カテゴリー別検索
Soils and Foundations 2002年
出版
soils and Foundations
| タイトル | 表紙（論文報告集） | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | -〜- | 発行 | 2002/02/15 | 文書ID | 20431 |
| 内容 | |||||
| ログイン | |||||
| タイトル | 目次（論文報告集） | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | -〜- | 発行 | 2002/02/15 | 文書ID | 20432 |
| 内容 | |||||
| ログイン | |||||
| タイトル | 表紙（Soils and Foundations） | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | -〜- | 発行 | 2002/02/15 | 文書ID | 20433 |
| 内容 | |||||
| ログイン | |||||
| タイトル | Contents（Soils and Foundations） | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | -〜- | 発行 | 2002/02/15 | 文書ID | 20434 |
| 内容 | |||||
| ログイン | |||||
| タイトル | Collapse Loads over Two-Layer Clay Foundation Soils | ||||
| 著者 | R. L. Michalowski | ||||
| 出版 | soils and Foundations | ||||
| ページ | 1〜7 | 発行 | 2002/02/15 | 文書ID | 20435 |
| 内容 | 表示 | ||||
| ログイン | |||||
| タイトル | seismic Passive/Active Thrust on Retaining Wall-Point of Application | ||||
| 著者 | D. M. Dewaikar ・S. A. Halkude | ||||
| 出版 | soils and Foundations | ||||
| ページ | 9〜15 | 発行 | 2002/02/15 | 文書ID | 20436 |
| 内容 | 表示 | ||||
| ログイン | |||||
| タイトル | Effects of the Stiffness of Soft Clay Layer on Strong Motion Response | ||||
| 著者 | Akira Yamaguchi・Motoki Kazama・Hirofumi Toyota・Masaki Kitazume・Takahiro Sugano | ||||
| 出版 | soils and Foundations | ||||
| ページ | 17〜33 | 発行 | 2002/02/15 | 文書ID | 20437 |
| 内容 | 表示 | ||||
| ログイン | |||||
| タイトル | Development of Sensor for Monitoring Seismic Liquefaction | ||||
| 著者 | Yoshihisa Shimizu・Susumu Yasuda・Iwao Morimoto・R. Orense | ||||
| 出版 | soils and Foundations | ||||
| ページ | 35〜52 | 発行 | 2002/02/15 | 文書ID | 20438 |
| 内容 | 表示 SOILS AND FOU*NDATJONSVol 42, No. i, 5369, Feb^ )_002Japanese C.eotechnical Society, ,a?lcp(1-situ )EXTERNAL STABILITY OF VERTICAL, EXCAVATIONS INanceslrnics,SOFT CLAY WITH SELF-SUPPORTED DMM WALLSvaterhiba-ALA'A EL NAHAsi) and JIRO TAKElvIURAii);as (inte andABSTRACTh It*a+vSix centrifuge tests ¥vere conducted to study the possible failure mechanisms for open excavations in soft clay withDMM self-supported valls, and the pre-failure soil and ¥vall behavior, as well as the effect of some parameters on thewall external stability. In the tests, in-flight excavation was conducted until failur'e. The DMM wall was modeled by awall made from aluminum and acrylic plates, which ¥vere instrumented with pressure cells to measure the active andpassi¥'e earth pressures, and the base contact pressure of the ¥vall during excavation. Upper bound analysis ¥vasconducted to verify the efficiency of the currently used design method, and to identify the main parameters which affect)n onSi e,)19ion of; underthe ex. ternal ¥vail stabilityr andIt ¥1'as found that the failur'e of the excavations with DMM self-supported walls floating in the clay, took placesuddenly ¥vithout marked pre-failure soil and wall movements. The main parameters which affect the wall stability arethe ¥vall dimensions, the soil strength profile, the adhesion between the ¥1'all surfaces and the surrounding clay, thestrength anisotropy, and the surcharge on the clay surface. The soil strength profile and the adhesion between the ¥vallsurfaces and the clay ¥vere found to be the most important parameters.arnin, Earth)ance aiA SCE.Kev. ,1=0rds: centrifuge test, deformation, DMM, open excavation, self-supported wall, soft clay, stability,bound calculation (IGC: H2)economical reasons.INTRODUCTIONThe external wall stability is normally estimated usin_",_Self-supported ¥valls (SSW) made by the deep mixingmethod (DlvlM) are a relatively recent application forthe classic desi_ n method of the self-supported wallsexcavations in soft clay. This type of wall is relativelyexpensi¥*e compared to strutted or anchored excavations.Chen et al. (1996), and Azuma et al. (1999). In this(gra¥'ity type ¥valls) as described by Shiomi et al. (1996),method, Rankine earth pressure distributions on the ¥vallsides are used, assuming smooth vertical ¥vall surfacesand isotropic soil conditions. As there are no recordedfailure cases for excavations supported by this wall type,the current design method is considered to provide safewall designs, althou*'h the actual safety factors are notHo¥vever, the strutted excavations are not economicalwhen a Jarge area of open excavation is required. Eveninstalling and removing the struts during constructionresults in complicating and slowing do¥vn theju p perconstFucrion process For soft soils where no *"oodbearing strata for ground anchors is availabie, usingclearly recognized. This design method has someuncertainty. For example, the possible failureanchors is also expensive. Therefore, this type of ¥vallbecomes economically feaslble for lar*'e open excavationsmechanisms for this wall type have not been thoroughlyin soft thick clay layers.investigated yet, the factors affecting the wail stability areAs the stiffness of the treated soil ¥vith DMlvl is farhigher than that of the untreated soft soil, e.g., mor'enot kno¥vn, and further ambiguity is caused by ignoringboth strength anisotropy, and the adhesion between thethan t¥vo order difference, the external stability andsoil and the ¥vall verticai surfaces. This has lead to over-internal stability are evaluated separately in the design ofdesigning walls to avoid sudden failures, as reported byShiomi et al. (1996).the ¥vall (Kita2;ume et al., 1996a). Due to the lo¥v tensilestrength of the non-reinforced DM columns, the currentdesi_ n practices adopt a ratio of height/breadth (H/B)of the valls of not more than 2 to avoid subjecting theKitazume et al. (1996a) pointed out in their JGS-TCReport that neglecting the adhesion on the interfacesbet¥veen the DM improved ground under marinewall cross sections to any tensile stresses. On the otherhand, that ratio is not allowed to be less than l.O forconstructions and the surrounding soft grounds, ¥vhich isadopted in the current design practices, results in)Lecturer, Department of Civil and Water Engineerin_g, National University of Science and Technolo_gy, Bulawayo, Zimbabwe.i) Associate PFofessor, c.ET/SCE,,Asian Institute of Technology, P O. Box. 4, Klong Luang, Pathumthani l)-120, Thailand.Manuscript ¥vas Feceived for review on January 31, 2000.¥Vritten discussions on this paper shouid be submitted before September I , 200'_ to the Japanese Geotechnical Society, Sugayama Bldg. 4F,Kanda A¥vaji-cho 2-23, Chiyoda-ku, Tokyo 101-0063, JapanUpon request the closing date may be extended one month.53sL' 54NAHAS AND TAKE*lviURAunderestimatin*･ the external stability of the improvedground against the horizontal and vertical forces. Theyalso sho¥ved that considering the adhesion is importantunstrutted sheet pile and cliaphra_ :m ¥valls. Kimura et al.for proper evaluation of the field behavior of theimproved ground mass.simulating excavation problems. Bolton et al. (1987,The internal stability of this type of walls has beenstudied by some researchers. To reduce the wall breadth,Kitazume et al. (1996b) and Babasaki et al. (1998) studiedthe failure mechanisms of the reinfor'ced DMM gravitywalls and the applicability of the reinforced concrete's¥vall excavations in clay and presented a method tostructural calculations in its design.Centrifuge modeling has been used for studying thestability of excavations in clay, supported by strutted and(1993), and Takemura et al. (1999) presented the benefitsof using centrlfuge modeling and an in-flight excavator in1988) conducted a series of centrifuge tests on diaphragmpredict the deformation of the ground due to excavationwith the diaphragm walls unpropped and propped at thetop. Centrifu*'e research on possible external failuremechanisms and the parameters affecting the externai stability of the self-supported DMM ¥valls is very limited.Among these studies are Chen et al. (1996) and El Nahaset al. (1999).In this paper results of six centrifu*'e model testsconducted to study the failure mechanism for the ¥valls¥vrth "H/B 1 2" are presented. The soil and wallin-fiight excavator upper sandgate TnotoFL,VDTsIayerdisplacements ¥vere monitored until failure, and theL DTS sur ace markerseffects of the ¥vall dimensions, and the adhesion bet¥veenvflter supplysolenoid valve (a)solenoidvalve (a)the soil and¥'all surfaces on the ¥vall external stability arediscussed. Upper bound analysis was also conducted toverify the current design method and to study the factors{>solenoid'vlvalve (b)Vs;v)vltankdumpeaffecting the external wall stability.VlCENTRIFUGF, MODF,L TF.STSTest Systelns a/7cl ConditionsTIT Mark 111 Centrifuge, in-fiight exca¥'ator and steelmade model container' ¥vith a tr'ansparent acrylic ¥vindo¥vsoiimm¥¥'ere used in the tests. Their details and specifications aregiven by Kimura et al. (1993) and Takemura et al. (1999).Test setup used in this study is sho¥vn in Fig. 1.' pore pressure transdilcerFig. 1. Test setupLDT target plateL,VDTswall extension platesctaluminum platesJacrylic plates8]vertical holes9]back sidefront side10]1l][12&13& 14]149.481[]Fig. 2.)lN)voo10 3 @ 20.3 Iounlt: mm.vlSchematic lal_ out for model wallPressure Cell No.cr¥ 55STABILiTY SELF-SUPPORT D D d¥* ,1 ¥¥,ALLItor in(thickness t = 20.7 mm) and the side aiuminum plates (t =10 mm) were used in all the tests, and the ¥vall breadth¥vas adjusted by adding additional vertical acrylic plates(1987,between the central acrylic plate and the tlvo side[ et al.enefitshragmaluminum plates. In SSW-O, 3, 4, and 6 t¥vo additionallod tovationthe central acrylic plate and the aluminum plates, asat theshown in Fi**. 2. In SS¥V-5, four additional vertical platesf ailure¥vith the same thickness ¥vere used. In SSW-7, twolal sta-additional vertical plates with different thickness (t = 10. 1irnited.mm) ¥vere used. To increase the wall height, t¥vo andvertical acrylic plates (t = 20.3 mm) ¥vere inserted betweenthree additional horizontal plates lvere also assembled onNahasthe vertical plates in SSW-4 and SSW-6 respectively, assho¥vn in Fig. '-. The ¥vall unit ¥veight was adjusted by31 testse vallsputtin*' Iead shot inside the vertical holes in the vertical･;･･･ *acrylic plates in SSW-4 and 5, and by making additlonalvertical holes in the acrylic and aluminum plates in SSW7. However, some difference in the unit ¥veight cou]d notld wallnd the)etlveeniliry arebe avoided in the testF](, 3. Model wallunit wei*･ht ¥vas 16.8 kN/m3 in SSW-O, 3, 4, and 5. InSSW-6 and 7, the wail unit vei__･ht ¥vas 17.9 kN/m; and19.4 kN/m3, respectively. In SS¥V-O, polished surfacesicted tof actors(a) lvlodelvith different dimensions. The ¥vallvallAs the purpose of the centrifuge model t,ests ¥vas tostudy the external stability of the self-supported DIMM¥vere provided on the wall of the aluminum plates towith a lot of instrumentation using real cement-treatedcreate the smooth wall condition. In the other tests, therough ¥vall condition ¥vas created by *'1uing sandpapersheets (No. 100) on the ¥vall vertical surfaces, and on thetnd steelsoil, the Dlvl ¥vall ¥vas modeled using different materials.wall bottom.¥vindo¥1*The model ¥vall used in the tests consisted of 2 aluminumplates and several acrylic plates, as shown In Figs. 2 and3. The aluminum plates ¥vere instrumented ¥vith 6 and 5pressure cells on the back and front sides of the ¥vall respectively. One pressure cell was also installed on the tip(b) Soils used in the tests and test setupThe model ground consisted of three layers: upper dry'all and it ¥¥'as rather difficult to make the DMM ¥ 'allions are(1999).of each of the t¥¥'o aluminum plates and the central acrylicloose Toyoura sand, soft kaolin clay, and lo¥ver denseToyoura sand as sho¥vn in Fi**. 1. Under the centrifugalacceleration of 70G adopted in the tests, the thickness ofthe layers in the prototype scale ¥vere I .O m, 10.7 m, andplate. The capacity of pressure cells No. l, 2, 3, 4, 7, 8and 9 ¥vas 7-00 kPa, and the capacity of the other cells hvas500 kPa. In each test, the ¥vall ¥vas reassembled to adjustits dimensions.2.45 m, respectively. . Table 2 gives the physical andThe ¥vall dimensions (H: hei_ :ht and B: breadth) forvertical consolidation pressure ((T(.) and axial strainseach test are sho¥vn in Table I . The central acrylic platewhich ¥vere obtained from undrained compression andTable 1.support condition (kN /m3 )condition¥)excess pore water pressures (Au) normalized by theTest conditions and resultsVertical Surf ace y * 1Test Nomechanical properties of the kaolin clay. Figure 4 sho¥vsthe relationships bet¥veen deviator stresses (q) and thek*2c 3(kN/m3)(kPa)H*4(mm)*5(mm)ObservedH/B(z*) *6(mm):'-/]SS¥¥f-O 'Floatin *SS¥¥r_3SS¥¥r_4FloatingFloatingSS¥¥r_5-Floating:SS V-6SSIV-7Resting*FloatingSmoothRoughRoughRoughRoughRough15.4l .43*43 4l'-3 (8.6)8, (5 7)l .543(3.0)15.5l .33 ,4163(1 1 .4)8, (5.7)2.016.016.0l .43 *4124 (8.7)64(4.5)67(4.7)l .415.51.33*43 4*co is undFained strength at the clay surfaceH and B are the lvall hei lht and breadth: 6( *)- is Ehe excavation depth at faiiurethe earth pressure on the vall surfaces ¥vas not measuredhe ¥vall is floating in the soft ciay layeFlhe ¥vall is resting on the lower dense sand layer(!L:)the dimension in the prototype scale (m)32(2 2)15.7}, is average bulk density of clayk is undrained strength increasing ratio of clay ¥ 'ith depth*-l .5123 (8,6): i*4 and8, (5 . 7)l ^4l 65(1 1 .6)122 (8.5)1 ,_3(8.6)82 (5 . 7)6 1 (4 3)1 .O2.02.0lOO(7.0)50(3.5) 56NAHAS AND TAKEMURA top plate蕊掛・ q：△u嚢 り20．5セ 10 15 2．丁＞．ヤトcKoこ！c営ぐ南一断・ 睾bb 13CKoUEぺぴ 一一 榊 180Sec“ona賑S韮de V藍ew（2−2） Sectiona叢E屡evat崖on（1−1） cu賃er hand（2）σ膠Vc：ve貢icalconsilidationpressureσ’v。篇392kPa一〇竜51510Sec。P藍an（3−3）團（％）Flg．4． Resui重s of CκoUC and CκoUE重es芝s for NTC kaoli臓clayTable2． Physical呂nd mecba鷺曇c田proper重ies of kaolln clay錘Liquld販mlt，（HZl）嚢（1） （1） 1L，77．5％（2）All〔1imensions are in田m．Cu償ers∼vere use〔i∼vith different、v圭dths（b）；64，84，and126mm，Fig．5．αayc瞭erforinstail韮ngmodelwallPlasticlimlt，（以P）30．3％Plasti￠ity index，（∫P）47、2Spec呈負c gravity（（二｝、）2。6三condltion was created in SSW−0，while in the other tests，Compresslonindex（q）〇．65the wall surface condit圭ons were a11 τough to ful豆yS、ve1至ing index（C、）0。10VQ玉d fat1o at98kPa on N。C，1ine1．66κ。forN．C。clay．0．61（c砦1：m・1f・ Ul…・0．24mobillze the adhesion on the surfaces．In all由e testsexcept SSW−6，the wall noated in the soft clay as aaoatlng type wal1，whle the wall in SSW−6rested on由esurfεtce of the正ower sand。It is noted that the thickness ofthe clay between the wal璽base and the lower sand was Crlticalstateparameter（M）Permeablhty at98kPa on N．C．Iine1．02。0×王o庸9m／seconly5mm ia SSW−4．ハ40‘ノθ1P1ゆ（∼Pαrα！ion‘7η（ノTθ5！P1層ocθφ11で3 互n由e preparatlon of the model setup，acrylic plateskaol三n clay。This figure shows that even in the extensionwere nrst placed on由e bottom of the container asspacers、Toyoura sand was then poured aad compactedtests，positiveexcessporewaterpressuregeneratesfortheuu（ier the sllbmerged condit圭on with surface vibrεttionexteasion triaxial tests on κo−normally consolidated＆x量a正strain鼓igher than2％unti正failure． As s数own in Fig．1，the upper sand layer was connectedtothesoildumpingareathroughasolenoidvalve（a），andt紅e so猛一dumped area portlon was connected to a tankoutside the container裳熱rough another solenoid valve（b），肇A wa宅er supply Iine was pτovided to the model containerthrough a s圭de hole above the soil layers in t鉦e＆ct玉ve s玉de・The Iower san（i layer was con鳳ected to the soll−dllmpeduutil the relative density（Z），）became90％．Clay slurryremolded at water content玉．5times the Ilquid limit wascarefully de−aired and poured into the containeLLabor＆tory旦oQrconsolid飢ionw＆sthencQ歎ductedstepwlse under the pressure of15kPa．After completionof the conso玉idation， pore pressure transduceτs wereinsertedintheclayfromthebacksidewallofthecontainer． Subsequently brass rods g三v量ng rise to aportion．Twopairsofspongetape∼veregluedon由e surchargepressureln70G盒eldequ＆1to由econsolidatlonupPerparts ofthe front andbεしck sidecorners ofthewalL垂and centrifugal consolidatlon was carried out at70G toen鍍app重ng any sand partic豆es ofthe uppeτsand layer be−form a normally consoli（iated cla》・with streng由tween the mo（iel wall aa（1each of the front window andincreasingwitbdepth．the back side wal正of the mo（ie孟container。（c）Testconditions Table三黛ives the test conditions for由e six tests．Asexp至ained＆bove，tぬe ground cond呈tions，i．e．レthick歎ess of難霧t｝集e星ayers an（i strength pro負1e of the clay，are the same inall the tests．The dimens至ons and surface roughness of the Oa completion of the centrifugαI consoli（iation，thecentrifuge was once stopped． The brass rods wereremove（i a勲d then the front、vlndow of tぬe contalner wasdetached．The clay 食ont suτface was covered by twoguideplatesbetween・vhichthemodelwallposltionremained llncovere（i．The box−shaped steel cutter waswa11were parameters in the tests．As discussed ln thehorlzontallylnsertedintotheclaythroughthespacebe−lntroductlon，thewa11height／breadthratlo（H／β）wastween the gui（ie plates to cut and remove the clay imhechanged from 1．O to 2．0．A smooth wall surface、嚢pressureontheia団oor“・ereplacedattheclaysurfaceThe function of the sponge tapes was to preventmodel wall position．Figure5shows a schematlc drawing STABILITY SELF-SUPPORTEDD¥. 1¥._1_ c :_! I}DTS "L1 DTs+;Ij I--Calculated froivl if?' ) 132"i': /uppersandlsl26129t301 !O 50* +)c'the stress historyi:pressilre ce] sjc'$MeasuredI f' i! 'l , tJ'i[21E8[7]it(S) :I +i.jrilELa ppTi lavprl)l'vCF1IJ1, 40,.tJ ':?'f'*: l;PPT (3)' [1l]I l[-1)o ppT (4) PPT(If[6] ' PPT(7_)1'_] [131 [14] kaolin c ay c'l 50$t 82 200h :._-[ 60t( ) pore pressure tFn * ducee>i1*o[ 1 1 'all pressure cell Noa : diuiensions are in InmFig. 6. Positions of sensors used in ceutrifuage modeling tests (SS¥ '-O,SS¥406s-+* :lower sand layer. J2oLW )･ PPT (6)(1)Ol I :1.>r hand/57¥VALL_3, SSW-4, SSW-5, SS¥ '-6, and SS¥ r_7)ld I '-6 mm.;::tQo100.8 0.6 1020 100 200water content (cu)eomp vertical stressof the cutter. Three cutters were made to suit threedifferem ¥vall breadths tested The outer ¥vidth of thether tests,cutter (b) ¥vas 3.0 mm lar'ger than the ¥vail breadth. Latexto fullymembranes coated ¥vith silicon grease ¥vere put on bothfront and back surfaces of the model wall, and the ¥vallwas ther} placed in the wail position. The purpose of the_greased membranes ¥vas to reduce the friction bet¥veenthe wail and the container and also to prevent the ¥vaterflow bet¥veen them. Having placed the model vall in thel the testsclay as ated on thelickness ofsand ¥ *asvere placed on it and the fr'ont ¥vido v ¥vas re-soil in the active side. Also, t vo pairs of laserLrcers ¥vereinstalled to monitor the ¥vall tilting and displacement.Figure 6 sho¥vs the positions of all sensors used in thedisplacement transducers (LDTS) and LVDTS ¥veremodel. Having completed all the preparations, theexcavator was mounted on the model container. The¥ 'ater levels in the soil layers and in the dumping arealvere adjusted to be at the upper sand layer's surface.The ¥¥'hole test setup ¥vas taken on the centrifu_ e andthe model groun ¥vas re-consolidated in a 70CJ field untilthe excess pore ¥vater pressure ¥vas dissipated. During thelay surface[ at 70G to[ stren thdation, thentainer ¥vasreconsolidation, solenoid valve (a) vas kept open andsorne lvater lvas drained from the dumping area to thered by t¥ 'ol[1 positiontank through solenoid ¥'alve (b) to keep the _ground ¥vaterlevel at the ievel of the clay upper surface, ¥vhich settledrods ¥verecutter ¥vase space be'clay in thetic dralvingAt the end of the reconsolidation, solenoid valve (a) wasclosed, and the excavation ¥vas conducted step by step,mm, and the in-flight excavator cut 10 mm thickness ofthe soil (0.7 m in the protot.ype scale) in front of theconductedompletionnsolidationincreasing ratio ((c ).. ,plcr(*) are also sho¥vn in the figure.remo¥'ed from the front surface of the clay, surfaceclay upper surface, and the sand ¥vas then lain on the clayand leveled to form the upper loose sand layer' ¥vith a relative density of 400/0. Then, LVDTS ¥vere instailed behindthe*all to measure the surface settlements of the retainedrise to athe effective vertical stress of the clay and the strengthusing the in-fli**ht excavator as follolvs. In everyfitted on the face of the model container. Water ¥vaspoured into the container to about 10 mm depth from theail of theprofiies at end of centrifugal reconsolidationexcavation step, the soil-retainin_markerscontainer.Fig. 7. Measured and calculated water content and shear strengthcontainer as sho¥vn in Fig. l. The two guide plates wereylic plates_i limit ¥vas(kPa)cut portion, a soi]-retainin*' _"*ate ¥vas installed in thentainer as,om pactedvlbrationllay slurry(kPa)gate ¥vas lo¥vered by 10model wall and thre¥v it into the dumping area. The ¥vaterlevel in the excavated area was lolvered by drainin_ : ¥vaterfrom the box throu*'h solenoid valve (b) to the tank untilthe ¥vater level reached the excavation bottom.The excavation step ¥vas repeated until a clear failureoccurred or until the maximum excavation depth. ForSSW-6, the maximurn excavation depth was achieved¥vithout observin*' any failure (z* = 7.0 m in the prototypescale). So, from the ¥vater supply line, ¥vater ¥vas pouredon the upper loose sand layer behind the ¥vall until thefailure took place. The increase of water level by theadded water can be transformed into an equivalent claylayer depth, ¥vith the same ¥veight. Since increasing theretained soil height has the same effect on the stabilitynumber as excavating the same height from the passiveside, the virtually added cla).' heiccrht due to the added¥vater can be assumed as an equivalent excavation ¥viththe same height. From this assumption, the finalexcavation hei_"*ht ¥vas estimated to be 7.6m in theprototype scale for SSW-6.due to the consolidation of the clay. Profiles of theFi**ure 8 shows the progress of the excavation process¥vith time. Each exca¥'ation step was conducted in fivemeasured and calculated vater contents in the ciay afterthe centrifugal consolidation are sho¥vn in Fig. 7. Theundrained compressive strength (c**)*.* estimated fromminutes, vhjch means O.7 m excavation 1,as cut e¥'ery 17days in the prototype scale. This excavation speed ¥vas theaaL:";maximum that the in-fiight excavator could achieve. +*'; {58NAHAS AND TAKEMURA,,,*1000 2000 3000 4000oii8;=;'1:i!,"ilH7N;'6o4>13,;:;:;{{ 'oooo ,oecoo1o' ;':;; ;;;" 'ooeoooSSW-4 (H/B= 2.0)SSW-5 (H/B= I .O)e)ooe)'SSW-O (H/B= I .5)SSW-3 (H/B= I .5)10lOO '-)ii12time in model scale (sec),,, "'*-e-sSW-o)-ssW-3- -SSw-4-sSW-5:IHSSw-6-SSW-740 80 120 160 200 240<a9h875 'N"(D4HIHo16;*o･ SSW-7 (H/B= 2.0)S50 '25SSW-6 (H/B= 2.0)eJOe)e)oo2time in prototype scale (day)o1 ,eFig. 8. Process of excavation!*,',;'<*1 .6,: " "';: failure point{{::;'During excavation, ¥vall and ground displacements, pore¥vater pressures and pressures on the front and backsurfaces and the base of the ¥vall vere measured.1 .41displacements. The test results are given in prototype0.8scale in the follo ving section. The water pressure in theg... '.' *lo¥ver sand layer 1¥'as lo vered as the exca¥rationprogressed because the lo¥ver sand layer ¥vas connected tothe soil-dumping portion where the ¥vater table ¥vas*/' ".adjusted to the excavation surface le¥'el. It lvoulcl havebeen expected that negative pore ¥vater pressure had beenobserved due to the removal of soils. Ho¥vever, the ¥vaterpressure measurements during the excavation did notsho¥v the negative pore ¥vater pressure,vhich meant that- -_ 1.2Photo_ raphs were also taken to observe the wall and soil:ic/o 0.60.4o0.2O-oooOthe assumption of undrained conditions could bez* (m)reasonably assumed for the test condition. A similar ofpore ¥ 'ater pressure behavior ¥vas observed in thecentrifug:e model tests on the braced ¥vall excavation insoft normally consolidated clay (Takemura et al., 1999).** i:.TEST RESULTS AND DISCUSSIONS"'",'**"*_ /',;""' fi'; ,' ,'maximum tilting angles of 6' ¥vas measured. Ho vever,even for the maximum tiltin_ : angle the 31lmid caused bthe ¥vall tiling was O. 14 m smaller than 6hb * at the end oiHoriz,ontal displacements at the ¥vall bottom ( /1b.*)and the ¥vall-tilting angle (e, *ll) during exca¥'ation areplotted against the excavation depth (4-*) in Fi**. 9. 1lb.*and e+.* ¥vere obtained from the measurements of the t¥vothe test in SSW-7 (O.3 ln). In the other' tests with thefloating type ¥vall, displacement of the lvall due to thrsets of LDTS and LVDTS on the ¥vall. As explained in theprevious chapter, the soll was excavated step vise by 0.7m depths in one step. With this increment of excavationdepth in one step, very small horiz,ontal displacements¥vall base sliding ¥vas much larger than that caused by the¥vall tilting. This may imply that the floating type ¥valk¥vith H/B up to 2 first fail by sliding; thereafter some ¥val]tilting to¥vards the excavation side takes place. Therefore,the failure excavation depth, (z*)f, for experiments ¥viththe floatin_g type wall should be determined from the z* -excavation depths where the sudden large displacementstook place lvere the same or one step ear'lier than thehb.* rclation. In this study (z*)f was defined as threxcavation depth at the intersection of the tangents fcuthe z* - /1 .* relationship before and after the sudderincrease in 61lb.*. In SSW-O, ho¥vever, it ¥vas ratheldepths lvhere the marked increase in the ¥vall tilting ¥vasdifficult to define the failure point in this ¥vay, because thtobserved, except for SSW-6 ¥vith the wall resting on theexcavation depth in the 4th step ¥vas relatively large]compared ¥vith the failure depth. Hence the average oiplace in the fioating type ¥valls (SSW-O, 3, 4, 5 and 7). Thelo ver dense sand layer. The horizontal walldisplacements at the mid depth of the ¥vall caused by thetilting (6h ,id) is approximately given by: H/2 x e,..u (inradians). In SS¥V-7 where H/B=2, and B=4.3 m, the!! ,･ . #wail during excavation,Va!! Movenlellts ancl Grotlnc! Defol-n7atiol7were observed before a sudden large displacement took,. "' .Frg. 9. Variations of horizontai bottom displacement and tiltin"* ofthe excavation depths before and after the sudderincreases ¥vas taken as ( ･-*)f for SS¥ J-O. The failure depthsare indicated ¥vith arro¥vs in the fig:ure. It should be notec STABILiTY SELF-SIJPPORTEDDiv+ I¥, i¥¥*59L Lz* (m)o1 2 3 4 5 6 7 8__ :_ 2.25m from the walupperproppingE O,f_o.,_f), IowerproppingcE(i)f(1)o(L)co O,/o.4Mf_f_, *- e- - caseO: no embedment into sand- - case7: embedment into sand by Im*fvo.o.6- -56eXCaVation depth()mh'SsW-o-0 ssW-3- -sSw-4o.81 2 3 4Fio. 1 1 . Resu Its of centrifu e model tests on braced sheet pile lva lexcavation: (after Takemura et a ', 1999)-sSw-5{hSsW-6' failureSSW-7relationship in a similar way to the other tests.1Fig, lO(a),s *,(* relationshiPsRelationships bet¥veen the maximum settlement behindthe ¥valls and the excavation depth are sho vn in, "***,Fig, lO. The horizontal axes in Figs. lO(a) and (b) are theZ J(Ze) fo02 O.4 O.6 O.8 1 1,2 14 16excavation depth and the excavation depth normalized by(z*)f respecti¥'ely. As ¥vith the ¥vall displacements, onlyvery small settlements ¥vere obser¥'ed before a suddenincrease in the settlement took place. Figure 1 1 sho¥vs theo.7_78l+Jand tilting olHo¥vever,o.8l due to thaused by thg type ¥¥*all;and the marked increase could be prevented by adding-ssw-o-o-ssw-3., caused b]}t the end oivith thesettlement gradually increased ¥¥"ith the excavation depth,o.4o.6tsexcavation depth and settlement relationships, ¥vhich¥¥'ere observed in the centrifuge model tests on bracedvaH excavations in normally consolidated kao]in clay(Takemura et a]., 1999). For the excavation ¥vith thebraced vall embedded into the lo¥ver sand layer, thestruts that sometimes resulted in larger settlements thanl ssw-4( ssw-5{ ssw-6the allo¥ 'able values ¥¥'ithout sho¥vin_ any failure. Whilefor the braced excavation with a sheet pile vall floatin**" inssw-7 ffatturethe clay (Case O in Fig. 1 1)vhichvas propped only at thetop, a marked increase of settlement and clear failuretook place. From the observation, it can be concludedthat brittleness is a typical behavior for self-supported orless supported floating type walls. In the case of a multi-braced wall with embedment into the lo¥ver sand iayer,the resisting forces from the struts and the lo¥ver sand1er some ¥valilayer also increase, as the horizontal deflection of the ¥vallFig, 10(b), s ../(4 )f relatronships. Therefore,increases due to excavation. But this is not the case forined as til:that the defined failure excavation depth is limit,ed in itstang:ents fo;accuracy due to the step¥vise exca¥'ation of O.7 m inself-supported or less supported floating type ¥vall, ¥vhichmight explain the brittle behavior of those types of ¥vall.This means that the stability against failure is the crucialsubject in the evaluation of the external stabilit.¥' of thedepth.DMM ¥vall rather than the-imentsvitrorn the z*the sudde:round deformation. As tileIn SSW-6 ¥vith the ¥vall base resting on the lo¥ver densefailure excavation depth is different in tests ¥vith different-, because thsand layer, no remarkable horizontal displacement waslrively largeseen at the ¥vall bottom even after the failure, as shown inconditlons, it is ditncult to compare the brittle behaviorof the different tests in Fi**, lO(a). Ho¥vever, from thele avera e ciFi_･.. 9. The faiiure happened ¥vith a marked increase ofthe ¥¥'all tilting ¥vhen ¥vater ¥vas poured on the retainedsoil surface after the 10th excavation step. Therefore, thefailure hei_g:ht in SS¥¥1_6 ¥ *as defined from the e,**u *¥vas rathe;the suddef:ailure depthiould be notetLrelat.ionship between s .* and z*/( ･*)f sho¥vn in Fig, lO(b),it can be seen that SSW-3 and 7 sho¥v more apparentbrittle behavior than SSW-4 and 5 havin*" relatively largerH and B. This might be attributed to the larger 60NAHAS AND TAKEMURA( m)( m)o.O0.0I3,5' 'b'b'l'l7.0.1, , ,.10.5///'///'l3,5ll"'l"'' bll･ ' ' '.,,7.0///ll'p.' '/'/ ' ',1'b"10.5･"I-Cm)m)14.014.0oO 3.5 7.0 10.5 14.017.5 21.0 7_4.5 7_8.03.5 7 O 10.5 14.0 17.52 1 .O.5 28.0SSW-3 (Ha = 1.5, ze= 3.6 m)SSW-O (lm= 1.5, ze= 2.8 m)(m)(m)0.00.0l3.53,5l7.07.010.510.514.014.0l,¥ZZZ7,7i7/, :'b'b( m)O 3.5 7.0 10.5 14.0 17.521.024.5 28.0O 3.5 7.0 10.5 14.017.521.024.5 28.0SSW-4 (Ha = 2.0, ze= 5.6 m)SSW-5 (H/B= 1.0, ze= 5.6 m)(m)(m)0.0O.O3,53,5,////'// l" i7.0ll.1l lb10.5, 1,･ ,,"'1''ll"'f"'l""'14.07.010.5, .,( m))14.0O 3.5 TO 10.5 14,0 175. 21:O 24.5 2810O 3.5 7.0 10.514.017.5 21.0 24.5 28.0SSW-6 (H/B:: 2.0, z.= 7 6 m)SSW-7 (H/;B= 2.0, ze=: 4. 9 m)Fig. 12.Observed ground displacements after failuresdeformation area for a ¥vall with lar*'e dimensions, Ivhichcauses more apparent progressive failure than a ¥vall ¥vithsmall dimensions.Figure 1'_ sho¥vs the observed displacements of the ¥valland the surface markers after failure. In all the tests,except for SSW-6, Iarger horizontal displacements of thewall and smaller vertical ones ¥vere observed at the ¥vallbase, which confirms the conclusion about Fig. 9 that theexternal instability for excavations supported by floatingtype ¥valls ¥vith H/B Iess than 2 is caused by slidin*'failure. Kimura et al. (1993) conducted centrifuge modeltests on a vertical excavation with unsupported floatingtype sheet pile ¥vall (H/B>>2) for clay ¥vith uniformstrength and increasing strength ¥vith depth. From thesetests, they observed that the failure mode for the latterclay was tilting, while for the former one the wall movedtranslationally without showin*' marked tilting. Thismeans that the ¥vall tends to tilt more in normallyconsolidated clay with increasing strength than the clay¥vith uniform strength. From these observation it mightbe said that the ¥'alue of H/B='-, which was obtainedfrom the normally consolidated clay, is not an overestimated value belo¥v vhich the sliding failure dominatesfor the fioating type self-supported DMlvi ¥vall. ¥ rhile for STAB L TY SELF-SUPPORTED D *1vall tiltingstrain concentration on the failure plane in the passivezone. From these observations above it can be expectedthan the ¥vall sliding for self-supported ¥valls ¥vith relatively high H/B ratio ( 2) resting on the dense layers.that the adhesion bet¥veen the lvall surfaces and the soilplays an important role in the external wall stability.SSW-6, the lvall moved with tilting mode, showing thatthe external instability occurs more due to theOn the active sldes, the failed zones were bounded bySettlement profiles behind the ¥valls just before andclear failure planes, in all the tests, as seen in Fig. 12. Theafter failure are illustrated in Fi . 13. The settlements andfailure plane in SSW-O with smooth surface is steeper'the distances from the ¥vall are normalized by thethan those in the other tests ¥vith rou*'h ¥vall surface,resulting in ¥vider failure zones in the latter than theformer. Outside these faiiure planes and belo¥v the ¥vall,no marked displacement vas observed even after failure.excavation height and the ¥vall height respecti¥'ely. Assome LVDTS didn't ¥vork in SS¥ l_7, the profiles couldnot be drawn in the test. Vfidth of the z,one of largeOn the passive sides, the soil deformed laterally withsome vertical heave without showing any clear' failureplanes. For the floating type walls in SSW-3, 4, 5 and 7the experiments and beyond a distance of the ¥vall height,very small settlements took place, even after the failure.with rough wall surfaces, the displacement vectors of thesurface markers in the first column in front of the ¥vallMobi!ized Strength on the Wa!1 Sui:facesho¥v only lateral displacements. However, in SSW-Oconducted on normally consolidated clay and normallywith a smooth wall surface, the displacement vectors ofthe same surface markers have vertical components. Thismeans that the full mobilization of the adhesion betweenthe ¥vall surface and the clay restrained the relativevertical displacements bet¥veen the ¥vall and the soil andmade the deformed zone in front of the ¥vall ¥vider thanthat for the smooth ¥vall. No clear failure plane was observed in the passive side. This may be attributed to the)61¥VALLstress-strain relationships sho vn in Fig. 4. In thecompression test (active coi7ditiol7), the deviator stressreaches its peak value and shows strain softenin*'. On theother hand, in the extension test (passive corldition) thede¥'iator stress increases continuously to large strain le¥'el.This strain hardening characteristic might prevent thesettlements didn't exceed 800/0 of the ¥vall height, H, in allTwo series of undrained direct shear tests wereconsolidated clay on a rigid aluminum disc. Theobjectives of these tests were to assess the mobiliz,edadhesion on the rough wall surfaces and also toinvestigate the effect of the strength anisotr'opy on themobilized undrained strength on the ¥vall surfaces. In thesecond series, an aluminum disc covered with roughsandpaper sheet ¥vas put in the lower haif of the shear boxto simulate the interface between the clay and the wallsurfaces. The tests ¥vere conducted according to thestandard test procedures "JGS 0560" (JGS, 2000) untilfailure. Figure 14 shows the results of the direct sheartests. There are quite similar relationships bet¥veen theshear stress (r) and the displacement ( h) for both testseries (Fig. 14(a)). Furthermore, the relationship betweenthe shear strength (rf) and the consolidation pressure(a(*) is almost the same for the two conditions. From Fig.14 it can be said that the mobiliz,ed strength at theinterface bet¥veen the rough wall surface and the sur-orounding clay (c,,.) ¥vas practically identical to that on theOfailure plane with the same direction of the wall surface in1the clay (c*), giving:just before failure;SWSSW- SSW-SSW{HSSW-o. ?_o.3O: 2; = 1.S m13: 2; = '_'9 m4: 2;;= 4'3 m5: z; = 4 ' m6: 2;3= 7.0 mcFrom the tangent of relationship between T nd (T(* ( =0.18) and [(c )* *p/Gf(*]eo*p=0.24, the following relationcan be derived for the undrained strength of the normallyconsolidated kaolin clay:¥ s'o.･4o[ :.JDs 0.75x ¥c ,,. p (2)[cr cT*(,0. lrh uniforrn)r the latterjuso, ,_strength increasing ratios for [CKoU]..*p triaxial tests andafter failureSSW- O: 2 = )- 7 m¥vall movedthe direct shear tests respectively.=SSW- 3: 2 = 3 6 milting. ThisCasagrande and Carillo (i944) proposed the following=SSW- 4: 2 = 4･8 m>-SSW- 5: 2;f 4･9 m03in normall =relationship to express the strength anisotropy:{ SSW- 6: 2;f 7.6 m:lan the cla =c (e) = c.h + [c vion it mighi'as obtaine0,oan overesti-'e dominatrll. While fo'. p¥vhere: [(c )*.*p/(T(*],. p and [c /(T(*]DS are the undrainedFrom theseFig. 13.!LO.5 x/H1^51_s/ze x/H relationships before and after failures= c*c hl x cos2 e (3-1)>< { m + (1 - m) >< cos2 e } (3-2)where: c v and c*h are the apparent undrained soil shearstrengths when the major principal stresses are vertical 62NAHAS AND TAKEMURAPressures Acting on the Wa!lThe measured total earth pressure distributions on thewall before excavation and just before failure in SSW-3,4, 5, 6 and 7 are sho¥vn in Fi**. 15(a-e). For SSW-O,･_o(a'vc= 60 kPa)Clay15rA :pressures acting on the wall were not available because amodel wall without pressure cells was used. Ko Pressure isalso shown, as well as the active and passive earth10, :;l5pressure distributions calculated from the formula of the' :!Civil Engineering Code of Practice (CP2) in UK, ¥vhichwas proposed by Rowe (1957):interface behveen clayp.,p(z) = yz + q :and sand paperowhere p*,p(z) is the intensity of the total active or passive_'6h4(mm)6 8 10o2c. (4-)vTT 7 : (5)earth pressure on the wall at a depth z from the upper claysurface, and c (z) is the undrained soil strength at depth<;-. Smooth and rough wall surface conditions were(a): 1:-5h relationshipsadopted in the calculation ofp* and pp, that is: c*,, O andO 8 x (c ) . The strength amsotropy was also taken mto. " '. paccount in this calculation by considering c* = (c )*.*p and1 20(c*)*** in the determination of p* and pp respectively.e ciay100Althou_g:h the differences of Ko Pressure and the calculatedactive pressures are small due to very low strengths of theC] interface between clayand sand paperclay, marked effects of the wall adhesion can be seen inc]80IF:Trthe calculated pressures. Equation (5) with c, =0.8x(c*)* *p Provides reasonable predictions for the earth0.18* a'vccs 60C]*pressure on the wall back just before failure in all the tests:¥vith rough wall surface. Ignoring the pressure cell No. 9,H 40which gave relatively higher values for observed earthpressures for all the cases, observed earth pressures on the･_oo[]front side of the walls fioating in the clay (SSW-3, 4, 5and 7) were smaller than pp with rough wall condition (c**O 8(c )..*p) and close to p'rth c,,,=0. In SSW-6, the100 _OO 300 400oobserved earth pressures on the front side were evena'+,c (kPa)Fig. 14.smaller than pp with smooth ¥vall condition (c,= O). These1;ra'vc relationshipresults show that considerin*' the wall surface adhesionon the mobilized active earth pressure on the wall backDirect shear test results of normaU ., consolidatcd kaolin clayleads to reasonable predictions for the active earthCb) :pressure distributions just before failure. On the otherhand, Rankine earth pressure theory (c,. = O) gives goodand horiz,ontal respectively. c*(e) rs the undrained soilshear strength when the major principal stress is directed¥vith an angle e, and e is the angle of the direction of theTakemura et al. (1999) expressed the mobilized soilmajor principal stress to the vertical. For the undrainedcondition (wit/1 c* = O), c ,, and c*h can be represented bythe shear strengths in the [CKoU]*.*p and [CKoU]*** re-strength ratio at the front of the sheet pile wall (MSR )f*' *spectively, and the angle of the failure plane to thestrength at the depth of the earth pressure cell on the walldirection of principal stress can be assumed 45'. Here lnduring excavation:is the coefficient of stren*"th anisotropy defined by c h/c"+ *Using Eqs. (1) and (3-2), the mobilized strength on thewall surface (e=45' and 135') can be expressed by:1 + mcw = c*{45) = c*(135)c ,*.= 2p X f ¥ (4)with smooth surface usin*" observed earth pressure ((Th)the total vertical pressure ((T ) and undrained compressive(MSR ) = ah - (T,. (6)f *. *r¥2¥c ,*.*pIn this study, the followin*' relationships were employedto assess the mobilized soil stren*"ths on both sides of thewall:Coefficient of strength anisotropy (m) of the normallyconsolidated kaolin clay is about O.6. Hence, Eq. (4)(MSR ) = (Thives: c,*= O 8 x (c ) for both the side surface and thebase of the rough ¥vall. This value compares ¥vell to theobtained value from the direct shear test (Eq. (2)), ¥vith(MSR)b ek= f2 Cu1)comp* " '. pabout 70/0 difference.{predictions for the maximum passive earth pressure onthe wall before failure.alfront 2(Cu )ext(7Y - CTh(7)(8) eqq(5)(cw=08(cu)cl;eq(5)((*=0.S(c)cQiTTP)(S)(c,.=0S(cnp))ceri')63STABILITY SELF-SUPPORTED D¥= i¥= { ¥¥,*ALLOhe4.Olz=. 29rQ- z=SsW-3l.3,,-O,front side3aback sidei4is"th･ *)////6ichl.l*'*+:¥-9 m:- - - ' - eq (5) (c7'P)'llSO 40 40=0)O20Iearth20pFessur'e80 4040 80 1 20(kPa) earth pressure (kPa)80 120earth pres5ure (kPa) earth pressure (kPa)O;iveq(5) (c*= O S(c ;)t(.,- - 1:q{5) (c+=0)- X(1 press re (ze=0)/c'*Pressvre ( ;= )for z.7s7 O Fn:lo8(5)back sideside79for z*=76firontze=7.0 m-+ -_-s/.*heH :c=0ssW- 6Fig. 15(d)Var ation of earth pressure profile on wall in SS¥ r.6; I ayFig. 15(a). Variation of earth pressure profile on the wall in SSW-3pthOereiandntoand4ely.)ItedSSW- 44i:**^8 x8/10o. 9,ll:arth//-Kepressure (ze; 0)'" - eq (5) (c Y=0)iO¥11¥¥80 40 40 80 1 _70Ol I Oearth pressure (kPa) earth pressure (kPa)4, 5Fig. 15(b),l-Ke PressureSSW- 5for zt=mVariation of earth presstlre profile on wall in SS ¥*-7back sidefront side 'otherood))+6d soil//l ,!/especially for very small displacement portion. Ho¥vever,it can be clearly seen from the figure that stren*･th at theback side of the wai] ¥vas mobiliz,ed before failure but notat the front side. The typical stress-strain relationships ofH ze:: O+1ze= 4.3 m/Sf ronll'Oe ((T *)SO40ear'th pressure (kPa)essivevallFig. i5(c)./1 + c,./c,,. For the rou*･h sur'faceabout 60 mm. Due to some error in the measurement, ofthe earth pressures and displacement, some scatterin_"*could not be avoided in the evaluation of MSR and h**u3earthi20so40earth pressure (kPa)The displacements of the ¥vall at the failure point ¥vere1:q (5) (c*=0),backOcondition, these values are 1.53 and 1.34 for the ¥vallfront and back respectively.OheseesioneFig. 15(e).SO40earth pressure (kPa)ultimate values becomeevenR)120Variation of earth pressure profile on waM in SSW-4, there oni q(5) (c*,=0)9foF z*= 4.3 m:/for z =2,S rr :S- Ko press 'rc (z *={))/l then (cwback Side/"*l*/- 6¥+¥*./9arthcests¥/li- 7n inrotlt' Slde;/'/fi/-6)*' theSSW- 7o40SO20earth pressure (kPa)Variation of earth pressure profile on wall in SSW-5A'o normaily consolidated clay sho¥vn in Fig. 4 can beconfirmed from these figures; that is, small strains atfailure in the acti¥'e side but very large str'ains in thepassive side. Potts (i991) sho¥ved similar results fromfinite element calculations. He also sho¥ved that forheavily overconsolidated clay with hi_..･h Ko values, the(6)For the smooth ¥vall condition, that is, shear stress alon_'the wall is zero, (1VISR ) = I means the full mobiliz,ation ofthe strength for the both sides.ployedof theFigures 16(a) and (b) sho¥v the relationships bet¥veenthe lateral displacement of the ¥vall at the depth of eachpressure ceil (6/1,,i!) and the mobilized strength ratios atthat depth for SSW-4. In the figures, t¥vo horizontal solid(7)and dashed lines ¥vere dra¥vn to represent the ultimate of(8), ,MSR for the smooth (c, =0) and the rough (c,. =0.8 x(c*)***p) ¥vall surface conditions respectively. TheseatLf t! 'lactl¥'e and passive conditions could be mobilized atsimilar ¥vall displacements. From the centrifuge modeltests on braced exca¥'ation of the kaolin clay using a sheetpile ¥vall lvith smooth surface, Takemura et al. (1999)made the figure about the similar relationship at the frontside of the sheet plle ¥vall as sho¥vn in Fig. 17. But theyused (c )* *p for normalization as sholvn in Eq. (6), sothat the ratio, (MSR)f*.**, of O.6 means the fullmobilization on the smooth wall condition. At the ver_¥*small ¥vall deflection, the relationships are very similar inthe DMM wall ¥vith rough surface and the sheet pile ¥vith NA} AS AND TAKE*MURA64front side E7( 7 5m from ground surface)41lower propping3,5i0.6;:'e3- : Ie'';:''e -' 2.5l: 2/ )o::efc¥l-**OI> 1.5Obb/lower propping!tx:11,-e )ase7-0.5oo.2O 1-13 -)ase90,05 0,1wall defiection (m)6hceH (m)Fig. 17. Relationship bctlveen mobilized strength and 11'all defiectionobtained from centrifuge model tests on braced sheet pile wall32.5Jexcavation: (after Takemura et al., 1999)Failure)* e)2, *r/ 1.5eq.It can be said from the calculatlons for the condition ¥vithc**,= O and c,+= 0.8 that the adhesion bet¥veen the vertical¥vall surfaces and the clay can significantly r'educe the> istress concentration at the front toe. Although somescattering ¥vas observed before exca¥'ation, it can beO.5clearly seen that variations of contact pressure were ¥'erysmall from the initial condition until the failure in SSW-OIto3, 5 and 7, ¥vith H/B= 1.5, 1, and 2.0 respectively. ForSSW-4 ¥vith H/B (=2), relatively lar_ ! e incr'eases anddecreases of the contact pressures ¥ 'ere observed at thefront side-o.5-1oO.1o.26hcell (m)Fig. 16. Relationships bet,veenh*.Ii and mobillzed strength forexperiment SS¥ '-4smooth surface, and a quite sharp increase in the ratiovas observed. Ho¥ve¥'er, some differences can be seenafter this sharp increase. For the sheet pile ¥vall,(MSR)f,* reached the full mobilization at about O.05 mand kept constant after that. While for the DMM, theratio didn't reach the le¥'el of full mobilization e¥'en forfront and back wall base edges. The difference in thevariation of the contact pressure in SS ¥r_4 and SSW-7¥vith the same H/B (='-) can be attributed to thethickness of the clay bet¥veen the ¥vall base and the lowersand. In SSW-4, the thickness ¥vas about 5 mm, ¥vhile forSSW-7 it ¥vas 45 mm in the model scale. Hence the lo¥versand layer affected the subgrade reaction of the ¥vall basein SSW-4 much greater than SSW-7, and the ¥vall tiltingcaused the larger increase in the contact pressure at thefront toe in SS¥¥f-4.Althou'_h some difference bet¥veen observed andcalculated contact pressures could be seen beforeexcavation, due to some difficulty in the measurements ofthe contact pressure, the observed increases and decreasesthat of the smooth wall condition at the dlsplacement ofabout 0.05 m and increased continuously after the failurepoints. As discussed in Fig. 12, the highly deformed areain contact pressures ¥vere much smaller than thein the passive side ¥vas larger for the rough ¥vall than thecurrent design method ¥vhere the adhesion on the ¥vallsmoothsurface is neg:lected overestimates the stress redistributionvall. The differences of the failure mode may bethe reason for the difference in the stren_2:th mobilization)*calculated ones with c,./(c,,)* ,,, O and slightly smallerthan those ¥vith c, /(c,, ).. ,p=0.8. This means that theat the ¥vall base due to exca¥'ation.Undrained strength of the clay at the base in SSW-4due to the wall surface rou hness.Figure 18 sho¥vs the measured contact pressures (q*) atthe ¥vall base before excavation and just before and after¥vas about 17 kPa, ¥vhich _･._ives the net bearing pr'essur'e ofthe ¥vall at about 90 kPa ( = 5. 14c**). The incr'ease for thefailure for SSW-3, 4, 5, and 7. The calculated valuescalculated contact pressure for the condition ¥vith c,./before excavation and at excavation depth just before thefailure are also sho¥vn in the fig:ure. This lvas obtainedfrom the moment equilibrium at the front toe of the ¥vall.!c ¥)* =0.8¥vas almost the same as the net bearing,pcapacity. From this it is considered that tilting failure due*,*to overstressing the ¥vall base might ha¥'e possiblys STABIL TY SELF-SUPPORT D65D¥, ,t 'i IVALLe=0,)::tebf2.9 m{Hze:::3.6 mr 1 OOe l) -1 OOSS W-4:¥Je)200*'i,e l*'ee)7300200SSW-3o2.9' e li ze:::1 .4 m300TZeb cwlOebf& cw::O 8rc ¥L ujcomp400=9e=0Calculated stresses:--Ze: Oebf4'3 m{Hze 4.8 m400o-2.92.92.9100SSW-7l OO1e) 2005aH defiectionQnn_CJ ')vveet pile wall200H ze:::Orl+ ebf4'3 mSSW-5e :{h e::5 .O mrhl300ee' 400ciition ¥¥'ith-4. 35he verticalreduce the)u :h someit can beO4,35distance from the wall center (m)Fig. 18.400-2. 1O2. 1distance from the wall center (m)Contact pressures under wall base for SS¥¥r_3/4/5/7vere ver}*re fn SS¥¥1_occurred,ti¥*ely. Forbefore sliding took place, if there had been afloatin*' type DMlvl self-supported walls ¥vith H/B?- isreases andthick clay layer belo¥v the ¥vall. The resistance against thesliding. Therefore the upper bound analysis ¥vas used torved at theence in thesliding and base failures are the function of many factors,conduct a parametric study using a sliding failuree.g., strength of the clay belolv the base, adhesion on theand SSVJ-7red to thebase and side surface of the clay, thickness of the claymechanism .The parameters which affect the externai stability oflc} the lo¥ *erso on. Holvever, for normally consolidated condition,n,vhile forthe strength and adhesion are not independentce the lo¥verparameters, highly dependin*･ on the depth, in otherbelo¥v the base, ground ¥vater level, top soil thickness andhe ¥vall base¥*all tilting:ssure at the,served andeen beforurements ofthe floating type DMlvl ¥vall in normally consolidated clayare schematically sho¥vn in Fig. 19. These parameters are:the wall hei_g:ht, H, the vall breadth, B, the surchargepressure, q, the excavation height, z*, the clay bulk unitwords, height of ¥vall. Considerin*" the discussions above,¥vith rather severe test conditions of thin top sand layerand high ¥vater table, it might be said that the ¥vall height-¥vei_ ht, y, the ratio bet¥veen the adhesion on the wailbreadth ratio (H/B) of around ,_ may not be an overesti-soil strength at the clay surface, co, the coefficient ofmated one as the threshold value vhere the failure patternchanges from sliding to bearin_9: failure for the floatingstrength anisotropy, m, the gradient of clay strengthtype self-supported DlvlMvall in the normallysurfaces and the soil strength on the slip plane parallel tothe vall surface at the same depth, c, lc , the compressi¥'eincreasing ¥vith depth, k.nd decreaseconsolidated clav. Fr'om the centrifug:e tests on the DMM'r than theas a foundation of break¥vater, Kitazume (1994) showedlhtly smallethat the local failure at the base of the DMlvl leads theans that theon the walibearin*･ failure in the case of the DMM ¥vith H/B=0.5As the exerted acti¥'e earth pressure by the upper dryloose sand layer on the ¥vall is small compared to that ofthe underlying submerged clay, its shear' str'ength ¥vasne*'1ected in the upper bound analysis and the layer' Ivasassumed to ¥vork as a surcharge pressure, q, on the upperedistributior=fioating in the clay. The threshold value of H/B from thesliding to the bearing failure for the self-supported DlvlMvall excavatlon is gr'eater than that of the floatin_g typetse in SSW-DMM foundation, ¥vhich is subjected to lateral forceclay surface in the calculations. The formula of C_asagrande and Carillo Eq. (3-'-) Ivas used to represent thestrength anisotropy.from the top through the superstructure.lg pressure 0=irease for thiion ¥vith c,*=UPPER BOUND ANALYSISnet bearininfailure du;lave possibl;The centrifuge modeling tests sho ved that the criticalfailure mechanism for the excavations supported by the-LL""'As the upper sand layer ¥vas represented by asurcharge, the ¥vall height ¥vas replaced by the embeddedwall depth into clay, H*1* , and the excavation height vasreplaced by the exca¥'ation height into the clay layer, z..From these parameters, the six non-dimensionalparameters: i71, cwlc., yH,1.'/co, yBlco, qlco, and kly,were deri¥'ed, ¥vhich affect the stability number at failure: NAHAS AND TAKEMURA66No*.**1=(q+y(z*)f)/co, ¥vhere (z*)f is 4-* at failure. TheThe observed displacements in SSW-O and 4 arefailure mechanism used in the upper bound calculationand its displacement diagram are shown in Fig. 20. Thecompared with the failure mechanisms obtained from theupper bound calculations in Fig. 21 . At the passive side,mechanism consists of t¥vo trian*'ular rigid blocks and athe mechanism compares well ¥vith the observations. Onfan between them for both sides of the wall with twothe other hand, the widths of the observed failure ¥vedgesbehind the ¥valls were smaller than the failur'e z,one obtained from the calculation for the rou*"h ¥vall case (SSW-variables oel and (x2. The calculation was first done for theconditions of the centrifu*'e model tests and then someparametric studies were conducted by changing the non-4) .dimensional parameters; yH,1*'1c0= I - 100, yB/c0=1 -66, kly=0 and 0.09, c, /c**=0 and 1.0, and n?=0.6and I .O. In the normally consolidated clay, the undrainedstrength at the clay surface co can be given by theproducts of vertical effective overburden stress ((7,'.*) and[(c,,)..*plcT(*] value. In the centrifuge tests, (T . at the claysurface was q from the top sand layer, because theground ¥vater ¥vas at the level of the clay surface. FromSSW-o(m)O.OI3.5"'b'b l-1b"I7.0//･"/// '･1'l･l, , .this and the ma*"nitude of [(c )*.*p/cr(.] on thecompression stren*"th of the kaolin clay (=0.24), qlcobecomes approximately 4.0. Hence q/c0=4 ¥vas used in1 0.5tt'the calculation.O 3.5 7.0 lO.514017521 0245 280;o.o(m) S SW-4l ZZ/ 7/'Z': ' :' ' t '3,57.0'I''tb¥¥"fIL'b j 4'/ : /: '' ''" 't 'tl'b,b,10.5I14.0(clc,,, Soil strength- iBm( u=)compprofileu )ext(m)O 3.5 7.0 10.514.017.521.024.528.0cFig. 21. Comparison of fajlure mecbanism obtained from upperFig. 19. Par8meters affecting external stabilitl.' of fioating type DMMwa]Ibound calculation with observed soil and wall displacements inexperiments SSW-O and 4q+Zcf45 A45-0eloelL<Fan I BalbO45-(XlOelwallo6CDwall O )*= B(a): Failure Mechanism.45-Ce,cd(b): Displacement diagram.F g. 20.Failure mechanism and displacement diagram used in upper bound calcuiationl 67STABILITY SELF-SUPPORTED D*¥IM ¥VALLd 4 are{from thesive side,ions. Onevedges +z,one obse (SSW- iTable 3. Observed and calculated stabilitl.' numbers at failure35(N *1)f'c=1DifferenceTest No Surfacecondit ionH/BLNot'1 (o/o )30o*,t*SS¥V-OSS¥V-3Smoothl .5Rcuigh1SS¥¥r_4RoughRoughRough7_.OSSW-5SS¥¥!_ !9,88 l13.513.515.91 .O20.221.616.I2.015.712 8521O.i5263423eAO Tn )6k/*f = O O:ob*rTT TI/'f = OO9:rTTchlcu:: ;]1'oA m )625m=1 Oc lcu:: o' om: 1 Op- 20r''oz sfB/c0= 26& q/c0= 4 .,eo. (5oTable 3 sho¥vs the stability numbers calculated fromo)O 40 60 80tests SS¥V-O, 3, 4, 5, and 7, the upper bound for the stability numbers, (No*.**1)c*!, and the difference betweenOO O 2040 60 80 1 OOvHd*) Jcethe observed failure heights, (No*.**i)ob*, in the centrifu*'eFig. 22. yH,I /co Net t'lrelatronships for smooth and rough wallsurface conditionsthem as a percentage of (No*.** )c*1' The upper boundsshould be equal to or higher than the ri*･orous ones intheory. However, (No* ** )ob= values were higher than35(NG*.,.])c,1 by 20 -330/0 for experiments SSW-O, 4, 5, and7, while for SSW-3 the observed and calculated stability30H (m)numbers ¥vere almost the same. The possible reasons for25l 8.0having (No*.**1)c*1<,(No*.**1)0 = are: 1) underestimation ofthe clay stren*'th because the shear strength parametersfrom the triaxlal tests were adopted to represent the soil7 t.:(m)the strong box, and 3) the difficulty in estimating theo}8.0from uppplacements i=0)¥'all conditions,n= O 6411= I On= o 641Tl= I Ok"r O O1'el:.ia}/cF 26& qlcf 415lOrough (c, /c = 1) and smooth (c,,./ck/f o. o :,'S 20;=strength in the plain strain condition, and aiso the strainrates in the model clay ¥vere much higher than that of theelement tests, 2) the friction between the model wall andexact failure excavation height, due to cutting relativelylarge excavated hei_ ht in each step (0.7 m).Figure 22 shows the relationships bet¥veen yH*1'y/co andNo*.**1 obtained from the upper bound calculations for the!I5--- o --.,t--Heo20 40 60 80 lOO O 20 40 60 80 100YB/coFig. 23 yB/c -N' o el't*irelationships forsmooth and rough wallsurface conditionsanisotropic (nl =0.6) and isotropic (/71 = I .O) conditions,and strengh profile conditions ¥vith uniform strength kly=0) and stren*'th increasing ¥vith depth (k/y=0.09).stability than increasin*' the wall breadth. Ho¥vever, if theFigure 23 sho¥vs similar relationships bet veen yB/co andNo*.**1' For the rough wall in the normally consolidatedclay ¥vith strength increasin_g: ¥vith depth (k/y 0.09),No****1 increases ¥vith increasin*' yHd*,'/co and yB/co.However, different relationships can be seen for groundsoil strength is uniform ¥vith depth, incr'easing thebreadth of the rou_ h floating type wall is the only ¥vay toincrease its stability.For the failure excavation heights of the cases of thecentrifuge tests obtained from the upper boundwith uniform stren_._"th (k/y=0) and smooth wallcalculations, limit equilibrium analyses were conducted.conditions (c,./c =0). For k/y=0, No*.**sli**htlyTwo assumptions were employed in the analyses. In thedecreases ¥vith increasin_g: yHd,v/co. From these results, itfirst one, Rankine's earth pressure distributions on the¥vall surfaces were used, ignoring the adhesion on thevertical wall surfaces and assuming isotropic conditionwith compression strength, which is similar to the currentdesign practices. In the second one, the roughness of thevertical ¥vall surfaces and the strength anisotropy, werecan be"considered that the effect of Hd*+ on the externalwall stability is hi*･hly dependent on the strengthincreasing rate (k). From Fig. 23, it can be also confirmedthat the effect of B on the external wall stability dependson cw/cand k/y. Furthermore it can be said that in thestability analysis of the excavations in the normallyconsolidated clay with strength increasing with depthusing self-supported ¥valls, i*･noring the adhesion on thevali surfaces may iead to significant underestimation ofthe externalvall stability.The slopes of the relationship bet¥¥'eenN ando*.**lyH,j,y/ca for k/y=0.09 in Fig. 2･-, where yB/c0=26, arehigher than the slopes of their counterparts in Fig. 23considered using Eqs. (3-2) and (5), by using thecompressive soil strength in the acti¥'e side, (c*)**^p, andthe extensive strength, (c )..*, in the passive side; cw/c =1.0 was used to express the ¥vall surface rou>'hness forSSW-3, 4, 5 and 7, and for SSW-O, cw/c* = O ¥vas used inthe second analyses.Table 4 shows the results of using the limit equilibriumanalyses. Here *1 and *2 denote the first and secondwith yH,1../c0=26. This means that in the normallyassumptions respectively. Except for SSW-O, the factorsconsolidated clay ¥vith increasing str'en*'th, increasing thewall height is more effective in increasing the external vall¥vere almost the same for every test condition. Ignorin_",_L!:of safety against sliding, (F. S. )=1idi**_, for both assumptions 68NAHAS AND TAKEMURATable 4.Factors of safetv.' and bearing stresses under wall base estimated by limit equilibrium methodSSw-o SS¥V-3*l(F S.) 'd g (I ^2) i(T 4 (kPa) ( q*h)l*3*'1 *2' I .O1 l.25i I}.06, 218.8i42.7168.8 i0.97151.7 fSSw-4SSw-7SSw-5*2 *1 *2*IO.961 .06 ! I .OI*1I .07o 96356.2 ! 231.9 j 181.6 ; 139.27 65 2l .07166.7lgnoring both the adhesion alon_ the vertical wall sides and the strength anisotropy and usin_ average strength (the current desig_n method).Considering both the adhesion along the vertical vall surfaces and the rength anisotropy and using average strength.Factor of safety a_ ainst sliding*4 Bearing stress of the ¥vall base at the front toe.the adhesion on the ¥vall surface leads to underestimatingthe ¥vall stabilit,y. On the other hand for the ¥valls innormally consolidated clay ¥vith high stren*･th anisotropydimensions on the stability are highly dependent onthe stren*'th profile of the clay and adhesion on the¥vall surface.(small /71 value), assuming the isotropic condition ¥viththe compression stren_g:th leads to overestimating the wallstability. For the clay vith relatively hi__*h strength(5) For clay with a relatively high strength increasinganisotropy, the current design method, ¥vhich does notincreasin*' the external stability of the ¥vall thanincreasing the ¥vall breadth. On the other hand, inconsider the stren*･th anisotropy and the ¥vall adhesionmay give a reasonable evaluation of the wall stabilityagainst sliding failure, because the effect of each factorcancels the effect of the other. However, ignorin_ boththe strength anisotropy and the adhesion on the vertical¥¥'all surfaces leads to overestimating the bearing stressredistribution due to the eccentricity caused by theexcavation as sho¥vn in Table 4. From this as ¥vell as thediscussion on the base contact pressure shown in Fig. 18,it can be said that the assumptions adopted in the currentdesi_g:n method overestimate the contact base pressur'e atthe front toe, ¥vhich may predict the bearin*･ capacityfailure as the critical condition.CO¥_ TCl.IjSIONSFrom the centrifuge model tests and the upper boundcalculations on the external stability of excavations insoft clay using fioating type Dlvlilvl self-supported walls,the follo¥ving conclusions have been drawn:(1) For the fioating type self-supported DMM vall ¥vith(H/B)- in normall)* consolidated clay, failuretakes place suddenly by sliding failure mode ¥vithoutsho¥ving marked pre-failure displacements.Therefore, the design of this type of ¥valls should bebased on the ¥vall stability rather than on theadjacent ground deformations.('_) On che interface bet veen rough lvail surfaces andthe surrounding saturated clay, undrained strengthof the clay can be mobilized. The mobilizedadhesion has significant effects on the stabilityagainst the sliding and base contact pressure.(3) The required ¥vall displacements to mobilize theminimum actlve earth pressure of the retainednormall.¥' consolldateci clav are less than thoserequired to mobilize the maximum passive earthpressure in front of the ¥vall.(4) The external ¥vall stability is affected by the soilstren_ :th profiie, the adhesion on the ¥vall surfacesand the lvail dimensions. The effects of the ¥vallratio ¥vith depth (k) Iike normally consolidated clay,increasing the wall height is more effective inclay ¥vith a small k-value, increasing the ¥vallbreadth can only lead to increase in the external ¥vallstability.(6) For clay with a relatively high strength anisotropy,the current design method, which does not considerstrength anisotropy and ¥vall adhesion, may *'ive areasonable evaluation of the ¥vall stability againstslidlng failure, because the effect of each parametercancels the effect of the other one. Ho¥vever,ignorin_9: wall adhesion leads to conservati¥'e anduneconomic estimations of the stability against thebearing capacity failure.NOTATIONSB:¥vaH breadth.[CA'oU]*omp:undrained triaxial compression test on Koconsolidated samples[CA'f]U]ex :undrained triaxial extension test on Koconsolidated sampiesco:(c )comp athe upper clay surface-cu(: :undrained shear s reng h of c]ay so l adepth z from the upper cla.v surface^(cti)com :undrained compressive shear strength of' theclay in the [C_KoU] empest(c**)e*E:undrained extensive shear strength of theclay in the [C_A'oU]e¥test.cL*i and ct*':apparent undrained soil shear s rengths'hen the major principai stresses arehorizontal and ¥,'ertical respectively.cul '):apparent undrairled soil shear strength ¥vhenthe major principal stress is directed lvith anangle e to the vertical axis.c**:adhesion bet¥veen the ¥vall surfaces and thesurrot ndin:g cla¥_*.H:lvali height embedded into thepper sandand clay layers.Hci *:lvall heigllt embedded into he clay layerH,:thickness of lhe upper sand layerk:strength increasing rate lvi h depth ,nl:coef icient of s rengEh anisolrop¥.'( = (c** )**E /(ct* )tomp )( t/SR ) * n and ( VSR)b**k:mobi ized soil srrength ra io a Ehe front andback sides of the lvall. 69ST．へBILITY S鷺LF−SUPPORTED DMM WALL No［o副：stabi韮ity number at fai亜し星re 呈n 【he upPer boundanalyslS、 ρ＆，P（ξ）：1ntensltiesof由eactlveandpassiveearth Pressures on t臨e wall surfaces at a depth漏竃， from t｝1e clay upやer surface． 1，0766．71eξhod）．de飢on｝on t聡ecreasmg’ledclay，、 σlsurc短argepressureontheclaysurface． 圭22一玉35、 （ξc）r：excavation dept巖 玉Rto 乞｝1e cLay iayer atconsider6）Cねe且，X。L．，Liu，Y．H、and Zわang，S．L）「 （1996）l Deslgn me由ods fa玉iure． ofceme飢一soilretainlng、valLPヂoc．2η41n’1．Coη∫ ξ，1亘otalexcavateddep由1nto出eupPersand ／ηψrovθ1ηθη’Gθo男乳∫’e1η，∫一αα廟9αη40θθρ1、五￥’η9，Tokyo， andclaylayers． ζ。bf＝toξalexcavateddepthinto由eupPersand 475−480曙 andclayiayersjustbefQrefalluretakes excavations i鳳soft day supPorted by工）M1〉I self−supPQrεed waHs， piace． 1S−710んyo99，Tokyo，Japan，583−588． （ξe）f：tota…excavate（王depth 1nto the upPer sandG1響α〃∼ゴ7）EI Naぬas，A．，Takemura，J．and Kouda，M，（1999〉：Stab1撫y of8） Japanese Geotechn玉cal Society，，IGS TO560−2000 （2000）：置ヤ1αhod anddaylayersatfailure．αlandαゴce煎alanglesfortriangularblocksiatぬe for conso玉玉dated constant vQiume direct box s琵ear test on so叢ls． fa難ure mechan玉sm，used in the upPer bound J．（1993）＝S［ab玉lity of unsupPorted and supPorted vert三cal cuヒs in calculat玉ons（Fig．20）． sof覧clay，Proo．11’1∼Sαイ∼hθα5扇5’α11Gεo’θごh．Coη∫，Sl服gapore， direcI S｝｝ear test．lsotropy，5） Casagrande，A．and Caril1Q，N．（1944）：Shear fai沁re of a錘sotropic ξc＝excavat1oR depI藍into￡be clay layer、all than’rnai wall4）Boiton，M。D．and Powrie，W．（1988）：Reむaviors of diapぬragm wallsinclaypriortoco賎apse，磁αθchn’σ置’θ，38（2），三67−189． so玉1s，Co∼πr’わμ”oη5 ’o Soi1ル旋∼ohαη’c∫，βεCE， 1941−1953， 1944， δh：measured shear displacements durlng the琵e wa1玉、3）Bolton，M。工）．and Powrle，YV．（1987）：丁姦e coliapse of d1ap姓ram wallsretainlngclay，磁αθ‘h’瞭’θ，37（3），335−353． ξ：dep【h from the clay upper surface．ctive ln ・halld，in Tokyo，Japan，673−678．9）K玉mura，τ．，τakemura，，L，｝｛玉ro−oka，A．，Okamura，M．and Park， 61−70．10） Kitazume，NI，（1994）：㌫憂ode玉and analytical stud呈es o艮stab玉lity of δhb。【＝measured horizontal dlsplacements of the improved ground by deep mixing met蝕od， Ph， 0， ’1reεな． （in wa至1bOt亡om． δhcξll：measured horlzontal dlsplacements of the11）1くltazume，M．，Mlyake，M、，Omine，K， and Fuj1sawa，H、（1996a）l Japanese）． waH at the pos玉tion of each pressure ce歪｝． JGS TC Report：Japanese deslgn procedures and recent actlvlties of δhmid：horizo鳳al waH displacement a慮s mid dep由 DMM，Proc．2nゴ1η∫1．Co’∼∫G〆o置“1ゴ11刀ρヂovθ，ηθ∼π（3θoり窟θ1η5一 d雛eto玉tst玉1ting． γ5照d：dry un圭t weig晦t of the upPer sand layer． αα廟8αηづρ卿雌κ’1∼9，Tokyo，Japan，925−930・玉2） Kitazume，真｛、，τabata，丁．，Is員iyama，S．andIshikawa，Y．，（1996b）：lygivea θ：angle of inclination of芝員e major princlpal Modehests o鷺fallure pattem of cemenureated retainlng、、・all， streSStO磁evertical． P∼o‘．2ηご／1π1．CoηゾGro瑚ご11ηρroソθ1ηθn’0θ05ツ5∼θ1η、∫一ααπ’n9ト・against θ、、al［＝angleof由ewalltlkingdu血gexcava“on αηゴP岬畝百119，Tokyo，Japa獄，509−514．arameter （degrees）．13）Potts，D．M．（1991）：Finiteelementsimulat玉onofembedded｛Owever， σ1、：observedlateraleartぬpressurebyeacぬ reta玉ning wa1豆s， 〆玉ごv‘7ηcεゴ （ヲθo’θご1π． ！垂ηαケ5Z∫， Elsev1er apP簸ed1tiveand三ainst the pressure ce韮董． ∫dence，131−167． στlbearlngstressof由e・vallbaseat出efro瓢14）Rowe，P．W．（1957）ISぬeeゆllewalislnc！ay，1η甜．αv、動9ヂ9∫，7， 覧oe． 629−654．15）S駄lomi，M．，Ito，K．，Nlshimura，D、，τanaka，H．andTanaka，M．REFERENCES王）Azuma，K．，Nogはc髄i，S．，Kurlsakl，1く．，Hyodo，H，andNagaoka， M．（玉999）：Moveme煎ofstablilzedcoa1−ashsollwallduringしes毛onκが excavation，1S−70幻yo99，Tokyo，Japan，459−4642）Babasaki，R，Suzukl，K．andNakama，T、（1998）：DesignprocedureleSt on KO・ for self supPorted waH us玉Ωg deep m玉x呈頁g method，C（∼n’ヂびμ9θ98，day soil alrface．ren鼠thoω1e3n9由of d腫arStreng藤s｛resses arξ、ely．，tre翁黛th wlle嚢ecしed w玉th a韮ゼaces and1hごeuppersan6claylayer・yer lePth，）Pythe front al矯 （1996）：Sbpe stabi1虻y貸sing the adm1xture metめod，P’・o‘、217ご／11f！、 Coη∫ Grα〃7ゴ 1’ηρro、7θ’ηθη’ （｝θo釧∫1θ’η5−Grα”加9 σ’∼4 五）θθP 1、4勧79，τokyo，563−56816） Takemura， ，1．， Ko【1doh， NI．， Esaki，T、and Kouda， NI，， （1999）： CeatrEfuge mode蓋tests on dQubLe propPed wa玉1excava雛on in soft clay，So’Z∫α1ガFα’ηゴ如0115，39（3），7シ87， | ||||
