clariˆed theconditions under which the air pressure head obtained bythe simulation was similar to that obtained by analyticalequations. We then developed procedures for obtainingthe air permeability coe‹cient and the radius of vacuumin‰uence based on the above comparisons and the analytical equations. Finally, we applied these procedures to airpermeability tests at ˆve sites. The numerical simulationincorporated the compressibility of air and the variationof water saturation in unsaturated soil.PROCEDURES FOR OBTAINING THE AIRPERMEABILITY COEFFICIENTFig. 1. The structure of an extraction well and the soil conditionsaround the well in cylindrical coordinatesMany studies have applied Darcy's law for air ‰ow tothe air phase in soil (Abriola and Pinder, 1985; Thorstenson and Pollock, 1989; Baehr and Bruell, 1991; Sleep andSykes, 1993; Lenhard et al., 1995; Reinecke and Sleep,2002; Hoeg et al., 2004). The equation for steady air ‰owwith compressibility of air in soil is given, in a cylindricalcoordinate system, by Eq. (1) (US Army Corps of Engineers, 2002) when the air permeability coe‹cient andthe viscosity of air do not change throughout the analytical domain:&2c2a 1 &c2a &2c2a++ 2 =0,&r 2 r & r&z(1)where ca is the air pressure head [L], r is the radial coordinate [L], and z is the vertical coordinate [L], which ispositive in the downward direction.The US Army Corps of Engineers (2002) developedanalytical equations based on Eq. (1) that are applicablewhen there is (1) radial air ‰ow toward an extraction wellpenetrating a permeable layer bounded on the top andbottom by impermeable layers, (2) radial air ‰ow towarda sink point in a space without boundaries, (3) air ‰owtoward a partly screened extraction well in a spacewithout boundaries, (4) air ‰ow toward a partly screenedextraction well from the ground surface, or (5) air ‰owtoward a partly screened extraction well in a permeablelayer bounded by the ground surface and the groundwater table. These equations are simple and suitable forobtaining the air permeability coe‹cient from the resultsof air permeability tests. These equations are evaluated asfollows:Radial Air Flow toward an Extraction Well Penetrating aPermeable Layer with Upper and Lower ImpermeableBoundariesIf an extraction well with a screen of length B [L] is installed with the center of the well at r=0, and air discharge, qa [L3/T], through the screen is constant (Fig. 1),then ca is equal to the atmospheric pressure head catm [L]at r=r0. Under these conditions Eq. (1) is solved as follows:c2atm-c2a=qacatm mraln (r0/r ),pBKa(2)Fig. 2. Unrestricted air ‰ow in a cylindrical coordinate system. The airpressure head is calculated at P(r, z )where Ka is the air permeability coe‹cient [L/T] and mra isthe relative viscosity of air (i.e., the ratio of the viscosityof air to that of water) [dimensionless].Radial Air Flow toward a Sink Point in a Space withoutBoundariesIf air is extracted from a point at z=z? and r=0 in theground (Fig. 2), the following formula can be derived ina spherical coordinate system if the eŠects of the groundsurface and the groundwater table boundaries are ignored. R in spherical coordinates is converted to the radial coordinate r and the vertical coordinate z in cylindricalcoordinates. Air ‰ows only toward the extraction point Ofrom the surrounding ground in this case (Shan et al.,1992)c2atm-c2a=qacatm mra2pKa r 2+(z-z?)2(3)Air Flow toward a Partly Screened Extraction Well in aSpace without BoundariesIf the screen is located between an lower point a and aupper point b in the extraction well (Fig. 3), a solution of AIR PERMEABILITY COEFFICIENT125The air pressure head should be equal to the atmospheric pressure head at the ground surface, but theair pressure head calculated by Eq. (4) does not becomeatmospheric pressure head. The mirror well, which is nota real well but an imaginary well, is installed in the symmetrical position above the ground surface. Air is extracted from the real well and injected into the mirrorwell. The condition of the ground surface is satisˆed bysuperposing the air pressure head obtained by Eq. (4) forthe real well on that obtained by Eq. (4) for the mirrorwell.Fig. 3. Unrestricted air ‰ow when air is extracted along a line fromOupper to Olower passing through the origin of a cylindrical coordinatesystem (r=0). The air pressure head is calculated at the pointP (r , z )Air Flow toward a Partly Screened Extraction Well in aPermeable Layer Bounded by the Ground Surface andthe Groundwater TableTherefore, a solution of Eq. (1) that takes into accountboth the ground surface and the groundwater table canalso be derived by using the above method of images, asfollows (Shan et al., 1992):c2atm-c2a=« Øqacatm mraz-b+ r 2+(z-b)2ln2pKa(a-b)z-a+ r 2+(z-a)2×»/z+b+ r 2+(z+b)2- S (-1)n22z+a+ r +(z+a)n= 1×lnFig. 4. The method of images applied to a well in the ground. Theground surface (thick solid line) is at z=0. The white circle and thegray circle at r=0 respectively describe a real well. The air pressurehead is calculated at point PEq. (1) can be obtained by integrating Eq. (3) from a tob, as follows (Shan et al., 1992).c2atm-c2a=Ø»qacatm mraz-b+ r 2+(z-b)2.ln2pKa(a-b)z-a+ r 2+(z-a)2(4)The air ‰ow in this case is inconsistent with that whichoccurs by extraction at a point because the air ‰ow in theradial direction is faster than that in the vertical direction.Air Flow toward a Partly Screened Extraction Well fromthe Ground SurfaceFurthermore, a solution of Eq. (1) that takes into account the ground surface (Fig. 4) can be derived by usingthe method of images, as follows (Shan et al., 1992).c2atm-c2a=Øqacatm mraz-b+ r 2+(z-b)2ln2 pK a ( a- b )z-a+ r 2+(z-a)2×»z+b+ r 2+(z+b)2.z+a+ r 2+(z+a)2(5)Ø zz++ba++ nhnh++ rr ++ zz++ab++ nhnh2222((22×z+a-2nh+ r 2+(z+a-2nh)2z+b-2nh+ r 2+(z+b-2nh)2×z-a+2nh+ r 2+(z-a+2nh)2z-b+2nh+ r 2+(z-b+2nh)2×z-a-2nh+ r 2+(z-a-2nh)2z-b-2nh+ r 2+(z-b-2nh)2)2)2»$(6)In addition to the condition of the ground surface described above, the method must satisfy the condition ofthe groundwater table. The air ‰ux should be zero at thegroundwater table, because the groundwater table restricts air ‰ow, and the air pressure head above thegroundwater table is smaller than that obtained by Eq.(5). Therefore, a mirror well from which air is extracted isinstalled in a symmetrical position to the groundwatertable. The method of images uses iteration to satisfy bothconditions of this case; the number of iterations (n in Fig.5) and of mirror wells and re‰ections of the ground surface and groundwater table is increased until the air pressure head obtained by Eq. (6) converges.The air permeability coe‹cient Ka is obtained usingEq. (2).K a=qacatm mrapB(c2atm-c2a )/ln (r0/r )(7)To obtain the air permeability coe‹cient using Eq. (7),an air permeability test must be conducted at an extraction well and several monitoring wells using a constant airdischarge rate qa. The change in the air pressure head ismeasured at the monitoring wells, which are at a knowndistance from the extraction well. The discharge rate qa, 126HIBI ET AL.tion well in Eqs. (3), (4), (5) and (6), respectively. Thedimension of L1 is length, and L2, L3, and L4 are ratesrepresenting the location of the monitoring well or the location where the air pressure head at the extraction well iscalculated. These coe‹cients become greater in theneighborhood of the extraction well and become smalleraway from the extraction well.L 1=1r +(z-z?)2(8a)2Ø zz--ba++ rr ++ zz--ba »Ø zz--ba++ rr ++ zz--ba ×zz++ba++ rr ++ zz++ba »2L2=ln22L3=ln2(()2)2(()2)222(((8b))2)2(8c)« ØL4= ln×z-b+ r 2+(z-b)2z-a+ r 2+(z-a)2»/z+b+ r 2+(z+b)2-(-1)nSz+a+ r 2+(z+a)2n= 1×lnØ2z+a+2nh+ r +(z+a+2nh)2z+b+2nh+ r 2+(z+b+2nh)2×z+a-2nh+ r 2+(z+a-2nh)2z+b-2nh+ r 2+(z+b-2nh)2×z-a+2nh+ r 2+(z-a+2nh)2z-b+2nh+ r 2+(z-b+2nh)2×z-a-2nh+ r 2+(z-a-2nh)2z-b-2nh+ r 2+(z-b-2nh)2»$(8d)The gradient E of the regression expression betweenc2atm-c2a and the coe‹cient for distance L1, L2, L3, or L4can be deˆned as follows:E=(c2atm-c2a )/Li,(9)where Li is L1 if Eq. (3), L2 if Eq. (4), L3 if Eq. (5), and L4if Eq. (6).By substituting the gradient E in Eq. (9) or E=c2atm-2ca/ln (r0/r ) into Eqs. (2) to (6) and rearranging, the airpermeability coe‹cient can be solved as follows:Fig. 5. The method of images applied to a well in the ground thatpenetrates the groundwater table. The ground surface and thegroundwater table are at z=0 and z=h, respectively. The white circle and the gray circles at r=0 respectively describe the real welland mirror wells. The air pressure head is calculated at point Pthe atmospheric pressure head catm, the relative viscosityof air mra, and the length of the screen in the extractionwell B must be known when the air permeability test iscarried out. Consequently, qacatm mra/pB is constant, andthe air permeability coe‹cient can be obtained from Eq.(7) if E, which indicates the strength for velocity of air,which is equal to (c2atm-c2a )/ln (r0/r ), becomes constantfor every value of ln (r0/r ) or some ln (r0/r ). Thus, ln (r0/r ) in Eq. (7) is a coe‹cient for distance from the extraction well. Moreover, L1, L2, L3, and L4 (deˆned in Eq.(8)) are the coe‹cients for the distance from the extrac-Ka=qacatm mra/pBEif(2)(10a)Ka=qacatm mra/2pEif(3)(10b)Ka=qacatm mra/2p(a-b)Eif(4), (5), or (6).(10c)Figure 6 shows the process for the calculation of the airpermeability coe‹cient. qa and the extraction point z orthe lower and upper depths of the extraction well screen(points a and b, respectively) are decided when the airpermeability test is designed (Fig. 6). catm is measuredwith a barometer, and mra is obtained from the temperature measured during the air permeability test. E in Eq.(9) can be obtained from the relationship between c2atm-c2a measured during the air permeability test, and Li forthe distance from the extraction well is calculated fromthe relative positions of the extraction well and amonitoring well (Fig. 6). The air permeability coe‹cientcan be calculated using Eq. (10) if E in Eq. (9) is indepen- AIR PERMEABILITY COEFFICIENT127is proportional to ln (r0/r ), L1, L2, L3, or L4 within everyrange or some range of these coe‹cients.ESTIMATION OF THE GRADIENT E AND THE AIRPERMEABILITY COEFFICIENT USING AFINITE-ELEMENT METHOD FOR AIR-WATERTWO-PHASE FLOW WITH COMPRESSION OF AIRIN SOILIn the present model, numerical simulations (Celia andBouloutas, 1990; Hibi et al., 2001) are carried out usingthe Galerkin Finite Element Method (GFEM) for porousmedia to estimate the gradient E and the air permeabilitycoe‹cient from calculated values of c2atm-c2a and ln (r0/r ), L1, L2, L3, and L4. The gradient E is evaluated whenthe degree of water saturation of the ground varies withdepth and also when it is essentially uniform. Theuniform air permeability coe‹cient without degree ofwater saturation is deˆned on the basis of the conditionsassumed for the derivation of Eqs. (2) to (6) from Eq.(1). The variable air permeability coe‹cient with degreeof water saturation, however, diŠers from that of Eqs.(2) to (6).Fig. 6.The process for calculation of the air permeability coe‹cientdent of Li in each Eq. (10). If E is dependent on Li, thenthe air permeability coe‹cient changes with Li and the airpermeability coe‹cient cannot be determined. c2atm-c2a(Eqs. (2) to (6)) should remain proportional to ln (r0/r ),L1, L2, L3, or L4 (Eq. (8)) provided that the air permeability coe‹cient is uniform over the analytical domain.However, this coe‹cient does not remain uniform inreality. The air permeability coe‹cient correlates withdegree of water saturation, increasing with a decreasingdegree of water saturation, and the degree of water saturation is at a minimum close to the ground surface and increases with depth in actual ground. Therefore, the airpermeability coe‹cient reaches a maximum close to theground surface where the degree of water saturation is ata minimum, decreases with depth from the ground surface, and becomes zero at the groundwater level, wherethe maximum degree of water saturation is reached.Nevertheless, previous studies have not proved that E isnot dependent on ln (r0/r ), L1, L2, L3, or L4 in actualground. It is therefore important to clarify the relationships between E and ln (r0/r ), L1, L2, L3, and L4 in theˆeld. This study aimed to ˆnd these relationships and theapplicable conditions necessary to reproduce ˆeld conditions with variable or uniform degree of water saturationfrom simulation results and air permeability test resultsfor ˆve sites. The results showed that the air permeabilitycoe‹cient could be calculated using ln (r0/r ), L1, L2, L3,or L4, and c2atm-c2a measured in monitoring wells, whichNumerical Model for Air-water Two-phase Flow Takinginto Account the Compression of Air in SoilEquation (11a) describes steady air ‰ow, and Eq. (11b)describes steady water ‰ow. Both equations are derivedfrom Darcy's law and the law of conservation of mass forthe air or water phase in soil in a cylindrical coordinatesystem.Ø»& ca ratm kra Ks &ca1 ca ratm kra Ks &ca+&r catm mra &rr catm mra &r& ca ratm kra Ks &+(ca-rraz) =0&z catm mra &z&&cwkrw Ks &cw+krw Ks&rr&r&r&&+krw Ks (cw-z) =0,&z&zØØ»(11a)»«$(11b)where rra is the relative density (i.e., the ratio of the density of air to that of water) [dimensionless] of air, ratm isthe density [M/L3 ] of air when the air pressure is equal tothe atmospheric pressure head, kra is the relative airpermeability coe‹cient (i.e., the ratio of the airpermeability coe‹cient to the saturated hydraulic conductivity) [dimensionless], krw is the relative hydraulicconductivity (i.e., the ratio of the hydraulic conductivityof the water phase to the saturated hydraulic conductivity) [dimensionless], Ks is the saturated hydraulic conductivity [L/T], and cw is the water pressure head [L]. Equations (11) are formulated using the GFEM in this numerical simulation (Hibi et al., 2001). Because the curve between the degree of water saturation and the capillarypressure head for water and air generally became continuous at the degree of water saturation 1.0 (Davis, 1994),the van Genuchten (1980) and Burdine (1953) was appliedin the present simulations to the constitutive equation be- HIBI ET AL.128tween degree of water saturation and capillary pressurehead as follows:˜Sw=Sw-Srw=s1+(acaw )bt-g1-Srw-Sra(12)where Sw is degree of water saturation (i.e., the ratio ofthe volume of water to that of voids in soil) [dimensionless], a and b are the Van Genuchten parameters (a is thereciprocal [L-1 ] of the entry pressure head, and b is aparameter [-] describing the pore space geometry of thesoil), g is [1-1/b ], Srw is the residual degree of watersaturation (i.e., the ratio of the volume of the residualwater to that of the voids in soil) [dimensionless], Sra isthe residual degree of air saturation (i.e., the ratio of thevolume of the residual air to that of the voids in soil)[dimensionless], ˜Sw is the eŠective degree of water saturation [dimensionless], and caw is the capillary pressurehead [L] between water and air.The Burdine model is also applied to the constitutiveequations between degree of water saturation and the relative air permeability coe‹cient or the relative hydraulicconductivity, as follows:g gkrw= ˜S 2ws1-(1- ˜S 1/w ) t(13a)g gkra=(1- ˜Sw )2(1- ˜S 1/w )(13b)The precision of this numerical simulation was validated by comparing the air pressure head determined by thissimulation with the air pressure head calculated by Eq.(2). The air pressure head obtained by this simulation wasconsistent with that of Eq. (2) (Hibi et al., 2006b).Modeling and Discretization for Numerical SimulationFigure 7 shows the analytical domain and boundaryconditions for the numerical simulation. The geometricaloutline of the analytical domain is a rectangle, and the extent of the domain is 0.05 mÃrÃ100 m and 0 mÃzÃ65m. In the GFEM numerical simulation, a total of 1435quadrangular elements with nodal spacing of 0.20 to 5.0m in the radial direction and 0.25 to 5.00 m in the verticaldirection are used and the analytical domain is discretizedwith 36×42=1512 nodes. The nodes in the neighborhood of the extraction well (in the range of 0.05mÃrÃ10.00 m) are 0.20 to 0.5 m apart in the radialdirection. The space between nodes increases with distance from the extraction well. The nodes in theneighborhood of the screen in the extraction well are ˆnely spaced in the vertical direction: 0.25 m apart in therange of 4.50 mÃzÃ5.50 m. It has been shown that theair pressure head obtained by the simulations is not improved if the simulations are carried out with ˆner nodalspacing (Hibi et al., 2006a).In the model, a 0.5-m-long screen is placed in an extraction well from z=4.75 to 5.25 m at r0=0.05 m. Theair discharge is 0.06 m3/min. The domain radius, equal to100 m, is su‹ciently large and the domain boundary issu‹ciently far from the extraction well that the assignedboundary conditions do not in‰uence the air pressurehead distribution in the domain. The air pressure head assigned at the boundary is equal to an atmospheric pressure head ca=10.34 m. The assigned discharge rate qa ofair at r0=0.05 m, excluding the depth from z=4.75 to5.25 m, is 0 m3/min. The ground surface is permeable,and the assigned air pressure head at the ground surface,z=0 m, is equal to an atmospheric pressure head ca=10.34 m. On the other hand, the assigned discharge rateof water is qw=0 m3/min at the ground surface becausethe ground surface is impermeable to water. An impermeable layer in the vertical direction is at z=65 m. Thedischarge rate of air qa and the discharge rate of water qwat z=65 m are both equal to zero. The water pressurehead hwL at the left boundary of the analytical domain,where the radial coordinate is r0=0.05 m, is equal to thewater pressure head hwR at the right boundary of the analytical domain, where the radial coordinate is r=100 m,and these water pressure heads are assigned the value 3.34Fig. 7. The analytical domain and boundary conditions for simulations by the ˆnite-element method for air-water two-phase ‰ow in the soil. Thewhole analytical domain and the boundary conditions for the air pressure head ca, the water pressure head hw, and the ‰uxes of air qa and waterqw, are shown on the right AIR PERMEABILITY COEFFICIENTm when the simulation is carried out with caw-kra-Swcurve No. 1 to reproduce the distribution of variablewater saturation, and the value 0.34 m with caw-kra-Swcurve No. 2 to reproduce the distribution of uniformdegree of water saturation. Therefore, the groundwater table is at ground level GL-7 m in the simulation using caw-kra-Sw curve No. 1, and at GL-10 m in the simulationusing caw-kra-Sw curve No. 2 from atmospheric pressure head at the ground surface and the water pressurehead at r0=0.05 m and r=100 m.Parameters Used in the Numerical SimulationAssumptions are made for sandy soil in order to carryout the numerical simulation to reproduce the conditionsfor air permeability tests carried out in sandy soils.Reasonable normal values for the saturated hydraulicconductivity and porosity for sand (Table 1) are therefore used in these simulations. A saturated hydraulic conductivity of 1.0×10-3 cm/s and a porosity of 0.4 are assumed. The densities and the viscosity of water are assumed to 1.0 g/cm3 and 1.0×10-3 Pa s, respectively, andthe density and viscosity of air are assumed to 0.012 g/cm3 and 1.8×10-5 Pa s, respectively. Numerical simulations were conducted to estimate the gradient E betweenc2atm-c2a and ln (r0/r ), L1, L2, L3, and L4 under the assumption that the degree of water saturation varied withTable 1. Soil and ‰uid parameters used in the numerical simulation bythe ˆnite-element method for air-water two-phase ‰ow in soilSaturatedhydraulicconductivityks (cm/s)Porosity1.0×10- 30.4WaterAirDensityViscosityDensity Viscosityrw (g/cm3) mw (Pa・S) ra (g/cm3) ma (Pa・S)11.0×10- 30.0121.8×10- 5129depth, whereas the analytical solution assumes that thedegree of water saturation is uniform everywhere in theanalytical domain. Therefore, in the numerical simulations, the air permeability coe‹cient varies with respectto the spatial coordinate, whereas the air permeabilitycoe‹cient is uniform in the analytical solution. The simulations using caw-kra-Sw curve No. 1 was carried outdue to reproduce the sandy ground that the degree ofwater saturation may have been varied with depth fromthe ground surface (Fig. 8(a)), whereas the simulationsusing caw-kra-Sw curve No. 2 was carried out due toreproduce the sandy ground that the degree of water saturation was uniform in the vapor zone except near thegroundwater table (Fig. 8(b)). Then these van Genuchtenparameters were assumed for the reproduction of thesandy ground with the uniform degree of water saturation and the sandy ground with the varied degree of watersaturation.The air and water parameter values used in the simulations are shown in Table 1. The density of air is approximately 1z that of water, and the eŠect of gravity isneglected. The viscosity of water is approximately 50times that of air; consequently, the air permeabilitycoe‹cient would be larger than the hydraulic conductivity by two orders of magnitude.Estimation of the Gradient E from the Results of the Numerical SimulationThe distribution of degree of water saturation was obtained by numerical simulations using the ˆnite-elementmethod for air-water two-phase ‰ow in soil for caw-kra-Sw curves No. 1 (Fig. 9(a)) and No. 2 (Fig. 9(b)). Withcurve No. 1, the degree of water saturation exceeds 0.2 atthe ground surface and rises to roughly 0.8 near the extraction well screen as a result of air extraction from theFig. 