| ログイン | |||||
| タイトル | External Stability of Vertical Excavations in Soft Clay with Self-Supported DMM Walls | ||||
| 著者 | Ala'a El Nahas・Jiro Takemura | ||||
| 出版 | soils and Foundations | ||||
| ページ | 53〜69 | 発行 | 2002/02/15 | 文書ID | 20439 |
| 内容 | 表示 | ||||
| ログイン | |||||
| タイトル | statnamic Load Tests on Model Piles and Their 3D-Elastoplastic FEM Analyses | ||||
| 著者 | Makoto Kimura・T. Boonyatee | ||||
| 出版 | soils and Foundations | ||||
| ページ | 71〜87 | 発行 | 2002/02/15 | 文書ID | 20440 |
| 内容 | 表示 SOIL,S AND FOUNDATIONSVol 4) N0. I, 71-87, Feb. 2002Japanese Geotechnical SocietylSTATNAMIC L,OAD TESTS ON MODEL, PILES ANDTHEIR 3D-ELASTOPLASTIC FEM ANALYSESMAKOTO Klh,lURAl) and TIRA¥vAT BOONYATEEii)ABSTRACTDur'ing the past ten years, the Statnamic load test has dr'awn attention from the piling community as one of the mosteconomical methods for pile load testin*･. Ho¥vever, almost all of the research and development have been based ondata from field tests. A consistent interpretation is difficuit to achieve with such data due to the uncertainty and thecomplexity of the *"round. To overcome this deficiency, the first objective of this research is to develop a systemwhereby Statnamic load tests can be performed under one constant condition. A small-scale Statnamic loading devicefor model tests has been developed vhereby pre-compressed air is applied instead of gas from an explosion. In thisstud.¥', two types of piles, friction piles and end bearing piles, are modeled and are loaded ¥vith two levels of forces,namely, small loads and large loads. The former loads are for determinin*' the initiai stiffness of piles and the latter fordetermining the ultimate capacity. The second objective of this study is to develop a 3D-FEM program that canianalyz,e various types of loading. For a dynamic analysis, the solution is determined by the direct integration in timedomain. The experimental results sho¥v the possibility of producing a loading curve similar to that in the originalStatnamic load test. The analysis also sho¥vs that the force distributions in piles under Statnamic loading are similar tothose under static loading.Kel.* Ivords:dynamic, finite element method, Ioad test, model test, pile, test equipment (IGC: E4/E8)plannin>" and the effect of the reaction piles (Poulos,INTRODUCTION1998) can be completely disregarded. Noting that theFor pile foundations, the static load test (SLT) Is_generally accepted as the most reliable method forSTN Ioads piles under a relatively lo¥v frequency, the pileestimating pile foundation capacities. Unfortunately, dueto the high cost and lengthy operating time, static loadtests are only performed for larc"e projects or at sitesto ) g.where the soil profile presents some unusual aspectsdynamic responses such as dampin_ and inertia forcebecome important, and they cannot be neglected as withthe SLT. Up until now, the results of the STN have usu-acceleration induced by the STN Ioading ranges from 0.5Although the STN has many advantages over the SLT,it loads piles at a hi_ :her rate than the SLT. Consequently,To avoid this situation, a Statnamic load test (STN) canbe used instead, as one of the rapid loading tests(Bermingham and Janes, 1989).)*ally been interpreted by a sirrrplified method called theThe STN uses a medium period load (100 ms - 200 ms)unloading point method. In this method, the dampin_"..to thrust a pile body into the ground. The lvordforce is calculated using a constant dampin_ coefficientthat can be estimated from the load-displacement curve.Assuming that a pile moves in a rigid body motion, theinertia force can be calculated from the pile mass and itsacceleration. For extensive details, see e.g., Bro¥vn"Statnamic" comes from the terms st(7tic and dyll(7lnic.By applying an explosive force to an explosion chamberinstalled on the top of pile head, an acceleration field ofabout 20 g, or t¥venty times the earth's acceleration, canbe obtalned. Placing a mass upon the explosion chamber(1994).At present, the primary approach to investi_9:atin*' pilecan generate a reaction force of magnitude twenty timesits o¥vn wei_ :ht. Since the applied load in this test isbehavior is to make a comparison between the results ofgenerated by the high degree of acceleration, a very highcapacity pile can be tested ¥vith a reaction mass of onlyfull-scale Statnamic and static load tests. One example isthe work done by Matsumoto et al. (1994a, 1994b).one-t¥ 'entieth the ma nitude of the desired load.Unfortunately, their calibration method has an inherentMoreover, there is no requirement for reaction piles ¥viththis method; the target pile can be tested ¥vithout priorproblem in its testin*' consistency, as ¥vas addressed by J.M. Amir and E. I. Amir (1995). Under the uncertainty') Assoc. Prof , Dept. of Civn Eng., K}'oto Universitv, Kyoto, Japan"; Lecturer, Deptofcivil E,n_"*., Chuialongkorn University, Bangkok, Thallandivlanuscript ¥vas received for reviel ' on Jul .* 26, 2000¥Vritten discussians on this paper should be submit ed before September I , 2002 to the Japanese Geotechnica] Society, Su_ ayama Bldg 4F,Kancia A¥vaji-cho 2-23, C_hiyoda-ku, Tokyo 101-0063, Japan Upon request the closiug date may be extended one month.i71);,l' 72KIMURA AND BOONYATEEand complexity of the target ground, the situationwhereby any model can be validated by calibratingStatnamic load tests against corresponding statlc loadtests can be demonstrated as follo¥vs:1. If a comparison is made of the results of tests onAlthough a t¥vo-dimensional analysis is simpler and thethe same pile, the tests have to be done in sequence.Therefore, the quality of the later tests invariablydimensional analysis, it cannot be applied to a complexsystem such as a pile-raft foundation or batter piles.deteriorates due to the induced residual stresses from theMoreover, it is obvious for a horizontal loading case thatthe analysis should be done in three-dimensional space.Therefore, the de¥'eloped code ¥vas made as a versatileformer tests.2. If a comparison is made bet¥veen the results of testson different piles, significant sampies should be tested inor'der to achieve some degree of reliability over theground uncertainty.analytical tool that can cope ¥vith several loadingconditions and pile types, and can find solutions in three-Since consistent systems for interpretation andcomparison can be provided under laboratory testconditions, it is thought that the model tests are anDYNA-3D, is used to simulate the vertical Statnamicindispensable tool for the study of pile-soil interactiondurin*" Statnamic loading. In this study, a small-scaleload test. A non-reflecting boundary was introduced instatnamic loading de¥'ice (3SLD-Mkl), driven by airpressure, has been developed for conducting the modeltests. Note that these model tests are not used for thereflections at boundaries of the soil mass. Since DYNA3D ¥vas designed for solving dynamic problems, a constant-loading duration was applied to obtain the pseudo-purpose of replacing the prototype tests, but are intendedstatic loading for the static load tests.to be a tool for the fundamental study of the physicalinteraction bet¥veen soil and piles during StatnamicIt is thought that before applyin_9: the DYSC to thesimulation of piles, its fidelity should be checked by aphysical model. For calibration purposes, a comparisontheir ability to carry out the STN in various types oftheir Statnamic analysis to prevent erroneous wavei'preferred to the results from the field tests because ofthe complexity of the ground and the qualities of theexperiments can be done under the same >'roundgeotechnical parameters required for the analysis. Afterconditions for each series of tests. Beginning ¥vith simplethe DYSC has been calibrated lvith the data from theground conditions, the mechanism bet¥veen the groundlaboratory tests, it ¥vill be used to simulate the prototype-and the piles can be grasped readily.For the determination of the ultimate bearin*' capacityscale tests. These simulations ¥vill ensure that the DYSCcan be applied to the analysis of Statnamic load tests. Inthe last part of this research, the DYSC ¥vill be used as aof piles, it is essential to load the piles up to their plastic{of the analytical results and the laboratory test, results isround can be achieved. Consistency means that the;' ･solution can be found faster than with a threedimensional space. One example of this kind of analysisis shown in the ¥vork done by Yamashita et al. (1995,1998). In their ¥vork, an explicit 3D-FEM code, calledloading.In laboratory tests, the conslstency of the tests andi*fact that the system of interest is axi-symmetric,Matsumoto (1998) applied a 2D-FEM program to analyzeIthe behavior of a single pile under verticai loading.range. Although many Statnamic load test results havereported that the static response of piles could besuccessfully estimated by the unloading point method, itappears that their loads ¥vere too small. In other words,the resistance of the piles ¥vas not fully mobiliz,ed.Therefore, in cases ¥vhere the piies are loaded by forceover their ultimate capacities and a lar*'e mobilizationoccurs, research on the application of the unloadingpoint method is necessary. Up until no¥v, there have beenfe¥v publications about this kind of test. One example isthe ¥vork by Nagaoka et al. (1995). To accomplish this*'oal, t¥ 'o types of loads are applied to the piles in thisstudy. The first kind of test is done by loading the pilesPile behavior under Statnamic loadingA4E (qualit tivejudgement)EE FE :odl :::of s'H ? Uncertainty of_ roundE physi*1 di*cu io sfJ-i }LIa,plied for the ftmdameTrtal study ofe single pilsso battef piiesQ group pilesof test is done by. Ioadin_ : the piles ¥vell over their ultimatee pile-raft foundationsothetwoarethemechanism of the piles during Statnamic loading can bethorou_ghly investigated by a numerical analysis. For thispurpose, a three-dimensional finite element analysisprogram called DYSC (dynamic and static systemsanalysis L0de) is developed in this stud_v. Applyin_g theHModel teStsbelow or up to their ultimate capacities. The second kindcapacities. Since it is thought that the responses toStatnamic load of piles also depend on the pile type,types of piles, friction piies and end bearing piies,used in this study.Instead of studying the data from the field tests,!E3D-ElastOPlastic FEM CDYSC)o adaptable to 2Jty e ofpil s s;1i loadings- UntSed s al)I is approacho centribution to the improvemcut ofsimplied estiTnution msLhodsResearch Framework+:,Fig. l. Outline of research framework STAlrNAlvllC TESTS ON MODEL PIL.ESImetric,tool for investi_9:atin*' the behavior of pile foundationsduring Statnamic loading. It ¥vill also be used to verifyanalyzeoading.and thel threeassumptions and to improve the estimation techniquese;nployed in the simplified methods. The frame¥vork ofthe ¥vhole research is sho¥vn diagrammatically in Fig. 1.r piles.In this paper, only the ¥vork done in step O, thedevelopment of the model tests and DYSC, and itsase thatapplication, are reported.omplexspace.ersatileOUTLI_¥'F, OF THE F.XPERIMF.NTSioadinn three-Deta!!s of the ApparafusA general vie¥v of the apparatus, developed in thisstudy, is sho¥vn in Fig. 2. The operation of loading by3SLD-Mkl can be divided into the follo¥ving fi¥'e stages:Inalysis(i995,calledrtnamic1) Initial stage (Fig. 3(a)).Lrced in'_) Air loading stage (Fig. 3(b)). In this stage, precompressed air is ailowed to flo¥v into the cylinder. Thes waveDYNA-air piston will start to load the pile head.a con)seudo- ;3) Launching-up stage (Fig. 3(c)). While the piston ispressing on the pile head, the air in the lower part of thecylinder ¥vill flo¥v out through the silencer. At the sametime, the upper part of the de¥'ice will be launched up dueto theid by aparison73to the reaction force from the pile head.4) Termination of air supply (Fig. 3(d)). When thehead of the piston is at the same level as the stoppers¥vitch, the magnetic ¥'aive will be trlggered and the pathof air will be shut off. At this stage, the upper part of thedevice ¥vill still be movin*' upward for a while because ofinertia force.5) Termination oftest (Fig. 3(e)). The free fall oftheupper part is gradually terminated by. the supportin__'boxes at the four corners of the lo¥ver base.The loading apparatus can be divided into t¥vo parts,namely the movable part and the fixed suppor'ting base.Components of the apparatus can be divided into thereaction-mass box, the cylinder and the piston, themagnetic valve, the speed controller, the stopper s¥vitch,the support legs, the sand box, the fixed base, the supportbeams, the measuring system, and the control circuit.The cylinder used in this study is made by the CKDCorporation (CKD Corp., SCA2-00-100B-150-R5-H). Ithas an effective diameter of 100 mm. The maximumallowable cylinder pressure is I .O MPa. The stroke lengthof the piston is 150 mm. The mass box as ¥vell as the¥veight of the cylinder is used for the same function as thereaction mass in the prototype. Four support legs areused to constr'ain the body of the apparatus on its ¥'ertical)sults Isaxis. These components, namely the mass box, theMagnetic valve Speed controller Reactionmassmse ofsupport legs, and the cylinder, are all fixed together bybolts at the top of the cylinder.of theAfterThe flo¥v of air is controlled by a magnetic valve that isshut in the normal state and open ¥vhen an electric currentAir supply tom thetoty pe-Stopper swrtchSilencerDYSCests. Inis received. In order to make an adjustable rate ofcylindereTPiston Model pile 420:ed as aLoad cell 300loading, the speed controller that regulates the rate ofairflow is also integrated into the air supply system. Astopper switch, ¥vhich is triggered by the magnetic field, isattached to the cylinder in order to stop the air supply*properly. This stopper s¥vitch ¥vill send a shut-off signal tothe magnetic valve ¥vhen the top portion of the pistonapproaches. The sand in the supporting boxes at the fourcorners of the lower base is used to _g radually stop the free)Soil chamber lUnit : mm6 OOSide viewfalling of the upper part after the launchin*･-up stage.After the base part of device is instailed on the top of asoil chamber, the legs of the movable part are put insidethe supporting boxes of the supporting base. Nex. t, thesand is filled Into the supportin*' boxes. Note that the tipsof these le*･s do not reach the base of the supporting:boxes. Therefore, the reaction mass and the ¥veight ofTo vieweach component are mainly supported by the pile. Thisdead weight from the upper part contributes to the initialstatic load and defiection. In the prototype, the initialload is about 50/0 of the peak load. Ho¥vever, the samee eT130_L130 JL-- -- I800iFig. 2. Details of apparatusiaS+". *""le¥'el of initial load cannot be produced in the developedmodel. From the SLT, the model pile has an ult,imatecapacity of 590 N. When compared to the full-scale tests,the initial load, which is 50/0 of the ultimate load, shouldbe 29 N. Ho¥vever, only the cylinder, ¥¥*hich is the mainpart of the apparatus, contributed to a downward forceof 130N. When all the components are assembledtogether, the lveight of the entire apparatus becomesquite heavy. From this limited condition, the least 74KllvIURA AND BOONYATEEMagnetic vatve¥Arr supplyyForce generatedThe air flows intoby air pressurethe cylinderCylinderPistonSilencerThe body isSandAction force atthe pile headmoving upPilea. Initial stagec. Launching upb. Air loadingInertia forced. Termination of air supply e. Termination oftestFrg. 3. Loading mechanism of3SLD-Mkl500possible initial load is about 230/0 of the ultimate load ofthe pile. Although this large initial load is not compatible¥vith the full-scale tests, it gives useful information for arough estimation of the static load-displacement r'elation.Another difficulty comes from the attempt to obtain anadjustable loading rate. Since the effect of the loadin_ :rate is one of the objectives of the study, an attempt tomake a distinctive change in the loading rate, i.e., achange in the loading duration from 100 ms to '_OO ms,400r:'300'c:5O200100has been made. Calibration tests are done by loadin_g therigid base ¥ 'ith the developed apparatus. Noting that thesand ¥vas not filled into the supporting boxes in thesetests, therefore, the dead ¥veight of the apparatus stillapplies on the pile head after the end of tests. Asconcluded from the calibration test results sho¥vn in Fig.4, the loading duration increases by only a small amount¥vhen the air pressure is increased.The same results are obtained lvhen the tests are doneon the model pile, as shown in Fig. 5. It is also found thatOO 20 40 60 80 100 120 140Tlme (ms)Fig. 4. Variation in loading rate with air pressure (calibration test withrigid base, reaction mass 30'- N)duration is still not an adjustable parameter. The loadingthe speed controller has absolutely no effect on theloading duration, although the maximum load can varyduration can be adjusted only by about Oo/o, dependin_"_.on the amount of solid fuel or the ven type (Karkee etwithin a 100/0 range by this unit.al., 1995).The other alternative for ad.justing the loadingduration is to increase the weight of the reaction mass. Asimilar trend is observed, ho¥vever, as sho vn in Fig. 6. Inaddition, increasing the ¥veight of the reaction mass hasan unpleasant effect brou_ ht on by the high initial load.For the above reasons, the distinctively di :erent rate ofloadin*･ cannot be produced at the present stage. Notethat even in the original Statnamic load test, the loadin_'._Test Conditions and MethodFour patterns of tests conducted in this study are summarized in Table I . T¥vo types of pile foundations, whichare the end bearin_g: piles and the friction piies, aremodeled. The properties of the model piles are sho¥vn inTable 2. Both types of piles are loaded by Statnamicforces that are lower and higher than their yielding 75STATNAMIC TESTS ON MODEL PILES600[I500EiiilJ::: ;:- - O'4 MP*Table 3. Properties of sand and modei ground,,¥l1l, ,400TISC:l300,¥.:t;¥t;¥-,L=100;¥OoFi,g. 5.40 60 80202.63Maximum void ratiol .03Minimum void ratioo.64Moisture ratioO 30/0D603 10 prnDIO120 ,JmUniformity coef.2.58Density1,467 kg/m'Relative density59.60/0Frictional an le36'Diiatancy angle90¥l200Specific ¥ 'eightl i120100Time (ms)Variation in loading rate with air pressure (experiment)350a) Friction pile tests300For the tests of the friction piles, a pile made of mor'tarl; 250¥j200:'150and piano wire, used for centrifugal model tests in ourresearch group (Kimura et al., 1997), is used. The model'_round is made of No. 6 silica sand. The properties ofsand are shown in Table 3. The frictional and dilatancy100ang:1es are determined from the direct shear tests. The soil50chamber and the location of the model pile are sho¥vn inFig. 7. The preparation of ground is divided into t voc:lO:loo4060 80Time (ms)20steps. At first, a lower layer, '_O cm thick, is compacted bylOOFig. 6. Variation in loading rate with reaction mass (calibration testwith rigid base, air pressure 0.2 MPa)Table 1.Test patternsEnd bearin*' pilesSmaH IoadPattern 1Pattern 3Large loadPattern 2Pattern 4! Friction piiesEnd bearing pilesMortarBrassDiaJneter (cm)2.42.4Len_ th (cm)4648Weight (kg)Youn_ 's modulus (lvlPa) :0.447o 2995.0X 038.5 x 104cudy are sun 'Points. The dimensions of the soil chamber are 80x 80lations, ¥vhict;cm wide and 60 cm high, and pro¥'ide a distance from thepile to the boundary of about 15 times the pile diameter.Since the ground models of the friction pile tests and the. are sho¥vn iby Statnarni*their yieldin;After the model pile is set up, the soil chamber is filledto the top ¥vith sand Then, an immersion vibrator is usedfor ground compaction. The vibrator is put into theUnder this preparation method, the model pile isProperties of modei pilesMaterialion piles, artconstrain the pile to the ¥'ertical axis.ground at tlventy-four uniformly distributed locations.I)ration test wiihpe (Karkee e{soil chamber. In this step, a 3 cm hole is dug in theground, the pile is installed, and then it is buried.attached to the top of the soil chamber are used toFriction pilesTable 2.The loadingspacin*'. Then, the model pile is placed in the center of theTherefore, the thickness of the layer beneath the pile isequal to 17 cm. At this stage, only four lines of thread20 140'b, dependingthe hammer used in the standard Proctor test. Thehammer is dropped 162 times under ¥vell-distributedend bearing pile tests are different, their preparations areexplained separately as follo¥vs:ILsupposed to behave as a friction pile. Vibro-compactionis not possible for the lower layer, because there is notenou9:h thickness for the sand to absorb the vibrationenergy from the vibrator. Ho¥vever, an attempt is madeto produce a uniform ground and to control the relativedensity of both upper and lower layers to about 600/0 . Theoverall density of the sandy ground is about I ,467 kg/m3.b) End bearing pile testsThe end bearing piles are modeled by a hollo¥v brasspipe, which has a small shaft friction. The thickness ofthe pipe is 1.0 mm with an outer diameter of 24.0 mm.Because the brass pipe is hollo¥v, the pile tip is cappedwith an aluminum plate in order to model the closed-endtype of piles. With the small shaft friction., almost ail ofthe resistance of the brass pile is due to the hard layerbelo¥v the pile tip. Therefore, the model pile is supposedto behave as an end bearing pile. In this kind of test, rigid 76Kllv URA AND BOONYATEEMortar model PileUnit:cmt80O+"20JGround material: N0.6 Silica sandJL_Side viewTo viewFig. 7.Ground model (friction piles)Brass pileUnit:cm80O60Ground material: N0.6 Silica sand-r-' 35 -To viewFig. 8.ISide viewGround model (end bearing piles)blocks made of plaster and dolomite are placed under thepile tip in order to model the support layer of the endbearing piles. The dimensions of the plaster blocks are 35x 35 cm ¥vide and 15 cm hig:h. These blocks are mademodel pile is set up, silica sand is filled up to the top of thesoil chamber. Then, an immersion vibrator is used forground compaction. The relative density similar to thewith a ratio of plaster to dolomite to ¥vater equal to I :2:5friction pile-type tests can be made by maintainin_ : thesame compaction time and locations. The overall densityby weight. The Young's modulus and the compressi¥'estren*'th of the plaster blocks, determined from theof the sandy ground is similar to the tests of the frictionpiles, which is 1,467 k_ /m3.uniaxial compression tests, are 41 .83 MPa and O.2 MPa,respectively. The outline of the ground model is sho¥vn inAfter the model ground is prepared, support beams areplaced across the top of the soil chamber and fixed byFi**. 8.clamps. The upper part of the device ¥vill then be set uponThe preparation of _2:round is divided into t¥vo steps. Atfirst, a plaster block is placed in the center of the soilthe pile head, and then the sand is filled into thechamber and then the model pile is installed. Again, fourlines of thread attached to the top of the soil chamber areused to constrain the pile to the vertical axis. After thesupported boxes of the lower base.The applied loads are measured from a load cell placedon the top of the pile cap. The displacement of the pile ismeasured from the fiange of the pile cap. This flange is 77STATNAMIC_ TESTS ON lvIODEL PILESSTN 1500Support frame for measuring device5test ' STN 2ndtest -SLT¥, , , . ,Laser displacement gauge400;- 300cso 200h:1Soi chamberlOOLoad cellOTo view0.0Side viewFig. 9. Measuring systcmFig. 10.made as short as possible to minimiz,e the effect of its ownvibration. A Iaser displacement gauge is used to measurethe settlement of the pile This displacement gau_ :e isinstalled on an additional frame that isolates it from theobserved system^ The measuring system is sho¥vn in FigLoad (N)0.2 0.4 0.6 0.8 1.0Displacement (mm)1 .2Load-displacement relation (Pattern l)Displacement (mm)5001.254001.00the reduced-scale tests, the wires of the strain gauge arerelatively large compared to the model piles. Therefore,3000.75the piles in these tests are not instrumented ¥vith the straingauges because they ¥vill disturb the pile-soil interactions2000.50around the pile shafts.lOOo.259. Note that there are no strain records in these tests^ ForoEXPERIMF,NT RESULTSFour patterns of tests lvere conducted in this study. Anattempt ¥vas made to load the pile ¥vith forces smaller andlarger than the ultimate capacity of piles. The first patternis the tests on a friction pile in ¥vhich the pile is loadedbelo¥¥* its ultimate capacity. The second pattern is a teston the same model pile in ¥vhich the pile is loaded wellover its ultimate capacity. The third and the fourthpatterns are similar tests performed on the end bearingpiles. Details of the test patterns are summarized in TableoFig. 11.0.0010 20 30 40 50 60 70 80Tlme (ms)Load and displacement vs time (Ist test of Pattern 1)the tests, a maximum Statnamic load of 440 N and amaximum displacement of about I .O mm are observed.The relation between the load and the displacement4. In oFder to ensure that there is no disparity in thewith time are shown in Fig. 1 1 . The measured data showthat maximum displacement occurs a short time after therecords, the test is done twice for each pattern bypeak load and that only a small displacement reboundcompletely reproducin*' the model ground.occurs.Pattern I-F/'iction Piles tinder Sma!! LoadingThe ¥vave number of loading has been calculated fromthe stress wave velocity, the duration of the Statnamicle top of theIn this pattern, a pressure of 0.2MPa is used toloading, and the pile length. The definition of waveis used forgenerate the Statnamic load. No additional reaction massnumber is the ratio between the loading duration and theis put in the reaction-mass box. The load and thetime it took the stress ¥ 'ave to travel from the pile head todisplacement of the pile head are sho¥vn in Fig, lO. Fromthe pile tip. With a stress wave velocity of 1,607 m/s, theTrilar to thentainin*' theduration of loading of 50 ms, and a pile length of 0.46 m,the calculated wave nulnber is 175. Since this value is inerall densitythe frictionTable 4. Summarl of each test pattern*rt bearns areand fixed by;1 be set upon*ed into theid cell placed;of the pile i irhis fiange ithe range of 12 to 1,000, it can be concluded that theexperiments do satisfy the STN philosophy (MiddendorpPatiern1)34O.2 = O 4Air pressuFe (*¥･IPa)O.2 O 4Max. Ioad (N),lax. dlsp. (mm)Max. vel. (cm/s)589280l O 5 403 1 37_5 37 o 2 5 14.0et al., 1995). For this large ¥vave number, it is thoughtthat the duration of loading is long enough to eliminatethe effect of the stress ¥vave.The velocity and the acceleration of the piie versus timeare sho vn in Fi*･. 12. The maximum velocity is about 7.5cm/s in a downward direction. A small value for the velocity in an upward direction indicates a gradual change KIMIJRA AND BOONYATEE78Velocity (cm/s) Acceleration (m/s2)STN 1test , STN 2600108stndtest -SLT¥//6l45, t/21:,a:l:¥ r¥ lf¥ l L r==/J:= ;i1 1=io400'-/Ii - / l500f;ro300O:!//200/100-5/oOl /2/l;/JO 1,0 20 30 40 50 60 70 8010Time (ms)lDisplacement2 3 4( mm)56Load-displacement re atton (Pattern 2)Fig. 13.Fig. 1'-. Velocity and acceleration vs time (Ist test of Pattern l)Displacement (mm)Load (N)in the displacement of the pile after the unloading point,or a point of maximum displacement. Maximum600accelerations during loading and unloading are 10 and9.5 m/s2, respectively. When compared to the data fromthe SLT, the load-displacement plot from the STN shows500a stiffer relation. As shown in Fig. 10, the loaddisplacement curves from SLT and STN intersect near300the unloading point under an applied load of 340 N.200Patte/'n 2-Friction Pi!es under Large LoadingAir pressure of 0.4MPa is used in this pattern. Nosettlement, ¥vhich is about 200/0 of the pile diameter, is5=14400/3//2//=]1 OO1l.Oadditional reaction mass is put in the reaction-mass box.The maximum Statnamic load in this pattern is about 590N. The load-displacement relations of the pile headare shown in Fig. 13. A very large amount of residual6/OO 10 20 30 40 50 60 70Time (ms)Fig. 14.Load and displacement vs time (Ist test of Pattern 2)noticed at the end of the tests. Maximum displacementVelocity (cm/s) Acceleration (m/s2)occurred after the peak load at a longer time lag than that40shown in the results of Pattern I . The wave number forPattern 2 is 222, due to the longer loading duration than3060/Pattern I .The relation between the load and the displacement,and the velocity and the acceleration with time are shownin Figs. 14 and 15, respectively. From the velocity-time,l20in displacement after an unloading point similar to that inPattern I is also measured.20It/l:!10l:l,,,olo/1-/1when compared with Pattern I . The maximumaccelerations during loading and unloading are equal to48 m/s2 and 35 m/s2, respectively. The gradual rebound40tplot, the maximum velocity is about 37cm/s in adownward direction, a change of more than four orders¥,-20¥;/-10Fio. 15.Olo 20 30 40 50 60 7040Time (ms)Velocitv.･ and acceleration vs time (Ist test of Pattern 2)Static I,oad Tests on the Friction Pi!esStatic load tests are also conducted on the model pile inorder to make a comparison between different loadingconditions. The tests are carried out with the sameLoad-displacement plots from both patterns and theSLT are shown in Fig. 16. An almost identical load-apparatus. After piling a large amount of reaction massupon the cylinder, a series of loads can be applied bydisplacement relation bet¥veen the two patterns in theincreasing the air pressure. For this experiment, the pile isdisplacement of the pile exceeds 2 mm, the rate of thedisplacement to load-increment in Pattern 2 increasesloaded under 50 N Ioadin*' steps until failure occurs. Thetime interval for each load increment is about 10 min.launching-up stage is observed. However, after theconsiderably. A Iarg'e deformation in Pattern 2 indicates 79STATNAlvIIC TESTS ON MODEL PILES600500::,,400::c:} 300O1 200lOO/// 1, ti -, t,- - :": i¥:¥;1"t25 o-; 200SLT- pattern 2t -¥ -i'I･i --Pattem I300:, 150; t;-1_f･cSO 100- - -;f_50ifOoo Displacement1 2 3 4(mm)5 60.00.2 0,30.1Displacement (mm)Fig. 16. l,oad-displacementrelationbetween Sl,T and STN of frictionFig. 18.Load-displacement relation (Pattern 3)piles700600500400)*3000.352500.302000.251500.201 OO0.1 5500.10o0.05ir;¥J 300::'csO:1200lOO10O. lDisplacement (mm)n 2)o4080120Time (ms)160Fig. 17. Static ko3d-displacement of friction･type pile ou iog-log scaleFig. 19.that the pile ¥vas loaded over its ultimate capacity. Fromthe plot of the static ioad-displacement in log-10g scale(Fig. 17), it can be seen that the yielding load of the modelpile is 5･_O N. This load corresponds to a displacement of2.2 mm.)Displacement (mm)Load (N)i_Patte,'rl 3-End Bea/'ing Piles under Si77a!! I,oadinglo0ttern 2)lal load- ;force of the piston. With a stress ¥vave velocity of 3,574m/s, the calculated wave number of this pattern is about305.From the velocity-time plot shown in Fig. 20, theHowever, the weight of reaction mass is increased to 20.0kg, or equal to the downward force of 196.0 N. To lessenthe initial dead weight, a chain is used to hang the mainbody of the apparatus from the ceiling and only a smallfraction of the dead weight is applied to the piles at thebeginning. This small initial load is allowed to act on thepile in order to ensure that there is no gap between thedirection. The maximum accelerations during loadingthis pattern is about 280 N. It is concluded from the staticload tests that will be shown later that this load is a littlebit higher than the yielding point of the target piles. Thete of theincreasesthou*･ht that the first fall-off (around the 20 ms in Fig. 19)indicatesis due to the air supplement being shut off before thefter theforce after the first fall-off is due to the remaining inertiamaximum velocity is about 2.5cm/s in a do¥vnwardload-displacement relations of the pile head are shown inPig. 18. When looking at the load-displacement relationand the load-time history plot, it is found that the forcedecreased once before reaching its maximum value. It isIs in thepiston could generate its full load, and the increase ofAir pressure of 0.2MPa is used in this pattern.pile cap and the piston. The maximum Statnamic load inand the jLoad and displacement vs time (Ist test of Pattern 3)aL';".",,and unloading are equal to 4.0 m/s2 and 2.6 m/s2, respectively. When compared with the friction piles, the velocity of pile is very small. It is thought that the hard layerbelow the pile tip makes the model pile displace at aslower rate than the friction pile.Pattern 4-End Bearing Piles under I,arge LoadingAir pressure of 0.4MPa is used in this pattern. Theweight of reaction mass is increased to 32.5 kg, or equalto the downward force of 3 18.8 N. A chain is used againto hang the main body of the apparatus from the ceiling.The maximum Statnamic load in this pattern is about 520N. The load-displacement relations of the pile head areshown in Fig. 21. The calculated wave number of thispattern is about 916.The relation between the load and the displacement, KiMURA AND BOONYATEE80Velocity (cm/s) Acceleration (m/s2)632jll1it,1 :l.t5002.544002.023001 .5ILt I , IIf"$ = II I/ ' =ot- ･$1 1 'la.j ,t=1,otl _-2l=i 'W I :-lt'2001 ,O100o.5o0,0o 80Time120(ms) 160Time (ms)Frg 20. Veiocity and acceleration vs time (Ist test of Pattern 3)Fig. '-2. Load and displacement vs time (Ist test of Pattern 4)Velocity (cm/s) Acceleration (m/s2)500Ol2015400)i10¥-/ 300::cslo 40 80 120 160 200 24040f;Displacement (mm)Load (N)10_ l;,t, l2005lOO,4'/- - :/ I ifj =ll' -- S. ;/ 'l- -"oloOi'*lOt'o' oisplacemento 5 l'o 1.5(mm)2.02.5.5*20o 40 80 120 160 200 240Time (ms)Fig. 21. Load-displacement relation (Pattern 4)Fl'* 23. Velocity and acce]eration vs time (Ist test of Pattern 4)and the velocity and the acceleration with time are sho¥vnm Figs. 22 and 23, respectively. From Fi*･. 23, theyielded ¥vhen the applied load exceeded 161 N, corresponding to a displacement of 0.1 1 mm.direction. The maximum accelerations during loadingand unloading are equal to 14 m/sl and 14 m/s2, respectively. As was observed in Pattern 3, it can be concludedthat the model pile displaces at a slo¥ver rate than theSince the yield displacement is smaller than themaximum displacement of Pattern 3, it can be thoughtthat the target piles were loaded beyond their staticyielding points. However, when an air pressure smallerfriction pile.than that applied in Pattern 3 is used, the inertia effect ofStatic Load Tests on the End Bearillg Pi!esthe piston, as described in the previous section, becomeslarge. Since the characteristic of force will be dominatedmaximum velocity is about 12cm/s in a downwardAfter the Statnamic tests have been conducted, theby the inertia of the piston when the air pressure is small,static load tests are done. The static load-displacementa force smaller than the one applied in Pattern 3 cannotbe produced. Currently, the improvement of the device torelation of a pile is shown in Fig. 24. For the end bearingpile, an improved static loading de¥'ice made after thecompletion of the friction pile tests is used. The maindifference from that used in the previous tests is that amechanical jack is adopted instead of the cylinder. Usin*this jack, the constraint displacement is applied to thecorrect this effect is under ¥vay.Danlping Coefficient of the Un!oading Point MethodAccompanyin*' the data from the SLT, dampiugpiles are loaded in four cycles before reaching the tar*･etcoefficient C, used in the unloadin*' point method, can beback calculated. Firstly, dampin_g: force Fd is calculatedby subtracting the Statnamic loading (F** ) ¥vith staticdisplacement, ¥vhich equals the maximum displacementresistance and inertia force (F*1* and M･ a, respecti¥'ely) asof the model piles in Pattern 4. The plot of static loaddisplacement in log-lo*' scale determines the yield point ofshopile. The rate of displacement is 1.5 mm per min. Thethe model pile. As shown in Fig. 25, the model pile'n in the following relationship:Fd = F*** - F*1*M･ a (1)=;']' i"" 81STATNAMIC TESTS ON MODEL, PILESpattern 45001/ t;I,_, 400:-/ 300c l200lOO¥_8,0___: , ._ _¥ */= =!/i ; ;i _ .;._ _;D D:-f 6.0./'; Statmic test =l'iij- fi,1 '; -.+c,D4'oC (ulp, patterT:+¥JJ 2,0C (Ulp, parterT' 2)0,0,0.0 0.51.0 1,5 ･_.ODisplacement(mm) 2.5Fig. 24. Load-displacement relation betlveen SLT and STN of endbearing piles;t 2002Displacement( mm)Fig. '-6. Damping coefficient vs displacement (Ist test of Pattern I and{---1 --i -8.0D DD4 o:;20s s os' patterT' 3ij :i _'_'i :iI_i Cavi = 5'07 kN-s/mf 6.0v'l'____ I, ! ----c:to:Ii iii !{ 'ii i-[iij titji;1 OOI- "* C'D4･O)l 2.0j0.00.1Displacement (mm)scale4'19 kN-5!m I c (ulp' pattem 3)4'79_ i_lr'¥:L_I Pattern 3Iv'l' ::: 3'09 kN-s/mL I' Il' t I'l' " : "c (ulp' pattem 4)' - 1'61i ¥ 4 1"l!il' ' PatternTT :' TYielding displacement!i / 'o.o 0.5 1.0 l.5 2.0Displacement (mm)Fig. 25. Static load-displacement of end bearing-t¥.'pe pile on log-]og4)43Pattern 2)400300i)2.47O^86tb =o),D selsl,20 5 l*SOFig. 1,*7. Damping coefficient vs displacement (Ist test of Pattern 3 andPattern 4)orre-Then, the damping force is divided by pile velocity V, toobtain the damping coefficient, as in the followingtheught 'lrelation:C V = Fd (2)static "lallerct ofomesThe ¥'ariation of Fd and the variation in C with pileinterpretation of Pattern I will be done in a zone ofinterest, which ranges from Dl,209to the Dl,809 ･ Thedefinition of D*,+, 6 is the displacement 'y' in percentage ofthe maximum displacement of pattern 'x' . For making acomparative study, the zone of interest for Pattern 2 alsostarts from D1,20',and stops at D2,809 ･ To quantitativelynateddisplacements for Patterns I and 2, and Patterns 3 and 4,mall,are sho¥vn in Figs. 26, and 27, respectively. Since the ve-the followed paragraphs. The first parameter is theannotlocity of piles is close to zero around the beginning oftests and the unloading point, the calculated C grows to avery lar_ e value (a value close to infinity) around thesevariation index of the damping coefficient, V.1., which isice tozones. Consequently, no meaningful information can beevaluate the variation of C, two parameters are used indefined as the difference between the maximum value andthe minimum value of C in a zone of interest. The secondparameter is the average value of C, C..,g, which is takenfrom the same zone that V.1. is calculated. For simplifiedestimation methods such as the Unloading point method,iodm pingcan beobtained from these areas. Although the tests are:ulatedC from the small load tests and large load tests are not inthe same ran*"e. These differences are due to the velocitiesthe value of C is assumed as a constant value. Consequently, it can be thought that the accuracy of theirpredictions should be related to the magnitude of V.1..of piles in the large load tests being higher than those inthe small load tests (see Figs. 12, 15, 20, and 23).As shown in Fig. 26, the V.1. of Patterns I and 2 are 1.02Since the values of C are large at the beginning andPattern I is larger than that of Pattern 2, it is expectedthat the prediction quality of Pattern I should be poorerstaticely) as(1).conducted on the same piles and ground, it can be seenfrom the C-displacement relations that the magnitude ofaround the point of maximum displacement, theitLkN-s/m and 0.86 kN-s/m, respectively. Since the V.1. of ･*"K1*¥,lURA AND BOONYATEE82600400i500f;¥J:;300l400l300200'CScO200lOO100ooo Displacement1 2 3 4(mm)5Fio. 28. Estimatcd static load-displacement relations b .･ unioadingpoint method0,0Estimatedpoiut methodF er. 29 .than that of Pattern 2 due to the use of constant C.However, as shown by Fig. 28, the prediction by the250,0unloading point znethod of Pattern I is much better thanthat of Pattern 2. Note that the C of the Unloading point200,0method for Patterns I and 2 are 2.47 kN-s/m and 0.86kN-s/m, respectively. From the prediction results, it isthought that the characteristic of damping force can bedivided into two parts, which are the major trend andminor trend. The major trend is controlled by onelumped parameter, say C* ,g, and the minor trend iso ,5 1 ,o I .5 2 .o 2 ,5Displacement (mm)static ioad -displacement relationsb) unloading/ Ylelding polnt)r;, '1,50.0csO:]lO0.050.0effected by the V.1.. The value of C*..*_ for Pattern I andPattern 2 are 2.77 kN-s/m and 0.55 kN-s/m, respec-0,0tively. For Pattern 1, although V.1. is large, it has a rela-o2 34IDisplacement (mm)tively small effect when compared to that from C. g. Onthe other hand, the V.1. of Pattern 2 has a large impacton the characteristic of damping resistance since the valueof C*+,g is small. It is also found that the V.1. of Pattern 2Fig. 30. Variation of dampingf orce5with dis placement (Ist tcst ofPattern I and Pattern 2)reduces to a small value and C converges to a constantvalue after the piles yield./Yleldmg polntSince the model pile experienced one drop of loading250before it reached its maximum displacement, thesettlement characteristic of pile in Pattern 3 is differentfrom the others. Consequently, the variation of C, whichdepends on the velocity, is also affected. Therefore, theresult of Pattern 3 is not used for the interpretation.However, the correspondin*' parameters are also shownin the plots for comparison. The V.1. of Patterns 3 and 4are 4. 19 kN-s/m and 3.09 kN-s/m, respectively.Although the variations of C in Fi**. 27 are larger thanthose of the friction piles, the Unloading point methodcan acceptably estimate the static responses of piles evenfor Pattern 4, which load the piles exceedingly over theiryielding points. These estimations for Patterns 3 and 4are shown in Fig. 29. Since the C-displacement plotscannot give any clues for the differences in behavior between Pattern 2 and 4, the Fd-displacement plots, which::i'.200';J1501:,co]lOO50O 0.0 0.5 1.0 1.5 2.0Displacement (mm)Fig. 31. VaTiation of damping force with displacement (lst test ofPattern 3 and Pattern 4)are not infiuenced by the piles velocities, are used instead.As shown in Figs. 30 and 31, it can be seen clearly thatdamping resistance of the friction piles reducesTherefore, although it cannot be concluded from the C-considerably after the piles yield. The same characteris-displacement plots, the difference in behavior between thetics are not observed for the tests of the end bearing piles.friction piles and the end bearing piles against the*,*i'i:･! .83STATNAMIC_ TESTS ON MODEL PIL,ESTo viewStatnamic force can be validated by the Fd-displacementplots .l,Since the main difference between the end bearing andthe friction pile is either the pile is supported mainly bythe shaft resistance or the tip resistance, the dampingcharacteristics also come from the same source. For thefriction piles, the damping resistance comes from theshaft portion and becomes small or zero after the slipoccurs. On the contrary, the end bearing piles gain theirdamping resistances mainly from the pile tip and theseresistances still remain even after their yielding point.When C is assumed to be constant, a good estimationfor the friction piles can only be obtained when the)magnitude of loading is not close to its ultimate///?¥1.3 5.09¥resistance. Note that C converges to a constant valueIoading/1./2 2.4/11.0(Unit cm)J27.0 f 0.0+¥18.0-3¥after the yielding point of piles, or the displacement of 2mm. Hence, it is thought that the damping resistance ofpiles is not only non-linearly related to its velocity (Coyleand Gibson, 1970; Lee et al., 1988), but it also has some2-o¥relation to the ratio bet¥veen applied loads and theultimate capacities of the piles. For the end bearing piles,lthe constant C can be applied to all ranges ofdisplacement, even after the yielding of piles.-35¥-31¥-43¥ a-49¥ANALYSIS BY A 3D-FEM CODF. (DYSO,-5 6¥(In order to develop a unified tool that can be appliedfor various types of problems, a 3D-FEM code, DYSC, isoriginally developed in this study. To demonstrate theSide viewFig. 32.application of DYSC, a simulation of a friction pileunder Statnamic loading is presented. No-tension criteriaand a simple elasto-plastic model based on the DruckerPrager theory are applied as the yield functions for themodel ground. An interface layer element is inserted atthe interface bet¥veen the pile and the soil. For the pilebody, a linear elastic relation is used since the applied5;ttest ofTable 5.Geometn.' of FEM meshPropertics of materials for FEM analysisSandforce is lower than its yielding point.To determine the necessary parameters used in the STNsimulation, trial calculations are made. As shown inDensity (k_ */ms)l ,467bPoisson's ratioo.333e0.200'Youn_ 's modulus (MPa)4.90n5.00 x lO;bFrictional an :le360 bFig. 32, an analysis is conducted in the half area of theIcalculated from the fiexural test results. Poisson's ratiosfor the pile and the soil material are assumed to be 0.20014and 0.333, respectively. Direct shear tests have been done2, 1 50b90Dilatancy angiepile-soil system. Young's modulus of the pile is backPilefrom inversed anai_vsisbfrom material testassumedto determine the frictional and dilatancy angles of thesand. The dilatancy angle, defined as a constantparameter, is approximated from the average change involume of sand during shearing. The frictional an*"le ofthe pile-soil interface is assumed to be 0.9 times thefrictional angle of sand. Based on the static load testresults, Young's modulus of sand can be estimated froma parametric study. The properties of each material deternxined from an inverse analysis are summariz,ed in TableIsi test of5.are calculated from the displacement by the Newmarkmethod. The stiffness matrix, the damping matrix, andthe mass matrix are calculated from the followingequations:l, .lK= BDBdvol (3)J .lC = NplNd vo! (4)¥veen theIn the next step, a dynamic FEM analysis of a pileunder Statnamic loading is done and then compared withthe experiment results. The loading rate dependency ofthe ground response is represented by a constant dampingM= NpNdvol (5)iinst the ;parameter. In this simulation, velocity and accelerationwhere N is a so-called shape function or displacementrrl the C-' .".i:si!Jl 84KIMURA AND BOONYATEEinterpolation function, B denotes a displacement to thestrain transformation function, and D is a strain to stress-400strain transformation function. Parameter p is used torepresent the damping constant per volume of thematerial of interest in the same manner as the density (p)is applied in the mass matrix.' ,;¥jI300::lcO:!Pi!e-Soil Intelface Mode!The Mohr-Coulomb yield criterion is used for the200100interaction between the pile and the soil. It states thatfailure will take place if the magnitude of shear stress (r)Oon the failure plane is equal to the value given by thefollowing relationship:l ri = (TDisplacement (mm)tan co + co (6)in which I I denotes the absolute value, (T is the normalstress on the failure plane, and co and co are material constants for the pile-soil interface. In this study, adhesion,or co, is assumed to be zero. Since the pile is not made bythe cast-in-place method, the frictional strength of thepile-soil interface should be deteriorated compared withthe surrounding soil. Therefore, the frictional angle, orco, is assumed to be 0.9 times the corresponding value ofsand. Equation (6) can be written in the form of yieldfunction F asF= I rl - a* tan 60. (7)0.0 0.2 0.4 0.6 0.8 1 OFl" 33' Variationin pilestiffnessagninstYoung's modutusofground400i' '; 300J:,ceO200hl OOIf the material is sheared to the yield surface and the as-sociated flow rule is adopted, the rates of plastic normalstrain ds and shear strain yP are given byd8P tan c[d y P lO0.0 0.2 O. 4.O (6 .)O 8 1.0Displacement mmFig. 34. Variation in pile stiffness against fricttonal angie of groundwhich impliesdePdyP = tan co (9)The same calculations are also done for ft'ictionalangies of 32eand 30'. When the amount of settlement isIncrernents in shear displacement along the plane areaccompanied by increments in normal displacement. Thethe pile behavior. However, the disparity in load-dilation of the shear plane will go unbound underyielding. To avoid this unfavorable behavior, the non-associated flow rule is adopted for the pile-soil interface.By introducing dilatancy. angle v/, the plastic potentialfunction can be ¥vritten asQ= ITI cr tan v/ (10)In this study, no dilation is assumed for the pile-soilinterface, i.e.,/H'O.small, the frictional an_g:1e of soil has little influence ondisplacement relations increases ¥vhen the displacement is )large, as sho¥vn in Fig. 34.From various trial calculations and comparisons withdata from static load tests, a Young's modulus of 4.9MPa and a frictional angle of 32' are selected as rationalquantities for the ground materials. Using these values, asatisfactory approximation for pile response can be obtained. The frictional angle of 32' for soil gi¥'es thecalculated ultimate load at more or less the same level asthe measured data. A Young's modulus of 4.9MPacontrols the shape of the load-displacement of the pileCALCULATION RF,SULTSStatic CapacityIn order to find the material constants, a parametricstudy has been made. Based on the data from the directshear tests, a frictional angle of 36' and a dilatancy angleof 9' for sand are used. When Young's modulus of soil isvaried, changes in pile stiffness are achieved as sho¥vn inFi**. 33.before failure.It can be seen that the determined frictional angle is notequal to the data obtained from the direct shear tests. Theground conditions in the experiment may not be as denseas the sand sample in the direct shear tests, and thiscontributes to there being a smaller value than in thedirect shear test results. The load-displacement plot frorrlcalculations and measured data is sho¥vn in Fig. 35.i 85STATNAMIC TESTS ON lvIOD L PILESStatnalnic CapacityBased on the calculated parameters determined in theI.is shifted to the right in order to match the 'true'displacement in the static load tests.previous section, simulations of pile responses underStatnamic loading are carried out. Since the pile is loadedto its ultimate capacity in Pattern 2, the solutions of thefinite element calculation diverge at about the yieldingpoint of pile and the response of the pile cannot becompletely determined. For the above reason, only theelastic contraction represented by the difference inThe damping force of the system is assumed to bemm. When compared to the overall settlement, thislinearly dependent on the velocity, and a damping constant of 3.9 MN/(m/s)/m3 (p as defined in Eq. (4)) iscontraction is about 50/0 of the pile head settlement. Thedistribution of axial force along the pile is sho¥vn in Fig.37(b). The application of load is sustained almost totallyby friction resistance, with only a small amount of forceused after trial calculations as the material constant forfurther calculations. The estimated load-displacementrelation and the test data are shown in Fig. 36. Note thatthe initial displacement in Statnamic load tests does notof groundShown in Fig. 37(a) are distributions of displacementalong a pile under static loading. At the peak load, thesettlement between the pile head and the toe is about 0.05results from Pattern I are presented here.1.0Comparison between Computed Static and StatnalnicLoading Resultsconform to that in the static load tests. The initialdisplacement in the Statnamic load tests is a little bitsmaller than the corresponding value in the static loadtests. This may be attributed to the loading rate effectduring the equipment installation process because theinitial dead weight in the Statnamic tests is applied to thepile head at once. To correct this inconsistency, the load-displacement relation (from the experiment) of the STNbeing transmitted to the pile tip. The ratio of the endbearing resistance to the shaft resistance is about 1:4.5.The pile velocity versus time relation is sho¥vn in Fig.38. At the maximum displacement, the velocity of the pilehead is equal to zero. At the same time, the velocity of thepile tip is almost identical to that of the pile head. Thisimplies that the pile behaves as a rigid body at theunloading point. Axial force distributions of the pileduring Statnamic loading as well as a comparison withthose of the SLT are shown in Fig. 39. At the same600600!500l . . Or' ,400c'300OI200;SSl- - Experiment/ if rictional {i ilOOrtlement isji200500,,_r/___'i' ____ i;O]// 7l; 400l 300le of groundli100Ifiuence on;,lacemento 1Displacement2 3 4(mm)5 6.risons withulus of 4.9Ooin load-Fig. 35.Load-displacement relations from SLT simulation and0.2 0,4 0.6 0.8 1.0DiSplacement (mm)Fig. 36. Load-dispiacement retattons from sTN stmu ation andex perimentexperimeuti as rationaise values,can be oboil 9:ives thame level aiof 4.9MPglOof the pil/V} an..,* le is no;J::_ 20flar tests. Th ;c be as den(.fts, and thi;than in th ;nt plot fror.･jFi . 35.30iiiiiiiili*- iili*!i:i iiiii io.2 o 4ri-S･lOON ,H -200N -A-300N i-400Niil{ i__iiFig. 37.ltilPs: 20 - i---o' ii ii ii i!ie'30 /;1//- --'- -r'-- i-; I-hIi -iI-- -"-Iirl i !Displacement (mm)a. D splacementij- -ll40 o, 6 o.8ijl{} i! i!Ii i!ro ' -I-- Id';T]oi¥J!lOO200300Load (N)b. Axial loadDistribution of displacement and axial force along pile under static loadingsOe _}/ _'rr 1'86' t Fl"TKIMURA AND BOONYATEEapplied load level, the axial force distributions of the twocases are almost identical. As shown in Fig. 39, when pilemined from trial calculations, a finite element analysiswas carried out. A comparison of pile behavior under ahead settlements are equated, the pile in the STN canstatic loading and a Statnamic loading was conducted.sustain a higher load than that in the SLT. There are nosubstantial changes in load sustained by the pile tip.Based on the results from the tests, which use relativelyIncreases in capacity mainly contributed to the shaftresistance. The effect of a stress wave is not observed inthis analysis.short piles and relatively loose soil, the followingconclusions can be summarized:1) The large wave numbers of all patterns imply thelong duration of Statnamic loading which results in a pilebehavior no longer dominated by the action of the stresswave. From this evidence, it can be concluded that the developed small-scale loading device has the potential toCONCLUSIONWhen compared to field tests that have the inherentsimulate Statnamic loading in laboratory tests.problem of ground uncertainty, the model tests presentedhere show the possibility for conducting Statnamic loadtests under one uniform condition. Only by this approachcan the data be interpreted on absolutely the same basis.Moreover, the experimental results also reveal oneadvantage of laboratory tests over full-scale tests. Forfull-scale load tests, it is difficult to load the piles up todisplacement of the pile cannot be compared to those ofthe prototype. Nevertheless, the experimental data agreetheir ultimate bearing capacities due to the condition ofsafety. However, the tests in Pattern 2 show that this kindof load can be applied readily in the laboratory tests.2) Due to the presence of dynamic resistance, there is awell with the original Statnamic signal.After input parameters for the simulation were det,er-time lag between the points of maximum displacementand the peak Statnamic load. The load-displacementAt present, such results as load magnitude andplots of the STN also show higher capacities than those8-!l :6lPile head- - Pile tip,¥J43) In Patterns 1, 3, and 4, the load-displacement plotsfrom the SLT and the STN meet at about the unloading1' 2:>0-2/s2 to 50m/s2. However, the inertia force is relativelysmall since the mass of the pile is small./ogiven in the results of the SLT because of these additionalforces. The acceleration of the pile varies from about 5 mo lo 2030 40 50Time (ms)Fig. 38. Variation in velocity of pile head and toe along timepoint. This evidence a*"rees well with the assumption ofthe unloading point method (Horvath et al., 1993), whichstates that dynamic forces at an unloading point are verysmall and can be disregarded. However, in Pattern 2, theSTN plot shows the unloading point to be quite far awayfrom the SLT Iine.4) It can be concluded from the C-displacement plotsand Fd-displacement plots that when C is assumed to beconstant, a good estimation of the friction piles can beobtained only when the magnitude of loading is not closeSiL C Sl:0 ･_8 mrrl-0.28 mm-c- O.55 mm -O.56 mm- -O.86 mm ^ O.85 mrnoo1010oo:: 20: 20,C- I i- Ii iii ; i !Li -'t i----"-- f- -'e)e,C:}i I"' 7 - - - yjl'lTI't I'T"'---r l"I" I"-^ i30i30T}401 oo300400Displacement (mm)a. Applied force equatedFig. 39.40lOO 200Load (N) 400 soo300b. Head displacement equatedComparison of statnamic and static simulations 87STATNAMIC TESTS ON lv iODEL PILESrelatively ;to its ultimate resistance. It is thought that the dampingresistance of the friction piles is not only non-linearlyrelated to the pile velocity, but also has some relation tothe degree of loading compared to the ultimate capacitiesfollowing jof piles.imply the ithe stress jresistances of Patterns 3 and 4 vary within a small range.Consequently, the damping coefficient of the end bearingpiles can be considered as a constant value. This is ob-lat the de- {served whether the piles yield or not. The damping)tential to jresistance of the pile, or the hard layer, does not decreaseeven if the applied load exceeds their yielding stress.t analysis :)r under a {onducted. ;5) From the variation of C and Fd, the dampings in a pile =ry tests, I3veal one i6) The finite element analysis (DYSC) shows that thetests. For ;elastic contraction of the pile is relatively small. This)iles up to jvalue represents about 50/0 of the total displacement.From the load distribution plot, the applied load ismainly supported by shaft friction. The model pile isndition of {t this kind {there is a {thought to be a friction pile. The ratio of shaft resistanceto end bearing resistance is about I :4.5. Velocities of theplacement ;pile head and the pile tip are almost identical and equalplacement izero at the unloading point. This supports the:han those {additional ;assumption that a pile moves as a rigid body at they tests. jREFERENCES1) Amir, J. M. and Amir, E. . (1995): A Iumped-Parameter modei forstatnamic testing, Proc. of the Ist Int'! Statnamic Serninar,Vancouver, 2232) Bermingham, P. and Janes, M. (1989): An innovative approach toload testing of high capacity piles, Proc. of the Int'! Co,rf, on Pi!ingand Deep Foundations. London, 409-413.3) Bermingham, P, and ¥rhite, J. (1995): Pyrotechnics and theaccurate prediction of statnamic peak loading and fuel charge size,Proc. of t/7e Jst Int'/ Statnanlic Serninar, Vancouver, I -12.4) Bro vn, D. A. (1994): Evaluation of static capacity of deepfoundations f'rom statnamic testin_ :, Geotech. Testing J.. GTJODJ,17 (4), 403=414.5) Coyle, H. M. and Gibson, G. C (1970): Empirical damping constants for sands and clays, J. Soi! Mech. and Found. Div.. ASCE,96 (SM3), 949-965.6) Karkee, M. B., Kojlma, I. and Shinoda, Y. (1995): Infiuence ofdifferent test conditions on the results of STATNAMIC Ioad tests atthe Shonan test site, Proc. of the Ist Int'! Statnamic Senlinar.Vancouver, 137-147.7) Kimura, M., Adachi, T., Yamanaka, T., Fukubayashi, Y, andBoonyatee, T. (1997). Failure mechanism of laterally loadedconcrete piles by centrifugal model tests, Proc. of the Int'/ Conf, onFol!ndation Faih!res. Singapore, 417-426.8) Kimura, M . Boonyatee, T, and Adachi, T, (1999): Experimentalunloading point.study of laterai statnamic ioad tests on group piles, Procabout 5 m i7) The axial force distribution from the STN is veryInt'! Conf. on Deep Fot!ndation Practice in Corporatingrelatively jsimilar to that from the SLT. The stress wave effect, as ina dynamic load test, is not observed in the present. Thisunloadin2mption ofimplies that in the STN, the pile is loaded in the samemanner as in the SLT.Although the outline of the research can be divided93), which iinto three parts, as sho¥vn in Fig. I , only the work on StepTlent plots ;:rt are very jtern 2, the ie far away ;Tlent plots ;med to be jles can bejs not close ;) is reported in this paper. The horizontal load tests ongroup piles have been conducted and reported elsewhere(Kimura et al., 1999). In order to perform vertical loadtests on pile-raft foundations, the improvement of theloading equipment is presently under planning.As a ¥vhole, the equipment presented here and DYSChave the potential to perform and analyze small-scaleStatnamic load tests. The 3SLD-Mkl may be used as atool for investigating pile behaviors under Statnamicloading and the application of Statnamic load tests to pilefoundations. As the second step of the research, theexamination of pile behavior will be done through thenumerical analyses of the full-scale tests.PII.ETALK '99. Singapore, '-63-271.9) Lee. S. L., Chow, Y. K., Karunaratne, Gof the 4thP, and Wong, K. Y.(1988): Rational wave equation model for pile-drivin_ : analysis, J.Geotech. Eng.. ASCE, 114 (3), 306-325.10) Matsumoto, T. and Tsuzuki, M. (1994a): Statnamic tests on steelpipe piies driven in a soft rock, Proc. of the Int'! Conf, on Design(Tnd Construction of Deep Found.. Orlando. F!orida, 586-600.l 1) Matsumoto, T., Tsuzuki, M. and Michi, Y. (1994b): Comparativestudy of static loadin_test and statnamic on a steel pipe pile drivenin a soft rock, Proc. of the 5th In!'! Conf, on Pi!ing and DeepFound.. Bruges. Be!gium, 5.3.1-5.3.7.12) Matsumoto, T. (1998): A FEM analysis of Statnamic test on openended steel pipe pile, Proc. of tlle 2nd Int'! Statnainic Seminar,Tokyo, 287-294.13) Middendorp, P. and Bielefeld, M. W. (1995): Statnamic ioadtesting and the nfiuence of stress wave phenomena, Proc, of t!1e Is!Int'/ Statnan7ic Serninar. Varlcouver, 207-22214) Nagaoka, T., Sakamoto, K., Fujisawa, H. and Kubo, Y. (1995): Acornparative study of the Statnamic ioad test on a steel pipe pileunder diff rent loadin_2: conditions at the Shonan test site, Proc. oftJle Ist Int'! Statnanlic Seminar. Vancouver, 149-164.15) Poulos, H. CJ. (1998): Pile testing - from the desi_gner's viewpoint,Proc. of the 2,Id Int'/ Statna,nic Seminar. Tokyo, 3-'-1.16) Yamashita, K., Tsubakihara, Y., Kakurai, M. and Fukuhara, T.ACKNOWLEDC.F,MENTSThe authors ¥vish to express their sincere appreciationto Professor Toshihisa Adachi of Kyoto University forhis advice. Special thanks are also due to Mr. AtsushiYoshida, former master course student of Kyoto University, for his help in performing the laboratory tests.j:i';,';i#Ei:-(1995): Load-settlement behavior during kinetic pile test. Proc, ofthe IOth Asian Regiona! Conf, on SMFE. Beljing. Cllina, 233-236.17) Yamashita, K , Tsubakihara, Y. and Kakurai, M. (1998): Methodfor estimatin_g static load-settlement relation by rapid pile loadtests, Proc. of tlle 7th Int'/ C0,If. and E;t:-hibition on Pi!illg a,rdDeep Found . Vienna. Austria, I .29. 1-1 .29.6. | ||||
| ログイン | |||||
| タイトル | Earthquake-Induced Flow Slides of Fills and Infinite Slopes | ||||
| 著者 | Osamu Matsuo・Yukiko Saito・Tetsuya Sasaki・Koichi Kondoh・Takashi Sato | ||||
| 出版 | soils and Foundations | ||||
| ページ | 89〜104 | 発行 | 2002/02/15 | 文書ID | 20441 |
| 内容 | 表示 | ||||
| ログイン | |||||
| タイトル | Torsion Shear Tests on Cyclic Stress-Dilatancy Relationship of Sand | ||||
| 著者 | H. Shahnazari・Ikuo Towhata | ||||
| 出版 | soils and Foundations | ||||
| ページ | 105〜119 | 発行 | 2002/02/15 | 文書ID | 20442 |