8. Soil-water characteristic curves (caw-Sw ) and the relationships between the relative permeability of air and degree of water saturation ( kra-Sw ) used in the numerical simulations by the ˆnite-element method for air-water two-phase ‰ow in soil 130HIBI ET AL.Fig. 9. Distributions of water saturation obtained with the ˆnite-element method for air-water two-phase ‰ow in soil using caw-kra-Sw curve No.1 (a) and No. 2 (b). Gray lines show the mesh for the ˆnite-element method, and the thick black lines are the contours of water saturationscreen (Fig. 9(a)). On the other hand, with curve No. 2,the degree of water saturation is apparently uniform closeto the screen of the extraction well.Figures 10(a) and (b) show the distributions of the airpressure head corresponding to the degree of water saturation distributions shown in Figs. 9(a) and (b), respectively. The air pressure head obtained by the numericalsimulation with caw-kra-Sw curve No. 1 decreases gradually from the atmospheric pressure head, 10.34 m, to10.15 m directly above the groundwater table in theneighborhood of the extraction well (Fig. 10(a)). This indicates that the groundwater table in‰uences the distribution of air pressure when air is extracted from the extraction well. On the other hand, the air pressure head obtained by the numerical simulation with caw-kra-Swcurve No. 2 decreases from 10.34 to 10.30 m directlyabove the groundwater table (Fig. 10(b)); this rate ofdecrease is thus smaller than that obtained by the numerical simulation using caw-kra-Sw curve No. 1. Theseresults suggest that the groundwater table does not in‰uence the distribution of the air pressure head.The distance from the extraction well at which the airpressure head approaches 10.30 m in the radial directionis 4.4 m for curve No. 1 and 3.0 m for curve No. 2 (Fig.10(a) and (b), respectively). The radius of vacuum in‰uence in ground with caw-kra-Sw curve No. 2, inwhich the air pressure head decreases as air is extracted, islower than that in ground with caw-kra-Sw curve No. 1.This diŠerence in the radius of vacuum in‰uence resultsfrom degree of water saturation close to the extractionwell in the case of caw-kra-Sw curve No. 1. The radiusof vacuum in‰uence is larger when the air permeabilitycoe‹cient is lower, which occurs where the degree ofwater saturation is greater close to the extraction well andthe groundwater table (Fig. 10). Since the contour linesof the air pressure head in Fig. 10(b) are concentric semicircles at the screen, the boundary conditions assigned tothe numerical simulation for air-water two-phase ‰ow insoil are similar to those assumed for Eq. (5). On the otherhand, the contour lines in Fig. 10(a) are not regular concentric semicircles because the groundwater table and theground surface obstruct the air ‰ow. Therefore, theboundary conditions used in the numerical simulationsatisfy those assumed for Eq. (6).Figure 11 shows the relationships between c2atm-c2aand ln (r0/r ), L1, L2, L3, and L4 at z=5 m, at the center ofthe screen in the extraction well. Although c2atm-c2a increases with ln (r0/r ), the increase is not linear withrespect to ln (r0/r ) (Fig. 11).This nonlinearity is caused by a diŠerent between theupper boundary condition of the analytical and that ofnumerical domain. Air ‰ow is restricted and the air pres- AIR PERMEABILITY COEFFICIENT131Fig. 10. Distributions of the air pressure head obtained with the ˆnite element method for air-water two-phase ‰ow in soil using caw-kra-Sw curveNo. 1 (a) and No. 2 (b). Gray lines show the mesh for the ˆnite-element method, and the thick black lines are the contours of the air pressurehead (in meters)Fig. 11. The relationships between c2atm-c2a obtained by the simulations and ln (r/r0 ), L1, L2, L3, and L4, coe‹cients for distance from the extraction well HIBI ET AL.132sure head is varied on the upper boundary of analyticaldomain, but the air pressure head is equal to atmosphericpressure head and air ‰ow is permitted on the upperboundary of numerical domain.Therefore, the air permeability coe‹cient cannot beobtained from the relationship between c2atm-c2a and ln(r0/r ). On the other hand, c2atm-c2a is proportional to L1for L1 less than 1.0 (Fig. 11). The air permeabilitycoe‹cient can thus be calculated from the gradient E ofthe regression expression between c2atm-c2a and L1 whereL1 does not exceed 1.0. Similarly, the gradient E can beobtained from the numerical solution by the ˆnite-element method for L2, L3, and L4 less than 0.4, 0.3, and0.6, respectively (Fig. 11) with a high correlationcoe‹cient of approximately 1.0. c2atm-c2a is not proportional to L1, L2, L3, or L4 in the neighborhood of the extraction well for two reasons: (1) the air pressure head obtained analytically with Eqs. (3) to (6) is not assigned atthe extraction well, while the air pressure head used in thesimulations satisˆes the speciˆed boundary condition atthe extraction well, and (2) the air permeability coe‹cientobtained with the simulations becomes smaller as thedegree of water saturation increases close to the extraction well. The analytical solutions of Eqs. (3) to (6) arederived under the assumption that the air permeabilitycoe‹cient is uniform in the analytical domain.Tables 2 and 3 list the air permeability coe‹cients calculated from the gradient E of the regression expressionsobtained by the simulations of air-water two-phase ‰owin soil with caw-kra-Sw curves No. 1 and No. 2, respectively (Fig. 11). Since the correlation coe‹cient of theregression expression is approximately 1.0 in each case(Table 2), the value of c2atm-c2a obtained by the numerical simulation with caw-kra-Sw curve No. 1 correlateswith L1, L2, L3, and L4. The air permeability coe‹cientscalculated from gradient E shown in Table 2 are diŠerentfrom that used in the numerical simulation. The largestdiŠerence is that between the air permeability coe‹cientused in the simulation and that obtained from gradient Ebetween c2atm-c2a and L4; the air permeability coe‹cientobtained using gradient E between c2atm-c2a and L4 is approximately twice as large as that used in the numericalsimulation. The diŠerence in the air permeabilitycoe‹cient obtained using gradient E between c2atm-c2aand L4 is approximately 1.2 to 1.3 times that obtained using gradient E between c2atm-c2a and L2 or L3.On the other hand, the correlation coe‹cients betweenc2atm-c2a and L1, L2, L3, and L4 calculated using caw-kra-Sw curve No. 2 are approximately 1.0 (Table 3); in fact,they are closer to 1.0 than those obtained with the caw-kra-Sw curve No. 1 (Table 2). Each air permeabilitycoe‹cient calculated from gradient E between c2atm-c2aand L1, L2, L3, or L4 is approximately equal to that usedin the numerical simulation (Table 3). If caw-kra-Swcurve No. 1 is used for the numerical simulation, a largevariation in the degree of water saturation might cause asigniˆcant diŠerence between the air permeabilitycoe‹cient calculated from the air pressure head and thatused in the simulation. However, whichever caw-kra-Swcurve, No. 1 or No. 2, is used, the coe‹cient of airpermeability can be calculated from the gradient E between c2atm-c2a and L1, L2, L3, or L4, and the estimatedTable 2. Comparison between the air permeability coe‹cient used in the simulation and the air permeability coe‹cients calculated from the distribution of the air pressure head obtained by the ˆnite-element method for air-water two-phase ‰ow in soil using caw-kra-Sw curve No. 1caw-kra-Sw curve No. 1Location of thescreenCoe‹cientwithdistanceL1L2L3L4Volumetricdischargeof air(m3/min)0.06Upper(m)Lower(m)——4.755.25Relativeviscosityof air1.80E-02Atmospherepressurehead (m)10.34Regresion expression betweenL1, L2, L3, L4 and c2atm-c2aCorrelationcoe‹cienGradient(m 2)0.99710.99750.99750.9984.7129.89910.6748.267Airpermeabilitycoe‹cient(cm/s)6.290E-045.988E-045.553E-047.170E-04Airpermeabilitycoe‹cientused in thesimulation(cm/s)DiŠerence(cm/s)3.81E-042.480E-042.178E-041.743E-043.360E-04Table 3. Comparison between the air permeability coe‹cient used in the simulation and the air permeability coe‹cients calculated from the distribution of the air pressure head obtained by the ˆnite-element method for air-water two-phase ‰ow in soil using caw-kra-Sw curve No. 2caw-kra-Sw curve No. 2Location of thescreenCoe‹cientwithdistanceVolumetricdischargeof air(m3/min)L1L2L3L40.06Upper(m)Lower(m)——4.755.25Relativeviscosityof airAtmospherepressurehead (m)1.80E-0210.34Regresion expression betweenL1, L2, L3, L4 and c2atm-c2aCorrelationcoe‹cienGradient(m 2)Airpermeabilitycoe‹cient(cm/s)0.99950.99960.99460.99942.9255.8676.3035.9561.013E-031.010E-039.404E-049.952E-04Airpermeabilitycoe‹cientused in thesimulation(cm/s)DiŠerence(cm/s)9.81E-043.223E-052.929E-05-4.059E-051.420E-05 AIR PERMEABILITY COEFFICIENTair permeability coe‹cient should be accurate within oneorder of magnitude. The coe‹cient of air permeabilitycalculated from the gradient E indicates the value depending on the degree of water saturation from the extraction well to the monitoring well, but this coe‹cient ofair permeability is not necessarily equal to that in theneighborhood of the monitoring.r0 =The radius of vacuum in‰uence can be deˆned as thelocation where c2atm-c2a becomes zero in radial coordinates at the level of the center of the screen in the extraction well. The radius of vacuum in‰uence is useful fordetermining the region in which hazardous chemical substances are removed from the air phase of the soil.The regression line between c2atm-c2a and L3 or L4 intersects the origin of the coordinate systems, where L3 orL4=0 and c2atm-c2a=0 (Fig. 11). In contrast, the regression line between c2atm-c2a and L1 or L2 crosses the L1 orL2 axis, where c2atm-c2a=0, with positive values. This canbe clearly seen in Fig. 12, where the values of both L1 andL2 become small far from the extraction well. The pointof intersection with the L1 or L2 axis can be used to determine the radius of vacuum in‰uence when the airpermeability test is conducted. The regression expressiondoes not cross the origin of the coordinate system in Fig.12 because the boundary conditions for Eqs. (3) and (4)are diŠerent from those of the numerical model in whichboth the groundwater table and the ground surface aretaken into consideration. On the other hand, the boundary conditions assigned to Eqs. (5) and (6) are more similar to those of the numerical simulation.L10 and L20 are the points where the regression line between c2atm-c2a and L1 or L2 crosses the L1 or L2 axis, respectively (Fig. 12). For L1, the radius r0 of vacuum in‰uence can be obtained by using Eq. (14a), which is derived from Eq. (8a) for z=z?:1.L10(14a)Similarly, for L2, the radius r0 of vacuum in‰uence isobtained by Eq. (14b), which is derived from Eq. (8b) forz=(a+b)/2.r0 =PROCEDURE FOR DETERMINING THE RADIUSOF VACUUM INFLUENCE133{Ø» Ø »}a-b (1+eL ) 2 a-b-2 1- e L2202021/2(14b)ESTIMATION OF THE APPLICABILITY OF EQS.(2) TO (6) TO AIR PERMEABILITY TESTSAs shown above, it was conˆrmed on the basis of theresults of numerical simulations using the ˆnite-elementmethod that the gradient E between c2atm-c2a and L1, L2,L3, or L4 can be obtained and the air permeabilitycoe‹cient can be calculated with an accuracy within oneorder of magnitude, in comparison with the airpermeability coe‹cient used in the numerical simulation,by the proposed procedures using Eqs. (2) to (6).Moreover, formulas used to estimate the radius ofvacuum in‰uence have been also presented in this study.However, it is necessary to conˆrm the applicability ofthese procedures by performing air permeability tests atactual ˆeld sites. Therefore, this study evaluated theapplicability of these proposed procedures using theresults of air permeability tests at ˆve sites. The airpermeability test data presented in this study were provided by the Taisei Corporation and Kajima Corporationand have not been previously published, except those forsite A, which have been published by Yasumoto andKawabata (2000).Soil Conditions at Each SiteAt site A, Kuroboku soil was distributed from 0 to 2.2m depth below the ground surface, and loam from 2.2 to5.5 m depth. Silty sand was found at depths below 5.5 m.The groundwater table at this site was 8.2 m below theFig. 12. The relationships between c2atm-c2a and L1 (left) and L2 (right) when L1 and L2 are less than 0.5 and 0.3, respectively. L10 and L20 are thepoints where the regression lines intersect the L1 and L2 axes, respectively HIBI ET AL.134Fig. 13.The disposition of wells and the geological proˆle in site AFig. 14.The disposition of wells and the geological proˆle in site Bground surface, and the screen of the extraction well wasinstalled at depths from 3.5 to 3.75 m, in the loam layer(Fig. 13). At site B, loam was distributed from 0 to 12.0m depth, and gravel from 12.0 m below the ground surface. The groundwater at site B was 16.0 m below theground surface, and the screen of the extraction well wasinstalled between 4.0 and 8.0 m depth (Fig. 14).At site C, loam was found from 0 to 2.5 m depth, andclay at depths below 2.5 m. The groundwater table was at3.65 m below the ground surface at site C, and the screensof the extraction well and the monitoring wells were in-stalled at depths between 1.2 and 2.7 m (Fig. 15). At siteD, loam, gravel, and clay were distributed from 0 to 4.5m, from 4.5 to 6.0 m, and below 6.0 m depth, respectively. The groundwater at site D was 6.5 m below theground surface, which was below the top of the clay. Thescreen of the extraction well was installed between 2.0and 3.5 m in loam. Site E was similar to site D except thescreen of the extraction well was installed at 4.5 to 5.5 mbelow the ground surface in gravel (Fig. 16).The air permeability tests at sites A, B, C, and D werethus conducted in the loam, which was composed of silty AIR PERMEABILITY COEFFICIENTFig. 15.Fig. 16.135The disposition of wells and the geological proˆle in site CThe disposition of wells and the geological proˆle in site D and Evolcanic ash. On the other hand, at site E the test wasconducted in gravel. Degree of water saturation in theloam, which had high water retentiveness, was more than0.86 (Yasumoto and Kawabata, 2000). The groundwatertable at site C was a short distance below the screen of theextraction well. Therefore, the screen of the extractionwell was closest to the groundwater table at the presentsites. The conditions at site C were similar to those assumed in Eq. (6); because it is generally most di‹cult toobtain the gradient E in such a situation, it is necessary toshow that the gradient E can be obtained from airpermeability tests despite the high degree of water satura-tion of the soil. If the gradient E can be obtained in thissituation, then it is possible to derive the air permeabilitycoe‹cient from the air permeability test data. The purpose of the air permeability test at site E was to evaluategradient E in a layer with higher permeability than loam.Evaluation of Gradient E and the Air PermeabilityCoe‹cient at Each SiteTable 4 lists the distances of the monitoring wells fromthe extraction well, the depth of the screen in the wells,the groundwater table depth, the discharge rate of air,and ca and catm at sites A, B, C, D, and E. Figures 17, 18, HIBI ET AL.136Table 4. Well systems used for the air permeability tests, including the groundwater level, the air discharge rate, and the measured air pressurehead at sites A, B, C, D, and ESiteADistancefrom theextractionwell (m)Upper level(GL-m)Lower level(GL-m)Extraction wellNo. 101.253.53.53.753.75No. 22.503.53.75No. 35.003.53.75No. 47.503.53.75No. 510.003.53.75WellMonitoringwellScreenBExtraction wellNo.No.No.MonitoringNo.wellNo.No.123456034634642.52.52.56668444888CExtraction wellNo.No.No.MonitoringNo.wellNo.No.12345602462461.21.21.21.21.21.21.22.72.72.72.72.72.72.7023.5No. 122.03.5No. 232.03.5No. 362.03.5No. 47.52.03.502367.54.54.54.54.54.55.55.55.55.55.5Extraction wellDEMonitoringwellExtraction wellNo.MonitoringNo.wellNo.No.123419, 20, and 21 show the relationships between c2atm-c2aand L1, L2, L3, and L4 at sites A–E, respectively, wherethe screen in the extraction well is in loam (sites A–D) orgravel (site E).Monitoring wells at site A were installed 1.25, 2.50,5.0, 7.5, and 10.0 m away from the extraction well, whichhad a screen from GL-3.5 m to GL-3.75 m (Table 4). c2atm-c2a was proportional to L1, L2, L3, and L4, except forthe highest values of L1, L2, L3, and L4 for all dischargerates, which were 1.4, 2.1, or 2.8 m3/min at site A (Fig.17). The maximum value of Li was in the neighborhoodGroundwaterlevel(GL-m)Dischargerate of air(m3/min)Genarated airpressure headca (m)Atmosphericpressure headcatm (m)8.21.4, 2.1, 2.81.42.12.81.42.12.81.42.12.81.42.12.81.42.12.8—10.336210.324010.300010.338010.329010.314010.339010.336010.328010.339610.338010.333010.339810.339010.335010.3416.00.14——————8.340010.338610.339310.339910.337810.339010.339810.342.31.15——————10.210010.255010.307010.320010.308010.333010.335010.346.52.53.1672.53.1672.53.1672.53.1672.53.16710.240010.160010.329010.325010.332010.329010.337010.337010.339010.338510.346.53.5————10.280010.334510.333510.336510.337010.34of the extraction well. This tendency was similar to therelationships between c2atm-c2a and L1, L2, L3, and L4 obtained by the numerical simulations. c2atm-c2a wasproportional to L1, L2, L3, and L4 within the entire rangeof variation of L1, L2, L3, and L4 at site B (Fig. 18). Allmonitoring wells at site B had two screens, from 2.5 to4.0 m and from 6.0 to 8.0 m below the ground surface,and they were at 3, 4, and 6 m from the extraction well,which had a screen from 4 to 8 m. The gradients E between c2atm-c2a and L1, L2, L3, and L4 from 2.5 to 4.0 mbelow the ground surface were similar to those from 6.0 AIR PERMEABILITY COEFFICIENTFig. 17.Fig. 18.137Evaluation of the proportional relationships between c2atm-c2a and L1, L2, L3, and L4, at site A for diŠerent discharge ratesEvaluation of the proportional relationships between c2atm-c2a and L1, L2, L3, and L4 at site B for diŠerent screen depthsto 8.0 m (Fig. 18). The system for the air permeabilitytest at site C consisted of an extraction well with a screenplaced from GL-1.2 m to GL-2.7 m and six monitoringwells, which were installed at 2, 4, or 6 m from the extraction well and had a screen from GL-1.2 m to GL-2.7 m.Monitoring wells No. 1 to No. 3 were installed oppositethe other three monitoring wells (No. 4 to No. 6). Themonitoring wells at site D were installed 2, 3, 6, and 7.5 mfrom the extraction well. The monitoring wells and theextraction well were screened from 2.0 to 3.5 m depth.Figures 19 and 20 show the relationship between c2atm-c2aand L1, L2, L3, and L4 at sites C and D, respectively; c2atm-c2a is proportional to L1, L2, L3, and L4 over the entirerange of L1, L2, L3, and L4. However, gradient E between HIBI ET AL.138Fig. 19.Fig. 20.Evaluation of the proportional relationships between c2atm-c2a and L1, L2, L3, and L4 at site CEvaluation of the proportional relationships between c2atm-c2a and L1, L2, L3, and L4 at site D for diŠerent discharge ratesc2atm-c2a and L1, L2, L3, and L4 determined at monitoringwells No. 1 to No. 3 diŠers from that determined frommonitoring wells No. 4 to No. 6 (Fig. 19). Therefore, thesoil conditions or groundwater table must diŠer betweenwells No. 1 to No. 3 and wells No. 4 to No. 6 at site C. Itis obvious that c2atm-c2a at site D is proportional to L1,L2, L3, and L4 for a discharge rate at the extraction well of2.5 or 3.167 m3/min (Fig. 20). Figure 21 shows therelationships between c2atm-c2a and L1, L2, L3, and L4 atsite E when the discharge rate at the extraction well was3.5 m3/min. As mentioned above, the conditions of theair permeability test at site E were similar to those at siteD, except that the screens of the extraction well and themonitoring wells were from GL-4.5 m to GL-5.5 m at siteE. Although the relationships between c2atm-c2a and L1,L2, L3, and L4 at site E appear to be proportional (Fig. AIR PERMEABILITY COEFFICIENTFig. 21.139Evaluation of the proportional relationships between c2atm-c2a and L1, L2, L3, and L4 at site E21), the values are more widely scattered than those observed at other sites. The correlation coe‹cients betweenc2atm-c2a and L1, L2, L3, and L4 are more than 0.9 at sitesA, B, C, and D; thus, c2atm-c2a is correlated with L1, L2,L3, and L4 (Table 5). On the other hand, the correlationcoe‹cients between c2atm-c2a and L1, L2, L3, or L4 areonly 0.60 to 0.65 at site E, presumably because of the fast‰ow of air in gravel. Therefore, it can be concluded thatgradients E between c2atm-c2a and L1, L2, L3, and L4 canbe calculated in a highly permeable layer as well as onewith lower permeability, but in the former case, moreprecise measurement of the air pressure head is requiredto obtain gradient E.Table 5 also shows the air permeability coe‹cients obtained from the gradients E at each site. The airpermeability coe‹cient obtained from L1 at site A is approximately 16 times those obtained from L2, L3, or L4. Asimilar diŠerence between the air permeability coe‹cientobtained from L1 and those obtained from L2, L3, or L4was not found at the other sites. Although at site C the airpermeability coe‹cients obtained from L1, L2, L3, and L4are scattered, the diŠerences do not exceed one order ofmagnitude. The air permeability coe‹cients frommonitoring wells No. 1 to No. 3 are smaller than thosefrom wells No. 4 to No. 6 at site C because of theanisotropic soil conditions. Therefore, it can be concluded that the position of the monitoring wells is important,as revealed by the results at site C, because the airpermeability coe‹cient diŠers among monitoring wellswhere the soil conditions is anisotropic. The simpliˆedprocedure suggested here yields realistic estimates of theair permeability coe‹cient for all tested conditions (Table 5). Therefore, the air permeability coe‹cient can beobtained by the proposed procedures with L2, L3, or L4,and the accuracy of the results with these procedures iswithin one order of magnitude.Figure 22 shows the relationship between the air discharge rate from the extraction well and the airpermeability coe‹cient at sites A and D, in loam.Although the air permeability coe‹cient is independentof the discharge rate if the air ‰ow obeys Darcy's law, theair permeability coe‹cients obtained at sites A and Ddecreased as the discharge rates increased (Fig. 22). Thenumerical solution shown in Fig. 9(a) suggests that theair permeability coe‹cient decreases with increasingdegree of water saturation near the screen in the extraction well when air is extracted from soils with high degreeof water saturation. The loams at sites A and D had ahigh degree of water saturation. The increase in degree ofwater saturation during the extraction of air occurredclose to the screen in the extraction well and decreased theair permeability coe‹cient as the air discharge rate increases. Therefore, the proposed procedure can be usedto obtain the air permeability coe‹cient from the airpermeability test data provided that the discharge ratefrom the extraction well is adequate and the monitoringwell is appropriately located. However, we should avoidemploying data from close to the extraction well to obtain the air permeability coe‹cient. The simpler procedure proposed in this study is useful for obtaining the airpermeability coe‹cient in heterogeneous and anisotropicsoil. Air permeability tests conducted in a laboratory canobtain the air permeability coe‹cients only of local soiland cannot take into account heterogeneity of the soil oranisotropy. When monitoring wells are installed in concentric circles around the extraction well, the proposed HIBI ET AL.140Table 5. Soils, groundwater levels, L1, L2, L3, and L4 coe‹cients for distance, correlation coe‹cients and the gradients of the regression expressionsbetween c2atm-c2a and L1, L2, L3, and L4, and the air permeability coe‹cients obtained at sites A, B, C, D, and EExtraction wellSiteSoilWaterlevelMonitoring wellScreenAir permeabilityScreenDischargeCoe‹cient Correlation Gradient E (m 2, except coe‹cient (cm/s)rate of airUpperLowerUpperLower for distance coe‹cientfor L1, l/m if L1)3(GL-m) (GL-m) (m /min) (GL-m) (GL-m)2.82.1ALoamGL-8.2 m3.53.753.53.752.54.06.08.01.4BLoamGL-8.2 m480.141.22.3*No. 1 to 3CDELoamLoamGL-2.3 mGL-6.5 mGravel GL-6.5 mRelationship between pressure and distances1.22.04.52.73.55.51.151.22.3*No. 4 to 63.162.03.52.52.03.54.55.53.5L1L2L3L4L1L2L3L4L1L2L3L40.99970.99970.99570.99830.99880.99880.99830.99990.98470.98470.96420.97481.45495.82296.81696.42870.69322.77423.33433.06660.12340.49400.58770.54309.5062E-025.9380E-035.0722E-035.3784E-031.4964E-019.3477E-037.7774E-038.4564E-035.6040E-013.4996E-022.9417E-023.1838E-02L1L2L3L4L1L2L3L40.99190.99480.99770.99760.98270.98030.98270.98210.28300.06840.07890.07850.27180.07340.07630.07572.4436E-024.0440E-013.5058E-013.5237E-012.5443E-023.7685E-013.6253E-013.6540E-01L1L2L3L4L1L2L3L40.99730.99700.98620.99920.96940.96830.94260.99084.07323.77192.78575.40921.76251.63151.19532.36411.3946E-022.2590E-023.0587E-021.5752E-023.2229E-025.2226E-027.1284E-023.6042E-02L1L2L3L4L1L2L3L40.97490.97730.98880.95710.97110.97350.98790.95070.77890.53540.44670.64250.55160.37910.31680.45442.0040E-014.3730E-015.2414E-013.6441E-012.8297E-016.1760E-017.3905E-015.1525E-01L1L2L3L40.61870.62220.65220.60750.15910.16170.14970.16731.0866E+001.0692E+001.1549E+001.0334E+00*1 Atmospheric pressure head catm=10.34 m*2 Relative viscosity of air ma=1.8×10- 2procedures can be used to obtain air permeabilitycoe‹cients in heterogeneous and anisotropic soils,without complex methods or procedures, from airpermeability test data.Evaluation of the Radius of Vacuum In‰uenceTable 6 shows the radius of vacuum in‰uence obtainedby using Eqs. (14a) and (14b) at each site. The radius ofvacuum in‰uence obtained from L10 is similar to that obtained from L20 (Table 6). As a result, Eqs. (14a) and(14b) can both be used to calculate the radius of vacuumin‰uence from results of air permeability tests. Equation(14a) has an advantage over Eq. (14b) that the calcula-tion of the radius is simpler. The quantities L10 or L20 atthe intersection between the regression line and the radialaxis are negative at site E (Fig. 21). For this reason thecorrelation coe‹cient of the regression is far from 1.0,and c2atm-c2a and L1 or L2 do not correlate well with eachother. Therefore, it is necessary to measure the air pressure head precisely to determine the radius of vacuum in‰uence. The radius of vacuum in‰uence obtained by theproposed procedures is useful for determining the spacebetween wells from which contaminated air in soil is extracted by vacuum pumps. A varying radius of vacuumin‰uence can be obtained when the monitoring wells areinstalled in concentric circles and the air permeability AIR PERMEABILITY COEFFICIENTcoe‹cient diŠers among wells because of anisotropicconditions.CONCLUSIONIn this study, the air permeability coe‹cient is evaluated from Eq. (10) and gradients E of the regression linesbetween c2atm-c2a and L1, L2, L3, and L4, and the radiusof vacuum in‰uence is obtained from point where theregression line intersects the L1 or L2 axis, where c2atm-c2ais zero. Gradients E and the radius of vacuum in‰uencewere obtained from air permeability test data in gravelsoil and loam soil with high degree of water saturation using the proposed procedure for air permeability and Eq.(14). The accuracy of the air permeability coe‹cient obtained by the proposed procedure was within one order ofmagnitude. Therefore, these procedures are applicable toˆeld conditions.A simple equation with acceptable precision is more141convenient than the complex equation to calculate the airpermeability coe‹cient from air permeability test data onsite. It was easy to calculate the air permeabilitycoe‹cient from Eq. (4) or Eq. (5), and both equationsyielded su‹ciently accurate values for the air permeability coe‹cient, which was validated by using numericalsimulation results. The radius of vacuum in‰uence calculated with Eq. (14a) was equal to that calculated with Eq.(14b), but Eq. (14a) is simpler to use than Eq. (14b).Therefore, the radius of vacuum in‰uence can be mosteasily obtained with Eq. (14a).ACKNOWLEDGMENTSWe acknowledge Taisei Corporation and Kajima Corporation for providing the air permeability test data. Wethank Dr. Halim MD. Abdul of Kyushu University forhis helpful advice. We are also most grateful for the comments of the reviewers of this article.REFERENCES1) Abriola, L. M. and Pinder, G. F. (1985): A multiphase approach tothe modeling of porous media contamination by organic compounds 2. Numerical simulation, Water Resources Research, 21(1),19–26.2) Baehr, A. L. and Bruell, C. J. (1990): Application of Stefan-Maxwell equation to determine limitations of Fick's low when modelingorganic vapor transport in sand column, Water ResourcesResearch, 26(6), 1155–1163.3) Baehr, A. L. and Hult, M. F. (1991): Evaluation of unsaturatedzone air permeability through pneumatic tests, Water ResourcesResearch, 27(10), 2605–2617.4) Burdine, N. T. (1953): Relative permeability calculations frompore-size distribution data, Technical report, Petroleum transactions, American Instrument Mining Metal Engineering, 98, 71–77.5) Celia, M. and Bouloutas, E. T. (1990): A General mass-conservative numerical solution for the unsaturated ‰ow equation, WaterResources Research, 26(7), 1483–1496.Fig. 22. The relationships between the discharge rate of air and the airpermeability coe‹cient measured at sites A (white symbols) and D(black symbols)Table 6. Values of intersection L10, where the regression line between c2atm-c2a and L1 intersects the L1 axis, and of intersection L20, where theregression line between c2atm-c2a and L2 intersects the L2 axis, and the radius of vacuum in‰uence values obtained using Eq. (14) and L10 or L20 atsites A, B, C, D, and EExtraction wellSiteMonitoring wellScreenScreenSoilUpper(GL-m)Lower(GL-m)L10L20Discharge ofair (m3/min)Upper(GL-m)Lower(GL-m)L10 (l/m)Radius of vacuumin‰uence (m)L20Radius of vacuumin‰uence (m)ALoam3.53.752.82.11.43.53.750.030790.074150.0575432.513.517.40.00770.01850.014432.413.517.4BLoam480.142.56.04.08.00.146290.154896.86.50.57750.61176.86.41.2*No. 1 to 31.2*No. 4 to 62.30.0727213.80.082113.402.30.133677.50.14787.41.15CLoam1.22.3DLoam2.03.53.162.52.02.03.53.50.081010.0678012.314.70.1250.105812.014.2EGravel4.55.53.54.55.5———— HIBI ET AL.1426) Davis, E. L. (1994): EŠect of temperature and pore size on thehydraulic properties and ‰ow of a hydrocarbon oil in the subsurface, Journal Contaminant Hydrology, 16, 55–86.7) Gerke, H. H., Hormung, U., Kelanemer, Y., Slodicka, M. andSchumache, S. (1999): Optimal Control of Soil Venting Mathematical Modeling and Applications, Birkhauser Verlag, Base, 6–42.8) Helmig, R. (1997): Multiphase Flow and Transport Process in theSubsurface, Springer, Berlin, 5–16.9) Hibi, Y., Fujinawa, K. and Fujiwara, Y. (2001): A comparison ofˆnite element solution for pressure based and mixed type equationsof two-phase ‰ow in porous media, International Association forResearch Committee on Groundwater Hydraulics 1st GroundwaterSeminar between China, Korea and Japan, International Association for Hydraulic Research, Fukuoka, 41–52.10) Hibi, Y., Jinno, K., Egusa, N., Kawabata, J. and Shimomura, M.(2006a): Prediction of in‰uence radius of vacuum pumping in unsaturated soil and evaluation air permeability by in situ vacuumtest, Journal of Environmental System and Engineering, 62(2),488–501.11) Hibi, Y., Jinno, K., Egusa, N., Kawabata, J. and Shimomura, M.(2006b): Comparison of the theoretical and numerical solution bythe ˆnite element method for steady state air ‰ow in soil toward anextraction well, Journal of Environmental System and Engineering,62(4), 391–402.12) Hoeg, S., Scholer, H. F. and Warnatz, J. (2004): Assessment of interfacial mass transfer in water-unsaturated soils during vapor extraction, Journal of Contaminant Hydrology, 74, 163–193.13) Lenhard, R. J., Oostrom, M., Simmons C. S. and White, M. D.(1995): Investigation of density-dependent gas advection oftrichloroethylene: Experiment and a model validation exercise,Journal Contaminant Hydrology, 19, 47–67.14) McWhorter, D. B. (1990): Unsteady radial ‰ow of gas in the vadosezone, Journal of Contaminant Hydrology, 5, 297–314.15) Reinecke, S. A. and Sleep, B. E. (2002): Knudsen diŠusion, gaspermeability, and water saturation in an unconsolidated porousmedium, Water Resource Research, 38(12), 16-1–16-15.16) Shan, C., Falta, R. W. and Javandel, I. (1992): Analytical solutionfor steady state gas ‰ow to a soil vapor extraction well, WaterResources Research, 28(4), 1105–1120.17) Sleep, B. E. and Sykes, J. F. (1993): Compositional simulation ofgroundwater contamination by organic compounds 1. Model development and veriˆcation, Water Resource Research, 29(6),1697–1708.18) Thorstenson, D. C. and Pollock, D. W. (1989): Gas transport inunsaturated zones: Multicomponent system and the adequacy ofFick's laws, Water Resource Research, 23(3), 477–507.19) US Army Corps of Engineers (2002): Soil Vapor Extraction andBioventing Engineer Manual, 1-1–21-22, D-8–E-9.20) van Genuchten, M. T. (1980): A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Science Society American Journal, 44, 892–898.21) Yasumoto, K. and Kawabata, J. (2000): Evaluation of in-situpermeability test for designing soil, Groundwater Updates,393–398.kra Ks &(ca-rra z ).(16b)mra&zThe density of air can be expressed by the ideal airequation:Vz=-ra=ca Ma rw g/RT(17)where R is the gas constant [ML2/mol kT2 ], T is the temperature [k], and Ma is the molecular weight [M/mol].When the air pressure head is equal to the atmosphericpressure head catm, the density of air can be expressed as,ratm=catm Ma rw g/RT.(18)Dividing Eq. (17) by Eq. (18) with a constant temperature and rearranging the result gives the following equation:ra=ca ratm/catm.(19)By substituting Eqs. (16) and (19) into Eq. (15), the following equation governing steady air ‰ow in soil is derived:Ø»& ca ratm Kra ks &ca1 ca ratm Kra ks &ca+r catm mra &r&r catm mra &r+Ø»& ca ratm Kra ks &(ca-rra z ) =0.&z catm mra &z(20)The velocities of water in soil can be expressed by Darcy'slaw:&c wVwr=-krw Ks(21a)&r&c w- z(21b)&zThe law of conservation of mass for steady water ‰owin soil can be expressed in the cylindrical coordinate system as follows:Vwz=-krw Ks&Vwr 1&Vwz+ Vwz+=0&rr&z(22)where Vwr is the velocity of water in the radial directionand Vwz is the velocity of water in the vertical direction.The equation governing water ‰ow in soil can then be derived by substituting Eq. (21) into Eq. (22).APPENDIX: EQUATIONS GOVERNINGAIR-WATER TWO-PHASE FLOWThe law of conservation of mass for steady air ‰ow insoil can be expressed in a cylindrical coordinate system asfollows:&raVar 1&raVaz+ raVar+=0,&rr&zVaz is the velocity of air in the vertical direction. Thevelocities obey Darcy's law and can be expressed usingthe following equations:kra Ks &caVr=-(16a)mra &r(15)where Var is the velocity of air in the radial direction andØ»&&c wkrw Ks &cw+krw Ks&rr&r&r+«$&&krw Ks (cw-z ) =0&z&r(23)
  • ログイン
  • タイトル
  • Investigation for Necessity of Dispersivity and Tortuosity in the Dusty Gas Model for a Binary Gas System in Soil
  • 著者
  • "Yoshihiko Hibi, Katsuyuki Fujinawa, Seiji Nishizaki, Kazuo Okamura, Masaharu Tasaki"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 143〜159
  • 発行
  • 2010/02/15
  • 文書ID
  • 64348