| 内容 | 表示 SOILS AND FOUNDA'TIONSVol. 42. No. l, 105-119, Feb_ 2002Japanese Geotechnical SocietyTORSION SHEAR TESTS ON C 'YCLIC STRESS-DILATANCYRELATIONSHIP OF SANDHABiB SHAHNAZARli) and IKUO To¥¥,HATAii)ABSTRACTSeveral cyclic torsional drained simple shear tests were performed on Toyoura sand in order to investigate the stressdilatancy relationship under a large number of re*'ular and irregular loadin*' cycles. In particular, effects of differentfactors such as initial anisotropic stress state, initial confinin*" pressure, density and shear history on this relationshipwere studied. It was found that the stress-dilatancy relationship changes suddenly after each loading reversal with acontractive behavior. When loading reversal occurs at a higher value of stress ratio, more contractive behavior is observed after the reversal. Although the stress-dilatancy diagrams of different cycles start from a different extent ofcontraction in irregular loading, they converge to a common one as stress loading continues. Test results showed thatinitial confining pressure and initial anisotropic stress state do not have any important effects on the stress-dilatancyrelationship. It was found that density and shear history affect the stress-dilatancy relation. Change of stress-dilatancyrelationship due to increase of density or shear history leads to less contractive behavior. Results of this researchprovide complete and accurate information on the stress-dilatancy relationship under a large number of regular orirregular cyclic loading and effects of different factors on this r'elationship. This information can be used in themodeling of cyclic stress-dilatancy relations and volumetric strain. The investigated volume change and stressdilatancy relationship in this study together with seepage analysis can predict the excess pore water pressure forliquefaction analysis.Key words: constitutive eauqation of soils, dilatancy, drained shear, sand, torsion (IGC: D7)INTRODUCTIONVolume change in dramed shear which can beconsidered as a mirror image of pore water pressurebuild-up during undrained shear, is one of the key}}horizontal and vertical stresses. Pradhan et al. (1989)performed a series of cyclic triaxial and torsional sheartests on isotropically consolidated specimens of Toyourasand. Although their number of loading cycles wasparameters that affect the behavior of sand under cyclicloading. Change of volurnetric strain in different stageslimited, a unique relationship between the stress ratio andthe dilatancy ratio (strain increment ratio) was observedin each testing method irrespective of void ratio and stressof loading can be described by the stress-dilatancylevel.relationship, which relates the ratio of strain incrementsto stress ratio. Many stress-dilatancy relations have beenAs a part of a research program for the modeling ofsand behavior under cyclic loading and for a better understanding of the cyclic stress-dilatancy relationship,proposed so far for monotonic loading (Rowe, 1962;Roscoe et al., 1963; Oda, 1975 amon*･ others). Forseveral tests were performed on Toyoura sand in thetriaxial tests, Tatsuoka (1978) obtained a stress-dilatancypresent study. Significant volume change was generatedrelationship, which appears to be independent of theafter a large number of loading cycles. Effects of differentsample density, the initial fabric and the mean pressure.parameters such as density, anisotropic consolidation,confining pressure and change of shear strain amplit.udeAlthough the study of soil behavior under dynarnicloading is an important issue in geotechnical engineering,there have been few studies on stress-dilatancy relationsof sand under cyclic loading. Based on the results of aseries of simple shear tests, Nemat-Naser and Takahashiel984) suggested that the stress-dilatancy behavior maybe independent of sample density (at least when only afew cycles are involved). They also stated that theilatancy is affected by the K= o'",/a¥vhich is the ratio ofon cyclic stress-dilatancy relations were also studied.A Iarge number of cycles are applied to soil structuresduring most real dynamic loading cases such as earthquake loading. Effects of cyclic loading on differentparameters of sand under a large number of cycles wereinvestigated in this study in a more comprehensive waythan with a limited number of cycies.Results of this study on the experimental stress-Assistaut Professor. Civil Engineering Department, Iran University of Science and Technology.professor, Civil Engineering Department, The University of Tokyo.Manuscript was received for revie¥¥' on February 6, 2001 .Written discussions on t is paper should be submitted before September I , _'002 to the Japanese Geotechnical Society, Su_ ayama Bld*Kanda A 'aji-cho 2-23, Chiyoda-ku, Tokyo lol-0063, Japan.';,jUpon request the closing date may be extended one month.1054F, l06SHAHNAZARI AND TO¥¥,HATAdilatancy relationship can be used in modeling cycliccircumferential strain (det) are kept zero. Moreover thestress-dilatancy. Liquefaction modeling based onmeasured pore water pressure (CU tests) is not invertical stress was kept constant. Stress and strainuniversal use. This is because, in reality, seepage andconsolidation change the volume of sand. CD tests whilemode are shown in Fig. 1. Independent control of thecomponents in hollow specimens under simple shearmonitoring dilatancy are more useful because themeasured volume change together ¥vith 2-D (or 3-D)axial force, the outer cell pressure and the inner cellpressure can produce this mode of shearing by using acomputer program. The torsional shear strain rate wasseepage analysis can predict the excess pore pressure. Themaintained constant at dy=0.30/0/min through thel-degree of freedom observation in this study can becombined with a multi nonlinear-inelastic spring model(Towhata and Ishihara, 1985) to achieve a 2-D modeling.10ading cycles. In some tests the shear strain amplitudewas constant in all the cycles but in some others, shearstrain amplitude was variable.SHEAR APPARATUS AND TESTED SPECIMF,NSISOTROPIC COMPRESSION TESTSA hollow cylindrical torsion shear apparatus was usedin this study. In this apparatus the vertical load, the innerSince the present study aims at the volume change ofsand due to torsion shear, it is important to make aand the outer cell pressures and torsional shear werecorrection to membrane penetration and also volumedynamically applied to a specimen with 19.5 cm height aswell as 10 cm outer and 6 cm inner diameters. To ensurechange due to the change of confining pressure. in orderan accurate measurement of volume change of themeasured volume changes and also the relationship ofspecimen, an electronic balance was used in place of thedifferential pressure transducer used by Pradhan et al.volumetric strain (8,,.1) and mean effective principal stress(1986).hollow cylindrical specimens with different densities.to investigate effects of membrane penetration on(P'), isotropic compression tests were performed onToyoura sand ¥vas tested in the present study, whichSivathayalan and Vaid (1998) showed that themainly consists of quartz (around 900/0) and chertmembrane penetration effect on a hollow cylindrical(around 40/0). Its physical properties are G* = 2.65, Dso =specimen of granular soil can be assessed by Eq. (1):O. 16 mm, U* = I .46, e*** = 0.977 and e*i = O. 597 .Specimens were prepared by air-pluviation of air-driedsand particles. By changing the drop height and the rateof pluviation, specimens ¥vith different relative densitieswere prepared (220/0 to 760/0). Carbon dioxide (C02) andsubsequently de-aired ¥vater were percolated through aspecimen to achieve a high degree of saturation. Then asaturation backpressure of 100 kPa was applied to thespecimen to achieve saturation with a B-value exceeding0.98. The specimen was subsequently consolidated underdifferent confining pressures and different anisotropicconsolidation ratios (K=crfla , which af and cr areeffective radial and vertical stress).c* = [A V, - A Vj*(x2 - l)] / (A*i +A**)] (1)in which e* is the unit membrane penetration (volumechange due to membrane penetration per unit area). A V*and A Vi* are the recorded volume change of the specimenand the inner cell and X is the ratio between the outer andinner radii of the specimen, while A i and A * are thesurface areas of the specimen covered by the inner andouter membranes. This equation is valid for the case¥vhere identical pressures are applied to the inside andoutside of the cylindrical specimen.In order to investigate the effects of density onmembrane penetration, isotropic compression tests lvereperformed on specimens with different densities. TheseSHEARINC. PROCEDURESpecimens were sheared after consolidation under aIsotropic compression and sweliing testdrained cyclic torsional simple shear manner. The simple0.005shear deformation is defined as that in which theincrement of the radial strain (ds*) and theToyoura sand{o¥i: r'0.004v_!;'Fzt:so,003o::C, = Constants 'Tzrtibir-Po,'¥,t rt¥ d8t=0LYL Yrt1 tlr>¥Or zF:e'E2'59E'5" P' P'o/ ¥l8--h-- No.251 Or=37'1e:t,::o.oolol l0 , oyl indrioal speciElenFig. 1. Stress and strain components in simple sheaf mode '･-No.255 Drs56e/e- -* No.253 Ors76e,/.Average valuee):o ooorP'Q: )- - N0.2S4 Dr=24e/oe's$o 't3'56E " P'0.002t2*de so¥-e;50 150 300iOO200250Effective con ning pressur8 (kPa)Fig. 2. Effects of densrt,_, on membrane penetration3 51 *:;107C_YC_LIC STRESS-DILATANCY,,,;il!!ltests were performed with the same method ascalculated and listed in Table I , which were corrected forSiva:thayalan and Vaid (i998) suggested. Membranemembrane penetration.Results of this section are used to estimate themembrane penetration. However, it is not clear how thetorsional deformation affects the extent of membranepenetration for specimens was determined by using ther.;"results of these tests and Eq. (1). Figure 2 compares the;,membrane penetration for specimens with differentl.**adensities. Thickness of membrane in the present studywas 0.3 mm. Although the membrane penetration curvesin Fi :. '- changed with density, the limited number ofis;;I[etests makes it impossible to find a consistent relation foreffects of density. Therefore, an average of the membranepenetrarion curves for different densities was used in thislelr' *i.study.*The relationship between volumetric strain and mean",effective confining pressure for medium dense sandbefore and after membrane penetration correction arepenetration. In this study no effort was made to considerthese effects on membrane penetration, and Eq. (1) wasused for estimation of membrane penetration in simpleshear mode.CAI.CUl.ATION OF VOLUMETRIC STRAININCREMF,NT AND DILATANCY RATIOVolumetric strain increment ds .consists of a:ierchange measurement.onFor calculatin*' the coefficients of volume compressibility or s¥velling (m ), Eq. (2) ¥vas used;dilatancy component de9. induced by plastic shear strainincrement and the r'emainin*' component de,',.1 induced bythe change in P', the effective confining pressure. For agiven change of P', the value of de,'..1 was calculated byusing Eq. (2).In this paper the ratio of volumetric strain increment tom = ds 1 Id!og o P (2)(-de9. /dyP). Increment of plastic shear strain isof, *sholvn in Fig. 3. It is clearly seen that the membranepenetration correction is very important in a volumei,a!eofi,essonin which ds .i stands for an increment of volumetric strainthedue to change of effective confining' pressure (P'). Theicalvalues of n7calculated by Eq. (3):d yP = dy - dy' (3)for compression and swelling wereIn this equation, y* stands for the elastic component ofshear strain, which was evaluated by dividing the shear(1)o.766umerO 7G2menandNo'255 :calculated by fitting a mathematical equation (in the form:: e:v_iv¥ : l,O.7Gotheos ,oandL'5 O 756>andO, 754v ons !o.7581:caseO.752S ShlAfter membrane penet. correctionh' before membrane pef?et correction0,750i: lIsotropjc eonsolidation fToyourasandh 1ie02:sO'764Dro s::Ss e/o¥ i¥1'erestress increment by the maximum tangent shear modulus(G***) The value of G ** for each speclmen wasHo 764!IV,Theseplastic shear strain increment is called the dilatancy ratioo 200Effective oonfining pressure(kPa)of a hyperbolic equation) to the stress-strain curve ofeach cycle. The derivative of each equation at thebe*"inning of loadin*" or unloading is denoted by G .*.The dilatancy ratio can not be calculated directly fromshear strain (yP) and volumetric strain (e . ) due tofluctuation of the recorded data. This fluctuation isunavoidable during experimental investigation. Thedilatancy ratio ( - ds,d. /dyP) is strongly affected by thisfluctuation. Therefore to calculate the dilatancy ratio,volumetric strain (8 *f) was plotted against plastic shearstrain for all the cycles. A mathematical equation (in theform of a polynomial equation, c,d,1 =A + BFig. 3. Effects of membrane penetration correction on isotropicCoefficients of volume compressibilit .･ and swelling (m.*) in isotropic consolidation tests (The unit of P' is kPa)C_onining eo 'tl) = O 885pressure Dro 2 = 240/0(kPa) fPts:)'r-"IS eS¥vellin :ee ' = O.764 eo 2 = O.690Dro 2 = 560/0 Dre 2 = 760/0O . 005 3 lO.00424 O 00360O150300O.0041 10.00364O.00349O OO,-74l OO25O . 0043 ll ooO . 003_, O1 50O.00207O.O01333 oo(i) e0.2=vcnd rauo at effectrve con nmg pressure of 20 kPa ( O ' kgf/cm )'eo ' = O.837Dr0.2 = 380/0O.00693O 00556,-5Compression+unloading part of cycles (Fig. 4(a)). The derivative of thisconsolidation test resultsTabte 1.yP + B2(yP)B3(yP)3 + B4(yP)4) was fitted to the curve of each loading or00443O 003?_1 O.002800.00_ 63 O.00228O . OO-,OO O . OO i 74O.00386 O.003390.00261 0.00235O.O0188 0.00185O.OOI 21 O.OOI 1 9O.003 1 4O.OO'_21O.OO 1 8 ,_O.OOI 1 8 108SHAHN_ AZ,ARI AND TO¥¥rHATA1 oo32cl data3110th loa ing of No.159 j40C:,2,8CL!･:e',i 2.720P(QL 2.6u)E d SA +Blfe,B2(7' )' *BS T P f +B4(? F )$,C,,Palameter Vaiue'oE 24L,T:,A a9soee2.3B1C,J)512BB2).0475sB4.001 45CO-40-60";-80Y =t3.0 '/.21-20J::Orained cyelic simple sheaFAnisotropic cons. K=2.5p' ;8 kPase o.ooe312 2'o"',1,Polynomia] Regression2 2.52.0::::!eo: 2,9>;lT TkNo.16180Polynomia] fit of data3.0or..-1 oo-3 -2Pl stic torsional shear strain, V P (%)-11-32-2o-1213****Shear strain, Y (%),,*_O//Ae1l vol/n*20iAe 1410ut loading of No.169 IO.8L vol /n * 1l+ {306i204e5 1¥ 02P-ds p d/ d7 P s -BI -2B2T P - 3B:(72 - 4Bs(!i,c;?sLcaOCQOOL;co:).2-1c 'e)c,)u)e)CODrained cyelicsimpleshear l)4.Cl)Anisotropic cens. Ks2.5).63p' s98 kPar7 s:!:3.0o/p)8-1 O) 752o0.00 0.50 0.75Dilatancy ratio, -d8..Id/d Y P) 50 H),250,2510dilatancl.' relation for half of cl.'clecurve with respect to yP is the dilatancy ratio ( ds,i 1ldyP,.1¥eycle no.¥;oe!e' S ee;¥fori*teycf e-o 2-1 oand changes of shear strain amplitude on stiffness andin dilation.¥;e:ixs ;O., Rotation of line c) 75H).50].25 O.OO O 25o.50o.75-deYold/d Y 'stress-dilatancy relations were studied. In this section theresults of one test are discussed in detail as a control case.Results of other tests will be discussed in the followingsections on the effects of different parameters such as density, confinin*" pressure, etc. In this paper volumetricstrain is considered positive in compression and negative**; e: "e:t¥6sity, initial anisotropic consolidation, confining pressure,ef'!lLlne c)8･"f "/2..:/;/-. 7 5o.oBased on the results of different tests, the effects of den-.'1. '"4./'C1Line c-c tor40thcycleH)*4RESULTS OF TORSIONAl. SIMPI.F. SHF,AR TF,STS. .vo/ ; .,,1002e*6(ei e)11 Tl N0'16104= B - 2B2(yP) - 3B3(yP)2 - 4B4(yP)3). The relation between -ds, .1/dyP and the stress ratio (rz;/(T =torsiondilatancy relationship (Fig. 4(b)).d08oeshear stress/effective vertical stress) is called the stress-4 5321Volumetrie strain, LFig. 4. (a) Fitting mathematical relation to yP-ed.] diagram, (b) Stress-;if .T iNo-1 6 {-4Fig. 5. (a) Stress-strain curves of medium dense specimeu subjeeted tocl_'clic simple shear, (b) Volumetric strain of medium densespecimen subjected to c_vclic simple shear, (c) Stress-dilatancyrelationship for medium dense specimen subjected to cyclic simpleshearFigure 5(a) sho¥vs a stress-strain diagram for aspecimen with initial void ratio of 0.756 (relative densityof 580/e). Figures 5(b) and 5(c) reveal volumetric strainstiffness increased with the increasing number of cycles.The increment of the soil stiffness in the course of drainedand stress-dilatancy relations for this specimen. Thesefi_ ures indicate that volume contracted and the soilshearing is not only due to change of density. It is also iaffected by shearin>" in previous cycles. This point will be'E! iI109C_YC*LIC STRESS*DILATANCYf:discussed in the next section, which concerns effects ofo 8rfi ThNo 161density and shear history on cyclic behavior of sand.j Due ro the accumulation of volume change during 40, cycles, the void ratio of the specimen changed fr'om 0.756I to 0.658 (relative density from 580/0 to 84010). Aithough' the tested sand had both contractive and dilative behaviorj, within individual cycles, the incremental volume change; after the end of each cycle was contr'active. The rate ofvolume contraction decreased with the increasing number'of cycles (see Fig. 5(b) for example). In other words, the"'- volume contraction was remarkably larc"er than volume; dilation in early cycles. After a large number of cycles,g0.Go 4end of a complete cycle decreased and the volumecontraction was slightly larger than dilation.¥eee .02K) o ,o¥P)2D! ned cyelie si ?ple shear1 0tropie cens , P* 8 kPa)4eH].e.1"-o 8.?Se * Dre*d = O.858 * D,5T =the difference of volume contraction and dilation at thei,,4 /' /¥:( :84%: 3%).6 ) 2 O O 04 O.6O.2), 4-de d / dYP. . Ficaure 5(c) shows that the dilatancy ratio starts from a' hi*,_"her vaJuei.vhen the loading is reversed at a higher level! of stress ratio. For example the dilatancy ratio afterFi**. 6. Stress-dilatancy relationship of medium dense specimen duringinitial (vir',*in) and first cycle of loading"{ Ioading re¥'ersal in the first cycle at the stress ratio of 0.47was 0.44. In contrast, when loading was reversed at astress ratio of 0.78 in the 40th cycle, the dilatancy ratio'as about O.6. This figure also shows that after loading{ reversal, each stress-dilatancy curve starts from aj diagonal line (c-c), ¥vhich passes through the center of; coordinates. In other words, the diagonal iine c-cconnects the beginning of the stress-dilatancy curves of10ading and unloading of each cycle. Moreover when theloading continues after reversal, stress-dilatancy curvesof different cycles become closer to each other in theloading parts (in this paper the loading part is a part ofshearing in ¥vhich the shear stress and increment of shearstress ha¥'e the same sign, which means dT*r>0). It canalso be seen in this figure that the diagonal line c-c slightlydiscontinuity in the stress-dilatancy curve and it restartedfrom point 7.Another important point in Fig. 6 is that the stressdilatancy curve of 7-9 (reloadin*') did not pass throughpoint I . Therefore a stress-dilatancy relation of virginloading appears to be different from those relations in thefollowing cycles (see Fig. 5(c)).In order to examine the effects of confining pressure onstiffness and volume chan*'e of sand, difi:erent tests were- number of cycles ¥vill be discussed later with regards to- the effects of density and shear history.^ In general, the stress-dilatancy curve (see Fig. 5(c)) for; each cycle consists of two parallel segments of positivej slopes and t¥vo nearly vertical segments immediately afterstrain with three percent amplitude ¥¥'as applied tospecimens No. 171, No. 161 and No. 168 with an averagedensity of 580/0 and isotropic consolidation. InitialIoading reversals. The stress-dilatancy relationship of the{ following cycles is different from that in the first cycle.7(a) shows the stress-strain curves of these tests.j Stress-dilatancy relationships in the first cycle areI demonstrated in detail in Fig. 6. At the beginning of; shearing, the stress-dilatancy curve started from a-" ,=during cyclic simple shear). Since the torsional shearstress is mobilized in the horizontal plane, it is clear that anormalizin*" the shear stress by the vertical stress, thestress-strain diagrams of these specimens become similar.Fi**ure 7(b) reveals the normalized stress-strain diagramsof these specimens. It can be seen in this figure that thefaric .'mple ;, Point 3, the value ofds,4.1ldyP changed discontinuously'; and remained positive (point 4). Immediately afterj loading reversal, the dilatancy ratio took the maximum; lyalue. After loading reversal soil exhibited a contractive;behavior, rn the follo¥ving cycles, the soil demonstrated ainedsirnilar behavior. The diiatancy ratio was zero at points 5cles,alsoSpecimens ¥vith a higher initial confining pressure andconsequently a higher value of vertical stress had higherstrength in this figure (vertical stress was kept constant; ratio became zero. After point 2, it took a positive value.iensei}; and 8. After loading reversal at point 6, there was a;isotropic confining pressures for these specimens beforeshearing ¥vere 53, 98 and 184 kPa, respectively. Figurehi_ :her value of normal stress on this plane leads to aj This point is equivalent ¥vith the phase transformationPoint, 1 'hich ¥vas introduced for undrained loading byIshihara (i996). When the loading direction reversed atll beinitial mean confining pressures. Cyclic torsional shear{ negative value of dilatancy ratio, - de,ldyP (point I inj Fig. 6). ¥Vhen loading continued to point 2, the dilatancyed to{BEHAVIOR OF SANDperformed on specimens consolidated under different; For a large number of cycles this difference is remarkable.;F.FFECTS OF CONFINING PRF.SSURF. ON CYCLICrotates counterclockwise with the number of cycles.Change of the slope of the diagonal line c-c with the:{hi**her shear stress. Therefore, it seems that afternormalized stress-strain relationship of differentspecimens are almost identical for the same number of;cycles. Althou*"h the (T.*/(fL)-y relationships changes ¥viththe number of cycles, (7 is not so important in this figure.This fact can be seen clearly in Figs. 7(c) and 7(d). Thesefigures compare the stress-strain curves of specimens inthe fifth cycle of shearing before and after normaliz,in_"._.; . . j*=**;SHAHNAZARI AND TOl 'HATAllO*101 6020H:}-N0.171 Dr s57% P'=53 cr':Hhlo.17 Or s571;, p's53 o' ::se- =No.161 Drss'rts58% P': e8 c'*s98e'No.168 Dr$:sr's58% P*=1B4 cr'*s e4o.8-c N0.16e Dr s58,X, P*=1840'¥80Pc,,a,P';o '-89u)-{ 20oHH:]2,,,7:col'I:G)e),,,o.Q1"3 kPa-40'T:,Il4JoL*'(1)02coq,il,!;1 84!(1704ui40:io eecl:O_x:'53-4No.1S1 Or s58% P' 8 cr'==981'].4e)N5H).6oHD.8P's o '*:sl35 kPaZ-1 eo3 2Isetroplc conso!idation35 cycles I :s:s 3'o-1 oO13 2- -1212Torsion sheer strain, Y (%)Torsion shear strain, Y (%);{,;'*;10160e 120, .C,:cH:HYo.171 Orss, rts579,'* P' 53 e'*s53No.151 Ort *rts58e/* P' ::98 (;'tsg808ONo.1S8 Or$$ t 5B% P' =184 o'.::184e. 40c,c':clee)OnttvOeo 1208 e'*s98ii06Po.4u)a)o 2:,Fifth cyele,,)Lcea):o)::r/) _80$58% P'i.'1u;Pe)H o^161 Dr;P' s53 c,'* 3)No,168 Dr$t '::5e% p* =184 o**=1e4¥/ 80lo.171 Or 5T;.10/r!Fifth cyc:eo oH) 2).4)N.c:lOH _160oZo-3 -2Torsion shear strain,Y (%)l)6l8-1 o2-32Torsion shear strain, Y (%)-11Fig. ?. (a) Effects of confinin"* pressure on stress-strain diagrams, (b) Effects of confining pressure on normalized stress-strain diagrams, (c) Effects {;of confining pressure on stress-strain diagrams (fifth cycle), (d) Effects of confining pressure on norma ized stress-strain diagrams (fifth cycle)specimens with different initial anisotropic confiningconcluded that the initial confining pressure did not affectthe stress-dilatancy remarkably after initial loading.In order to verify this conclusion on effects of confiningpressures. However, after normalizing the shear stress bypressure, some other tests were performed on loosevertical effective stress the stress-strain curves are almostspecimens with a relative density of 230/0 . Figures 10(a)the shear stress by effective vertical stress. It can be seenthat the stress-strain curves are completely different foridentical.and 10(b) compare the stress-dilatancy relationship ofFigure 8(a) compares the stress-dilatancy diagrams inthese specimens in the first and tenth cycle of shearing.the first cycle of shearing for these tests. It can be seen inExcept for the initial loading, the stress-dilatancyrelationship of these specimens was almost identical,this figure that the difference of stress-dilatancyrelationship for different specimens occurs mainly at thebeginning of the first loading and afterwards, there is noverifying that the stress-dilatancy relationship after initialremarkable difference. Comparison of stress-dilatancypressure.dia*'rams for the tenth cycle of shearing is shown in Fig.8(b). This figure demonstrates that the stress-dilatancydiagrams were almost identical when shearing continued.In other words the initial confining pressure did not haveany remarkable effect on the stress-dilatancy relationshipliloading ¥vas nearly independent of initial confiningEFFECTS OF INITIAL ANISOTROPICCONSOLIDATION ON CYCl,IC BEHAVIOUR OFSANDexcept at the beginnin*' of first loading. This fact can alsoDifferent tests were performed to investigate the effectsbe seen in Fig. 9 which shows the developed volumeof initial anisotropic consolidation on strength and stress-change in the first, second, fifth and tenth cycle ofdilatancy relations of sand. Tests No. 165, No. 164 andshearin*'. In this figure the volume chan_g:es of specimens¥vith different initial confinin*' pressures ¥vere almost theNo. 172 were performed under initial anisotropicsame except for the initial ioadin*'. Therefore, it can beand the mean consolidation pressure of 98 kPa. Theconsolidation stress ratios (K= (7/ Ia ) of I .6, 1.0 and O.6,{i lllCYCLIC_ STRESS-DILATANCYo#-No 171 OrH 1 D･1 S10.8e-No.1G805i,79,'*8%8%DrDr10P' 3 e ' ;3p' 8 (; 'o.8p'=1e4 o **=1 B4¥ ¥e ereInitiai loading Fir$t eycle0.6¥e: ;o ¥. e:'" jl0402Pio o,O-o 2e¥PNu)a)!-0.4)*No.168Dr* ,s=23'1.;e7 c,' nj7P =98e' ;8P s:135 e ' =135=": ¥e: o e:¥¥¥ce ", . . ..=! {( 'o.oHD2!_!' ' "' il' _ ').4'Cl)24P/o PtOFsmjs22e/.o.24)' -1:i;N0.174 DrHNo.16104'e¥Hc J8c .H)6-o.el' ;r":u::n^!o -se;F"nP_!e^vlsil i hrt e.atai,ir", ,[ir]'" ; "ii_ ･'.. :';: . :'.',,, ,','.;) 8' t'- Oi,'isotroplc consolidation)^8i-1) 25 0.00 O.25).50-o 75o 507 :s:#3'O %Initial loading+fiFst oyc[eoo 75) 75).25-d8vold O.,25/ dYPH),50o 500.00-d8void / dYPo 75*'10**,,;08li08:H o.171 Or- No. 1 51 DrNo.168 Or7%P's53 (,' ;310:hNo.174 Or8%8p*=1 e4 eF ' =1 B4O^8H o.16iN0.168;8% P' 8 a 'r10- eycl:e{04i¥e/';o ¥2¥¥sj'lO.6t) O.OooPN -o 2¥tlP__!･･")43%35 o '73c'=135;oTenul cyc ef, 2.!.,!..).4!-o 6sl-o 8-? c-o 75 H), 25-dE*dOI d25 0.50 O.75o oo) 50=ectshL!P'=¥¥,,,',1'e')" i02¥JT24% P' 7 cr*=22% P'::98 o '040.2erTOrDr/ j'rat_ t_:irn<0jioe;;mo :e'").6)8 c.-1 O50).75H) H),25Od8.,doo / 0.250.50 o 75dYP,relationship of medium dense specimen (initial loading and firstFig. 10. (a) Effects of iuitial confining pressure on stress-dilatanc _'relationship of loose specimen (initial loading and first cycle), (b)e _'cle), (b) F,ffects of initial confining pressure on stress-dilatancv.'Effects of initial confining pressure on stress-dilatancy relationshiprelationship of medium dense specimen (tenth c,_'cle).of loose spe(:imen (tenth cycfe)Fig. 8. (a) Effects of initiai confining pressure cn stress-dilatanc,.')fectlln)oser !nFtrai::: ltosdln9*O ( a)rT: T::T:lIst eyc err;:T:, 1:l21ld eyc eTi:;:5ul eye erT:T l1 oth eyeleaverage initial relative density of these specimens was 23o/o. Figures 1 1(a) and 1 1(b) show the change of the radialstress of these specimens durin*' the first and thefollowing cycles. Since shearing was conducted in asimple shear mode, the outer and inner cell pressures3J) of2l ng .changed to keep the lateral strain equal to z,ero. It can beseen in Fig. 11(a) that for the specimen ¥vith initial K= ltncyical,oitlal(No. 164) the value of radial stress reduced quickly from98 kPa to about 62 kPa during the initiai loading andf ingthen fiuctuated around this level (Fig. 11(b)). In-2 'subsequent cycles the average level of the radial stress-3O.o O 4F08 oo 0408 0.0 0.4 O.8 OODT I 58- ne. 171r ctsress-sotrelc CensalldationP1ekPa,ne･1S1,P'Fig. 9. Effects of initial confiningandmedium dense specimenopic-i 0.6,iTheO.4 O.8 OO 04 03Volumet,ic strain. s d ( )1,pi8kPs, Apressureloading. At the initial stage of shearing, the radial stressof a specimen with K= 1.6 (No. 165) decreased sharplyT= $ 3no 1 e9, p'slightly increased. Anisotropically consolidatedspecimens showed a similar behavior under cyclic=184kPaon volume change offrom 112 kPa to 47 kPa. For a specimen with K=0.6(No. 172), conversely the radial stress increased from 80kPa to 84 kPa. In the subsequent cycles, the radial stressfiuctuated with a gradual increase of its average level.Pradhan et al. (1989) also observed this behavior. As isshown in Fig. 1 1(b), after the substantial chang'e of stress+,;i 1:'?jii'; "' L, ･ !!' ;;'* S ' SHAHNAZARI AND TOll2HATA.- No., 65* or : 24e/., K .1 201 40A No.1e4. DrFssl.6, a ';10 kPa=229 , K:* t"=1.0, CF ':s98 kPa!No.Is5, K*:s's=1^S ,o '==70 kPaoNo 172, DrFtv's239t, l($s'IsO.6, e '*:sl34 kPa- a.164, K$srt:;1.0 *e ';9B kPac-No.172* KFsstsO e *,1 's*134 kPa1 30/1 20,QcL 110J(10090t)80o;L'start 0Test K:; e '* /e '* after first cyclerN0'165n0165startrl of n0172{ I . 'r _ofi'J v r? _ O ( !hastartoti,aOCAn J¥/¥--i'l"-n5040cJ,_.=-.- :'-' ;-<='-__'-_ -- ;_' : :-/a: ; fi :::2j-;c,,f(os:Drained cyclic siFnple shearo'J/i f '"55 -80p,= g8kPa20 cycles ToH-1 20First cyclefnitiai load.'_'1'f'LL Os: -40'!':',,)e)l '¥4 J- =u)a)Na'l72eo:540(,;.,'r-'-'( j'(_PNa'le470U)o'65o G3o'e3nol5480CL3.0 %_3 -2 -1 O 1 2 3*Torsional shear strain, Y (%)" i1301 20""' r;o* 110Test I 1,'*lc,' aftsTfiTstcycleO G5nole5O JS3nol 54-No.155* XF:"rfl G ,:T 'sss70 kPa- H o.1e4, Ks 1 l.O ,o ':s98 kPaH o.1 12, KFs't 0,e tc"s:sl 34 kPan0172Si]' "" ="ea'oO, Seo.8c:; I 0.165* Drss't::24, X$:s"' 1.6, e'sf10No.,1S4, Or, ,s229 * Kstss"si-e -No.1 72, Drl s,rt: 23}kPaO, e '*g98 kPa, XF: tse 6* e '*s:134 kPa,s,x."+.*I]= }1' }"{ oo' ,i * I=.=,.*1'*"'i,*t"'l"'i*{"' '" **, A.'ijlliil:= , :!:Iiil:iT;IIII} I{I80,*^ "*.'+..: =' :" '1 "I t}70CQ!02i'oou)i'C,, 7) 2)Illll IIIi! I5040)*_ r'1:so'SfXo,4cne)4'U)o.6Put) 90u,o)¥{]i! IfJ:co1:,(DN15o 5 1 o1205Cycle no302sFig. 11. (a) Change of radial stress for specimens with different initialEIoZ) 4;;rH).6)8-1 oDrained cyellc simple shearp ' = g8KPa20 eycles T s 3.0 %-3 -2 -1 o 1 2 3Torsiona[ shear strain' Y (%)anisotropic stress states under c,.'clic simple shear (initial to rdingand first cvcle), (b) Change of radial stress for specimens withlid t'on on stress-strainFig' ::rve:a:fEl eo::ss::Idni:lb;l S:scot:rooF::1: oanlsaonis[oat:opicconsolidatioudifferent initial snisotropic stress states subjected to cyclic simpleshearon normalized stress-strain curves of loose sandilratio (K=(7f la ) during the initial loading, its avera_ evalue ¥vas about 0.65 for all specimens independent of theinitial anisotropic stress state.Figure 12(a) illustrates the stress-strain diagrams ofspecimens. The stiffness of specimen No. 172 was hi*･herthan that of others, because of the higher value of normalstress on the horizontal piane. After normalization ofshear stresses by vertical stresses, the stress-strain curvesin Fig. 12(b) became almost identical (Shahnazari andtenth cycle of shearing are compared in Fi**. 14. It can beseen that the stress-dilatancy relationship of thesespecimens are nearly identical, suggesting that the initialanisotropic consolidation did not have any remarkableeffect on the stress-dilatancy relationship of sand after theinitial stage of loading. A comparison of the volumechange of specimens during 20 cycies is illustrated in Fig.15. It can be seen that the difference bet¥veen thesevolume changes after 20 cycles was srnall. This differenceTowhata, 2000). This implies that the vertical stress onthe horizontal plane strongly affects the torsional shearoccurred mainly during the first loading. For example,the differences of volume changes for specimen No. 165and No. 164 after initial loading and at the end of '-Ostiffness of sand.cycles, which are denoted by A***** and ll**d respectively,Figure 1 3(a) demonstrates the stress-dilatancyrelationship of specimens in the first cycle of loadin*'. Thestress-dilatancy relationship in initial stages of loadingwas affected by the initial anisotropic stress state.Ho 'ever, it seems that ¥vhen shearing continued thiseffect decreased. A comparison of volume change in thefirst cycle of shearin_-' in Fig. 13(b) also indicates that theeffects of initial anisotropic stress state on the volumechange were important mainly durin_ the initial loading.The stress-dilatanc.v diagrams of these specimens in the::::,,are nearly identical. Therefore, it can be said that thevolume change of sand is independent of the initialanisotropic stress state except during the initial stage ofIn order to investi**ate the effects of initial anisotroplcconsolidation on the cyclic behavior of sand some othertests were performed on specimens with the averageinitial relative density of 570/0 (No. 169, No. 161 and No.::.::,:.167). Each specimen was consolidated ¥vith a greater***g i '{113CYCLIC STRESS-DILATANCY1 .O1 .o-{h･No.1e5. Dr$: s'l=24%, K$so.4.tl '/ ':1f' ';;rrE- "'Rrsteycle ""i/l 7f /ol:7 ::1:;i'!jL! '1 Ii!If! P'fl'fP!1'' .1 ! ItliHD･2HD*4-o 6' lc-o 8-1 o.(¥ ;c) o.o¥t5-O^8¥10 eycle04-o 4i's23s ' K' s c e' c' tiB134 kPH c02e oo¥P )2*'10H o 172' Dr'o e" l"'!/' / _j ' _02:H otl55t Dr's 'F24 ' K'# ' l sl 0: t:s7o kParNo l64' Dr' 1 ts22 ' x' t:;110"' I:$ ee kPao.8(v'r9in) eadin9: ¥e: D¥¥slee: rl'"'*i'c- No.172* Dr., Is23%. K$ lse.e, (; '*sla4 kPao.'.*l 1 5, CF '$s 70 kPa- H Io,1e4, Drt t 22%* K srtsl .O* CF '*s98 kPao-O.50H),25-o. 7 5O,OO O,50 O,15O.25c .--{ o.50 l .250.000.25 0.50 O. 75-devo d / df75-dB+0:d / dY P;{;Fig, 14. F,ffects of initial anisotropic consolida:tion on stress dilatancyS5, ors l:t249 t K5sst'=1"51 o 1;t::70 kPai - rNa-'-'--No'l1e4, orEsrts22%, X':$rt=1^Of 'T tEseB kP54l -;3i,_lF¥/ 2*,:,1'u,O!L,:!Oe,**/_j_/r"v-c:Ijl lc::1'h If' /rh!)l2+ss32' o"tJr'¥! i fi]ins!::P:!clie simple sheaF/:o-1-2-3// lHO _3A eT,dA startrlJrr15EOrelationship of hoose sand (tenth cycle)'r-Nol72 Or s23 K$:: rtsOGe$s5134kPa.,532; ' i+' i¥ i'l i +; L*'i Iti' L'/ : ¥'¥it}}!1 !>-' :}';/:+1 l' '1*i"I ' ** = '*::j/ V 'i/1 !1!)i!'1i)1!1;!il):J!!':i)1)li li'ce0.0 1 .O 2.0 2 50515Volumetnc stra n 8.,t ( )c'Dx:9' r ' r rnrlrr'rl i' '!i)i==! 't='<il= l*'*"o1cn2c:3o;1 SLJj ! ,] flj i!"'1;i'!!_ /L'-4l 1 : : !,,)!linFig. 13. ( ) Effects of initial anisotropic consolidation on stress-'ondilatanc . ralationship of loose sand durin"* initial and first cl_'cle ofloading, (b) Effects of initiaE anisotropic consolidation on volumechange of loose sand during initial and first cycle of loadingHo;il;iiil) ".*ol"i, il ･=- .-2-3beeserange of anisotropic stress state than in previous figures.[ial IFigures 16(a), 16(b) and 16(c) illustrate the stress-bledilatancy relationship of these specimens in the first, fifththeand tenth cycle of shearing. These fi*･ures also indicatethat the stress-dilatancy relations of sand becameme-1"*independent of the initial anisotropic consolidation afterlesethe initial sta*'e of loading.nceThe results of this section su_ :gest that the effects ofple,initial anisotropic consolidation appeared mainly at theinitial stages of shearing. After the initial stage ofshearing, anisotropically and isotropically consolidated16520specimens had almost identical stress-dilatancyely,relationshi ps .theirialBesides the initial anisotropic stress state and its changee ofin inltial stages of shearing, the fabric anisotropy thatO 1 2 Volumetrio3 4 5 6strain,7 8e+.Id9 10( ) 11 12Fig. 15. Effects of anisotropic consolidatio l on volumetric strai iunder cyclic ioading (20 cycles)the initial loading may be considered as factors whichaffect the stress-dilatancy relationship of isotropically oranisotropically consolidated specimens in initial sta_ es ofshearing.EFFECTS OF DENSITY AND SHEAR HISTORY ONCYCLIC BEHAVIOUR OF SANDopicpreparation techniques can affect the behavior of sand)thernlainly in the initial stages of shearing. Ho¥vever, in thefollo¥ving stages, initial fabric anisotropy diminishes dueWhen a soil specimen is subjected to cyclic loading, itsdensity increases due to shear deformations. This changeaffects the stress-strain and volume chan*'e behavior ofsoil in the following stages of shearing. During cyclicshear, besides the effects of density, shear history alsoto shear deformations. Therefore, the initial fabricaffects the behavior of sand. These effects are due to sheararises in laboratory specimens from the sample:ra eNo.eateri,anisotropy and change of anisotropic stress state duringdeformations in previous sta*･es of shearing. Shear;,i ;"'ill4SHAHNAZ,ARl AND TO1 1HATAiN0'169' Dr s57%' K ' s2'5";'108049 kPaNo'l64' or*= 2-No 151 ' Drsssrts58'x" KFiprt 1'or a':s9B kPa !;'108Initial loadin9 tirst cyele [r'i !0.6o j""'!rf:"r-!/?'-r": Q¥ee /1'1 :::qo ¥ :!'_ _ _"i/'*1:::::e *:'0.4"(1e : ¥ $ " 1!11/o.2;¥- -o 2PNHD.4j"6).8T__J!40･ ･-P 20(ie)IIc,)iir// !lrr]ljl'' Ofl'(1:;ju,c' :40=_4_n'ngf{ ;;elie sir7lple shear l_!!h : -*i{ !!ou)Lo -50-i1_ -' ; ;; ' !s7 [. ^ rvIf!oa!n 03iics:menP: ' sh pekPsta I fhle-80-1 o-3).SO ) 25O 09 9.25 0.50 O 75-dE*,d / d7P), 75--i;ir/ : --La) -20/f-No 16e ":or' "=7i;i f J) jt 'r_'ifc:,CL_1'ANo 162' Drs* 8'/*No'l61 ' or*= ;8""(,,;f ' je 0,0!{60-e-No'l 67' ofetpl: 7 ie'KFl ss0'3' at::sl84kPa-1 O-2Torsionai shear stra[n,Y ( )2 3*Effects of density on stress-strain curves of sandFig. 17(a).*: -No.159, Dr$tsrts5le.!c' K,t"I::2.S, o '.: 49 kP10- -ND.151, Dr*s ' 5B%, K*ssrl 1 .o, e '=s98 kP- N0.157* Dr 4T9 ,, K . 0'3*o'si84kPa (S e¥･･ "i}+ c0.8r;rhFifth cyele06/4i¥e el/':}je )r; ;2i0.2ic) o.o¥Pi¥3¥e: io(¥ ; ¥ (1' cr I jo.4I.:.o 2' ics:mo:: 'sph =_ag'8tkeps:iIL-a,/ Eiil' !noc:f!?' fll/G')4:c,)-1f/::HD6ompie shear.8eep, = SekPac.7-1 o50 0,25 O.50 O,75-0.25-o. 7 52/ohs3*o %j¥ c:i1,/f' i/" = - Na'le4'or=22%H - N0'162* Dr'= 8 t-3-No'lG1'Dr;8%- No Is5' or =759O_OO-4-dE , d / d-o.52 O 3.50.5 1 o I .50.02.53.0VolvmetHo strajn, 8v*i (%)--"'11"""I'NoJe9' Dr'#rt 57S4' K'$s" 2 5' CF tts49 kPa101 'tNo'i61 ' Drt: It 5Be/st t($ :srt :1Effects of densitr.' on volume cbange of sandFig. 17(b).o' e ': 98 kPaY"'<) No'hl67' Drt ls57%' Ks'stls013"' I:::1e4kPa o e¥e / i'1 c08P'flJ jth cycie ¥eh''!1P'io. e'c¥5; JycieI ¥¥/'e ¥ ¥¥¥ 1e e o ro1004Na.1e4, Dr02i08- {1- - N0.1S2, Droe- h No. 61, Or-e- Na.1Ge, Dr2%8%Line e'e tor leose sand 't 'il7¥ ':!'' "f 1;8%=75%it) o o¥O. 4) 2!ILJ'P '!!1 f"P'Iff L ! r471;4'; tl/e¥ O, 2/P- OOo).6-o 8C /-1 .o) 75, ' 1J1'h L;-O 50 O,OO O.7525O 25O 501 :L -0.2c ,c,'T / " i'/ I ',J,G;)4L'fC"' "I"f "' !f / f / /). 6-de+.rd / dyP/ ! " Une eT'c for der'se::_ dto delsii..).8ISi:1Rot tlen ofdia90na Ilne e'c dUe to de sityFig, 16. (a) Effects of initial anisotropic consolidation on stressdilatancy of medium dense sand (initial loading and first cv. cle), (b)-1 o).75) 25O OOO.25o.500.75Dilatanoy ratio, -dg*Id/dYFEffect of initial anisotropic consolidation on stress-dilatancv.' ofmedium dense sand (fifth e 'cle), (c) Effects of initial anisotropicconsolidation on stress-dilatancy of medium dense sand (tenth).50Fig. 17(c).F,ffects of densitv., on stress-dilatancy relation of sandcycle)**;i=L:s･ 115C_YC L,1 C_ STRESS*DILATANCY; .history can be studied in terms of the number of cycles,i{1o.8accumulated shear energy, cumulative shear strain*0increment and/or any combination of these parameters.The number of cycles is used as an index for shear history+in this study.IIn order to investigate the effects of density and shearhistory on the cyclic behavior of sand, several tests wereperformed on specimens ¥¥'ith different initial densities ofi22, 38, 58 and 75 percent. Comparison of results at theo 4t) 02¥P- OOo: 5CQ(,,)2,,,beginning and also at different sta*"es of loadin*･ revealsthe effects of density and shear history and theircombination.Specimens ¥vere sheared under a constant strainamplitude of three percent. The shear history effect isminimum in the first cycle of shearing and increases withi*{cycles. When the effects of density are studied, data fromthe first cycle is employed, because the history effect isilnd.4) 6-o 8H).75H:] 50 -O 25 O.500.75O.250.00Dilatancy ratb, - e+.Id/dyPFig. 18. Effects of density on stress-dilatancy of sandnegligible in this cycle. Strictly speakin*･, the experienceof the first cycle of loadin*･ generates the history effects inthe specimen during this cycle. This is ho¥vever ignored inthe present discussion on the first cycle.Figure 17(a) examines the stress-strain curves of thesespecimens in the first cycle. It is evident that the stiffnessIlll Iof dense sand is greater than that of loose sand. Fi**ure17(b) sho¥vs the volumetric str'ain of these specimens inthe first cycle of loading. It can be seen that the loosespecimen (No. 164) vas contractive at all stages of thefirst cycle. Dense specimen No. 166 ¥vas contractive onlyat a lo¥ver magnitude of shear stress or stress ratio. Intkeps:sg8kPaz_ ="'//a 3-5mdNo 164¥ : 11 ¥¥oe4 0'6G o iB 0'70 0'72 i 0'74 0'7e 0'78 0'80 0'82: o'B4 o'B6 o'8B O906cldes :- (j((((r(j(((!ijr ¥lri30_:lf(1' 'T'j' 11 Dri_rted5impsatropesh:ar?,_ ::f11lilt(e conso: :";'elp ; es kPa" o'o15) 30No I G2¥ ¥¥r¥064 o'G6 o'eB 0'70 o'72 ;074 o'7s 078 080 082: 0'84 08G 0'88 o'90: 3 ')":'esi ::dense sand the increment of residual contractive3()Figure 17(c) sho¥vs the stress-dilatancy relationship of*15 p ':9akPa3 J)1 n5100se sand.:L Io o tsatropccensoFor all the loose and dense specimens there was a residualpositive ¥'olume chan_ge after completion of a cycle. Forvolumetric strain after each cycle ¥vas smaller than for9 ele!es :4j lht_1 5 DrEined simp e shearhigher values of stress ratio, ho¥vever, it became dilative.'-rl;SrOO.5tIt I¥':Di:_nsj/ simpleshserIsotlropic eonsilP =9s kPNo I G1O'G4 O'e5 0'58 070 O'72 : O'74 O'^7e 078 O'80 082 O 84 0'85 O'88 O'90z : : :VOid RatioFig. 19. Effects of shear history on volume change of sandthese specimens in the first cycle of shearin*". The startingpoint of the stress-dilatancy relationship ¥vas stronglyaffected by density. For denser specimens it started at alower value of negative dilatancy ratio, vhich means a' .':)*d ' ･ ,7)¥.:.smaller extent of contraction. Besides the startin*･ point,the stress-dilatancy diagrams were different in otherparts. It can be seen that for denser sand the diagonal linec-ch ltp';l1'as steeper (counterclockwise rotation with the8kPao 0'75This means that a specimen with shear history had asmaller volume change per cycle than a specimen withoutEffects of shear history can be separately studied bycornparison of test results for specimens ¥vith differentinitial densities at the same current void ratio. Fig:ure 19i!_**For a similar change of void ratio, specimen No. 162 ¥vithsix previous cycles needed five cycles. Nine cycles ¥vereapplied to specimen No. 162 with eleven previous cycles.Fi**ure 18 compares the stress-dilatancy relations forspecimens ¥vith different densities in the first cycle ofshearing under a reduced shear strain amplitude of onesand .;1 of sandneeded a different number of cycles. Three cycles ¥vereapplied to specimen No, 161 without any shear history.increase of relative density).percent. This figure reveals similar effects of density onstress-dilatancy relationships, which are a smaller valueof negati¥'e dilatancy ratio and steeper line c-c for denser;: .ea!'s..tvoid ratio from section M-M to N-N, each specimenshear history. This difference is clear in Fi** 20(a), ¥vhichcompares the volume chan*･es just after section M-M.Increase of stiffness (hardening) only due to shearhistory is shown in Fig. 20(b). Specimens in this figurehad identical current void ratios but different shearhistories. Since the constant shear strain amplitude wasthe same for specimens, shear stress amplitude is arepresentative parameter for the stiffness. The shearstress amplitude of specimen No. 161 Ivithout sheareontpares the volumetric strain of three specimens at thesanle current void ratio. At the section M-M, all threehistory lvas about 60 kPa. Shear stress amplitude was 66specirnens had the same void ratio of 0.756. Under thesanle amplitude of shear strain and identical change of68 kPa for specimen no, 164 in the twelfth cycle. Thus theincreasing rate of stiffness ¥vas greater in initial cycleskPa for specimen No. 162 in the seventh cycle ¥vhile it ¥vas 'j.S}{AHNAZARI AND TO¥ 'HATA116(shorter shear history). In contrast after a larger number {N0.164, i2t cycle;3iT7.No.1 5'!2of cycles (longer shear history) t.his rate became smaller. ;T:h eyeleFor example, in Fig. 20(b) shear stress amplitudeNe'l61, 1't eycle {1i{.Figure 20(c) compares the stress-dilatancy relations for ;these tests. It is clear in this figure that shear history j:c,,o!o:affected the stress-dilatancy relations. It seems that, ;-1:similar to the case of soil stiffness (shear stress ;oohincreased about 6 kPa after six more cycles (No. 161 to 'jNo. 162). The increase of shear stress amplitude for the {later five cycles was only 2 kPa (No. 162 to No. 164). ";amplitude), for initial cycles the effects of shear history jwere greater.This effect decr'eased after a large number of jcycles. For example, in this figure difference of stress- {,-2Pls98 kPaes0'756-3o 7 9 8 o 9 1.0O.O O 1 O.2 O.3 O.4 O 5 O eAe old (%)dilatancy relations is greater for specimens No. 161 to ;No. 162 (initial 6 cycles) than for specimens No. 162 to iNo. 164 (following 5 cycles). It can be seen that diagonal {Effects of shear histor_v on volume chwge of medium denseFig. 20(a).line c-c rotates counterclockwise due to shear history, jwhich is similar to the effects ofdensity (Fig.17c). Besides jsail!dthe rotation of line c-c, when shearing continued, the idirection of stress-dilatancy curves slightly changed in jrjjL;: ;:':'1T'{';::::':;, :" .__.___1"':i= "'1'No.1G4, 12t't cycle80¥,.L:"s'::J60c(JNo 152, 7e' cycl40Pgraph in loading parts. When these changes of stress- ;zodilatancy relationship combine with the effects of shear jc,;c,,e,ce)sv,::history on stress-strain curves, smaller volume ;ocontraction is generated for sand-20o-40effects on the volume change of sand under one-percent {shear strain amplitude. Specimens had different initial IN0.161, 1*t eycie-50void ratios but at the section M-M, void ratios ¥1*ere ;-80-2 Torsion-1 shear Ostrain, Y (Ek)-31100'8 j::i2 3Increase of stiffness (hardeniv,g) due to shear historl.'Fig. 20(b).Line c4 for 15t cyole: ;:L;ceyyyc!::ei: f'o_rl2 lcyc!: 'F'> :'i;' "' ' ' ' - No e'$' 12 cyclee¥PcF,g0'6'r li::,,,fshrinka9e in laadi::::/; :/i/::: //:i::::;:/::;:'l jj04:. _ _ T:1';;; _ _ ::(:; 111.:::: 7'! t0'2O'ON':'161 f cyete i: :.. :' Is) ///1tilf I ; ""!'1 !f4 ,t;'' ii!/;' ot:stres' "dilatancy'r' '// ' shrinka9eH)'2l/"c,,(,,o)'4(D)'61e! l $: /:e¥s;;r:I/ diagra!11 in toad n9 part {!/1/t/ '" '/'/- ;¥;oSS'jlf:;::1;ii"'; ! *?/ !' '/ /-e,8 ' " '-1 Ovith shear history. ;Figure 21 sho¥vs another example of shear history ;os,10ading parts (the loading part is where, dr*r>0). By thisslight changae, the curve for a larger number of cy. cles +came inside, resulting in more dilative behavior. In this jpaper this behavior is called shrinka_g:e of stress-dilatancy jRotatian et dia9anaPI ::9e kPa: eso'75enne c-G due to sh ar history) 6 H).4 ].20.0O 2Diiataney ratio, -deve d/d Y Po.4 o 6Fig. 20(c). Effects of sl]ear historl.' on stress-relationship of mediumdense sandequal. However, shear histories of specimens ¥vere jdifferent. In this section specimen No. 177 had no shearhistory (effect ofvirgin loading is neglected) but specimenNo. 188 had experienced 21 previous cycles. The stressdilatancy relationship for specimens at section M-M isshown in Fig. 22. Diagonal line c-c for specimen No. 188after 21 cycles was steeper than that for specimen No. 177jI;j}jwithout any previous cycle. In other words, Iine c-c ;rotated counterclockwise due to shear history, Ieadin_*," toless contraction after loading reversal. The other effect of !shear history on the stress-dilatancy relationship of jspecimen No. 188 was shrinkage in the loading part, jwhich means more dilation in this part of loading. jBased on the discussions in this section on the effects of jdensity and shear history on stress-dilatancy relationships ;of sand, it can be stated that increasing sand density and Ishear history has similar effects on stress-dilatancy !relationship. These effects were the counterclock¥vise }rotation of diagonal line c-c and shrinkage of the stress- ;dilatancy diagram in the loading part. Therefore, it is {expected that the combination of density and shear jhistory ¥vill have the same effects on stress-dilatancy Irelationships. Effects of this combination are sho¥vn in jFig. 23, which illustrates the stress-dilatancy relationships {for specimen No. 176 with initial relative density of 240/0 ;,and under cyclic shear strain of lo/o. The density of the jspecimen changed from 240/0 to 690/0 after 20 cycles. Itl,"LL;_ii ;,*117CYC_LIC STRESS-DILATANCY{;,5#deto{ll!11{Itf{((Ifll'!il liiN"IB8O. B*'{t'llt¥*t{o 6- ¥ '801 ,*50 i;5./. C:4 .' . . 1'-! o^o?11'f.2 .'1,1. ': *o.41 ' tso 62 o e4 o G6'-! l'or¥'. ** *.7' "" *"4 '1* "* "*' "*' '*+)ry' 11!i:=*{/**/*,., , io*!¥11 *w'l 5O G2 O S4 O.5G O.Sg O 70}*o.72 0.74 0.7G¥P])6.8-i_:$eShHnkageC. .k"I10iLine¥ O. 2;.this:;s*,.ancy)y){ress-U)' for 215tcyc!e .!¥/ j'/ / ll'' !/' I'*1 /:/ No'l.77'1$t cycle)4.6L rN_o 1::i2. 1.:iy.:ie)2hearShrinkage ot stress ffata;1cydia9ram in loadlng partrRotati:: of diagonal liRe c ; due to shear history tlO:ii_i.ned siFTxple shaer ,Isotropjc cansolldation)8lumep 598 kPa- .O)i;b-tor¥.' i4:rcent ;O,2 O 6H),2 O o0.4Dilatancy ratio, d8vold/d Y PFig. 22. Effeets of shear histon.' on stress-dilatanc_v relationship of08stress- ;SSlf,:j:,,:";:fiii+;:=+,:,!;:,,lNa '175 cycle no1. .･- _80::[-iivl is !o,6o. 188 !1o.4o. 177 ;10'20' C' [sh nks9e in 7i;:ne c"e I.part, }o,2e oo¥PH32¥,1 l:-*;:/, s;Lb ';YQr shrlnkagenodln9 part fC l)nship;,ity and iH:)'! IinEc ;forl' c cl l'.8f¥¥; ;::::J:s::. 75 O 25-o 50latanc)ckl¥*i .e ;stress' i}"e, rt iS;Fig. 24. C1_'clic stress-diiatancy relationships of medium dense sand(effects of density and shear history)changes of stress-dilatancy rclationships also reducedvolume contraction with the increasing number of cycles.Another example of the change of the stress-dilatancyrelationship due to both the change of density and shearhistory is demonstrated in Fig. 24 for a denser specimen.Relative density of the specimen changed from 56010 tocombined effects of density and shear history, diagonalline c-c rotated counterclock¥vise and shrinkage of the), 25 O.OO-de* ti/d Y PFig. 23. Stress-dilatanc_v relationships for loose0.50 o.75as ¥vell.In order to investigate the _ :eneral shape of stressdilatancy relationship under irregular loading, some testswere performed under simple and complicated irregularstrain amplitudes. To study the shape of the stress-Figure 25(a) shows the stress-strain curves for aspecimen subjected to irregular shear strain. In this test,strain amplitude in the first two initial cycles was t¥vopercent while in the following cycles it was reduced to firstone and then 0.5 percent. The stress-dilatancy relation ofthis specimen is sho¥vn in Fig. 25(b). The shape of thestress-dilatancy curves of this test follows the generaltrends of cyclic stress-dilatancy curves, explained earlier.sand under cyclicloading (effects of density and shear histon_')The diagonal line c-c can easily explain the shape of thestress-dilatancy curves for irregular shear strain. It can beseen in Fig. 25(b) that after loadin*' reversal, the stress-rl shear;ilatanc"dilatancy changes discontinuously and starts from ao l*n l{.stress-dilatancy relationships occurred in the loading partdilatancy relationship under irregular loading, results oftests with both irre*"ular shear stress and strain amplitudeare shown and discussed in this section.5; LYe).4rects of jo 75SHAPE OF THE STRESS-DILATANCY CIJRVESFOR IRRF,GULAR 1.0ADINGshear ;cirnen !ilip cf io.50medium dense sandvere !ling to ;Tect of ;),25 O.OO O.25800/0 under a large number of cycles. Due to thenitial :.lvere :) 50/::( :/1ij::i; :! !7S '/" f"/ r / " ' [i Othisune cH: for 160!s eycleShrinka9e in lo; din9 part-+'clesfor f: cvele* _ '" r.f:._04d inLine cne c eLine e*e for Ist cyc[e05;.then lc,ading part-dE* d/d Y P08ory,･'.' Rotation ofH).75) nal;iLoii onshiP;'/H:). 4ess-ides¥p /1: -o 78 o ao o 82 o.e4Effects of shear history on volume change of sandFig. 21'I es;iLf!'¥;o*'to;)2Void Ratiooryofn laading parte o. oat ,essShrinksge02'ts?'- o'ol toCycle no: ;'oheI10=: 2* *>d***,,ercan be seen that the stress-dilatancy relationship changedith cycles due to the combination of density and shearof 240, jhistory. Counterclockwise rotation of line c-c and alsov of tlycles. l{jshrinkage of the stress-dilatancy diagram in loading partsoccurred ¥vith the increasing number of cyc.les. Thesediagonal line. Therefore, the stress-dilatancy. curve afterreversal from smaller amplitudes is located inside of acurve after reversal from a larger amplitude. The slope ofdiagonal line c-c changes continuously with the chan*"e ofdensity and shear history. After each loadin_ : reversal the"{; SHAHNAZARI AND TO¥¥,HATA11S+:80r;7N0'156rr ;GOe,Q3gP 2040J.:2 cye es 7 s2,0 ,2 eycles T s 1 O3 eye]es? s:: 0.5 ,O- 40bNo. 1 55ieess = 0.738 , Ore#ti =e2e/.P 20!!J)u;o Ocou,L Oo!'coI'u)cL ' _20oco-20e)sJ:c,,*,,,'c,)c,"c: _40c2 -40Lo7e ::0.764 . Dr . ::56".'o0 7e3 . Dr sS5e D･738 .DrCUDrained eyelic simple shearIsotropic eons., P' =98 kPa50OTalned cyciic s mple shearsotrepis eQns. P' *98 kPsroL.Ho -6060- 80-2 1Oi-2 -11 21}Torsion shear strain, Y (u! Q)Torsion shear strain, Y (a70');Fig. 25(a).Stress-strain curves of sand under irregular el.'clic loadingFrg '6(a). Stress-strain curves of dense sand subjected to irregu]arc .'clic loading;{OO.B0604e¥rrh ; JNo.1 5G R A¥ -C.-.7e3 ,*O1*$=S3Dt= 55 3. 7i'I" ''ee O.73S2eyeleT2 eyele I s : .OO Go. 2eO. o02dOOPll). 2H). 4u;'eD)e) 8.,. '+JC,,ine c<; for the first eyc e' une o for le last c e eo),75) 50O. OO0.25 o 75O.50Dilataney ratio, -dE+*d/d Y Pl" - ':;;P'/ : " t!=j' i - ihNo'l55!/Ir't; ftt'_;'1._::;. .,t r " :1r'L F;j/;'}(;.;";(Tj:'c=F;'/: is 't ';i;' ' ;1; 's' rP';!;f f'1 rt/ir ;d7:s r" s'; 'TY'!""IJ ?'r'i,_ {'1/Jo '!'H)2f;)4'f::)fr/J!/ s' #'f// : F: ' ''1/u' u's" ' /F'l'/ f :'1 ';:'j ,･･ ;: i)8).25i: ///ir ';//' c:(::( ; ;1::!6. . ' /.c Ratat:on of line o s-r! Ifs ' ' Emj- te '11 'F' 'sr' $s- /Y*r''N '?;¥csU;/O. 4ss,une s ; fof Ist syctB08a,O% 5 .' +,SSS ;;:ji::{{:}L:;L:;::i l!l1'61ea' I¥.J3 cycle T s:t 0.5Pii.10Orained cyelcons.,c simpleshearno ;"" ! '!15atFepiep' sS8oyclekPa ';,r';'v5C"/-1 O-O 75une c'e at t e ead et test0 HD.2SO OOO 25 0.75O 50Dilataney ratio, -de*Id/d yPFig. 25(b). Stress-dilatancy relations of medium deuse sand underirregular c _'clic loadingFig. '-6(b). Stress*dilatanc .' relationshipsof medium dense sandsubjected to irreguiar c .'clic loading*,stress-dilatancy curves of different cycles become closerto each other.Figure 26(a) sho¥vs the stress-strain curves for amedium specimen sand under irregular cyclic shearstrain. The stress-dilatancy rclationship for this test issho¥vn in Fig. 26(b). The general shape of stress-dilatancyrelationship for this test can be explained by usingdia onal line c-c. After loading reversal, stress-dilat,ancycurves start from this line and when shearing continues,all the curves become closer to each other.reversais .(2) The stress-dilatancy relationship during the firstloading is different from stress-dilatancy relationships ofthe subsequent cycles. The starting point of the stressdilatancy curve at the be_g:inning of the first loading isaffected by the initial anisotropic stress state and relative(3) For each direction of loading, the dilatancy ratlo( - de .1 /d yP) changes continuously . Upon loadingreversal, it changes suddenly and after¥vards stressdilatancy curves start from a diagonal line that passesCONCLUSIONSThe follo¥ving major conclusions ¥vere dra¥vn from thetest results of hollolv torsional specimen under drainedsimple shear mode:(1) For each complete cycle of shearing after initialthrou_9:h the center of coordinates. When loading reversaloccurs at a higher level of stress-ratios, the absolute valueof dilatancy ratio ( : = de,d.1ldyP I ) becomes larger.(4) When shearing continues after loadin*' reversal,stress-dilatancy curves become closer to each other.loadin_g:, the stress-dilatancy curve consists of tlvo almost(5) Confining pressure does not affect the stress-parallel nonlinear segments of positive slopes and t¥vodilatancy relationship remarkably.nearly vertical segments immediately after loadin_l,(6) Effects of initial anisotropic consolidation are,{;lL･_ CYCLIC STRESS−DILAτ、ANCY量mPortantmainlyintheinitialstageQfl・ading・Theseelfects diminlsh in the subsequent cycles。Radial stressa薙dco旦seqaentlytheratioofradialstresstoverticaIstress （ratio of stress anisotropy，κ需σ！／σ≦） chaageduring initial stages of shearing、After this chaage，the1atioofstressan量sotτopybecomesconstant，independentofitsinitialvalue．（7）Tぬestress−d1la伽cyrelati・nshipisa任ectedbys・il｛denslty， The stress一（i呈latancy d呈agram of Iooser san（istarts from a greater value of negative dilatancy ratio atthe begi艮ning of the first Ioa（iing．For the fo至low量ngcycles，魚creasing the density｝ea（ls to a cou凱erclockwise τotationof宅hediagona11宝nec−candshr1nkageofstress−dilata蓑cyrelationshlpintkeloadingpart．Aconsequence「lrregula曙 150−158．7）Prad熱an，丁．B，S．and Tatsuoka，E and Rorll，N．（1988a）l Simple sheaτtestingonsandlnaヒorsionalsぬearapParatus，Soi’∫αηゴ Fα〃1面’ioη5，28（2），95一玉12、8）Pradhan，T。B．S．andTatsuoka，F．andHorli，N．（玉988b）lStreng由 and deformation c裕aracterlstics of sand ln torsional slmple曲ear， 50’Z5α114Fα’nゴα∼10175，28（3），BH48、9）Pradhan，T。B．S．，Tatsuoka，F，andSato，Y．（玉989）：薦xperlmentaI stress−dilatancyrelatlonsofsandsubjectedtocyclicload玉ng，SoiZ5 αnゴFoμηゴα∼’oπ5，29（1），45−64．10）Roscoe，K．H．，Sc益o負eld，A，N、and Thura玉raja賑，A，（茎963）： Yieldlngofclaysinstatesweuer由ancrltica1，G60’θ‘17nゆ’θ，13（3）， 211−240，11）Rowe，P．W，（1962）：τ簸e stress−dllatancy relatlon for static equlllb由m ofan assembly ofpart三cles in co瓶act，Proc．Roy。50ら 、乙onゴoηンSθノブθ5141η，269，500−527．of tbese changes is smalier vo夏ume contractionぐor denser12）Sha熱nazari，H。andTowhata，L（1999）：E輝ectofanisotropic consol量dationondrainedcyclicsimpleshearofsand，X1廊’σηsand． Rθ9’oηα1CoηゾoゾSo’1A4θごhαη’c5αnげFα〃14‘71’011Eη9・，κoヂθα・（8）Shear history a錨ects the stress−dilatancyrelationsbip．1tse伍ectsaresimilartothee伍ectsofincreas呈ng the （iensity on stress−dHatancy diagrams，αangesofstress−dilatancyrelationshipduetoshearざ飛119historyleadtosmallervolumecontractlon． Proc，155一玉56．13）Sh麟nazarl， 鷺． and Towhata， L （2000）： Harde頭ng and dens玉丘cat玉on of sand due to drained cyc1玉c玉oading，Gθo∼εch．｝セ‘77 2000Conブ．，Bα119たoκ，rhσ’1α1τゴ，1，9−16・14）S熱a無nazari，H．a獄d Towhata，L（2001）：Predictlon of volumetrlc stralnforsand自ndercycllcloadlngズα！だh∫1∼’．Co11∫oηRθcεn∼ ！4ゴvαn‘ε5∫n G8α．Eσr’h．E119．，SαηD’θgo，US！4，Pヂoc，CP−Ro1η， 1．REFERENCES箋“lse sandサhe負rSl、撮ps of streSS’、tdingisrelativeこyrati。i1・adin鷺streSS・萎毛passe纏revers旦壕lteva1曜reversaLher． stresシ110n a罐藝髪婁 of gramlar solls w曲no membrane−penetratlon e拝ects，Co11・圭）lsむihara，K。（19％）：So’1βεhαvio1ゴnEαπ1冨σε磁θGθo’εoh17’c5， Gθo∼θch。／．，35，730−739． Oxford Sc玉ence Publication．2）NemaトNaser，S、（1980）：On behav玉or of granロ1ar mater玉als 玉ni6）Tatsuoka，F．（1978）：Ont歓e出eoreticalstudiesondefomatlon simPle sむear，So1なα’1ゴFoμnゴα∼’01∼s，20（3），59−73・ 0、7515）Sivatぬayalan，S．andVa呈d，Y・P・（1998〉：Tru玉yundra魚edresponse be卜avlorofgranularmaterlaII，τ5εκ11iぜo乱50，／5SM圧，26（6）， 82−89．3）Nemat一醤aser，S．andτakallashl，K，（1984）：Liquefacτlon and fabrlc17）Tatsuoka，F．，lwas＆kl，T．，Fukus扁撮a，S．andSudo，S・（1979）l ofsand，P∼oc．。4SC君，110（9），129レBO6．4）Oda，M，（1975）：Onstress−dllatancyrelatlonofsandlnsilnpleshear S底ressconditlonsandstressわistorlesa押ectlngs甦earmodulusand damplngofsandundercycllcloading，So’Z5α17ゴFαぜnゴ副0115，19 test，50’Z∫αηゴノroμηゴα‘io175，15（2〉，17−29・ （2），29−43。5）Pradhan，τ，B．S、an（i Tatsuoka，F、（1989）＝On stress−d玉互atancy18）Tatsuoka，F，，Sonoda，S。，Hara，K，Fukushi斑a，S、and Pradぬan， equatbns of sand subjected to cycllc loading，50’15θ11ゴ T．B．S（1986b）：Fallureanddeforma霞onofsandintorsiona至sれear， 1；oど〃1（ノ‘π10η5，29（1），65−8L So1Z5α11ゴFo∼〃7ごαが0115，26（4），79−97。6）Pradi｝an，T、B・S・，Tatsuoka，F。and Molenkamp，F。（1986）：19）Towhata，王，andls臨ara，K（1985）：Modellngsollbehavlo田nder Accuracyofautomatedvolumechangemeasurementbymeansofa prlnclpalstressaxesrotation，P1’oσ、5！h加。Co17∫0ηノ〉εイ1ηθ伽1 a玉fferential pressure transducers，So〃5απごFoε’n6α”0175，26 （4）， ルfαhoゴ5’1zGθo’ηθc12傭c5，ノ〉αgの7α，1，523−530． | ||||
| ログイン | |||||
| タイトル | Effects of Air Bubbles on B-Value and P-Wave Velocity of a Partly Saturated Sand | ||||
| 著者 | shuji Tamura・Kohji Tokimatsu・Akio Abe・Masayoshi Sato | ||||
| 出版 | soils and Foundations | ||||
| ページ | 121〜129 | 発行 | 2002/02/15 | 文書ID | 20443 |
| 内容 | 表示 | ||||
| ログイン | |||||
| タイトル | A Displacement Prediction Method for Retaining Walls under Seismic Loading | ||||
| 著者 | Mitsu Okamura・Osamu Matsuo | ||||
| 出版 | soils and Foundations | ||||
| ページ | 131〜138 | 発行 | 2002/02/15 | 文書ID | 20444 |
| 内容 | 表示 | ||||
| ログイン | |||||
| タイトル | On the Yielding and Plastic Compression of Sand | ||||
| 著者 | G. R. Mcdowell | ||||
| 出版 | soils and Foundations | ||||
| ページ | 139〜145 | 発行 | 2002/02/15 | 文書ID | 20445 |