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 143–159, Feb. 2010INVESTIGATION FOR NECESSITY OF DISPERSIVITY AND TORTUOSITYIN THE DUSTY GAS MODEL FOR A BINARY GAS SYSTEM IN SOILYOSHIHIKO HIBIi), KATSUYUKI FUJINAWAii), SEIJI NISHIZAKIiii),KAZUO OKAMURAiv) and MASAHARU TASAKIiv)ABSTRACTDiŠusion, dispersion, and advection are important processes in multi-gas systems in soils. To date, both Fick'smodel and the Dusty Gas (DG) model have been used to model the movement of gases in these systems. Dispersion isincluded in the dispersion-advection equation with Fick's Model for the movement of gases in gas-phase of soil, yet themovement of gases in multi-component gas-soil systems is considered to be expressed more accurately by the DGmodel than by Fick's model. However to date, no study has investigated the necessity of considering dispersion in theDusty Gas (DG) model. We carried out column experiments for nitrogen-methane, nitrogen-carbon dioxide, and carbon dioxide-methane binary gas systems in sandy soil, and also did simulations on the same systems using both Fick'smodel and the DG model. A comparison of the results of the column experiments with our simulations conˆrmed thatthere was no need to consider the dispersion in the advection-diŠusion equations with the DG model when the velocityof gas was 0.05–0.4 cm/s in Toyoura sand. Furthermore, our experiments and simulations with the DG model showedthat, rather than dispersion, tortuosity should be taken into account in application of the DG model to the above condition.Key words: diŠsion, dispersivity, dusty gas model, Fick's model, gas phase in soil, tortuosity (IGC: D4/E7/E13)in the background gas in front of the advancing tracer gas(Hibi, 2008).Dispersion in water in a porous medium is referred toas ``mechanical mixing dispersion'' in the advectiondispersion equation of Fick's model (Bear, 1972). Mendoza and Frind (1990a, 1990b), Sleep and Sykes (1993a,1993b), and Hoeg et al. (2004) formulated an advectiondispersion equation that included a mechanical mixingdispersion term derived from Fick's model to simulatethe migration of a component gas in a gas-soil system.Sleep (1998) considered mechanical mixing dispersion inthe advection-dispersion equation of the DG model;however, the necessity of the mechanical mixing dispersion term in this model has not been investigated in anystudy. The concept of mechanical mixing dispersion isused to account for the diŠerence between experimentallyobserved dispersion and the molecular diŠusion calculated from Fick's model. The dispersion coe‹cient of Fick'smodel includes the mechanical mixing dispersioncoe‹cient and the molecular diŠusion coe‹cient withtortuosity. Fick's model does not include Knudsen diŠusion as a component of mechanical mixing dispersion.Hibi et al. (2007) conducted column experiments forINTRODUCTIONDiŠusion and dispersion are important processes in themigration of chemical substances in multi-component gassystems in soils. Fick's model and the Dusty Gas model(hereafter referred to as the DG model) (Mason et al.,1967; Cunningham and Williams, 1980; Mason andMalinauskas, 1983; Thorstenson and Pollock, 1989;Massmann and Farrier, 1992) have been used to modelthe diŠusion of gas in porous media. Molar ‰uxes calculated using Fick's model diŠer from those obtained fromthe DG model. Thorstenson and Pollock (1989) andMassmann and Farrier (1992) investigated the in‰uenceof the Knudsen diŠusion ‰ux on multi-component gasdiŠusion in soils and concluded that the value of theKnudsen diŠusion coe‹cient in‰uenced the movement ofchemical substances in the vapor zone of soils whenpermeability is less than 10-10 cm2. Fick's model does notinclude the Knudsen diŠusion, and the diŠusioncoe‹cient in Fick's model is the same for all molar fractions of gas. In contrast, the DG model includes theKnudsen diŠusion coe‹cient and the molecular diŠusioncoe‹cient of the DG model varies according to changesi)ii)iii)iv)Department of Environmental Science and Technology, Faculty of Science and Technology, Meijo University, Nagoya, Aichi, Japan (hibiy@ccmfs.meijo-u.ac.jp).Department of Civil Engineering, Faculty of Engineering, Shinshu University, Nagano, Nagano, Japan.Nippon Koei, Chiyoda, Tokyo, Japan.Institute of Technology, Shimizu Corporation, Koto-ku, Tokyo, Japan.The manuscript for this paper was received for review on February 10, 2009; approved on September 29, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.143 144HIBI ET AL.two binary gas systems: a nitrogen-oxygen gas system anda nitrogen-carbon dioxide gas system. Dispersivities related to mechanical mixing dispersion were determinedfrom the gradients of regression lines of plots of gas velocity versus the diŠusion coe‹cient optimized withbreakthrough curves of these experiments. Hibi et al.(2007) found that the dispersivity of a gas depends on thecomponents of the gas system of which it is part. Costanza-Robinson and Brusseau (2002) also conducted columnexperiments for binary gas systems in wet soil but wereunable to conˆrm that the dispersivities of the gas systems were dependent on the dispersivities of the component gases. Zheng and Bennett (2002) reported that dispersivity is independent of the component gases of a multi-gas system because the structure of the porous mediumcauses mechanical mixing dispersion; that is, dispersivityshould be the same for all multi-gas systems. As statedabove, the dipersivities of Fick's model have been obtained in some studies, but the dispersivity of the DGmodel was not been investigated to date. The aim of thisstudy is to investigate the necessity of both dispersivityand tortuosity in the DG model in a multi-gas system andto obtain values for them. To this end, we conductedcolumn experiments for nitrogen-methane, nitrogen-carbon dioxide, and carbon dioxide-methane binary gas systems. We simulated our column experiments by usingboth Fick's model and the DG model. A comparison ofthe experimentally determined dispersivities with those ofthe DG model simulations clearly showed that mechanical mixing dispersion was not included in the DG modelwhen the velocity of gas was 0.05–0.4 cm/s in Toyourasand.The purpose of this study was to determine not only thedispersivities, but also the tortuosities from both thecolumn experiments and the DG model simulations.Although Costanza-Robinson and Brusseau (2002) determined tortuosities using the Penman-Millington Quirkmodel (Moldrup et al., 1997), and Fen and Abriola (2004)determined tortuosities with the DG model for a binarygas system, tortuosities for multi-component gas systemshave not yet been obtained directly from column experiments.COLUMN EXPERIMENTS FOR THE BINARY GASSYSTEM IN DRY SANDColumn experiments were conducted to estimate themechanical mixing dispersion and tortuosity in a binarygas system in dry sand. The length and diameter of theacrylic resin column we used in our experiments were 90and 50 cm, respectively, and the column was equippedwith ˆve syringe ports for gas sampling and ˆve electricalpressure gauges to measure the gas pressure within thecolumn (Figs. 1 and 2). The gas pressures at the inlet andoutlet of the column were measured with a precision pressure gauge. A valve was used to control the gas ‰ow intothe precision gauge (Fig. 1). We used paired combinations of methane, nitrogen, and carbon dioxide to formthe background and tracer gases of our experimental bi-Fig. 1.Fig. 2.Schematic diagram of the experimental setupStructural diagram of the column experiment apparatusnary systems because of their relative molecular weights(molecular weights increase in the order methaneºnitrogenºcarbon dioxide).First, dry standard Toyoura sand of grain size 0.08 to2.0 mm was compacted in a column standing on thelaboratory ‰oor. The column was initially ˆlled withbackground gas. Next, the valve at the base of the columnwas opened and, after reaching a speciˆed pressure at theinlet to the column, the tracer gas was injected at the baseof the column. The discharge rate of the tracer gas fromthe top of the column was measured by a ‰ow meter, andthe gas pressures in the column were measured by the ˆvepressure gauges. Then, gas samples were extracted viasyringes at the sampling ports. The time of extraction wasrecorded, and the extracted gas samples were analyzed bygas chromatography to obtain the molar concentrationsof the tracer and background gases. Samples were repeatedly extracted until the tracer gas was detected at the uppermost sample port (No. 5).Three porous media were used in our experiments. Thegas-ˆlled porosity and intrinsic permeability of porousmedium 1 were 0.429 and 2.076E–11 m2, respectively;those of porous medium 2 were 0.429 and 2.093E–11 m2,and those of porous medium 3 were 0.432 and 2.026E–11m2 (Table 1). The molecular weights and viscositiesshown in Table 1 are from Poling et al. (2001).The Knudsen diŠusion coe‹cient can be described asfollows:Di=ksbm/M 1/2i ,(1)where bm is the intrinsic Klinkenberg parameter (M1/2/mol1/2T2). The intrinsic Klinkenberg parameter in Eq. DISPERSIVITY AND TORTUOSITY(1) can be calculated from the Klinkenberg parameter ofair. Thorstenson and Pollock (1989) investigated published data on the Klinkenberg parameter for air and derived the following correlation between the Klinkenbergparameter and intrinsic permeability:Table 1. Transport properties of the three porous media and KnudsendiŠusion coe‹cients of the gases used in the column experimentsand simulationsPorous Medium 1PorosityPermeabilityKnudsen coe‹cient0.4292.076E-11 m 2bair=0.1ks-0.39,Porous Medium 2PorosityPermeabilityKnudsen coe‹cientbm=bairM 1/2air /mair,0.4292.093E-11 m 2Porous Medium 3PorosityPermeability0.4322.026E-11 m 2Knudsen coe‹cientMethaneCarbon dioxideNitrogen24.541 cm2/s14.815 cm2/s18.571 cm2/sGasesMolecular weightMethaneCarbon dioxideNitrogen16.04 g/mol44.01 g/mol28.01 g/molMolecular diŠusion coe‹cientMethane-NitrogenCarbon dioxide-MethaneCarbon dioxide-NitrogenTable 2.Viscosity1.08E-05 Pa・S1.47E-05 Pa・S1.76E-05 Pa・S0.21187 cm2/s0.16041 cm2/s0.14988 cm2/sColumn temperatures, inlet and outlet column pressures, and pressure diŠerences during the column experimentsPressure of gasGasesMedium123(3)where Mair is the molecular weight of air (28.75 g/mol)and mair is the viscosity of air (1.8E–5 Pa s).Table 2 shows the binary gas combinations, the gaspressures at the inlet and outlet of the column, and thediŠerences between the gas pressures at the column inletand the outlet during the experiments. All of the columnexperiments were conducted at a temperature of about219C. For experimental runs using either methane or carbon dioxide as the tracer gas in porous medium 1 ˆlledwith a background gas of nitrogen, the tracers were injected when the diŠerences between the inlet and outletgas pressures were approximately 0.18, 0.37, and 0.75kPa. The column experiments for porous medium 2 wereconducted for each of the following as the backgroundgas: methane, carbon dioxide, and nitrogen. The diŠerences between the inlet and outlet gas pressures when thetracer gases were injected to porous medium 2 were approximately 0.18, 0.37, and 0.76 kPa for the nitrogenbackground gas and 0.39 and 0.78 kPa for methane andcarbon dioxide background gases. The diŠerences be-25.032 cm2/s15.112 cm2/s18.943 cm2/sMethaneCarbon dioxideNitrogen(2)where bair is the Klinkenberg parameter (M/LT2) of air.The intrinsic Klinkenberg parameter bm can then be calculated from the Klinkenberg parameter and the viscosityand molecular weight of air:24.857 cm2/s15.006 cm2/s18.810 cm2/sMethaneCarbon dioxideNitrogen145Back GroundTracerN2CH 4N2CO2CH 4N2CO2N2CO2CH 4CH 4CO2N2CH 4N2CO2CH 4N2CO2N2Temperature9CVelocityInletkPaOutlet(initial condition)kPaDiŠerencekPaPort 2cm/sPort 3cm/s20.921.121.121.221.121.398.16698.37498.77498.17098.35698.75097.97898.00098.02597.99497.98897.9860.1880.3740.7490.1760.3680.7640.0710.1430.2860.0590.1300.2770.0740.1530.3100.0760.1420.29321.021.021.021.421.121.120.920.819.620.220.821.421.221.696.46696.86597.50497.97398.37498.77497.39097.86296.98397.20897.62796.12296.24196.60696.07096.08497.11297.19398.00098.02597.02297.09296.80796.83296.87295.93795.86995.8480.3960.7810.3920.7800.3740.7490.3680.7700.1760.3760.7550.1850.3720.7580.2010.3750.1580.3230.1590.3270.1990.4170.0640.1390.2890.0620.1310.2770.1980.3980.1560.3270.1690.3580.1980.4110.0770.1530.3100.0670.1410.29121.021.021.021.0————————0.4000.8000.4000.8000.2640.5470.2640.4550.2590.5030.2390.392 HIBI ET AL.146tween the inlet and outlet gas pressures in porous medium3 were measured only to obtain the dispersion coe‹cientand gas velocity optimized with the breakthrough curvefor tracer gas nitrogen in background gases of methaneand carbon dioxide.FORMULATION OF DUSTY GAS MODELEQUATIONS FOR A MULTI-COMPONENTGAS SYSTEM IN SOILIf gas slip does not occur, the velocity of gas movement in soil can be described by Darcy's law as follows:Vg=-Krgks(;Pg+rgg;z),mg(4)where Vg is the velocity of the gas in soil (L/T); ks and Krgare the intrinsic permeability (L2) and the relativepermeability of the gas (dimensionless), respectively; mg isthe viscosity of the mixed gas; Pg is the total gas pressure(M/LT2); rg is the gas density (M/L3); g is the gravitational constant (L/T2); and z is the vertical coordinate and ispositive upward.Assuming that the gas is incompressible because of itsslow velocity, the gas ‰ow equation can be described interms of the continuity equation and Darcy's law as«$&u gKrgKs=;・(;Pg+rgg;z) ,&tmg(5)where t is the time (T) and ug is the gas-ˆlled porosity(dimensionless), which is the ratio of the volume of gas tothat of the voids in the soil.The density of a mixed gas in a binary gas system in soilcan be calculated from the molecular weight and molarconcentration of each component as follows:rg=CAMA+CBMB,(6)where CA and CB are the molar concentrations (mol/L3)of components A and B, respectively, and MA and MB arethe molecular weights (g/mol) of components A and B,respectively. Furthermore, the viscosity of the mixed gascan be obtained from the following equation proposed byPoling et al. (2001):m g=X gAmgAX gBmgB+ g,gX cAA+X BcBA X AcAB+X gBcBBgA(7)where, X gA and X gB are the molar fractions (dimensionless)of components A and B, respectively, and mgA and mgB arethe viscosities (M/LT) of components A and B, respectively. cAA, cBB, cAB, and cBA in Eq. (7) can be calculatedfrom the molecular weights of components A and B byusing the following equations:Ø MM »M=ØM »cAA=A1/2=1cBB=AcABBAØ MM »B1/2=1B1/2=1.cBA(8)The diŠusion molar ‰uxes of components A and B of abinary gas system in soil are described by the DG modelequations as follows:XANDB-XBNDANDA1-=;( PA+rAgz)tugDABtugDA RT(9a)XBNDA-XANDBNDB1-=;( PB+rBgz),tugDABtugDB RT(9b)where NDA and NDB are the molar ‰uxes (mol/L2T) of components A and B, respectively; PA and PB are the partialpressures (M/LT2) of components A and B, respectively;R is the gas constant (M L2/molKT2); T is the temperature (K); DAB is the molecular diŠusion coe‹cient (L2/T)between components A and B; DA and DB are the Knudsen diŠusion coe‹cients (L2/T) of components A and B,respectively; rA and rB are the densities (M/L3) of components A and B, respectively; and t is the tortuosity(dimensionless).Substituting CA=PA/RT, CB=PB/RT, rA=MACA, andrB=MBCB into Eqs. (9a) and (9b) givesØØ»MC +C »RTXANDB-XBNDA NDAM Ag- =tug ;CA+CADABDARTXBNDA-XANDB NDB- =tug ;DABDBgBBB.(10a)(10b)By summing Eqs. (9a) and (9b) and re-arranging them,the following equation can be derived:-NDA NDB tug- =;( Pg+rggz).DA DB RT(11)Then, substituting Eq. (11) into Eq. (10), NDA becomesugt;CAD B XA X B1++DA DAB DAB DAu gt M A g-CADB XA XB1++RTDA DAB DAB DAug tXA-DB;( Pg+rggz).DB XA XB1DAB++RTDA DAB DAB DA(12)NDA=-ػػػThe total molar ‰ux NTA of component A is equal to thesum of the advective molar ‰ux VgCA and the above NDA.Applying Darcy's law for the velocity of a gas, the totalmolar ‰ux NTA of component A can be derived from theabove Eqs. (4) and (12) as DISPERSIVITY AND TORTUOSITYugt;CADB XA X B1++DA DAB DAB DAug t M A g-D B X A XB1++RTDA DAB DAB DAug tDB Kgks++;( Pg+rgg) CADB XA XB1 DAB mg++CRTDA DAB DAB DANTA=-ػػØ»Assuming that dispersion is not considered, and substituting Eq. (14) into Eq. (13), the total molar ‰ux NTican be given asNTi=-D *i ;Ci+V*giCi.&u gC A+;・V*gCA=;・(D*A;CA).&tØV*gA=-u gtDB XA XB1++DA DAB DAB DA(14a)»ug t M A gD B X A XB1++RTDA DAB DAB DAØ»ug tDB K gk s ;+( Pg+rggz)DB XA XB1 DAB mg ++CRTDA DAB DAB DA(14b)-ØTable 3.»NDA=-tugDAB;CA.12(17)The following Eq. (18) expresses the advection-dispersionequation for component A according to Fick's model.& ug C A+;・VgCA=;・ug(Dmech+tDAB);CA,&t(18)where Dmech is the matrix for the mechanical mixing dispersion coe‹cient deˆned as:Dmech ij=aL`Vg`dij+(aL-aT)VgiVgj,`Vg`(19)where aL is the longitudinal dispersivity (L); aT is thetransverse dispersivity (L); i and j are the coordinates ofx, y and z; `Vg` is the norm of the velocity; and dln isKronecker's delta.To obtain the molar concentration of component A,we applied the characteristic ˆnite element method (similar to the Euler-Lagrange method used by Neuman (1981)and Fujinawa, (1986)) to Eqs. (16) and (18). Then, themolar concentration of component A is calculated asCB=Pg-CA.RT(20)The molar fractions of components A and B are then calculated from XA=CA/C and XB=CB/C with total molarconcentration C (mol/L3).Column temperatures and inlet and outlet tracer gas pressures and concentrations for the column experiments and simulationsGasesMedium(16)The diŠusion molar ‰ux is expressed for Fick's Model as(13)D *A=-(15)The advection-dispersion equation of component A forthe DG model can be expressed asThe diŠusion coe‹cient of the ˆrst term of the right sideof Eq. (13) includes both the molecular diŠusion and theKnudsen diŠusion. The second term of the right side ofEq. (13) is an advective term associated with gradationalgas pressure. Darcy velocity, molecular diŠusion, andKnudsen diŠusion aŠect this advective term in thehorizontal and vertical directions, and gravitation aŠectsit in the vertical direction. The diŠusion coe‹cient D *Aand the velocity Vg*A in the above diŠusion and advectiveterms are hereafter called the 'composite diŠusioncoe‹cient' and the 'composite velocity' of component A,respectively, and are deˆned as follows:147Pressure of gasBackGround TracerN2CH4N2CO2CH4N2CO2N2CO2CH4CH4CO2Temperature9CInletkPaConcentrationOutletInletOutlet(initial condition)DiŠernce(initial condition)kPakPaBack Ground Gas Tracer Gas Back Ground Gas Tracer Gasmol/cm3mol/cm 3mol/cm3mol/cm320.921.121.121.221.121.398.16698.37498.77498.17098.35698.75097.97898.00098.02597.99497.98897.9860.1880.3740.7490.1760.3680.7640.00.00.00.00.00.04.017E-054.023E-054.039E-054.013E-054.022E-054.036E-054.010E-054.008E-054.009E-054.006E-054.007E-054.004E-050.00.00.00.00.00.021.021.021.021.421.221.020.920.896.46696.86597.50497.97397.20797.49697.39097.86296.07096.08497.11297.19396.82796.73997.02297.0920.3960.7810.3920.7800.3800.7570.3680.7700.00.00.00.00.00.00.00.03.946E-053.963E-053.989E-054.002E-053.979E-053.988E-053.979E-054.006E-053.930E-053.931E-053.973E-053.971E-053.958E-053.957E-053.970E-053.975E-050.00.00.00.00.00.00.00.0 148HIBI ET AL.We simulated the column experiments shown in Table3 with both the DG model and Fick's model in this study.The analytical domain was consistent with the dimensions of the experimental column (length 90 cm, width 5cm). The ˆnite element grid consisted of 362 nodes deˆning 160 elements in this domain. The grid comprised 361cells of 0.5 cm vertical dimension and 5 cm horizontaldimension. This ˆnite grid allows for the simulation ofvertical one-dimensional gas ‰ow.For each simulation, the analytical domain was initially ˆlled with the background gas at the outlet gas pressures listed in Table 3. The molar concentration of thebackground gas at the outlet was derived from the idealgas equation by using the gas pressures and temperaturesin the analytical domain and a molar concentration ofbackground gas of zero at the inlet (Table 3). The tracergas was injected into the analytical domain by raising thepressure and molar concentration of the tracer gas at theinlet according to the ideal gas equation at pressures andtemperatures as shown in Table 3. The molar ‰ux of thebackground gas was taken to be zero at the outlet of thecolumn. Details of the porous media and gases used in thesimulations are provided in Table 1.RESULTS AND DISCUSSIONComparisons of Experimental Results and SimulationsFigures 3(a) and (b) show the breakthrough curves ofmethane at gas sample ports 2 and 3, respectively, in thegas system ˆlled with nitrogen. Figures 3(c) and (d) showthe breakthrough curves of nitrogen at gas sample ports 2and 3, respectively, in the gas system ˆlled with methane.The simulations shown in Fig. 3 were conducted witheŠective gas-ˆlled porosity of 0.365.We found that the molar fraction of tracer gas methanedetermined by column experiment was consistent with themolar fraction obtained by simulation according to boththe DG Model and Fick's model when the diŠerence between the inlet and outlet gas pressures was highest (0.749kPa) and gas velocity was fastest (Figs. 3(a) and (b)). Onthe other hand, slight diŠerences between the experimental and simulated molar fractions of methane were observed when the diŠerence in gas pressures was lowest(0.188 kPa) and gas velocity was slowest (Figs. 3(a) and(b)). The molar fraction of methane in the simulationrose earlier than in the column experiment and reached avalue of 1.0 later than in the experiment. This trend isrelated to the dependence of gas velocity on the diŠerencein inlet and outlet gas pressures. There are slight diŠerences between the molar fractions of methane obtainedusing the two models, but the ratio of the increase of theFig. 3. Comparison of the temporal changes of molar fractions of tracer gases obtained by column experiments with those simulated with the DGmodel and with Fick's model for the nitrogen-methane binary gas system. Tracer gas methane at (a) sample port 2 and (b) sample port 3. Tracergas nitrogen at (c) sample port 2 and (d) sample port 3 DISPERSIVITY AND TORTUOSITYmolar fraction of methane from Fick's model was greaterthan that from the DG model. This is because the DGmodel uses the composite diŠusion coe‹cient of Eq.(14a) and Fick's model incorporates only the binary diŠusion coe‹cient. The Knudsen diŠusion coe‹cient (included in the composite diŠusion coe‹cient) does not in‰uence the migration of gas in soils of high permeabilityexceeding 10-10 cm2 (Thorstenson and Pollock, 1989;Massmann and Farrier, 1992).We found that the experimental molar fraction oftracer gas nitrogen determined by the column experimentwas consistent with the molar fraction obtained by simulation when the diŠerence between the inlet and outlet gaspressures was 0.781 kPa (Figs. 3(c) and (d)). A slightdiŠerence was observed between the experimental andsimulated molar fractions of nitrogen when the diŠerenceof the gas pressure was 0.396 kPa. The molar fractions ofnitrogen rose earlier in the simulations than in the columnexperiments and reached a value of 1.0 later than in theexperiment (Figs. 3(c) and (d)). This result was similar tothat for tracer gas methane in the nitrogen-methane gassystem (Figs. 3(a) and (b)). These simulations were performed assuming a tortuosity value of 1.0 (no tortuosity).The magnitude of the diŠusion coe‹cient without tortuosity is greater than that with tortuosity, and the molarfraction of the tracer gas obtained by a simulation149without tortuosity rises earlier than that obtained by asimulation with tortuosity. The ratio of the increase inthe molar fraction of the tracer gas obtained by a simulation with tortuosity is greater than that obtained using asimulation without tortuosity. Therefore, the observeddiŠerences in the experimental and simulated molar fractions of the tracer gases are related to the tortuosity of theporous media. There was a slight diŠerence between themolar fractions of nitrogen simulated with the twomodels. The ratio of increase of the molar fraction ofnitrogen simulated with the DG model was greater thanthat for Fick's model (Figs. 3(c) and (d)), contrary to theresults for tracer gas methane in the methane-nitrogengas system (Figs. 3(a) and (b)).The simulated molar fractions of tracer gas carbon dioxide in the nitrogen-carbon dioxide system were consistent with those obtained experimentally at sample port 2when the diŠerences of the inlet and outlet gas pressuresof the column were 0.764 and 0.368 kPa (Fig. 4(a)). Similarly, the simulated molar fractions of tracer gas nitrogenwere consistent with those obtained experimentally atsample port 2 when the diŠerences of gas pressures were0.780 and 0.392 kPa (Fig. 4(c)) and when the diŠerencesof gas pressures were 0.764 and 0.780 kPa at sample port3 (Figs. 4(b) and (d)). The molar fractions of the tracergas obtained by simulation with the DG model were con-Fig. 4. Comparison of the temporal changes of molar fractions of tracer gases obtained by column experiments with those simulated by the DGmodel and by Fick's model for the nitrogen-carbon dioxide binary gas system. Tracer gas carbon dioxide at (a) sample port 2 and (b) sampleport 3. Tracer gas nitrogen at (c) sample port 2 and (d) sample port 3. The simulations for the nitrogen-methane gas system were conducted withan eŠective gas-ˆlled porosity of 0.365 150HIBI ET AL.sistent with those obtained by simulation with Fick'smodel when the diŠerences of gas pressures were greaterthan 0.368 kPa at sample port 2 (Figs. 4(a) and (c)) andgreater than 0.764 kPa at gas sample port 3 (Figs. 4(b)and (d)). When pressures are high, and, consequently,gas velocities are fast, migration of the tracer gas is by advection with little in‰uence of diŠusion or dispersion.There were slight diŠerences between the simulated andexperimental molar fractions of carbon dioxide at sampleport 2 when the diŠerence of the gas pressure was 0.176kPa (Fig. 4(a)). Moreover, these slight diŠerences werealso observed at sample port 3 when the diŠerence of thegas pressures was 0.368 kPa for the background gasnitrogen-tracer gas carbon dioxide gas system (Fig. 4(b))and at sample port 3 when the diŠerence of the gas pressure was 0.392 kPa for the background gas carbon dioxide-tracer gas nitrogen system (Fig. 4(d)). However, themolar fractions of carbon dioxide obtained by the simulations were not consistent with those obtained experimentally at sample port 3 when the diŠerence in gaspressure was 0.176 kPa (Fig. 4(b)). We inferred from thescatter of experimental data (Fig. 4(b)) that this inconsistency re‰ects disturbed gas ‰ow during the extractionof gas samples from the column. DiŠusion governs themigration of tracer gas in these situations where thediŠerence in the gas pressure is low and its velocity istherefore slow.The simulated molar fractions of tracer gas for thenitrogen-carbon dioxide gas system rose earlier andreached a value of 1.0 later in comparison to the columnexperiments, as was the case for the nitrogen-methane gassystem (Figs. 4(a), (b), and (d)). These results suggestthat tortuosity aŠected the nitrogen-carbon dioxide gassystem. The ratio of the increase of the molar fractionsimulated with the DG model was greater than that simulated with Fick's model for the background gas nitrogentracer gas carbon dioxide gas system (Figs. 4(a) and (b)).For the background gas carbon dioxide-tracer gas nitrogen gas system, the ratio of the increase of the molar fraction of nitrogen simulated with the DG model wassmaller than that simulated with Fick's model.The Knudsen diŠusion coe‹cients for carbon dioxideand nitrogen in porous medium 1 were 15.006 and 18.810cm2/s, respectively (Table 1), and the Knudsen diŠusioncoe‹cient for carbon dioxide was smaller than that fornitrogen. The Knudsen diŠusion coe‹cients for methaneand nitrogen in porous medium 2 were 25.032 and 18.943cm2/s, respectively (Table 1), and the Knudsen diŠusioncoe‹cient for nitrogen was smaller than that formethane. These results suggest that the ratio of the increase in the molar fraction of the tracer gas simulatedwith the DG model was greater than that simulated withFick's model when the Knudsen diŠusion coe‹cient ofthe tracer gas was smaller than that of the backgroundgas ( see Figs. 3(c), 3(d), 4(a), and 4(b)). This is becausethe composite diŠusion coe‹cient includes the KnudsendiŠusion coe‹cient.The simulated and experimental molar fractions oftracer gas were consistent for the methane-carbon dioxidegas system when the diŠerences of gas pressure were0.790 and 0.749 kPa (Fig. 5), that is, for faster gas velocities, as was the case for the nitrogen-methane andnitrogen-carbon dioxide gas systems. On the other hand,the simulated molar fractions of the tracer gas wereslightly inconsistent with those of the column experiments for the methane-carbon dioxide gas system for theslower gas velocities when the diŠerences of gas pressureswere 0.368 kPa (Figs. 5(a) and (b)) and 0.374 kPa (Figs.5(c) and (d)). A comparison of the molar fractions of thetracer gas at gas sample ports 2 and 3 for the methanecarbon dioxide system (Fig. 5) shows that the diŠerencesbetween the simulated and experimental results increasewith increasing distance from the gas inlet of the column.The ratio of the increase in the molar fraction of thetracer gas obtained using the simulation without tortuosity was smaller than that obtained experimentally, as wasthe case for both the nitrogen-methane and nitrogen-carbon dioxide gas systems (Figs. 5(b) and (d)). These resultssuggest that tortuosity must be included in the diŠusioncoe‹cient for both the DG model and Fick's model.The diŠerence between the molar fractions simulatedby the two models for the methane-carbon dioxide gassystem with slower gas velocities was greater than thatwith faster gas velocities, and the ratio of the increase inthe molar fraction of carbon dioxide simulated with theDG model was greater than that simulated with Fick'smodel when the Knudsen diŠusion coe‹cient for carbondioxide (14.815 cm2/s) was smaller than that for methane(24.541 cm2/s) (Figs. 5(a) and (b)). These trends observedfor the methane-carbon dioxide system are similar tothose of the nitrogen-methane and nitrogen-carbon dioxide systems. Therefore, the experimentally obtainedmolar fractions of tracer gas were consistent with thesimulated molar fractions for both models when thediŠerence between the inlet and the outlet gas pressures ofthe column were greater than about 0.75 kPa, and the gasvelocity was therefore faster than at lower pressure diŠerences. Moreover, the molar fraction of the tracer gassimulated with the DG model was similar to that of Fick'smodel. The composite diŠusion coe‹cient of Eq. (14a)had little in‰uence on the migration of tracer gas in thegas system when gas velocities were relatively fast. On theother hand, diŠerences between the simulated and experimental molar fractions of tracer gas were observedwhen gas velocities were slow, and hence, diŠusiongoverned gas migration. Then, the ratio of the increase ofthe simulated molar fraction of tracer gas was smallerthan that derived experimentally, and tortuosity in‰uenced the migration by diŠusion of the tracer gas.For a gas system in a porous media, the diŠusioncoe‹cients for both the DG model and Fick's modelmust include tortuosity, as shown by Eqs. (14a) and (17).The migration of tracer gas predicted by the DG modeldiŠers slightly from that predicted by Fick's model. Theratio of the increase in the molar fraction of tracer gaspredicted by the DG model is greater than that predictedby Fick's model when the Knudsen diŠusion coe‹cient ofthe tracer gas is smaller than that of the background gas. DISPERSIVITY AND TORTUOSITY151Fig. 5. Comparison of the temporal changes of molar fractions of tracer gases obtained by column experiments with those simulated by the DGmodel and by Fick's model for the methane-carbon dioxide binary gas system. Tracer gas carbon dioxide at (a) sample port 2 and (b) sampleport 3. Tracer gas methane at (c) sample port 2 and (d) sample port 3. The eŠective gas-ˆlled porosity used in the simulation for the methanecarbon dioxide gas system was 0.365This shows the in‰uence of the Knudsen diŠusioncoe‹cient (which is included in the composite diŠusioncoe‹cient expressed in Eq. (14a)) on the migration oftracer gas.The eŠective gas-ˆlled porosity of the porous mediathat we used for all simulations was 0.365 and was not dependent on gas velocity, or the particular backgroundand tracer gases used.Relationships between Gas Velocity and the DiŠusionCoe‹cientThe dispersion coe‹cient is generally proportional tothe gas velocity in the water phase of a soil system with aone-dimensional water ‰ow, as follows (Bear, 1972):D=aLV+tD0,(21)2where D is the dispersion coe‹cient (L /T), aL is longitudinal dispersivity (L), t is tortuosity (dimensionless),V is gas velocity (L/T), and D0 is the molecular diŠusioncoe‹cient (L2/T). Gidda et al. (2006) experimentally conˆrmed that the dispersion coe‹cient is directly proportional to the gas velocity in the binary gas system of soil.Then Costanza-Robinson et al. (2002) experimentallyderived the dispersivity of gas in soil from Eq. (21). Theˆrst term of the right side of Eq. (21) is the mechanicalmixing term of dispersion diŠusion; it is determined bythe soil type and is independent of chemical substancesmoving in the soil system. According to Eq. (21), themechanical mixing term is proportional to the gas velocity, independent of gas moving in the soil system, and thedispersivities, which are the gradients of regression linesfrom plots of gas velocity versus the dispersioncoe‹cient, are constant for all gases.Figure 6(a) shows the relationship between gas velocityand the dispersion coe‹cient optimized by the PowellConjugate Gradient Method (Fujinawa, 1983) by usingthe methane breakthrough curves shown in Fig. 3(a). Theoptimized gas velocity for the background gas nitrogentracer gas methane system is proportional to the optimized diŠusion coe‹cient (Fig. 6(a)). The breakthrough curves of Fig. 3(a) were obtained by simulationsusing the DG model for the background gas nitrogentracer gas methane binary gas system, without themechanical mixing term and without tortuosity. If Fick'smodel is applied for the migration of gas in the gas-soilsystem without mechanical mixing, the diŠusioncoe‹cient should be constant over the range of all optimized gas velocities. However, the regression line foroptimized gas velocity plotted against the optimizeddiŠusion coe‹cient (Fig. 6(a)) has a gradient of 0.0958cm, although the mechanical mixing term was not considered in this simulation with the DG Model. 152HIBI ET AL.Fig. 6. Relationships between gas velocities and diŠusion coe‹cients for tracer gases optimized with breakthrough curves simulated with the DGmodel for binary gas systems nitrogen-methane, nitrogen-carbon dioxide and methane-carbon dioxide. Regression lines for tracer gases (a)methane and (b) nitrogen in the nitrogen-methane gas system; (c) carbon dioxide and (d) nitrogen in the nitrogen-carbon dioxide gas system;and (e) methane and (f) carbon dioxide in the methane-carbon dioxide gas systemFigure 6(b) shows the regression line for gas velocityplotted against the diŠusion coe‹cient optimized withthe breakthrough curves of tracer gas nitrogen, whichwere simulated using the DG model for the nitrogenmethane gas system by means of the Powell conjugategradient method (Fujinawa, 1983). By comparing thegradients of the regression line for the tracer gasesmethane and nitrogen (Figs. 6(a) and (b), respectively)with Eq. (21), it can be seen that the gradients of theregression lines are equivalent to the dispersivity of Eq.(21). The lower gradient of the regression line for tracergas nitrogen than that for tracer gas methane in thenitrogen-methane gas system conˆrms that dispersivity isdependent on the tracer gas in the gas system simulatedby the DG model. However, these gradients do notrepresent the dispersivity generated by the mechanicalmixing term. Because the ratio of the increase in the molar fraction of the tracer gas obtained with the DG modelwas diŠerent to that obtained with Fick's model (asshown in Fig. 3), the diŠusion coe‹cient optimized byusing the results of the simulation with the DG model isnot equal to that obtained by simulation with Fick's DISPERSIVITY AND TORTUOSITYmodel. For a gas velocity of 0 cm/s, the diŠusioncoe‹cient of methane (0.1959 cm2/s) was slightly smallerthan that of nitrogen (0.2298 cm2/s), which was slightlylarger than the binary molecular diŠusion coe‹cient(0.2119 cm2/s) in the nitrogen-methane binary gas system(Figs. 6(a) and (b)).The gradient of the regression line for gas velocity plotted against the diŠusion coe‹cient optimized with thebreakthrough curves of the tracer gas carbon dioxidesimulated using the DG model for the nitrogen-carbon dioxide gas system was 0.073 cm and the diŠusioncoe‹cient at gas velocity 0 cm/s was 0.1207 cm2/s (Fig.6(c)). For tracer gas nitrogen optimized using the breakthrough curves simulated with the DG model for thenitrogen-carbon dioxide gas system the gradient of theregression line and the diŠusion coe‹cient at gas velocityof 0 cm/s were 0.0674 cm and 0.1824 cm2/s, respectively(Fig. 6(d)). The gradient of the regression line for carbondioxide approximated that for nitrogen. For a gas velocity of 0 cm/s, the diŠusion coe‹cient for carbon dioxide(0.1207 cm2/s) was smaller, and that of nitrogen (0.1824cm2/s) was larger, than the molecular diŠusion coe‹cient(0.14988 cm2/s) for the nitrogen-carbon dioxide binarygas system.The gradient of the regression lines for gas velocityplotted against diŠusion coe‹cient optimized with thebreakthrough curves for tracer gases methane and carbondioxide simulated with the DG model for the carbon dioxide-methane gas system were 0.0728 and -0.011 cm,respectively (Figs. 6(e) and (f)). This indicates that thegradients of the regression lines obtained from the breakthrough curves simulated with the DG model are diŠerentfor tracer gases methane and carbon dioxide. The diŠusion coe‹cients for methane and carbon dioxide at a gasvelocity of 0 cm/s were 0.1741 and 0.1591 cm2/s, respectively. The diŠusion coe‹cient of methane was slightlygreater and that of carbon dioxide was slightly smallerthan the binary molecular diŠusion coe‹cient (0.16041cm2/s) for the methane-carbon dioxide gas system.The diŠerence between the Knudsen diŠusioncoe‹cients of carbon dioxide and nitrogen is the smallestamong the binary gas systems used in this study. TheKnudsen diŠusion coe‹cients of carbon dioxide andnitrogen in porous medium 2 were 15.122 and 18.943cm2/s, respectively (Table 1). For this case, the value ofDB/DA in Eq. (14a) was 0.798 for background gas carbondioxide and tracer gas nitrogen, and 1.253 for background gas nitrogen and tracer gas carbon dioxide. Onthe other hand, the diŠerence between the Knudsen diŠusion coe‹cients of methane and carbon dioxide isgreatest among the binary gas systems used in this study,and the value of DB/DA was 0.604 for background gascarbon dioxide and tracer gas methane, and 1.656 forbackground gas methane and tracer gas carbon dioxide.When DB/DA of Eq. (14a) equals 1.0, and for high valuesof the Knudsen diŠusion coe‹cient, the diŠusioncoe‹cient included in the Knudsen diŠusion coe‹cientfor the DG model approximates the binary moleculardiŠusion coe‹cient.153The relationships between the diŠusion coe‹cients calculated from Eq. (14a) and the molar fractions for tracergases methane and nitrogen in the nitrogen-methane gassystem (Fig. 7(a)) show that the diŠusion coe‹cient oftracer gas methane is greater than the binary moleculardiŠusion coe‹cient (0.21187 cm2/s) because DB/DA is lessthan 1.0, but the diŠusion coe‹cient of tracer gas nitrogen is smaller than the binary molecular diŠusioncoe‹cient for this gas system because DB/DA for nitrogenis greater than 1.0.Figure 7(b) shows the diŠusion coe‹cients for tracergases carbon dioxide and nitrogen calculated from Eq.