| 内容 | 表示 SOILS AND FOUNDATIONSiVol, 42, No, l, 139-145, Feb. 7_002Japanese C.eotechnicai Society'otech.gra¥*ityON THE YIELDING AND PLASTIC COMPRESSION OF SAND-469.. earingngrg.,G. R. McDo¥VELL,i)itesholdJ.of, -759.ABSTRACT{(2000):=ct andThis paper presents an analysis of the yielding and plastic hardening of uniformly-graded samples of a silica sandsubjected to one-dimensional normal compression. Single *'rains of silica sand have been compressed diametrically between fiat platens to measure indirectly tensile strength. Approximately 30 grains were tested for each of the follo¥vingnominal particle sizes: 0.5 mm, I mm and 2 mm diameter. It was found that the data could be described by the Weibullstatistics of brittle ceramics, and the Weibull modulus could be taken to be about 3 . I . Uniform aggregates of the samesand lvere then compacted to maximum density and subjected to one-dimensional compression. The initiai particle sizedistributions were 0.3-0.6 mm, 0.6-1 .18 mm and I .18-2 mm, and aggregates were subjected to stresses of up to 100MPa. All particies were initially of sirnilar shape, and hence the initial voids ratios of the aggregates at maximum density were approximately equal. The yield stress was defined to be the point of maximum curvature on a plot of voidsratio against the logarithm of effective stress, and found to increase ¥vith decreasing particle size, and to beapproximately proportional to the tensile strength of the constituent grains. However, the plastic compressibility index¥vas found to be approximately constant and independent of the initial grading, and a fractal distribution of particlesizes appeared to evolve under increasing stress. There is evidence to su*'gest that the aggregates evolve towards afractai dimension of 2.5 under high stresses.hquakei(1999):ainingof Civi!selsmrc='tion ofnlp., 2icity ofEngrg..w stripgineers,ldrainedry, J. ofKey w'ords: micro mechanics, particle crushing, sands, statistical analysis, strength (IGC:65 276.thod forD5/D6)*h. andwhere m is the Weibull modulus and (T**,d is the value ofINTRODUCTIONcharacteristic stress for a particle of size d such that 37010;,=iIt has long been recognised that the constitutiveof tested particles survive, or "370/0 tensile strength".behaviour of an aggregate of soil grains is strongly de-McDowell and Amon (2000) showed that a*. d ispendent on the crushing strength of the individualproportional to and approximately equal to the averageparticles (Billam, 1972; Bolton, 1986; Lee, 1992; Nakatatensile strength (7*.,d, and is a function of the particle sizeet al. , 1 999). Followin*" Jaeger (1 967), the tensile stren*'thd according to the equationof a singl soil grain is usually measured indirectly bycompressing the grain between fiat platens until failure(7,. d oc d - 3/* (3)occurs. McDowell and Amon (2000) reviewed much ofFor nl=3, for example, cT*.,d=0.89 cF* , . McDo¥vell andAmon (2000) showed that data for calcareous Quiou sandthe work on quasi-static compression of brittle spheresand showed that if the particle-platen contact area couldi.particles could be adequately described by Weibullbe assumed to be negligible, and that if all loadingstatistics. Nakata et al. (2001) measured Weibull moduligeometries were similar, then Weibull statistics (Weibull,for silica sand grains of different sizes, and also plottedfailure characteristic stress as a function of size on a log-i951) could be applied to characterise soil particle*,strength. For grains of siz,e d loaded diametrically under aforce F, they defined a characteristic induced tensile stressa* as:F(7c = d 2 (1)Eq. (3). However it may be possible to improve theconsistency of those data if the average strength for eachparticle size ¥vere to be plotted as a function of size. Thus,and sholved that the survival probability of a particle ofas yet it is not known of any data which has demonstratedsize d is _ iven bysuccessfully the applicability of Weibull statistics to silica[ ( )Jm crc (2)Ps(d)=exp(7co'd*)l10g plot for all particles tested. The values of Weibullmodulus varied greatly across the range of sizes, and wereinconsistent with the size effect on strength according tosand.McDowell and Bolton (1998) examined the micromechanics of soils subjected to one dimensionalLecturer, School of Civil Engineering, University of Nottin_ ham, Nottin_! ham NG7 2RDManuscript was received for review on February 13, 2001Written discussions on this paper shou d be submitzed before September I , 200'- to the Jap nese CJeotechnical Society, Sugayama Bldg. 4F,Kanda Awaji-cho 2-23, Chiyoda-ku, Tokyo 101-0063, Japan. Upon request the closin_g date may be extended one month.139 ;;lvICDO¥¥rELL140which 500/0 by mass of particles are finer than), for arange of sands. They calculated tensile strength as thecharacteristic stress at first peak in load, and proposedthat the tensile strength should be proportional to ael 6142o*{dense oarbonate sanddid not, however, examine the compression of uniformly*'raded aggregates of a given sand, with particle si2:evarying between the aggregates. Nakata et al. (2001) examined the one-dimensional compression of a range ofuniformly-*'raded sands, and related the macroscopicloose silica sand08cdense silica sand06¥o(1){crushability index K, defined as the logarithm of the yieldstress for a sample at z,ero initial relative density. They1,¥¥¥I;!behaviour to the strengths of the constituent soil i0. 4:particles. They found that for silica sand, the yield stress07_Ol O crJ (MPa)IOFig. l. One-di,nensiona compression plots for carbol]ate and silicasands (Golightly, 1990)decreased with increasing particle size. However, the sizeeffect on yield stress was small, and was not consistent !with the size effect on tensile stren*"th determined for theindividual * rains (though they did not isolate the effect ofrelative density). Thus Nakata et al. (2001) were unable totensile strength.{McDo¥vell and Bolton (1998) noted that the onecompression, and proposed mechanisms for yielding anddimensional plastic compression of soil leads to theplastic hardening. Figure I (CJolightly, 1990) sho¥vs plotsof voids ratio against the logarithm of effective stress forevolution of a fractal distribution of particle sizes, suchthat the percentage by mass M(1,<d) of particles finersands subjected to one-dimensional compression.than size d is _9:iven by the equation:Consider the dense silica sand in Fig. I . At low stresses(region 1) the behaviour is quasi-elastic. Beyond yield(re*'ion 2), an approximately linear normal compressionline emerges. Coop and Lee (1993) showed that normalcompression results from particle crushing, andattributed yield to the onset of particle crushing. Hardin(1985) related the amount of particle breakage in triaxialtests to the applied stress levels but did not relate yieldstress to the tensile strengths of the soil grains. Hardin(1987) studied one-dimensional compression ofcohesionless soils and proposed that instead of plottingvoids ratio e against lo*'arithm of effective stress (7' , a plotof I /e against ((T')should be used (where p is the powermdex) Hardm (1987) defined a "breakpoint" stress atM ( I , <, d ) cc d 3,**,D (4)¥vhere D is the fractal dimension. Remarkably, for manygranular materials subjected to pure crushing, a fractaldimension of about 2.5 emerges (MCDO¥vell and Daniell,,i*{{2001). McDo¥vell and Daniell (2001) showed thatiinumerical simulations of fracturing fault gouge by Steacyand Sammis (1991) c.ould explain the observed dimensionof 2.5 in soils. McDowell and Bolton (1998) showed thatthe evolution of fractals could explain the existence oflinear normal compression lines when voids ratio e isplotted against the logarithm of macroscopic stress (T.They proposed that for initially uniform aggregates,although the yield stress should depend on the initialattributed to the onset of crushing. He related thisparticle size, the plastic compressibility index (defined asthe slope of the e-log (T plot) might be a fundamental con-breakpoint stress to initial particle size distribution andstant. McDo¥vell and Daniell (2001) found that forparticie shape, but not to the tensile strengths of theparticles. McDowell and Bolton (1998) also attributedyield to the onset of grain fracture, and coined the termoedometer tests on calcareous Quiou sand, samples with¥vhich the slope of the plot becomes non-linear, ¥vhich he*explicitly show that yield stress is proportional to particle*,,,=:}:.different initial particle siz:e distributions all appeared to"clastic yielding" to describe this process. Because yieldevolve towards a fractal with dimension 2.5, and thecompressibility index was independent of the initialIoccurs gradually, a suitable definition of yield is required.particle size distribution. Ho¥vever, in their tests, the;In this paper yield will be taken to correspond to the pointan*'ularity of the particles varied between differentof maximum curvature on the plot of voids ratio againstparticle sizes, so that it was impossible to relate yieldloganthm of stress. McDo¥vell and Bolton (1998)stress to the average tensile strength of the constituentgrains. Nakata et al. (2001) demonstrated that for uniformly-graded silica sand subjected to one-dimensionalproposed that the yield stress for a uniformly gradeda*'*'regate should be proportional to the average tensilestrength of the constituent grains but as yet it is notkno vn of any available data to support this proposition.Kwag et al. (1999) did not use Weibull statistics,related the yield stress (Casagrande definition)aggregates subjected to isotropic compression tosample relative density and the tensile strength ofbutforthetheconstituent particles corresponding to size d50 (i.e. the siz,ecompression, the plastic c.ompression index isindependent of the initial particle size, but they did not; "*attempt to demonstrate that this was linked to the"',evolution of a fractal distribution of particle sizes.This paper aims to make several contributions. Firstly,the paper aims to demonstrate the applicability ofi.!iWeibull to silica sand *･rains. New data is presented fori ;' 141YIELDING* AND PLASTIC C_O* ,iPRESSION OF SANE)S,r aItheIsedoaieldheygrains of Leighton Buz,zard silica sand, crushed betweencompressed bet¥veen flat platens to determine theflat pia:tens. The distribution of strengths is presented fordistribution of strengths for grains of a _given size, and 37grains of diameter 0.5 mm, I mm and 2 mm, and theapplicability of Weibull is examined. The second ando/o tensile strength as a function of size, in order todetermine whether Weibull statistics can reasonably bemost significant contribution of the paper is to provideapplied. Fi_ :ure 2 shows a simple particle crushing device,support for the proposition by MCDOwell and Boltonwhich is described by McDowell and Amon (2000). Theload measuring capacity of the device is 320N with a(1998) that the clastic yield stress for uniform aggregatesmlysubjected to one-dimensional compression should beptoportional to the average tensile strength of theconstituent grains. IJniform aggregates of the sameLei_9:hton Buz,zard sand were compacted to maximumsizeiI ex-e ofopici*density and subjected to one-dimensional normalsoilItresssizecompression (one-dimensional compression tests ¥verei!conducted as opposed to isotropic tests for convenience).The initial particle size distributions were 0.3-0.6 mm,stentr theiO.6-1.18mm and 1.18-2mm, and aggregates ¥ 'er'e'ct ofsubjected to stresses of up to 100 MPa. A11 particles)le toinitially of similar shape, so that after compaction torticle;i''ere(4 )diameter 5 mm. For the 2 mm grains the 20 mm diarnetertop platen ¥'as used. For the 0.5 mm and I mm *'rains,the 5 mm diameter top platen was used to ensure that thetop and bottom platens could not come into contact witheach other without crushing the particle. Thirty particleswere tested for each nominal particle size.For a single particle of size d under a diametral force F,the characteristic stress (7* induced ¥vithin the particle isdefined according to (1) and the survival probability isapproximately equal for each a_ :gregate. Thus thegiven by Eq. (2) if Weibull is applicable. Small asperitiesmay fracture before final failure of the particle, and careis needed in adoptin*' a suitable definition of failure. Inyield stress is constant in these experiments. The effect offineravailable: a 20 mm diameter platen and a platen ofmaximum density the initial voids ratios ¥vereinfluence of initial voids ratio and relative density onone) thesuchresolution of 0.001N. Three nominal particle sizes weretested: 0.5 mm, I .O mm and 2 mm. Two top platens wererelative density on yield stress has been studied by Kwa_ :et al, (1999) and the effect of initial voids ratio has beenstudied by Nakata et al. (2001), and so these effects arethis paper the approach proposed by McDowell andAmon (2000) is adopted whereby failure is taken tonot studied here. The yield stress is determined as aof the particle is still greater than 500/0 of the initial size.function of average initial particle size, and the results arecorrespond to the largest force such that the current sizemiell,that for this Lei**hton Buzzard silica sand, thethatcompressibility index is independent of the initial particleIn all cases this was found to correspond to catastrophicsplitting of the particle, for this Leighton Buzz,ard sand.Characteristic stress at failure is defined in this paper asthe diametral force at failure divided by the square. of thenominal particle diameter. It is also possible to calculatesize distribution, and is linked to the evolution of athe characteristic stress based on the diameter of thefractal geometry. The ra¥v data for the single particle testsrelated to the avera*'e tensile strength of the constituentmanyparticles. Finally, this paper also aims to demonstrateractalSteacyension*,'*tests in Oweis (2000).particle at failure. However, the aim here is to correlatethe yield stress for approximately uniform aggregates inoedometer tests ¥vith the average tensile strength of theo e isconstituent grains, and for this purpose the use of aess (T.SINGLF, PARTIC_LE CRUSHING TF,STSnominal diameter is sufficient.Follo¥ving Eq. (2), by plotting In (In (1/P*)) against;.d that=nce ofe"*ates,initialcan be found in Voo (2000) and for the one-dimensionalSingle grains of Lei_ *hton Buzzard sand have beeniIn (7*, the Weibull modulus can be determined from theined asal con"lat fores ¥vithared tond theinitialSS*'" :(i*;.* *.:i: ;r;; :,'i'*r;:' ;" ** ' *""';*.= s* * * -*: "**{,i* :' "=;" ..:.**""'* "---*f'*"*;;. ; ;s.. ;'':i;'"' " s'. ";* '- - i* fS ' ?';; +.r'*":;* ; i20rnm diametertop platents, the!if erenttest specimene yieldstituent;'or uni*Insionaldex Isdid notbottom platento thealternative 5mmdiameterFirstly,top platenility ofir ted forFig. 2.Particle crushing device b:sIMCZ)OWELL1 42ilOOO -0.5mm grains2J(y = 3 44t3x + 17 lS2 ._ IlR2 = O 9449- o-l_- i! :5_-l2;[ y = 74 288x o 910s:[¥ =D2O9786I10..-J*3_4 J{olOlIn (T'!n d( a){Fig. 4. 370/0 tensile strength 8s a function of sizemm grainsITable l. WeibuH modulus, 370/0 tensile strenogth and fverage force atf ailurel2ll y-' 3395x - 9'8273 IFle-o::Q,0.5 3 .44l-2ll f 2 34,e3 ll, ' failure/N1Nominal j i 370/0Weibulltensile stren"thcr* d /MPasize/mm j modulus m ,R2 =: o'95962 3 14,}Avera_ge force at'{1 47 .4 33 . 1 266,75 9 Ol41 .7149.05iiIn cr.The results for average force at failure for each of the(b)three nominal particle sizes are given in Tabie I , and thisindeed found to be the case.2mm grains21y= 3 136x -_ ll-oONE-DIMENSIONAL COMPRESSION TESTSi 698 -R- = O 9776i:lDll3,2314),j,-4In cr*(c)Fig. 3. ¥ 'eibuH plots for each set of grainsTests were performed in an Instron testing machineusing an oedometer made from EN24 steel with internal,{diameter 80 . 5 mm and a sample thickness ofapproximately 15mm. Figure 5 shows compression}Icurves obtained for oedometric compression of denselycompacted dry silica Leighton Buzzard sand of variousinitial gradings. The initial uniform gradings ¥vere0.30.6rnm, 0.6-1.18mm and 1.18-2mm, and eachsample was compacted to maximum density in theoedometer by vibration. All particles were of similar Ian*"ularity and hence the initial voids ratio wasapproximately the same for each sample compacted toslope of the line of best fit, and the value of (7*.,d determined as the value of cr* when In(In (1 /P*)) = O. Figure 3shows the distribution of strengths for each of thenominal particle sizes. The results are summarised inTable I . The average Weibull modulus is found to be2.97. The 370/0 tensile strengths are plotted againstnominal particle size on a log-10g scale in Fig. 4.maximum density. The experimen.tai procedure for thesetests is described by Oweis (2000). It is clear from Fig. )that the stress level of the yielding region depends on theinitial grain size distribution and increases with reducingparticle size. Here the yield stress has been taken to be theFollowing equation (3), the slope of the plot is -3/m,point of maximum curvature on the e-log (T plot, and determined by fitting a 6th order polynomial to the yieldingregion with a correlation coefficient of I .O. The yieldwhich corresponds to a Weibull modulus of 3.29. Thestress for each particle size distribution is given in Tableresults are therefore in *'ood agreement and it seems that2, and is plotted as a function of the average initialWeibull can be applied. Taking the average of the twoWeibull moduli calculated from Figs. 3 and 4 it seemsparticle size in Fig. 6 (here the average particle siz,e is sim-that an m value of 3 , I could be assumed for this material.particle size distribution). In order to determine ¥vhetherIn this case, followin*' McDowell and Amon (2000), thethe results are commensurate with the results from theavera*'e force at failure should be approximatelysingle particle crushin*' tests, it is useful to first exarnineproportional to d2-3/* so that for ln = 3. 1, average forceat failure should be approximately proportional to size.":.{:;;.ply taken to be the average of the two extreme siz,es in theFig. 7(a), ¥vhich sho¥vs the result of a test on an array ofIi .. ';*!i,'.photoelastic str'ess discs (de Josselin de Jon*' and !tLti-. ;.YI LDING AND PLASTIC COMPRESSION OF SANDSI.iary force FH, such that FH/Fv=0.39, which is6-i'O 3TT1;n < d <; O.6mrncomparable to typical Ko Values measured in one-O 6 uT1 <d<: I ISmmdimensional compression tests on sand in the triaxialiJapparatus. In Fig. 7(b) (Cundall and Strack, 1979) FH /FV=0.43. Both figures show that the stress distributionswithin particle assemblies are extremely heterogeneous.The width of the rectangles plotted through the particlecontacts in each array is proportional to the magnitude ofthe contact force. For each of the arrays in Fig. 7, whichare approximately 12 particles wide, it can be seen thatLil lgmul<d< 'mm**OIeO1o}lO1lcoOoOStress CT / . iPaFig. )-Compression plots for different uniform gradings of sand40 -it30 -might anticipate that the yield stress might be about fourtimes less than the 370/0 (or average) tensile strength ofthe constituent grains in the aggregate. For the aggregatesl o True yield strengtho25x Yield strength predictedX20 -e5 >*lfrom single particle testsxlOthe 370/0 tensile strength of 0.5 mm diameter particles is15}Average particle size / mmiFig.5. Yield stress predicted from siugle particle crush ingtests,assuming yield stress = (370/0 tensile strength)/4{tensile strength has been estimated for the averageaggregate assuming a Weibull modulus of 3.1, and thatOhis0.3-0.6mm, 0.6-1.18mm and 1.18-2mm, the 37010paFticle size (average of the two extreme sizes) in each#iheapproximately three columns of strong force form totransmit the major principal stress. If it is then supposedthat at yield, the characteristic stress induced in theparticles forming the columns of strong force might beabout four times the applied macroscopic stress, one45 -at143147.4 MPa, as given in Table l. Thus, for the particlesranging in size I .18-2 mm, for example, an average siz,eof 1.59 mm is assumed so that the 370/0 tensile strengthfor particles in this aggregate is estimated to be 147.4 ><(1.59/0.5)3/3 1=48 MPa. The values of 370/0 tensile{ofstrength for each average particle size are given in Table2. The values have then been divided by 4 to predict theyield stress of the aggregate. These values are also givenin Table 2 and plotted together ¥vith the measured yieldstresses in Fig. 6. The results are very pleasing and cer-10ntainly support the proposition made by McDowell and{*...* ,'+ Ei,InenalIBolton (i998) that yield stress should be proportionalto the tensile strength of the individual grains. Thediscrepancies between the values can be explained by the.elyous}ereachfact that yield is a gradual process, and at the yield stress,(b)(a)ithethe particle size distribution will already be different from.ilar,vasi toFig. 7. (a) Test on an array of photoelastic discs with FH/Fv=0.39the initial distribution, such that the average particle size(De Josselin de Jong, 1969) and (b) discrete element simulation of(a) (Cundall and Strack, 1979) with FH /Fv= 0.43will have changed. In addition, the average of the two. 5Table 2. Yield stress for each aggregatc, estimatedthescaling factor of four deduced from Fi**. 7 can only be37 o/otensilestrength and estimated yield stresscingtheextreme particle sizes in the ag*'regate is unlikely to equalthe true mean size of the constituent grains. Finally, theeseAg *regate;Yield iFollowing yield, an approximately linear normalAvera e370/0 tensile(370/. tensileinitialstressparticlestrengthstrength)/4dinggrading/MPasize/mm/MPa/MPaield0.3-0 6 mm37o 45l 6341O 6-l270.898421lg1 .594812i de-'*ablel itial. 8 mml. i 8_2 mmsim"a p proximate.*thecompression line emerges in Fig. 5 for each of the threeaggregates tested. At very high stresses the voids ratiosare extremely low, and it would be anticipated that thecurvature of the plot would change as the materialbehaves more rock-like. Indeed, follo¥ving the oedometertests, the sand was found to be extremely interlocked, butcould be easily crumbled to a powder in the fingers. Itappears that the slope of the plot, the plasticthercompressibility index is a constant, independent of initiall theVerruijt, 1969) and Fig. 7(b) (Cundall and Strack, 1979)ininewhich sho¥vs a discrete element simulation of the.v ofexperiment in Fig. 7(a). In Fig. 7(a) the array is subjectedand }to a vertical boundary force Fv and a horizontal bound-grading, and can be taken to be about 0.4. The particlesize distributions which evolve under increasing stress areshown in Fig. 8 for the 1.18-2 mm ag*"regate. It can beseen that the rate of crushing with increasing stress Lii_ ;I144+ (COO¥ 'ELLI.evolution of a fractal _e:eometry, in agreement withMcDowell and Bolton (1998).Initial gradiug: l. 8-2mmOO90 -* 8070= - initialI-h･iO iPa :60*-e-20ivlPa* SO40j- .50MPa i,-75MPa j;h 30,)* )-O' 100(Pa 'lOOI I O I OO I OOOOl OOOParticle size / umFig. 8. Evolvmg particle slze distnbutrons for 1 18 ･ mm aggregateCONCLI JSIONSSingle *'rains of L,eighton Buzzard silica sand have beencompressed diametrically between fiat platens in order tomeasure the tensile strength. Thirty}"rains were tested foreach of the follo¥ving nominal particle sizes: 0.5 mm, 1mm and 2 mm. For each nominal siz,e, the distribution ofi;strengths was found, and the 370/0 tensile strength ¥vas determined as a function of particle size. It ¥vas found thatthe results were consistent with the Weibull statistics ofifracture of brittle ceramics, and the Weibull moduluscould be taken to be about 3.1. Oedometer tests were1 ooperformed on uniform ag"-regates of the same sand up toan applied stress of 100 MPa. Tests were performed ona gre*"ates of the followin' "radings' 0.3O 6 mm!-S.18mm-2mm ;l--e-O 6mm - I ISmmlt;:lOl '-- O 3mm - O 6mm- ' ' " ' FFacta}, D*2.5 [,)}0.6-1.18 mm and 1.18-2 mm. The yield stress ¥¥'as defined as the point of maximum curvature on the plot ofvoids ratio versus the logarithm of stress and was found ito increase with decreasin*" particle size. Results of testson arrays of photoelastic discs and discrete elementsimulations were examined, and it was found that forstress ratios similar to those found in one-dimensionalcompression of sand, the major macroscopic stress islI I OO10OOOOOOOParticle size / umFig. 9. Particle size distributions at 100 MPaplotted on a lo"*-tog scalecarried by stron*' columns of force at an average spacingof four particle diameters. Based on this observation, theresults from the single grain crushing tests ¥vere used to,*;predict the yield stresses of the aggregates on theassumption that yield stress should be approximatelyequal to one quarter of the 370/0 (or average) tensilestrength calculated for the average particle size in thereduces considerably at very high stresses: presumablyaggre*'ate. The predictions ¥vere found to be in reasonablelarge particles are well protected by many neighbours, sothat the tensile stresses induced within them are very low,approximately linear normal compression line emergeswhilst the smallest particles have reached thecomminution limit, so that fracture is no longer possible.This is consistent with the change in curvature of theagreement ¥vith the measured values. Following yield, anfor each a*'gregate and the plastic compressibility indexwas found to be independent of the initial grading. Theparticle size distributions were determined after normalcompression plots in Fig. 5 at very high stresses. Similarparticles size distributions were found to evolve for thedistributions appeared to evolve to vards a fractal ofother uniform aggregates.dimension 2.5, thou*'h in this case the degree of particleThe particle size distribution for' each aggregate at 100MPa is plotted in Fig. 9, with percentage by mass passingand particle size each plotted on a lo_ :arithmic scale. According to Eq. (4) a fractal ¥vould appear as a linear plot.fracture occurring si_ nificantly reduces at high stresses. Itcompression to various stress levels, and the particle sizeIt appears in Fig. 9 that a fractal distribution hasemerged, but as previously stated, the rate of crushingaverage tensile stren*'th of the constituent grains, but thewith increasing stress has significantly reduced at higherstresses. A Iine of slope 0.5, corresponding to a fractalcompressibility index is a constant, and is linked to theformation of a fractal geometry. There is also evidence tosu_ :gest that ag>'regates subjected to one-dimensionaicompression evolve to¥vards a fractal distribution 1 'ithappears that the particle siz,e distributions would evolvetowards a fractal ¥'ith dimension of 2.5, if crushing ¥vereI::t/j-therefore seems reasonable to propose that for uniforma_g:gregates subjected to one-dimensionai normalcompression, the yield stress can be assumed to beapproximately equal to one quarter of the 370/0 ordimension of 2.5, has also been drawn on Fig. 9. It*ii,:"*,,,*dimension 2.5 at high stress levels.allowed to continue at extremely lo v voids ratios. Theslope of the upper part of the particle size distribution forithe 1.18mm-2 mm sample corresponds to a fractalACKNOWLEDC.EMF,NTSdimension of 2.35. It appears that the existence of linearThe author wishes to thank Mr Zeid O¥veis and Mr VunKion*" Voo for performin*' the laboratory testing.normal compression lines is inextricably linked to the*,*,';j; YIELDING AND PLASTIC COMPRESSION OF SANDS145 fragmentation strength，Eηgrg．，〆ior Cα1cαヂεo∼イ5Sθグ’〃1θ1π5（ed．by’ithREFE盆ENCES玉）Blllam・」・（王972）：Some aspects of the behaviour of granular ma篭erials at high pressures，S’ヂθ5∫一Sぴα’ηZ）θhαv’oμ∼oゾrSoiな，Pro（ン． ゴ醜θ加∫10η，CambridgeUniversity． o∫’hθRo5ωθ漉’ηor’α燭7ηψ・（ed・byParry，R澱・G．），69−80、12）McDQwell，G．R、and Bolton，M．D．（1998）：On the micro2）Bolto員・M・D・（1986）：The strength and dilatancy of sands・een A1−Shafel，K、A。），Ealkema，79−87。11）Lee，D．M．（1992）：Yheangles of frictlon ofgranular負ils，Ph。n 磁Ofθ‘ノ∼nゆθ，36（1），65−78， mechanicsofcrushab互eaggregates，G60ガεohnゆe，48（5），667−679，13）McDowell，G．R．and Amon，A．（2000）：The appllcation ofWelbull statistics Io t簸e fracture of soil pa貸icles，So”5αηゴFo㍑ηdαfめη5，40『to3）CooP，M・R・andLee・LK・（玉993）：Thebeねaviourofgranularsollsfoτ at high stresses，P7（∼ゴ’cず’vεSo〃ルノθごhαη’c5， Proc． oゾ『∫hθ 昭ro∼h （5），玉33−14L 1砿乏∼1πor1‘71S』y1ηρ，（ed，by｝｛oulsby，G、T．and Schof｝eld，A．N．），I4） ∼lcDoweU，G，R．aad Daniel董，C．M．（2001）：Fτactal compression of 圭86−198．4）Cunda11，P・A・and Strack，0・Σ）・L（1979）：A dlscrete element15〉Nakata，Y，，Hyde，A．F、L．，｝｛yodo，M．andMurata， ｛．（1999）：A1，110fde． model for granular assemb践e5，G（多o∫ε（ンhn’9μθ，29（1），47−65。11at5）De Iosselin de Jong，G．and Verruljt，A．（1969）：孟tude photQ−lof 61astique d’un empllement de dlsques，Cαh．Gψθ戸，E飯ごe，Rh601，IIUS 2，73−86．6）Goiightly，CR・（1990）：Eng量neerlngPropertlesofcarbonatesands，一『ere⊃toon so11，磁αεchnゆe，51（2），173−176。 probabilistic apPrQach to sand part玉c玉e cr越shing in the tr玉axial test， G60∼θoh’11（1μθ，49（5），567−583．王6）Nakata，Y．，Kato，Y．，｝｛yQdo，M．，壬｛yde，A，F，L。and Murata，M， （2001）＝One−d玉mensionalcompressionbe益avlourofuniformly gradedsandrelatedtoslngleparticlecrusぬlngstrength，50iZ5αnゴ Ph．P．ゴ’55ε加∼’oπ，BradfordUnlverslty、 ハαイ層頗oη5，4三（2），39づ1，7）狂ardin，B・O・（1985）：Crushlngofsoilparticles，河SCE訊oゾ17）Oweis，Z、W．（2000）：The compressibility and crus頁ing of sllica σθorθ‘h、Engrg．，111（玉0），1177−1192。 sand，ハグ，五『η9．‘ノな5θπα’1011，Un玉versity of Nottingわam。8）Hardin，B・0、（1987）：1−D s亡ra玉n ln normally consol量dated co島esionlesssoils，。4SC君∫oゾ（3εαεch．Eπgrg。，113（…2）， i449−1467．9）Jaeger，」．C（1967）：Fallureofrocksundertensilecondltions，加．18）Steacy，S．」．and Sammis，C，G．（1991〉：An automaton for fractaI 」」Rooた．ハ4’11．So’，，4，2玉9−227。20）Weibull，W，（195王）l A statistlcal distrlbution function of wldeests！0）Kwag，」，M．，Ochiai，H．and Yasufuku，N．（1999）：Yield圭ng stress appHcability，∫．沌ρp1．Mθch，，18，293−297．／entfor characterlsticsofcarbonatesandinrelatlo財olndividualparticlelm，de．tofmd）na1、SISomg由e⊂1totheしtely／siletheable 嚢1，anIrges膿rmallsize嚢ほof蒙1ticlelヨs・ltl＝ormlrmall）bel き∩or萎 きtthe萎）thelceto嚢麟 警謬婁Vuロ嚢黙嚢髪 patterns of fragmentat呈on，ハ∴α々’rθ353，（6341），250一一252．19） Voo，V．K，（2000）：Stat呈stics of part玉cle strength in a si1三ca sand，ハ4Pゆ Eng．ゴ趣θr∫副on，University of Nottingham． | ||||
| ログイン | |||||
| タイトル | Effects of Initial Fabric and Shearing Direction on Cyclic Deformation Characteristics of Sand | ||||
| 著者 | s. K. Chaudhary・Jiro Kuwano・Satoshi Hashimoto・Yutaka Hayano・Yuhei Nakamura | ||||
| 出版 | soils and Foundations | ||||
| ページ | 147〜157 | 発行 | 2002/02/15 | 文書ID | 20446 |
| 内容 | 表示 {!*SOILS AND FOUNDATIONS;iVol 42 No. l, 147-157. Feb, 2002Japanese C.eotechnical Society;!iEFFECTS OF INITIAL, FABRIC AND SHEARlNG DIRECTION ONCYCL,IC DEFORMATION CHARACTERISTICS OF SANDI';::;I;;IiSUSHIL K. CHAUDHARYi), JIRO KU¥¥,ANoii), SATOSHI HAShllvroTOiii),'jYIJTAKA HAYANof*･) and YUHEI NAKAMURAi).ii=1{ABSTRACTI{I.The paper presents a study of the effects of initial fabric and shearing direction on cyclic deformation characteristicssuch as stress-strain response, shear modulus and damping ratio from drained static cyclic tests on medium denseToyoura sand using hollow cylinder apparatus. The apparatus allo¥vs independent control of stress components, (T=,a , * and r, , and accurate measurement of strain components, 8., e, 8* and y.e, over a wide range of strains from10-30/0 ro 100/0. Three methods of sample preparation, air pluviation, water pluviation and dry rodding, wereIiemployed to produce different initial fabrics. Samples were sheared cyclically in p'-constant plane along the directionof major principal stress O' (90'), 22.5' ( - 67.5') and 45' ( - 45') relative to the direction of deposition. Anisotropicbehaviour ¥vas observed in stress-strain response and the secant shear moduli defined separately for each direction ofmajor pFincipal stress. Ho¥vever, the equivalent shear modulus was found to be little affected by the direction of theznajor principal stress. In addition, the effect of initial fabrics ¥vas not significant. The same ¥vas found for thehysteretic damping ratio.i*{Ke .' words:damping ratio, deformation, repeated load, sand, shear modulus, special shear test, torsion (IGC:D6/D7);Ladd, 1974; Mulilis et al., 1975; Silver and Park, 1976;Ladd, 1976; Tatsuoka et al., 1986). On the other hand,lNTRODUCTIONIt is essential to properly estimate strain-dependentshear moduli and damping properties of soils inanalyzing soi]-structure interactions and earthquakeresponses of gr'ounds and soil struc.tures where thedirection of the major principal stress is not alwaysvertical, as in the ordinary condition of level ground(Ishihara, 1983; Kuwano and Ishihara, 1988). Soils areiianisotropic fabric (Kallstenius and Bergau, 1961) and(Oda, 1972). The response was stiffer along the directiontherefore anisotropic response (Shibuya and Hight,of deposition than along its perpendicular. Ho¥vever,past studies have all been confined to either triaxial,where the direction of major principal stress is eitherby air plu "iarion and by moist tampin*" or moist rodding.In addition, many researchers have found that the cyclicundrained stren_ th of reconstituted sands determined bycyclic triaxial tests and torsional shear tests are stronglyaffected by sample pr'eparation methods (for example,t,iiiFormer CJraduate Student, Dept;stress revealed that the properties of sand, such asmobilized stress ratio and secant modulus, are highly de-deposition (Oda, 1972). L,aboratory tests conducted by, ,iiura and Toki (1982) indicated large differences intriaxial behaviour bet¥veen clean sand samples prepared{deposition direction and the direction of major principalinherently anisotropic in response. Even spherical glassballs deposited with free fall under gravity give rise to1987). The nature and degree of fabric anisotropy of sanddepends upon the shape of sand grains and the method of.the same fabric (the same sample preparation method)gives different responses when sheared in differentdirections. A comprehensive series of static triaxialcompression tests on specimens prepared in a tiltingmould with various angles of inclination between thependent on the direction of the major principal stressifivertical or horizontal, or torsional shear tests, where themajor principal stress direction is 45'. The hollowcylinder apparatus used in this study controls torsionalshear stress and deviatoric stress independently andtherefore allows shearin*' of the specimen in any directionin the z- e plane. Specimens were sheared cyclically indifferent directions in the p'-constant plane. Differentinitial fabrics in the specimens were produced by differentof Civil Engr_ ., Tokyo inst, of Technology, 2-1)_-1 0-0kayama, Meguro, Tokyo i52-8552.AssociaLe Professor, ditto.EngineeF, Kuma_"_,ai Gurni C_orporation, Japan^The Japan Research Ins itute. Tokyo, Japan.i,Manuscript ¥vas received for revie¥v on ivlarch 16, 2001.¥Vritten dlscussions on this paper should be submitted before September I , 2002 to the Japanese Geotechnical Society, Sugayama Bld_g:. 4F,iKanda A¥vaji-cho 2-23, Chiyoda-ku, Tokyo 101-0063, Japan. Upon request the closing date ma_v be extended one month.;11471 148CHAUDHARY ET AL{sample preparation techniques. Their effects on stressstrain response, shear modulus and hysteretic dampingare studied in this paper.Firstly, a short description of the apparatus and testingsystem will be presented. Secondly, the test conditionsand program will be described. Finally, the results will bepresented and discussed.Table 1. Calculation of average stresses and strains in hoHow cyiinderspecimenAvera :e strainsAverage stressesW , por pjrh , Ahlz(ry'r ) 2r r ezllj(FZro Po I 'Cir ro + ri(roPier=roiro PoHOLLOW CYLINDER APPARATIJS;rj Pie =(Tro 'A hollow cylinder apparatus with the specimendimensions of height (h) = 100 mm, inner radius (rj) = 30mm and outer radius (r.) = 50 mm ¥'ras used in this study.The testing system was fully automated. Schematic(r_ +rzPe)yze 3h (r;roi)(rirji)ri(rj,rofrirji)- r;･)rjj)4M:T (r - rj)rzeillustration is given in Fig. 1. Details of the systemdevelopment have been reported by Nakamura et al.(ro2e(r1r:roi)3lr (rrt)(r; - ri2)3MTrzPe 21T(r30rsl)(1998). All the measurements and control were made byPC throu*'h 16-bit A/D and D/A converters. The stress;,;.components, vertical stress (T., circumferential stress (Te,e plane r.e, ¥verep., independently (see Fig. 2 also). The axiai load wasapplied to the specimen by controlling axiai load W,controlled by air pressure through a double actingtorque MT inner cell pressure pj, and outer cell pressureBellofram cylinder. But the torque was controlled by oilpressure through a hydraulic pressure control unit. Theradial stress (T*, and shear stress in the zlinner and outer cell pressures were controlled by airpressure. The axial load and torque were measured byinternal load cells over the top cap of the specimen andthe pand p. ¥vere measured by pressuremeters at thebase. The average stresses and corresponding strains ¥verecalculated as shown in Table I . The a¥'erage stress (7, isbased on the equilibrium of forces at the mid-height ofthe specimen. The stresses (Te and (7* are based on the;"";Iassumptions of linear elastic stress distribution across the;-wall of the specimen (Hight et al., 1983). The shear stress,r,e, has been taken as the average of the values given byithe assumptions of linear elastic and perfectly plasticstates of the specimen. It has been sho¥vn by I¥vasaki et al,(1978) that the difference bet¥veen the values of r,e givenby the above t¥¥'o assumptions is very small.The vertical strain, 8., and shear strain in the z-eplane, y,e, are based on strain compatibility whereas theFig. l. Automated hollow cylinder testing s,.'stemcircumferential strain, ea, and radial strain, 8*, are basedon the assumption that the radial displacement varieslinearly across the wall of the specimen (Hight et al.,1983). The vertical displacement, Ah, and the sheardisplacement, 6, were measured by proximity transducersrtl(gap sensors) at the top cap. The current inner and outerradii of the specimen, / and r , at any moment during thr<jtest were calculated from the volume changes of the4 Jronspecimen, A V*, and its hollo¥v, A Vj, as follo¥vs:i;;Ii*,,,r,= ( - AV,)- rj'-ihjh ,Tr =l A(Vj - A)V= (2)a T '. crl- r jhjaa(7CrrCT, cr3Fig. 2. Stress component in hollow c_vlinder specimenL';iwhere hj, rjj and r.j are the initial dimensions ofspecimen. The initial dimensions ¥vere measured asetting the specimen (under suction of 19.6 kPa).they ¥vere updated and reinitialized at the start; i *i149CYC_L,lC DEFORMATION CHARACTER STICS OF SANDderiO 110'o¥**<t,-O4 timesf1eJ))i>-o3;UnloadingApi=16-134 kPa-o 4¥5l-o. _uToyoura Sand:)*'e = 0.68o20Isotropic unloading40 60 80 100100503 timescf. (kPa)Inner pressure, Api (kPa)Fig. 4. Membrane penetration per unit surface areaFig. 3. Volume change of hollow due to change in membranethickness;i¥vas:tingmade at burettes by differential pressure transducers.¥* oild byandmade for the membrane penetration and for the change inthe thickness of the inner membrane. The thickness of themembrane used was 0.3 mm. The thickness change of theinner membrane was evaluated by inserting a steel tubewhich had the same inner diameter as the specimen. If theL thesteel tube is used, the membrane penetration can beCorrections to the volume change measurements wereTheai rneglected for the change in the inner cell pressure. The¥vere(7= isvolume change of the hollo¥v would then be due to the;ht ofC o rrectedg e Eerc suhsconsolidation and shearing to calculate strains in therespective processes. Volume change measurements werei100Er8r,w ithoutbc o rre ctio nr50T r hcom rcssion-O.1 O 1 O 2 0_3O8r' 8e (%)Fig. 5. 8e and 8 wlth and wlthout correctlonchange in membrane thickness only. It is plotted against[1 thethe inner cell pressure, pj, in Fig. 3. It should bementioned, however, that other system compliances,}ss the19.6 - 137 kPa. This value is close to the value obtainedsuch as the volume change at the drainage tube, were alsoincluded in it. It can be seen from the figure that A Vj*by Goto (1986).)lasticchanged almost linearly with A pi, and the amount ofcycles in isotropic compression. Cell pressure (Tg waset al.system compliance was of the order of 0.050/0 in terms ofvolumetric strain for the stress change of 100 kPa, whichincreased and decreased bet¥veen 19.6 and 98. I kPa threewas si nificant for small strain measurements.Ioading. It can be seen that after applying correctionsRelationship bet¥veen A Vj* and A pj can be written asusing Eqs. (3) and (5), the variation of e* with theconfinin*' pressure became almost equal to that of 8e,tress,en byiig:iveui'z-e;as theA V{* = CA pj (3)based¥'ariesshearC= - 2.87 x 103 cm3/kPa was obtained for the range ofApi= 16 - 134 kPa.Volume change due to membrane penetration per unitducersarea is expressed as follows if the deformation inet al,,iAhdrawes, 1972; Vaid and Negussey, 1984):;;of thetimes and then increased to 137 kPa in the fourthexcept in the first loading. The discrepancy in the first10ading may be attributed to localized fabric around thelateral boundary (Ishibashi et al., 1996). With thesecorrections, small strains down to 1030/0 ¥vere measuredprecisely for all strain components.isotropic unloading is isotropically elastic (E1-Sohby andl outering theFigure 5 shows ee and e* during loading-unloadingAMP= A VT. '*rj/ - (4);;;'27z(/'. + rj)h3e.2TEST PROCEDIJREToyoura sand specimens with a relative density ofabout 500/0 ¥vere used in this investigation. Toyoura sand(1)where A VT* and s.*''*(2)are the total volume change includingis a uniform sand with subangular particles, mainlym:enibrane penetration and the vertical strain duringquartz, and is ¥videly used in Japan for research purposes.isotropic unloading respectively. A MP is plotted againstThe physical properties are as follo¥vs: mean grain sizeD50= O. 19 mm, specific gravity G* = 2.645, minimum voidthe logarithm of effective confinin*' stress, (Tg , as sho¥vn inof the:d aftea). B;tartPig. 4. The following relationship can be obtained:agAMP=Slogloa *(5)6.1 l!m was obtained for the stress range of (T* =ratio e*i*=0.609, maximum void ratio e***=0.973 anduniformity coefficient U*=1.56. The samples ¥vereprepared by three different methods, air pluviation (A.P.), water pluviation (W. P.) and dry rodding (D. R.) toproduce different soil fabrics. Details of the test program :150CHAUDHARY ET AL.Table 2.TestprogrammeCyclic shearing testsMethod of sampleDirection ofpreparation !sheaFing ((x.)Void Fatio at thebeginning of shearingo' (90 )1 22.5'(67 5')Air pluviation45' (=45')45' (45')0.793o.788o.780oe (90e)o. 76622.50 (67.50)45o (_450)0.767o.762O' (90e)22.5' (-67.4')Water pluviationDry roddin0.789o 792o.800;diameter from a constant height above the sand surface,as shown in Fig. 6. Samples of various densities can beobtained by changing the nozzle diameter and/or heightof fall. In this study, a nozzle diameter of 5 mm and aheight of fall of 140 - 150 mm were used to achieve therelative density of 500/0. It is considered that the fabric ofa sample produced by this method is similar to that ofaeolian deposits of sand (Tatsuoka et al., 1986; Kuerbisand Vaid, 1988).Water Pluviation MethodIn the water pluviation method, sand is phrviatedsimilarly to the air pluviation method, but through water.A constant depth of 30mm of deaired water ¥vasmaintained above the sand surface and the sand wasMonotonic shearin9: testsAir pluviationo'90"o.800o 782Water piuviationo'90'o.777o 820Dry roddin_go'90'o . 784o.778pluviated through a nozzle I .5 mm in diameter from aheight of 170 - 180 mm above the water level. The densityof the specimen was far lower than 500/0. Vaid andNegussey (1988) reported that the soil grains of meandiameter 0.4 mm reach terminal velocity almost instantly,in a drop height of 2 mm through water. Therefore, thedrop height is ineffective in controlling the density of awater-pluviated sample. To achieve a relative density ofare given in Table 2.500/0, the mould was tapped gently ¥vith a ¥voodenhammer. The fabric produced by this method simulatesthe deposition of sand through water found in manyA il' P!uviation Methodnatural environments and mechanically placed hydraulicIn the air pluviation method, dry Toyoura sand ispluviated into the mould through a nozz,le of a certainfills. Oda et al. (1978) reported that natural alluvial soilsand water-pluviated soils have a similar fabric andbehaviour.;Dry Rodding Metl70dThe dry rodding method was mainly designed to IAir Pluviation MethodFixed inner diameterproduce a relatively isotropic sample by destroying anypreferred orientation of sand particles in the air+{Constant height of fallpluviation method. The sand was pluviated in layers andeach layer ¥vas rodded (fully penetrated) 20 times with awooden rod 4 mm in diameter to destroy any preferredAir dry Toyoura sandorientation.}*The samples were saturated by first applying a vacuumand then a backpressure of 196 kPa. B-vaiues higher thanWater Pluviation Method0.95 were obtained in all tests. The samples wereconsolidated isotropically to 98. I kPa for about 4 hours.They were then sheared statically in a cyclic manner alongithree (Tf-directions, O' (90'), 22.5' (-67,5') and 45'(-45'), keeping the mean effective stress, p', and theintermediate principal stress parameter, b, constant atDeaired ¥vater 3 cm deepDrv Roddin MethodWooden rod diameter 4 mmSand p]uviatcd in layersand rodded a fixed no. oftimesO', 22.5' and 45' and then the direction ¥vas reversedalong 90', -67.5' and -45' respectively. The cyclicshear stress amplitude was increased gradually from onecycle to another. The number of cycle, N, was kept to one}at any amplitude. The stress paths follo¥ved in the testsare illustrated schematically in Fig. 7. The drainage ¥1'askept open during shearing. Monotonic loading tests werealso carried out on the three types of samples along the(Tf-directions of O' and 90' to see the anisotrop .' of the'6.Illustration of sample preparation methods*,98. I kPa and 0.5 respectively. The shearing started alongsamples.F oi*ii CYCLIC DCTZtce,at* a lzlaP'J>!,2bea cTght'Ida< Htheoft<-H>, 2rbis(TzCTlp' = 98 lkPa = const.Conditlon for b = cr2 - (y3 = 0.5, = constshearing (71cr3a(7 (deg.) = (0,90),(2 L5, ;7.) ,(45,p<hA[ ofT+151FORMATION CHARACTERISTICS OF SANDcTZD = consL(J }p ! ::: COnSt.21 Z1tedIter,2avasTmax =vasm apIsityIsotropic consolidation Cand4 1?rleanntly,Failure surfacetheFig. 7.of aStress conditions in test seriesv of)den1latesO[1anyaullcO150soilsand:( 100l*¥Od to::s 100o TOyoura Sando^:Jse)2,,17 - eto b=05)¥l;I+ v/aterpluviation' Dr}rroddinge)+'eo pr= 98'1 kPa, ,;{+ waterpluYiationDry roddinga, ,S[ any' Tr-1!i:st l'i-u IJi50F(e) (s' 50O4 1+e'*i,airandol O )ith a1 0 4lO-31 O2l0 lYmaxer ed*',,;uum s+Toyoura Sand' Ae P'*988rt}-e a .b*05Pa_. ',_ F(e) 2- 17-e( )l+eO I 0 3 1 0 11 O )1 O 41 0 2YiT)ax(a) c a = O'(b) (x. = 90'*,thanFig. 8.Secant shear modulus vs. maximum shear strajn from monotonic testsvereours.aiong-1 45'RESUl,TS AND DISCUSSIONd the!Stress Strain ResponseTypical plots of maximum shear stress, r*** { = ((TIint aiResults from the monotonic shearing tests are shown in(T )/2} , versus maximum shear strain, y*..(= ei - e3), foralongFig. 8. The shear moduli were normalized by the voidersedratio function, F(e)=(2.17-e)2/(1+e) (Hardin andwater pluviated samples are sho¥vn in Fig. 9. Anisotropyin stress-strain response can be seen comparing the threecases. Hysteresis loops ¥vere not symmetrical at highercyclicRichart, 1963), to take account of the effect of any slightTl onevariation in void ratio. The response was different for thethree sample preparation methods. It was stiffest for air:o onetestspluviation method alon*' O'. Comparing Figs. 8(a) and'e ¥vas8(b), it can be seen that the response was almost isotropicfor the dry rodding method, being close for both O' and90', compared to the other two methods. Anisotropy washighest for the air pluviation method, especially at as wereilg: theof the;snlall strain range of l0-4 or smaller. Results from cyclictests are discussed below.I"' "strain levels for positive and negative shear stressamplitudes, r **, ¥vhen the specimen was sheared along O'(90'), but they ¥vere symmetrical when sheared along 45'( - 45'). At very small stress amplitude, the response ¥vasapproximately linear ¥vith an extremely small hysteresis100p. But ¥vith increasing stress amplitude, the responsebecame increasingly non-1inear with larger loops. Thesamples were sheared until a shear strain response, y **,of about 30/0 was observed. H'c;l max (kP a)1 Ol(kPa)max10 IJ (kPa).*'l:fgi ?.'88' '2nd cycle10 ID max (kPa)*n ax, e '2nd cycle2nd cycleafa>C:z:-0.010'O1-0.010.01i-10:tmax-103rd - 6thcycles3oYm lx (olo)(b) a J :: 22.50 (_67.50)(a) a = O' (90')Fig. 9.Ls,, ･--Typicai strcss-strain plot for water ph viatioR method (p' =98.1 kPa=coust., /; =0.5): :(( o)100-3c:i>Vtdl n ax (kPa)O.O1d'oecolYmax (olo)v max(a/o)-10-0.01(c) a. = 45' (-45')lH 玉53CYCLIC DEFORMAτ10N C賊ARACT￡RISTICS OF SAND ｝ασ窯0。（90。）5一轍一ασ＝225。（一675。）囎り一一ασ＝45。（一45。）40．3 、（登一！ 一 一 一 、！ 1！F岬’ ｛、 3 一一 、、5■一 、一、、 齢、 1 ＼＼ ／戸 ｝ 一 、 ， 一 、 、 卿、ノ ＼ ， 一 、’ 、 、㌔ 、、“1 ＼0．i 輸馬 、 一’聯ぐ 甲’ρ一 鱒ノ ”ノ ーノ ’ ■ 、4 ・一諾 欄、 、 榊 、 、＼ 、， 爾幅9一興一、♂ フ0 、・、 1 ■、一0．2”求ω＞ 2‘． 、 ’ 一 一輌00 0．5一6 −4 −2 0 2 4 6 Ymax（％）symbol start ofcycle◇ 3rd（＆）緬pluvia亡ion O 4th ㊤ 5th2 ☆ 6￡h ασ嵩0。（90。）”一ασ露225。（一675。）榊”一卿一ασ謀45σ（一45。） 〆イニー囎’幽一’一曽一“嚇｝需一一隔榊、 、、・￥ 41・一一P一一一一験一一 ．＿二Σ，0ユま） 1♂ 4 1ρ．，鱒一一■一 ◇ 7一馬，”一金’一、 、 出臥く二，一一卿一騨一一幽一一一曽 團隔略隔卿、一 、” 、 、・￥、 ／1＼． σ岬 鰍、㌧ 桑 覧、 、、くs、 ／ ノ’ 轟一ぐ一瞬一｝葡囎一、一一噺輪噸乳00一〇．00、10．2一3 γmax（％）Symbolstartofcycle◇ 3rd（b）WatefPluvlation O 4th ㊥ 5th ☆ 6由 》3 ασ＝0。（90。）鼎一一ασ＝22．5。（一675。）疇一“騨｝ασ糾5。（一45。） ＄2 き丈 ／、 ／ ！ン’一一・｝』一、＼、／ ！欄一一’欄需曹醐騨爾一”ヘー 、轟ま ヤ ノ1 ’＼0．2莫 メ ＿＿＿ 一く￥＞ 0．3 乙ウつシ蔚 へ級ω1 霧〆二〆！’働一’・♪＼ ，，＿＿、 噛、、 リヤ めひイ0，1 つ、0 藝 蒙 馨 嚢 多0一4一2 0240 Ymax（％） 華 馨（c）Dryrodding 嚢 Fig．10、 Volume重ric s重raiηvs．maxi瓢um she訂strain0．51 154CHAUDHARY ET AL、100σ CS CC0。，22．5。，45。口τm器80隊oθ eq1［ o浅 60o 隠冨1⋮90。，一67．5。，一45。σ cs ec1i 1iYmaxじ▲、 （2、17一ε）2葦 400（Y灘x）A201oF（ε）留臓 1＋θo △ ▲ロ国夕 o0三〇 5Fl9．1玉。De6nit量o脆ofsec段臓tandequiva巽en柚e謎rmodu藍i10’41σ210り10一（Ymax）A （a）Airp豆uviation Figure10shows plots of vo互umetric strain versusmaximum shear strain for all three methods of sampleprep＆ration．The starting Point of the new loadlng cycle100has been marked on every plot．Anisotropy was observedin tbe volumetτic strain due to shearing direction and alsodue to sample preparation metho（is．The volumetric80strain was veτy small up to the secoad cycle（τm鍼一土7離臓okPa），but圭ncreased rapi（ily with increεlsing amplitude，oΣ 60The overall magn玉tude oぞvolumetric strain wεls l3rgestfor22．50（一67．50）in generaL T鉦e resi（1ua星shear stra圭nβ田隔 （2，王7一ε）2、develope（i for the a圭r pluv呈ated samples was larger than茎 40F（ε）躍0that for the water p互uv圭ated and （1ry ro（i（ied samp豆es。 o 1＋ε▲妬Moreover，the residual strain was larger for O。（900）an（1 擁2022．50 （一67．5。） compared to 45Q （一45Q） for anyparticular method。｝○口姫0 510−4i O’Shθα1・ル∫oゴ乙〃μ5秘 口1σ2 三〇r5圭0’（Ym昆x）A Secant shear moduli for cyclic loading，G。、，。，were（1e一且ned separate正y for positive and negative peak shearStreSSeS，τm抵，aS ShOWn in F三g．n．ReSUI総are ShOwn in（b）W＆terpluvlation藍Fig．12。Anisotropy of the specimen shown in F圭g．8formonotonic shearlng is also clear in the cyclic secant shear霧100mo（luli for（1i∬erent shearlng directions，ασ，For t難e airpluviatlou met｝10d，蜘e largest anisotropy was observed80between Oo an（i900，Tbe anisotropy was largest at sma至Istra重n near the beginning of shearing（reflects the ef㌶ect of露ごinitia1／inherent anisotropy）an（i gradua11y re（1uced as theΣ 60sheaぎ strain increased （re且ects stress−state 圭nduced♂ 宏 ｝Oanisotropy）． The ＆nisotropy was also af罫ected by the o§40samp豆e preparat量on method．It was the highest for the a圭r 図 （2．17一θ）26pluviation method，fo110wed by山e water p玉uviationmethod．It was lowest or almost non−ex至stent for t鼓e dryF（ε〉＝ 1＋ε▲瀦o20 ⑫ro（iding metho（1， This， αlong with the results from髪闇陪鳥漁o o01α5the＆nlsotropy developed by air pluviation was indee（i（iestroyed by the penetration ofthe woo（1en ro（1，giving a！oP410’310萎10P（Y田3x）A 霧 嚢 董more or Iess isotrop量c fabrlc．The three methods forme（icli任erent fabric structures in sand specimens g三ving rise to （cl Dry rodding 嚢 蓑di賃erentin重tialanisotropy．Fig．・2．Cychcseca繊ts勧earm。dul蒙vs．single践mplitude田ax蓋m腿嶢 Equiva互ent shear mo（iulus，（｝，q，on the other紅and，is 曲earst蘭 馨繭nedastheslope・fthestraightlinepassingthroughthe peak shear stress points as shown in Fig．11．Thisgives a di任erent value than the secant moduli clefined彗ハmonoton量c tests，indicates that in t数e dry ro（id呈ng metho（i 妻 aboveandincludesresp・nsesinthetw・・PP・site 盤 王55CYCUC D￡FORMATION CHARACTERISTICS OF SAND100 80阻oQ餓餌芝鮒覧なむ▲ 9）60ζ ▲ △ふασ＝225c，一675。 脇 口田 αα＝45②，一450o．στ maxA P W P D R o Goασ瓢0。，906難舞雛箋 ％鍾騒謹懸・ToyouraSand N＝三鯛o△研も①20’［1Il ﹁［10IIγmグ＝981kPa＝cons虹P40 （2．！フーθ）2 ムF（ε）＝雛 1＋θ 蜘o 陶亟1σ4玉0’1σ2 10弓1﹃10王0’1σ2（γ職a1）銅 1（Yma罵）SAFig．13．Va罫iation of equivalent shear mod観亘雛s with single騒mpmude shears重ra韮nFig。15・De舳t韮o凱ofbystere重icdRmpiロgrat隻o14 A PW P D、R o 、 ▲ 〔 、 雁1。2 圃 、 1o①ασニoc，90。ムムασ記25c，一6フ5c贋康ασ；45。，・45。0．5A P W P．D R0恥0．80 0．6㊤ 0 0ασ瓢0。，90。▲ △ △ασ諸225￠，一675。0、4 m （》 ￥ 喚＼、＼τoyouraSand ∼、▲ 、p『瓢981kPa雛conSt 穿 、、田 o 彊ασ＝45。，45。 ￥》，㎎、㎞＿濡極P’尋81kPa耗・ns皇， ／！瓢 仏 N＝1 ノノヒoここ0、20．4霞co沁maand是orsion＆lshcar 、tヒStsf・rN＝2（lw巳s謹kl ＾’0、2c国，1978）o10』⊃玉0冒4 1σ31σ2 、・幽 繭〆り儀臨稀謙綴鷲臨，、（艀転嚇e＝062−091圭0’監 ▲o ① 9T・y・uraSand ノ／ ノ ノ・灘 0．3 N＝1ノ函《① o雛釦ム ノ ノの0．1 〆重／ f・・N＝2（Tats・・kactal，1978） ⊂ン ε鷹062−0、91王σ1詩瓜ぞ（Y職）SA牙。・510甲21σ3玉0認1σ1（Ymaエ）SAF蓑g、14． Comparison of eqqivale蹴she3r modulus with publlshed 穿es曲SFigほ6， 殺ys重ere重ic dampi獄g ratio vs。si鳳gle a磁pl董tude s赴ear sαa置銀d董rectlons、The results are shown in Fig．13．丁簸ere was0．⊃almost簸odi狂ereuceduetoshe段ringdirectionforanyPartic婆1ar sample preparation method，Though some護萎due to the three sample prepara重ion methods，most of the萎data points plotted together in a very narrow zone for aの二 〇．3艶き「esponses in the t、vo oPPosite directions．If the samp玉eα0．つ妻direction，the equivalent mod111us woul（i represent an嚢婁霧 §馨 we「e sti貸マin one （iirection aad soft 三n the oPPositeThismaybeareas・nwhytheanis・tr・pyinequiva互entshear modulus due to sぬear量ng directions was neg圭iglble．D R． o oOασ＝0。，90。 ▲ oムασ＝225。，一6フ5。田ασ＝45P，一45。 曝 e△ 、eoToyouraSand ＼璽、。 N傭1葵Qドどむゆ ドじ の しじロしししゆほ ゑの ずヤヤ0．i【・Ts…。n融ls旨cartcstsf・丁／ 滋・K鷲2侮tsuok昼ct田，1978）ε灘062−09まaverage of modu員加the two directions．Tぬe anisotropicτespQnse in any particulaτtest is，therefore，obscure（1，A P，W，PP，講981匙Pa；co鳶5εequivalentm・dulusis，inasense，anaverage・fthe蓬嚢義ax漁ロmwide range of shear strain（less t簸an10鱗to10皿！）．The0、・、諭馨菱109minoτdi鉦erences were observed at very small strain leveI00奄・襲 o、、、o 、 o 田、・ 田0．204 0．60．8玉Gcq／Gγ筥106 To compare the results of this investigatlon with thoseaPPearing in the literature，shear modu1圭were noτma王ize（iF韮9．17。 Re置at董o鶏sbip betw’een damp韮ng raIio a爺d equiva董e賑〔 shearもy蟻es鉦eaτm・dul圭atashearstraln。f10−4f。rFig．14 modul豚Sa越d10−6f・rFig．17，w舳werecalc噸edusingthe娩・wingrelati・nspr・P。sedbyIwasakietal。（玉978）． CHAUDHARY ET AL156- 700 (2. 17 - e)2 p'o 5 (kgf /cm2)G?=10+ =GT=10 '1+e(2.17 e) p'04 (kgf/cm2)- 9001+eC. G. S. units have been used in the equations to keep theoriginality.istress, and in monotonic shearing tests. Anisotropy waslargest in samples prepared by the air pluviation method,follo¥ved by the water pluviation method. The samplesprepared by the dry rodding method exhibited an almostisotropic response. The equivalent shear modulusobscured an anisotropic response as it averaged responsesfrom the stiff and soft directions of anisotropic sand. TheThe normalized plot of shear modulus is given in Fig.equivalent shear modulus and the hysteretic damping14. It can be seen that the data points fell very close to theratio were bo, th very little affected by the initial soil fabricrange of data from torsional shear and resonant columnand the direction of major principal stress.tests on loosest to densest sand samples by lwasaki et al.(1978). Slight variations at small strain range may beattributed to the test conditions and difference in thenumber of cycles, N, (Alarcon-Guz,man et a]., 1989;Tatsuoka et al., 1991). In the present study, N= I wasadopted ¥vhereas lwasaki et al. applied 10 cycles at everyamplitude in torsional shear tests from medium to largestrain range and a large number of cycles in resonantcolumn tests for the strain amplitude up to l0-4. Thelarge number of cycles might have stiffened the responseof the sand. The dotted lines in the figure show the rangeof data for N= 2.ACKNOWLEDC.F,MENTS*The work presented in this paper is part of a researchprogram supported by Taisei Corporation. The help pro-vided by Dr. S. Goto of Yamanashi University, MessersA. Tateishi, K. Fukushima, K. Watanabe, T. Shida, Y.Shiba of Taisei Corporation is greatly appreciated.iiREFERENCF,Sl) AlaFcon-Guzman, A., Chameau, J^ L_, Leonards, CJA. and Frost,J. D. (1989): Shear moduius and cyclic undrained behavior ofHysteretic Damping RatioThe hysteretic damping ratio, h, is defined as shown inFig. 15. Like the equivalent shear modulus, the area ofthe hysteretic loop for the calculation of damping ratiosands, Soils and Foundations, 29 (4), 1051 19.'_) El-sohby, M. A. and Andrawes. K. Z. (197,-): Deformatiou characteristics of granular materia! under hydrostatic compression, Can.Geotech. J , 9 (9), 338350.3) Goto, S(1986): Strength and deformation characteristics ofincludes both the stiff side and soft side of the anisotropicgranular materials in triaxial tests, Drmaterial and therefore the anisotropy is averaged. Thedamping ratios are plotted in Fig. 16. The values fellTokyo.within the range given by Tatsuoka et al. (1978) based onresonant column and torsional shear tests on sand with awide range of density. Slight variations may be attributedto the test conditions and the number of cycles similar tothe equivalent shear modulus as the damping ratios byTatsuoka et al. (1978) were derived from the same testsreported by lwasaki et al. (1978). There was no significantdifference in values for the three methods of samplepreparation, or for the various directions of majorprincipal stress.Figure 17 shows the plot of damping ratio versus shearmodulus, which again indicates aimost no effect ofsample preparation methods and direction of shearing.Data points are very close to the dotted line suggested byTatsuoka et al. (1978).Engr*". Tllesis, University of4) Hardin, B. O_ and Richart, F. E., Jr. (1963): Elastic ¥vave velocitiesin _granular soils, J. Soi! Mech. Foi!nd. Engrg. Div , ASCE, 89(Slvll), 33-655) Hight, D. W., Gens. A. and S.vmes, M. J. (1983): The developmentof a new holio¥v cylinder apparatus for investigating the effects ofiprincipal stress rotation in soils, G otec/7niq:re, 33 (4), 355-3836) Ishibashi, ., Jenkins, J. T., Choi, J. W, and Parker IV, C_. L.(1996): The infiuence of boundaries on the volumetFic behaviour ofsolid and hollo v cyiindFical specimens of glass beads, Soi!,s airdi,Foundations, 36 (2), 45-55.7) Ishihara, K. (1983): Soil response in cyclic loading induced byearthquakes, traf c andvaves, Proc. 7th ARCSMFE, Haifa,Israel, 2, 42-66.!}8) Iwasaki, T., Tatsuoka, F, and Takagi, Y. (1978): Shear moduli ofsands under cyclic torsional shear loading. Soi!s and Foundations,18 (1), 39-56.9) Kallstenius, T. and Bergau, ¥V. (1961): Research on the texture ofgranular masses, Proc 5tll ICSMFE, 1, 165-170.lO) Kuerbis, R, and Vaid, Y. P. (1988): Sand sample preparation - theslurry deposition method, Soi!s and Foundations, 28 (4), 107-1 18.i}i:CONCl.USIONSStatic cyclic loading tests were conducted successfullyalong O' (90'), 22.5' (-67.5') and 45' (-45') onsamples prepared by air pluviation, ¥vater pluviation anddry rodding methods to study the effects of initial fabricand shearing direction on the stress-strain response, shearmodulus and damping ratio of medium dense Toyourasand over a wide range of strain. Anisotropy was observed in the stress-strain response and volumetric strainL11) Kuwano, J. and Ishihara, K. (1988): Analysis of permanentdeformation of earth dams due to earthquakes, Soi!s andFoundations, 28 (1), 41-) 5.!12) Ladd, R. S. (1974): Specimen preparation and liquefaction ofsands. J. Geotech. Engrg. Div.. ASCE, 100 (GTIO), 1 180=1 184.13) Ladd, R. S. (1976): Specimen preparation and cyclic stability ofsands, Liquefaction Proble,77s in Geotech. E,7grg. ASCE, National',;Convention, 199-226.,"'*14) Miura, S, and Toki, S (1982): A sample preparation Inethod and itseffect on static and cyclic deformation-strength properties of sand,Soi!s and Foundations, 22 (1), 61-77.15) Mulilis, J. P., C_han, C. K. and Seed, H. B,, (1975): The effects ofdue to the shearing direction. Anisotropy was also ob-method of sample preparation on the cyclic stress-strain behaviorof sands, Report No. EERC 7 -18, Univ of California, Berkeley.served in the secant shear modulus both in cyclic tests, de-16) Nakamura, Y., Hashimoto, S. and Kuwano, J. (1998): Thefined separately for each direction of major principaldevelopment of a hollo¥ ' cylinder apparatus for a measurement iu aI*; CYCLIC DεFORMAnON CHARACT￡RISTICS OF SAND157 wide Strain rangeラPノ’oc．33rゴ∫αPσπN‘π10〃‘τ1Co11プ1．o〃Gθo∼εch， damp加g of sands under c｝℃1ic玉oadiag and 萎！s relat茎o鶏 to shear βη9／3、，Yamaguch圭，JapaneseGeotec熱。Soclety，1，519−520。17）Oda・M・（1972）：三nitialfabrlcsandtheirrelati・nst・mechanlcaI modulus，Soi’5αnゴFo姻ゴφon5，18（2），25−40、22）Tatsuoka，F．，Ochi，K，，Fujii，S．and Okamαo，M．（三986）：Cyclic、』as）d，lles難 propertiesofgranula罫material，So’Z5α”ゴFoμηゴαf’oη5，12（1）， undrained tr玉a』x玉al and tors玉onal shear streηgth of sands forost 17弓6 di貿erent sample preparation methods，So鉱∫αηゴFoμηゴαだ0133，26iUS18）Oda・M・・Koishika・va・La澱d磁9αch呈」・（1978〉：鷺xpe曲e繊allses「hem91rch）ro−sersY，7rOS乞，or of1arac−cα11．Gs ofミi［yof）citles五，89pm巳nt∋cts of垂383、C L「o田of 嚢r’∫α’τごきごed byHa1fa， 舞ui1・礁‘π’0η5，ture of）n一由e莚）7−118、ma蘇eロしlz5σηづ妻幾裟糞［ion of4184．董）趣ofねtiQna！iandltS）fsand，挿ec〔5σf、ehaviOferke互ey・8）1τilelent ipa23） Tatsuoka， F，， Shibuya， S。 and Teachavorasinskun， S． （1991）： So’Z∫01∼ゴEα〃1伽10115，18（1），2シ38． Dlscussion，So’なαπゴ召o雄磁！’o’15，31（2〉，202−209．lg）Shlbuya・S・a鷺d田ght・D・W・（1987）l A bounding surface for24）Vaid，Y。P，andNegussey，D、（1984）＝Acriticalassessmentof 郎anularmaterials，So’なα11ごFo醐ゴ頗oη5，27（4），123−i36， membranepenetrationin出etrlaxlahest，σeoごθごh．71ε5励9／，，720〕Sllver，M・L and Park・T・K・（1976）：Liquefaction potentlaI）r1C蓬妻嚢 （3），23−4董． study of aa玉sotropic she＆r strength Qf sand by plane strain test， （2），70−76． evaluaτed from cycllc strain−controi1燈d properties tests on sands，25）Vaid，Y．P，and Negussey，D．（1988）：Prepa影atlon Qf reconstlωted So115αηゴEo瑚吻ioπ5，16（3），51−66。 sand spec茎mens，／痩4y‘7ηα∼ゴ 7ン’i鳳Yノ‘71 71851iηg oゾSoi1 ‘7ηごRocκン21）IaIsuoka，E・Iwasak玉・τ・and Takagl・Y・（1978）＝｝｛ysteretic ASTM SτP977，405−417． | ||||
| ログイン | |||||
| タイトル | stress Rate-Elastic Stretching Relations in Elastoplastic Constitutive Equations for Soils | ||||
| 著者 | I. Einav・A. M. Puzrin | ||||
| 出版 | soils and Foundations | ||||
| ページ | 159〜160 | 発行 | 2002/02/15 | 文書ID | 20447 |
| 内容 | 表示 SOILS AND FOUNDATIONSVol42, No, l, Feb. 2002Japanese Geotechnical SocietyIt would be interesting to assess what effect the missingDISCIJSSIONSterm would have on calculation of elastic strains duringplastic loading. The authors define the Gibbs free energyfunction (36) as:STRESS RATE-ELASTIC STRETCHINGRELATIONS IN ELASTOPLASTICG(crjj,F) y(p+ F) InP+ F 1po +CONSTITIJTIVE EQUATIONS FOR SOILS=)1+ 2 F tr((ri*Discussion by I. ElNAVi ) and A. M. PUZRINii)where y,The paper emphasizes the importance of the First Lawof Thermodynamics in description of elastic componentof elasto-plastic behaviour of soils. To ensure that theFirst La¥1' is satisfied, existence of energy potential shouldandare material constants, pto introduce thermomechanical principles into soil(7i*j = (Tij+pajj is the deviatoric stress tensor and F is theyield surface and is given by Eq. (28):-8 )F= Fo exp (9 1)ywhere 8 =8*Pi is the volumetric plastic strain, and p is amaterial constant. Differentiation of the Gibbs freeenergy function with respect to the stress tensor yields theelastic small strain tensor (38):modellin*', yet they seem to overlook this subtlety.In Eq. (1) the authors make an assumption with respectto decomposition of the stretching tensor D into elastic8i'J aG(aij,F)acfij(L +- -3 y6ijIno ++c_F F (Tstudied in the paper, this assumption reduces to convenjj =j'j +)1and plastic parts Djj =Dj*j + D ;Pj. In a case of small strains,tional decomposition of the strain rate tensor:(+ F8,'.= e i y In,P is defined by Eq. (68) using associated fiow rule(60) and extended consistency condition (59), while theelastic component (Eqs. (2) and (5)) is given by the ex-F I (92)Then the volumetric elastic strain is given byiP ･ In the model proposed in the paper, the plastic component- (Ti /3 is theisotropic hardening function related to the size of therelationship is easily derived by double differentiation ofalso made dependent on plastic strains, derivation of incremental elastic stress-strain relationship becomes subtler. The authors are to be congratulated on their attemptCTk J ) (90)mean effective stress, po is the initial mean effective stress,be assumed. Then the incremental elastic stress-strainthis potential. However, when this energy potential isF0+F (93)and its correct rate of change bypression:'.* aG(cr;j, iPj) .a(Tija(Tkl akl- yp +y( p - po) 'FF)( po + F)F ( p +while the rate of chan*"e calculated using Eqs. (2) and (5),i:';'where ((Tij, 8,Pj) is the Gibbs free energy potential func-as suggested by the authors, is simplytion.( ,')A-y -. p + F P (95)Unfortunately, Eq. (87) represents only a part of the"elastic" strain rate tensor. In fact, following Eq. (38),from definition of the CJibbs free energy potential we ob*,,tain:tic component of volumetric strain. Expression (95), on8i=j = aG((Tij, e iPj)I(88)acr *;**i;,,", a (orij, eiPj) aG((T ;, eiPj) .='jaai -j a (cTk klla(7i +j a 8lthe contrary, is not a full differential and its integrationwill depend on the integration path. The simplest example to consider would be isotropic consolidation, when F=p and F0=po, so that integration of expression (95)and the full differential of this equation is *'iven byi{Obviously, because Eq. (94) is a full differential, when in-tegrated it wiil produce a correct expression (93) for elas-(89)yields:(e, I)Ay In P (96)+ powhich reduces to Eq. (87) only for a case of non-plasticfoading. Therefore, for a general case of plastic loading(Eq. (69)), the authors have missed the term (a( !((Tij, e iPj) /while the correct expression for volumetric elastic strain isaaija 1) l' reflecting changes in elastic strains dueobtained by substituting F=p into expression (93):toges in plastic strains.By Koichi Hashi_ uchi and lan- F. CoHins., Vol. 41, No 2, April 2001, pp. 77-87Doctoral Studen and Associate Professor respectively at the Technion, Israel Institute of Technology, Haifal 59 DISC_tJSSIONS16050[200a [i40- 301500 [eo 20-ce- f' : e* Iooo r*'50a [Correctedplastic[Eq. (4110the ela:oof e' ir500 1000 20001500op [kPa]Authorsrowhere i*o oa8o o 002 o 004 o 006o olwhereFig. 7. The relative error in elastic strainssYFig. 6. Comparison betll'een the non-plastic volumetric-strain fornormally consolidated clay in isotropic consoiidationsiderable step forward as compared to models where;!neither elastic nor plastic behaviour satisfies the FirstLaw. However, as we have seen, an attempt to model thedependency of eiastic properties on plastic strains withinthis mixed frame¥vork may lead to inconsistencies.(1 +pe = - y In p0+p (97)The error resulting from the missing term can be quantified by considering a particular parametric case suggestedby the authors: = O.1, y =0.004 and p0= 100 kPa. Elastic stress-strain curves obtained in isotropic consolidationare compared in Fig. 6, while the relative error 6 = { [(e,'.)A-8,*,]/e,*,} >< 1000/0 is plotted versus the mean effectivestress in Fig. 7. In conclusion, it is worth mentioning thatin the writers' vie¥v this mistake could have been avoided.Necessity to satisfy the la¥vs of Thermodynamics whenmodeling behaviour of materials has been reco*"nized bymany researchers. Unfortunately, some of them limit;;IThis problem can be easily avoided by applying a moreconsistent thermomechanical framework to modeling of Ielasto-plastic behaviour, (e.*'. Collins and Houlsby,1997). Important feature of this framework is that theand thlGibbs free energy represents a potential for total strainsand not just elastic ones. In this case, assumption of dependency of elastic properties on plastic strains would automatically lead to appearance of additional strain termscoupling between elastic and plastic strains. As a resultboth elastic and plastic behaviour ¥vill be consistent ¥vithThethe First and the Second Laws of Thermodynamics andno terms will be missed.TheEqs. (1their efforts to satisfy the First L,aw only by elastic com-REFERENCE,ponent of this behaviour, while the plastic component isfound from more or less conventional frame¥vork, ¥vhichhas nothing to do vith Thermodynamics. Still it is a con-36) Col ins, I. F. and Houlsby, G. T_ (1997): Application of thermomechanical principles to the modeling of geomaterials. Proc.jRoya! Societ_v of I,0,Idon. Series A, 453, 1975-2001 .fSTRESS RATE-ELASTIC STRETCHINGRELATIONS IN ELASTOPLASTICCONSTITUTIVE EQIJATIONS FOR SOIL,S*)Closure by KOICHI HASHIGUCHlii)and IAN F. ColuNsiii)tegration of Eq. (32) or (33) under the condition F=const.whereOn this circumstance the discussers derived the elasticvolumetric stretching Eq. (94) inversely from the com-a :O a'The telplementary energy function (36) ¥vithout fixing F. In ¥vhatfollows let the novel elastoplastic constitutive equation be(35), the complementary energy function (36) and thestress-elastic strain relation (37) or (38) ¥vas sho¥vn as aForderived by the first author formulating the complete setconstitthe halof strain energy function, complementary energy function, stress-elastic strain relation and stress rate-elasticstretching relation, whilst the Hooke's type elastic laThe stress rate-elastic stretching relation (32) or (33)¥vas formulated based on the physical considerations. Onthe other hand, the novel set of the strain energy functionelastic;'lp(8e,does not hold any more, and further the complexity is**"caused by the elastic-plastic coupling in not only elasticibut also elastoplastic constitutive equations.Assume the following complementary energy function'G (a,G for infinitesimal elastic strain 8*.supplement, ¥¥'hich is derived formally by the time-in,;i) Voi. 41, No. -?, April 200i, pp^ 77-87. (Previous discussion by I_ Einav and A. M. Puzrin, Vol 42, N0. l, February 2002, pp 159- 60.)i professor. CJraduate School of Bioresources and Environmemal Sciences, Kyushu University, Hakozaki 6-l0-1 . Hi_gashi-ku, Fukuoka 812i)'*i"':from8581. Japan{ii) pFofessor. Department of En*aineering Science, School of Engineering, University of Auckland, Auckland. Ne¥v Zeaiand.# | ||||
| ログイン | |||||
| タイトル | stress Rate-Elastic Stretching Relations in Elastoplastic Constitutive Equations for Soils(closure) | ||||
| 著者 | Koichi Hashiguchi | ||||
| 出版 | soils and Foundations | ||||
| ページ | 160〜164 | 発行 | 2002/02/15 | 文書ID | 20448 |
| 内容 | 表示 DISC_tJSSIONS16050[200a [i40- 301500 [eo 20-ce- f' : e* Iooo r*'50a [Correctedplastic[Eq. (4110the ela:oof e' ir500 1000 20001500op [kPa]Authorsrowhere i*o oa8o o 002 o 004 o 006o olwhereFig. 7. The relative error in elastic strainssYFig. 6. Comparison betll'een the non-plastic volumetric-strain fornormally consolidated clay in isotropic consoiidationsiderable step forward as compared to models where;!neither elastic nor plastic behaviour satisfies the FirstLaw. However, as we have seen, an attempt to model thedependency of eiastic properties on plastic strains withinthis mixed frame¥vork may lead to inconsistencies.(1 +pe = - y In p0+p (97)The error resulting from the missing term can be quantified by considering a particular parametric case suggestedby the authors: = O.1, y =0.004 and p0= 100 kPa. Elastic stress-strain curves obtained in isotropic consolidationare compared in Fig. 6, while the relative error 6 = { [(e,'.)A-8,*,]/e,*,} >< 1000/0 is plotted versus the mean effectivestress in Fig. 7. In conclusion, it is worth mentioning thatin the writers' vie¥v this mistake could have been avoided.Necessity to satisfy the la¥vs of Thermodynamics whenmodeling behaviour of materials has been reco*"nized bymany researchers. Unfortunately, some of them limit;;IThis problem can be easily avoided by applying a moreconsistent thermomechanical framework to modeling of Ielasto-plastic behaviour, (e.*'. Collins and Houlsby,1997). Important feature of this framework is that theand thlGibbs free energy represents a potential for total strainsand not just elastic ones. In this case, assumption of dependency of elastic properties on plastic strains would automatically lead to appearance of additional strain termscoupling between elastic and plastic strains. As a resultboth elastic and plastic behaviour ¥vill be consistent ¥vithThethe First and the Second Laws of Thermodynamics andno terms will be missed.TheEqs. (1their efforts to satisfy the First L,aw only by elastic com-REFERENCE,ponent of this behaviour, while the plastic component isfound from more or less conventional frame¥vork, ¥vhichhas nothing to do vith Thermodynamics. Still it is a con-36) Col ins, I. F. and Houlsby, G. T_ (1997): Application of thermomechanical principles to the modeling of geomaterials. Proc.jRoya! Societ_v of I,0,Idon. Series A, 453, 1975-2001 .fSTRESS RATE-ELASTIC STRETCHINGRELATIONS IN ELASTOPLASTICCONSTITUTIVE EQIJATIONS FOR SOIL,S*)Closure by KOICHI HASHIGUCHlii)and IAN F. ColuNsiii)tegration of Eq. (32) or (33) under the condition F=const.whereOn this circumstance the discussers derived the elasticvolumetric stretching Eq. (94) inversely from the com-a :O a'The telplementary energy function (36) ¥vithout fixing F. In ¥vhatfollows let the novel elastoplastic constitutive equation be(35), the complementary energy function (36) and thestress-elastic strain relation (37) or (38) ¥vas sho¥vn as aForderived by the first author formulating the complete setconstitthe halof strain energy function, complementary energy function, stress-elastic strain relation and stress rate-elasticstretching relation, whilst the Hooke's type elastic laThe stress rate-elastic stretching relation (32) or (33)¥vas formulated based on the physical considerations. Onthe other hand, the novel set of the strain energy functionelastic;'lp(8e,does not hold any more, and further the complexity is**"caused by the elastic-plastic coupling in not only elasticibut also elastoplastic constitutive equations.Assume the following complementary energy function'G (a,G for infinitesimal elastic strain 8*.supplement, ¥¥'hich is derived formally by the time-in,;i) Voi. 41, No. -?, April 200i, pp^ 77-87. (Previous discussion by I_ Einav and A. M. Puzrin, Vol 42, N0. l, February 2002, pp 159- 60.)i professor. CJraduate School of Bioresources and Environmemal Sciences, Kyushu University, Hakozaki 6-l0-1 . Hi_gashi-ku, Fukuoka 812i)'*i"':from8581. Japan{ii) pFofessor. Department of En*aineering Science, School of Engineering, University of Auckland, Auckland. Ne¥v Zeaiand.# 161DISCUSSIONSNote that the Hooke's type elastic law does not hold by8' aG((T, H. H) (98)the appearance of the second and third terms in the righthand side of Eq. (99) due to the elastic-plastic coupling.The substitution of the flow rule (60) into Eq. (99) Ieadsa(7-/where H and H are the second-order and the scalar valuedplastic internal variables, respectively, as described forEq. (41) of the yield condition. Further, if we assume thatthe elastic stretching is given by the time-differentiationtotr (N ) ( a2G a2G )+ Mp_ acraHh+aaaHof 8' in Eq. (98), it holds that. a2G . a2G2000D'=E (T+aaaH H+ aaaH HThe stretching D is obtained from Eqs. (1), (60), (61)and (101) as follows:(99)' (N'+ ( I 02)M p aaaH aaaHD E-la+tr(N ) a2G h+ a2G- )hwhereElwherea2Gfrom Eq. (102) as follows:e Firstdel the_M +tr(NEN)+trtr (NED)NE aG¥vithina moreiia( aH:ling ofDulsby,(NE-h) +h tr)a2Ga(1 aHand thus the plastic stretching is described ashat theDP_ __ (___N(104)(NE- 2_)M +tr(NEN)+tr NE aGaaaHtr (NED)strainsl of de-a(TaH,uld au-n termsh) +h tra2GThe loading criterion is given as follows (Hashiguchi, 2000):a resultntThe positive proportionality factor in the flow rule (60)is expressed in terms of the stretching D, rewritingas A ,(1 OO)acFaoFDPvith.*;0:A > O,D P = O:)i:ics andThe inverse expression of Eq. (102), i.e. the expression of the stress rateEqs. (1), (l02), (103) and (105) asO. (105)in terms of the stretching D is given froma 'h+h/ (N+_ tr(N'D) (-2d2Ga2G() IaG-p - --E (-acFaHaaaHof ther-=EDls, ProcM +tr(NEN)+tr NE aoraH*)06)h) + h tr NE a(7aH:'=const.where < > is the McCauley's bracket, i,e. <a>=a forelasticle com"a :O and <a> = O for a<0 for arbitrary scalar variable.The terms containing in Eq. (106) are induced by theIn ¥vhatelastic-plastic coupling.ation bcFor the present soil modei the complete set of elasticconstitutive equations taken account of the variation inthe hardening function F can be given as follows:)lete sety func'* ;e-elasticV/(8',F)=y(p0+ Fo)exp -tr8' + Ftr8'stic lal ',lexity isyv elastic+1Ftr s'*2+ - Ftr (a 8'*)2FoG(a, F) = y(p+ F) Jlln ( p+ F ) _ IIJi'unctiono +oka S12,{I,ifrom which it holds that+e_8F + - aF8e*Fo(109)e aG((5f'F)8-aa)yln/P+ F )I++('-(7-Foo +FO' p0+ Fo(trD )1+ FDe + FI+F(107)a=(110)8e*+(To. (111)_Fo+ I tra* ' l2 FFO tr (a'a'); 59- 1 60.)(F) tr(1aW(8e,= - (p0+ Fo)exp(l08)_p + yF) F*-3( FI_D*3(d.1+py+ F)F2CF'(1 12) 王62DISCUSS三〇NS2，000’鞭■！1，500 P（kPa）EinavandP面nl ， （1＋9）P ゆ！1，000Eq（97）1εソ鳶ザ｝n跳仰1■5001 ’ ’ ’ ○ ε PE“（118）1εv甑｝71nπ‘一● ，E“（119）・阜1柔9暢 ’00一〇〇〇2a一〇〇〇6 −0008 −0010一〇〇〇485韮Fig．8．Co即朗so獄ofe隻as窒董cvo夏ume皇ricstrainsca匪cu藍atedbythreee簾asl鑑ceoロs舳tiverelat董onsin伽e簸ormaトcoロso蓋ida重ionprocess一〇〇30．5y一〇．02石6v0．25一〇〇1罰000 1，000 2，000 3，000ヂ P（kpa）eIsoPセopic consolidatio且霧O605 0、677 9一，碕い嘘，一’匿甲 n 騨 ■ ” P 囎 一 孕 ’ ゆ■甲’ 』 甲一一？，酔，囎圏脚 ’ひ7一’ ●狩1’■，’一’”一 騨 一 〆．牢1﹃8置﹂8 掃r 趣『 ヌεγ O。3025，！ 3P ’1r1門 齢鼎0．25’ミ’’ノli卜’ 警 ’！i’ i 000、2llε＊1001一〇〇2一〇〇5 き薫嚢8v O005εv O0、02讐嚢0，1 O、04 0．1 0、2 0 005 0．10 1ε＊l l蕊＊l T船頭alc・mpress孟on T打a滋alextensio簸wi出c・nstandateralpress町e wi血const瓢1ateralpress肛eFig。9。（114）Meas級red cu罫マe（・セt刃’’’81 ’＝ri1ε＊ll1一’’『0，夏嚢 1σ州P 『i3ρ！華弄（！陛謬﹃iI lfI i，1σ＊llγ’’膠1 ， ’置 ’00．5■鱈 − ’ 一甲叫’，0、3tlうa獄dpredictedcurve（ （一一一P。蚤ss。n・srat量。））by重hee蓋as童卿sticc。。stit櫨iveEq。（106）wi撫Eqs，（113）臼・δ藝 __ yI+ I a*1J F'i{163DISC_USSIONSE,jkl(p+y F 32 ii6kl+ F(6ik6i +6il6jk)The maximum relative difference due to f is(113)( -1) i f y I IJ 6ijakk :_3 3(p+ F) 2 Fi jkl1+ 4 F (a k6, + 6* 6Jk)(113)'anda2G{acFaH3( P +F)F2(1 14)noting the relationsp + = Fex tr )8p( e(1 1 5)po + FO yof* a _F Fo8e*(1 1 6)/(1 +atmost as known by comparing Eqs. (1 18) and (1 19). Thus,the relative difference is 9.090/0 constantly in the monotonic isotropic normal-consolidation process with = O. 1used in Fig. 4 as shown in Fig. 8, although it increases upto 400/0 in Figs. 6 and 7 calculated by the discussers usingtheir Eq. (97) which involves the inappropriate replacement of the initial pressure to the current pressure asknown by comparing it with Eq. (1 18).Further, the prediction by Eq. (106) with Eqs. (113)and (1 14) with the full elastic-plastic coupling shown inFig. 9 is almost same as the prediction by Eq. (71) withEqs. (34) and (72) shown in Fig. 4, whilst same values ofmaterial parameters are used for these figures. Eventually, the difference of the prediction due to p would not beso large as examined for the monotonic normal-consolidation process in which the difference exhibits maximum,whilst not only the elastic but also the elastoplastic con-The elastic volumetric strain eis given exactly fromEq. (110) asP/i!^'I8/p+ Ftr 8'= y In 0+ FO (1 17)vhich reduces toe = ylnP (118)po{;for the monotonic isotropic normal-consolidation process (F=p) studied by the discussers, in which the ratio ofthe increment of hardening function F to that of pressureI,p is maximum, i.e, the maximum elastic-plastic coupling(fr/p = max.) is realized, the elastic volumetric strain*i.being independent of the material constantprescribingthe elastic-plastic coupling. On the other hand, the elasticIvolumetric strain due to the stress rate-elastic stretchingrelation (32) is given by{=_ y In Po (1'8'1 9)' (1(-)+p{**'{i;'!;.*artd;"'*I;*;'stitutive equations becomes complex by incorporating therate-type elastic constitutive equation with the term of frbringing about the full elastic-plastic coupling.The therrnomechanical approach at the present stagewould not play an inevitable role for modeling concreteforms of constitutive equations as was indicated againstthe conclusion of Collins and Houlsby (1997) by the firstauthor (Hashiguchi, 2001). The elastic constitutive equation formulated in the article would give sufficiently exactprediction for practical use, whilst a more elaborateelastoplastic constitutive equation taken account of thefull elastic-plastic coupling is given in this closure.REFERENCE37) Hashiguchi. K. (2001): On the thermomechanical approach to theformulation of constitutive equations, Soi!s and Foundations, 41(4), 89 94. | ||||