(14a) for the nitrogen-carbon dioxide gas system. Figure7(c) shows the diŠusion coe‹cients for tracer gasesmethane and carbon dioxide calculated from Eq. (14a)for the carbon dioxide-methane gas system. The diŠusioncoe‹cients of tracer gases simulated with the DG modelwere greater than the binary diŠusion coe‹cients whenDB/DA of the tracer gas was less than or equal to 1.0, andtheir values increased as the molar fraction of the tracergas increased (Fig. 7). On the other hand, when DB/DAfor the tracer gas was greater than 1.0, the diŠusioncoe‹cients simulated with the DG model were smallerthan the binary molecular diŠusion coe‹cient anddecreased as the molar fraction increased (Fig. 7). ThediŠerence between the diŠusion coe‹cients of the tracergases for DB/DAº1.0 and DB/DAÀ1.0 was greatest forthe methane-carbon dioxide gas system and smallest forthe nitrogen-carbon dioxide gas system, among the gassystems studied here. A comparison of the gradients ofthe regression lines (Fig. 6) and diŠusion coe‹cients (Fig.7) show that the gradient of the regression line for gas velocity plotted against the diŠusion coe‹cient is dependent on the tracer gas used and approximates that of a gassystem for which the tracer and background gases areswitched when the diŠerence of the diŠusion coe‹cientsof the component gases (Fig. 7) is small. The diŠerencesin the diŠusion coe‹cients shown in Fig. 7 re‰ect the inclusion of the Knudsen diŠusion coe‹cient in Eq. (14a)for the DG model. Therefore, the gradient of the regression line for gas velocity plotted against the diŠusioncoe‹cient simulated with the DG model is greater thanzero as shown in Fig. 7, even though mechanical mixingis not considered in the simulation with the DG model.This gradient is equal to dispersivity if Fick's model is applied, but does not represent dispersivity if the DG modelis applied. The gradient of the regression line for gas velocity plotted against the diŠusion coe‹cient optimizedwith the results of the simulation with the DG modelre‰ects the diŠerent diŠusion coe‹cient in the background gas immediately in front of the advancing tracergas. This variation of the diŠusion coe‹cient in front ofthe tracer gas is caused by Knudsen diŠusion.Figure 8(a) shows the composite viscosities of thetracer gases methane and nitrogen in the nitrogenmethane gas system; the viscosities were calculated fromEq. (7). Figure 8(b) compares the breakthrough curvesfor tracer gases methane and nitrogen obtained from thecolumn experiments with those from simulations with the 154HIBI ET AL.Fig. 7. Relationships between molar fractions and composite diŠusion coe‹cients for tracer gases in the three binary gas systems of this study: (a)nitrogen-methane, (b) nitrogen-carbon dioxide and (c) methane-carbon dioxideDG model for the nitrogen-methane gas system. ThediŠerence between the viscosities of methane (1.08E–05Pa s) and nitrogen (1.76E–05 Pa s) is greatest among thegas systems of this study (Table 1). The composite viscosity of the system for tracer gas methane in thenitrogen-methane gas system decreased and that of tracergas nitrogen increased with the increasing molar fractionof tracer gas. The velocity of tracer gas nitrogen wasfaster than that of tracer gas methane in the nitrogenmethane system (Fig. 8(b)), and the viscosity of methanewas smaller than that of nitrogen, as stated above. Figure8(c) shows the composite viscosities of tracer gases carbon dioxide and nitrogen in the nitrogen-carbon dioxidegas system; the viscosities were obtained from Eq. (7).Figure 8(d) compares the breakthrough curves for tracergases carbon dioxide and nitrogen obtained from thecolumn experiments with those from simulations with theDG Model for the nitrogen-carbon dioxide gas system.The diŠerence between the viscosities of nitrogen and carbon dioxide is the smallest among the gas systems studiedhere. The composite viscosity of the system for tracer gascarbon dioxide decreased from the viscosity of nitrogen(1.76E–05 Pa s) to the viscosity of carbon dioxide(1.47E–05 Pa s) with the increasing molar fraction oftracer gas. Conversely, the composite viscosity of the sys-tem for tracer gas nitrogen increased from 1.47E–05 to1.76E–05 Pa s with the increasing molar fraction oftracer gas. The velocity of tracer gas nitrogen was fasterthan that of tracer gas carbon dioxide (Fig. 8(d)). Thecomposite viscosity of the system for tracer gas methane,which has lower viscosity than the other gases used here,decreased from the viscosity of the carbon dioxide(1.47E–05 Pa s) to the viscosity of methane (1.08E–05Pa s) with the increasing molar fraction of tracer gasmethane (Fig. 8(e)). Conversely, the composite viscosityof the system for tracer gas carbon dioxide increasedfrom the viscosity of methane (1.08E–05 Pa s) to the viscosity of carbon dioxide (1.47E–05 Pa s) with the increasing molar fraction of tracer gas carbon dioxide (Fig.8(e)). The velocity of tracer gas carbon dioxide in background gas methane was faster than that of tracer gasmethane in background gas carbon dioxide with greaterviscosity (Fig. 8(f)). Therefore, the composite viscosity ofthe tracer gas calculated from Eq. (7) changed from theviscosity of the background gas to that of the tracer gaswith the increasing molar fraction of the tracer gas. Thevelocity of the tracer gas depends on the viscosity of thebackground gas and became faster as the viscosity of thebackground gas decreased. A comparison of the gradientof the regression line for gas velocity plotted against the DISPERSIVITY AND TORTUOSITY155Fig. 8. Relationships between composite viscosities and molar fractions of tracer gases and comparisons of experimental and DG model simulatedbreakthrough curves of tracer gases: (a) and (b) in the nitrogen-methane gas system; (c) and (d) in the nitrogen-carbon dioxide gas system; and(e) and (f) in the methane-carbon dioxide gas systemdiŠusion coe‹cient (Fig. 6) and composite viscosity(Figs. 8(a), (c) and (e)) shows that the gradients of theregression lines for the tracer gases with high viscosity arelower than those for tracer gases with low viscosity, andthe diŠerence between the gradients of the regression lineswhen the tracer gas was replaced with the background gaswas greater the larger the diŠerence in viscosity. Therefore, the gradients of the regression lines for gas velocityplotted against diŠusion coe‹cients, which are optimizedwith the results of the simulations with the DG modelwhen tortuosity is 1.0 and mechanical mixing is neglected, depend on both the viscosity of the gas and the Knudsen diŠusion coe‹cient, and are diŠerent for diŠerent binary gas systems.Gas velocity optimized by the Powell conjugategradient method (Fujinawa, 1983) with the experimentalresults is shown in Table 2. Figure 9(a) compares thesimulated relationship between the gas velocity and dis- 156HIBI ET AL.Fig. 9. Relationships between optimized gas velocities and the optimized dispersion coe‹cient of tracer gases. The solid and dotted lines indicateregression lines from the column experiments and those from the DG model simulations, respectively: (a) and (b) the nitrogen-methane gas system; (c) and (d) the nitrogen-carbon dioxide gas system; and (e) and (f) the methane-carbon dioxide gas systempersion coe‹cient optimized with the experimentally obtained results for tracer gas methane in the nitrogenmethane gas system. The gradient of the regression linefor the experiment was 0.0507 cm and the dispersioncoe‹cient was 0.1037 cm2/s for a gas velocity of 0 cm/s(Fig. 9(a)). Figure 9(b) shows the same comparison fortracer gas nitrogen in the methane-nitrogen gas system.The gradient of the regression line for the experiment was0.037 cm and the dispersion coe‹cient was 0.1575 cm2/sfor a gas velocity of 0 cm/s. The gradient of the regression line for velocity plotted against the dispersioncoe‹cient is generally equal to the dispersivity, and thediŠusion dispersion at a velocity of 0 cm/s is the diŠusioncoe‹cient, as shown by Eq. (21). Thus, the dispersivityof tracer gas methane in the nitrogen-methane gas systemwas 0.0507 cm and the dispersivity of tracer gas nitrogenin the nitrogen-methane gas system was 0.037 cm.Moreover, the diŠusion coe‹cients for methane andnitrogen in the nitrogen-methane gas system were 0.1037and 0.1575 cm2/s, respectively, if Fick's law is applicablefor a binary gas system in soil. The experimental dispersivity of methane was greater than that of nitrogen in thenitrogen-methane gas system, as was the case for thesimulated dispersion coe‹cient of the tracer gas obtained DISPERSIVITY AND TORTUOSITYwith the DG model. Moreover, the experimentally derived diŠusion coe‹cient for methane at a gas velocity of 0cm/s in the nitrogen-methane gas system was smallerthan that of the nitrogen tracer; this trend is consistentwith that of the simulations with the DG model.Figures 9(c) and (d) show the relationships between gasvelocity and the dispersion coe‹cient optimized with theexperimental breakthrough curves for tracer gases carbondioxide and nitrogen, respectively, for the nitrogen-carbon dioxide gas system. The dispersivities of carbon dioxide and nitrogen in the nitrogen-carbon dioxide gassystem were 0.0402 and 0.0702 cm, respectively, and theirdiŠusion coe‹cients were 0.0761 and 0.1267 cm2/s, respectively (Figs. 9(c) and (d)). The experimentally deriveddispersivity for carbon dioxide was smaller than that fornitrogen, contrary to the results of the simulation withthe DG model. The experimental dispersivity and diŠusion coe‹cient for tracer gas methane in the carbon dioxide-methane were 0.0274 cm and 0.110 cm2/s, respectively (Fig. 9(e)). Moreover, the experimentally deriveddispersion and diŠusion coe‹cient of tracer gas carbondioxide were 0.0347 cm and 0.0803 cm2/s, respectively(Fig. 9(f)). The experimentally derived diŠusioncoe‹cient for methane were greater than those for carbon dioxide, as was the case for the simulation with theDG model.Estimation of Dispersivity and TortuosityThe diŠusion coe‹cients from DG model simulations(Fig. 6) do not consider tortuosity. The simulated diŠusion coe‹cient at a gas velocity of 0 cm/s (as projectedon the regression lines of Fig. 6) should be equal to theexperimental diŠusion coe‹cient at a gas velocity of 0cm/s (as projected on the regression lines of Fig. 9). It isnecessary to deal with tortuosity when applying the DGmodel because the diŠusion coe‹cients for the DG model(Fig. 6) are greater than the experimental diŠusioncoe‹cients (Fig. 9). Eq. (14a) shows that tortuosity isequal to the ratio of the experimental diŠusion coe‹cientto the DG model simulated diŠusion coe‹cient at a gasvelocity of 0 cm/s. That is,t=DExper/DDGM,(22)where t is tortuosity, DExper is the experimental diŠusioncoe‹cient (L2/T) at a gas velocity of 0 cm/s (projected onthe experimental regression line of Fig. 9), and DDGM isthe DG model simulated diŠusion coe‹cient (L2/T) at agas velocity of 0 cm/s (projected on the regression line ofFig. 6). The modiˆed diŠusion coe‹cients, which wereobtained by multiplying the DG model simulated diŠusion coe‹cient by tortuosity, are shown in Fig. 9. TheeŠect of dispersion is not included in the modiˆed diŠusion coe‹cients of the DG model simulations because themodel does not deal with mechanical mixing dispersion.The dispersion coe‹cient comprises the mechanical mixing dispersion coe‹cient and the diŠusion coe‹cient:Ddisp=Dmecha+Ddiff,(23)2where Ddisp is the dispersion coe‹cient (L /T), Dmecha is157the mechanical mixing dispersion coe‹cient (L2/T), andDdiff is the diŠusion coe‹cient (L2/T). The dispersioncoe‹cient is equal to the experimental dispersioncoe‹cient of Fig. 9 and the DG model simulated modiˆed diŠusion coe‹cient is equal to the diŠusioncoe‹cient of Fig. 9. Thus, mechanical mixing dispersioncan be derived from Eq. (23) by subtracting the DGmodel simulated diŠusion coe‹cient from the experimental dispersion coe‹cient. Then, dispersivity is equal tothe diŠerence of the gradients of the regression lines forgas velocity plotted against the DG model simulated modiˆed diŠusion coe‹cient of Fig. 9 and the equivalentgradient for experimentally derived dispersivity of Fig. 9as follows:a=aexper-Gsimu,(24)where a is the dispersivity (L) of the tracer gas, aexper is theexperimental dispersivity (L) and Gsimu is the gradient ofthe regression line for gas velocity plotted against the DGmodel simulated modiˆed diŠusion coe‹cient. Table 4shows the experimental dispersivities and dispersioncoe‹cients at a gas velocity of 0 cm/s, the DG modelsimulated modiˆed diŠusion coe‹cients at a gas velocityof 0 cm/s, and the gradients of the regression lines for gasvelocity plotted against diŠusion coe‹cient and modiˆeddiŠusion coe‹cient. The calculated dispersivities and tortuosities of the tracer gas are also shown in Table 4. Tortuosities range from 0.630 to 0.685, with the exception ofthe tracer gas methane in the nitrogen-methane system(0.529) and tracer gas carbon dioxide in the methane-carbon dioxide system (0.505). The experimental data werenot exactly reproduced by the model data (Table 4) because of the limited amount of experimental data fortracer gas carbon dioxide in the methane-carbon dioxidegas system. The data of Table 4 show that tortuosity isindependent of the gas system for these binary gas systems. Thus, tortuosity of the soil used in our analyses is inthe range from 0.53 to 0.70, regardless of the gas system.The dispersivities of Table 4 are negative (in the range-0.009 to -0.0186 cm) for tracer gas methane in thenitrogen-methane gas system, for tracer gas carbon dioxide in the nitrogen-carbon dioxide gas system, and fortracer gas methane in the carbon dioxide-methane gassystem. In nature, dispersivity can never be negative because the mechanical mixing diŠusion coe‹cient is greater than zero. These negative dispersivities indicate errorsin our measurements and suggest either that mechanicalmixing does not occur in the gas-soil systems we investigated here, or it is unnecessary to account for mechanicalmixing in the DG model. On the other hand, the dispersivity of tracer gas nitrogen in the methane-nitrogen gassystem was 0.0235 and that of tracer gas nitrogen in thecarbon dioxide-nitrogen gas system was 0.0234. Becausethe minimum negative dispersivity was -0.0186 cm, theaccuracy of our measurements was better than ±0.02 cmand, because the dispersivities we measured were withinthis error range, our results show that mechanical mixingdispersion need not be considered in the DG model in therange of gas velocity (0.05–0.4 cm/s) used in this study. HIBI ET AL.158Table 4.Estimated dispersivities and tortuosities for tracer gases in the three binary gas systemsGasesBackground gasTracer gasRegression lineSimulations withthe DG ModelExperimentsModiˆed gradientDispersivityTortuosity=aexper-Gsimu=DExper/DsimuN2CH4Gradient G1 (cm)DiŠusion coe‹cient at the velocity0 cm/s DDGM (cm 2/s)Experimental Dispersivity aexper (cm)DiŠusion coe‹cient at the velocity0 cm/s DExper (cm2/s)(cm) Gsimu(cm)Correlation coe‹cients for gas velocity versus the DGmodel simulated diŠusion coe‹cient were less than 0.55,except for tracer gas nitrogen in the carbon dioxide-nitrogen gas system (Fig. 6). Moreover, the DG model diŠusion coe‹cients varied widely for tracer gas methane inthe nitrogen-methane gas system and for tracer gas carbon dioxide in the methane-carbon dioxide gas system(Fig. 6). The experimental correlation coe‹cients for gasvelocity versus the dispersion coe‹cient were smallerthan those with the DG model, with a maximum of 0.23(Fig. 9). Although gas velocity does not correlate wellwith the dispersion coe‹cient or the diŠusion coe‹cient,it can still be used to investigate mechanical mixing andtortuosity.CONCLUSIONSWe investigated the mechanical mixing dispersion andtortuosity for several binary gas systems in soil. Mechanical mixing dispersion should be considered in gas systemsfor which the diŠusion coe‹cient is constant and Fick'smodel is applicable. Dispersivity, which is equal to thegradient of the regression line for gas velocity plottedagainst the dispersion coe‹cient, is dependent on thecomponent gases of the binary gas system. This dependence was proved by the results of our column experiments.The breakthrough curves derived by the column experiment were consistent with the DG model simulatedbreakthrough curves only near the column inlet or in theearlier stages of the experiments, indicating that tortuosity must be considered in the DG model. We calculatedtortuosities in the range from 0.53 to 0.70 by dividing theexperimental dispersion coe‹cient and the DG modelsimulated diŠusion coe‹cient at a gas velocity of zeroand showed that tortuosity is independent of the component gases of the binary gas system.The gradients of the regression lines for gas velocityversus DG model simulated diŠusion coe‹cient were dependent on the components of the gas system, as was thecase for experimentally determined dispersivity. By comparing this gradient determined from the column experiments with that from DG model simulations using themodiˆed diŠusion coe‹cient with tortuosities we wereable to conclude that there was no need to consider theCH 4N2N2CO2CO2N2CO2CH4CH4CO20.09580.01970.0730.06740.0728-0.01110.19590.22980.12070.18240.17410.15910.04980.0370.04020.07020.02740.03470.10370.15750.07610.12670.110.05070.01350.04600.04680.0460-0.0056-0.00090.5290.02350.685-0.00580.6300.02340.695-0.01860.6320.04030.5050.0803mechanical mixing dispersion in the DG model withoutdispersivity in the range of gas velocity (0.05–0.4 cm/s).ACKNOWLEDGMENTSWe are most grateful for advice and guidance fromTomiharu Toyoda of Shinshu University for our columnexperiments. Without his advice, this study would nothave been completed.REFERENCES1) Bear, J. (1972): Dynamic of ‰uid in porous media, Amsterdam,764.2) Costanza-Robinson, M. S. and Brusseau, M. L. (2002): Gas phaseadvection and dispersion in unsaturated porous media, WaterResources Research, 38(4), 7–1¿–7–10.3) Cunningham, R. E. and Williams, R. J. J. (1980): DiŠusion inGases and Porous Media, Plenum, New York.4) Fen, C. and Abriola, L. M. (2004): A comparison of mathematicalmodel formulations for organic vapor transport in porous media,Advances in Water Resources, 27, 1005–1016.5) Fujinawa, K. (1983): Asymptotic solutions to the convectiondispersion equation and Powell's optimization method for evaluating groundwater velocity and diŠusion coe‹cient from observeddata of single dilution tests, Journal of Hydrology, 62, 333–353.6) Fujinawa, K. (1986): A Characteristic ˆnite element scheme forconvective-dispersion transport with non-equilibrium reaction, International Journal Numerical Methods Engineer, 23, 1161–1178.7) Gidda, T., Cann, D., Stiver, W. H. and Zytner, R. G. (2006): Air‰ow dispersion in unsaturated soil, Journal of ContaminantHydrology, 82, 118–132.8) Hibi, Y., Fujinawa, K., Okamura, K. and Tazaki, M. (2007): Experiments on the dispersion of gas phase components in soil, Journal of Environmental Systems and Engineering, 63(1), 30–39.9) Hibi, Y. (2008): Formulation of a dusty gas model for multi-component diŠusion in the gas phase of soil, Soils and Foundations,48(3), 419–432.10) Hoeg, S., Scholer, H. F. and Warnatz, J. (2004): Assessment of interfacial mass transfer in water-unsaturated soils during vapor extraction, Journal of Contaminant Hydrology, 74, 163–193.11) Mason, E. A. (1967): Flow and diŠusion of gases in porous media,Journal of Chemical Physics, 46, 3199–3216.12) Mason, E. A. and Malinauskas, A. P. (1983): Gas Transport inPorous Media the Dusty Gas Model, Elsevier, 30–49.13) Massmann, J. and Farrier, D. F. (1992): EŠects of atmosphericpressures on gas transport in the vapor zone, Water ResourcesResearch, 28(3), 777–791.14) Mendoza, A. and Frind, E. O. (1990a): Advective-Dispersion transport of dense organic vapor in unsaturated zone 1. Model development, Water Resources Research, 26(3), 379–387. DISPERSIVITY AND TORTUOSITY15) Mendoza, A. and Frind, E. O. (1990b): Advective-Dispersion transport of dense organic vapor in unsaturated zone 2. Sensitivity analysis, Water Resources Research, 26(3), 388–398.16) Moldrup, P., Olesen, T., Rolston, D. E. and Yamaguchi, T. (1997):Modeling diŠusion and reaction in soils, VII: Predicting gas diŠusivity in undisturbed and sieved soil, Soil Science, 162(9), 632–640.17) Neuman, S. P. (1981): A Eulerian-Lagrangian numerical schemefor the dispersion-convection equation using conjugate space-timegrids, Journal of Computational Physics, 41, 270–294.18) Poling, B. E., Prausnitz, J. M. and O'Connell, J. P. (2001): TheProperties of Gases and Liquids, McGraw-Hill, 11.19–11.20.19) Sleep, B. E. (1998): Modeling transient organic vapor transport inporous media with the dusty gas model, Advance in WaterResource, 22(3), 247-256.20) Sleep, B. E. and Sykes, J. F. (1993a): Compositional simulation of21)22)23)24)159groundwater contamination by organic compounds 1. Model development and veriˆcation, Water Resources Research, 29(6),1697–1708.Sleep, B. E. and Sykes, J. F. (1993b): Compositional simulation ofgroundwater contamination by organic compounds 2. Model applications, Water Resources Research, 29(6), pp. 1709–1718.Thorstenson, D. C. and Pollock, D. W. (1989): Gas transport inunsaturated zones: Multi component systems and the adequacy ofFick's Laws, Water Resource Research, 23(3), 477–507.Webb, S. W. and Pruess, K. (2003): The use of Fick's law formodeling tracer gas diŠusion in porous media, Transport in PorousMedia, 51, 327–341.Zheng, C. and Bennett, G. D. (2002): Applied Contaminant Transport Modeling 2nd Edition, Wiley Interscience, 35–41.