| ログイン | |||||
| タイトル | scale-Modelling of Fluid Flow in Geotechnical Centrifuges(closure) | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | 164〜164 | 発行 | 2002/02/15 | 文書ID | 20449 |
| 内容 | |||||
| ログイン | |||||
| タイトル | Announcements | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | 165〜165 | 発行 | 2002/02/15 | 文書ID | 20450 |
| 内容 | |||||
| ログイン | |||||
| タイトル | JGS NEWS | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | I〜II | 発行 | 2002/02/15 | 文書ID | 20451 |
| 内容 | 表示 | ||||
| ログイン | |||||
- タイトル
- 表紙（論文報告集）
- 著者
- 出版
- soils and Foundations
- ページ
- -〜-
- 発行
- 2002/02/15
- 文書ID
- 20431
- 内容
- ログイン
- タイトル
- 目次（論文報告集）
- 著者
- 出版
- soils and Foundations
- ページ
- -〜-
- 発行
- 2002/02/15
- 文書ID
- 20432
- 内容
- ログイン
- タイトル
- 表紙（Soils and Foundations）
- 著者
- 出版
- soils and Foundations
- ページ
- -〜-
- 発行
- 2002/02/15
- 文書ID
- 20433
- 内容
- ログイン
- タイトル
- Contents（Soils and Foundations）
- 著者
- 出版
- soils and Foundations
- ページ
- -〜-
- 発行
- 2002/02/15
- 文書ID
- 20434
- 内容
- ログイン
- タイトル
- Collapse Loads over Two-Layer Clay Foundation Soils
- 著者
- R. L. Michalowski
- 出版
- soils and Foundations
- ページ
- 1〜7
- 発行
- 2002/02/15
- 文書ID
- 20435
- 内容
- ログイン
- タイトル
- seismic Passive/Active Thrust on Retaining Wall-Point of Application
- 著者
- D. M. Dewaikar ・S. A. Halkude
- 出版
- soils and Foundations
- ページ
- 9〜15
- 発行
- 2002/02/15
- 文書ID
- 20436
- 内容
- ログイン
- タイトル
- Effects of the Stiffness of Soft Clay Layer on Strong Motion Response
- 著者
- Akira Yamaguchi・Motoki Kazama・Hirofumi Toyota・Masaki Kitazume・Takahiro Sugano
- 出版
- soils and Foundations
- ページ
- 17〜33
- 発行
- 2002/02/15
- 文書ID
- 20437
- 内容
- ログイン
- タイトル
- Development of Sensor for Monitoring Seismic Liquefaction
- 著者
- Yoshihisa Shimizu・Susumu Yasuda・Iwao Morimoto・R. Orense
- 出版
- soils and Foundations
- ページ
- 35〜52
- 発行
- 2002/02/15
- 文書ID
- 20438
- 内容
- SOILS AND FOU*NDATJONSVol 42, No. i, 5369, Feb^ )_002Japanese C.eotechnical Society, ,a?lcp(1-situ )EXTERNAL STABILITY OF VERTICAL, EXCAVATIONS INanceslrnics,SOFT CLAY WITH SELF-SUPPORTED DMM WALLSvaterhiba-ALA'A EL NAHAsi) and JIRO TAKElvIURAii);as (inte andABSTRACTh It*a+vSix centrifuge tests ¥vere conducted to study the possible failure mechanisms for open excavations in soft clay withDMM self-supported valls, and the pre-failure soil and ¥vall behavior, as well as the effect of some parameters on thewall external stability. In the tests, in-flight excavation was conducted until failur'e. The DMM wall was modeled by awall made from aluminum and acrylic plates, which ¥vere instrumented with pressure cells to measure the active andpassi¥'e earth pressures, and the base contact pressure of the ¥vall during excavation. Upper bound analysis ¥vasconducted to verify the efficiency of the currently used design method, and to identify the main parameters which affect)n onSi e,)19ion of; underthe ex. ternal ¥vail stabilityr andIt ¥1'as found that the failur'e of the excavations with DMM self-supported walls floating in the clay, took placesuddenly ¥vithout marked pre-failure soil and wall movements. The main parameters which affect the wall stability arethe ¥vall dimensions, the soil strength profile, the adhesion between the ¥1'all surfaces and the surrounding clay, thestrength anisotropy, and the surcharge on the clay surface. The soil strength profile and the adhesion between the ¥vallsurfaces and the clay ¥vere found to be the most important parameters.arnin, Earth)ance aiA SCE.Kev. ,1=0rds: centrifuge test, deformation, DMM, open excavation, self-supported wall, soft clay, stability,bound calculation (IGC: H2)economical reasons.INTRODUCTIONThe external wall stability is normally estimated usin_",_Self-supported ¥valls (SSW) made by the deep mixingmethod (DlvlM) are a relatively recent application forthe classic desi_ n method of the self-supported wallsexcavations in soft clay. This type of wall is relativelyexpensi¥*e compared to strutted or anchored excavations.Chen et al. (1996), and Azuma et al. (1999). In this(gra¥'ity type ¥valls) as described by Shiomi et al. (1996),method, Rankine earth pressure distributions on the ¥vallsides are used, assuming smooth vertical ¥vall surfacesand isotropic soil conditions. As there are no recordedfailure cases for excavations supported by this wall type,the current design method is considered to provide safewall designs, althou*'h the actual safety factors are notHo¥vever, the strutted excavations are not economicalwhen a Jarge area of open excavation is required. Eveninstalling and removing the struts during constructionresults in complicating and slowing do¥vn theju p perconstFucrion process For soft soils where no *"oodbearing strata for ground anchors is availabie, usingclearly recognized. This design method has someuncertainty. For example, the possible failureanchors is also expensive. Therefore, this type of ¥vallbecomes economically feaslble for lar*'e open excavationsmechanisms for this wall type have not been thoroughlyin soft thick clay layers.investigated yet, the factors affecting the wail stability areAs the stiffness of the treated soil ¥vith DMlvl is farhigher than that of the untreated soft soil, e.g., mor'enot kno¥vn, and further ambiguity is caused by ignoringboth strength anisotropy, and the adhesion between thethan t¥vo order difference, the external stability andsoil and the ¥vall verticai surfaces. This has lead to over-internal stability are evaluated separately in the design ofdesigning walls to avoid sudden failures, as reported byShiomi et al. (1996).the ¥vall (Kita2;ume et al., 1996a). Due to the lo¥v tensilestrength of the non-reinforced DM columns, the currentdesi_ n practices adopt a ratio of height/breadth (H/B)of the valls of not more than 2 to avoid subjecting theKitazume et al. (1996a) pointed out in their JGS-TCReport that neglecting the adhesion on the interfacesbet¥veen the DM improved ground under marinewall cross sections to any tensile stresses. On the otherhand, that ratio is not allowed to be less than l.O forconstructions and the surrounding soft grounds, ¥vhich isadopted in the current design practices, results in)Lecturer, Department of Civil and Water Engineerin_g, National University of Science and Technolo_gy, Bulawayo, Zimbabwe.i) Associate PFofessor, c.ET/SCE,,Asian Institute of Technology, P O. Box. 4, Klong Luang, Pathumthani l)-120, Thailand.Manuscript ¥vas Feceived for review on January 31, 2000.¥Vritten discussions on this paper shouid be submitted before September I , 200'_ to the Japanese Geotechnical Society, Sugayama Bldg. 4F,Kanda A¥vaji-cho 2-23, Chiyoda-ku, Tokyo 101-0063, JapanUpon request the closing date may be extended one month.53sL' 54NAHAS AND TAKE*lviURAunderestimatin*･ the external stability of the improvedground against the horizontal and vertical forces. Theyalso sho¥ved that considering the adhesion is importantunstrutted sheet pile and cliaphra_ :m ¥valls. Kimura et al.for proper evaluation of the field behavior of theimproved ground mass.simulating excavation problems. Bolton et al. (1987,The internal stability of this type of walls has beenstudied by some researchers. To reduce the wall breadth,Kitazume et al. (1996b) and Babasaki et al. (1998) studiedthe failure mechanisms of the reinfor'ced DMM gravitywalls and the applicability of the reinforced concrete's¥vall excavations in clay and presented a method tostructural calculations in its design.Centrifuge modeling has been used for studying thestability of excavations in clay, supported by strutted and(1993), and Takemura et al. (1999) presented the benefitsof using centrlfuge modeling and an in-flight excavator in1988) conducted a series of centrifuge tests on diaphragmpredict the deformation of the ground due to excavationwith the diaphragm walls unpropped and propped at thetop. Centrifu*'e research on possible external failuremechanisms and the parameters affecting the externai stability of the self-supported DMM ¥valls is very limited.Among these studies are Chen et al. (1996) and El Nahaset al. (1999).In this paper results of six centrifu*'e model testsconducted to study the failure mechanism for the ¥valls¥vrth "H/B 1 2" are presented. The soil and wallin-fiight excavator upper sandgate TnotoFL,VDTsIayerdisplacements ¥vere monitored until failure, and theL DTS sur ace markerseffects of the ¥vall dimensions, and the adhesion bet¥veenvflter supplysolenoid valve (a)solenoidvalve (a)the soil and¥'all surfaces on the ¥vall external stability arediscussed. Upper bound analysis was also conducted toverify the current design method and to study the factors{>solenoid'vlvalve (b)Vs;v)vltankdumpeaffecting the external wall stability.VlCENTRIFUGF, MODF,L TF.STSTest Systelns a/7cl ConditionsTIT Mark 111 Centrifuge, in-fiight exca¥'ator and steelmade model container' ¥vith a tr'ansparent acrylic ¥vindo¥vsoiimm¥¥'ere used in the tests. Their details and specifications aregiven by Kimura et al. (1993) and Takemura et al. (1999).Test setup used in this study is sho¥vn in Fig. 1.' pore pressure transdilcerFig. 1. Test setupLDT target plateL,VDTswall extension platesctaluminum platesJacrylic plates8]vertical holes9]back sidefront side10]1l][12&13& 14]149.481[]Fig. 2.)lN)voo10 3 @ 20.3 Iounlt: mm.vlSchematic lal_ out for model wallPressure Cell No.cr¥ 55STABILiTY SELF-SUPPORT D D d¥* ,1 ¥¥,ALLItor in(thickness t = 20.7 mm) and the side aiuminum plates (t =10 mm) were used in all the tests, and the ¥vall breadth¥vas adjusted by adding additional vertical acrylic plates(1987,between the central acrylic plate and the tlvo side[ et al.enefitshragmaluminum plates. In SSW-O, 3, 4, and 6 t¥vo additionallod tovationthe central acrylic plate and the aluminum plates, asat theshown in Fi**. 2. In SS¥V-5, four additional vertical platesf ailure¥vith the same thickness ¥vere used. In SSW-7, twolal sta-additional vertical plates with different thickness (t = 10. 1irnited.mm) ¥vere used. To increase the wall height, t¥vo andvertical acrylic plates (t = 20.3 mm) ¥vere inserted betweenthree additional horizontal plates lvere also assembled onNahasthe vertical plates in SSW-4 and SSW-6 respectively, assho¥vn in Fig. '-. The ¥vall unit ¥veight was adjusted by31 testse vallsputtin*' Iead shot inside the vertical holes in the vertical･;･･･ *acrylic plates in SSW-4 and 5, and by making additlonalvertical holes in the acrylic and aluminum plates in SSW7. However, some difference in the unit ¥veight cou]d notld wallnd the)etlveeniliry arebe avoided in the testF](, 3. Model wallunit wei*･ht ¥vas 16.8 kN/m3 in SSW-O, 3, 4, and 5. InSSW-6 and 7, the wail unit vei__･ht ¥vas 17.9 kN/m; and19.4 kN/m3, respectively. In SS¥V-O, polished surfacesicted tof actors(a) lvlodelvith different dimensions. The ¥vallvallAs the purpose of the centrifuge model t,ests ¥vas tostudy the external stability of the self-supported DIMM¥vere provided on the wall of the aluminum plates towith a lot of instrumentation using real cement-treatedcreate the smooth wall condition. In the other tests, therough ¥vall condition ¥vas created by *'1uing sandpapersheets (No. 100) on the ¥vall vertical surfaces, and on thetnd steelsoil, the Dlvl ¥vall ¥vas modeled using different materials.wall bottom.¥vindo¥1*The model ¥vall used in the tests consisted of 2 aluminumplates and several acrylic plates, as shown In Figs. 2 and3. The aluminum plates ¥vere instrumented ¥vith 6 and 5pressure cells on the back and front sides of the ¥vall respectively. One pressure cell was also installed on the tip(b) Soils used in the tests and test setupThe model ground consisted of three layers: upper dry'all and it ¥¥'as rather difficult to make the DMM ¥ 'allions are(1999).of each of the t¥¥'o aluminum plates and the central acrylicloose Toyoura sand, soft kaolin clay, and lo¥ver denseToyoura sand as sho¥vn in Fi**. 1. Under the centrifugalacceleration of 70G adopted in the tests, the thickness ofthe layers in the prototype scale ¥vere I .O m, 10.7 m, andplate. The capacity of pressure cells No. l, 2, 3, 4, 7, 8and 9 ¥vas 7-00 kPa, and the capacity of the other cells hvas500 kPa. In each test, the ¥vall ¥vas reassembled to adjustits dimensions.2.45 m, respectively. . Table 2 gives the physical andThe ¥vall dimensions (H: hei_ :ht and B: breadth) forvertical consolidation pressure ((T(.) and axial strainseach test are sho¥vn in Table I . The central acrylic platewhich ¥vere obtained from undrained compression andTable 1.support condition (kN /m3 )condition¥)excess pore water pressures (Au) normalized by theTest conditions and resultsVertical Surf ace y * 1Test Nomechanical properties of the kaolin clay. Figure 4 sho¥vsthe relationships bet¥veen deviator stresses (q) and thek*2c 3(kN/m3)(kPa)H*4(mm)*5(mm)ObservedH/B(z*) *6(mm):'-/]SS¥¥f-O 'Floatin *SS¥¥r_3SS¥¥r_4FloatingFloatingSS¥¥r_5-Floating:SS V-6SSIV-7Resting*FloatingSmoothRoughRoughRoughRoughRough15.4l .43*43 4l'-3 (8.6)8, (5 7)l .543(3.0)15.5l .33 ,4163(1 1 .4)8, (5.7)2.016.016.0l .43 *4124 (8.7)64(4.5)67(4.7)l .415.51.33*43 4*co is undFained strength at the clay surfaceH and B are the lvall hei lht and breadth: 6( *)- is Ehe excavation depth at faiiurethe earth pressure on the vall surfaces ¥vas not measuredhe ¥vall is floating in the soft ciay layeFlhe ¥vall is resting on the lower dense sand layer(!L:)the dimension in the prototype scale (m)32(2 2)15.7}, is average bulk density of clayk is undrained strength increasing ratio of clay ¥ 'ith depth*-l .5123 (8,6): i*4 and8, (5 . 7)l ^4l 65(1 1 .6)122 (8.5)1 ,_3(8.6)82 (5 . 7)6 1 (4 3)1 .O2.02.0lOO(7.0)50(3.5) 56NAHAS AND TAKEMURA top plate蕊掛・ q：△u嚢 り20．5セ 10 15 2．丁＞．ヤトcKoこ！c営ぐ南一断・ 睾bb 13CKoUEぺぴ 一一 榊 180Sec“ona賑S韮de V藍ew（2−2） Sectiona叢E屡evat崖on（1−1） cu賃er hand（2）σ膠Vc：ve貢icalconsilidationpressureσ’v。篇392kPa一〇竜51510Sec。P藍an（3−3）團（％）Flg．4． Resui重s of CκoUC and CκoUE重es芝s for NTC kaoli臓clayTable2． Physical呂nd mecba鷺曇c田proper重ies of kaolln clay錘Liquld販mlt，（HZl）嚢（1） （1） 1L，77．5％（2）All〔1imensions are in田m．Cu償ers∼vere use〔i∼vith different、v圭dths（b）；64，84，and126mm，Fig．5．αayc瞭erforinstail韮ngmodelwallPlasticlimlt，（以P）30．3％Plasti￠ity index，（∫P）47、2Spec呈負c gravity（（二｝、）2。6三condltion was created in SSW−0，while in the other tests，Compresslonindex（q）〇．65the wall surface condit圭ons were a11 τough to ful豆yS、ve1至ing index（C、）0。10VQ玉d fat1o at98kPa on N。C，1ine1．66κ。forN．C。clay．0．61（c砦1：m・1f・ Ul…・0．24mobillze the adhesion on the surfaces．In all由e testsexcept SSW−6，the wall noated in the soft clay as aaoatlng type wal1，whle the wall in SSW−6rested on由esurfεtce of the正ower sand。It is noted that the thickness ofthe clay between the wal璽base and the lower sand was Crlticalstateparameter（M）Permeablhty at98kPa on N．C．Iine1．02。0×王o庸9m／seconly5mm ia SSW−4．ハ40‘ノθ1P1ゆ（∼Pαrα！ion‘7η（ノTθ5！P1層ocθφ11で3 互n由e preparatlon of the model setup，acrylic plateskaol三n clay。This figure shows that even in the extensionwere nrst placed on由e bottom of the container asspacers、Toyoura sand was then poured aad compactedtests，positiveexcessporewaterpressuregeneratesfortheuu（ier the sllbmerged condit圭on with surface vibrεttionexteasion triaxial tests on κo−normally consolidated＆x量a正strain鼓igher than2％unti正failure． As s数own in Fig．1，the upper sand layer was connectedtothesoildumpingareathroughasolenoidvalve（a），andt紅e so猛一dumped area portlon was connected to a tankoutside the container裳熱rough another solenoid valve（b），肇A wa宅er supply Iine was pτovided to the model containerthrough a s圭de hole above the soil layers in t鉦e＆ct玉ve s玉de・The Iower san（i layer was con鳳ected to the soll−dllmpeduutil the relative density（Z），）became90％．Clay slurryremolded at water content玉．5times the Ilquid limit wascarefully de−aired and poured into the containeLLabor＆tory旦oQrconsolid飢ionw＆sthencQ歎ductedstepwlse under the pressure of15kPa．After completionof the conso玉idation， pore pressure transduceτs wereinsertedintheclayfromthebacksidewallofthecontainer． Subsequently brass rods g三v量ng rise to aportion．Twopairsofspongetape∼veregluedon由e surchargepressureln70G盒eldequ＆1to由econsolidatlonupPerparts ofthe front andbεしck sidecorners ofthewalL垂and centrifugal consolidatlon was carried out at70G toen鍍app重ng any sand partic豆es ofthe uppeτsand layer be−form a normally consoli（iated cla》・with streng由tween the mo（iel wall aa（1each of the front window andincreasingwitbdepth．the back side wal正of the mo（ie孟container。（c）Testconditions Table三黛ives the test conditions for由e six tests．Asexp至ained＆bove，tぬe ground cond呈tions，i．e．レthick歎ess of難霧t｝集e星ayers an（i strength pro負1e of the clay，are the same inall the tests．The dimens至ons and surface roughness of the Oa completion of the centrifugαI consoli（iation，thecentrifuge was once stopped． The brass rods wereremove（i a勲d then the front、vlndow of tぬe contalner wasdetached．The clay 食ont suτface was covered by twoguideplatesbetween・vhichthemodelwallposltionremained llncovere（i．The box−shaped steel cutter waswa11were parameters in the tests．As discussed ln thehorlzontallylnsertedintotheclaythroughthespacebe−lntroductlon，thewa11height／breadthratlo（H／β）wastween the gui（ie plates to cut and remove the clay imhechanged from 1．O to 2．0．A smooth wall surface、嚢pressureontheia団oor“・ereplacedattheclaysurfaceThe function of the sponge tapes was to preventmodel wall position．Figure5shows a schematlc drawing STABILITY SELF-SUPPORTEDD¥. 1¥._1_ c :_! I}DTS "L1 DTs+;Ij I--Calculated froivl if?' ) 132"i': /uppersandlsl26129t301 !O 50* +)c'the stress historyi:pressilre ce] sjc'$MeasuredI f' i! 'l , tJ'i[21E8[7]it(S) :I +i.jrilELa ppTi lavprl)l'vCF1IJ1, 40,.tJ ':?'f'*: l;PPT (3)' [1l]I l[-1)o ppT (4) PPT(If[6] ' PPT(7_)1'_] [131 [14] kaolin c ay c'l 50$t 82 200h :._-[ 60t( ) pore pressure tFn * ducee>i1*o[ 1 1 'all pressure cell Noa : diuiensions are in InmFig. 6. Positions of sensors used in ceutrifuage modeling tests (SS¥ '-O,SS¥406s-+* :lower sand layer. J2oLW )･ PPT (6)(1)Ol I :1.>r hand/57¥VALL_3, SSW-4, SSW-5, SS¥ '-6, and SS¥ r_7)ld I '-6 mm.;::tQo100.8 0.6 1020 100 200water content (cu)eomp vertical stressof the cutter. Three cutters were made to suit threedifferem ¥vall breadths tested The outer ¥vidth of thether tests,cutter (b) ¥vas 3.0 mm lar'ger than the ¥vail breadth. Latexto fullymembranes coated ¥vith silicon grease ¥vere put on bothfront and back surfaces of the model wall, and the ¥vallwas ther} placed in the wail position. The purpose of the_greased membranes ¥vas to reduce the friction bet¥veenthe wail and the container and also to prevent the ¥vaterflow bet¥veen them. Having placed the model vall in thel the testsclay as ated on thelickness ofsand ¥ *asvere placed on it and the fr'ont ¥vido v ¥vas re-soil in the active side. Also, t vo pairs of laserLrcers ¥vereinstalled to monitor the ¥vall tilting and displacement.Figure 6 sho¥vs the positions of all sensors used in thedisplacement transducers (LDTS) and LVDTS ¥veremodel. Having completed all the preparations, theexcavator was mounted on the model container. The¥ 'ater levels in the soil layers and in the dumping arealvere adjusted to be at the upper sand layer's surface.The ¥¥'hole test setup ¥vas taken on the centrifu_ e andthe model groun ¥vas re-consolidated in a 70CJ field untilthe excess pore ¥vater pressure ¥vas dissipated. During thelay surface[ at 70G to[ stren thdation, thentainer ¥vasreconsolidation, solenoid valve (a) vas kept open andsorne lvater lvas drained from the dumping area to thered by t¥ 'ol[1 positiontank through solenoid ¥'alve (b) to keep the _ground ¥vaterlevel at the ievel of the clay upper surface, ¥vhich settledrods ¥verecutter ¥vase space be'clay in thetic dralvingAt the end of the reconsolidation, solenoid valve (a) wasclosed, and the excavation ¥vas conducted step by step,mm, and the in-flight excavator cut 10 mm thickness ofthe soil (0.7 m in the protot.ype scale) in front of theconductedompletionnsolidationincreasing ratio ((c ).. ,plcr(*) are also sho¥vn in the figure.remo¥'ed from the front surface of the clay, surfaceclay upper surface, and the sand ¥vas then lain on the clayand leveled to form the upper loose sand layer' ¥vith a relative density of 400/0. Then, LVDTS ¥vere instailed behindthe*all to measure the surface settlements of the retainedrise to athe effective vertical stress of the clay and the strengthusing the in-fli**ht excavator as follolvs. In everyfitted on the face of the model container. Water ¥vaspoured into the container to about 10 mm depth from theail of theprofiies at end of centrifugal reconsolidationexcavation step, the soil-retainin_markerscontainer.Fig. 7. Measured and calculated water content and shear strengthcontainer as sho¥vn in Fig. l. The two guide plates wereylic plates_i limit ¥vas(kPa)cut portion, a soi]-retainin*' _"*ate ¥vas installed in thentainer as,om pactedvlbrationllay slurry(kPa)gate ¥vas lo¥vered by 10model wall and thre¥v it into the dumping area. The ¥vaterlevel in the excavated area was lolvered by drainin_ : ¥vaterfrom the box throu*'h solenoid valve (b) to the tank untilthe ¥vater level reached the excavation bottom.The excavation step ¥vas repeated until a clear failureoccurred or until the maximum excavation depth. ForSSW-6, the maximurn excavation depth was achieved¥vithout observin*' any failure (z* = 7.0 m in the prototypescale). So, from the ¥vater supply line, ¥vater ¥vas pouredon the upper loose sand layer behind the ¥vall until thefailure took place. The increase of water level by theadded water can be transformed into an equivalent claylayer depth, ¥vith the same ¥veight. Since increasing theretained soil height has the same effect on the stabilitynumber as excavating the same height from the passiveside, the virtually added cla).' heiccrht due to the added¥vater can be assumed as an equivalent excavation ¥viththe same height. From this assumption, the finalexcavation hei_"*ht ¥vas estimated to be 7.6m in theprototype scale for SSW-6.due to the consolidation of the clay. Profiles of theFi**ure 8 shows the progress of the excavation process¥vith time. Each exca¥'ation step was conducted in fivemeasured and calculated vater contents in the ciay afterthe centrifugal consolidation are sho¥vn in Fig. 7. Theundrained compressive strength (c**)*.* estimated fromminutes, vhjch means O.7 m excavation 1,as cut e¥'ery 17days in the prototype scale. This excavation speed ¥vas theaaL:";maximum that the in-fiight excavator could achieve. +*'; {58NAHAS AND TAKEMURA,,,*1000 2000 3000 4000oii8;=;'1:i!,"ilH7N;'6o4>13,;:;:;{{ 'oooo ,oecoo1o' ;':;; ;;;" 'ooeoooSSW-4 (H/B= 2.0)SSW-5 (H/B= I .O)e)ooe)'SSW-O (H/B= I .5)SSW-3 (H/B= I .5)10lOO '-)ii12time in model scale (sec),,, "'*-e-sSW-o)-ssW-3- -SSw-4-sSW-5:IHSSw-6-SSW-740 80 120 160 200 240<a9h875 'N"(D4HIHo16;*o･ SSW-7 (H/B= 2.0)S50 '25SSW-6 (H/B= 2.0)eJOe)e)oo2time in prototype scale (day)o1 ,eFig. 8. Process of excavation!*,',;'<*1 .6,: " "';: failure point{{::;'During excavation, ¥vall and ground displacements, pore¥vater pressures and pressures on the front and backsurfaces and the base of the ¥vall vere measured.1 .41displacements. The test results are given in prototype0.8scale in the follo ving section. The water pressure in theg... '.' *lo¥ver sand layer 1¥'as lo vered as the exca¥rationprogressed because the lo¥ver sand layer ¥vas connected tothe soil-dumping portion where the ¥vater table ¥vas*/' ".adjusted to the excavation surface le¥'el. It lvoulcl havebeen expected that negative pore ¥vater pressure had beenobserved due to the removal of soils. Ho¥vever, the ¥vaterpressure measurements during the excavation did notsho¥v the negative pore ¥vater pressure,vhich meant that- -_ 1.2Photo_ raphs were also taken to observe the wall and soil:ic/o 0.60.4o0.2O-oooOthe assumption of undrained conditions could bez* (m)reasonably assumed for the test condition. A similar ofpore ¥ 'ater pressure behavior ¥vas observed in thecentrifug:e model tests on the braced ¥vall excavation insoft normally consolidated clay (Takemura et al., 1999).** i:.TEST RESULTS AND DISCUSSIONS"'",'**"*_ /',;""' fi'; ,' ,'maximum tilting angles of 6' ¥vas measured. Ho vever,even for the maximum tiltin_ : angle the 31lmid caused bthe ¥vall tiling was O. 14 m smaller than 6hb * at the end oiHoriz,ontal displacements at the ¥vall bottom ( /1b.*)and the ¥vall-tilting angle (e, *ll) during exca¥'ation areplotted against the excavation depth (4-*) in Fi**. 9. 1lb.*and e+.* ¥vere obtained from the measurements of the t¥vothe test in SSW-7 (O.3 ln). In the other' tests with thefloating type ¥vall, displacement of the lvall due to thrsets of LDTS and LVDTS on the ¥vall. As explained in theprevious chapter, the soll was excavated step vise by 0.7m depths in one step. With this increment of excavationdepth in one step, very small horiz,ontal displacements¥vall base sliding ¥vas much larger than that caused by the¥vall tilting. This may imply that the floating type ¥valk¥vith H/B up to 2 first fail by sliding; thereafter some ¥val]tilting to¥vards the excavation side takes place. Therefore,the failure excavation depth, (z*)f, for experiments ¥viththe floatin_g type wall should be determined from the z* -excavation depths where the sudden large displacementstook place lvere the same or one step ear'lier than thehb.* rclation. In this study (z*)f was defined as threxcavation depth at the intersection of the tangents fcuthe z* - /1 .* relationship before and after the sudderincrease in 61lb.*. In SSW-O, ho¥vever, it ¥vas ratheldepths lvhere the marked increase in the ¥vall tilting ¥vasdifficult to define the failure point in this ¥vay, because thtobserved, except for SSW-6 ¥vith the wall resting on theexcavation depth in the 4th step ¥vas relatively large]compared ¥vith the failure depth. Hence the average oiplace in the fioating type ¥valls (SSW-O, 3, 4, 5 and 7). Thelo ver dense sand layer. The horizontal walldisplacements at the mid depth of the ¥vall caused by thetilting (6h ,id) is approximately given by: H/2 x e,..u (inradians). In SS¥V-7 where H/B=2, and B=4.3 m, the!! ,･ . #wail during excavation,Va!! Movenlellts ancl Grotlnc! Defol-n7atiol7were observed before a sudden large displacement took,. "' .Frg. 9. Variations of horizontai bottom displacement and tiltin"* ofthe excavation depths before and after the sudderincreases ¥vas taken as ( ･-*)f for SS¥ J-O. The failure depthsare indicated ¥vith arro¥vs in the fig:ure. It should be notec STABILiTY SELF-SIJPPORTEDDiv+ I¥, i¥¥*59L Lz* (m)o1 2 3 4 5 6 7 8__ :_ 2.25m from the walupperproppingE O,f_o.,_f), IowerproppingcE(i)f(1)o(L)co O,/o.4Mf_f_, *- e- - caseO: no embedment into sand- - case7: embedment into sand by Im*fvo.o.6- -56eXCaVation depth()mh'SsW-o-0 ssW-3- -sSw-4o.81 2 3 4Fio. 1 1 . Resu Its of centrifu e model tests on braced sheet pile lva lexcavation: (after Takemura et a ', 1999)-sSw-5{hSsW-6' failureSSW-7relationship in a similar way to the other tests.1Fig, lO(a),s *,(* relationshiPsRelationships bet¥veen the maximum settlement behindthe ¥valls and the excavation depth are sho vn in, "***,Fig, lO. The horizontal axes in Figs. lO(a) and (b) are theZ J(Ze) fo02 O.4 O.6 O.8 1 1,2 14 16excavation depth and the excavation depth normalized by(z*)f respecti¥'ely. As ¥vith the ¥vall displacements, onlyvery small settlements ¥vere obser¥'ed before a suddenincrease in the settlement took place. Figure 1 1 sho¥vs theo.7_78l+Jand tilting olHo¥vever,o.8l due to thaused by thg type ¥¥*all;and the marked increase could be prevented by adding-ssw-o-o-ssw-3., caused b]}t the end oivith thesettlement gradually increased ¥¥"ith the excavation depth,o.4o.6tsexcavation depth and settlement relationships, ¥vhich¥¥'ere observed in the centrifuge model tests on bracedvaH excavations in normally consolidated kao]in clay(Takemura et a]., 1999). For the excavation ¥vith thebraced vall embedded into the lo¥ver sand layer, thestruts that sometimes resulted in larger settlements thanl ssw-4( ssw-5{ ssw-6the allo¥ 'able values ¥¥'ithout sho¥vin_ any failure. Whilefor the braced excavation with a sheet pile vall floatin**" inssw-7 ffatturethe clay (Case O in Fig. 1 1)vhichvas propped only at thetop, a marked increase of settlement and clear failuretook place. From the observation, it can be concludedthat brittleness is a typical behavior for self-supported orless supported floating type walls. In the case of a multi-braced wall with embedment into the lo¥ver sand iayer,the resisting forces from the struts and the lo¥ver sand1er some ¥valilayer also increase, as the horizontal deflection of the ¥vallFig, 10(b), s ../(4 )f relatronships. Therefore,increases due to excavation. But this is not the case forined as til:that the defined failure excavation depth is limit,ed in itstang:ents fo;accuracy due to the step¥vise exca¥'ation of O.7 m inself-supported or less supported floating type ¥vall, ¥vhichmight explain the brittle behavior of those types of ¥vall.This means that the stability against failure is the crucialsubject in the evaluation of the external stabilit.¥' of thedepth.DMM ¥vall rather than the-imentsvitrorn the z*the sudde:round deformation. As tileIn SSW-6 ¥vith the ¥vall base resting on the lo¥ver densefailure excavation depth is different in tests ¥vith different-, because thsand layer, no remarkable horizontal displacement waslrively largeseen at the ¥vall bottom even after the failure, as shown inconditlons, it is ditncult to compare the brittle behaviorof the different tests in Fi**, lO(a). Ho¥vever, from thele avera e ciFi_･.. 9. The faiiure happened ¥vith a marked increase ofthe ¥¥'all tilting ¥vhen ¥vater ¥vas poured on the retainedsoil surface after the 10th excavation step. Therefore, thefailure hei_g:ht in SS¥¥1_6 ¥ *as defined from the e,**u *¥vas rathe;the suddef:ailure depthiould be notetLrelat.ionship between s .* and z*/( ･*)f sho¥vn in Fig, lO(b),it can be seen that SSW-3 and 7 sho¥v more apparentbrittle behavior than SSW-4 and 5 havin*" relatively largerH and B. This might be attributed to the larger 60NAHAS AND TAKEMURA( m)( m)o.O0.0I3,5' 'b'b'l'l7.0.1, , ,.10.5///'///'l3,5ll"'l"'' bll･ ' ' '.,,7.0///ll'p.' '/'/ ' ',1'b"10.5･"I-Cm)m)14.014.0oO 3.5 7.0 10.5 14.017.5 21.0 7_4.5 7_8.03.5 7 O 10.5 14.0 17.52 1 .O.5 28.0SSW-3 (Ha = 1.5, ze= 3.6 m)SSW-O (lm= 1.5, ze= 2.8 m)(m)(m)0.00.0l3.53,5l7.07.010.510.514.014.0l,¥ZZZ7,7i7/, :'b'b( m)O 3.5 7.0 10.5 14.0 17.521.024.5 28.0O 3.5 7.0 10.5 14.017.521.024.5 28.0SSW-4 (Ha = 2.0, ze= 5.6 m)SSW-5 (H/B= 1.0, ze= 5.6 m)(m)(m)0.0O.O3,53,5,////'// l" i7.0ll.1l lb10.5, 1,･ ,,"'1''ll"'f"'l""'14.07.010.5, .,( m))14.0O 3.5 TO 10.5 14,0 175. 21:O 24.5 2810O 3.5 7.0 10.514.017.5 21.0 24.5 28.0SSW-6 (H/B:: 2.0, z.= 7 6 m)SSW-7 (H/;B= 2.0, ze=: 4. 9 m)Fig. 12.Observed ground displacements after failuresdeformation area for a ¥vall with lar*'e dimensions, Ivhichcauses more apparent progressive failure than a ¥vall ¥vithsmall dimensions.Figure 1'_ sho¥vs the observed displacements of the ¥valland the surface markers after failure. In all the tests,except for SSW-6, Iarger horizontal displacements of thewall and smaller vertical ones ¥vere observed at the ¥vallbase, which confirms the conclusion about Fig. 9 that theexternal instability for excavations supported by floatingtype ¥valls ¥vith H/B Iess than 2 is caused by slidin*'failure. Kimura et al. (1993) conducted centrifuge modeltests on a vertical excavation with unsupported floatingtype sheet pile ¥vall (H/B>>2) for clay ¥vith uniformstrength and increasing strength ¥vith depth. From thesetests, they observed that the failure mode for the latterclay was tilting, while for the former one the wall movedtranslationally without showin*' marked tilting. Thismeans that the ¥vall tends to tilt more in normallyconsolidated clay with increasing strength than the clay¥vith uniform strength. From these observation it mightbe said that the ¥'alue of H/B='-, which was obtainedfrom the normally consolidated clay, is not an overestimated value belo¥v vhich the sliding failure dominatesfor the fioating type self-supported DMlvi ¥vall. ¥ rhile for STAB L TY SELF-SUPPORTED D *1vall tiltingstrain concentration on the failure plane in the passivezone. From these observations above it can be expectedthan the ¥vall sliding for self-supported ¥valls ¥vith relatively high H/B ratio ( 2) resting on the dense layers.that the adhesion bet¥veen the lvall surfaces and the soilplays an important role in the external wall stability.SSW-6, the lvall moved with tilting mode, showing thatthe external instability occurs more due to theOn the active sldes, the failed zones were bounded bySettlement profiles behind the ¥valls just before andclear failure planes, in all the tests, as seen in Fig. 12. Theafter failure are illustrated in Fi . 13. The settlements andfailure plane in SSW-O with smooth surface is steeper'the distances from the ¥vall are normalized by thethan those in the other tests ¥vith rou*'h ¥vall surface,resulting in ¥vider failure zones in the latter than theformer. Outside these faiiure planes and belo¥v the ¥vall,no marked displacement vas observed even after failure.excavation height and the ¥vall height respecti¥'ely. Assome LVDTS didn't ¥vork in SS¥ l_7, the profiles couldnot be drawn in the test. Vfidth of the z,one of largeOn the passive sides, the soil deformed laterally withsome vertical heave without showing any clear' failureplanes. For the floating type walls in SSW-3, 4, 5 and 7the experiments and beyond a distance of the ¥vall height,very small settlements took place, even after the failure.with rough wall surfaces, the displacement vectors of thesurface markers in the first column in front of the ¥vallMobi!ized Strength on the Wa!1 Sui:facesho¥v only lateral displacements. However, in SSW-Oconducted on normally consolidated clay and normallywith a smooth wall surface, the displacement vectors ofthe same surface markers have vertical components. Thismeans that the full mobilization of the adhesion betweenthe ¥vall surface and the clay restrained the relativevertical displacements bet¥veen the ¥vall and the soil andmade the deformed zone in front of the ¥vall ¥vider thanthat for the smooth ¥vall. No clear failure plane was observed in the passive side. This may be attributed to the)61¥VALLstress-strain relationships sho vn in Fig. 4. In thecompression test (active coi7ditiol7), the deviator stressreaches its peak value and shows strain softenin*'. On theother hand, in the extension test (passive corldition) thede¥'iator stress increases continuously to large strain le¥'el.This strain hardening characteristic might prevent thesettlements didn't exceed 800/0 of the ¥vall height, H, in allTwo series of undrained direct shear tests wereconsolidated clay on a rigid aluminum disc. Theobjectives of these tests were to assess the mobiliz,edadhesion on the rough wall surfaces and also toinvestigate the effect of the strength anisotr'opy on themobilized undrained strength on the ¥vall surfaces. In thesecond series, an aluminum disc covered with roughsandpaper sheet ¥vas put in the lower haif of the shear boxto simulate the interface between the clay and the wallsurfaces. The tests ¥vere conducted according to thestandard test procedures "JGS 0560" (JGS, 2000) untilfailure. Figure 14 shows the results of the direct sheartests. There are quite similar relationships bet¥veen theshear stress (r) and the displacement ( h) for both testseries (Fig. 14(a)). Furthermore, the relationship betweenthe shear strength (rf) and the consolidation pressure(a(*) is almost the same for the two conditions. From Fig.14 it can be said that the mobiliz,ed strength at theinterface bet¥veen the rough wall surface and the sur-orounding clay (c,,.) ¥vas practically identical to that on theOfailure plane with the same direction of the wall surface in1the clay (c*), giving:just before failure;SWSSW- SSW-SSW{HSSW-o. ?_o.3O: 2; = 1.S m13: 2; = '_'9 m4: 2;;= 4'3 m5: z; = 4 ' m6: 2;3= 7.0 mcFrom the tangent of relationship between T nd (T(* ( =0.18) and [(c )* *p/Gf(*]eo*p=0.24, the following relationcan be derived for the undrained strength of the normallyconsolidated kaolin clay:¥ s'o.･4o[ :.JDs 0.75x ¥c ,,. p (2)[cr cT*(,0. lrh uniforrn)r the latterjuso, ,_strength increasing ratios for [CKoU]..*p triaxial tests andafter failureSSW- O: 2 = )- 7 m¥vall movedthe direct shear tests respectively.=SSW- 3: 2 = 3 6 milting. ThisCasagrande and Carillo (i944) proposed the following=SSW- 4: 2 = 4･8 m>-SSW- 5: 2;f 4･9 m03in normall =relationship to express the strength anisotropy:{ SSW- 6: 2;f 7.6 m:lan the cla =c (e) = c.h + [c vion it mighi'as obtaine0,oan overesti-'e dominatrll. While fo'. p¥vhere: [(c )*.*p/(T(*],. p and [c /(T(*]DS are the undrainedFrom theseFig. 13.!LO.5 x/H1^51_s/ze x/H relationships before and after failures= c*c hl x cos2 e (3-1)>< { m + (1 - m) >< cos2 e } (3-2)where: c v and c*h are the apparent undrained soil shearstrengths when the major principal stresses are vertical 62NAHAS AND TAKEMURAPressures Acting on the Wa!lThe measured total earth pressure distributions on thewall before excavation and just before failure in SSW-3,4, 5, 6 and 7 are sho¥vn in Fi**. 15(a-e). For SSW-O,･_o(a'vc= 60 kPa)Clay15rA :pressures acting on the wall were not available because amodel wall without pressure cells was used. Ko Pressure isalso shown, as well as the active and passive earth10, :;l5pressure distributions calculated from the formula of the' :!Civil Engineering Code of Practice (CP2) in UK, ¥vhichwas proposed by Rowe (1957):interface behveen clayp.,p(z) = yz + q :and sand paperowhere p*,p(z) is the intensity of the total active or passive_'6h4(mm)6 8 10o2c. (4-)vTT 7 : (5)earth pressure on the wall at a depth z from the upper claysurface, and c (z) is the undrained soil strength at depth<;-. Smooth and rough wall surface conditions were(a): 1:-5h relationshipsadopted in the calculation ofp* and pp, that is: c*,, O andO 8 x (c ) . The strength amsotropy was also taken mto. " '. paccount in this calculation by considering c* = (c )*.*p and1 20(c*)*** in the determination of p* and pp respectively.e ciay100Althou_g:h the differences of Ko Pressure and the calculatedactive pressures are small due to very low strengths of theC] interface between clayand sand paperclay, marked effects of the wall adhesion can be seen inc]80IF:Trthe calculated pressures. Equation (5) with c, =0.8x(c*)* *p Provides reasonable predictions for the earth0.18* a'vccs 60C]*pressure on the wall back just before failure in all the tests:¥vith rough wall surface. Ignoring the pressure cell No. 9,H 40which gave relatively higher values for observed earthpressures for all the cases, observed earth pressures on the･_oo[]front side of the walls fioating in the clay (SSW-3, 4, 5and 7) were smaller than pp with rough wall condition (c**O 8(c )..*p) and close to p'rth c,,,=0. In SSW-6, the100 _OO 300 400oobserved earth pressures on the front side were evena'+,c (kPa)Fig. 14.smaller than pp with smooth ¥vall condition (c,= O). These1;ra'vc relationshipresults show that considerin*' the wall surface adhesionon the mobilized active earth pressure on the wall backDirect shear test results of normaU ., consolidatcd kaolin clayleads to reasonable predictions for the active earthCb) :pressure distributions just before failure. On the otherhand, Rankine earth pressure theory (c,. = O) gives goodand horiz,ontal respectively. c*(e) rs the undrained soilshear strength when the major principal stress is directed¥vith an angle e, and e is the angle of the direction of theTakemura et al. (1999) expressed the mobilized soilmajor principal stress to the vertical. For the undrainedcondition (wit/1 c* = O), c ,, and c*h can be represented bythe shear strengths in the [CKoU]*.*p and [CKoU]*** re-strength ratio at the front of the sheet pile wall (MSR )f*' *spectively, and the angle of the failure plane to thestrength at the depth of the earth pressure cell on the walldirection of principal stress can be assumed 45'. Here lnduring excavation:is the coefficient of stren*"th anisotropy defined by c h/c"+ *Using Eqs. (1) and (3-2), the mobilized strength on thewall surface (e=45' and 135') can be expressed by:1 + mcw = c*{45) = c*(135)c ,*.= 2p X f ¥ (4)with smooth surface usin*" observed earth pressure ((Th)the total vertical pressure ((T ) and undrained compressive(MSR ) = ah - (T,. (6)f *. *r¥2¥c ,*.*pIn this study, the followin*' relationships were employedto assess the mobilized soil stren*"ths on both sides of thewall:Coefficient of strength anisotropy (m) of the normallyconsolidated kaolin clay is about O.6. Hence, Eq. (4)(MSR ) = (Thives: c,*= O 8 x (c ) for both the side surface and thebase of the rough ¥vall. This value compares ¥vell to theobtained value from the direct shear test (Eq. (2)), ¥vith(MSR)b ek= f2 Cu1)comp* " '. pabout 70/0 difference.{predictions for the maximum passive earth pressure onthe wall before failure.alfront 2(Cu )ext(7Y - CTh(7)(8) eqq(5)(cw=08(cu)cl;eq(5)((*=0.S(c)cQiTTP)(S)(c,.=0S(cnp))ceri')63STABILITY SELF-SUPPORTED D¥= i¥= { ¥¥,*ALLOhe4.Olz=. 29rQ- z=SsW-3l.3,,-O,front side3aback sidei4is"th･ *)////6ichl.l*'*+:¥-9 m:- - - ' - eq (5) (c7'P)'llSO 40 40=0)O20Iearth20pFessur'e80 4040 80 1 20(kPa) earth pressure (kPa)80 120earth pres5ure (kPa) earth pressure (kPa)O;iveq(5) (c*= O S(c ;)t(.,- - 1:q{5) (c+=0)- X(1 press re (ze=0)/c'*Pressvre ( ;= )for z.7s7 O Fn:lo8(5)back sideside79for z*=76firontze=7.0 m-+ -_-s/.*heH :c=0ssW- 6Fig. 15(d)Var ation of earth pressure profile on wall in SS¥ r.6; I ayFig. 15(a). Variation of earth pressure profile on the wall in SSW-3pthOereiandntoand4ely.)ItedSSW- 44i:**^8 x8/10o. 9,ll:arth//-Kepressure (ze; 0)'" - eq (5) (c Y=0)iO¥11¥¥80 40 40 80 1 _70Ol I Oearth pressure (kPa) earth pressure (kPa)4, 5Fig. 15(b),l-Ke PressureSSW- 5for zt=mVariation of earth presstlre profile on wall in SS ¥*-7back sidefront side 'otherood))+6d soil//l ,!/especially for very small displacement portion. Ho¥vever,it can be clearly seen from the figure that stren*･th at theback side of the wai] ¥vas mobiliz,ed before failure but notat the front side. The typical stress-strain relationships ofH ze:: O+1ze= 4.3 m/Sf ronll'Oe ((T *)SO40ear'th pressure (kPa)essivevallFig. i5(c)./1 + c,./c,,. For the rou*･h sur'faceabout 60 mm. Due to some error in the measurement, ofthe earth pressures and displacement, some scatterin_"*could not be avoided in the evaluation of MSR and h**u3earthi20so40earth pressure (kPa)The displacements of the ¥vall at the failure point ¥vere1:q (5) (c*=0),backOcondition, these values are 1.53 and 1.34 for the ¥vallfront and back respectively.OheseesioneFig. 15(e).SO40earth pressure (kPa)ultimate values becomeevenR)120Variation of earth pressure profile on waM in SSW-4, there oni q(5) (c*,=0)9foF z*= 4.3 m:/for z =2,S rr :S- Ko press 'rc (z *={))/l then (cwback Side/"*l*/- 6¥+¥*./9arthcests¥/li- 7n inrotlt' Slde;/'/fi/-6)*' theSSW- 7o40SO20earth pressure (kPa)Variation of earth pressure profile on wall in SSW-5A'o normaily consolidated clay sho¥vn in Fig. 4 can beconfirmed from these figures; that is, small strains atfailure in the acti¥'e side but very large str'ains in thepassive side. Potts (i991) sho¥ved similar results fromfinite element calculations. He also sho¥ved that forheavily overconsolidated clay with hi_..･h Ko values, the(6)For the smooth ¥vall condition, that is, shear stress alon_'the wall is zero, (1VISR ) = I means the full mobiliz,ation ofthe strength for the both sides.ployedof theFigures 16(a) and (b) sho¥v the relationships bet¥veenthe lateral displacement of the ¥vall at the depth of eachpressure ceil (6/1,,i!) and the mobilized strength ratios atthat depth for SSW-4. In the figures, t¥vo horizontal solid(7)and dashed lines ¥vere dra¥vn to represent the ultimate of(8), ,MSR for the smooth (c, =0) and the rough (c,. =0.8 x(c*)***p) ¥vall surface conditions respectively. TheseatLf t! 'lactl¥'e and passive conditions could be mobilized atsimilar ¥vall displacements. From the centrifuge modeltests on braced exca¥'ation of the kaolin clay using a sheetpile ¥vall lvith smooth surface, Takemura et al. (1999)made the figure about the similar relationship at the frontside of the sheet plle ¥vall as sho¥vn in Fig. 17. But theyused (c )* *p for normalization as sholvn in Eq. (6), sothat the ratio, (MSR)f*.**, of O.6 means the fullmobilization on the smooth wall condition. At the ver_¥*small ¥vall deflection, the relationships are very similar inthe DMM wall ¥vith rough surface and the sheet pile ¥vith NA} AS AND TAKE*MURA64front side E7( 7 5m from ground surface)41lower propping3,5i0.6;:'e3- : Ie'';:''e -' 2.5l: 2/ )o::efc¥l-**OI> 1.5Obb/lower propping!tx:11,-e )ase7-0.5oo.2O 1-13 -)ase90,05 0,1wall defiection (m)6hceH (m)Fig. 17. Relationship bctlveen mobilized strength and 11'all defiectionobtained from centrifuge model tests on braced sheet pile wall32.5Jexcavation: (after Takemura et al., 1999)Failure)* e)2, *r/ 1.5eq.It can be said from the calculatlons for the condition ¥vithc**,= O and c,+= 0.8 that the adhesion bet¥veen the vertical¥vall surfaces and the clay can significantly r'educe the> istress concentration at the front toe. Although somescattering ¥vas observed before exca¥'ation, it can beO.5clearly seen that variations of contact pressure were ¥'erysmall from the initial condition until the failure in SSW-OIto3, 5 and 7, ¥vith H/B= 1.5, 1, and 2.0 respectively. ForSSW-4 ¥vith H/B (=2), relatively lar_ ! e incr'eases anddecreases of the contact pressures ¥ 'ere observed at thefront side-o.5-1oO.1o.26hcell (m)Fig. 16. Relationships bet,veenh*.Ii and mobillzed strength forexperiment SS¥ '-4smooth surface, and a quite sharp increase in the ratiovas observed. Ho¥ve¥'er, some differences can be seenafter this sharp increase. For the sheet pile ¥vall,(MSR)f,* reached the full mobilization at about O.05 mand kept constant after that. While for the DMM, theratio didn't reach the le¥'el of full mobilization e¥'en forfront and back wall base edges. The difference in thevariation of the contact pressure in SS ¥r_4 and SSW-7¥vith the same H/B (='-) can be attributed to thethickness of the clay bet¥veen the ¥vall base and the lowersand. In SSW-4, the thickness ¥vas about 5 mm, ¥vhile forSSW-7 it ¥vas 45 mm in the model scale. Hence the lo¥versand layer affected the subgrade reaction of the ¥vall basein SSW-4 much greater than SSW-7, and the ¥vall tiltingcaused the larger increase in the contact pressure at thefront toe in SS¥¥f-4.Althou'_h some difference bet¥veen observed andcalculated contact pressures could be seen beforeexcavation, due to some difficulty in the measurements ofthe contact pressure, the observed increases and decreasesthat of the smooth wall condition at the dlsplacement ofabout 0.05 m and increased continuously after the failurepoints. As discussed in Fig. 12, the highly deformed areain contact pressures ¥vere much smaller than thein the passive side ¥vas larger for the rough ¥vall than thecurrent design method ¥vhere the adhesion on the ¥vallsmoothsurface is neg:lected overestimates the stress redistributionvall. The differences of the failure mode may bethe reason for the difference in the stren_2:th mobilization)*calculated ones with c,./(c,,)* ,,, O and slightly smallerthan those ¥vith c, /(c,, ).. ,p=0.8. This means that theat the ¥vall base due to exca¥'ation.Undrained strength of the clay at the base in SSW-4due to the wall surface rou hness.Figure 18 sho¥vs the measured contact pressures (q*) atthe ¥vall base before excavation and just before and after¥vas about 17 kPa, ¥vhich _･._ives the net bearing pr'essur'e ofthe ¥vall at about 90 kPa ( = 5. 14c**). The incr'ease for thefailure for SSW-3, 4, 5, and 7. The calculated valuescalculated contact pressure for the condition ¥vith c,./before excavation and at excavation depth just before thefailure are also sho¥vn in the fig:ure. This lvas obtainedfrom the moment equilibrium at the front toe of the ¥vall.!c ¥)* =0.8¥vas almost the same as the net bearing,pcapacity. From this it is considered that tilting failure due*,*to overstressing the ¥vall base might ha¥'e possiblys STABIL TY SELF-SUPPORT D65D¥, ,t 'i IVALLe=0,)::tebf2.9 m{Hze:::3.6 mr 1 OOe l) -1 OOSS W-4:¥Je)200*'i,e l*'ee)7300200SSW-3o2.9' e li ze:::1 .4 m300TZeb cwlOebf& cw::O 8rc ¥L ujcomp400=9e=0Calculated stresses:--Ze: Oebf4'3 m{Hze 4.8 m400o-2.92.92.9100SSW-7l OO1e) 2005aH defiectionQnn_CJ ')vveet pile wall200H ze:::Orl+ ebf4'3 mSSW-5e :{h e::5 .O mrhl300ee' 400ciition ¥¥'ith-4. 35he verticalreduce the)u :h someit can beO4,35distance from the wall center (m)Fig. 18.400-2. 1O2. 1distance from the wall center (m)Contact pressures under wall base for SS¥¥r_3/4/5/7vere ver}*re fn SS¥¥1_occurred,ti¥*ely. Forbefore sliding took place, if there had been afloatin*' type DMlvl self-supported walls ¥vith H/B?- isreases andthick clay layer belo¥v the ¥vall. The resistance against thesliding. Therefore the upper bound analysis ¥vas used torved at theence in thesliding and base failures are the function of many factors,conduct a parametric study using a sliding failuree.g., strength of the clay belolv the base, adhesion on theand SSVJ-7red to thebase and side surface of the clay, thickness of the claymechanism .The parameters which affect the externai stability oflc} the lo¥ *erso on. Holvever, for normally consolidated condition,n,vhile forthe strength and adhesion are not independentce the lo¥verparameters, highly dependin*･ on the depth, in otherbelo¥v the base, ground ¥vater level, top soil thickness andhe ¥vall base¥*all tilting:ssure at the,served andeen beforurements ofthe floating type DMlvl ¥vall in normally consolidated clayare schematically sho¥vn in Fig. 19. These parameters are:the wall hei_g:ht, H, the vall breadth, B, the surchargepressure, q, the excavation height, z*, the clay bulk unitwords, height of ¥vall. Considerin*" the discussions above,¥vith rather severe test conditions of thin top sand layerand high ¥vater table, it might be said that the ¥vall height-¥vei_ ht, y, the ratio bet¥veen the adhesion on the wailbreadth ratio (H/B) of around ,_ may not be an overesti-soil strength at the clay surface, co, the coefficient ofmated one as the threshold value vhere the failure patternchanges from sliding to bearin_9: failure for the floatingstrength anisotropy, m, the gradient of clay strengthtype self-supported DlvlMvall in the normallysurfaces and the soil strength on the slip plane parallel tothe vall surface at the same depth, c, lc , the compressi¥'eincreasing ¥vith depth, k.nd decreaseconsolidated clav. Fr'om the centrifug:e tests on the DMM'r than theas a foundation of break¥vater, Kitazume (1994) showedlhtly smallethat the local failure at the base of the DMlvl leads theans that theon the walibearin*･ failure in the case of the DMM ¥vith H/B=0.5As the exerted acti¥'e earth pressure by the upper dryloose sand layer on the ¥vall is small compared to that ofthe underlying submerged clay, its shear' str'ength ¥vasne*'1ected in the upper bound analysis and the layer' Ivasassumed to ¥vork as a surcharge pressure, q, on the upperedistributior=fioating in the clay. The threshold value of H/B from thesliding to the bearing failure for the self-supported DlvlMvall excavatlon is gr'eater than that of the floatin_g typetse in SSW-DMM foundation, ¥vhich is subjected to lateral forceclay surface in the calculations. The formula of C_asagrande and Carillo Eq. (3-'-) Ivas used to represent thestrength anisotropy.from the top through the superstructure.lg pressure 0=irease for thiion ¥vith c,*=UPPER BOUND ANALYSISnet bearininfailure du;lave possibl;The centrifuge modeling tests sho ved that the criticalfailure mechanism for the excavations supported by the-LL""'As the upper sand layer ¥vas represented by asurcharge, the ¥vall height ¥vas replaced by the embeddedwall depth into clay, H*1* , and the excavation height vasreplaced by the exca¥'ation height into the clay layer, z..From these parameters, the six non-dimensionalparameters: i71, cwlc., yH,1.'/co, yBlco, qlco, and kly,were deri¥'ed, ¥vhich affect the stability number at failure: NAHAS AND TAKEMURA66No*.**1=(q+y(z*)f)/co, ¥vhere (z*)f is 4-* at failure. TheThe observed displacements in SSW-O and 4 arefailure mechanism used in the upper bound calculationand its displacement diagram are shown in Fig. 20. Thecompared with the failure mechanisms obtained from theupper bound calculations in Fig. 21 . At the passive side,mechanism consists of t¥vo trian*'ular rigid blocks and athe mechanism compares well ¥vith the observations. Onfan between them for both sides of the wall with twothe other hand, the widths of the observed failure ¥vedgesbehind the ¥valls were smaller than the failur'e z,one obtained from the calculation for the rou*"h ¥vall case (SSW-variables oel and (x2. The calculation was first done for theconditions of the centrifu*'e model tests and then someparametric studies were conducted by changing the non-4) .dimensional parameters; yH,1*'1c0= I - 100, yB/c0=1 -66, kly=0 and 0.09, c, /c**=0 and 1.0, and n?=0.6and I .O. In the normally consolidated clay, the undrainedstrength at the clay surface co can be given by theproducts of vertical effective overburden stress ((7,'.*) and[(c,,)..*plcT(*] value. In the centrifuge tests, (T . at the claysurface was q from the top sand layer, because theground ¥vater ¥vas at the level of the clay surface. FromSSW-o(m)O.OI3.5"'b'b l-1b"I7.0//･"/// '･1'l･l, , .this and the ma*"nitude of [(c )*.*p/cr(.] on thecompression stren*"th of the kaolin clay (=0.24), qlcobecomes approximately 4.0. Hence q/c0=4 ¥vas used in1 0.5tt'the calculation.O 3.5 7.0 lO.514017521 0245 280;o.o(m) S SW-4l ZZ/ 7/'Z': ' :' ' t '3,57.0'I''tb¥¥"fIL'b j 4'/ : /: '' ''" 't 'tl'b,b,10.5I14.0(clc,,, Soil strength- iBm( u=)compprofileu )ext(m)O 3.5 7.0 10.514.017.521.024.528.0cFig. 21. Comparison of fajlure mecbanism obtained from upperFig. 19. Par8meters affecting external stabilitl.' of fioating type DMMwa]Ibound calculation with observed soil and wall displacements inexperiments SSW-O and 4q+Zcf45 A45-0eloelL<Fan I BalbO45-(XlOelwallo6CDwall O )*= B(a): Failure Mechanism.45-Ce,cd(b): Displacement diagram.F g. 20.Failure mechanism and displacement diagram used in upper bound calcuiationl 67STABILITY SELF-SUPPORTED D*¥IM ¥VALLd 4 are{from thesive side,ions. Onevedges +z,one obse (SSW- iTable 3. Observed and calculated stabilitl.' numbers at failure35(N *1)f'c=1DifferenceTest No Surfacecondit ionH/BLNot'1 (o/o )30o*,t*SS¥V-OSS¥V-3Smoothl .5Rcuigh1SS¥¥r_4RoughRoughRough7_.OSSW-5SS¥¥!_ !9,88 l13.513.515.91 .O20.221.616.I2.015.712 8521O.i5263423eAO Tn )6k/*f = O O:ob*rTT TI/'f = OO9:rTTchlcu:: ;]1'oA m )625m=1 Oc lcu:: o' om: 1 Op- 20r''oz sfB/c0= 26& q/c0= 4 .,eo. (5oTable 3 sho¥vs the stability numbers calculated fromo)O 40 60 80tests SS¥V-O, 3, 4, 5, and 7, the upper bound for the stability numbers, (No*.**1)c*!, and the difference betweenOO O 2040 60 80 1 OOvHd*) Jcethe observed failure heights, (No*.**i)ob*, in the centrifu*'eFig. 22. yH,I /co Net t'lrelatronships for smooth and rough wallsurface conditionsthem as a percentage of (No*.** )c*1' The upper boundsshould be equal to or higher than the ri*･orous ones intheory. However, (No* ** )ob= values were higher than35(NG*.,.])c,1 by 20 -330/0 for experiments SSW-O, 4, 5, and7, while for SSW-3 the observed and calculated stability30H (m)numbers ¥vere almost the same. The possible reasons for25l 8.0having (No*.**1)c*1<,(No*.**1)0 = are: 1) underestimation ofthe clay stren*'th because the shear strength parametersfrom the triaxlal tests were adopted to represent the soil7 t.:(m)the strong box, and 3) the difficulty in estimating theo}8.0from uppplacements i=0)¥'all conditions,n= O 6411= I On= o 641Tl= I Ok"r O O1'el:.ia}/cF 26& qlcf 415lOrough (c, /c = 1) and smooth (c,,./ck/f o. o :,'S 20;=strength in the plain strain condition, and aiso the strainrates in the model clay ¥vere much higher than that of theelement tests, 2) the friction between the model wall andexact failure excavation height, due to cutting relativelylarge excavated hei_ ht in each step (0.7 m).Figure 22 shows the relationships bet¥veen yH*1'y/co andNo*.**1 obtained from the upper bound calculations for the!I5--- o --.,t--Heo20 40 60 80 lOO O 20 40 60 80 100YB/coFig. 23 yB/c -N' o el't*irelationships forsmooth and rough wallsurface conditionsanisotropic (nl =0.6) and isotropic (/71 = I .O) conditions,and strengh profile conditions ¥vith uniform strength kly=0) and stren*'th increasing ¥vith depth (k/y=0.09).stability than increasin*' the wall breadth. Ho¥vever, if theFigure 23 sho¥vs similar relationships bet veen yB/co andNo*.**1' For the rough wall in the normally consolidatedclay ¥vith strength increasin_g: ¥vith depth (k/y 0.09),No****1 increases ¥vith increasin*' yHd*,'/co and yB/co.However, different relationships can be seen for groundsoil strength is uniform ¥vith depth, incr'easing thebreadth of the rou_ h floating type wall is the only ¥vay toincrease its stability.For the failure excavation heights of the cases of thecentrifuge tests obtained from the upper boundwith uniform stren_._"th (k/y=0) and smooth wallcalculations, limit equilibrium analyses were conducted.conditions (c,./c =0). For k/y=0, No*.**sli**htlyTwo assumptions were employed in the analyses. In thedecreases ¥vith increasin_g: yHd,v/co. From these results, itfirst one, Rankine's earth pressure distributions on the¥vall surfaces were used, ignoring the adhesion on thevertical wall surfaces and assuming isotropic conditionwith compression strength, which is similar to the currentdesign practices. In the second one, the roughness of thevertical ¥vall surfaces and the strength anisotropy, werecan be"considered that the effect of Hd*+ on the externalwall stability is hi*･hly dependent on the strengthincreasing rate (k). From Fig. 23, it can be also confirmedthat the effect of B on the external wall stability dependson cw/cand k/y. Furthermore it can be said that in thestability analysis of the excavations in the normallyconsolidated clay with strength increasing with depthusing self-supported ¥valls, i*･noring the adhesion on thevali surfaces may iead to significant underestimation ofthe externalvall stability.The slopes of the relationship bet¥¥'eenN ando*.**lyH,j,y/ca for k/y=0.09 in Fig. 2･-, where yB/c0=26, arehigher than the slopes of their counterparts in Fig. 23considered using Eqs. (3-2) and (5), by using thecompressive soil strength in the acti¥'e side, (c*)**^p, andthe extensive strength, (c )..*, in the passive side; cw/c =1.0 was used to express the ¥vall surface rou>'hness forSSW-3, 4, 5 and 7, and for SSW-O, cw/c* = O ¥vas used inthe second analyses.Table 4 shows the results of using the limit equilibriumanalyses. Here *1 and *2 denote the first and secondwith yH,1../c0=26. This means that in the normallyassumptions respectively. Except for SSW-O, the factorsconsolidated clay ¥vith increasing str'en*'th, increasing thewall height is more effective in increasing the external vall¥vere almost the same for every test condition. Ignorin_",_L!:of safety against sliding, (F. S. )=1idi**_, for both assumptions 68NAHAS AND TAKEMURATable 4.Factors of safetv.' and bearing stresses under wall base estimated by limit equilibrium methodSSw-o SS¥V-3*l(F S.) 'd g (I ^2) i(T 4 (kPa) ( q*h)l*3*'1 *2' I .O1 l.25i I}.06, 218.8i42.7168.8 i0.97151.7 fSSw-4SSw-7SSw-5*2 *1 *2*IO.961 .06 ! I .OI*1I .07o 96356.2 ! 231.9 j 181.6 ; 139.27 65 2l .07166.7lgnoring both the adhesion alon_ the vertical wall sides and the strength anisotropy and usin_ average strength (the current desig_n method).Considering both the adhesion along the vertical vall surfaces and the rength anisotropy and using average strength.Factor of safety a_ ainst sliding*4 Bearing stress of the ¥vall base at the front toe.the adhesion on the ¥vall surface leads to underestimatingthe ¥vall stabilit,y. On the other hand for the ¥valls innormally consolidated clay ¥vith high stren*･th anisotropydimensions on the stability are highly dependent onthe stren*'th profile of the clay and adhesion on the¥vall surface.(small /71 value), assuming the isotropic condition ¥viththe compression stren_g:th leads to overestimating the wallstability. For the clay vith relatively hi__*h strength(5) For clay with a relatively high strength increasinganisotropy, the current design method, ¥vhich does notincreasin*' the external stability of the ¥vall thanincreasing the ¥vall breadth. On the other hand, inconsider the stren*･th anisotropy and the ¥vall adhesionmay give a reasonable evaluation of the wall stabilityagainst sliding failure, because the effect of each factorcancels the effect of the other. However, ignorin_ boththe strength anisotropy and the adhesion on the vertical¥¥'all surfaces leads to overestimating the bearing stressredistribution due to the eccentricity caused by theexcavation as sho¥vn in Table 4. From this as ¥vell as thediscussion on the base contact pressure shown in Fig. 18,it can be said that the assumptions adopted in the currentdesi_g:n method overestimate the contact base pressur'e atthe front toe, ¥vhich may predict the bearin*･ capacityfailure as the critical condition.CO¥_ TCl.IjSIONSFrom the centrifuge model tests and the upper boundcalculations on the external stability of excavations insoft clay using fioating type Dlvlilvl self-supported walls,the follo¥ving conclusions have been drawn:(1) For the fioating type self-supported DMM vall ¥vith(H/B)- in normall)* consolidated clay, failuretakes place suddenly by sliding failure mode ¥vithoutsho¥ving marked pre-failure displacements.Therefore, the design of this type of ¥valls should bebased on the ¥vall stability rather than on theadjacent ground deformations.('_) On che interface bet veen rough lvail surfaces andthe surrounding saturated clay, undrained strengthof the clay can be mobilized. The mobilizedadhesion has significant effects on the stabilityagainst the sliding and base contact pressure.(3) The required ¥vall displacements to mobilize theminimum actlve earth pressure of the retainednormall.¥' consolldateci clav are less than thoserequired to mobilize the maximum passive earthpressure in front of the ¥vall.(4) The external ¥vall stability is affected by the soilstren_ :th profiie, the adhesion on the ¥vall surfacesand the lvail dimensions. The effects of the ¥vallratio ¥vith depth (k) Iike normally consolidated clay,increasing the wall height is more effective inclay ¥vith a small k-value, increasing the ¥vallbreadth can only lead to increase in the external ¥vallstability.(6) For clay with a relatively high strength anisotropy,the current design method, which does not considerstrength anisotropy and ¥vall adhesion, may *'ive areasonable evaluation of the ¥vall stability againstslidlng failure, because the effect of each parametercancels the effect of the other one. Ho¥vever,ignorin_9: wall adhesion leads to conservati¥'e anduneconomic estimations of the stability against thebearing capacity failure.NOTATIONSB:¥vaH breadth.[CA'oU]*omp:undrained triaxial compression test on Koconsolidated samples[CA'f]U]ex :undrained triaxial extension test on Koconsolidated sampiesco:(c )comp athe upper clay surface-cu(: :undrained shear s reng h of c]ay so l adepth z from the upper cla.v surface^(cti)com :undrained compressive shear strength of' theclay in the [C_KoU] empest(c**)e*E:undrained extensive shear strength of theclay in the [C_A'oU]e¥test.cL*i and ct*':apparent undrained soil shear s rengths'hen the major principai stresses arehorizontal and ¥,'ertical respectively.cul '):apparent undrairled soil shear strength ¥vhenthe major principal stress is directed lvith anangle e to the vertical axis.c**:adhesion bet¥veen the ¥vall surfaces and thesurrot ndin:g cla¥_*.H:lvali height embedded into thepper sandand clay layers.Hci *:lvall heigllt embedded into he clay layerH,:thickness of lhe upper sand layerk:strength increasing rate lvi h depth ,nl:coef icient of s rengEh anisolrop¥.'( = (c** )**E /(ct* )tomp )( t/SR ) * n and ( VSR)b**k:mobi ized soil srrength ra io a Ehe front andback sides of the lvall. 69ST．へBILITY S鷺LF−SUPPORTED DMM WALL No［o副：stabi韮ity number at fai亜し星re 呈n 【he upPer boundanalyslS、 ρ＆，P（ξ）：1ntensltiesof由eactlveandpassiveearth Pressures on t臨e wall surfaces at a depth漏竃， from t｝1e clay upやer surface． 1，0766．71eξhod）．de飢on｝on t聡ecreasmg’ledclay，、 σlsurc短argepressureontheclaysurface． 圭22一玉35、 （ξc）r：excavation dept巖 玉Rto 乞｝1e cLay iayer atconsider6）Cねe且，X。L．，Liu，Y．H、and Zわang，S．L）「 （1996）l Deslgn me由ods fa玉iure． ofceme飢一soilretainlng、valLPヂoc．2η41n’1．Coη∫ ξ，1亘otalexcavateddep由1nto出eupPersand ／ηψrovθ1ηθη’Gθo男乳∫’e1η，∫一αα廟9αη40θθρ1、五￥’η9，Tokyo， andclaylayers． ζ。bf＝toξalexcavateddepthinto由eupPersand 475−480曙 andclayiayersjustbefQrefalluretakes excavations i鳳soft day supPorted by工）M1〉I self−supPQrεed waHs， piace． 1S−710んyo99，Tokyo，Japan，583−588． （ξe）f：tota…excavate（王depth 1nto the upPer sandG1響α〃∼ゴ7）EI Naぬas，A．，Takemura，J．and Kouda，M，（1999〉：Stab1撫y of8） Japanese Geotechn玉cal Society，，IGS TO560−2000 （2000）：置ヤ1αhod anddaylayersatfailure．αlandαゴce煎alanglesfortriangularblocksiatぬe for conso玉玉dated constant vQiume direct box s琵ear test on so叢ls． fa難ure mechan玉sm，used in the upPer bound J．（1993）＝S［ab玉lity of unsupPorted and supPorted vert三cal cuヒs in calculat玉ons（Fig．20）． sof覧clay，Proo．11’1∼Sαイ∼hθα5扇5’α11Gεo’θごh．Coη∫，Sl服gapore， direcI S｝｝ear test．lsotropy，5） Casagrande，A．and Caril1Q，N．（1944）：Shear fai沁re of a錘sotropic ξc＝excavat1oR depI藍into￡be clay layer、all than’rnai wall4）Boiton，M。D．and Powrie，W．（1988）：Reむaviors of diapぬragm wallsinclaypriortoco賎apse，磁αθchn’σ置’θ，38（2），三67−189． so玉1s，Co∼πr’わμ”oη5 ’o Soi1ル旋∼ohαη’c∫，βεCE， 1941−1953， 1944， δh：measured shear displacements durlng the琵e wa1玉、3）Bolton，M。工）．and Powrle，YV．（1987）：丁姦e coliapse of d1ap姓ram wallsretainlngclay，磁αθ‘h’瞭’θ，37（3），335−353． ξ：dep【h from the clay upper surface．ctive ln ・halld，in Tokyo，Japan，673−678．9）K玉mura，τ．，τakemura，，L，｝｛玉ro−oka，A．，Okamura，M．and Park， 61−70．10） Kitazume，NI，（1994）：㌫憂ode玉and analytical stud呈es o艮stab玉lity of δhb。【＝measured horizontal dlsplacements of the improved ground by deep mixing met蝕od， Ph， 0， ’1reεな． （in wa至1bOt亡om． δhcξll：measured horlzontal dlsplacements of the11）1くltazume，M．，Mlyake，M、，Omine，K， and Fuj1sawa，H、（1996a）l Japanese）． waH at the pos玉tion of each pressure ce歪｝． JGS TC Report：Japanese deslgn procedures and recent actlvlties of δhmid：horizo鳳al waH displacement a慮s mid dep由 DMM，Proc．2nゴ1η∫1．Co’∼∫G〆o置“1ゴ11刀ρヂovθ，ηθ∼π（3θoり窟θ1η5一 d雛eto玉tst玉1ting． γ5照d：dry un圭t weig晦t of the upPer sand layer． αα廟8αηづρ卿雌κ’1∼9，Tokyo，Japan，925−930・玉2） Kitazume，真｛、，τabata，丁．，Is員iyama，S．andIshikawa，Y．，（1996b）：lygivea θ：angle of inclination of芝員e major princlpal Modehests o鷺fallure pattem of cemenureated retainlng、、・all， streSStO磁evertical． P∼o‘．2ηご／1π1．CoηゾGro瑚ご11ηρroソθ1ηθn’0θ05ツ5∼θ1η、∫一ααπ’n9ト・against θ、、al［＝angleof由ewalltlkingdu血gexcava“on αηゴP岬畝百119，Tokyo，Japa獄，509−514．arameter （degrees）．13）Potts，D．M．（1991）：Finiteelementsimulat玉onofembedded｛Owever， σ1、：observedlateraleartぬpressurebyeacぬ reta玉ning wa1豆s， 〆玉ごv‘7ηcεゴ （ヲθo’θご1π． ！垂ηαケ5Z∫， Elsev1er apP簸ed1tiveand三ainst the pressure ce韮董． ∫dence，131−167． στlbearlngstressof由e・vallbaseat出efro瓢14）Rowe，P．W．（1957）ISぬeeゆllewalislnc！ay，1η甜．αv、動9ヂ9∫，7， 覧oe． 629−654．15）S駄lomi，M．，Ito，K．，Nlshimura，D、，τanaka，H．andTanaka，M．REFERENCES王）Azuma，K．，Nogはc髄i，S．，Kurlsakl，1く．，Hyodo，H，andNagaoka， M．（玉999）：Moveme煎ofstablilzedcoa1−ashsollwallduringしes毛onκが excavation，1S−70幻yo99，Tokyo，Japan，459−4642）Babasaki，R，Suzukl，K．andNakama，T、（1998）：DesignprocedureleSt on KO・ for self supPorted waH us玉Ωg deep m玉x呈頁g method，C（∼n’ヂびμ9θ98，day soil alrface．ren鼠thoω1e3n9由of d腫arStreng藤s｛resses arξ、ely．，tre翁黛th wlle嚢ecしed w玉th a韮ゼaces and1hごeuppersan6claylayer・yer lePth，）Pythe front al矯 （1996）：Sbpe stabi1虻y貸sing the adm1xture metめod，P’・o‘、217ご／11f！、 Coη∫ Grα〃7ゴ 1’ηρro、7θ’ηθη’ （｝θo釧∫1θ’η5−Grα”加9 σ’∼4 五）θθP 1、4勧79，τokyo，563−56816） Takemura， ，1．， Ko【1doh， NI．， Esaki，T、and Kouda， NI，， （1999）： CeatrEfuge mode蓋tests on dQubLe propPed wa玉1excava雛on in soft clay，So’Z∫α1ガFα’ηゴ如0115，39（3），7シ87，