  • ログイン
  • タイトル
  • Effects of Dry Density and Grain Size Distribution on Soil-Water Characteristic Curves of Sandy Soils
  • 著者
  • "C. P. K. Gallage, Taro Uchimura"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 161〜172
  • 発行
  • 2010/02/15
  • 文書ID
  • 64349
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, 161–172, Feb. 2010EFFECTS OF DRY DENSITY AND GRAIN SIZE DISTRIBUTIONON SOIL-WATER CHARACTERISTIC CURVES OF SANDY SOILSCHAMINDA PATHMA KUMARA GALLAGEi) and TARO UCHIMURAii)ABSTRACTThe soil-water characteristic curve (SWCC) of soil plays the key roll in unsaturated soil mechanics which is a relatively new ˆeld of study having wide applications particularly in Geotechnical and Geo-environmental Engineering. Toencourage the geotechnical engineers to apply unsaturated soil mechanics theories in routine practice, numericalmethods, based on the SWCC and saturated soil properties, have been developed to predict unsaturated permeabilityfunction and unsaturated shear strength properties which are expensive and time consuming to measure in laboratories. Further, several methods have been proposed to predict the SWCC in order to avoid di‹culties in measuring theSWCC in laboratories. It is time consuming and it may require special techniques or apparatus to measure the SWCCin laboratories. However, it is important to have laboratory measured data of SWCCs to enhance and verify theproposed numerical methods. Hence, employing a Tempe pressure cell apparatus, the present study aims to investigatethe eŠects of dry density and grain-size distribution on the SWCCs of sandy soils. Drying and wetting SWCCs were obtained for four sandy soils with diŠerent dry densities. The test data were best-ˆtted using the Fredlund and Xing(1994) equation and found that the ˆtting parameter, a, increases linearly with increasing the air-entry value of theSWCC and the ˆtting parameter, m, decreases with increasing the residual suction of the SWCC. The results revealedthat soils with a low density have lower air-entry value and residual suction than soils with a high dry density. Further,the maximum slope of drying SWCC and hysteresis of drying and wetting SWCCs decrease with increasing density ofsoil. The air-entry value, residual suction, and hysteresis (the diŠerence between the drying and wetting SWCCs) tendsto decrease when the eŠective D10 of the soil increases. A soil with uniform grain-size distribution (the steeper slope ingrain-size distribution) has a less hysteresis and a greater slope of drying SWCC than those of a non-uniform soil.Key words: dry density, grain-size distribution, hysteresis of suction, model ˆtting, soil-water characteristic curve(IGC: F4)INTRODUCTIONThe relationship between water content and suction ofa soil is termed as the soil-water characteristic curve(SWCC). The most commonly used form of water content is volumetric water content (Houston et al., 1999), uw(deˆned as the volume of water in the soil divided by thetotal volume of soil, Vw/V ). The degree of saturation, S,is also used sometimes as a measure of water content forthe SWCC. The suction used for the SWCC is usually thematric suction, ua-uw (deˆned as the diŠerence betweenthe pore-air pressure and the pore-water pressure in thesoil), but the total suction is occasionally used as well.Figure 1 illustrates typical drying and wetting SWCCs.The air entry value, AEV or ca, refers to the matric suction that must be exceeded before air recedes into thepores of the soil during drying process (Brooks and Corey1964, 1966). As suction increases from zero to the AEVof the soil, the volumetric water content, uw, is nearlyconstant. Then the water content steadily decreases to thei)ii)Fig. 1.Typical soil-water characteristic curvesresidual water content, ur, as matric suction increases beyond the AEV. The residual water content is the watercontent at residual state, at which water phase is discontinuous. The suction corresponding to the residual waterLecturer, School of Urban Development, Queensland University of Technology, Brisbane, Australia.Associate Professor, University of Tokyo, Department of Civil Engineering, Tokyo, Japan (uchimura@civil.t.u-tokyo.ac.jp).The manuscript for this paper was received for review on March 10, 2008; approved on December 2, 2009.Written discussions on this paper should be submitted before September 1, 2010 to the Japanese Geotechnical Society, 4-38-2, Sengoku,Bunkyo-ku, Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.161 162GALLAGE AND UCHIMURAcontent is called residual soil suction. cr. Absorption anddesorption curves refer to the wetting and drying processes, respectively. The diŠerence in water content at thesaturation between drying and wetting processes is theresidual (trapped) air content. The water-entry value, cw,on the wetting SWCC, is deˆned as the matric suction atwhich the water content starts to increase signiˆcantlyduring the wetting process.In Fig. 1, the SWCC during wetting process is not thesame as that in drying process. This is referred to as hysteresis, i.e., the soil's ability under similar suction to havetwo diŠerent water contents when the soil is being wettedor dried. For a speciˆed suction value, the soil being wetted has less water content than the soil being dried. Suchhysteresis is due to the following. Within a group of soilgrains or aggregate, pores of various sizes exist that canbe visualized as many interconnecting bottlenecks. Thesmallest pores at the outermost of an aggregate governsthe maximum matric suction (or air entry value) of a particular aggregate. Since the pore sizes are not uniformthrough an aggregate, larger pores can be found insidethe aggregate. These pores does not control or aŠect airentry value of the aggregate. They have the tendency toretain water if they are surrounded by pores of smaller diameter when the soil is being dried under constant matricsuction. However, these larger pores don't contain waterwhen the soil has been previously dried prior to beingwetted under similar matric suction. Hence, soil at dryingalways has greater water content than the soil at wetting(Orense, 2003).A number of empirical models or equations have beendeveloped to describe the highly nonlinear SWCC (e.g.,van Genuchten, 1980; Mualem, 1986; Rossi and Nimmo,1994; Fredlund and Xing, 1994; Assouline et al., 1998;Aubertin et al., 1998). Among these equations, the vanGenuchten (1980) equation and the Fredlund and Xing(1994) equation were found to be the best SWCC modelsfor a variety of soils (Leong and Rahardjo, 1997).The soil-water characteristic curve is central to the behavior of an unsaturated soil (e.g., Fredlund and Rahardjo, 1993; Barbour, 1998). The SWCC can be relatedto other properties describing the behavior of the soil,such as the unsaturated coe‹cient of permeability (Fredlund et al., 1994) and the shear strength (Vanapalli et al.,1996). Therefore, to encourage geotechnical engineers toimplement unsaturated soil mechanics theory in routinepractice, a number of methods for prediction of theSWCC have been developed (e.g., Gupta and Larson,1979; Arya and Paris, 1981; Haverkamp and Parlange,1986; Fredlund et al., 1997) to avoid time and moneyconsumption in measuring the SWCC in laboratories.The method proposed by Fredlund et al. (1997) uses thepore distribution in soil obtained from grain size distribution curve to obtain the SWCC. The methods proposedby Arya and Paris (1981) and Gupta and Larson (1979)use statistical approach to predict SWCC using percentages of sand, silt and clay and bulk density. They conducted regression analyses using the cubic spline methodon experimental data to predict the SWCC. Any of theseprevious studies has not investigated quantitatively theeŠects of grain size distribution and density on hysteresisof drying and wetting SWCCs, and ˆtting parametersused in respective methods. Therefore, it is important toconduct such a quantitative investigation to enhance thepredictive methods of the SWCC.In this study, drying and wetting SWCCs for foursandy soils were obtained in the laboratory using a Tempepressure cell and the experimental data were ˆtted usingthe Fredlund and Xing (1994) equation. The obtained ˆtting parameters are correlated to the soil parameterswhich governs the shape of the drying SWCC. The eŠectsof dry density and grain size distributions of soils on theirdrying and wetting hysteresis and SWCCs parameters arethen discussed.TEST MATERIALS AND APPARATUSTest MaterialsFour diŠerent materials, namely Edosaki sand, Inagesand, Tsukuba River sand, and Chiba soil, were employed in the experimental work of this study. Edosakiand Inage sands were procured from two diŠerent naturalslopes in Ibaraki and Chiba Prefectures (Japan), respectively. Tsukuba River sand was obtained from a river bedin Tsukuba area in Ibaraki prefecture (Japan). Chiba soilwas excavated from a railway embankment in Chibaprefecture (Japan).Wet sieving analysis and hydrometer tests were performed on Edosaki sand, Inage sand, and Chiba soil asthese materials contain ˆnes (particles ˆner than 0.075mm) contents of 17.1, 18.0, and 36z, respectively. Drysieving analysis was performed on Tsukuba River sand.These sieve and hydrometer analyses were conducted using JGS (Japanese geotechnical Society) standard testmethod. The grain-size distributions of the four soils areshown in Fig. 2. Other basic soil properties such asspeciˆc gravity, maximum void ratio, minimum void ratio, compaction properties, and plasticity index weremeasured for the four soils using JGS standard testmethod and are shown in Table 1. These soils were classiˆed in accordance with the Uniˆed Soil ClassiˆcationSystem using JGS standard test method and it was foundFig. 2.Grain-size distributions of test materials EFFECTS OF DENSITY AND GRAIN SIZE ON SUCTIONthat Edosaki sand, Inage sand, and Chiba soil were siltysand whereas Tsukuba River sand was well-graded.Test ApparatusThe schematic diagram of the Tempe pressure cellwhich was used in the laboratory to obtain soil-watercharacteristic curves of tests materials is shown in Fig. 3.This apparatus was designed and manufactured in thelaboratory. It consists of a brass cylinder with the innerdiameter of 50 mm and the height of 60 mm, a base plateon which a high air-entry (300 kPa) ceramic disk is embedded, and a top cap. A soil specimen is placed on thehigh air entry ceramic disk inside the retaining brasscylinder of the Tempe pressure cell. A tube connected tothe base plate (underneath the high air entry disk) allowsin and out water ‰ow of the soil specimen. Air pressure issupplied through the tube connected to the top cap. Thetop and the bottom plate are fastened together during thetest. It is worthy to note that this Tempe pressure cell issimilar to a conventional one which can not be used toTable 1.Basic properties of test materialsEdosakisandInagesandTsukubaRiversandChibasoilSpeciˆc gravity, Gs2.752.722.712.72Mean Grain size, D50 [mm]0.220.150.550.14Coe‹cient ofuniformity,Uc=D60/D1017.1018.004.5054.40Coe‹cient of gradation,Cc=(D30)2/(D10*D60)3.974.500.941.95Sand content, [z]83.6073.5398.0064.00Fines content, [z]16.4026.472.0036.00Plastic indexNPNPNP2.26Maximum void ratio, emax1.591.350.961.74Minimum void ratio, emin1.010.840.521.11PropertiesFig. 3.Schematic diagram of Tempe pressure cell163apply conˆning pressure and to measure possible soilvolume change. However, in the conventional Tempepressure cell, the change in water content in the sample ismeasured by weighing or measuring the amount of out/in ‰ow during the test and therefore, the evaporation ofwater could lead to inaccurate water content calculation.In the Tempe pressure cell used in this study, change inwater content in the soil sample is measured by weighingthe assembly of the apparatus and therefore, the evaporation of out/in ‰ow water does not aŠect the calculation ofsoil water content.TEST METHODThe test procedure of the Tempe pressure cell mainlyinvolved saturation of the ceramic disk, sample preparation, and obtaining drying and wetting SWCCs.Saturation of the Ceramic DiskA test was started by saturating the high air-entry ceramic disk and the associated measuring system (the compartment between the ceramic disk and the base plate, thetube connected to the base plate). In order to saturate theceramic disk and the associated system, ceramic disk embedded base plate was immersed in a vacuum cylinderand left for one day. During this time, tapping was doneto the cylinder in order to expel the trapped air in thewater and the disk itself.After this process, a check was made to ensure the saturation of the associated system following the proceduredescribed by Huang (1994). To do the check, the fullysaturated system (the ceramic disk, the compartment below the ceramic disk, and the tube connected to the baseplate) was connected to a pore pressure transducer by thetube connected to the base plate. The surface of the ceramic disk was then wiped using a soft dry paper and thereading of the pressure transducer was observed withtime. The saturation of the disk and the associated systemwas considered perfect when a negative pore-water pressure of about 60¿70 kPa was observed after drying thesurface of the disk by a soft dry paper (Huang, 1994).Otherwise, the described process of saturation was con-Fig. 4. Saturation check of the high air-entry ceramic disk embeddedin the base plate of Tempe pressure cell GALLAGE AND UCHIMURA164Fig. 5.Saturation of the specimenducted again. Figure 4 shows the typical result of saturation check of the ceramic disk and the associated system.After conˆrming the saturation, the water was ‰ushedthrough the bottom of the ceramic disk in order tosaturate the upper portion of the disk which dried-upduring the saturation-check.Sample PreparationAfter the saturation check of the disk and the associated system, the base plate was connected to a water tankto maintain the saturation of the disk and the associatedsystem. The brass-cylinder was then mounted andfastened to the base plate. Before sample preparation wasstarted, the soil was oven-dried and the mass of the soilrequired to achieve the target density was computed. Thesoil was then mixed with water to achieve the gravimetricwater content of 10z (for all tests). After closing the lineconnecting the base plate and the water tank and wipingout the surface of the ceramic disk, the required amountof soil was placed cylinder and compacted to the targetdensity (moist tamping technique). Then the preparedspecimen was saturated by sending water through thebase plate as shown in Fig. 5. During the saturation, theweight of the assembly (the base plate, cylinder, and thespecimen) was measured (after removing the excess waterfrom the surface of the specimen) time to time. When theconstant weight of the assembly was observed, the topcap was mounted and tightened. Generally the saturationof the sample took 2¿3 days.Obtaining Drying and Wetting Soil-water CharacteristicCurvesThe Tempe pressure cell was connected to a system asshown in Fig. 3. The water level of the water collectingtank was maintained at the middle height of the soil specimen and the tank was always vented to atmospheric pressure (pore-water pressure in the sample (uw) was assumedto be zero throughout the test). As ˆrst step, without applying any air-pressure (air-pressure in the specimen (ua)is zero) into the specimen, the weight of the assembly wasmeasured until constant weight was observed. The con-stant weight of the assembly corresponding to zero suction (ua-uw=0) was recorded. Then the air-pressure (ua)was increased to another value (i.e., 0.5, 1.0, 2.0, 3.0,5.0, 7.0, 10.0, 20.0, 50.0, 100.0, 200.0 kPa) through theinlet tube on the top plate and the outlet tube located atthe base plate allowed water to drain out to the water collecting tank, which was opened to atmospheric pressure,and its water level was maintained at the middle height ofthe soil specimen. When the air pressure was applied,water was draining from the specimen through the highair-entry disk until the equilibrium was reached. When equilibrium was ensured (the assembly reached a constantweight) the weight of the assembly was noted (corresponding air-pressure was equal to the suction (ua-uw) asthe water pressure was maintained atmospheric). Duringthe weighting of the assembly, both tubes (inlet and outlet) were closed. The procedure was then repeated at ahigher applied air pressure (i.e., higher matric suction)and the drying process was stopped at the suction of 200kPa (applied air pressure 200 kPa).This apparatus cannot be used to obtain SWCC for the suction greater than300 kPa as the air entry value of the used ceramic disk is300 kPa.The wetting process was simulated by decreasing the airpressure from 200 kPa keeping the water pressure at theconstant value of zero. Once the air pressure wasdecreased, water ‰owed into the cell through the disk until the equilibrium was reached. The weight of the assembly was noted when it reached the equilibrium. Thisprocedure was repeated at lower water pressure (i.e., lower matric suction).When the specimen reached zero matric suction in thewetting process (i.e., water pressure was equal to the airpressure), the assembly was disconnected from the systemand the water content corresponding to zero suction onwetting was measured by oven-drying the soil specimen.This water content together with previous change inweight of the assembly was used to back-calculate thewater contents corresponding to the other suction values.The suctions were then plotted against their corresponding water contents to obtain the SWCCs.RESULTS AND DISCUSSIONThe Fredlund and Xing (1994) equation which wasused in this study to ˆt the SWCC test data can be writtenas follows:uw=«usmsln [e+(c/a)n]t$«1-ln (1+c/cr)ln (1+106/cr)$(1)where uw in the volumetric water content; us is the saturated volumetric water content; a is a soil parameter relatedto the AEV of the soil (kPa); n is a soil parameter relatedto the slope between the AEV and the residual suction onthe SWCC; m is a parameter related to the residual watercontent portion of the curve; e is the natural number2.71828 . . .; c is any soil suction (kPa); cr is the residualsoil suction (kPa) corresponding to the residual watercontent, ur. EFFECTS OF DENSITY AND GRAIN SIZE ON SUCTIONFredlund and Xing (1994) model has the following advantages over the van Genuchten model:(1) Provides a good ˆt for general soils over the entiresuction range of 0 to 106 kPa.(2) Since there are three ˆtting parameters (a, m, n)better data ˆtting can be obtained (van Genuchtenmodel has only two ˆtting parameters).(3) Some ˆtting parameters used in FX model havephysical meaning: a has unit of pressure and closelyrelated to AEV of soil, n controls the slope of theSWCC curve.The ˆtting parameters in Eq. (1) (a, n, m) describe theshape of the SWCC. To best-ˆt the experimental data,these parameters can be obtained by the least square optimization method using experimental data and nonlinearcurve-ˆtting algorithms as explained by Fredlund andXing (1994).Soil-water Characteristic Curves of Test MaterialsDrying and wetting soil-water characteristic curves(SWCCs) for the four test materials were obtained using aTempe pressure cell in the laboratory. Inage and Tsukubasand samples with dry density of 1.35 g/cm3, Edosakisand samples with dry densities of 1.22, 1.35, and 1.50g/cm3, and Chiba soil samples with dry densities of 1.25,1.35, and 1.42 g/cm3 were used in this experimental program. The experimental data were best-ˆt using the equation Eq. (1) proposed by Fredlund and Xing (1994). Thisequation provides a good ˆt for sand, silt, and silt soilsover entire suction range from 0 to 106 kPa. The air-entryvalue, residual suction, maximum slope, and ˆttingparameters (a, m, n) of SWCCs were obtained using theSoilVision computer software (SoilVision systems Ltd.Ver. 4.14). The obtained ˆtting parameters and residualsuction values of SWCCs are listed in Table 2.The experimental data and the best-ˆt SWCC results oftest materials for diŠerent densities are shown in Figs.6–13. The results show that the best-ˆt SWCCs using theFredlund and Xing (1994) equation closely describes theSWCC data of test materials. The best-ˆt parameters ofthe Fredlund and Xing (1994) are further discussed in thisstudy.The laboratory obtained drying SWCCs are diŠerenteach other due to the eŠects of the grain-size distributionand the initial dry density. The diŠerences of the SWCCsare determined by the diŠerences of the SWCCparameters such as the air-entry value, ca, residual suction, cr, and the slope of SWCC. In this study, an attempt was made to correlate the SWCC parameters to theˆtting parameters (a, n, and m) of the Fredlund and Xing(1994) equation. As Shown in Fig. 14, the air-entryvalues, ca, and the ˆtting parameter, a, are closely relatedand have an apparent linear relationship. The greater theca value, the greater the a value. Similarly, the residualsuction values, cr, are related to the ˆtting parameter m(Fig. 15) such a way that the larger the cr value, thesmaller the m value. These ˆndings are consistent withLeon and Rahardjo (1997) and Hong et al. (2004).The maximum slope of SWCC was obtained by extend-Table 2.Fredlund and Xing (1994) best-ˆt parametersResidualsuction[kPa]Drydensity[g/cm3]Inage sand1.35Tsukuba sand1.351.22Edosaki sand1.351.501.25Chiba soil1651.351.42Fredlund and Xingbest-ˆt parametersCra [kPa]mnDrying11.7494.8340.2189.956Wetting4.8051.8180.154 20Drying5.0872.2930.203Wetting2.4650.9700.164 20Drying6.5252.2330.4436.893Wetting6.5581.2730.5522.927Drying10.1303.3200.4035.453Wetting6.0861.6740.4005.512Drying11.2553.9790.2916.845Wetting6.0951.8630.2546.964Drying11.9133.6960.195 10.729Wetting3.0390.6420.163Drying12.2835.1150.162 12.283Wetting2.3481.3150.116Drying19.5557.1230.130 14.099Wetting6.4161.2820.1265.0876.4061.3156.137Fig. 6. Soil-water characteristic curves of Inage sand for dry densityof 1.35 g/cm 3ing the steepest straight portion of the SWCC as shown inFig. 16. Two points on the extended line were selectedand the corresponding water content and suction valueswere used in the following equation to calculate the maximum slope of the SWCC.u1 - u 2(2)c2logc1The maximum slope of drying SWCC was plotted againstthe ˆtting parameter n as shown in Fig. 17. A clear correlation can not be observed between these two. However,Hong et al. (2004) observed that the steeper the slope ofThe maximum slope of the SWCC=Ø » 166GALLAGE AND UCHIMURAFig. 7. Soil-water characteristic curves of Tsukuba sand for dry density of 1.35 g/cm3Fig. 8. Soil-water characteristic curves of Edosaki sand for dry densityof 1.22 g/cm 3Fig. 9. Soil-water characteristic curves of Edosaki sand for dry densityof 1.35 g/cm 3the SWCC, the larger the parameter n. Note, the valuesshown within brackets in Figs. 14, 15 and 17 are the initial dry density values for which the drying SWCCs wereobtained.Fig. 10. Soil-water characteristic curves of Edosaki sand for dry density of 1.50 g/cm3Fig. 11. Soil-water characteristic curves of Chiba soil for dry densityof 1.25 g/cm 3Fig. 12. Soil-water characteristic curves of Chiba soil for dry densityof 1.35 g/cm 3EŠects of the Initial Dry Density on Soil-water Characteristic CurvesThe initial dry density of silty soils has some signiˆcanteŠects on the soil-water characteristic curve as shown inFigs. 18 and 19. In order to observe the eŠects of the initial density on the SWCC parameters, the laboratory obtained drying SWCCs of Edosaki sand and Chiba soil for EFFECTS OF DENSITY AND GRAIN SIZE ON SUCTIONFig. 16.167The maximum slope of the soil-water characteristic curveFig. 13. Soil-water characteristic curves of Chiba soil for dry densityof 1.42 g/cm 3Fig. 14. Fitting parameter a in Fredlund and Xing (1994) equation versus air-entry (AEV) of drying SWCCs of test materials (the valuesshown in brackets are initial dry density)Fig. 17. Fitting parameter n in Fredlund and Xing (1994) equationversus slope of drying SWCCs of test materials (the values shown inbrackets are initial dry density)Fig. 18.Fig. 15. Fitting parameter m in Fredlund and Xing (1994) equationversus residual suction of drying SWCCs of test materials (thevalues shown in brackets are initial dry density)the diŠerent dry densities are considered. As the initialdry density of silty soil increases, the air entry value of thesoil increases (Fig. 20). As shown in Fig. 21, the highdensity specimens de-saturate at a slower rate than thelow-density specimens. As a result, the high-densityEŠects of dry density on drying SWCCs for Edosaki sandspecimens have higher water contents than the low-density specimens at matric suctions beyond their air entryvalues (Figs. 18 and 19). Therefore, the residual suction,cr, increases eventually with the increase in the initial drydensity (Fig. 22). These ˆndings are consistent with theresults of Croney and Coleman (1954). For comparison,the AEV is plotted with void ratio and relative density asshown in APPENDIX A and found the same R2 value for GALLAGE AND UCHIMURA168Fig. 19.EŠects of dry density on drying SWCCs for Chiba soilFig. 