- ログイン
- タイトル
- External Stability of Vertical Excavations in Soft Clay with Self-Supported DMM Walls
- 著者
- Ala'a El Nahas・Jiro Takemura
- 出版
- soils and Foundations
- ページ
- 53〜69
- 発行
- 2002/02/15
- 文書ID
- 20439
- 内容
- ログイン
- タイトル
- statnamic Load Tests on Model Piles and Their 3D-Elastoplastic FEM Analyses
- 著者
- Makoto Kimura・T. Boonyatee
- 出版
- soils and Foundations
- ページ
- 71〜87
- 発行
- 2002/02/15
- 文書ID
- 20440
- 内容
- SOIL,S AND FOUNDATIONSVol 4) N0. I, 71-87, Feb. 2002Japanese Geotechnical SocietylSTATNAMIC L,OAD TESTS ON MODEL, PILES ANDTHEIR 3D-ELASTOPLASTIC FEM ANALYSESMAKOTO Klh,lURAl) and TIRA¥vAT BOONYATEEii)ABSTRACTDur'ing the past ten years, the Statnamic load test has dr'awn attention from the piling community as one of the mosteconomical methods for pile load testin*･. Ho¥vever, almost all of the research and development have been based ondata from field tests. A consistent interpretation is difficuit to achieve with such data due to the uncertainty and thecomplexity of the *"round. To overcome this deficiency, the first objective of this research is to develop a systemwhereby Statnamic load tests can be performed under one constant condition. A small-scale Statnamic loading devicefor model tests has been developed vhereby pre-compressed air is applied instead of gas from an explosion. In thisstud.¥', two types of piles, friction piles and end bearing piles, are modeled and are loaded ¥vith two levels of forces,namely, small loads and large loads. The former loads are for determinin*' the initiai stiffness of piles and the latter fordetermining the ultimate capacity. The second objective of this study is to develop a 3D-FEM program that canianalyz,e various types of loading. For a dynamic analysis, the solution is determined by the direct integration in timedomain. The experimental results sho¥v the possibility of producing a loading curve similar to that in the originalStatnamic load test. The analysis also sho¥vs that the force distributions in piles under Statnamic loading are similar tothose under static loading.Kel.* Ivords:dynamic, finite element method, Ioad test, model test, pile, test equipment (IGC: E4/E8)plannin>" and the effect of the reaction piles (Poulos,INTRODUCTION1998) can be completely disregarded. Noting that theFor pile foundations, the static load test (SLT) Is_generally accepted as the most reliable method forSTN Ioads piles under a relatively lo¥v frequency, the pileestimating pile foundation capacities. Unfortunately, dueto the high cost and lengthy operating time, static loadtests are only performed for larc"e projects or at sitesto ) g.where the soil profile presents some unusual aspectsdynamic responses such as dampin_ and inertia forcebecome important, and they cannot be neglected as withthe SLT. Up until now, the results of the STN have usu-acceleration induced by the STN Ioading ranges from 0.5Although the STN has many advantages over the SLT,it loads piles at a hi_ :her rate than the SLT. Consequently,To avoid this situation, a Statnamic load test (STN) canbe used instead, as one of the rapid loading tests(Bermingham and Janes, 1989).)*ally been interpreted by a sirrrplified method called theThe STN uses a medium period load (100 ms - 200 ms)unloading point method. In this method, the dampin_"..to thrust a pile body into the ground. The lvordforce is calculated using a constant dampin_ coefficientthat can be estimated from the load-displacement curve.Assuming that a pile moves in a rigid body motion, theinertia force can be calculated from the pile mass and itsacceleration. For extensive details, see e.g., Bro¥vn"Statnamic" comes from the terms st(7tic and dyll(7lnic.By applying an explosive force to an explosion chamberinstalled on the top of pile head, an acceleration field ofabout 20 g, or t¥venty times the earth's acceleration, canbe obtalned. Placing a mass upon the explosion chamber(1994).At present, the primary approach to investi_9:atin*' pilecan generate a reaction force of magnitude twenty timesits o¥vn wei_ :ht. Since the applied load in this test isbehavior is to make a comparison between the results ofgenerated by the high degree of acceleration, a very highcapacity pile can be tested ¥vith a reaction mass of onlyfull-scale Statnamic and static load tests. One example isthe work done by Matsumoto et al. (1994a, 1994b).one-t¥ 'entieth the ma nitude of the desired load.Unfortunately, their calibration method has an inherentMoreover, there is no requirement for reaction piles ¥viththis method; the target pile can be tested ¥vithout priorproblem in its testin*' consistency, as ¥vas addressed by J.M. Amir and E. I. Amir (1995). Under the uncertainty') Assoc. Prof , Dept. of Civn Eng., K}'oto Universitv, Kyoto, Japan"; Lecturer, Deptofcivil E,n_"*., Chuialongkorn University, Bangkok, Thallandivlanuscript ¥vas received for reviel ' on Jul .* 26, 2000¥Vritten discussians on this paper should be submit ed before September I , 2002 to the Japanese Geotechnica] Society, Su_ ayama Bldg 4F,Kancia A¥vaji-cho 2-23, C_hiyoda-ku, Tokyo 101-0063, Japan Upon request the closiug date may be extended one month.i71);,l' 72KIMURA AND BOONYATEEand complexity of the target ground, the situationwhereby any model can be validated by calibratingStatnamic load tests against corresponding statlc loadtests can be demonstrated as follo¥vs:1. If a comparison is made of the results of tests onAlthough a t¥vo-dimensional analysis is simpler and thethe same pile, the tests have to be done in sequence.Therefore, the quality of the later tests invariablydimensional analysis, it cannot be applied to a complexsystem such as a pile-raft foundation or batter piles.deteriorates due to the induced residual stresses from theMoreover, it is obvious for a horizontal loading case thatthe analysis should be done in three-dimensional space.Therefore, the de¥'eloped code ¥vas made as a versatileformer tests.2. If a comparison is made bet¥veen the results of testson different piles, significant sampies should be tested inor'der to achieve some degree of reliability over theground uncertainty.analytical tool that can cope ¥vith several loadingconditions and pile types, and can find solutions in three-Since consistent systems for interpretation andcomparison can be provided under laboratory testconditions, it is thought that the model tests are anDYNA-3D, is used to simulate the vertical Statnamicindispensable tool for the study of pile-soil interactiondurin*" Statnamic loading. In this study, a small-scaleload test. A non-reflecting boundary was introduced instatnamic loading de¥'ice (3SLD-Mkl), driven by airpressure, has been developed for conducting the modeltests. Note that these model tests are not used for thereflections at boundaries of the soil mass. Since DYNA3D ¥vas designed for solving dynamic problems, a constant-loading duration was applied to obtain the pseudo-purpose of replacing the prototype tests, but are intendedstatic loading for the static load tests.to be a tool for the fundamental study of the physicalinteraction bet¥veen soil and piles during StatnamicIt is thought that before applyin_9: the DYSC to thesimulation of piles, its fidelity should be checked by aphysical model. For calibration purposes, a comparisontheir ability to carry out the STN in various types oftheir Statnamic analysis to prevent erroneous wavei'preferred to the results from the field tests because ofthe complexity of the ground and the qualities of theexperiments can be done under the same >'roundgeotechnical parameters required for the analysis. Afterconditions for each series of tests. Beginning ¥vith simplethe DYSC has been calibrated lvith the data from theground conditions, the mechanism bet¥veen the groundlaboratory tests, it ¥vill be used to simulate the prototype-and the piles can be grasped readily.For the determination of the ultimate bearin*' capacityscale tests. These simulations ¥vill ensure that the DYSCcan be applied to the analysis of Statnamic load tests. Inthe last part of this research, the DYSC ¥vill be used as aof piles, it is essential to load the piles up to their plastic{of the analytical results and the laboratory test, results isround can be achieved. Consistency means that the;' ･solution can be found faster than with a threedimensional space. One example of this kind of analysisis shown in the ¥vork done by Yamashita et al. (1995,1998). In their ¥vork, an explicit 3D-FEM code, calledloading.In laboratory tests, the conslstency of the tests andi*fact that the system of interest is axi-symmetric,Matsumoto (1998) applied a 2D-FEM program to analyzeIthe behavior of a single pile under verticai loading.range. Although many Statnamic load test results havereported that the static response of piles could besuccessfully estimated by the unloading point method, itappears that their loads ¥vere too small. In other words,the resistance of the piles ¥vas not fully mobiliz,ed.Therefore, in cases ¥vhere the piies are loaded by forceover their ultimate capacities and a lar*'e mobilizationoccurs, research on the application of the unloadingpoint method is necessary. Up until no¥v, there have beenfe¥v publications about this kind of test. One example isthe ¥vork by Nagaoka et al. (1995). To accomplish this*'oal, t¥ 'o types of loads are applied to the piles in thisstudy. The first kind of test is done by loading the pilesPile behavior under Statnamic loadingA4E (qualit tivejudgement)EE FE :odl :::of s'H ? Uncertainty of_ roundE physi*1 di*cu io sfJ-i }LIa,plied for the ftmdameTrtal study ofe single pilsso battef piiesQ group pilesof test is done by. Ioadin_ : the piles ¥vell over their ultimatee pile-raft foundationsothetwoarethemechanism of the piles during Statnamic loading can bethorou_ghly investigated by a numerical analysis. For thispurpose, a three-dimensional finite element analysisprogram called DYSC (dynamic and static systemsanalysis L0de) is developed in this stud_v. Applyin_g theHModel teStsbelow or up to their ultimate capacities. The second kindcapacities. Since it is thought that the responses toStatnamic load of piles also depend on the pile type,types of piles, friction piies and end bearing piies,used in this study.Instead of studying the data from the field tests,!E3D-ElastOPlastic FEM CDYSC)o adaptable to 2Jty e ofpil s s;1i loadings- UntSed s al)I is approacho centribution to the improvemcut ofsimplied estiTnution msLhodsResearch Framework+:,Fig. l. Outline of research framework STAlrNAlvllC TESTS ON MODEL PIL.ESImetric,tool for investi_9:atin*' the behavior of pile foundationsduring Statnamic loading. It ¥vill also be used to verifyanalyzeoading.and thel threeassumptions and to improve the estimation techniquese;nployed in the simplified methods. The frame¥vork ofthe ¥vhole research is sho¥vn diagrammatically in Fig. 1.r piles.In this paper, only the ¥vork done in step O, thedevelopment of the model tests and DYSC, and itsase thatapplication, are reported.omplexspace.ersatileOUTLI_¥'F, OF THE F.XPERIMF.NTSioadinn three-Deta!!s of the ApparafusA general vie¥v of the apparatus, developed in thisstudy, is sho¥vn in Fig. 2. The operation of loading by3SLD-Mkl can be divided into the follo¥ving fi¥'e stages:Inalysis(i995,calledrtnamic1) Initial stage (Fig. 3(a)).Lrced in'_) Air loading stage (Fig. 3(b)). In this stage, precompressed air is ailowed to flo¥v into the cylinder. Thes waveDYNA-air piston will start to load the pile head.a con)seudo- ;3) Launching-up stage (Fig. 3(c)). While the piston ispressing on the pile head, the air in the lower part of thecylinder ¥vill flo¥v out through the silencer. At the sametime, the upper part of the de¥'ice will be launched up dueto theid by aparison73to the reaction force from the pile head.4) Termination of air supply (Fig. 3(d)). When thehead of the piston is at the same level as the stoppers¥vitch, the magnetic ¥'aive will be trlggered and the pathof air will be shut off. At this stage, the upper part of thedevice ¥vill still be movin*' upward for a while because ofinertia force.5) Termination oftest (Fig. 3(e)). The free fall oftheupper part is gradually terminated by. the supportin__'boxes at the four corners of the lo¥ver base.The loading apparatus can be divided into t¥vo parts,namely the movable part and the fixed suppor'ting base.Components of the apparatus can be divided into thereaction-mass box, the cylinder and the piston, themagnetic valve, the speed controller, the stopper s¥vitch,the support legs, the sand box, the fixed base, the supportbeams, the measuring system, and the control circuit.The cylinder used in this study is made by the CKDCorporation (CKD Corp., SCA2-00-100B-150-R5-H). Ithas an effective diameter of 100 mm. The maximumallowable cylinder pressure is I .O MPa. The stroke lengthof the piston is 150 mm. The mass box as ¥vell as the¥veight of the cylinder is used for the same function as thereaction mass in the prototype. Four support legs areused to constr'ain the body of the apparatus on its ¥'ertical)sults Isaxis. These components, namely the mass box, theMagnetic valve Speed controller Reactionmassmse ofsupport legs, and the cylinder, are all fixed together bybolts at the top of the cylinder.of theAfterThe flo¥v of air is controlled by a magnetic valve that isshut in the normal state and open ¥vhen an electric currentAir supply tom thetoty pe-Stopper swrtchSilencerDYSCests. Inis received. In order to make an adjustable rate ofcylindereTPiston Model pile 420:ed as aLoad cell 300loading, the speed controller that regulates the rate ofairflow is also integrated into the air supply system. Astopper switch, ¥vhich is triggered by the magnetic field, isattached to the cylinder in order to stop the air supply*properly. This stopper s¥vitch ¥vill send a shut-off signal tothe magnetic valve ¥vhen the top portion of the pistonapproaches. The sand in the supporting boxes at the fourcorners of the lower base is used to _g radually stop the free)Soil chamber lUnit : mm6 OOSide viewfalling of the upper part after the launchin*･-up stage.After the base part of device is instailed on the top of asoil chamber, the legs of the movable part are put insidethe supporting boxes of the supporting base. Nex. t, thesand is filled Into the supportin*' boxes. Note that the tipsof these le*･s do not reach the base of the supporting:boxes. Therefore, the reaction mass and the ¥veight ofTo vieweach component are mainly supported by the pile. Thisdead weight from the upper part contributes to the initialstatic load and defiection. In the prototype, the initialload is about 50/0 of the peak load. Ho¥vever, the samee eT130_L130 JL-- -- I800iFig. 2. Details of apparatusiaS+". *""le¥'el of initial load cannot be produced in the developedmodel. From the SLT, the model pile has an ult,imatecapacity of 590 N. When compared to the full-scale tests,the initial load, which is 50/0 of the ultimate load, shouldbe 29 N. Ho¥vever, only the cylinder, ¥¥*hich is the mainpart of the apparatus, contributed to a downward forceof 130N. When all the components are assembledtogether, the lveight of the entire apparatus becomesquite heavy. From this limited condition, the least 74KllvIURA AND BOONYATEEMagnetic vatve¥Arr supplyyForce generatedThe air flows intoby air pressurethe cylinderCylinderPistonSilencerThe body isSandAction force atthe pile headmoving upPilea. Initial stagec. Launching upb. Air loadingInertia forced. Termination of air supply e. Termination oftestFrg. 3. Loading mechanism of3SLD-Mkl500possible initial load is about 230/0 of the ultimate load ofthe pile. Although this large initial load is not compatible¥vith the full-scale tests, it gives useful information for arough estimation of the static load-displacement r'elation.Another difficulty comes from the attempt to obtain anadjustable loading rate. Since the effect of the loadin_ :rate is one of the objectives of the study, an attempt tomake a distinctive change in the loading rate, i.e., achange in the loading duration from 100 ms to '_OO ms,400r:'300'c:5O200100has been made. Calibration tests are done by loadin_g therigid base ¥ 'ith the developed apparatus. Noting that thesand ¥vas not filled into the supporting boxes in thesetests, therefore, the dead ¥veight of the apparatus stillapplies on the pile head after the end of tests. Asconcluded from the calibration test results sho¥vn in Fig.4, the loading duration increases by only a small amount¥vhen the air pressure is increased.The same results are obtained lvhen the tests are doneon the model pile, as shown in Fig. 5. It is also found thatOO 20 40 60 80 100 120 140Tlme (ms)Fig. 4. Variation in loading rate with air pressure (calibration test withrigid base, reaction mass 30'- N)duration is still not an adjustable parameter. The loadingthe speed controller has absolutely no effect on theloading duration, although the maximum load can varyduration can be adjusted only by about Oo/o, dependin_"_.on the amount of solid fuel or the ven type (Karkee etwithin a 100/0 range by this unit.al., 1995).The other alternative for ad.justing the loadingduration is to increase the weight of the reaction mass. Asimilar trend is observed, ho¥vever, as sho vn in Fig. 6. Inaddition, increasing the ¥veight of the reaction mass hasan unpleasant effect brou_ ht on by the high initial load.For the above reasons, the distinctively di :erent rate ofloadin*･ cannot be produced at the present stage. Notethat even in the original Statnamic load test, the loadin_'._Test Conditions and MethodFour patterns of tests conducted in this study are summarized in Table I . T¥vo types of pile foundations, whichare the end bearin_g: piles and the friction piies, aremodeled. The properties of the model piles are sho¥vn inTable 2. Both types of piles are loaded by Statnamicforces that are lower and higher than their yielding 75STATNAMIC TESTS ON MODEL PILES600[I500EiiilJ::: ;:- - O'4 MP*Table 3. Properties of sand and modei ground,,¥l1l, ,400TISC:l300,¥.:t;¥t;¥-,L=100;¥OoFi,g. 5.40 60 80202.63Maximum void ratiol .03Minimum void ratioo.64Moisture ratioO 30/0D603 10 prnDIO120 ,JmUniformity coef.2.58Density1,467 kg/m'Relative density59.60/0Frictional an le36'Diiatancy angle90¥l200Specific ¥ 'eightl i120100Time (ms)Variation in loading rate with air pressure (experiment)350a) Friction pile tests300For the tests of the friction piles, a pile made of mor'tarl; 250¥j200:'150and piano wire, used for centrifugal model tests in ourresearch group (Kimura et al., 1997), is used. The model'_round is made of No. 6 silica sand. The properties ofsand are shown in Table 3. The frictional and dilatancy100ang:1es are determined from the direct shear tests. The soil50chamber and the location of the model pile are sho¥vn inFig. 7. The preparation of ground is divided into t voc:lO:loo4060 80Time (ms)20steps. At first, a lower layer, '_O cm thick, is compacted bylOOFig. 6. Variation in loading rate with reaction mass (calibration testwith rigid base, air pressure 0.2 MPa)Table 1.Test patternsEnd bearin*' pilesSmaH IoadPattern 1Pattern 3Large loadPattern 2Pattern 4! Friction piiesEnd bearing pilesMortarBrassDiaJneter (cm)2.42.4Len_ th (cm)4648Weight (kg)Youn_ 's modulus (lvlPa) :0.447o 2995.0X 038.5 x 104cudy are sun 'Points. The dimensions of the soil chamber are 80x 80lations, ¥vhict;cm wide and 60 cm high, and pro¥'ide a distance from thepile to the boundary of about 15 times the pile diameter.Since the ground models of the friction pile tests and the. are sho¥vn iby Statnarni*their yieldin;After the model pile is set up, the soil chamber is filledto the top ¥vith sand Then, an immersion vibrator is usedfor ground compaction. The vibrator is put into theUnder this preparation method, the model pile isProperties of modei pilesMaterialion piles, artconstrain the pile to the ¥'ertical axis.ground at tlventy-four uniformly distributed locations.I)ration test wiihpe (Karkee e{soil chamber. In this step, a 3 cm hole is dug in theground, the pile is installed, and then it is buried.attached to the top of the soil chamber are used toFriction pilesTable 2.The loadingspacin*'. Then, the model pile is placed in the center of theTherefore, the thickness of the layer beneath the pile isequal to 17 cm. At this stage, only four lines of thread20 140'b, dependingthe hammer used in the standard Proctor test. Thehammer is dropped 162 times under ¥vell-distributedend bearing pile tests are different, their preparations areexplained separately as follo¥vs:ILsupposed to behave as a friction pile. Vibro-compactionis not possible for the lower layer, because there is notenou9:h thickness for the sand to absorb the vibrationenergy from the vibrator. Ho¥vever, an attempt is madeto produce a uniform ground and to control the relativedensity of both upper and lower layers to about 600/0 . Theoverall density of the sandy ground is about I ,467 kg/m3.b) End bearing pile testsThe end bearing piles are modeled by a hollo¥v brasspipe, which has a small shaft friction. The thickness ofthe pipe is 1.0 mm with an outer diameter of 24.0 mm.Because the brass pipe is hollo¥v, the pile tip is cappedwith an aluminum plate in order to model the closed-endtype of piles. With the small shaft friction., almost ail ofthe resistance of the brass pile is due to the hard layerbelo¥v the pile tip. Therefore, the model pile is supposedto behave as an end bearing pile. In this kind of test, rigid 76Kllv URA AND BOONYATEEMortar model PileUnit:cmt80O+"20JGround material: N0.6 Silica sandJL_Side viewTo viewFig. 7.Ground model (friction piles)Brass pileUnit:cm80O60Ground material: N0.6 Silica sand-r-' 35 -To viewFig. 8.ISide viewGround model (end bearing piles)blocks made of plaster and dolomite are placed under thepile tip in order to model the support layer of the endbearing piles. The dimensions of the plaster blocks are 35x 35 cm ¥vide and 15 cm hig:h. These blocks are mademodel pile is set up, silica sand is filled up to the top of thesoil chamber. Then, an immersion vibrator is used forground compaction. The relative density similar to thewith a ratio of plaster to dolomite to ¥vater equal to I :2:5friction pile-type tests can be made by maintainin_ : thesame compaction time and locations. The overall densityby weight. The Young's modulus and the compressi¥'estren*'th of the plaster blocks, determined from theof the sandy ground is similar to the tests of the frictionpiles, which is 1,467 k_ /m3.uniaxial compression tests, are 41 .83 MPa and O.2 MPa,respectively. The outline of the ground model is sho¥vn inAfter the model ground is prepared, support beams areplaced across the top of the soil chamber and fixed byFi**. 8.clamps. The upper part of the device ¥vill then be set uponThe preparation of _2:round is divided into t¥vo steps. Atfirst, a plaster block is placed in the center of the soilthe pile head, and then the sand is filled into thechamber and then the model pile is installed. Again, fourlines of thread attached to the top of the soil chamber areused to constrain the pile to the vertical axis. After thesupported boxes of the lower base.The applied loads are measured from a load cell placedon the top of the pile cap. The displacement of the pile ismeasured from the fiange of the pile cap. This flange is 77STATNAMIC_ TESTS ON lvIODEL PILESSTN 1500Support frame for measuring device5test ' STN 2ndtest -SLT¥, , , . ,Laser displacement gauge400;- 300cso 200h:1Soi chamberlOOLoad cellOTo view0.0Side viewFig. 9. Measuring systcmFig. 10.made as short as possible to minimiz,e the effect of its ownvibration. A Iaser displacement gauge is used to measurethe settlement of the pile This displacement gau_ :e isinstalled on an additional frame that isolates it from theobserved system^ The measuring system is sho¥vn in FigLoad (N)0.2 0.4 0.6 0.8 1.0Displacement (mm)1 .2Load-displacement relation (Pattern l)Displacement (mm)5001.254001.00the reduced-scale tests, the wires of the strain gauge arerelatively large compared to the model piles. Therefore,3000.75the piles in these tests are not instrumented ¥vith the straingauges because they ¥vill disturb the pile-soil interactions2000.50around the pile shafts.lOOo.259. Note that there are no strain records in these tests^ ForoEXPERIMF,NT RESULTSFour patterns of tests lvere conducted in this study. Anattempt ¥vas made to load the pile ¥vith forces smaller andlarger than the ultimate capacity of piles. The first patternis the tests on a friction pile in ¥vhich the pile is loadedbelo¥¥* its ultimate capacity. The second pattern is a teston the same model pile in ¥vhich the pile is loaded wellover its ultimate capacity. The third and the fourthpatterns are similar tests performed on the end bearingpiles. Details of the test patterns are summarized in TableoFig. 11.0.0010 20 30 40 50 60 70 80Tlme (ms)Load and displacement vs time (Ist test of Pattern 1)the tests, a maximum Statnamic load of 440 N and amaximum displacement of about I .O mm are observed.The relation between the load and the displacement4. In oFder to ensure that there is no disparity in thewith time are shown in Fig. 1 1 . The measured data showthat maximum displacement occurs a short time after therecords, the test is done twice for each pattern bypeak load and that only a small displacement reboundcompletely reproducin*' the model ground.occurs.Pattern I-F/'iction Piles tinder Sma!! LoadingThe ¥vave number of loading has been calculated fromthe stress wave velocity, the duration of the Statnamicle top of theIn this pattern, a pressure of 0.2MPa is used toloading, and the pile length. The definition of waveis used forgenerate the Statnamic load. No additional reaction massnumber is the ratio between the loading duration and theis put in the reaction-mass box. The load and thetime it took the stress ¥ 'ave to travel from the pile head todisplacement of the pile head are sho¥vn in Fig, lO. Fromthe pile tip. With a stress wave velocity of 1,607 m/s, theTrilar to thentainin*' theduration of loading of 50 ms, and a pile length of 0.46 m,the calculated wave nulnber is 175. Since this value is inerall densitythe frictionTable 4. Summarl of each test pattern*rt bearns areand fixed by;1 be set upon*ed into theid cell placed;of the pile i irhis fiange ithe range of 12 to 1,000, it can be concluded that theexperiments do satisfy the STN philosophy (MiddendorpPatiern1)34O.2 = O 4Air pressuFe (*¥･IPa)O.2 O 4Max. Ioad (N),lax. dlsp. (mm)Max. vel. (cm/s)589280l O 5 403 1 37_5 37 o 2 5 14.0et al., 1995). For this large ¥vave number, it is thoughtthat the duration of loading is long enough to eliminatethe effect of the stress ¥vave.The velocity and the acceleration of the piie versus timeare sho vn in Fi*･. 12. The maximum velocity is about 7.5cm/s in a downward direction. A small value for the velocity in an upward direction indicates a gradual change KIMIJRA AND BOONYATEE78Velocity (cm/s) Acceleration (m/s2)STN 1test , STN 2600108stndtest -SLT¥//6l45, t/21:,a:l:¥ r¥ lf¥ l L r==/J:= ;i1 1=io400'-/Ii - / l500f;ro300O:!//200/100-5/oOl /2/l;/JO 1,0 20 30 40 50 60 70 8010Time (ms)lDisplacement2 3 4( mm)56Load-displacement re atton (Pattern 2)Fig. 13.Fig. 1'-. Velocity and acceleration vs time (Ist test of Pattern l)Displacement (mm)Load (N)in the displacement of the pile after the unloading point,or a point of maximum displacement. Maximum600accelerations during loading and unloading are 10 and9.5 m/s2, respectively. When compared to the data fromthe SLT, the load-displacement plot from the STN shows500a stiffer relation. As shown in Fig. 10, the loaddisplacement curves from SLT and STN intersect near300the unloading point under an applied load of 340 N.200Patte/'n 2-Friction Pi!es under Large LoadingAir pressure of 0.4MPa is used in this pattern. Nosettlement, ¥vhich is about 200/0 of the pile diameter, is5=14400/3//2//=]1 OO1l.Oadditional reaction mass is put in the reaction-mass box.The maximum Statnamic load in this pattern is about 590N. The load-displacement relations of the pile headare shown in Fig. 13. A very large amount of residual6/OO 10 20 30 40 50 60 70Time (ms)Fig. 14.Load and displacement vs time (Ist test of Pattern 2)noticed at the end of the tests. Maximum displacementVelocity (cm/s) Acceleration (m/s2)occurred after the peak load at a longer time lag than that40shown in the results of Pattern I . The wave number forPattern 2 is 222, due to the longer loading duration than3060/Pattern I .The relation between the load and the displacement,and the velocity and the acceleration with time are shownin Figs. 14 and 15, respectively. From the velocity-time,l20in displacement after an unloading point similar to that inPattern I is also measured.20It/l:!10l:l,,,olo/1-/1when compared with Pattern I . The maximumaccelerations during loading and unloading are equal to48 m/s2 and 35 m/s2, respectively. The gradual rebound40tplot, the maximum velocity is about 37cm/s in adownward direction, a change of more than four orders¥,-20¥;/-10Fio. 15.Olo 20 30 40 50 60 7040Time (ms)Velocitv.･ and acceleration vs time (Ist test of Pattern 2)Static I,oad Tests on the Friction Pi!esStatic load tests are also conducted on the model pile inorder to make a comparison between different loadingconditions. The tests are carried out with the sameLoad-displacement plots from both patterns and theSLT are shown in Fig. 16. An almost identical load-apparatus. After piling a large amount of reaction massupon the cylinder, a series of loads can be applied bydisplacement relation bet¥veen the two patterns in theincreasing the air pressure. For this experiment, the pile isdisplacement of the pile exceeds 2 mm, the rate of thedisplacement to load-increment in Pattern 2 increasesloaded under 50 N Ioadin*' steps until failure occurs. Thetime interval for each load increment is about 10 min.launching-up stage is observed. However, after theconsiderably. A Iarg'e deformation in Pattern 2 indicates 79STATNAlvIIC TESTS ON MODEL PILES600500::,,400::c:} 300O1 200lOO/// 1, ti -, t,- - :": i¥:¥;1"t25 o-; 200SLT- pattern 2t -¥ -i'I･i --Pattem I300:, 150; t;-1_f･cSO 100- - -;f_50ifOoo Displacement1 2 3 4(mm)5 60.00.2 0,30.1Displacement (mm)Fig. 16. l,oad-displacementrelationbetween Sl,T and STN of frictionFig. 18.Load-displacement relation (Pattern 3)piles700600500400)*3000.352500.302000.251500.201 OO0.1 5500.10o0.05ir;¥J 300::'csO:1200lOO10O. lDisplacement (mm)n 2)o4080120Time (ms)160Fig. 17. Static ko3d-displacement of friction･type pile ou iog-log scaleFig. 19.that the pile ¥vas loaded over its ultimate capacity. Fromthe plot of the static ioad-displacement in log-10g scale(Fig. 17), it can be seen that the yielding load of the modelpile is 5･_O N. This load corresponds to a displacement of2.2 mm.)Displacement (mm)Load (N)i_Patte,'rl 3-End Bea/'ing Piles under Si77a!! I,oadinglo0ttern 2)lal load- ;force of the piston. With a stress ¥vave velocity of 3,574m/s, the calculated wave number of this pattern is about305.From the velocity-time plot shown in Fig. 20, theHowever, the weight of reaction mass is increased to 20.0kg, or equal to the downward force of 196.0 N. To lessenthe initial dead weight, a chain is used to hang the mainbody of the apparatus from the ceiling and only a smallfraction of the dead weight is applied to the piles at thebeginning. This small initial load is allowed to act on thepile in order to ensure that there is no gap between thedirection. The maximum accelerations during loadingthis pattern is about 280 N. It is concluded from the staticload tests that will be shown later that this load is a littlebit higher than the yielding point of the target piles. Thete of theincreasesthou*･ht that the first fall-off (around the 20 ms in Fig. 19)indicatesis due to the air supplement being shut off before thefter theforce after the first fall-off is due to the remaining inertiamaximum velocity is about 2.5cm/s in a do¥vnwardload-displacement relations of the pile head are shown inPig. 18. When looking at the load-displacement relationand the load-time history plot, it is found that the forcedecreased once before reaching its maximum value. It isIs in thepiston could generate its full load, and the increase ofAir pressure of 0.2MPa is used in this pattern.pile cap and the piston. The maximum Statnamic load inand the jLoad and displacement vs time (Ist test of Pattern 3)aL';".",,and unloading are equal to 4.0 m/s2 and 2.6 m/s2, respectively. When compared with the friction piles, the velocity of pile is very small. It is thought that the hard layerbelow the pile tip makes the model pile displace at aslower rate than the friction pile.Pattern 4-End Bearing Piles under I,arge LoadingAir pressure of 0.4MPa is used in this pattern. Theweight of reaction mass is increased to 32.5 kg, or equalto the downward force of 3 18.8 N. A chain is used againto hang the main body of the apparatus from the ceiling.The maximum Statnamic load in this pattern is about 520N. The load-displacement relations of the pile head areshown in Fig. 21. The calculated wave number of thispattern is about 916.The relation between the load and the displacement, KiMURA AND BOONYATEE80Velocity (cm/s) Acceleration (m/s2)632jll1it,1 :l.t5002.544002.023001 .5ILt I , IIf"$ = II I/ ' =ot- ･$1 1 'la.j ,t=1,otl _-2l=i 'W I :-lt'2001 ,O100o.5o0,0o 80Time120(ms) 160Time (ms)Frg 20. Veiocity and acceleration vs time (Ist test of Pattern 3)Fig. '-2. Load and displacement vs time (Ist test of Pattern 4)Velocity (cm/s) Acceleration (m/s2)500Ol2015400)i10¥-/ 300::cslo 40 80 120 160 200 24040f;Displacement (mm)Load (N)10_ l;,t, l2005lOO,4'/- - :/ I ifj =ll' -- S. ;/ 'l- -"oloOi'*lOt'o' oisplacemento 5 l'o 1.5(mm)2.02.5.5*20o 40 80 120 160 200 240Time (ms)Fig. 21. Load-displacement relation (Pattern 4)Fl'* 23. Velocity and acce]eration vs time (Ist test of Pattern 4)and the velocity and the acceleration with time are sho¥vnm Figs. 22 and 23, respectively. From Fi*･. 23, theyielded ¥vhen the applied load exceeded 161 N, corresponding to a displacement of 0.1 1 mm.direction. The maximum accelerations during loadingand unloading are equal to 14 m/sl and 14 m/s2, respectively. As was observed in Pattern 3, it can be concludedthat the model pile displaces at a slo¥ver rate than theSince the yield displacement is smaller than themaximum displacement of Pattern 3, it can be thoughtthat the target piles were loaded beyond their staticyielding points. However, when an air pressure smallerfriction pile.than that applied in Pattern 3 is used, the inertia effect ofStatic Load Tests on the End Bearillg Pi!esthe piston, as described in the previous section, becomeslarge. Since the characteristic of force will be dominatedmaximum velocity is about 12cm/s in a downwardAfter the Statnamic tests have been conducted, theby the inertia of the piston when the air pressure is small,static load tests are done. The static load-displacementa force smaller than the one applied in Pattern 3 cannotbe produced. Currently, the improvement of the device torelation of a pile is shown in Fig. 24. For the end bearingpile, an improved static loading de¥'ice made after thecompletion of the friction pile tests is used. The maindifference from that used in the previous tests is that amechanical jack is adopted instead of the cylinder. Usin*this jack, the constraint displacement is applied to thecorrect this effect is under ¥vay.Danlping Coefficient of the Un!oading Point MethodAccompanyin*' the data from the SLT, dampiugpiles are loaded in four cycles before reaching the tar*･etcoefficient C, used in the unloadin*' point method, can beback calculated. Firstly, dampin_g: force Fd is calculatedby subtracting the Statnamic loading (F** ) ¥vith staticdisplacement, ¥vhich equals the maximum displacementresistance and inertia force (F*1* and M･ a, respecti¥'ely) asof the model piles in Pattern 4. The plot of static loaddisplacement in log-lo*' scale determines the yield point ofshopile. The rate of displacement is 1.5 mm per min. Thethe model pile. As shown in Fig. 25, the model pile'n in the following relationship:Fd = F*** - F*1*M･ a (1)=;']' i"" 81STATNAMIC TESTS ON MODEL, PILESpattern 45001/ t;I,_, 400:-/ 300c l200lOO¥_8,0___: , ._ _¥ */= =!/i ; ;i _ .;._ _;D D:-f 6.0./'; Statmic test =l'iij- fi,1 '; -.+c,D4'oC (ulp, patterT:+¥JJ 2,0C (Ulp, parterT' 2)0,0,0.0 0.51.0 1,5 ･_.ODisplacement(mm) 2.5Fig. 24. Load-displacement relation betlveen SLT and STN of endbearing piles;t 2002Displacement( mm)Fig. '-6. Damping coefficient vs displacement (Ist test of Pattern I and{---1 --i -8.0D DD4 o:;20s s os' patterT' 3ij :i _'_'i :iI_i Cavi = 5'07 kN-s/mf 6.0v'l'____ I, ! ----c:to:Ii iii !{ 'ii i-[iij titji;1 OOI- "* C'D4･O)l 2.0j0.00.1Displacement (mm)scale4'19 kN-5!m I c (ulp' pattem 3)4'79_ i_lr'¥:L_I Pattern 3Iv'l' ::: 3'09 kN-s/mL I' Il' t I'l' " : "c (ulp' pattem 4)' - 1'61i ¥ 4 1"l!il' ' PatternTT :' TYielding displacement!i / 'o.o 0.5 1.0 l.5 2.0Displacement (mm)Fig. 25. Static load-displacement of end bearing-t¥.'pe pile on log-]og4)43Pattern 2)400300i)2.47O^86tb =o),D selsl,20 5 l*SOFig. 1,*7. Damping coefficient vs displacement (Ist test of Pattern 3 andPattern 4)orre-Then, the damping force is divided by pile velocity V, toobtain the damping coefficient, as in the followingtheught 'lrelation:C V = Fd (2)static "lallerct ofomesThe ¥'ariation of Fd and the variation in C with pileinterpretation of Pattern I will be done in a zone ofinterest, which ranges from Dl,209to the Dl,809 ･ Thedefinition of D*,+, 6 is the displacement 'y' in percentage ofthe maximum displacement of pattern 'x' . For making acomparative study, the zone of interest for Pattern 2 alsostarts from D1,20',and stops at D2,809 ･ To quantitativelynateddisplacements for Patterns I and 2, and Patterns 3 and 4,mall,are sho¥vn in Figs. 26, and 27, respectively. Since the ve-the followed paragraphs. The first parameter is theannotlocity of piles is close to zero around the beginning oftests and the unloading point, the calculated C grows to avery lar_ e value (a value close to infinity) around thesevariation index of the damping coefficient, V.1., which isice tozones. Consequently, no meaningful information can beevaluate the variation of C, two parameters are used indefined as the difference between the maximum value andthe minimum value of C in a zone of interest. The secondparameter is the average value of C, C..,g, which is takenfrom the same zone that V.1. is calculated. For simplifiedestimation methods such as the Unloading point method,iodm pingcan beobtained from these areas. Although the tests are:ulatedC from the small load tests and large load tests are not inthe same ran*"e. These differences are due to the velocitiesthe value of C is assumed as a constant value. Consequently, it can be thought that the accuracy of theirpredictions should be related to the magnitude of V.1..of piles in the large load tests being higher than those inthe small load tests (see Figs. 12, 15, 20, and 23).As shown in Fig. 26, the V.1. of Patterns I and 2 are 1.02Since the values of C are large at the beginning andPattern I is larger than that of Pattern 2, it is expectedthat the prediction quality of Pattern I should be poorerstaticely) as(1).conducted on the same piles and ground, it can be seenfrom the C-displacement relations that the magnitude ofaround the point of maximum displacement, theitLkN-s/m and 0.86 kN-s/m, respectively. Since the V.1. of ･*"K1*¥,lURA AND BOONYATEE82600400i500f;¥J:;300l400l300200'CScO200lOO100ooo Displacement1 2 3 4(mm)5Fio. 28. Estimatcd static load-displacement relations b .･ unioadingpoint method0,0Estimatedpoiut methodF er. 29 .than that of Pattern 2 due to the use of constant C.However, as shown by Fig. 28, the prediction by the250,0unloading point znethod of Pattern I is much better thanthat of Pattern 2. Note that the C of the Unloading point200,0method for Patterns I and 2 are 2.47 kN-s/m and 0.86kN-s/m, respectively. From the prediction results, it isthought that the characteristic of damping force can bedivided into two parts, which are the major trend andminor trend. The major trend is controlled by onelumped parameter, say C* ,g, and the minor trend iso ,5 1 ,o I .5 2 .o 2 ,5Displacement (mm)static ioad -displacement relationsb) unloading/ Ylelding polnt)r;, '1,50.0csO:]lO0.050.0effected by the V.1.. The value of C*..*_ for Pattern I andPattern 2 are 2.77 kN-s/m and 0.55 kN-s/m, respec-0,0tively. For Pattern 1, although V.1. is large, it has a rela-o2 34IDisplacement (mm)tively small effect when compared to that from C. g. Onthe other hand, the V.1. of Pattern 2 has a large impacton the characteristic of damping resistance since the valueof C*+,g is small. It is also found that the V.1. of Pattern 2Fig. 30. Variation of dampingf orce5with dis placement (Ist tcst ofPattern I and Pattern 2)reduces to a small value and C converges to a constantvalue after the piles yield./Yleldmg polntSince the model pile experienced one drop of loading250before it reached its maximum displacement, thesettlement characteristic of pile in Pattern 3 is differentfrom the others. Consequently, the variation of C, whichdepends on the velocity, is also affected. Therefore, theresult of Pattern 3 is not used for the interpretation.However, the correspondin*' parameters are also shownin the plots for comparison. The V.1. of Patterns 3 and 4are 4. 19 kN-s/m and 3.09 kN-s/m, respectively.Although the variations of C in Fi**. 27 are larger thanthose of the friction piles, the Unloading point methodcan acceptably estimate the static responses of piles evenfor Pattern 4, which load the piles exceedingly over theiryielding points. These estimations for Patterns 3 and 4are shown in Fig. 29. Since the C-displacement plotscannot give any clues for the differences in behavior between Pattern 2 and 4, the Fd-displacement plots, which::i'.200';J1501:,co]lOO50O 0.0 0.5 1.0 1.5 2.0Displacement (mm)Fig. 31. VaTiation of damping force with displacement (lst test ofPattern 3 and Pattern 4)are not infiuenced by the piles velocities, are used instead.As shown in Figs. 30 and 31, it can be seen clearly thatdamping resistance of the friction piles reducesTherefore, although it cannot be concluded from the C-considerably after the piles yield. The same characteris-displacement plots, the difference in behavior between thetics are not observed for the tests of the end bearing piles.friction piles and the end bearing piles against the*,*i'i:･! .83STATNAMIC_ TESTS ON MODEL PIL,ESTo viewStatnamic force can be validated by the Fd-displacementplots .l,Since the main difference between the end bearing andthe friction pile is either the pile is supported mainly bythe shaft resistance or the tip resistance, the dampingcharacteristics also come from the same source. For thefriction piles, the damping resistance comes from theshaft portion and becomes small or zero after the slipoccurs. On the contrary, the end bearing piles gain theirdamping resistances mainly from the pile tip and theseresistances still remain even after their yielding point.When C is assumed to be constant, a good estimationfor the friction piles can only be obtained when the)magnitude of loading is not close to its ultimate///?¥1.3 5.09¥resistance. Note that C converges to a constant valueIoading/1./2 2.4/11.0(Unit cm)J27.0 f 0.0+¥18.0-3¥after the yielding point of piles, or the displacement of 2mm. Hence, it is thought that the damping resistance ofpiles is not only non-linearly related to its velocity (Coyleand Gibson, 1970; Lee et al., 1988), but it also has some2-o¥relation to the ratio bet¥veen applied loads and theultimate capacities of the piles. For the end bearing piles,lthe constant C can be applied to all ranges ofdisplacement, even after the yielding of piles.-35¥-31¥-43¥ a-49¥ANALYSIS BY A 3D-FEM CODF. (DYSO,-5 6¥(In order to develop a unified tool that can be appliedfor various types of problems, a 3D-FEM code, DYSC, isoriginally developed in this study. To demonstrate theSide viewFig. 32.application of DYSC, a simulation of a friction pileunder Statnamic loading is presented. No-tension criteriaand a simple elasto-plastic model based on the DruckerPrager theory are applied as the yield functions for themodel ground. An interface layer element is inserted atthe interface bet¥veen the pile and the soil. For the pilebody, a linear elastic relation is used since the applied5;ttest ofTable 5.Geometn.' of FEM meshPropertics of materials for FEM analysisSandforce is lower than its yielding point.To determine the necessary parameters used in the STNsimulation, trial calculations are made. As shown inDensity (k_ */ms)l ,467bPoisson's ratioo.333e0.200'Youn_ 's modulus (MPa)4.90n5.00 x lO;bFrictional an :le360 bFig. 32, an analysis is conducted in the half area of theIcalculated from the fiexural test results. Poisson's ratiosfor the pile and the soil material are assumed to be 0.20014and 0.333, respectively. Direct shear tests have been done2, 1 50b90Dilatancy angiepile-soil system. Young's modulus of the pile is backPilefrom inversed anai_vsisbfrom material testassumedto determine the frictional and dilatancy angles of thesand. The dilatancy angle, defined as a constantparameter, is approximated from the average change involume of sand during shearing. The frictional an*"le ofthe pile-soil interface is assumed to be 0.9 times thefrictional angle of sand. Based on the static load testresults, Young's modulus of sand can be estimated froma parametric study. The properties of each material deternxined from an inverse analysis are summariz,ed in TableIsi test of5.are calculated from the displacement by the Newmarkmethod. The stiffness matrix, the damping matrix, andthe mass matrix are calculated from the followingequations:l, .lK= BDBdvol (3)J .lC = NplNd vo! (4)¥veen theIn the next step, a dynamic FEM analysis of a pileunder Statnamic loading is done and then compared withthe experiment results. The loading rate dependency ofthe ground response is represented by a constant dampingM= NpNdvol (5)iinst the ;parameter. In this simulation, velocity and accelerationwhere N is a so-called shape function or displacementrrl the C-' .".i:si!Jl 84KIMURA AND BOONYATEEinterpolation function, B denotes a displacement to thestrain transformation function, and D is a strain to stress-400strain transformation function. Parameter p is used torepresent the damping constant per volume of thematerial of interest in the same manner as the density (p)is applied in the mass matrix.' ,;¥jI300::lcO:!Pi!e-Soil Intelface Mode!The Mohr-Coulomb yield criterion is used for the200100interaction between the pile and the soil. It states thatfailure will take place if the magnitude of shear stress (r)Oon the failure plane is equal to the value given by thefollowing relationship:l ri = (TDisplacement (mm)tan co + co (6)in which I I denotes the absolute value, (T is the normalstress on the failure plane, and co and co are material constants for the pile-soil interface. In this study, adhesion,or co, is assumed to be zero. Since the pile is not made bythe cast-in-place method, the frictional strength of thepile-soil interface should be deteriorated compared withthe surrounding soil. Therefore, the frictional angle, orco, is assumed to be 0.9 times the corresponding value ofsand. Equation (6) can be written in the form of yieldfunction F asF= I rl - a* tan 60. (7)0.0 0.2 0.4 0.6 0.8 1 OFl" 33' Variationin pilestiffnessagninstYoung's modutusofground400i' '; 300J:,ceO200hl OOIf the material is sheared to the yield surface and the as-sociated flow rule is adopted, the rates of plastic normalstrain ds and shear strain yP are given byd8P tan c[d y P lO0.0 0.2 O. 4.O (6 .)O 8 1.0Displacement mmFig. 34. Variation in pile stiffness against fricttonal angie of groundwhich impliesdePdyP = tan co (9)The same calculations are also done for ft'ictionalangies of 32eand 30'. When the amount of settlement isIncrernents in shear displacement along the plane areaccompanied by increments in normal displacement. Thethe pile behavior. However, the disparity in load-dilation of the shear plane will go unbound underyielding. To avoid this unfavorable behavior, the non-associated flow rule is adopted for the pile-soil interface.By introducing dilatancy. angle v/, the plastic potentialfunction can be ¥vritten asQ= ITI cr tan v/ (10)In this study, no dilation is assumed for the pile-soilinterface, i.e.,/H'O.small, the frictional an_g:1e of soil has little influence ondisplacement relations increases ¥vhen the displacement is )large, as sho¥vn in Fig. 34.From various trial calculations and comparisons withdata from static load tests, a Young's modulus of 4.9MPa and a frictional angle of 32' are selected as rationalquantities for the ground materials. Using these values, asatisfactory approximation for pile response can be obtained. The frictional angle of 32' for soil gi¥'es thecalculated ultimate load at more or less the same level asthe measured data. A Young's modulus of 4.9MPacontrols the shape of the load-displacement of the pileCALCULATION RF,SULTSStatic CapacityIn order to find the material constants, a parametricstudy has been made. Based on the data from the directshear tests, a frictional angle of 36' and a dilatancy angleof 9' for sand are used. When Young's modulus of soil isvaried, changes in pile stiffness are achieved as sho¥vn inFi**. 33.before failure.It can be seen that the determined frictional angle is notequal to the data obtained from the direct shear tests. Theground conditions in the experiment may not be as denseas the sand sample in the direct shear tests, and thiscontributes to there being a smaller value than in thedirect shear test results. The load-displacement plot frorrlcalculations and measured data is sho¥vn in Fig. 35.i 85STATNAMIC TESTS ON lvIOD L PILESStatnalnic CapacityBased on the calculated parameters determined in theI.is shifted to the right in order to match the 'true'displacement in the static load tests.previous section, simulations of pile responses underStatnamic loading are carried out. Since the pile is loadedto its ultimate capacity in Pattern 2, the solutions of thefinite element calculation diverge at about the yieldingpoint of pile and the response of the pile cannot becompletely determined. For the above reason, only theelastic contraction represented by the difference inThe damping force of the system is assumed to bemm. When compared to the overall settlement, thislinearly dependent on the velocity, and a damping constant of 3.9 MN/(m/s)/m3 (p as defined in Eq. (4)) iscontraction is about 50/0 of the pile head settlement. Thedistribution of axial force along the pile is sho¥vn in Fig.37(b). The application of load is sustained almost totallyby friction resistance, with only a small amount of forceused after trial calculations as the material constant forfurther calculations. The estimated load-displacementrelation and the test data are shown in Fig. 36. Note thatthe initial displacement in Statnamic load tests does notof groundShown in Fig. 37(a) are distributions of displacementalong a pile under static loading. At the peak load, thesettlement between the pile head and the toe is about 0.05results from Pattern I are presented here.1.0Comparison between Computed Static and StatnalnicLoading Resultsconform to that in the static load tests. The initialdisplacement in the Statnamic load tests is a little bitsmaller than the corresponding value in the static loadtests. This may be attributed to the loading rate effectduring the equipment installation process because theinitial dead weight in the Statnamic tests is applied to thepile head at once. To correct this inconsistency, the load-displacement relation (from the experiment) of the STNbeing transmitted to the pile tip. The ratio of the endbearing resistance to the shaft resistance is about 1:4.5.The pile velocity versus time relation is sho¥vn in Fig.38. At the maximum displacement, the velocity of the pilehead is equal to zero. At the same time, the velocity of thepile tip is almost identical to that of the pile head. Thisimplies that the pile behaves as a rigid body at theunloading point. Axial force distributions of the pileduring Statnamic loading as well as a comparison withthose of the SLT are shown in Fig. 39. At the same600600!500l . . Or' ,400c'300OI200;SSl- - Experiment/ if rictional {i ilOOrtlement isji200500,,_r/___'i' ____ i;O]// 7l; 400l 300le of groundli100Ifiuence on;,lacemento 1Displacement2 3 4(mm)5 6.risons withulus of 4.9Ooin load-Fig. 35.Load-displacement relations from SLT simulation and0.2 0,4 0.6 0.8 1.0DiSplacement (mm)Fig. 36. Load-dispiacement retattons from sTN stmu ation andex perimentexperimeuti as rationaise values,can be oboil 9:ives thame level aiof 4.9MPglOof the pil/V} an..,* le is no;J::_ 20flar tests. Th ;c be as den(.fts, and thi;than in th ;nt plot fror.･jFi . 35.30iiiiiiiili*- iili*!i:i iiiii io.2 o 4ri-S･lOON ,H -200N -A-300N i-400Niil{ i__iiFig. 37.ltilPs: 20 - i---o' ii ii ii i!ie'30 /;1//- --'- -r'-- i-; I-hIi -iI-- -"-Iirl i !Displacement (mm)a. D splacementij- -ll40 o, 6 o.8ijl{} i! i!Ii i!ro ' -I-- Id';T]oi¥J!lOO200300Load (N)b. Axial loadDistribution of displacement and axial force along pile under static loadingsOe _}/ _'rr 1'86' t Fl"TKIMURA AND BOONYATEEapplied load level, the axial force distributions of the twocases are almost identical. As shown in Fig. 39, when pilemined from trial calculations, a finite element analysiswas carried out. A comparison of pile behavior under ahead settlements are equated, the pile in the STN canstatic loading and a Statnamic loading was conducted.sustain a higher load than that in the SLT. There are nosubstantial changes in load sustained by the pile tip.Based on the results from the tests, which use relativelyIncreases in capacity mainly contributed to the shaftresistance. The effect of a stress wave is not observed inthis analysis.short piles and relatively loose soil, the followingconclusions can be summarized:1) The large wave numbers of all patterns imply thelong duration of Statnamic loading which results in a pilebehavior no longer dominated by the action of the stresswave. From this evidence, it can be concluded that the developed small-scale loading device has the potential toCONCLUSIONWhen compared to field tests that have the inherentsimulate Statnamic loading in laboratory tests.problem of ground uncertainty, the model tests presentedhere show the possibility for conducting Statnamic loadtests under one uniform condition. Only by this approachcan the data be interpreted on absolutely the same basis.Moreover, the experimental results also reveal oneadvantage of laboratory tests over full-scale tests. Forfull-scale load tests, it is difficult to load the piles up todisplacement of the pile cannot be compared to those ofthe prototype. Nevertheless, the experimental data agreetheir ultimate bearing capacities due to the condition ofsafety. However, the tests in Pattern 2 show that this kindof load can be applied readily in the laboratory tests.2) Due to the presence of dynamic resistance, there is awell with the original Statnamic signal.After input parameters for the simulation were det,er-time lag between the points of maximum displacementand the peak Statnamic load. The load-displacementAt present, such results as load magnitude andplots of the STN also show higher capacities than those8-!l :6lPile head- - Pile tip,¥J43) In Patterns 1, 3, and 4, the load-displacement plotsfrom the SLT and the STN meet at about the unloading1' 2:>0-2/s2 to 50m/s2. However, the inertia force is relativelysmall since the mass of the pile is small./ogiven in the results of the SLT because of these additionalforces. The acceleration of the pile varies from about 5 mo lo 2030 40 50Time (ms)Fig. 38. Variation in velocity of pile head and toe along timepoint. This evidence a*"rees well with the assumption ofthe unloading point method (Horvath et al., 1993), whichstates that dynamic forces at an unloading point are verysmall and can be disregarded. However, in Pattern 2, theSTN plot shows the unloading point to be quite far awayfrom the SLT Iine.4) It can be concluded from the C-displacement plotsand Fd-displacement plots that when C is assumed to beconstant, a good estimation of the friction piles can beobtained only when the magnitude of loading is not closeSiL C Sl:0 ･_8 mrrl-0.28 mm-c- O.55 mm -O.56 mm- -O.86 mm ^ O.85 mrnoo1010oo:: 20: 20,C- I i- Ii iii ; i !Li -'t i----"-- f- -'e)e,C:}i I"' 7 - - - yjl'lTI't I'T"'---r l"I" I"-^ i30i30T}401 oo300400Displacement (mm)a. Applied force equatedFig. 39.40lOO 200Load (N) 400 soo300b. Head displacement equatedComparison of statnamic and static simulations 87STATNAMIC TESTS ON lv iODEL PILESrelatively ;to its ultimate resistance. It is thought that the dampingresistance of the friction piles is not only non-linearlyrelated to the pile velocity, but also has some relation tothe degree of loading compared to the ultimate capacitiesfollowing jof piles.imply the ithe stress jresistances of Patterns 3 and 4 vary within a small range.Consequently, the damping coefficient of the end bearingpiles can be considered as a constant value. This is ob-lat the de- {served whether the piles yield or not. The damping)tential to jresistance of the pile, or the hard layer, does not decreaseeven if the applied load exceeds their yielding stress.t analysis :)r under a {onducted. ;5) From the variation of C and Fd, the dampings in a pile =ry tests, I3veal one i6) The finite element analysis (DYSC) shows that thetests. For ;elastic contraction of the pile is relatively small. This)iles up to jvalue represents about 50/0 of the total displacement.From the load distribution plot, the applied load ismainly supported by shaft friction. The model pile isndition of {t this kind {there is a {thought to be a friction pile. The ratio of shaft resistanceto end bearing resistance is about I :4.5. Velocities of theplacement ;pile head and the pile tip are almost identical and equalplacement izero at the unloading point. This supports the:han those {additional ;assumption that a pile moves as a rigid body at they tests. jREFERENCES1) Amir, J. M. and Amir, E. . (1995): A Iumped-Parameter modei forstatnamic testing, Proc. of the Ist Int'! Statnamic Serninar,Vancouver, 2232) Bermingham, P. and Janes, M. (1989): An innovative approach toload testing of high capacity piles, Proc. of the Int'! Co,rf, on Pi!ingand Deep Foundations. London, 409-413.3) Bermingham, P, and ¥rhite, J. (1995): Pyrotechnics and theaccurate prediction of statnamic peak loading and fuel charge size,Proc. of t/7e Jst Int'/ Statnanlic Serninar, Vancouver, I -12.4) Bro vn, D. A. (1994): Evaluation of static capacity of deepfoundations f'rom statnamic testin_ :, Geotech. Testing J.. GTJODJ,17 (4), 403=414.5) Coyle, H. M. and Gibson, G. C (1970): Empirical damping constants for sands and clays, J. Soi! Mech. and Found. Div.. ASCE,96 (SM3), 949-965.6) Karkee, M. B., Kojlma, I. and Shinoda, Y. (1995): Infiuence ofdifferent test conditions on the results of STATNAMIC Ioad tests atthe Shonan test site, Proc. of the Ist Int'! Statnamic Senlinar.Vancouver, 137-147.7) Kimura, M., Adachi, T., Yamanaka, T., Fukubayashi, Y, andBoonyatee, T. (1997). Failure mechanism of laterally loadedconcrete piles by centrifugal model tests, Proc. of the Int'/ Conf, onFol!ndation Faih!res. Singapore, 417-426.8) Kimura, M . Boonyatee, T, and Adachi, T, (1999): Experimentalunloading point.study of laterai statnamic ioad tests on group piles, Procabout 5 m i7) The axial force distribution from the STN is veryInt'! Conf. on Deep Fot!ndation Practice in Corporatingrelatively jsimilar to that from the SLT. The stress wave effect, as ina dynamic load test, is not observed in the present. Thisunloadin2mption ofimplies that in the STN, the pile is loaded in the samemanner as in the SLT.Although the outline of the research can be divided93), which iinto three parts, as sho¥vn in Fig. I , only the work on StepTlent plots ;:rt are very jtern 2, the ie far away ;Tlent plots ;med to be jles can bejs not close ;) is reported in this paper. The horizontal load tests ongroup piles have been conducted and reported elsewhere(Kimura et al., 1999). In order to perform vertical loadtests on pile-raft foundations, the improvement of theloading equipment is presently under planning.As a ¥vhole, the equipment presented here and DYSChave the potential to perform and analyze small-scaleStatnamic load tests. The 3SLD-Mkl may be used as atool for investigating pile behaviors under Statnamicloading and the application of Statnamic load tests to pilefoundations. As the second step of the research, theexamination of pile behavior will be done through thenumerical analyses of the full-scale tests.PII.ETALK '99. Singapore, '-63-271.9) Lee. S. L., Chow, Y. K., Karunaratne, Gof the 4thP, and Wong, K. Y.(1988): Rational wave equation model for pile-drivin_ : analysis, J.Geotech. Eng.. ASCE, 114 (3), 306-325.10) Matsumoto, T. and Tsuzuki, M. (1994a): Statnamic tests on steelpipe piies driven in a soft rock, Proc. of the Int'! Conf, on Design(Tnd Construction of Deep Found.. Orlando. F!orida, 586-600.l 1) Matsumoto, T., Tsuzuki, M. and Michi, Y. (1994b): Comparativestudy of static loadin_test and statnamic on a steel pipe pile drivenin a soft rock, Proc. of the 5th In!'! Conf, on Pi!ing and DeepFound.. Bruges. Be!gium, 5.3.1-5.3.7.12) Matsumoto, T. (1998): A FEM analysis of Statnamic test on openended steel pipe pile, Proc. of tlle 2nd Int'! Statnainic Seminar,Tokyo, 287-294.13) Middendorp, P. and Bielefeld, M. W. (1995): Statnamic ioadtesting and the nfiuence of stress wave phenomena, Proc, of t!1e Is!Int'/ Statnan7ic Serninar. Varlcouver, 207-22214) Nagaoka, T., Sakamoto, K., Fujisawa, H. and Kubo, Y. (1995): Acornparative study of the Statnamic ioad test on a steel pipe pileunder diff rent loadin_2: conditions at the Shonan test site, Proc. oftJle Ist Int'! Statnanlic Seminar. Vancouver, 149-164.15) Poulos, H. CJ. (1998): Pile testing - from the desi_gner's viewpoint,Proc. of the 2,Id Int'/ Statna,nic Seminar. Tokyo, 3-'-1.16) Yamashita, K., Tsubakihara, Y., Kakurai, M. and Fukuhara, T.ACKNOWLEDC.F,MENTSThe authors ¥vish to express their sincere appreciationto Professor Toshihisa Adachi of Kyoto University forhis advice. Special thanks are also due to Mr. AtsushiYoshida, former master course student of Kyoto University, for his help in performing the laboratory tests.j:i';,';i#Ei:-(1995): Load-settlement behavior during kinetic pile test. Proc, ofthe IOth Asian Regiona! Conf, on SMFE. Beljing. Cllina, 233-236.17) Yamashita, K , Tsubakihara, Y. and Kakurai, M. (1998): Methodfor estimatin_g static load-settlement relation by rapid pile loadtests, Proc. of tlle 7th Int'/ C0,If. and E;t:-hibition on Pi!illg a,rdDeep Found . Vienna. Austria, I .29. 1-1 .29.6.