20. The variation of the air-entry value (AEV) with the dry density of sandFig. 21. The variation of the slope of drying SWCC with the dry density of sandlinear correlation which is obtained by plotting AEV withdry density.Aitchison (1960) pointed out that the matric suction (ua-uw) obeys a simple capillary model as follows:u a- u w=2T sRs(3)Fig. 22. The variation of the residual suction with the dry density ofsandWhere Ts=the surface tension force of water (N/m)Rs=Radius of curvature of meniscus (m)With the increase of density of a soil sample, the size andthe number of pores in the soil matrix reduces. As aresult, the radius of curvature of meniscus decreases andthe corresponding suction increases. Therefore, the suction required for air to enter into the soil matrix (air-entryvalue) increases. Similarly, for the same volumetric watercontent, the higher the initial density is the greater thesuction value. Increasing in the initial density of a soilsample, the permeability of soil is decreased. This canlead to slower the de-saturation process and also to increase the air-entry value and the residual suction.Croney and Coleman (1954) further revealed that theeŠect of initial water content on the drying curves of incompressible soils has similar eŠect, as was illustrated bythe initial dry densities. An increase in the initial watercontent of the soil results in a decrease in the air entryvalue. This can be attributed to the large pore sizes in thehigh initial water content mixtures. This soils drainquickly at relatively low matric suctions. As a result, thewater content in the soil with the large pores is less thanthe water content in the soil with the small pores at matricsuctions beyond the air entry value. In other wards, soilswith low initial water content (or small pore sizes) requirea large matric suction value in order to commence desaturation. There is then a slower rate of water drainagefrom the pores.In this study, the hysteresis between the drying andwetting SWCCs is quantiˆed as shown in Fig. 23, wherethe area between the drying and wetting SWCCs as computed on logarithm scale over the suction range from 0.1to 106 kPa. First, drying and wetting SWCC data were ˆtted using Eq. (1) and corresponding ˆtting parameterswere obtained. Then, the two curves were integrated overthe suction range of 0.1 to 106 kPa. The diŠerence of thetwo integrated values would give the hysteresis as shownin the following equation: EFFECTS OF DENSITY AND GRAIN SIZE ON SUCTIONFig. 23. The deˆnition of hysteresis of the soil-water characteristiccurvesFig. 24.169Fig. 25. The variation of air-entry value and residual suction of dryingSWCC with grain-size parameter D10The variation of the hysteresis with the dry density of sand106f(u )Hysteresis=f(u )dc -w drying0.1Fig. 26. The variation of slope of drying SWCC with the slope ofgrain-size distribution curve106w wettingdc(4)0.1where, (uw)drying is Eq. (1) ˆtted for drying data, (uw)wetting isEq. (1) ˆtted with wetting data, c is suction.Water content is unit less quantity and suction has theunit of pressure. Therefore, as shown in Eq. (4), the hysteresis could have the unit of pressure and in this study, itis kPa.As shown in Fig. 24, the hysteresis associated with thehigh-density specimens is less than the hysteresis exhibited by the low-density specimens. The possible reasons forthis behavior may be less pore-volume and greater capillary potential created by the denser soil sample.EŠects of Grain Size Distributions on Soil-water Characteristic CurvesSince the SWCC depends on the pore-size distributionof the soil, it is directly related to the grain-size distribution. Holtz and Kovacs (1981) assumed that the averagepore-diameter is about 20z of the mean grain-size, D10,hence, the attempt was made in this study to relate D10 ofa soil to its SWCC parameters. To examine the eŠects ofD10 on SWCC parameters, the drying SWCCs obtainedfor the four test materials with initial dry density of 1.35g/cm3 were considered. It could be reasonable to compare with the same value of density as their speciˆc gravity (Gs) are similar (2.71¿2.75). Further, AEV, residualsuction, and hysteresis were correlated with D10, D30, D50,D60, and Uc ( see APPENDIX B) and found that D10would give better correlation with AEV, residual suction,and hysteresis.As shown in Fig. 25, both the AEV and the residualsuction correlate well with the D10 of the soils. The AEVand the residual suction decrease with the increase in theD10. The larger the D10 the coarser the soils, the coarsegrained soils have bigger voids and hence, air can easilyenter into the soil skeleton (small AEV). It can also beseen in Fig. 24 that the diŠerence between the residualsuction and the AEV decrease with the increase in the D10.From Figs. 25 and 26, it can be extracted that the maximum slope of drying SWCC increases with the increase inthe D10.Figure 26 depicts the relationship between the maximum slope of the drying SWCC and the slope of grainsize distribution curve of sandy soils. The results showthat a steep slope of drying SWCC is caused by a steepgrain size distribution curve. This observation indicates GALLAGE AND UCHIMURA170CONCLUSIONSFig. 27.The eŠects of the slope of grain-size distribution on hysteresisFig. 28.In the present study, drying and wetting soil-watercharacteristic curves were investigated for four sandysoils. The experimental data of SWCCs obtained fromTempe pressure cell were best-ˆtted using the Fredlundand Xing (1994) equation. The ˆtting parameters andSWCC's parameters were then correlated. The eŠects ofdry density and the grain-size distribution on the SWCC'sparameters and the hysteresis in drying and wettingSWCCs were investigated. Accordingly, the followingconclusions were drawn.(1) The ˆtting parameter, a, exhibits a linear relationship with the air-entry of drying SWCC. a increaseswith increasing the air-entry value,(2) As the residual suction of drying SWCC increases,the ˆtting parameter, m, may decrease. The ˆttingparameter, n, does not exhibit any clear correlationwith the maximum slope of drying SWCC.(3) Both the air-entry value and the residual suction ofdrying SWCC may increase as dry density of sandysoil increases. However, the area between dryingand wetting SWCCs (i.e., hysteresis) seems todecrease with increasing dry density of soils.(4) A coarse-grained soil has a lower air-entry value,lower residual suction than a ˆne-grained soil.(5) The SWCC of a uniform soil has a steeper slopethan that of a less uniform soil. In other word, thesteeper the slope of grain-size distribution curve thegreater the slope of the SWCC.(6) A uniform coarse-grained soil has a smaller hysteresis than a less uniform, ˆne-grained soil.The eŠects of D10 on hysteresisACKNOWLEDGEMENTthat the drying SWCC is closely related to the grain sizedistribution of the soil. Because of this strong correlationbetween the drying SWCC and the grain size distributioncurve, many empirical methods have been developed topredict the drying SWCC directly from the grain-size distribution of the soil (Fredlund et al., 1997).Figures 27 and 28 show how the hysteresis of SWCCs isaŠected by the slope of grain size distribution curve andthe grain-size parameter, D10, respectively. The resultssuggest that the hysteresis between the drying and thewetting SWCCs decreases with increasing the slope of thegrain size distribution curve of the soils. It can be furtherdecreased by increasing the grain-size parameter, D10. Auniform particle distribution (i.e., a steep slope of grainsize distribution) creates uniform pore-sizes and hencethe diŠerence between water contents in drying and wetting at the same suction decreases (less histeresis). Withincreasing grain size (D10), the numbers of bigger poresincrease and the number of smaller pores which signiˆcantly aŠect the hysteresis of drying and wettingSWCCs decrease. Hence, the increase in D10 may reducethe diŠerence between the drying and wetting SWCCs.The authors gratefully acknowledge the PromotingFundamental Transport Technology Research of theJapan Railway Construction, Transport and TechnologyAgency (JRTT), and Grants-in-Aid for ScientiˆcResearch of the Japan Society for the Promotion ofScience (JSPS) for the ˆnancial support for this study.The ˆrst author acknowledges the scholarship receivedfrom the Ministry of Education, Science and Culture,Government of Japan (MONBUSHO) for reading doctoral degree at the University of Tokyo, Japan.REFERENCES1) Aitchison, G. D. (1960): Relationships of moisture stress and eŠective stress functions in unsaturated soils, Proc. Conference on PorePressure and Suction in Soils, London, 47–52.2) Arya, L. M. and Paris, J. F. (1981): A physicoempirical model topredict the soil moisture characteristic from particle-size distribution and bulk density data, Soil Science Society of America Journal, 45, 1023–1030.3) Assouline, S., Tessier, D. and Bruand, A. (1998): The conceptualmodel of the soil water retention curve, Water Resources Research,34(2), 223–231.4) Aubertin, M., Ricard, J. F. and Chapuis, R. P. (1998): A predictivemodel for the water retention curve: application to tailings fromhard-rock mines, Canadian Geotechnical Journal, 35, 55–69. EFFECTS OF DENSITY AND GRAIN SIZE ON SUCTION5) Barbour, S. L. (1998): The soil-water characteristic curve: a historical prospective, Canadian Geotechnical Journal, 35, 873–894.6) Brooks, R. H. and Corey, A. T. (1964): Hydraulic properties ofporous medium, Colorado State University (Fort Collins), Hydrology Paper No. 3.7) Brooks, R. H. and Corey, A. T. (1966): Properties of porous mediaaŠecting ‰uid ‰ow, Journal of the Irrigation and Drainage Division, ASCE, 92(IR2), 61–89.8) Croney, D. and Coleman, J. D. (1954): Soil structure in relation tosoil suction (pF), Journal of Soil Science, 5(1), 75–84.9) Fredlund, D. G. and Rahardjo, H. (1993): The role of unsaturatedbehaviour in geotechnical engineering practice, Proc. 11thSoutheast Asian Geotechnical Conference, Singapore, March 1993,Southeast Asian Geotechnical Society, Pathumthani, Tailand,37–49.10) Fredlund, D. G. and Xing, A. (1994): Equation for the soil-watercharacteristic curve, Canadian Geotechnical Journal, 31, 521–532.11) Fredlund, D. G., Xing, A. and Huang, S. (1994): Prediction of thepermeability function for unsaturated soils using the soil-watercharacteristic curve, Canadian Geotechnical Journal, 31, 533–546.12) Fredlund, M. D., Wilson, G. W. and Fredlund, D. G. (1997):Prediction of the soil-water characteristic curve from the grain-sizedistribution curve, UNSAT '97: Proc. 3rd Symposium on Unsaturated Soil, Rio de Janeiro, Brazil, 20–22 April 1997 (eds. by M. P.de Campos and E. A. Vargas), 13–23.13) Gupta, S. C. and Larson, W. E. (1979): Estimating soil water retention characteristic from particle size distribution, organic mattercontent, and bulk density, Water Resources Research, 15(6),1633–1635.14) Haverkamp, R. and Parlange, J. Y. (1986): Predicting the waterretention curve from particle size distribution: 1. Sandy soil withoutorganic matter, Soil Science, 142, 325–339.15) Holtz, R. D. and Kovacs, W. D. (1981): An Introduction to Geotechnical Engineering, Prentice-Hall, Inc., Englewood CliŠs, NJ.16) Hong, Y., Rahardjo, H., Eng-Choon, L. and Fredlund, D. G.(2004): Factors aŠecting drying and wetting soil-water characteristic curves of sandy soils, Canadian Geotechnical Journal, 41,908–920.17) Houston, W. N., Houston, S. L., Zapata, C. E., Manepally, C.and Lawrence, C. (1999): In‰uence of compressibility on use of interpretation of soil water characteristic curves, Proc. 11thPanamerican Conference on Soil Mechanics and Geotechnical Engineering, Foz do Iguassu, Brazil, 947–954.18) Huang, Y. (1994): EŠects of suction on strength and deformationbehavior of unsaturated collapsible soils, Ph.D. Thesis, Universityof Tokyo, Japan.19) Leong, E. C. and Rahardjo, H. (1997): Review of soil-water characteristic curve equations, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 123(12), 245–246.20) Mualem, Y. (1986): Hydraulic conductivity of unsaturated soils:prediction and formulas, Methods of soil analysis, part 1 (ed. by A.Klute) Agronomy Monograph 9, 2nd ed. American Society ofAgronomy and Soil Science Society of America, Madison, WI,799–823.21) Orense, R. P. (2003): Geotechnical Hazards: Nature, Assessmentand Mitigation, The University of the Philippines Press, E. de losSantos St., U. P. Campus, Philippines.22) Rossi, C. and Nimmo, J. R. (1994): Modeling of soil water retention from saturation to oven dryness, Water Resources Research,30(3), 701–708.23) Vanapalli, S. K., Fredlund, D. G., Pufahl, D. E. and CliŠton, A.W. (1996): Model for the prediction of shear strength with respectto soil suction, Canadian Geotechnical Journal, 33, 379–392.24) Van Genuchten, M. T. (1980): A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Science Society of America Journal, 44, 892–898.171APPENDIX AFig. AA1. The variation of air-entry value of drying SWCC with initial void ratioFig. AA2. The variation of air-entry value of drying SWCC with initial relative densityAPPENDIX BFig. AB1. The variation of air-entry value of drying SWCC withgrain-size parameters 172GALLAGE AND UCHIMURAFig. AB2. The variation of air-entry value of drying SWCC withcoe‹cient of uniformityFig. AB3. The variation of residual suction of drying SWCC withgrain-size parametersFig. AB4. The variation of hysteresis of drying SWCC with grain-sizeparameters
  • ログイン
  • タイトル
  • The Effect of Fines on Critical State and Liquefaction Resistance Characteristics of Non-Plastic Silty Sands
  • 著者
  • C. A. Stamatopoulos
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 173〜176
  • 発行
  • 2010/02/15
  • 文書ID
  • 64350
  • 内容
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 50, No. 1, Feb. 2010dinated by Prof. Bouckovalas of the National TechnicalUniversity of Athens (NTUA) and included three laboratories: The laboratory of the Aristotle University of Thessaloniki (AUTH) under the direction of Prof. Tika, thelaboratory of NTUA under the direction of Prof. Georgiannou and the laboratory of the author (STAM). Testsby AUTH and STAM were performed in the triaxialdevice, while tests by NTUA were in the torsional-sheardevice. The ˆrst common tests were performed by allthree laboratories in order to ensure that they producecompatible results. Then, tests proposed by Prof. Bouckovalas, as well as additional tests, were performed byeach laboratory.The discusser wishes to present results of the tests thathe performed in order to enrich some of the ˆgurespresented by the authors and to use the enriched ˆgures toobtain the eŠect of relative density (Dr) on the relationship between the ˆnes content (fc) and the cyclic strength(CRR15). Tests of the STAM laboratory focussed at fc of0, 15z and 25z. Figures 20 and 21 enrich Figs. 11 andDISCUSSIONSTHE EFFECT OF FINES ON CRITICALSTATE AND LIQUEFACTION RESISTANCECHARACTERISTICS OF NON-PLASTICSILTY SANDSi)Discussion by CONSTANTINE A. STAMATOPOULOSii)The authors present an elaborate experimental studyon the combined eŠect of void ratio, conˆning stress andˆnes content on the cyclic strength. To the discusser'sknowledge, such studies are sparse in the literature. Thedata presented is primarily on artiˆcial sand-silt mixtures.Tests performed in these sand-silt mixtures were part of aresearch program funded by the General Secretriat ofResearch and Development of Greece that was coor-Fig. 20. Variation of CRR15 with void ratio for mixtures with fc=0, 15 and 25%. This ˆgure enriches Fig. 11 (for fc=0, 15 and 25%) of the original paper using data from both the AUTH and STAM laboratoriesi)ii)Anthi Papadopoulou and Theodora Tika, Vol. 48, No. 5, October 2008, pp. 713–725.Stamatopoulos and Associates Co. Ltd., Athens, Greece (k.stam @saa-geotech.gr).173 DISCUSSIONS174Fig. 21. Variation of CRR15 with intergranular void ratio for mixtures with fc=0, 15 and 25%. This ˆgure enriches Fig. 13 (for fc=0, 15 and 25%)of the original paper using data from both the AUTH and STAM laboratories13 of the paper using the test results of both the AUTHand STAM laboratories. Unlike Figs. 11 and 13, Figs. 20and 21 give results for mixtures of only fc=0, 15 and 25z. The following can be observed: (a) the results of thetwo laboratories are consistent and the STAM data extends Figs. 11 and 13 to larger and smaller void ratios, (b)similar to the previous data, the extended data predictsthat at fc 0 to 25z the cyclic strength (i) with a similarvoid ratio and conˆning stress decreases as fc increases,and (ii) with a similar intergranural void ratio and conˆning stress increases as fc increases.The eŠect of ˆnes in the liquefaction susceptibility ofsand-silt mixtures can be studied in terms of the factor Ifdeˆned asTable 4. The parameters A and B of Eq. (11) that ˆt each case (for s?oand fc) of Fig. 20 and the coe‹cient of correlations?o (kPa)f c (z )ABR250028.7-6.870.9950158.18-5.870.9950253.26-5.110.9910006.2-4.870.95100154.29-5.260.94100250.47-2.200.9815008.77-5.330.99150154.58-5.220.97(9)150251.64-4.330.99where CRR15-fc=0 is the cyclic strength of the mixture withfc=0 at similar void ratio and conˆning stress (s?o).Bouckovalas et al. (2003) assumed that the factor Ifchanges linearly with ˆnes content. Thus, they deˆned thefactor af as3000-7.711.0030015-5.130.99If=CRR15/CRR15-fc=0af=100(If-1)/fc(10)The af factor equals zero if at similar void ratio and s?othere is no eŠect of fc on the cyclic strength and is nega-342.74tive when the cyclic strength decreases with fc.Figure 20 was used to obtain af factors in terms of thecombined eŠects of Dr-fc-0 and s?o, where Dr-fc-0 gives therelative density of the mixture with fc=0 at the same voidratio. In particular, the following procedure was used: (i) DISCUSSIONSAssume that the cyclic strength changes exponentiallywith the void ratio (e) for each case of fc and s?o, orCRR15=A exp (B・e)(11)where A and B are model parameters, (ii) obtain theparameters A and B that best ˆt each case of fc and s?o,(iii) use the obtained parameters to compute the If factorsfor fc=15z and 25z in terms of Dr-fc-0 and s?o and (iv) estimate the corresponding af factors for the If factors obtained. Table 4 gives the obtained parameters A and Bfor each case and the coe‹cient of correlation. Table 5gives the obtained af values in terms of Dr-fc-0 and s?o for fc=15z and 25z, as well as the average value. It can beobserved that (a) the exponential ˆt describes the eŠect ofTable 5. af coe‹cients obtained from the curves of Fig. 20 (with theparameters of Table 4) in terms of s?o, Dr-fc-0 and fce0.790.740.680.630.59s?o (kPa)Dr-fc-00.20.40.60.80.9650af-fc=15z-2.52-2.73-2.93-3.11-3.26af-fc=25z-2.18-2.34-2.49-2.62-2.72af-ave-2.35-2.53-2.71-2.87-2.99af-fc=15z-3.27-3.20-3.13-3.06-3.00af-fc=25z-1.51-1.83-2.11-2.36-2.53af-ave-2.39-2.52-2.62-2.71-2.76af-fc=15z-2.87-2.87-2.93-2.95-2.98af-fc=25z-2.36-2.44-2.52-2.65-2.73af-ave-2.61-2.65-2.73-2.80-2.85af-fc=15z-2.60-3.10-3.55-3.94-4.22100150300175void ratio on the cyclic strength very well and (b) the afapproximation reasonably describes the eŠect of ˆnes inthe three mixtures considered.Figure 22 plots the average af factors in terms of conˆning stress and relative density. It can be observed that(a) af decreases approximately linearly as Dr-fc-0 increasesand (b) the eŠect of consolidation stress on af does notshow a clear trend. The linear regression curve of the cyclic strength versus Dr-fc-0 is also presented. Its coe‹cientof correlation R2 is 0.73. Figure 22 illustrates that theeŠect of ˆnes on the cyclic strength increases as soil density increases.Table 6 compares the af factors obtained from theresults from previous investigations with the range ofvalues of af from Fig. 22. No comparison is made interms of Dr-fc-0 since this parameter, or the factors neededFig. 22. af coe‹cients obtained from Fig. 20 in terms of consolidationstress and densityTable 6. Comparison of af coe‹cients estimated from laboratory tests performed by other researchers with the range of values of Fig. 22 (-2.2 to-3.0)ReferenceTests bys?o (kPa)afComparisonXenaki and Athansopoulos (2003)Xenaki and Athansopoulos (2003)200-2.25OKBouckovalas et al. (2003)Yasuda et al. (1994)500.8No〃Troncoso (1990)196-2.4OK〃Vaid (1994)350-4.1No〃Polito and Martin (2001)100-3.2No〃Polito (1999)100-2.2OK〃Koester et al. (1994)103-2.4OK〃Koester et al. (1994)207-2.7OK〃Koester et al. (1994)103-3.5No〃Koester et al. (1994)207-4.1No〃Koester et al. (1994)103-1.9No〃Koester et al. (1994)207-2.4OK〃Koester et al. (1994)103-2.8OK〃Koester et al. (1994)207-2.9OK 176DISCUSSIONSto obtain it, are not available since they have not alwaysbeen reported. It can be observed that the range of af factors in Fig. 22 in most cases is in agreement with previousdata.In conclusion, the discusser presented the results of thetests he performed in order to enrich some of the ˆgurespresented by the authors and to use the enriched ˆgures toderive Fig. 22, which illustrates the eŠect of Dr-fc-0 on therelationship between fc and CRR15. It should be notedthat the eŠect of the ˆnes content on the cyclic strength isstrongly aŠected by the relative density, and that this hasnot been demonstrated before.REFERENCES36) Bouckovalas, G. D., Andrianopoulos, K. I. and Papadimitriou, A.G. (2003): A critical state interpretation for the cyclic liquefactionof silty sands, Soil Dynamics and Earthquake Engineering,2003(23), 115–125.37) Koester, J. P. (1994): The in‰uence of ˆne type and content on cyclic strength, ground failures under seismic conditions, Geotechnical Special Publication No. 44, ASCE, 17–33.38) Polito, C. P. (1999): The eŠects of non-plastic and plastic ˆnes onthe liquefaction of sandy soils, Ph. D. Thesis, Virginia PolytechnicInstitute.39) Troncoso, J. H. (1990): Failure risks of abandoned tailing dams,Proc. of International Symposium on Safety and Rehabilitation ofTailing Dams, Paris, International Commission on Large Dams,82–9.40) Yasuda, S., Wakamatsu, K. and Nagase, H. (1994): Liquefactionof artiˆcially ˆlled silty sands, Ground failures under seismic conditions, Geotechnical Special Publication No. 44, ASCE, 91–104.
  • ログイン
  • タイトル
  • The Effect of Fines on Critical State and Liquefaction Resistance Characteristics of Non-Plastic Silty Sands (closure)
  • 著者
  • "A. Papadopoulou, T. Tika"
  • 出版
  • Soils and Foundations Vol.50 No.1
  • ページ
  • 176〜176
  • 発行
  • 2010/02/15
  • 文書ID
  • 64351
  • 内容
  • 176DISCUSSIONSTHE EFFECT OF FINES ON CRITICALSTATE AND LIQUEFACTION RESISTANCECHARACTERISTICS OF NON-PLASTICSILTY SANDSi)Closure by ANTHI PAPADOPOULOUii)and THEODORA TIKAiii)The authors would like to thank the discusser for hiscomments. The discussion concerns the following points:a) the presentation of additional data for the liquefaction resistance, CRR15, for the same materials tested bythe authors at s?0=50, 100 and 150 kPa and ˆnes content,fc=0, 15 and 25z. A good agreement between the twosets of data is observed at s?0=50 and 100 kPa.b) the evaluation of a correction factor, If, expressingthe eŠect of ˆnes on CRR15, suggested by Bouckovalas etal. (2003):If=CRR15-f» 0CRR15-f=0(12)Bouckovalas et al. (2003) expressed If as a linear functionof fc:If=1+af・fc100(13)and stated that af depends on s?0 and is rather independenton void ratio. The discusser evaluates the If and af factorsfor all the test results from the non-plastic silty sands andexpresses af as a function of relative density, Dr-fc=0 ofsand (or void ratio).i)ii)ii)Vol. 48, No. 5, April 2006, pp. 713–725. (Previous discussion by C. A. Stamatopoulos, Vol. 50, No. 1, February 2010, pp. 173–176).Research Student, Department of Civil Engineering, Aristotle University of Thessaloniki, Greece.Professor, ditto (tika@civil.auth.gr).
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