- ログイン
- タイトル
- Earthquake-Induced Flow Slides of Fills and Infinite Slopes
- 著者
- Osamu Matsuo・Yukiko Saito・Tetsuya Sasaki・Koichi Kondoh・Takashi Sato
- 出版
- soils and Foundations
- ページ
- 89〜104
- 発行
- 2002/02/15
- 文書ID
- 20441
- 内容
- ログイン
- タイトル
- Torsion Shear Tests on Cyclic Stress-Dilatancy Relationship of Sand
- 著者
- H. Shahnazari・Ikuo Towhata
- 出版
- soils and Foundations
- ページ
- 105〜119
- 発行
- 2002/02/15
- 文書ID
- 20442
- 内容
- SOILS AND FOUNDA'TIONSVol. 42. No. l, 105-119, Feb_ 2002Japanese Geotechnical SocietyTORSION SHEAR TESTS ON C 'YCLIC STRESS-DILATANCYRELATIONSHIP OF SANDHABiB SHAHNAZARli) and IKUO To¥¥,HATAii)ABSTRACTSeveral cyclic torsional drained simple shear tests were performed on Toyoura sand in order to investigate the stressdilatancy relationship under a large number of re*'ular and irregular loadin*' cycles. In particular, effects of differentfactors such as initial anisotropic stress state, initial confinin*" pressure, density and shear history on this relationshipwere studied. It was found that the stress-dilatancy relationship changes suddenly after each loading reversal with acontractive behavior. When loading reversal occurs at a higher value of stress ratio, more contractive behavior is observed after the reversal. Although the stress-dilatancy diagrams of different cycles start from a different extent ofcontraction in irregular loading, they converge to a common one as stress loading continues. Test results showed thatinitial confining pressure and initial anisotropic stress state do not have any important effects on the stress-dilatancyrelationship. It was found that density and shear history affect the stress-dilatancy relation. Change of stress-dilatancyrelationship due to increase of density or shear history leads to less contractive behavior. Results of this researchprovide complete and accurate information on the stress-dilatancy relationship under a large number of regular orirregular cyclic loading and effects of different factors on this r'elationship. This information can be used in themodeling of cyclic stress-dilatancy relations and volumetric strain. The investigated volume change and stressdilatancy relationship in this study together with seepage analysis can predict the excess pore water pressure forliquefaction analysis.Key words: constitutive eauqation of soils, dilatancy, drained shear, sand, torsion (IGC: D7)INTRODUCTIONVolume change in dramed shear which can beconsidered as a mirror image of pore water pressurebuild-up during undrained shear, is one of the key}}horizontal and vertical stresses. Pradhan et al. (1989)performed a series of cyclic triaxial and torsional sheartests on isotropically consolidated specimens of Toyourasand. Although their number of loading cycles wasparameters that affect the behavior of sand under cyclicloading. Change of volurnetric strain in different stageslimited, a unique relationship between the stress ratio andthe dilatancy ratio (strain increment ratio) was observedin each testing method irrespective of void ratio and stressof loading can be described by the stress-dilatancylevel.relationship, which relates the ratio of strain incrementsto stress ratio. Many stress-dilatancy relations have beenAs a part of a research program for the modeling ofsand behavior under cyclic loading and for a better understanding of the cyclic stress-dilatancy relationship,proposed so far for monotonic loading (Rowe, 1962;Roscoe et al., 1963; Oda, 1975 amon*･ others). Forseveral tests were performed on Toyoura sand in thetriaxial tests, Tatsuoka (1978) obtained a stress-dilatancypresent study. Significant volume change was generatedrelationship, which appears to be independent of theafter a large number of loading cycles. Effects of differentsample density, the initial fabric and the mean pressure.parameters such as density, anisotropic consolidation,confining pressure and change of shear strain amplit.udeAlthough the study of soil behavior under dynarnicloading is an important issue in geotechnical engineering,there have been few studies on stress-dilatancy relationsof sand under cyclic loading. Based on the results of aseries of simple shear tests, Nemat-Naser and Takahashiel984) suggested that the stress-dilatancy behavior maybe independent of sample density (at least when only afew cycles are involved). They also stated that theilatancy is affected by the K= o'",/a¥vhich is the ratio ofon cyclic stress-dilatancy relations were also studied.A Iarge number of cycles are applied to soil structuresduring most real dynamic loading cases such as earthquake loading. Effects of cyclic loading on differentparameters of sand under a large number of cycles wereinvestigated in this study in a more comprehensive waythan with a limited number of cycies.Results of this study on the experimental stress-Assistaut Professor. Civil Engineering Department, Iran University of Science and Technology.professor, Civil Engineering Department, The University of Tokyo.Manuscript was received for revie¥¥' on February 6, 2001 .Written discussions on t is paper should be submitted before September I , _'002 to the Japanese Geotechnical Society, Su_ ayama Bld*Kanda A 'aji-cho 2-23, Chiyoda-ku, Tokyo lol-0063, Japan.';,jUpon request the closing date may be extended one month.1054F, l06SHAHNAZARI AND TO¥¥,HATAdilatancy relationship can be used in modeling cycliccircumferential strain (det) are kept zero. Moreover thestress-dilatancy. Liquefaction modeling based onmeasured pore water pressure (CU tests) is not invertical stress was kept constant. Stress and strainuniversal use. This is because, in reality, seepage andconsolidation change the volume of sand. CD tests whilemode are shown in Fig. 1. Independent control of thecomponents in hollow specimens under simple shearmonitoring dilatancy are more useful because themeasured volume change together ¥vith 2-D (or 3-D)axial force, the outer cell pressure and the inner cellpressure can produce this mode of shearing by using acomputer program. The torsional shear strain rate wasseepage analysis can predict the excess pore pressure. Themaintained constant at dy=0.30/0/min through thel-degree of freedom observation in this study can becombined with a multi nonlinear-inelastic spring model(Towhata and Ishihara, 1985) to achieve a 2-D modeling.10ading cycles. In some tests the shear strain amplitudewas constant in all the cycles but in some others, shearstrain amplitude was variable.SHEAR APPARATUS AND TESTED SPECIMF,NSISOTROPIC COMPRESSION TESTSA hollow cylindrical torsion shear apparatus was usedin this study. In this apparatus the vertical load, the innerSince the present study aims at the volume change ofsand due to torsion shear, it is important to make aand the outer cell pressures and torsional shear werecorrection to membrane penetration and also volumedynamically applied to a specimen with 19.5 cm height aswell as 10 cm outer and 6 cm inner diameters. To ensurechange due to the change of confining pressure. in orderan accurate measurement of volume change of themeasured volume changes and also the relationship ofspecimen, an electronic balance was used in place of thedifferential pressure transducer used by Pradhan et al.volumetric strain (8,,.1) and mean effective principal stress(1986).hollow cylindrical specimens with different densities.to investigate effects of membrane penetration on(P'), isotropic compression tests were performed onToyoura sand ¥vas tested in the present study, whichSivathayalan and Vaid (1998) showed that themainly consists of quartz (around 900/0) and chertmembrane penetration effect on a hollow cylindrical(around 40/0). Its physical properties are G* = 2.65, Dso =specimen of granular soil can be assessed by Eq. (1):O. 16 mm, U* = I .46, e*** = 0.977 and e*i = O. 597 .Specimens were prepared by air-pluviation of air-driedsand particles. By changing the drop height and the rateof pluviation, specimens ¥vith different relative densitieswere prepared (220/0 to 760/0). Carbon dioxide (C02) andsubsequently de-aired ¥vater were percolated through aspecimen to achieve a high degree of saturation. Then asaturation backpressure of 100 kPa was applied to thespecimen to achieve saturation with a B-value exceeding0.98. The specimen was subsequently consolidated underdifferent confining pressures and different anisotropicconsolidation ratios (K=crfla , which af and cr areeffective radial and vertical stress).c* = [A V, - A Vj*(x2 - l)] / (A*i +A**)] (1)in which e* is the unit membrane penetration (volumechange due to membrane penetration per unit area). A V*and A Vi* are the recorded volume change of the specimenand the inner cell and X is the ratio between the outer andinner radii of the specimen, while A i and A * are thesurface areas of the specimen covered by the inner andouter membranes. This equation is valid for the case¥vhere identical pressures are applied to the inside andoutside of the cylindrical specimen.In order to investigate the effects of density onmembrane penetration, isotropic compression tests lvereperformed on specimens with different densities. TheseSHEARINC. PROCEDURESpecimens were sheared after consolidation under aIsotropic compression and sweliing testdrained cyclic torsional simple shear manner. The simple0.005shear deformation is defined as that in which theincrement of the radial strain (ds*) and theToyoura sand{o¥i: r'0.004v_!;'Fzt:so,003o::C, = Constants 'Tzrtibir-Po,'¥,t rt¥ d8t=0LYL Yrt1 tlr>¥Or zF:e'E2'59E'5" P' P'o/ ¥l8--h-- No.251 Or=37'1e:t,::o.oolol l0 , oyl indrioal speciElenFig. 1. Stress and strain components in simple sheaf mode '･-No.255 Drs56e/e- -* No.253 Ors76e,/.Average valuee):o ooorP'Q: )- - N0.2S4 Dr=24e/oe's$o 't3'56E " P'0.002t2*de so¥-e;50 150 300iOO200250Effective con ning pressur8 (kPa)Fig. 2. Effects of densrt,_, on membrane penetration3 51 *:;107C_YC_LIC STRESS-DILATANCY,,,;il!!ltests were performed with the same method ascalculated and listed in Table I , which were corrected forSiva:thayalan and Vaid (i998) suggested. Membranemembrane penetration.Results of this section are used to estimate themembrane penetration. However, it is not clear how thetorsional deformation affects the extent of membranepenetration for specimens was determined by using ther.;"results of these tests and Eq. (1). Figure 2 compares the;,membrane penetration for specimens with differentl.**adensities. Thickness of membrane in the present studywas 0.3 mm. Although the membrane penetration curvesin Fi :. '- changed with density, the limited number ofis;;I[etests makes it impossible to find a consistent relation foreffects of density. Therefore, an average of the membranepenetrarion curves for different densities was used in thislelr' *i.study.*The relationship between volumetric strain and mean",effective confining pressure for medium dense sandbefore and after membrane penetration correction arepenetration. In this study no effort was made to considerthese effects on membrane penetration, and Eq. (1) wasused for estimation of membrane penetration in simpleshear mode.CAI.CUl.ATION OF VOLUMETRIC STRAININCREMF,NT AND DILATANCY RATIOVolumetric strain increment ds .consists of a:ierchange measurement.onFor calculatin*' the coefficients of volume compressibility or s¥velling (m ), Eq. (2) ¥vas used;dilatancy component de9. induced by plastic shear strainincrement and the r'emainin*' component de,',.1 induced bythe change in P', the effective confining pressure. For agiven change of P', the value of de,'..1 was calculated byusing Eq. (2).In this paper the ratio of volumetric strain increment tom = ds 1 Id!og o P (2)(-de9. /dyP). Increment of plastic shear strain isof, *sholvn in Fig. 3. It is clearly seen that the membranepenetration correction is very important in a volumei,a!eofi,essonin which ds .i stands for an increment of volumetric strainthedue to change of effective confining' pressure (P'). Theicalvalues of n7calculated by Eq. (3):d yP = dy - dy' (3)for compression and swelling wereIn this equation, y* stands for the elastic component ofshear strain, which was evaluated by dividing the shear(1)o.766umerO 7G2menandNo'255 :calculated by fitting a mathematical equation (in the form:: e:v_iv¥ : l,O.7Gotheos ,oandL'5 O 756>andO, 754v ons !o.7581:caseO.752S ShlAfter membrane penet. correctionh' before membrane pef?et correction0,750i: lIsotropjc eonsolidation fToyourasandh 1ie02:sO'764Dro s::Ss e/o¥ i¥1'erestress increment by the maximum tangent shear modulus(G***) The value of G ** for each speclmen wasHo 764!IV,Theseplastic shear strain increment is called the dilatancy ratioo 200Effective oonfining pressure(kPa)of a hyperbolic equation) to the stress-strain curve ofeach cycle. The derivative of each equation at thebe*"inning of loadin*" or unloading is denoted by G .*.The dilatancy ratio can not be calculated directly fromshear strain (yP) and volumetric strain (e . ) due tofluctuation of the recorded data. This fluctuation isunavoidable during experimental investigation. Thedilatancy ratio ( - ds,d. /dyP) is strongly affected by thisfluctuation. Therefore to calculate the dilatancy ratio,volumetric strain (8 *f) was plotted against plastic shearstrain for all the cycles. A mathematical equation (in theform of a polynomial equation, c,d,1 =A + BFig. 3. Effects of membrane penetration correction on isotropicCoefficients of volume compressibilit .･ and swelling (m.*) in isotropic consolidation tests (The unit of P' is kPa)C_onining eo 'tl) = O 885pressure Dro 2 = 240/0(kPa) fPts:)'r-"IS eS¥vellin :ee ' = O.764 eo 2 = O.690Dro 2 = 560/0 Dre 2 = 760/0O . 005 3 lO.00424 O 00360O150300O.0041 10.00364O.00349O OO,-74l OO25O . 0043 ll ooO . 003_, O1 50O.00207O.O01333 oo(i) e0.2=vcnd rauo at effectrve con nmg pressure of 20 kPa ( O ' kgf/cm )'eo ' = O.837Dr0.2 = 380/0O.00693O 00556,-5Compression+unloading part of cycles (Fig. 4(a)). The derivative of thisconsolidation test resultsTabte 1.yP + B2(yP)B3(yP)3 + B4(yP)4) was fitted to the curve of each loading or00443O 003?_1 O.002800.00_ 63 O.00228O . OO-,OO O . OO i 74O.00386 O.003390.00261 0.00235O.O0188 0.00185O.OOI 21 O.OOI 1 9O.003 1 4O.OO'_21O.OO 1 8 ,_O.OOI 1 8 108SHAHN_ AZ,ARI AND TO¥¥rHATA1 oo32cl data3110th loa ing of No.159 j40C:,2,8CL!･:e',i 2.720P(QL 2.6u)E d SA +Blfe,B2(7' )' *BS T P f +B4(? F )$,C,,Palameter Vaiue'oE 24L,T:,A a9soee2.3B1C,J)512BB2).0475sB4.001 45CO-40-60";-80Y =t3.0 '/.21-20J::Orained cyelic simple sheaFAnisotropic cons. K=2.5p' ;8 kPase o.ooe312 2'o"',1,Polynomia] Regression2 2.52.0::::!eo: 2,9>;lT TkNo.16180Polynomia] fit of data3.0or..-1 oo-3 -2Pl stic torsional shear strain, V P (%)-11-32-2o-1213****Shear strain, Y (%),,*_O//Ae1l vol/n*20iAe 1410ut loading of No.169 IO.8L vol /n * 1l+ {306i204e5 1¥ 02P-ds p d/ d7 P s -BI -2B2T P - 3B:(72 - 4Bs(!i,c;?sLcaOCQOOL;co:).2-1c 'e)c,)u)e)CODrained cyelicsimpleshear l)4.Cl)Anisotropic cens. Ks2.5).63p' s98 kPar7 s:!:3.0o/p)8-1 O) 752o0.00 0.50 0.75Dilatancy ratio, -d8..Id/d Y P) 50 H),250,2510dilatancl.' relation for half of cl.'clecurve with respect to yP is the dilatancy ratio ( ds,i 1ldyP,.1¥eycle no.¥;oe!e' S ee;¥fori*teycf e-o 2-1 oand changes of shear strain amplitude on stiffness andin dilation.¥;e:ixs ;O., Rotation of line c) 75H).50].25 O.OO O 25o.50o.75-deYold/d Y 'stress-dilatancy relations were studied. In this section theresults of one test are discussed in detail as a control case.Results of other tests will be discussed in the followingsections on the effects of different parameters such as density, confinin*" pressure, etc. In this paper volumetricstrain is considered positive in compression and negative**; e: "e:t¥6sity, initial anisotropic consolidation, confining pressure,ef'!lLlne c)8･"f "/2..:/;/-. 7 5o.oBased on the results of different tests, the effects of den-.'1. '"4./'C1Line c-c tor40thcycleH)*4RESULTS OF TORSIONAl. SIMPI.F. SHF,AR TF,STS. .vo/ ; .,,1002e*6(ei e)11 Tl N0'16104= B - 2B2(yP) - 3B3(yP)2 - 4B4(yP)3). The relation between -ds, .1/dyP and the stress ratio (rz;/(T =torsiondilatancy relationship (Fig. 4(b)).d08oeshear stress/effective vertical stress) is called the stress-4 5321Volumetrie strain, LFig. 4. (a) Fitting mathematical relation to yP-ed.] diagram, (b) Stress-;if .T iNo-1 6 {-4Fig. 5. (a) Stress-strain curves of medium dense specimeu subjeeted tocl_'clic simple shear, (b) Volumetric strain of medium densespecimen subjected to c_vclic simple shear, (c) Stress-dilatancyrelationship for medium dense specimen subjected to cyclic simpleshearFigure 5(a) sho¥vs a stress-strain diagram for aspecimen with initial void ratio of 0.756 (relative densityof 580/e). Figures 5(b) and 5(c) reveal volumetric strainstiffness increased with the increasing number of cycles.The increment of the soil stiffness in the course of drainedand stress-dilatancy relations for this specimen. Thesefi_ ures indicate that volume contracted and the soilshearing is not only due to change of density. It is also iaffected by shearin>" in previous cycles. This point will be'E! iI109C_YC*LIC STRESS*DILATANCYf:discussed in the next section, which concerns effects ofo 8rfi ThNo 161density and shear history on cyclic behavior of sand.j Due ro the accumulation of volume change during 40, cycles, the void ratio of the specimen changed fr'om 0.756I to 0.658 (relative density from 580/0 to 84010). Aithough' the tested sand had both contractive and dilative behaviorj, within individual cycles, the incremental volume change; after the end of each cycle was contr'active. The rate ofvolume contraction decreased with the increasing number'of cycles (see Fig. 5(b) for example). In other words, the"'- volume contraction was remarkably larc"er than volume; dilation in early cycles. After a large number of cycles,g0.Go 4end of a complete cycle decreased and the volumecontraction was slightly larger than dilation.¥eee .02K) o ,o¥P)2D! ned cyelie si ?ple shear1 0tropie cens , P* 8 kPa)4eH].e.1"-o 8.?Se * Dre*d = O.858 * D,5T =the difference of volume contraction and dilation at thei,,4 /' /¥:( :84%: 3%).6 ) 2 O O 04 O.6O.2), 4-de d / dYP. . Ficaure 5(c) shows that the dilatancy ratio starts from a' hi*,_"her vaJuei.vhen the loading is reversed at a higher level! of stress ratio. For example the dilatancy ratio afterFi**. 6. Stress-dilatancy relationship of medium dense specimen duringinitial (vir',*in) and first cycle of loading"{ Ioading re¥'ersal in the first cycle at the stress ratio of 0.47was 0.44. In contrast, when loading was reversed at astress ratio of 0.78 in the 40th cycle, the dilatancy ratio'as about O.6. This figure also shows that after loading{ reversal, each stress-dilatancy curve starts from aj diagonal line (c-c), ¥vhich passes through the center of; coordinates. In other words, the diagonal iine c-cconnects the beginning of the stress-dilatancy curves of10ading and unloading of each cycle. Moreover when theloading continues after reversal, stress-dilatancy curvesof different cycles become closer to each other in theloading parts (in this paper the loading part is a part ofshearing in ¥vhich the shear stress and increment of shearstress ha¥'e the same sign, which means dT*r>0). It canalso be seen in this figure that the diagonal line c-c slightlydiscontinuity in the stress-dilatancy curve and it restartedfrom point 7.Another important point in Fig. 6 is that the stressdilatancy curve of 7-9 (reloadin*') did not pass throughpoint I . Therefore a stress-dilatancy relation of virginloading appears to be different from those relations in thefollowing cycles (see Fig. 5(c)).In order to examine the effects of confining pressure onstiffness and volume chan*'e of sand, difi:erent tests were- number of cycles ¥vill be discussed later with regards to- the effects of density and shear history.^ In general, the stress-dilatancy curve (see Fig. 5(c)) for; each cycle consists of two parallel segments of positivej slopes and t¥vo nearly vertical segments immediately afterstrain with three percent amplitude ¥¥'as applied tospecimens No. 171, No. 161 and No. 168 with an averagedensity of 580/0 and isotropic consolidation. InitialIoading reversals. The stress-dilatancy relationship of the{ following cycles is different from that in the first cycle.7(a) shows the stress-strain curves of these tests.j Stress-dilatancy relationships in the first cycle areI demonstrated in detail in Fig. 6. At the beginning of; shearing, the stress-dilatancy curve started from a-" ,=during cyclic simple shear). Since the torsional shearstress is mobilized in the horizontal plane, it is clear that anormalizin*" the shear stress by the vertical stress, thestress-strain diagrams of these specimens become similar.Fi**ure 7(b) reveals the normalized stress-strain diagramsof these specimens. It can be seen in this figure that thefaric .'mple ;, Point 3, the value ofds,4.1ldyP changed discontinuously'; and remained positive (point 4). Immediately afterj loading reversal, the dilatancy ratio took the maximum; lyalue. After loading reversal soil exhibited a contractive;behavior, rn the follo¥ving cycles, the soil demonstrated ainedsirnilar behavior. The diiatancy ratio was zero at points 5cles,alsoSpecimens ¥vith a higher initial confining pressure andconsequently a higher value of vertical stress had higherstrength in this figure (vertical stress was kept constant; ratio became zero. After point 2, it took a positive value.iensei}; and 8. After loading reversal at point 6, there was a;isotropic confining pressures for these specimens beforeshearing ¥vere 53, 98 and 184 kPa, respectively. Figurehi_ :her value of normal stress on this plane leads to aj This point is equivalent ¥vith the phase transformationPoint, 1 'hich ¥vas introduced for undrained loading byIshihara (i996). When the loading direction reversed atll beinitial mean confining pressures. Cyclic torsional shear{ negative value of dilatancy ratio, - de,ldyP (point I inj Fig. 6). ¥Vhen loading continued to point 2, the dilatancyed to{BEHAVIOR OF SANDperformed on specimens consolidated under different; For a large number of cycles this difference is remarkable.;F.FFECTS OF CONFINING PRF.SSURF. ON CYCLICrotates counterclockwise with the number of cycles.Change of the slope of the diagonal line c-c with the:{hi**her shear stress. Therefore, it seems that afternormalized stress-strain relationship of differentspecimens are almost identical for the same number of;cycles. Althou*"h the (T.*/(fL)-y relationships changes ¥viththe number of cycles, (7 is not so important in this figure.This fact can be seen clearly in Figs. 7(c) and 7(d). Thesefigures compare the stress-strain curves of specimens inthe fifth cycle of shearing before and after normaliz,in_"._.; . . j*=**;SHAHNAZARI AND TOl 'HATAllO*101 6020H:}-N0.171 Dr s57% P'=53 cr':Hhlo.17 Or s571;, p's53 o' ::se- =No.161 Drss'rts58% P': e8 c'*s98e'No.168 Dr$:sr's58% P*=1B4 cr'*s e4o.8-c N0.16e Dr s58,X, P*=1840'¥80Pc,,a,P';o '-89u)-{ 20oHH:]2,,,7:col'I:G)e),,,o.Q1"3 kPa-40'T:,Il4JoL*'(1)02coq,il,!;1 84!(1704ui40:io eecl:O_x:'53-4No.1S1 Or s58% P' 8 cr'==981'].4e)N5H).6oHD.8P's o '*:sl35 kPaZ-1 eo3 2Isetroplc conso!idation35 cycles I :s:s 3'o-1 oO13 2- -1212Torsion sheer strain, Y (%)Torsion shear strain, Y (%);{,;'*;10160e 120, .C,:cH:HYo.171 Orss, rts579,'* P' 53 e'*s53No.151 Ort *rts58e/* P' ::98 (;'tsg808ONo.1S8 Or$$ t 5B% P' =184 o'.::184e. 40c,c':clee)OnttvOeo 1208 e'*s98ii06Po.4u)a)o 2:,Fifth cyele,,)Lcea):o)::r/) _80$58% P'i.'1u;Pe)H o^161 Dr;P' s53 c,'* 3)No,168 Dr$t '::5e% p* =184 o**=1e4¥/ 80lo.171 Or 5T;.10/r!Fifth cyc:eo oH) 2).4)N.c:lOH _160oZo-3 -2Torsion shear strain,Y (%)l)6l8-1 o2-32Torsion shear strain, Y (%)-11Fig. ?. (a) Effects of confinin"* pressure on stress-strain diagrams, (b) Effects of confining pressure on normalized stress-strain diagrams, (c) Effects {;of confining pressure on stress-strain diagrams (fifth cycle), (d) Effects of confining pressure on norma ized stress-strain diagrams (fifth cycle)specimens with different initial anisotropic confiningconcluded that the initial confining pressure did not affectthe stress-dilatancy remarkably after initial loading.In order to verify this conclusion on effects of confiningpressures. However, after normalizing the shear stress bypressure, some other tests were performed on loosevertical effective stress the stress-strain curves are almostspecimens with a relative density of 230/0 . Figures 10(a)the shear stress by effective vertical stress. It can be seenthat the stress-strain curves are completely different foridentical.and 10(b) compare the stress-dilatancy relationship ofFigure 8(a) compares the stress-dilatancy diagrams inthese specimens in the first and tenth cycle of shearing.the first cycle of shearing for these tests. It can be seen inExcept for the initial loading, the stress-dilatancyrelationship of these specimens was almost identical,this figure that the difference of stress-dilatancyrelationship for different specimens occurs mainly at thebeginning of the first loading and afterwards, there is noverifying that the stress-dilatancy relationship after initialremarkable difference. Comparison of stress-dilatancypressure.dia*'rams for the tenth cycle of shearing is shown in Fig.8(b). This figure demonstrates that the stress-dilatancydiagrams were almost identical when shearing continued.In other words the initial confining pressure did not haveany remarkable effect on the stress-dilatancy relationshipliloading ¥vas nearly independent of initial confiningEFFECTS OF INITIAL ANISOTROPICCONSOLIDATION ON CYCl,IC BEHAVIOUR OFSANDexcept at the beginnin*' of first loading. This fact can alsoDifferent tests were performed to investigate the effectsbe seen in Fig. 9 which shows the developed volumeof initial anisotropic consolidation on strength and stress-change in the first, second, fifth and tenth cycle ofdilatancy relations of sand. Tests No. 165, No. 164 andshearin*'. In this figure the volume chan_g:es of specimens¥vith different initial confinin*' pressures ¥vere almost theNo. 172 were performed under initial anisotropicsame except for the initial ioadin*'. Therefore, it can beand the mean consolidation pressure of 98 kPa. Theconsolidation stress ratios (K= (7/ Ia ) of I .6, 1.0 and O.6,{i lllCYCLIC_ STRESS-DILATANCYo#-No 171 OrH 1 D･1 S10.8e-No.1G805i,79,'*8%8%DrDr10P' 3 e ' ;3p' 8 (; 'o.8p'=1e4 o **=1 B4¥ ¥e ereInitiai loading Fir$t eycle0.6¥e: ;o ¥. e:'" jl0402Pio o,O-o 2e¥PNu)a)!-0.4)*No.168Dr* ,s=23'1.;e7 c,' nj7P =98e' ;8P s:135 e ' =135=": ¥e: o e:¥¥¥ce ", . . ..=! {( 'o.oHD2!_!' ' "' il' _ ').4'Cl)24P/o PtOFsmjs22e/.o.24)' -1:i;N0.174 DrHNo.16104'e¥Hc J8c .H)6-o.el' ;r":u::n^!o -se;F"nP_!e^vlsil i hrt e.atai,ir", ,[ir]'" ; "ii_ ･'.. :';: . :'.',,, ,','.;) 8' t'- Oi,'isotroplc consolidation)^8i-1) 25 0.00 O.25).50-o 75o 507 :s:#3'O %Initial loading+fiFst oyc[eoo 75) 75).25-d8vold O.,25/ dYPH),50o 500.00-d8void / dYPo 75*'10**,,;08li08:H o.171 Or- No. 1 51 DrNo.168 Or7%P's53 (,' ;310:hNo.174 Or8%8p*=1 e4 eF ' =1 B4O^8H o.16iN0.168;8% P' 8 a 'r10- eycl:e{04i¥e/';o ¥2¥¥sj'lO.6t) O.OooPN -o 2¥tlP__!･･")43%35 o '73c'=135;oTenul cyc ef, 2.!.,!..).4!-o 6sl-o 8-? c-o 75 H), 25-dE*dOI d25 0.50 O.75o oo) 50=ectshL!P'=¥¥,,,',1'e')" i02¥JT24% P' 7 cr*=22% P'::98 o '040.2erTOrDr/ j'rat_ t_:irn<0jioe;;mo :e'").6)8 c.-1 O50).75H) H),25Od8.,doo / 0.250.50 o 75dYP,relationship of medium dense specimen (initial loading and firstFig. 10. (a) Effects of iuitial confining pressure on stress-dilatanc _'relationship of loose specimen (initial loading and first cycle), (b)e _'cle), (b) F,ffects of initial confining pressure on stress-dilatancv.'Effects of initial confining pressure on stress-dilatancy relationshiprelationship of medium dense specimen (tenth c,_'cle).of loose spe(:imen (tenth cycfe)Fig. 8. (a) Effects of initiai confining pressure cn stress-dilatanc,.')fectlln)oser !nFtrai::: ltosdln9*O ( a)rT: T::T:lIst eyc err;:T:, 1:l21ld eyc eTi:;:5ul eye erT:T l1 oth eyeleaverage initial relative density of these specimens was 23o/o. Figures 1 1(a) and 1 1(b) show the change of the radialstress of these specimens durin*' the first and thefollowing cycles. Since shearing was conducted in asimple shear mode, the outer and inner cell pressures3J) of2l ng .changed to keep the lateral strain equal to z,ero. It can beseen in Fig. 11(a) that for the specimen ¥vith initial K= ltncyical,oitlal(No. 164) the value of radial stress reduced quickly from98 kPa to about 62 kPa during the initiai loading andf ingthen fiuctuated around this level (Fig. 11(b)). In-2 'subsequent cycles the average level of the radial stress-3O.o O 4F08 oo 0408 0.0 0.4 O.8 OODT I 58- ne. 171r ctsress-sotrelc CensalldationP1ekPa,ne･1S1,P'Fig. 9. Effects of initial confiningandmedium dense specimenopic-i 0.6,iTheO.4 O.8 OO 04 03Volumet,ic strain. s d ( )1,pi8kPs, Apressureloading. At the initial stage of shearing, the radial stressof a specimen with K= 1.6 (No. 165) decreased sharplyT= $ 3no 1 e9, p'slightly increased. Anisotropically consolidatedspecimens showed a similar behavior under cyclic=184kPaon volume change offrom 112 kPa to 47 kPa. For a specimen with K=0.6(No. 172), conversely the radial stress increased from 80kPa to 84 kPa. In the subsequent cycles, the radial stressfiuctuated with a gradual increase of its average level.Pradhan et al. (1989) also observed this behavior. As isshown in Fig. 1 1(b), after the substantial chang'e of stress+,;i 1:'?jii'; "' L, ･ !!' ;;'* S ' SHAHNAZARI AND TOll2HATA.- No., 65* or : 24e/., K .1 201 40A No.1e4. DrFssl.6, a ';10 kPa=229 , K:* t"=1.0, CF ':s98 kPa!No.Is5, K*:s's=1^S ,o '==70 kPaoNo 172, DrFtv's239t, l($s'IsO.6, e '*:sl34 kPa- a.164, K$srt:;1.0 *e ';9B kPac-No.172* KFsstsO e *,1 's*134 kPa1 30/1 20,QcL 110J(10090t)80o;L'start 0Test K:; e '* /e '* after first cyclerN0'165n0165startrl of n0172{ I . 'r _ofi'J v r? _ O ( !hastartoti,aOCAn J¥/¥--i'l"-n5040cJ,_.=-.- :'-' ;-<='-__'-_ -- ;_' : :-/a: ; fi :::2j-;c,,f(os:Drained cyclic siFnple shearo'J/i f '"55 -80p,= g8kPa20 cycles ToH-1 20First cyclefnitiai load.'_'1'f'LL Os: -40'!':',,)e)l '¥4 J- =u)a)Na'l72eo:540(,;.,'r-'-'( j'(_PNa'le470U)o'65o G3o'e3nol5480CL3.0 %_3 -2 -1 O 1 2 3*Torsional shear strain, Y (%)" i1301 20""' r;o* 110Test I 1,'*lc,' aftsTfiTstcycleO G5nole5O JS3nol 54-No.155* XF:"rfl G ,:T 'sss70 kPa- H o.1e4, Ks 1 l.O ,o ':s98 kPaH o.1 12, KFs't 0,e tc"s:sl 34 kPan0172Si]' "" ="ea'oO, Seo.8c:; I 0.165* Drss't::24, X$:s"' 1.6, e'sf10No.,1S4, Or, ,s229 * Kstss"si-e -No.1 72, Drl s,rt: 23}kPaO, e '*g98 kPa, XF: tse 6* e '*s:134 kPa,s,x."+.*I]= }1' }"{ oo' ,i * I=.=,.*1'*"'i,*t"'l"'i*{"' '" **, A.'ijlliil:= , :!:Iiil:iT;IIII} I{I80,*^ "*.'+..: =' :" '1 "I t}70CQ!02i'oou)i'C,, 7) 2)Illll IIIi! I5040)*_ r'1:so'SfXo,4cne)4'U)o.6Put) 90u,o)¥{]i! IfJ:co1:,(DN15o 5 1 o1205Cycle no302sFig. 11. (a) Change of radial stress for specimens with different initialEIoZ) 4;;rH).6)8-1 oDrained cyellc simple shearp ' = g8KPa20 eycles T s 3.0 %-3 -2 -1 o 1 2 3Torsiona[ shear strain' Y (%)anisotropic stress states under c,.'clic simple shear (initial to rdingand first cvcle), (b) Change of radial stress for specimens withlid t'on on stress-strainFig' ::rve:a:fEl eo::ss::Idni:lb;l S:scot:rooF::1: oanlsaonis[oat:opicconsolidatioudifferent initial snisotropic stress states subjected to cyclic simpleshearon normalized stress-strain curves of loose sandilratio (K=(7f la ) during the initial loading, its avera_ evalue ¥vas about 0.65 for all specimens independent of theinitial anisotropic stress state.Figure 12(a) illustrates the stress-strain diagrams ofspecimens. The stiffness of specimen No. 172 was hi*･herthan that of others, because of the higher value of normalstress on the horizontal piane. After normalization ofshear stresses by vertical stresses, the stress-strain curvesin Fig. 12(b) became almost identical (Shahnazari andtenth cycle of shearing are compared in Fi**. 14. It can beseen that the stress-dilatancy relationship of thesespecimens are nearly identical, suggesting that the initialanisotropic consolidation did not have any remarkableeffect on the stress-dilatancy relationship of sand after theinitial stage of loading. A comparison of the volumechange of specimens during 20 cycies is illustrated in Fig.15. It can be seen that the difference bet¥veen thesevolume changes after 20 cycles was srnall. This differenceTowhata, 2000). This implies that the vertical stress onthe horizontal plane strongly affects the torsional shearoccurred mainly during the first loading. For example,the differences of volume changes for specimen No. 165and No. 164 after initial loading and at the end of '-Ostiffness of sand.cycles, which are denoted by A***** and ll**d respectively,Figure 1 3(a) demonstrates the stress-dilatancyrelationship of specimens in the first cycle of loadin*'. Thestress-dilatancy relationship in initial stages of loadingwas affected by the initial anisotropic stress state.Ho 'ever, it seems that ¥vhen shearing continued thiseffect decreased. A comparison of volume change in thefirst cycle of shearin_-' in Fig. 13(b) also indicates that theeffects of initial anisotropic stress state on the volumechange were important mainly durin_ the initial loading.The stress-dilatanc.v diagrams of these specimens in the::::,,are nearly identical. Therefore, it can be said that thevolume change of sand is independent of the initialanisotropic stress state except during the initial stage ofIn order to investi**ate the effects of initial anisotroplcconsolidation on the cyclic behavior of sand some othertests were performed on specimens with the averageinitial relative density of 570/0 (No. 169, No. 161 and No.::.::,:.167). Each specimen was consolidated ¥vith a greater***g i '{113CYCLIC STRESS-DILATANCY1 .O1 .o-{h･No.1e5. Dr$: s'l=24%, K$so.4.tl '/ ':1f' ';;rrE- "'Rrsteycle ""i/l 7f /ol:7 ::1:;i'!jL! '1 Ii!If! P'fl'fP!1'' .1 ! ItliHD･2HD*4-o 6' lc-o 8-1 o.(¥ ;c) o.o¥t5-O^8¥10 eycle04-o 4i's23s ' K' s c e' c' tiB134 kPH c02e oo¥P )2*'10H o 172' Dr'o e" l"'!/' / _j ' _02:H otl55t Dr's 'F24 ' K'# ' l sl 0: t:s7o kParNo l64' Dr' 1 ts22 ' x' t:;110"' I:$ ee kPao.8(v'r9in) eadin9: ¥e: D¥¥slee: rl'"'*i'c- No.172* Dr., Is23%. K$ lse.e, (; '*sla4 kPao.'.*l 1 5, CF '$s 70 kPa- H Io,1e4, Drt t 22%* K srtsl .O* CF '*s98 kPao-O.50H),25-o. 7 5O,OO O,50 O,15O.25c .--{ o.50 l .250.000.25 0.50 O. 75-devo d / df75-dB+0:d / dY P;{;Fig, 14. F,ffects of initial anisotropic consolida:tion on stress dilatancyS5, ors l:t249 t K5sst'=1"51 o 1;t::70 kPai - rNa-'-'--No'l1e4, orEsrts22%, X':$rt=1^Of 'T tEseB kP54l -;3i,_lF¥/ 2*,:,1'u,O!L,:!Oe,**/_j_/r"v-c:Ijl lc::1'h If' /rh!)l2+ss32' o"tJr'¥! i fi]ins!::P:!clie simple sheaF/:o-1-2-3// lHO _3A eT,dA startrlJrr15EOrelationship of hoose sand (tenth cycle)'r-Nol72 Or s23 K$:: rtsOGe$s5134kPa.,532; ' i+' i¥ i'l i +; L*'i Iti' L'/ : ¥'¥it}}!1 !>-' :}';/:+1 l' '1*i"I ' ** = '*::j/ V 'i/1 !1!)i!'1i)1!1;!il):J!!':i)1)li li'ce0.0 1 .O 2.0 2 50515Volumetnc stra n 8.,t ( )c'Dx:9' r ' r rnrlrr'rl i' '!i)i==! 't='<il= l*'*"o1cn2c:3o;1 SLJj ! ,] flj i!"'1;i'!!_ /L'-4l 1 : : !,,)!linFig. 13. ( ) Effects of initial anisotropic consolidation on stress-'ondilatanc . ralationship of loose sand durin"* initial and first cl_'cle ofloading, (b) Effects of initiaE anisotropic consolidation on volumechange of loose sand during initial and first cycle of loadingHo;il;iiil) ".*ol"i, il ･=- .-2-3beeserange of anisotropic stress state than in previous figures.[ial IFigures 16(a), 16(b) and 16(c) illustrate the stress-bledilatancy relationship of these specimens in the first, fifththeand tenth cycle of shearing. These fi*･ures also indicatethat the stress-dilatancy relations of sand becameme-1"*independent of the initial anisotropic consolidation afterlesethe initial sta*'e of loading.nceThe results of this section su_ :gest that the effects ofple,initial anisotropic consolidation appeared mainly at theinitial stages of shearing. After the initial stage ofshearing, anisotropically and isotropically consolidated16520specimens had almost identical stress-dilatancyely,relationshi ps .theirialBesides the initial anisotropic stress state and its changee ofin inltial stages of shearing, the fabric anisotropy thatO 1 2 Volumetrio3 4 5 6strain,7 8e+.Id9 10( ) 11 12Fig. 15. Effects of anisotropic consolidatio l on volumetric strai iunder cyclic ioading (20 cycles)the initial loading may be considered as factors whichaffect the stress-dilatancy relationship of isotropically oranisotropically consolidated specimens in initial sta_ es ofshearing.EFFECTS OF DENSITY AND SHEAR HISTORY ONCYCLIC BEHAVIOUR OF SANDopicpreparation techniques can affect the behavior of sand)thernlainly in the initial stages of shearing. Ho¥vever, in thefollo¥ving stages, initial fabric anisotropy diminishes dueWhen a soil specimen is subjected to cyclic loading, itsdensity increases due to shear deformations. This changeaffects the stress-strain and volume chan*'e behavior ofsoil in the following stages of shearing. During cyclicshear, besides the effects of density, shear history alsoto shear deformations. Therefore, the initial fabricaffects the behavior of sand. These effects are due to sheararises in laboratory specimens from the sample:ra eNo.eateri,anisotropy and change of anisotropic stress state duringdeformations in previous sta*･es of shearing. Shear;,i ;"'ill4SHAHNAZ,ARl AND TO1 1HATAiN0'169' Dr s57%' K ' s2'5";'108049 kPaNo'l64' or*= 2-No 151 ' Drsssrts58'x" KFiprt 1'or a':s9B kPa !;'108Initial loadin9 tirst cyele [r'i !0.6o j""'!rf:"r-!/?'-r": Q¥ee /1'1 :::qo ¥ :!'_ _ _"i/'*1:::::e *:'0.4"(1e : ¥ $ " 1!11/o.2;¥- -o 2PNHD.4j"6).8T__J!40･ ･-P 20(ie)IIc,)iir// !lrr]ljl'' Ofl'(1:;ju,c' :40=_4_n'ngf{ ;;elie sir7lple shear l_!!h : -*i{ !!ou)Lo -50-i1_ -' ; ;; ' !s7 [. ^ rvIf!oa!n 03iics:menP: ' sh pekPsta I fhle-80-1 o-3).SO ) 25O 09 9.25 0.50 O 75-dE*,d / d7P), 75--i;ir/ : --La) -20/f-No 16e ":or' "=7i;i f J) jt 'r_'ifc:,CL_1'ANo 162' Drs* 8'/*No'l61 ' or*= ;8""(,,;f ' je 0,0!{60-e-No'l 67' ofetpl: 7 ie'KFl ss0'3' at::sl84kPa-1 O-2Torsionai shear stra[n,Y ( )2 3*Effects of density on stress-strain curves of sandFig. 17(a).*: -No.159, Dr$tsrts5le.!c' K,t"I::2.S, o '.: 49 kP10- -ND.151, Dr*s ' 5B%, K*ssrl 1 .o, e '=s98 kP- N0.157* Dr 4T9 ,, K . 0'3*o'si84kPa (S e¥･･ "i}+ c0.8r;rhFifth cyele06/4i¥e el/':}je )r; ;2i0.2ic) o.o¥Pi¥3¥e: io(¥ ; ¥ (1' cr I jo.4I.:.o 2' ics:mo:: 'sph =_ag'8tkeps:iIL-a,/ Eiil' !noc:f!?' fll/G')4:c,)-1f/::HD6ompie shear.8eep, = SekPac.7-1 o50 0,25 O.50 O,75-0.25-o. 7 52/ohs3*o %j¥ c:i1,/f' i/" = - Na'le4'or=22%H - N0'162* Dr'= 8 t-3-No'lG1'Dr;8%- No Is5' or =759O_OO-4-dE , d / d-o.52 O 3.50.5 1 o I .50.02.53.0VolvmetHo strajn, 8v*i (%)--"'11"""I'NoJe9' Dr'#rt 57S4' K'$s" 2 5' CF tts49 kPa101 'tNo'i61 ' Drt: It 5Be/st t($ :srt :1Effects of densitr.' on volume cbange of sandFig. 17(b).o' e ': 98 kPaY"'<) No'hl67' Drt ls57%' Ks'stls013"' I:::1e4kPa o e¥e / i'1 c08P'flJ jth cycie ¥eh''!1P'io. e'c¥5; JycieI ¥¥/'e ¥ ¥¥¥ 1e e o ro1004Na.1e4, Dr02i08- {1- - N0.1S2, Droe- h No. 61, Or-e- Na.1Ge, Dr2%8%Line e'e tor leose sand 't 'il7¥ ':!'' "f 1;8%=75%it) o o¥O. 4) 2!ILJ'P '!!1 f"P'Iff L ! r471;4'; tl/e¥ O, 2/P- OOo).6-o 8C /-1 .o) 75, ' 1J1'h L;-O 50 O,OO O.7525O 25O 501 :L -0.2c ,c,'T / " i'/ I ',J,G;)4L'fC"' "I"f "' !f / f / /). 6-de+.rd / dyP/ ! " Une eT'c for der'se::_ dto delsii..).8ISi:1Rot tlen ofdia90na Ilne e'c dUe to de sityFig, 16. (a) Effects of initial anisotropic consolidation on stressdilatancy of medium dense sand (initial loading and first cv. cle), (b)-1 o).75) 25O OOO.25o.500.75Dilatanoy ratio, -dg*Id/dYFEffect of initial anisotropic consolidation on stress-dilatancv.' ofmedium dense sand (fifth e 'cle), (c) Effects of initial anisotropicconsolidation on stress-dilatancy of medium dense sand (tenth).50Fig. 17(c).F,ffects of densitv., on stress-dilatancy relation of sandcycle)**;i=L:s･ 115C_YC L,1 C_ STRESS*DILATANCY; .history can be studied in terms of the number of cycles,i{1o.8accumulated shear energy, cumulative shear strain*0increment and/or any combination of these parameters.The number of cycles is used as an index for shear history+in this study.IIn order to investigate the effects of density and shearhistory on the cyclic behavior of sand, several tests wereperformed on specimens ¥¥'ith different initial densities ofi22, 38, 58 and 75 percent. Comparison of results at theo 4t) 02¥P- OOo: 5CQ(,,)2,,,beginning and also at different sta*"es of loadin*･ revealsthe effects of density and shear history and theircombination.Specimens ¥vere sheared under a constant strainamplitude of three percent. The shear history effect isminimum in the first cycle of shearing and increases withi*{cycles. When the effects of density are studied, data fromthe first cycle is employed, because the history effect isilnd.4) 6-o 8H).75H:] 50 -O 25 O.500.75O.250.00Dilatancy ratb, - e+.Id/dyPFig. 18. Effects of density on stress-dilatancy of sandnegligible in this cycle. Strictly speakin*･, the experienceof the first cycle of loadin*･ generates the history effects inthe specimen during this cycle. This is ho¥vever ignored inthe present discussion on the first cycle.Figure 17(a) examines the stress-strain curves of thesespecimens in the first cycle. It is evident that the stiffnessIlll Iof dense sand is greater than that of loose sand. Fi**ure17(b) sho¥vs the volumetric str'ain of these specimens inthe first cycle of loading. It can be seen that the loosespecimen (No. 164) vas contractive at all stages of thefirst cycle. Dense specimen No. 166 ¥vas contractive onlyat a lo¥ver magnitude of shear stress or stress ratio. Intkeps:sg8kPaz_ ="'//a 3-5mdNo 164¥ : 11 ¥¥oe4 0'6G o iB 0'70 0'72 i 0'74 0'7e 0'78 0'80 0'82: o'B4 o'B6 o'8B O906cldes :- (j((((r(j(((!ijr ¥lri30_:lf(1' 'T'j' 11 Dri_rted5impsatropesh:ar?,_ ::f11lilt(e conso: :";'elp ; es kPa" o'o15) 30No I G2¥ ¥¥r¥064 o'G6 o'eB 0'70 o'72 ;074 o'7s 078 080 082: 0'84 08G 0'88 o'90: 3 ')":'esi ::dense sand the increment of residual contractive3()Figure 17(c) sho¥vs the stress-dilatancy relationship of*15 p ':9akPa3 J)1 n5100se sand.:L Io o tsatropccensoFor all the loose and dense specimens there was a residualpositive ¥'olume chan_ge after completion of a cycle. Forvolumetric strain after each cycle ¥vas smaller than for9 ele!es :4j lht_1 5 DrEined simp e shearhigher values of stress ratio, ho¥vever, it became dilative.'-rl;SrOO.5tIt I¥':Di:_nsj/ simpleshserIsotlropic eonsilP =9s kPNo I G1O'G4 O'e5 0'58 070 O'72 : O'74 O'^7e 078 O'80 082 O 84 0'85 O'88 O'90z : : :VOid RatioFig. 19. Effects of shear history on volume change of sandthese specimens in the first cycle of shearin*". The startingpoint of the stress-dilatancy relationship ¥vas stronglyaffected by density. For denser specimens it started at alower value of negative dilatancy ratio, vhich means a' .':)*d ' ･ ,7)¥.:.smaller extent of contraction. Besides the startin*･ point,the stress-dilatancy diagrams were different in otherparts. It can be seen that for denser sand the diagonal linec-ch ltp';l1'as steeper (counterclockwise rotation with the8kPao 0'75This means that a specimen with shear history had asmaller volume change per cycle than a specimen withoutEffects of shear history can be separately studied bycornparison of test results for specimens ¥vith differentinitial densities at the same current void ratio. Fig:ure 19i!_**For a similar change of void ratio, specimen No. 162 ¥vithsix previous cycles needed five cycles. Nine cycles ¥vereapplied to specimen No. 162 with eleven previous cycles.Fi**ure 18 compares the stress-dilatancy relations forspecimens ¥vith different densities in the first cycle ofshearing under a reduced shear strain amplitude of onesand .;1 of sandneeded a different number of cycles. Three cycles ¥vereapplied to specimen No, 161 without any shear history.increase of relative density).percent. This figure reveals similar effects of density onstress-dilatancy relationships, which are a smaller valueof negati¥'e dilatancy ratio and steeper line c-c for denser;: .ea!'s..tvoid ratio from section M-M to N-N, each specimenshear history. This difference is clear in Fi** 20(a), ¥vhichcompares the volume chan*･es just after section M-M.Increase of stiffness (hardening) only due to shearhistory is shown in Fig. 20(b). Specimens in this figurehad identical current void ratios but different shearhistories. Since the constant shear strain amplitude wasthe same for specimens, shear stress amplitude is arepresentative parameter for the stiffness. The shearstress amplitude of specimen No. 161 Ivithout sheareontpares the volumetric strain of three specimens at thesanle current void ratio. At the section M-M, all threehistory lvas about 60 kPa. Shear stress amplitude was 66specirnens had the same void ratio of 0.756. Under thesanle amplitude of shear strain and identical change of68 kPa for specimen no, 164 in the twelfth cycle. Thus theincreasing rate of stiffness ¥vas greater in initial cycleskPa for specimen No. 162 in the seventh cycle ¥vhile it ¥vas 'j.S}{AHNAZARI AND TO¥ 'HATA116(shorter shear history). In contrast after a larger number {N0.164, i2t cycle;3iT7.No.1 5'!2of cycles (longer shear history) t.his rate became smaller. ;T:h eyeleFor example, in Fig. 20(b) shear stress amplitudeNe'l61, 1't eycle {1i{.Figure 20(c) compares the stress-dilatancy relations for ;these tests. It is clear in this figure that shear history j:c,,o!o:affected the stress-dilatancy relations. It seems that, ;-1:similar to the case of soil stiffness (shear stress ;oohincreased about 6 kPa after six more cycles (No. 161 to 'jNo. 162). The increase of shear stress amplitude for the {later five cycles was only 2 kPa (No. 162 to No. 164). ";amplitude), for initial cycles the effects of shear history jwere greater.This effect decr'eased after a large number of jcycles. For example, in this figure difference of stress- {,-2Pls98 kPaes0'756-3o 7 9 8 o 9 1.0O.O O 1 O.2 O.3 O.4 O 5 O eAe old (%)dilatancy relations is greater for specimens No. 161 to ;No. 162 (initial 6 cycles) than for specimens No. 162 to iNo. 164 (following 5 cycles). It can be seen that diagonal {Effects of shear histor_v on volume chwge of medium denseFig. 20(a).line c-c rotates counterclockwise due to shear history, jwhich is similar to the effects ofdensity (Fig.17c). Besides jsail!dthe rotation of line c-c, when shearing continued, the idirection of stress-dilatancy curves slightly changed in jrjjL;: ;:':'1T'{';::::':;, :" .__.___1"':i= "'1'No.1G4, 12t't cycle80¥,.L:"s'::J60c(JNo 152, 7e' cycl40Pgraph in loading parts. When these changes of stress- ;zodilatancy relationship combine with the effects of shear jc,;c,,e,ce)sv,::history on stress-strain curves, smaller volume ;ocontraction is generated for sand-20o-40effects on the volume change of sand under one-percent {shear strain amplitude. Specimens had different initial IN0.161, 1*t eycie-50void ratios but at the section M-M, void ratios ¥1*ere ;-80-2 Torsion-1 shear Ostrain, Y (Ek)-31100'8 j::i2 3Increase of stiffness (hardeniv,g) due to shear historl.'Fig. 20(b).Line c4 for 15t cyole: ;:L;ceyyyc!::ei: f'o_rl2 lcyc!: 'F'> :'i;' "' ' ' ' - No e'$' 12 cyclee¥PcF,g0'6'r li::,,,fshrinka9e in laadi::::/; :/i/::: //:i::::;:/::;:'l jj04:. _ _ T:1';;; _ _ ::(:; 111.:::: 7'! t0'2O'ON':'161 f cyete i: :.. :' Is) ///1tilf I ; ""!'1 !f4 ,t;'' ii!/;' ot:stres' "dilatancy'r' '// ' shrinka9eH)'2l/"c,,(,,o)'4(D)'61e! l $: /:e¥s;;r:I/ diagra!11 in toad n9 part {!/1/t/ '" '/'/- ;¥;oSS'jlf:;::1;ii"'; ! *?/ !' '/ /-e,8 ' " '-1 Ovith shear history. ;Figure 21 sho¥vs another example of shear history ;os,10ading parts (the loading part is where, dr*r>0). By thisslight changae, the curve for a larger number of cy. cles +came inside, resulting in more dilative behavior. In this jpaper this behavior is called shrinka_g:e of stress-dilatancy jRotatian et dia9anaPI ::9e kPa: eso'75enne c-G due to sh ar history) 6 H).4 ].20.0O 2Diiataney ratio, -deve d/d Y Po.4 o 6Fig. 20(c). Effects of sl]ear historl.' on stress-relationship of mediumdense sandequal. However, shear histories of specimens ¥vere jdifferent. In this section specimen No. 177 had no shearhistory (effect ofvirgin loading is neglected) but specimenNo. 188 had experienced 21 previous cycles. The stressdilatancy relationship for specimens at section M-M isshown in Fig. 22. Diagonal line c-c for specimen No. 188after 21 cycles was steeper than that for specimen No. 177jI;j}jwithout any previous cycle. In other words, Iine c-c ;rotated counterclockwise due to shear history, Ieadin_*," toless contraction after loading reversal. The other effect of !shear history on the stress-dilatancy relationship of jspecimen No. 188 was shrinkage in the loading part, jwhich means more dilation in this part of loading. jBased on the discussions in this section on the effects of jdensity and shear history on stress-dilatancy relationships ;of sand, it can be stated that increasing sand density and Ishear history has similar effects on stress-dilatancy !relationship. These effects were the counterclock¥vise }rotation of diagonal line c-c and shrinkage of the stress- ;dilatancy diagram in the loading part. Therefore, it is {expected that the combination of density and shear jhistory ¥vill have the same effects on stress-dilatancy Irelationships. Effects of this combination are sho¥vn in jFig. 23, which illustrates the stress-dilatancy relationships {for specimen No. 176 with initial relative density of 240/0 ;,and under cyclic shear strain of lo/o. The density of the jspecimen changed from 240/0 to 690/0 after 20 cycles. Itl,"LL;_ii ;,*117CYC_LIC STRESS-DILATANCY{;,5#deto{ll!11{Itf{((Ifll'!il liiN"IB8O. B*'{t'llt¥*t{o 6- ¥ '801 ,*50 i;5./. C:4 .' . . 1'-! o^o?11'f.2 .'1,1. ': *o.41 ' tso 62 o e4 o G6'-! l'or¥'. ** *.7' "" *"4 '1* "* "*' "*' '*+)ry' 11!i:=*{/**/*,., , io*!¥11 *w'l 5O G2 O S4 O.5G O.Sg O 70}*o.72 0.74 0.7G¥P])6.8-i_:$eShHnkageC. .k"I10iLine¥ O. 2;.this:;s*,.ancy)y){ress-U)' for 215tcyc!e .!¥/ j'/ / ll'' !/' I'*1 /:/ No'l.77'1$t cycle)4.6L rN_o 1::i2. 1.:iy.:ie)2hearShrinkage ot stress ffata;1cydia9ram in loadlng partrRotati:: of diagonal liRe c ; due to shear history tlO:ii_i.ned siFTxple shaer ,Isotropjc cansolldation)8lumep 598 kPa- .O)i;b-tor¥.' i4:rcent ;O,2 O 6H),2 O o0.4Dilatancy ratio, d8vold/d Y PFig. 22. Effeets of shear histon.' on stress-dilatanc_v relationship of08stress- ;SSlf,:j:,,:";:fiii+;:=+,:,!;:,,lNa '175 cycle no1. .･- _80::[-iivl is !o,6o. 188 !1o.4o. 177 ;10'20' C' [sh nks9e in 7i;:ne c"e I.part, }o,2e oo¥PH32¥,1 l:-*;:/, s;Lb ';YQr shrlnkagenodln9 part fC l)nship;,ity and iH:)'! IinEc ;forl' c cl l'.8f¥¥; ;::::J:s::. 75 O 25-o 50latanc)ckl¥*i .e ;stress' i}"e, rt iS;Fig. 24. C1_'clic stress-diiatancy relationships of medium dense sand(effects of density and shear history)changes of stress-dilatancy rclationships also reducedvolume contraction with the increasing number of cycles.Another example of the change of the stress-dilatancyrelationship due to both the change of density and shearhistory is demonstrated in Fig. 24 for a denser specimen.Relative density of the specimen changed from 56010 tocombined effects of density and shear history, diagonalline c-c rotated counterclock¥vise and shrinkage of the), 25 O.OO-de* ti/d Y PFig. 23. Stress-dilatanc_v relationships for loose0.50 o.75as ¥vell.In order to investigate the _ :eneral shape of stressdilatancy relationship under irregular loading, some testswere performed under simple and complicated irregularstrain amplitudes. To study the shape of the stress-Figure 25(a) shows the stress-strain curves for aspecimen subjected to irregular shear strain. In this test,strain amplitude in the first two initial cycles was t¥vopercent while in the following cycles it was reduced to firstone and then 0.5 percent. The stress-dilatancy relation ofthis specimen is sho¥vn in Fig. 25(b). The shape of thestress-dilatancy curves of this test follows the generaltrends of cyclic stress-dilatancy curves, explained earlier.sand under cyclicloading (effects of density and shear histon_')The diagonal line c-c can easily explain the shape of thestress-dilatancy curves for irregular shear strain. It can beseen in Fig. 25(b) that after loadin*' reversal, the stress-rl shear;ilatanc"dilatancy changes discontinuously and starts from ao l*n l{.stress-dilatancy relationships occurred in the loading partdilatancy relationship under irregular loading, results oftests with both irre*"ular shear stress and strain amplitudeare shown and discussed in this section.5; LYe).4rects of jo 75SHAPE OF THE STRESS-DILATANCY CIJRVESFOR IRRF,GULAR 1.0ADINGshear ;cirnen !ilip cf io.50medium dense sandvere !ling to ;Tect of ;),25 O.OO O.25800/0 under a large number of cycles. Due to thenitial :.lvere :) 50/::( :/1ij::i; :! !7S '/" f"/ r / " ' [i Othisune cH: for 160!s eycleShrinka9e in lo; din9 part-+'clesfor f: cvele* _ '" r.f:._04d inLine cne c eLine e*e for Ist cyc[e05;.then lc,ading part-dE* d/d Y P08ory,･'.' Rotation ofH).75) nal;iLoii onshiP;'/H:). 4ess-ides¥p /1: -o 78 o ao o 82 o.e4Effects of shear history on volume change of sandFig. 21'I es;iLf!'¥;o*'to;)2Void Ratiooryofn laading parte o. oat ,essShrinksge02'ts?'- o'ol toCycle no: ;'oheI10=: 2* *>d***,,ercan be seen that the stress-dilatancy relationship changedith cycles due to the combination of density and shearof 240, jhistory. Counterclockwise rotation of line c-c and alsov of tlycles. l{jshrinkage of the stress-dilatancy diagram in loading partsoccurred ¥vith the increasing number of cyc.les. Thesediagonal line. Therefore, the stress-dilatancy. curve afterreversal from smaller amplitudes is located inside of acurve after reversal from a larger amplitude. The slope ofdiagonal line c-c changes continuously with the chan*"e ofdensity and shear history. After each loadin_ : reversal the"{; SHAHNAZARI AND TO¥¥,HATA11S+:80r;7N0'156rr ;GOe,Q3gP 2040J.:2 cye es 7 s2,0 ,2 eycles T s 1 O3 eye]es? s:: 0.5 ,O- 40bNo. 1 55ieess = 0.738 , Ore#ti =e2e/.P 20!!J)u;o Ocou,L Oo!'coI'u)cL ' _20oco-20e)sJ:c,,*,,,'c,)c,"c: _40c2 -40Lo7e ::0.764 . Dr . ::56".'o0 7e3 . Dr sS5e D･738 .DrCUDrained eyelic simple shearIsotropic eons., P' =98 kPa50OTalned cyciic s mple shearsotrepis eQns. P' *98 kPsroL.Ho -6060- 80-2 1Oi-2 -11 21}Torsion shear strain, Y (u! Q)Torsion shear strain, Y (a70');Fig. 25(a).Stress-strain curves of sand under irregular el.'clic loadingFrg '6(a). Stress-strain curves of dense sand subjected to irregu]arc .'clic loading;{OO.B0604e¥rrh ; JNo.1 5G R A¥ -C.-.7e3 ,*O1*$=S3Dt= 55 3. 7i'I" ''ee O.73S2eyeleT2 eyele I s : .OO Go. 2eO. o02dOOPll). 2H). 4u;'eD)e) 8.,. '+JC,,ine c<; for the first eyc e' une o for le last c e eo),75) 50O. OO0.25 o 75O.50Dilataney ratio, -dE+*d/d Y Pl" - ':;;P'/ : " t!=j' i - ihNo'l55!/Ir't; ftt'_;'1._::;. .,t r " :1r'L F;j/;'}(;.;";(Tj:'c=F;'/: is 't ';i;' ' ;1; 's' rP';!;f f'1 rt/ir ;d7:s r" s'; 'TY'!""IJ ?'r'i,_ {'1/Jo '!'H)2f;)4'f::)fr/J!/ s' #'f// : F: ' ''1/u' u's" ' /F'l'/ f :'1 ';:'j ,･･ ;: i)8).25i: ///ir ';//' c:(::( ; ;1::!6. . ' /.c Ratat:on of line o s-r! Ifs ' ' Emj- te '11 'F' 'sr' $s- /Y*r''N '?;¥csU;/O. 4ss,une s ; fof Ist syctB08a,O% 5 .' +,SSS ;;:ji::{{:}L:;L:;::i l!l1'61ea' I¥.J3 cycle T s:t 0.5Pii.10Orained cyelcons.,c simpleshearno ;"" ! '!15atFepiep' sS8oyclekPa ';,r';'v5C"/-1 O-O 75une c'e at t e ead et test0 HD.2SO OOO 25 0.75O 50Dilataney ratio, -de*Id/d yPFig. 25(b). Stress-dilatancy relations of medium deuse sand underirregular c _'clic loadingFig. '-6(b). Stress*dilatanc .' relationshipsof medium dense sandsubjected to irreguiar c .'clic loading*,stress-dilatancy curves of different cycles become closerto each other.Figure 26(a) sho¥vs the stress-strain curves for amedium specimen sand under irregular cyclic shearstrain. The stress-dilatancy rclationship for this test issho¥vn in Fig. 26(b). The general shape of stress-dilatancyrelationship for this test can be explained by usingdia onal line c-c. After loading reversal, stress-dilat,ancycurves start from this line and when shearing continues,all the curves become closer to each other.reversais .(2) The stress-dilatancy relationship during the firstloading is different from stress-dilatancy relationships ofthe subsequent cycles. The starting point of the stressdilatancy curve at the be_g:inning of the first loading isaffected by the initial anisotropic stress state and relative(3) For each direction of loading, the dilatancy ratlo( - de .1 /d yP) changes continuously . Upon loadingreversal, it changes suddenly and after¥vards stressdilatancy curves start from a diagonal line that passesCONCLUSIONSThe follo¥ving major conclusions ¥vere dra¥vn from thetest results of hollolv torsional specimen under drainedsimple shear mode:(1) For each complete cycle of shearing after initialthrou_9:h the center of coordinates. When loading reversaloccurs at a higher level of stress-ratios, the absolute valueof dilatancy ratio ( : = de,d.1ldyP I ) becomes larger.(4) When shearing continues after loadin*' reversal,stress-dilatancy curves become closer to each other.loadin_g:, the stress-dilatancy curve consists of tlvo almost(5) Confining pressure does not affect the stress-parallel nonlinear segments of positive slopes and t¥vodilatancy relationship remarkably.nearly vertical segments immediately after loadin_l,(6) Effects of initial anisotropic consolidation are,{;lL･_ CYCLIC STRESS−DILAτ、ANCY量mPortantmainlyintheinitialstageQfl・ading・Theseelfects diminlsh in the subsequent cycles。Radial stressa薙dco旦seqaentlytheratioofradialstresstoverticaIstress （ratio of stress anisotropy，κ需σ！／σ≦） chaageduring initial stages of shearing、After this chaage，the1atioofstressan量sotτopybecomesconstant，independentofitsinitialvalue．（7）Tぬestress−d1la伽cyrelati・nshipisa任ectedbys・il｛denslty， The stress一（i呈latancy d呈agram of Iooser san（istarts from a greater value of negative dilatancy ratio atthe begi艮ning of the first Ioa（iing．For the fo至low量ngcycles，魚creasing the density｝ea（ls to a cou凱erclockwise τotationof宅hediagona11宝nec−candshr1nkageofstress−dilata蓑cyrelationshlpintkeloadingpart．Aconsequence「lrregula曙 150−158．7）Prad熱an，丁．B，S．and Tatsuoka，E and Rorll，N．（1988a）l Simple sheaτtestingonsandlnaヒorsionalsぬearapParatus，Soi’∫αηゴ Fα〃1面’ioη5，28（2），95一玉12、8）Pradhan，T。B．S．andTatsuoka，F．andHorli，N．（玉988b）lStreng由 and deformation c裕aracterlstics of sand ln torsional slmple曲ear， 50’Z5α114Fα’nゴα∼10175，28（3），BH48、9）Pradhan，T。B．S．，Tatsuoka，F，andSato，Y．（玉989）：薦xperlmentaI stress−dilatancyrelatlonsofsandsubjectedtocyclicload玉ng，SoiZ5 αnゴFoμηゴα∼’oπ5，29（1），45−64．10）Roscoe，K．H．，Sc益o負eld，A，N、and Thura玉raja賑，A，（茎963）： Yieldlngofclaysinstatesweuer由ancrltica1，G60’θ‘17nゆ’θ，13（3）， 211−240，11）Rowe，P．W，（1962）：τ簸e stress−dllatancy relatlon for static equlllb由m ofan assembly ofpart三cles in co瓶act，Proc．Roy。50ら 、乙onゴoηンSθノブθ5141η，269，500−527．of tbese changes is smalier vo夏ume contractionぐor denser12）Sha熱nazari，H。andTowhata，L（1999）：E輝ectofanisotropic consol量dationondrainedcyclicsimpleshearofsand，X1廊’σηsand． Rθ9’oηα1CoηゾoゾSo’1A4θごhαη’c5αnげFα〃14‘71’011Eη9・，κoヂθα・（8）Shear history a錨ects the stress−dilatancyrelationsbip．1tse伍ectsaresimilartothee伍ectsofincreas呈ng the （iensity on stress−dHatancy diagrams，αangesofstress−dilatancyrelationshipduetoshearざ飛119historyleadtosmallervolumecontractlon． Proc，155一玉56．13）Sh麟nazarl， 鷺． and Towhata， L （2000）： Harde頭ng and dens玉丘cat玉on of sand due to drained cyc1玉c玉oading，Gθo∼εch．｝セ‘77 2000Conブ．，Bα119たoκ，rhσ’1α1τゴ，1，9−16・14）S熱a無nazari，H．a獄d Towhata，L（2001）：Predictlon of volumetrlc stralnforsand自ndercycllcloadlngズα！だh∫1∼’．Co11∫oηRθcεn∼ ！4ゴvαn‘ε5∫n G8α．Eσr’h．E119．，SαηD’θgo，US！4，Pヂoc，CP−Ro1η， 1．REFERENCES箋“lse sandサhe負rSl、撮ps of streSS’、tdingisrelativeこyrati。i1・adin鷺streSS・萎毛passe纏revers旦壕lteva1曜reversaLher． stresシ110n a罐藝髪婁 of gramlar solls w曲no membrane−penetratlon e拝ects，Co11・圭）lsむihara，K。（19％）：So’1βεhαvio1ゴnEαπ1冨σε磁θGθo’εoh17’c5， Gθo∼θch。／．，35，730−739． Oxford Sc玉ence Publication．2）NemaトNaser，S、（1980）：On behav玉or of granロ1ar mater玉als 玉ni6）Tatsuoka，F．（1978）：Ont歓e出eoreticalstudiesondefomatlon simPle sむear，So1なα’1ゴFoμnゴα∼’01∼s，20（3），59−73・ 0、7515）Sivatぬayalan，S．andVa呈d，Y・P・（1998〉：Tru玉yundra魚edresponse be卜avlorofgranularmaterlaII，τ5εκ11iぜo乱50，／5SM圧，26（6）， 82−89．3）Nemat一醤aser，S．andτakallashl，K，（1984）：Liquefacτlon and fabrlc17）Tatsuoka，F．，lwas＆kl，T．，Fukus扁撮a，S．andSudo，S・（1979）l ofsand，P∼oc．。4SC君，110（9），129レBO6．4）Oda，M，（1975）：Onstress−dllatancyrelatlonofsandlnsilnpleshear S底ressconditlonsandstressわistorlesa押ectlngs甦earmodulusand damplngofsandundercycllcloading，So’Z5α17ゴFαぜnゴ副0115，19 test，50’Z∫αηゴノroμηゴα‘io175，15（2〉，17−29・ （2），29−43。5）Pradhan，τ，B．S、an（i Tatsuoka，F、（1989）＝On stress−d玉互atancy18）Tatsuoka，F，，Sonoda，S。，Hara，K，Fukushi斑a，S、and Pradぬan， equatbns of sand subjected to cycllc loading，50’15θ11ゴ T．B．S（1986b）：Fallureanddeforma霞onofsandintorsiona至sれear， 1；oど〃1（ノ‘π10η5，29（1），65−8L So1Z5α11ゴFo∼〃7ごαが0115，26（4），79−97。6）Pradi｝an，T、B・S・，Tatsuoka，F。and Molenkamp，F。（1986）：19）Towhata，王，andls臨ara，K（1985）：Modellngsollbehavlo田nder Accuracyofautomatedvolumechangemeasurementbymeansofa prlnclpalstressaxesrotation，P1’oσ、5！h加。Co17∫0ηノ〉εイ1ηθ伽1 a玉fferential pressure transducers，So〃5απごFoε’n6α”0175，26 （4）， ルfαhoゴ5’1zGθo’ηθc12傭c5，ノ〉αgの7α，1，523−530．
- ログイン
- タイトル
- Effects of Air Bubbles on B-Value and P-Wave Velocity of a Partly Saturated Sand
- 著者
- shuji Tamura・Kohji Tokimatsu・Akio Abe・Masayoshi Sato
- 出版
- soils and Foundations
- ページ
- 121〜129
- 発行
- 2002/02/15
- 文書ID
- 20443
- 内容
- ログイン
- タイトル
- A Displacement Prediction Method for Retaining Walls under Seismic Loading
- 著者
- Mitsu Okamura・Osamu Matsuo
- 出版
- soils and Foundations
- ページ
- 131〜138
- 発行
- 2002/02/15
- 文書ID
- 20444
- 内容
- ログイン
- タイトル
- On the Yielding and Plastic Compression of Sand
- 著者
- G. R. Mcdowell
- 出版
- soils and Foundations
- ページ
- 139〜145
- 発行
- 2002/02/15
- 文書ID
- 20445
- 内容
- SOILS AND FOUNDATIONSiVol, 42, No, l, 139-145, Feb. 7_002Japanese C.eotechnicai Society'otech.gra¥*ityON THE YIELDING AND PLASTIC COMPRESSION OF SAND-469.. earingngrg.,G. R. McDo¥VELL,i)itesholdJ.of, -759.ABSTRACT{(2000):=ct andThis paper presents an analysis of the yielding and plastic hardening of uniformly-graded samples of a silica sandsubjected to one-dimensional normal compression. Single *'rains of silica sand have been compressed diametrically between fiat platens to measure indirectly tensile strength. Approximately 30 grains were tested for each of the follo¥vingnominal particle sizes: 0.5 mm, I mm and 2 mm diameter. It was found that the data could be described by the Weibullstatistics of brittle ceramics, and the Weibull modulus could be taken to be about 3 . I . Uniform aggregates of the samesand lvere then compacted to maximum density and subjected to one-dimensional compression. The initiai particle sizedistributions were 0.3-0.6 mm, 0.6-1 .18 mm and I .18-2 mm, and aggregates were subjected to stresses of up to 100MPa. All particies were initially of sirnilar shape, and hence the initial voids ratios of the aggregates at maximum density were approximately equal. The yield stress was defined to be the point of maximum curvature on a plot of voidsratio against the logarithm of effective stress, and found to increase ¥vith decreasing particle size, and to beapproximately proportional to the tensile strength of the constituent grains. However, the plastic compressibility index¥vas found to be approximately constant and independent of the initial grading, and a fractal distribution of particlesizes appeared to evolve under increasing stress. There is evidence to su*'gest that the aggregates evolve towards afractai dimension of 2.5 under high stresses.hquakei(1999):ainingof Civi!selsmrc='tion ofnlp., 2icity ofEngrg..w stripgineers,ldrainedry, J. ofKey w'ords: micro mechanics, particle crushing, sands, statistical analysis, strength (IGC:65 276.thod forD5/D6)*h. andwhere m is the Weibull modulus and (T**,d is the value ofINTRODUCTIONcharacteristic stress for a particle of size d such that 37010;,=iIt has long been recognised that the constitutiveof tested particles survive, or "370/0 tensile strength".behaviour of an aggregate of soil grains is strongly de-McDowell and Amon (2000) showed that a*. d ispendent on the crushing strength of the individualproportional to and approximately equal to the averageparticles (Billam, 1972; Bolton, 1986; Lee, 1992; Nakatatensile strength (7*.,d, and is a function of the particle sizeet al. , 1 999). Followin*" Jaeger (1 967), the tensile stren*'thd according to the equationof a singl soil grain is usually measured indirectly bycompressing the grain between fiat platens until failure(7,. d oc d - 3/* (3)occurs. McDowell and Amon (2000) reviewed much ofFor nl=3, for example, cT*.,d=0.89 cF* , . McDo¥vell andAmon (2000) showed that data for calcareous Quiou sandthe work on quasi-static compression of brittle spheresand showed that if the particle-platen contact area couldi.particles could be adequately described by Weibullbe assumed to be negligible, and that if all loadingstatistics. Nakata et al. (2001) measured Weibull moduligeometries were similar, then Weibull statistics (Weibull,for silica sand grains of different sizes, and also plottedfailure characteristic stress as a function of size on a log-i951) could be applied to characterise soil particle*,strength. For grains of siz,e d loaded diametrically under aforce F, they defined a characteristic induced tensile stressa* as:F(7c = d 2 (1)Eq. (3). However it may be possible to improve theconsistency of those data if the average strength for eachparticle size ¥vere to be plotted as a function of size. Thus,and sholved that the survival probability of a particle ofas yet it is not known of any data which has demonstratedsize d is _ iven bysuccessfully the applicability of Weibull statistics to silica[ ( )Jm crc (2)Ps(d)=exp(7co'd*)l10g plot for all particles tested. The values of Weibullmodulus varied greatly across the range of sizes, and wereinconsistent with the size effect on strength according tosand.McDowell and Bolton (1998) examined the micromechanics of soils subjected to one dimensionalLecturer, School of Civil Engineering, University of Nottin_ ham, Nottin_! ham NG7 2RDManuscript was received for review on February 13, 2001Written discussions on this paper shou d be submitzed before September I , 200'- to the Jap nese CJeotechnical Society, Sugayama Bldg. 4F,Kanda Awaji-cho 2-23, Chiyoda-ku, Tokyo 101-0063, Japan. Upon request the closin_g date may be extended one month.139 ;;lvICDO¥¥rELL140which 500/0 by mass of particles are finer than), for arange of sands. They calculated tensile strength as thecharacteristic stress at first peak in load, and proposedthat the tensile strength should be proportional to ael 6142o*{dense oarbonate sanddid not, however, examine the compression of uniformly*'raded aggregates of a given sand, with particle si2:evarying between the aggregates. Nakata et al. (2001) examined the one-dimensional compression of a range ofuniformly-*'raded sands, and related the macroscopicloose silica sand08cdense silica sand06¥o(1){crushability index K, defined as the logarithm of the yieldstress for a sample at z,ero initial relative density. They1,¥¥¥I;!behaviour to the strengths of the constituent soil i0. 4:particles. They found that for silica sand, the yield stress07_Ol O crJ (MPa)IOFig. l. One-di,nensiona compression plots for carbol]ate and silicasands (Golightly, 1990)decreased with increasing particle size. However, the sizeeffect on yield stress was small, and was not consistent !with the size effect on tensile stren*"th determined for theindividual * rains (though they did not isolate the effect ofrelative density). Thus Nakata et al. (2001) were unable totensile strength.{McDo¥vell and Bolton (1998) noted that the onecompression, and proposed mechanisms for yielding anddimensional plastic compression of soil leads to theplastic hardening. Figure I (CJolightly, 1990) sho¥vs plotsof voids ratio against the logarithm of effective stress forevolution of a fractal distribution of particle sizes, suchthat the percentage by mass M(1,<d) of particles finersands subjected to one-dimensional compression.than size d is _9:iven by the equation:Consider the dense silica sand in Fig. I . At low stresses(region 1) the behaviour is quasi-elastic. Beyond yield(re*'ion 2), an approximately linear normal compressionline emerges. Coop and Lee (1993) showed that normalcompression results from particle crushing, andattributed yield to the onset of particle crushing. Hardin(1985) related the amount of particle breakage in triaxialtests to the applied stress levels but did not relate yieldstress to the tensile strengths of the soil grains. Hardin(1987) studied one-dimensional compression ofcohesionless soils and proposed that instead of plottingvoids ratio e against lo*'arithm of effective stress (7' , a plotof I /e against ((T')should be used (where p is the powermdex) Hardm (1987) defined a "breakpoint" stress atM ( I , <, d ) cc d 3,**,D (4)¥vhere D is the fractal dimension. Remarkably, for manygranular materials subjected to pure crushing, a fractaldimension of about 2.5 emerges (MCDO¥vell and Daniell,,i*{{2001). McDo¥vell and Daniell (2001) showed thatiinumerical simulations of fracturing fault gouge by Steacyand Sammis (1991) c.ould explain the observed dimensionof 2.5 in soils. McDowell and Bolton (1998) showed thatthe evolution of fractals could explain the existence oflinear normal compression lines when voids ratio e isplotted against the logarithm of macroscopic stress (T.They proposed that for initially uniform aggregates,although the yield stress should depend on the initialattributed to the onset of crushing. He related thisparticle size, the plastic compressibility index (defined asthe slope of the e-log (T plot) might be a fundamental con-breakpoint stress to initial particle size distribution andstant. McDo¥vell and Daniell (2001) found that forparticie shape, but not to the tensile strengths of theparticles. McDowell and Bolton (1998) also attributedyield to the onset of grain fracture, and coined the termoedometer tests on calcareous Quiou sand, samples with¥vhich the slope of the plot becomes non-linear, ¥vhich he*explicitly show that yield stress is proportional to particle*,,,=:}:.different initial particle siz:e distributions all appeared to"clastic yielding" to describe this process. Because yieldevolve towards a fractal with dimension 2.5, and thecompressibility index was independent of the initialIoccurs gradually, a suitable definition of yield is required.particle size distribution. Ho¥vever, in their tests, the;In this paper yield will be taken to correspond to the pointan*'ularity of the particles varied between differentof maximum curvature on the plot of voids ratio againstparticle sizes, so that it was impossible to relate yieldloganthm of stress. McDo¥vell and Bolton (1998)stress to the average tensile strength of the constituentgrains. Nakata et al. (2001) demonstrated that for uniformly-graded silica sand subjected to one-dimensionalproposed that the yield stress for a uniformly gradeda*'*'regate should be proportional to the average tensilestrength of the constituent grains but as yet it is notkno vn of any available data to support this proposition.Kwag et al. (1999) did not use Weibull statistics,related the yield stress (Casagrande definition)aggregates subjected to isotropic compression tosample relative density and the tensile strength ofbutforthetheconstituent particles corresponding to size d50 (i.e. the siz,ecompression, the plastic c.ompression index isindependent of the initial particle size, but they did not; "*attempt to demonstrate that this was linked to the"',evolution of a fractal distribution of particle sizes.This paper aims to make several contributions. Firstly,the paper aims to demonstrate the applicability ofi.!iWeibull to silica sand *･rains. New data is presented fori ;' 141YIELDING* AND PLASTIC C_O* ,iPRESSION OF SANE)S,r aItheIsedoaieldheygrains of Leighton Buz,zard silica sand, crushed betweencompressed bet¥veen flat platens to determine theflat pia:tens. The distribution of strengths is presented fordistribution of strengths for grains of a _given size, and 37grains of diameter 0.5 mm, I mm and 2 mm, and theapplicability of Weibull is examined. The second ando/o tensile strength as a function of size, in order todetermine whether Weibull statistics can reasonably bemost significant contribution of the paper is to provideapplied. Fi_ :ure 2 shows a simple particle crushing device,support for the proposition by MCDOwell and Boltonwhich is described by McDowell and Amon (2000). Theload measuring capacity of the device is 320N with a(1998) that the clastic yield stress for uniform aggregatesmlysubjected to one-dimensional compression should beptoportional to the average tensile strength of theconstituent grains. IJniform aggregates of the sameLei_9:hton Buz,zard sand were compacted to maximumsizeiI ex-e ofopici*density and subjected to one-dimensional normalsoilItresssizecompression (one-dimensional compression tests ¥verei!conducted as opposed to isotropic tests for convenience).The initial particle size distributions were 0.3-0.6 mm,stentr theiO.6-1.18mm and 1.18-2mm, and aggregates ¥ 'er'e'ct ofsubjected to stresses of up to 100 MPa. A11 particles)le toinitially of similar shape, so that after compaction torticle;i''ere(4 )diameter 5 mm. For the 2 mm grains the 20 mm diarnetertop platen ¥'as used. For the 0.5 mm and I mm *'rains,the 5 mm diameter top platen was used to ensure that thetop and bottom platens could not come into contact witheach other without crushing the particle. Thirty particleswere tested for each nominal particle size.For a single particle of size d under a diametral force F,the characteristic stress (7* induced ¥vithin the particle isdefined according to (1) and the survival probability isapproximately equal for each a_ :gregate. Thus thegiven by Eq. (2) if Weibull is applicable. Small asperitiesmay fracture before final failure of the particle, and careis needed in adoptin*' a suitable definition of failure. Inyield stress is constant in these experiments. The effect offineravailable: a 20 mm diameter platen and a platen ofmaximum density the initial voids ratios ¥vereinfluence of initial voids ratio and relative density onone) thesuchresolution of 0.001N. Three nominal particle sizes weretested: 0.5 mm, I .O mm and 2 mm. Two top platens wererelative density on yield stress has been studied by Kwa_ :et al, (1999) and the effect of initial voids ratio has beenstudied by Nakata et al. (2001), and so these effects arethis paper the approach proposed by McDowell andAmon (2000) is adopted whereby failure is taken tonot studied here. The yield stress is determined as aof the particle is still greater than 500/0 of the initial size.function of average initial particle size, and the results arecorrespond to the largest force such that the current sizemiell,that for this Lei**hton Buzzard silica sand, thethatcompressibility index is independent of the initial particleIn all cases this was found to correspond to catastrophicsplitting of the particle, for this Leighton Buzz,ard sand.Characteristic stress at failure is defined in this paper asthe diametral force at failure divided by the square. of thenominal particle diameter. It is also possible to calculatesize distribution, and is linked to the evolution of athe characteristic stress based on the diameter of thefractal geometry. The ra¥v data for the single particle testsrelated to the avera*'e tensile strength of the constituentmanyparticles. Finally, this paper also aims to demonstrateractalSteacyension*,'*tests in Oweis (2000).particle at failure. However, the aim here is to correlatethe yield stress for approximately uniform aggregates inoedometer tests ¥vith the average tensile strength of theo e isconstituent grains, and for this purpose the use of aess (T.SINGLF, PARTIC_LE CRUSHING TF,STSnominal diameter is sufficient.Follo¥ving Eq. (2), by plotting In (In (1/P*)) against;.d that=nce ofe"*ates,initialcan be found in Voo (2000) and for the one-dimensionalSingle grains of Lei_ *hton Buzzard sand have beeniIn (7*, the Weibull modulus can be determined from theined asal con"lat fores ¥vithared tond theinitialSS*'" :(i*;.* *.:i: ;r;; :,'i'*r;:' ;" ** ' *""';*.= s* * * -*: "**{,i* :' "=;" ..:.**""'* "---*f'*"*;;. ; ;s.. ;'':i;'"' " s'. ";* '- - i* fS ' ?';; +.r'*":;* ; i20rnm diametertop platents, the!if erenttest specimene yieldstituent;'or uni*Insionaldex Isdid notbottom platento thealternative 5mmdiameterFirstly,top platenility ofir ted forFig. 2.Particle crushing device b:sIMCZ)OWELL1 42ilOOO -0.5mm grains2J(y = 3 44t3x + 17 lS2 ._ IlR2 = O 9449- o-l_- i! :5_-l2;[ y = 74 288x o 910s:[¥ =D2O9786I10..-J*3_4 J{olOlIn (T'!n d( a){Fig. 4. 370/0 tensile strength 8s a function of sizemm grainsITable l. WeibuH modulus, 370/0 tensile strenogth and fverage force atf ailurel2ll y-' 3395x - 9'8273 IFle-o::Q,0.5 3 .44l-2ll f 2 34,e3 ll, ' failure/N1Nominal j i 370/0Weibulltensile stren"thcr* d /MPasize/mm j modulus m ,R2 =: o'95962 3 14,}Avera_ge force at'{1 47 .4 33 . 1 266,75 9 Ol41 .7149.05iiIn cr.The results for average force at failure for each of the(b)three nominal particle sizes are given in Tabie I , and thisindeed found to be the case.2mm grains21y= 3 136x -_ ll-oONE-DIMENSIONAL COMPRESSION TESTSi 698 -R- = O 9776i:lDll3,2314),j,-4In cr*(c)Fig. 3. ¥ 'eibuH plots for each set of grainsTests were performed in an Instron testing machineusing an oedometer made from EN24 steel with internal,{diameter 80 . 5 mm and a sample thickness ofapproximately 15mm. Figure 5 shows compression}Icurves obtained for oedometric compression of denselycompacted dry silica Leighton Buzzard sand of variousinitial gradings. The initial uniform gradings ¥vere0.30.6rnm, 0.6-1.18mm and 1.18-2mm, and eachsample was compacted to maximum density in theoedometer by vibration. All particles were of similar Ian*"ularity and hence the initial voids ratio wasapproximately the same for each sample compacted toslope of the line of best fit, and the value of (7*.,d determined as the value of cr* when In(In (1 /P*)) = O. Figure 3shows the distribution of strengths for each of thenominal particle sizes. The results are summarised inTable I . The average Weibull modulus is found to be2.97. The 370/0 tensile strengths are plotted againstnominal particle size on a log-10g scale in Fig. 4.maximum density. The experimen.tai procedure for thesetests is described by Oweis (2000). It is clear from Fig. )that the stress level of the yielding region depends on theinitial grain size distribution and increases with reducingparticle size. Here the yield stress has been taken to be theFollowing equation (3), the slope of the plot is -3/m,point of maximum curvature on the e-log (T plot, and determined by fitting a 6th order polynomial to the yieldingregion with a correlation coefficient of I .O. The yieldwhich corresponds to a Weibull modulus of 3.29. Thestress for each particle size distribution is given in Tableresults are therefore in *'ood agreement and it seems that2, and is plotted as a function of the average initialWeibull can be applied. Taking the average of the twoWeibull moduli calculated from Figs. 3 and 4 it seemsparticle size in Fig. 6 (here the average particle siz,e is sim-that an m value of 3 , I could be assumed for this material.particle size distribution). In order to determine ¥vhetherIn this case, followin*' McDowell and Amon (2000), thethe results are commensurate with the results from theavera*'e force at failure should be approximatelysingle particle crushin*' tests, it is useful to first exarnineproportional to d2-3/* so that for ln = 3. 1, average forceat failure should be approximately proportional to size.":.{:;;.ply taken to be the average of the two extreme siz,es in theFig. 7(a), ¥vhich sho¥vs the result of a test on an array ofIi .. ';*!i,'.photoelastic str'ess discs (de Josselin de Jon*' and !tLti-. ;.YI LDING AND PLASTIC COMPRESSION OF SANDSI.iary force FH, such that FH/Fv=0.39, which is6-i'O 3TT1;n < d <; O.6mrncomparable to typical Ko Values measured in one-O 6 uT1 <d<: I ISmmdimensional compression tests on sand in the triaxialiJapparatus. In Fig. 7(b) (Cundall and Strack, 1979) FH /FV=0.43. Both figures show that the stress distributionswithin particle assemblies are extremely heterogeneous.The width of the rectangles plotted through the particlecontacts in each array is proportional to the magnitude ofthe contact force. For each of the arrays in Fig. 7, whichare approximately 12 particles wide, it can be seen thatLil lgmul<d< 'mm**OIeO1o}lO1lcoOoOStress CT / . iPaFig. )-Compression plots for different uniform gradings of sand40 -it30 -might anticipate that the yield stress might be about fourtimes less than the 370/0 (or average) tensile strength ofthe constituent grains in the aggregate. For the aggregatesl o True yield strengtho25x Yield strength predictedX20 -e5 >*lfrom single particle testsxlOthe 370/0 tensile strength of 0.5 mm diameter particles is15}Average particle size / mmiFig.5. Yield stress predicted from siugle particle crush ingtests,assuming yield stress = (370/0 tensile strength)/4{tensile strength has been estimated for the averageaggregate assuming a Weibull modulus of 3.1, and thatOhis0.3-0.6mm, 0.6-1.18mm and 1.18-2mm, the 37010paFticle size (average of the two extreme sizes) in each#iheapproximately three columns of strong force form totransmit the major principal stress. If it is then supposedthat at yield, the characteristic stress induced in theparticles forming the columns of strong force might beabout four times the applied macroscopic stress, one45 -at143147.4 MPa, as given in Table l. Thus, for the particlesranging in size I .18-2 mm, for example, an average siz,eof 1.59 mm is assumed so that the 370/0 tensile strengthfor particles in this aggregate is estimated to be 147.4 ><(1.59/0.5)3/3 1=48 MPa. The values of 370/0 tensile{ofstrength for each average particle size are given in Table2. The values have then been divided by 4 to predict theyield stress of the aggregate. These values are also givenin Table 2 and plotted together ¥vith the measured yieldstresses in Fig. 6. The results are very pleasing and cer-10ntainly support the proposition made by McDowell and{*...* ,'+ Ei,InenalIBolton (i998) that yield stress should be proportionalto the tensile strength of the individual grains. Thediscrepancies between the values can be explained by the.elyous}ereachfact that yield is a gradual process, and at the yield stress,(b)(a)ithethe particle size distribution will already be different from.ilar,vasi toFig. 7. (a) Test on an array of photoelastic discs with FH/Fv=0.39the initial distribution, such that the average particle size(De Josselin de Jong, 1969) and (b) discrete element simulation of(a) (Cundall and Strack, 1979) with FH /Fv= 0.43will have changed. In addition, the average of the two. 5Table 2. Yield stress for each aggregatc, estimatedthescaling factor of four deduced from Fi**. 7 can only be37 o/otensilestrength and estimated yield stresscingtheextreme particle sizes in the ag*'regate is unlikely to equalthe true mean size of the constituent grains. Finally, theeseAg *regate;Yield iFollowing yield, an approximately linear normalAvera e370/0 tensile(370/. tensileinitialstressparticlestrengthstrength)/4dinggrading/MPasize/mm/MPa/MPaield0.3-0 6 mm37o 45l 6341O 6-l270.898421lg1 .594812i de-'*ablel itial. 8 mml. i 8_2 mmsim"a p proximate.*thecompression line emerges in Fig. 5 for each of the threeaggregates tested. At very high stresses the voids ratiosare extremely low, and it would be anticipated that thecurvature of the plot would change as the materialbehaves more rock-like. Indeed, follo¥ving the oedometertests, the sand was found to be extremely interlocked, butcould be easily crumbled to a powder in the fingers. Itappears that the slope of the plot, the plasticthercompressibility index is a constant, independent of initiall theVerruijt, 1969) and Fig. 7(b) (Cundall and Strack, 1979)ininewhich sho¥vs a discrete element simulation of the.v ofexperiment in Fig. 7(a). In Fig. 7(a) the array is subjectedand }to a vertical boundary force Fv and a horizontal bound-grading, and can be taken to be about 0.4. The particlesize distributions which evolve under increasing stress areshown in Fig. 8 for the 1.18-2 mm ag*"regate. It can beseen that the rate of crushing with increasing stress Lii_ ;I144+ (COO¥ 'ELLI.evolution of a fractal _e:eometry, in agreement withMcDowell and Bolton (1998).Initial gradiug: l. 8-2mmOO90 -* 8070= - initialI-h･iO iPa :60*-e-20ivlPa* SO40j- .50MPa i,-75MPa j;h 30,)* )-O' 100(Pa 'lOOI I O I OO I OOOOl OOOParticle size / umFig. 8. Evolvmg particle slze distnbutrons for 1 18 ･ mm aggregateCONCLI JSIONSSingle *'rains of L,eighton Buzzard silica sand have beencompressed diametrically between fiat platens in order tomeasure the tensile strength. Thirty}"rains were tested foreach of the follo¥ving nominal particle sizes: 0.5 mm, 1mm and 2 mm. For each nominal siz,e, the distribution ofi;strengths was found, and the 370/0 tensile strength ¥vas determined as a function of particle size. It ¥vas found thatthe results were consistent with the Weibull statistics ofifracture of brittle ceramics, and the Weibull moduluscould be taken to be about 3.1. Oedometer tests were1 ooperformed on uniform ag"-regates of the same sand up toan applied stress of 100 MPa. Tests were performed ona gre*"ates of the followin' "radings' 0.3O 6 mm!-S.18mm-2mm ;l--e-O 6mm - I ISmmlt;:lOl '-- O 3mm - O 6mm- ' ' " ' FFacta}, D*2.5 [,)}0.6-1.18 mm and 1.18-2 mm. The yield stress ¥¥'as defined as the point of maximum curvature on the plot ofvoids ratio versus the logarithm of stress and was found ito increase with decreasin*" particle size. Results of testson arrays of photoelastic discs and discrete elementsimulations were examined, and it was found that forstress ratios similar to those found in one-dimensionalcompression of sand, the major macroscopic stress islI I OO10OOOOOOOParticle size / umFig. 9. Particle size distributions at 100 MPaplotted on a lo"*-tog scalecarried by stron*' columns of force at an average spacingof four particle diameters. Based on this observation, theresults from the single grain crushing tests ¥vere used to,*;predict the yield stresses of the aggregates on theassumption that yield stress should be approximatelyequal to one quarter of the 370/0 (or average) tensilestrength calculated for the average particle size in thereduces considerably at very high stresses: presumablyaggre*'ate. The predictions ¥vere found to be in reasonablelarge particles are well protected by many neighbours, sothat the tensile stresses induced within them are very low,approximately linear normal compression line emergeswhilst the smallest particles have reached thecomminution limit, so that fracture is no longer possible.This is consistent with the change in curvature of theagreement ¥vith the measured values. Following yield, anfor each a*'gregate and the plastic compressibility indexwas found to be independent of the initial grading. Theparticle size distributions were determined after normalcompression plots in Fig. 5 at very high stresses. Similarparticles size distributions were found to evolve for thedistributions appeared to evolve to vards a fractal ofother uniform aggregates.dimension 2.5, thou*'h in this case the degree of particleThe particle size distribution for' each aggregate at 100MPa is plotted in Fig. 9, with percentage by mass passingand particle size each plotted on a lo_ :arithmic scale. According to Eq. (4) a fractal ¥vould appear as a linear plot.fracture occurring si_ nificantly reduces at high stresses. Itcompression to various stress levels, and the particle sizeIt appears in Fig. 9 that a fractal distribution hasemerged, but as previously stated, the rate of crushingaverage tensile stren*'th of the constituent grains, but thewith increasing stress has significantly reduced at higherstresses. A Iine of slope 0.5, corresponding to a fractalcompressibility index is a constant, and is linked to theformation of a fractal geometry. There is also evidence tosu_ :gest that ag>'regates subjected to one-dimensionaicompression evolve to¥vards a fractal distribution 1 'ithappears that the particle siz,e distributions would evolvetowards a fractal ¥'ith dimension of 2.5, if crushing ¥vereI::t/j-therefore seems reasonable to propose that for uniforma_g:gregates subjected to one-dimensionai normalcompression, the yield stress can be assumed to beapproximately equal to one quarter of the 370/0 ordimension of 2.5, has also been drawn on Fig. 9. It*ii,:"*,,,*dimension 2.5 at high stress levels.allowed to continue at extremely lo v voids ratios. Theslope of the upper part of the particle size distribution forithe 1.18mm-2 mm sample corresponds to a fractalACKNOWLEDC.EMF,NTSdimension of 2.35. It appears that the existence of linearThe author wishes to thank Mr Zeid O¥veis and Mr VunKion*" Voo for performin*' the laboratory testing.normal compression lines is inextricably linked to the*,*,';j; YIELDING AND PLASTIC COMPRESSION OF SANDS145 fragmentation strength，Eηgrg．，〆ior Cα1cαヂεo∼イ5Sθグ’〃1θ1π5（ed．by’ithREFE盆ENCES玉）Blllam・」・（王972）：Some aspects of the behaviour of granular ma篭erials at high pressures，S’ヂθ5∫一Sぴα’ηZ）θhαv’oμ∼oゾrSoiな，Pro（ン． ゴ醜θ加∫10η，CambridgeUniversity． o∫’hθRo5ωθ漉’ηor’α燭7ηψ・（ed・byParry，R澱・G．），69−80、12）McDQwell，G．R、and Bolton，M．D．（1998）：On the micro2）Bolto員・M・D・（1986）：The strength and dilatancy of sands・een A1−Shafel，K、A。），Ealkema，79−87。11）Lee，D．M．（1992）：Yheangles of frictlon ofgranular負ils，Ph。n 磁Ofθ‘ノ∼nゆθ，36（1），65−78， mechanicsofcrushab互eaggregates，G60ガεohnゆe，48（5），667−679，13）McDowell，G．R．and Amon，A．（2000）：The appllcation ofWelbull statistics Io t簸e fracture of soil pa貸icles，So”5αηゴFo㍑ηdαfめη5，40『to3）CooP，M・R・andLee・LK・（玉993）：Thebeねaviourofgranularsollsfoτ at high stresses，P7（∼ゴ’cず’vεSo〃ルノθごhαη’c5， Proc． oゾ『∫hθ 昭ro∼h （5），玉33−14L 1砿乏∼1πor1‘71S』y1ηρ，（ed，by｝｛oulsby，G、T．and Schof｝eld，A．N．），I4） ∼lcDoweU，G，R．aad Daniel董，C．M．（2001）：Fτactal compression of 圭86−198．4）Cunda11，P・A・and Strack，0・Σ）・L（1979）：A dlscrete element15〉Nakata，Y，，Hyde，A．F、L．，｝｛yodo，M．andMurata， ｛．（1999）：A1，110fde． model for granular assemb践e5，G（多o∫ε（ンhn’9μθ，29（1），47−65。11at5）De Iosselin de Jong，G．and Verruljt，A．（1969）：孟tude photQ−lof 61astique d’un empllement de dlsques，Cαh．Gψθ戸，E飯ごe，Rh601，IIUS 2，73−86．6）Goiightly，CR・（1990）：Eng量neerlngPropertlesofcarbonatesands，一『ere⊃toon so11，磁αεchnゆe，51（2），173−176。 probabilistic apPrQach to sand part玉c玉e cr越shing in the tr玉axial test， G60∼θoh’11（1μθ，49（5），567−583．王6）Nakata，Y．，Kato，Y．，｝｛yQdo，M．，壬｛yde，A，F，L。and Murata，M， （2001）＝One−d玉mensionalcompressionbe益avlourofuniformly gradedsandrelatedtoslngleparticlecrusぬlngstrength，50iZ5αnゴ Ph．P．ゴ’55ε加∼’oπ，BradfordUnlverslty、 ハαイ層頗oη5，4三（2），39づ1，7）狂ardin，B・O・（1985）：Crushlngofsoilparticles，河SCE訊oゾ17）Oweis，Z、W．（2000）：The compressibility and crus頁ing of sllica σθorθ‘h、Engrg．，111（玉0），1177−1192。 sand，ハグ，五『η9．‘ノな5θπα’1011，Un玉versity of Nottingわam。8）Hardin，B・0、（1987）：1−D s亡ra玉n ln normally consol量dated co島esionlesssoils，。4SC君∫oゾ（3εαεch．Eπgrg。，113（…2）， i449−1467．9）Jaeger，」．C（1967）：Fallureofrocksundertensilecondltions，加．18）Steacy，S．」．and Sammis，C，G．（1991〉：An automaton for fractaI 」」Rooた．ハ4’11．So’，，4，2玉9−227。20）Weibull，W，（195王）l A statistlcal distrlbution function of wldeests！0）Kwag，」，M．，Ochiai，H．and Yasufuku，N．（1999）：Yield圭ng stress appHcability，∫．沌ρp1．Mθch，，18，293−297．／entfor characterlsticsofcarbonatesandinrelatlo財olndividualparticlelm，de．tofmd）na1、SISomg由e⊂1totheしtely／siletheable 嚢1，anIrges膿rmallsize嚢ほof蒙1ticlelヨs・ltl＝ormlrmall）bel き∩or萎 きtthe萎）thelceto嚢麟 警謬婁Vuロ嚢黙嚢髪 patterns of fragmentat呈on，ハ∴α々’rθ353，（6341），250一一252．19） Voo，V．K，（2000）：Stat呈stics of part玉cle strength in a si1三ca sand，ハ4Pゆ Eng．ゴ趣θr∫副on，University of Nottingham．
- ログイン
- タイトル
- Effects of Initial Fabric and Shearing Direction on Cyclic Deformation Characteristics of Sand
- 著者
- s. K. Chaudhary・Jiro Kuwano・Satoshi Hashimoto・Yutaka Hayano・Yuhei Nakamura
- 出版
- soils and Foundations
- ページ
- 147〜157
- 発行
- 2002/02/15
- 文書ID
- 20446
- 内容
- {!*SOILS AND FOUNDATIONS;iVol 42 No. l, 147-157. Feb, 2002Japanese C.eotechnical Society;!iEFFECTS OF INITIAL, FABRIC AND SHEARlNG DIRECTION ONCYCL,IC DEFORMATION CHARACTERISTICS OF SANDI';::;I;;IiSUSHIL K. CHAUDHARYi), JIRO KU¥¥,ANoii), SATOSHI HAShllvroTOiii),'jYIJTAKA HAYANof*･) and YUHEI NAKAMURAi).ii=1{ABSTRACTI{I.The paper presents a study of the effects of initial fabric and shearing direction on cyclic deformation characteristicssuch as stress-strain response, shear modulus and damping ratio from drained static cyclic tests on medium denseToyoura sand using hollow cylinder apparatus. The apparatus allo¥vs independent control of stress components, (T=,a , * and r, , and accurate measurement of strain components, 8., e, 8* and y.e, over a wide range of strains from10-30/0 ro 100/0. Three methods of sample preparation, air pluviation, water pluviation and dry rodding, wereIiemployed to produce different initial fabrics. Samples were sheared cyclically in p'-constant plane along the directionof major principal stress O' (90'), 22.5' ( - 67.5') and 45' ( - 45') relative to the direction of deposition. Anisotropicbehaviour ¥vas observed in stress-strain response and the secant shear moduli defined separately for each direction ofmajor pFincipal stress. Ho¥vever, the equivalent shear modulus was found to be little affected by the direction of theznajor principal stress. In addition, the effect of initial fabrics ¥vas not significant. The same ¥vas found for thehysteretic damping ratio.i*{Ke .' words:damping ratio, deformation, repeated load, sand, shear modulus, special shear test, torsion (IGC:D6/D7);Ladd, 1974; Mulilis et al., 1975; Silver and Park, 1976;Ladd, 1976; Tatsuoka et al., 1986). On the other hand,lNTRODUCTIONIt is essential to properly estimate strain-dependentshear moduli and damping properties of soils inanalyzing soi]-structure interactions and earthquakeresponses of gr'ounds and soil struc.tures where thedirection of the major principal stress is not alwaysvertical, as in the ordinary condition of level ground(Ishihara, 1983; Kuwano and Ishihara, 1988). Soils areiianisotropic fabric (Kallstenius and Bergau, 1961) and(Oda, 1972). The response was stiffer along the directiontherefore anisotropic response (Shibuya and Hight,of deposition than along its perpendicular. Ho¥vever,past studies have all been confined to either triaxial,where the direction of major principal stress is eitherby air plu "iarion and by moist tampin*" or moist rodding.In addition, many researchers have found that the cyclicundrained stren_ th of reconstituted sands determined bycyclic triaxial tests and torsional shear tests are stronglyaffected by sample pr'eparation methods (for example,t,iiiFormer CJraduate Student, Dept;stress revealed that the properties of sand, such asmobilized stress ratio and secant modulus, are highly de-deposition (Oda, 1972). L,aboratory tests conducted by, ,iiura and Toki (1982) indicated large differences intriaxial behaviour bet¥veen clean sand samples prepared{deposition direction and the direction of major principalinherently anisotropic in response. Even spherical glassballs deposited with free fall under gravity give rise to1987). The nature and degree of fabric anisotropy of sanddepends upon the shape of sand grains and the method of.the same fabric (the same sample preparation method)gives different responses when sheared in differentdirections. A comprehensive series of static triaxialcompression tests on specimens prepared in a tiltingmould with various angles of inclination between thependent on the direction of the major principal stressifivertical or horizontal, or torsional shear tests, where themajor principal stress direction is 45'. The hollowcylinder apparatus used in this study controls torsionalshear stress and deviatoric stress independently andtherefore allows shearin*' of the specimen in any directionin the z- e plane. Specimens were sheared cyclically indifferent directions in the p'-constant plane. Differentinitial fabrics in the specimens were produced by differentof Civil Engr_ ., Tokyo inst, of Technology, 2-1)_-1 0-0kayama, Meguro, Tokyo i52-8552.AssociaLe Professor, ditto.EngineeF, Kuma_"_,ai Gurni C_orporation, Japan^The Japan Research Ins itute. Tokyo, Japan.i,Manuscript ¥vas received for revie¥v on ivlarch 16, 2001.¥Vritten dlscussions on this paper should be submitted before September I , 2002 to the Japanese Geotechnical Society, Sugayama Bld_g:. 4F,iKanda A¥vaji-cho 2-23, Chiyoda-ku, Tokyo 101-0063, Japan. Upon request the closing date ma_v be extended one month.;11471 148CHAUDHARY ET AL{sample preparation techniques. Their effects on stressstrain response, shear modulus and hysteretic dampingare studied in this paper.Firstly, a short description of the apparatus and testingsystem will be presented. Secondly, the test conditionsand program will be described. Finally, the results will bepresented and discussed.Table 1. Calculation of average stresses and strains in hoHow cyiinderspecimenAvera :e strainsAverage stressesW , por pjrh , Ahlz(ry'r ) 2r r ezllj(FZro Po I 'Cir ro + ri(roPier=roiro PoHOLLOW CYLINDER APPARATIJS;rj Pie =(Tro 'A hollow cylinder apparatus with the specimendimensions of height (h) = 100 mm, inner radius (rj) = 30mm and outer radius (r.) = 50 mm ¥'ras used in this study.The testing system was fully automated. Schematic(r_ +rzPe)yze 3h (r;roi)(rirji)ri(rj,rofrirji)- r;･)rjj)4M:T (r - rj)rzeillustration is given in Fig. 1. Details of the systemdevelopment have been reported by Nakamura et al.(ro2e(r1r:roi)3lr (rrt)(r; - ri2)3MTrzPe 21T(r30rsl)(1998). All the measurements and control were made byPC throu*'h 16-bit A/D and D/A converters. The stress;,;.components, vertical stress (T., circumferential stress (Te,e plane r.e, ¥verep., independently (see Fig. 2 also). The axiai load wasapplied to the specimen by controlling axiai load W,controlled by air pressure through a double actingtorque MT inner cell pressure pj, and outer cell pressureBellofram cylinder. But the torque was controlled by oilpressure through a hydraulic pressure control unit. Theradial stress (T*, and shear stress in the zlinner and outer cell pressures were controlled by airpressure. The axial load and torque were measured byinternal load cells over the top cap of the specimen andthe pand p. ¥vere measured by pressuremeters at thebase. The average stresses and corresponding strains ¥verecalculated as shown in Table I . The a¥'erage stress (7, isbased on the equilibrium of forces at the mid-height ofthe specimen. The stresses (Te and (7* are based on the;"";Iassumptions of linear elastic stress distribution across the;-wall of the specimen (Hight et al., 1983). The shear stress,r,e, has been taken as the average of the values given byithe assumptions of linear elastic and perfectly plasticstates of the specimen. It has been sho¥vn by I¥vasaki et al,(1978) that the difference bet¥veen the values of r,e givenby the above t¥¥'o assumptions is very small.The vertical strain, 8., and shear strain in the z-eplane, y,e, are based on strain compatibility whereas theFig. l. Automated hollow cylinder testing s,.'stemcircumferential strain, ea, and radial strain, 8*, are basedon the assumption that the radial displacement varieslinearly across the wall of the specimen (Hight et al.,1983). The vertical displacement, Ah, and the sheardisplacement, 6, were measured by proximity transducersrtl(gap sensors) at the top cap. The current inner and outerradii of the specimen, / and r , at any moment during thr<jtest were calculated from the volume changes of the4 Jronspecimen, A V*, and its hollo¥v, A Vj, as follo¥vs:i;;Ii*,,,r,= ( - AV,)- rj'-ihjh ,Tr =l A(Vj - A)V= (2)a T '. crl- r jhjaa(7CrrCT, cr3Fig. 2. Stress component in hollow c_vlinder specimenL';iwhere hj, rjj and r.j are the initial dimensions ofspecimen. The initial dimensions ¥vere measured asetting the specimen (under suction of 19.6 kPa).they ¥vere updated and reinitialized at the start; i *i149CYC_L,lC DEFORMATION CHARACTER STICS OF SANDderiO 110'o¥**<t,-O4 timesf1eJ))i>-o3;UnloadingApi=16-134 kPa-o 4¥5l-o. _uToyoura Sand:)*'e = 0.68o20Isotropic unloading40 60 80 100100503 timescf. (kPa)Inner pressure, Api (kPa)Fig. 4. Membrane penetration per unit surface areaFig. 3. Volume change of hollow due to change in membranethickness;i¥vas:tingmade at burettes by differential pressure transducers.¥* oild byandmade for the membrane penetration and for the change inthe thickness of the inner membrane. The thickness of themembrane used was 0.3 mm. The thickness change of theinner membrane was evaluated by inserting a steel tubewhich had the same inner diameter as the specimen. If theL thesteel tube is used, the membrane penetration can beCorrections to the volume change measurements wereTheai rneglected for the change in the inner cell pressure. The¥vere(7= isvolume change of the hollo¥v would then be due to the;ht ofC o rrectedg e Eerc suhsconsolidation and shearing to calculate strains in therespective processes. Volume change measurements werei100Er8r,w ithoutbc o rre ctio nr50T r hcom rcssion-O.1 O 1 O 2 0_3O8r' 8e (%)Fig. 5. 8e and 8 wlth and wlthout correctlonchange in membrane thickness only. It is plotted against[1 thethe inner cell pressure, pj, in Fig. 3. It should bementioned, however, that other system compliances,}ss the19.6 - 137 kPa. This value is close to the value obtainedsuch as the volume change at the drainage tube, were alsoincluded in it. It can be seen from the figure that A Vj*by Goto (1986).)lasticchanged almost linearly with A pi, and the amount ofcycles in isotropic compression. Cell pressure (Tg waset al.system compliance was of the order of 0.050/0 in terms ofvolumetric strain for the stress change of 100 kPa, whichincreased and decreased bet¥veen 19.6 and 98. I kPa threewas si nificant for small strain measurements.Ioading. It can be seen that after applying correctionsRelationship bet¥veen A Vj* and A pj can be written asusing Eqs. (3) and (5), the variation of e* with theconfinin*' pressure became almost equal to that of 8e,tress,en byiig:iveui'z-e;as theA V{* = CA pj (3)based¥'ariesshearC= - 2.87 x 103 cm3/kPa was obtained for the range ofApi= 16 - 134 kPa.Volume change due to membrane penetration per unitducersarea is expressed as follows if the deformation inet al,,iAhdrawes, 1972; Vaid and Negussey, 1984):;;of thetimes and then increased to 137 kPa in the fourthexcept in the first loading. The discrepancy in the first10ading may be attributed to localized fabric around thelateral boundary (Ishibashi et al., 1996). With thesecorrections, small strains down to 1030/0 ¥vere measuredprecisely for all strain components.isotropic unloading is isotropically elastic (E1-Sohby andl outering theFigure 5 shows ee and e* during loading-unloadingAMP= A VT. '*rj/ - (4);;;'27z(/'. + rj)h3e.2TEST PROCEDIJREToyoura sand specimens with a relative density ofabout 500/0 ¥vere used in this investigation. Toyoura sand(1)where A VT* and s.*''*(2)are the total volume change includingis a uniform sand with subangular particles, mainlym:enibrane penetration and the vertical strain duringquartz, and is ¥videly used in Japan for research purposes.isotropic unloading respectively. A MP is plotted againstThe physical properties are as follo¥vs: mean grain sizeD50= O. 19 mm, specific gravity G* = 2.645, minimum voidthe logarithm of effective confinin*' stress, (Tg , as sho¥vn inof the:d aftea). B;tartPig. 4. The following relationship can be obtained:agAMP=Slogloa *(5)6.1 l!m was obtained for the stress range of (T* =ratio e*i*=0.609, maximum void ratio e***=0.973 anduniformity coefficient U*=1.56. The samples ¥vereprepared by three different methods, air pluviation (A.P.), water pluviation (W. P.) and dry rodding (D. R.) toproduce different soil fabrics. Details of the test program :150CHAUDHARY ET AL.Table 2.TestprogrammeCyclic shearing testsMethod of sampleDirection ofpreparation !sheaFing ((x.)Void Fatio at thebeginning of shearingo' (90 )1 22.5'(67 5')Air pluviation45' (=45')45' (45')0.793o.788o.780oe (90e)o. 76622.50 (67.50)45o (_450)0.767o.762O' (90e)22.5' (-67.4')Water pluviationDry roddin0.789o 792o.800;diameter from a constant height above the sand surface,as shown in Fig. 6. Samples of various densities can beobtained by changing the nozzle diameter and/or heightof fall. In this study, a nozzle diameter of 5 mm and aheight of fall of 140 - 150 mm were used to achieve therelative density of 500/0. It is considered that the fabric ofa sample produced by this method is similar to that ofaeolian deposits of sand (Tatsuoka et al., 1986; Kuerbisand Vaid, 1988).Water Pluviation MethodIn the water pluviation method, sand is phrviatedsimilarly to the air pluviation method, but through water.A constant depth of 30mm of deaired water ¥vasmaintained above the sand surface and the sand wasMonotonic shearin9: testsAir pluviationo'90"o.800o 782Water piuviationo'90'o.777o 820Dry roddin_go'90'o . 784o.778pluviated through a nozzle I .5 mm in diameter from aheight of 170 - 180 mm above the water level. The densityof the specimen was far lower than 500/0. Vaid andNegussey (1988) reported that the soil grains of meandiameter 0.4 mm reach terminal velocity almost instantly,in a drop height of 2 mm through water. Therefore, thedrop height is ineffective in controlling the density of awater-pluviated sample. To achieve a relative density ofare given in Table 2.500/0, the mould was tapped gently ¥vith a ¥voodenhammer. The fabric produced by this method simulatesthe deposition of sand through water found in manyA il' P!uviation Methodnatural environments and mechanically placed hydraulicIn the air pluviation method, dry Toyoura sand ispluviated into the mould through a nozz,le of a certainfills. Oda et al. (1978) reported that natural alluvial soilsand water-pluviated soils have a similar fabric andbehaviour.;Dry Rodding Metl70dThe dry rodding method was mainly designed to IAir Pluviation MethodFixed inner diameterproduce a relatively isotropic sample by destroying anypreferred orientation of sand particles in the air+{Constant height of fallpluviation method. The sand was pluviated in layers andeach layer ¥vas rodded (fully penetrated) 20 times with awooden rod 4 mm in diameter to destroy any preferredAir dry Toyoura sandorientation.}*The samples were saturated by first applying a vacuumand then a backpressure of 196 kPa. B-vaiues higher thanWater Pluviation Method0.95 were obtained in all tests. The samples wereconsolidated isotropically to 98. I kPa for about 4 hours.They were then sheared statically in a cyclic manner alongithree (Tf-directions, O' (90'), 22.5' (-67,5') and 45'(-45'), keeping the mean effective stress, p', and theintermediate principal stress parameter, b, constant atDeaired ¥vater 3 cm deepDrv Roddin MethodWooden rod diameter 4 mmSand p]uviatcd in layersand rodded a fixed no. oftimesO', 22.5' and 45' and then the direction ¥vas reversedalong 90', -67.5' and -45' respectively. The cyclicshear stress amplitude was increased gradually from onecycle to another. The number of cycle, N, was kept to one}at any amplitude. The stress paths follo¥ved in the testsare illustrated schematically in Fig. 7. The drainage ¥1'askept open during shearing. Monotonic loading tests werealso carried out on the three types of samples along the(Tf-directions of O' and 90' to see the anisotrop .' of the'6.Illustration of sample preparation methods*,98. I kPa and 0.5 respectively. The shearing started alongsamples.F oi*ii CYCLIC DCTZtce,at* a lzlaP'J>!,2bea cTght'Ida< Htheoft<-H>, 2rbis(TzCTlp' = 98 lkPa = const.Conditlon for b = cr2 - (y3 = 0.5, = constshearing (71cr3a(7 (deg.) = (0,90),(2 L5, ;7.) ,(45,p<hA[ ofT+151FORMATION CHARACTERISTICS OF SANDcTZD = consL(J }p ! ::: COnSt.21 Z1tedIter,2avasTmax =vasm apIsityIsotropic consolidation Cand4 1?rleanntly,Failure surfacetheFig. 7.of aStress conditions in test seriesv of)den1latesO[1anyaullcO150soilsand:( 100l*¥Od to::s 100o TOyoura Sando^:Jse)2,,17 - eto b=05)¥l;I+ v/aterpluviation' Dr}rroddinge)+'eo pr= 98'1 kPa, ,;{+ waterpluYiationDry roddinga, ,S[ any' Tr-1!i:st l'i-u IJi50F(e) (s' 50O4 1+e'*i,airandol O )ith a1 0 4lO-31 O2l0 lYmaxer ed*',,;uum s+Toyoura Sand' Ae P'*988rt}-e a .b*05Pa_. ',_ F(e) 2- 17-e( )l+eO I 0 3 1 0 11 O )1 O 41 0 2YiT)ax(a) c a = O'(b) (x. = 90'*,thanFig. 8.Secant shear modulus vs. maximum shear strajn from monotonic testsvereours.aiong-1 45'RESUl,TS AND DISCUSSIONd the!Stress Strain ResponseTypical plots of maximum shear stress, r*** { = ((TIint aiResults from the monotonic shearing tests are shown in(T )/2} , versus maximum shear strain, y*..(= ei - e3), foralongFig. 8. The shear moduli were normalized by the voidersedratio function, F(e)=(2.17-e)2/(1+e) (Hardin andwater pluviated samples are sho¥vn in Fig. 9. Anisotropyin stress-strain response can be seen comparing the threecases. Hysteresis loops ¥vere not symmetrical at highercyclicRichart, 1963), to take account of the effect of any slightTl onevariation in void ratio. The response was different for thethree sample preparation methods. It was stiffest for air:o onetestspluviation method alon*' O'. Comparing Figs. 8(a) and'e ¥vas8(b), it can be seen that the response was almost isotropicfor the dry rodding method, being close for both O' and90', compared to the other two methods. Anisotropy washighest for the air pluviation method, especially at as wereilg: theof the;snlall strain range of l0-4 or smaller. Results from cyclictests are discussed below.I"' "strain levels for positive and negative shear stressamplitudes, r **, ¥vhen the specimen was sheared along O'(90'), but they ¥vere symmetrical when sheared along 45'( - 45'). At very small stress amplitude, the response ¥vasapproximately linear ¥vith an extremely small hysteresis100p. But ¥vith increasing stress amplitude, the responsebecame increasingly non-1inear with larger loops. Thesamples were sheared until a shear strain response, y **,of about 30/0 was observed. H'c;l max (kP a)1 Ol(kPa)max10 IJ (kPa).*'l:fgi ?.'88' '2nd cycle10 ID max (kPa)*n ax, e '2nd cycle2nd cycleafa>C:z:-0.010'O1-0.010.01i-10:tmax-103rd - 6thcycles3oYm lx (olo)(b) a J :: 22.50 (_67.50)(a) a = O' (90')Fig. 9.Ls,, ･--Typicai strcss-strain plot for water ph viatioR method (p' =98.1 kPa=coust., /; =0.5): :(( o)100-3c:i>Vtdl n ax (kPa)O.O1d'oecolYmax (olo)v max(a/o)-10-0.01(c) a. = 45' (-45')lH 玉53CYCLIC DEFORMAτ10N C賊ARACT￡RISTICS OF SAND ｝ασ窯0。（90。）5一轍一ασ＝225。（一675。）囎り一一ασ＝45。（一45。）40．3 、（登一！ 一 一 一 、！ 1！F岬’ ｛、 3 一一 、、5■一 、一、、 齢、 1 ＼＼ ／戸 ｝ 一 、 ， 一 、 、 卿、ノ ＼ ， 一 、’ 、 、㌔ 、、“1 ＼0．i 輸馬 、 一’聯ぐ 甲’ρ一 鱒ノ ”ノ ーノ ’ ■ 、4 ・一諾 欄、 、 榊 、 、＼ 、， 爾幅9一興一、♂ フ0 、・、 1 ■、一0．2”求ω＞ 2‘． 、 ’ 一 一輌00 0．5一6 −4 −2 0 2 4 6 Ymax（％）symbol start ofcycle◇ 3rd（＆）緬pluvia亡ion O 4th ㊤ 5th2 ☆ 6￡h ασ嵩0。（90。）”一ασ露225。（一675。）榊”一卿一ασ謀45σ（一45。） 〆イニー囎’幽一’一曽一“嚇｝需一一隔榊、 、、・￥ 41・一一P一一一一験一一 ．＿二Σ，0ユま） 1♂ 4 1ρ．，鱒一一■一 ◇ 7一馬，”一金’一、 、 出臥く二，一一卿一騨一一幽一一一曽 團隔略隔卿、一 、” 、 、・￥、 ／1＼． σ岬 鰍、㌧ 桑 覧、 、、くs、 ／ ノ’ 轟一ぐ一瞬一｝葡囎一、一一噺輪噸乳00一〇．00、10．2一3 γmax（％）Symbolstartofcycle◇ 3rd（b）WatefPluvlation O 4th ㊥ 5th ☆ 6由 》3 ασ＝0。（90。）鼎一一ασ＝22．5。（一675。）疇一“騨｝ασ糾5。（一45。） ＄2 き丈 ／、 ／ ！ン’一一・｝』一、＼、／ ！欄一一’欄需曹醐騨爾一”ヘー 、轟ま ヤ ノ1 ’＼0．2莫 メ ＿＿＿ 一く￥＞ 0．3 乙ウつシ蔚 へ級ω1 霧〆二〆！’働一’・♪＼ ，，＿＿、 噛、、 リヤ めひイ0，1 つ、0 藝 蒙 馨 嚢 多0一4一2 0240 Ymax（％） 華 馨（c）Dryrodding 嚢 Fig．10、 Volume重ric s重raiηvs．maxi瓢um she訂strain0．51 154CHAUDHARY ET AL、100σ CS CC0。，22．5。，45。口τm器80隊oθ eq1［ o浅 60o 隠冨1⋮90。，一67．5。，一45。σ cs ec1i 1iYmaxじ▲、 （2、17一ε）2葦 400（Y灘x）A201oF（ε）留臓 1＋θo △ ▲ロ国夕 o0三〇 5Fl9．1玉。De6nit量o脆ofsec段臓tandequiva巽en柚e謎rmodu藍i10’41σ210り10一（Ymax）A （a）Airp豆uviation Figure10shows plots of vo互umetric strain versusmaximum shear strain for all three methods of sampleprep＆ration．The starting Point of the new loadlng cycle100has been marked on every plot．Anisotropy was observedin tbe volumetτic strain due to shearing direction and alsodue to sample preparation metho（is．The volumetric80strain was veτy small up to the secoad cycle（τm鍼一土7離臓okPa），but圭ncreased rapi（ily with increεlsing amplitude，oΣ 60The overall magn玉tude oぞvolumetric strain wεls l3rgestfor22．50（一67．50）in generaL T鉦e resi（1ua星shear stra圭nβ田隔 （2，王7一ε）2、develope（i for the a圭r pluv呈ated samples was larger than茎 40F（ε）躍0that for the water p互uv圭ated and （1ry ro（i（ied samp豆es。 o 1＋ε▲妬Moreover，the residual strain was larger for O。（900）an（1 擁2022．50 （一67．5。） compared to 45Q （一45Q） for anyparticular method。｝○口姫0 510−4i O’Shθα1・ル∫oゴ乙〃μ5秘 口1σ2 三〇r5圭0’（Ym昆x）A Secant shear moduli for cyclic loading，G。、，。，were（1e一且ned separate正y for positive and negative peak shearStreSSeS，τm抵，aS ShOWn in F三g．n．ReSUI総are ShOwn in（b）W＆terpluvlation藍Fig．12。Anisotropy of the specimen shown in F圭g．8formonotonic shearlng is also clear in the cyclic secant shear霧100mo（luli for（1i∬erent shearlng directions，ασ，For t難e airpluviatlou met｝10d，蜘e largest anisotropy was observed80between Oo an（i900，Tbe anisotropy was largest at sma至Istra重n near the beginning of shearing（reflects the ef㌶ect of露ごinitia1／inherent anisotropy）an（i gradua11y re（1uced as theΣ 60sheaぎ strain increased （re且ects stress−state 圭nduced♂ 宏 ｝Oanisotropy）． The ＆nisotropy was also af罫ected by the o§40samp豆e preparat量on method．It was the highest for the a圭r 図 （2．17一θ）26pluviation method，fo110wed by山e water p玉uviationmethod．It was lowest or almost non−ex至stent for t鼓e dryF（ε〉＝ 1＋ε▲瀦o20 ⑫ro（iding metho（1， This， αlong with the results from髪闇陪鳥漁o o01α5the＆nlsotropy developed by air pluviation was indee（i（iestroyed by the penetration ofthe woo（1en ro（1，giving a！oP410’310萎10P（Y田3x）A 霧 嚢 董more or Iess isotrop量c fabrlc．The three methods forme（icli任erent fabric structures in sand specimens g三ving rise to （cl Dry rodding 嚢 蓑di賃erentin重tialanisotropy．Fig．・2．Cychcseca繊ts勧earm。dul蒙vs．single践mplitude田ax蓋m腿嶢 Equiva互ent shear mo（iulus，（｝，q，on the other紅and，is 曲earst蘭 馨繭nedastheslope・fthestraightlinepassingthroughthe peak shear stress points as shown in Fig．11．Thisgives a di任erent value than the secant moduli clefined彗ハmonoton量c tests，indicates that in t数e dry ro（id呈ng metho（i 妻 aboveandincludesresp・nsesinthetw・・PP・site 盤 王55CYCUC D￡FORMATION CHARACTERISTICS OF SAND100 80阻oQ餓餌芝鮒覧なむ▲ 9）60ζ ▲ △ふασ＝225c，一675。 脇 口田 αα＝45②，一450o．στ maxA P W P D R o Goασ瓢0。，906難舞雛箋 ％鍾騒謹懸・ToyouraSand N＝三鯛o△研も①20’［1Il ﹁［10IIγmグ＝981kPa＝cons虹P40 （2．！フーθ）2 ムF（ε）＝雛 1＋θ 蜘o 陶亟1σ4玉0’1σ2 10弓1﹃10王0’1σ2（γ職a1）銅 1（Yma罵）SAFig．13．Va罫iation of equivalent shear mod観亘雛s with single騒mpmude shears重ra韮nFig。15・De舳t韮o凱ofbystere重icdRmpiロgrat隻o14 A PW P D、R o 、 ▲ 〔 、 雁1。2 圃 、 1o①ασニoc，90。ムムασ記25c，一6フ5c贋康ασ；45。，・45。0．5A P W P．D R0恥0．80 0．6㊤ 0 0ασ瓢0。，90。▲ △ △ασ諸225￠，一675。0、4 m （》 ￥ 喚＼、＼τoyouraSand ∼、▲ 、p『瓢981kPa雛conSt 穿 、、田 o 彊ασ＝45。，45。 ￥》，㎎、㎞＿濡極P’尋81kPa耗・ns皇， ／！瓢 仏 N＝1 ノノヒoここ0、20．4霞co沁maand是orsion＆lshcar 、tヒStsf・rN＝2（lw巳s謹kl ＾’0、2c国，1978）o10』⊃玉0冒4 1σ31σ2 、・幽 繭〆り儀臨稀謙綴鷲臨，、（艀転嚇e＝062−091圭0’監 ▲o ① 9T・y・uraSand ノ／ ノ ノ・灘 0．3 N＝1ノ函《① o雛釦ム ノ ノの0．1 〆重／ f・・N＝2（Tats・・kactal，1978） ⊂ン ε鷹062−0、91王σ1詩瓜ぞ（Y職）SA牙。・510甲21σ3玉0認1σ1（Ymaエ）SAF蓑g、14． Comparison of eqqivale蹴she3r modulus with publlshed 穿es曲SFigほ6， 殺ys重ere重ic dampi獄g ratio vs。si鳳gle a磁pl董tude s赴ear sαa置銀d董rectlons、The results are shown in Fig．13．丁簸ere was0．⊃almost簸odi狂ereuceduetoshe段ringdirectionforanyPartic婆1ar sample preparation method，Though some護萎due to the three sample prepara重ion methods，most of the萎data points plotted together in a very narrow zone for aの二 〇．3艶き「esponses in the t、vo oPPosite directions．If the samp玉eα0．つ妻direction，the equivalent mod111us woul（i represent an嚢婁霧 §馨 we「e sti貸マin one （iirection aad soft 三n the oPPositeThismaybeareas・nwhytheanis・tr・pyinequiva互entshear modulus due to sぬear量ng directions was neg圭iglble．D R． o oOασ＝0。，90。 ▲ oムασ＝225。，一6フ5。田ασ＝45P，一45。 曝 e△ 、eoToyouraSand ＼璽、。 N傭1葵Qドどむゆ ドじ の しじロしししゆほ ゑの ずヤヤ0．i【・Ts…。n融ls旨cartcstsf・丁／ 滋・K鷲2侮tsuok昼ct田，1978）ε灘062−09まaverage of modu員加the two directions．Tぬe anisotropicτespQnse in any particulaτtest is，therefore，obscure（1，A P，W，PP，講981匙Pa；co鳶5εequivalentm・dulusis，inasense，anaverage・fthe蓬嚢義ax漁ロmwide range of shear strain（less t簸an10鱗to10皿！）．The0、・、諭馨菱109minoτdi鉦erences were observed at very small strain leveI00奄・襲 o、、、o 、 o 田、・ 田0．204 0．60．8玉Gcq／Gγ筥106 To compare the results of this investigatlon with thoseaPPearing in the literature，shear modu1圭were noτma王ize（iF韮9．17。 Re置at董o鶏sbip betw’een damp韮ng raIio a爺d equiva董e賑〔 shearもy蟻es鉦eaτm・dul圭atashearstraln。f10−4f。rFig．14 modul豚Sa越d10−6f・rFig．17，w舳werecalc噸edusingthe娩・wingrelati・nspr・P。sedbyIwasakietal。（玉978）． CHAUDHARY ET AL156- 700 (2. 17 - e)2 p'o 5 (kgf /cm2)G?=10+ =GT=10 '1+e(2.17 e) p'04 (kgf/cm2)- 9001+eC. G. S. units have been used in the equations to keep theoriginality.istress, and in monotonic shearing tests. Anisotropy waslargest in samples prepared by the air pluviation method,follo¥ved by the water pluviation method. The samplesprepared by the dry rodding method exhibited an almostisotropic response. The equivalent shear modulusobscured an anisotropic response as it averaged responsesfrom the stiff and soft directions of anisotropic sand. TheThe normalized plot of shear modulus is given in Fig.equivalent shear modulus and the hysteretic damping14. It can be seen that the data points fell very close to theratio were bo, th very little affected by the initial soil fabricrange of data from torsional shear and resonant columnand the direction of major principal stress.tests on loosest to densest sand samples by lwasaki et al.(1978). Slight variations at small strain range may beattributed to the test conditions and difference in thenumber of cycles, N, (Alarcon-Guz,man et a]., 1989;Tatsuoka et al., 1991). In the present study, N= I wasadopted ¥vhereas lwasaki et al. applied 10 cycles at everyamplitude in torsional shear tests from medium to largestrain range and a large number of cycles in resonantcolumn tests for the strain amplitude up to l0-4. Thelarge number of cycles might have stiffened the responseof the sand. The dotted lines in the figure show the rangeof data for N= 2.ACKNOWLEDC.F,MENTS*The work presented in this paper is part of a researchprogram supported by Taisei Corporation. The help pro-vided by Dr. S. Goto of Yamanashi University, MessersA. Tateishi, K. Fukushima, K. Watanabe, T. Shida, Y.Shiba of Taisei Corporation is greatly appreciated.iiREFERENCF,Sl) AlaFcon-Guzman, A., Chameau, J^ L_, Leonards, CJA. and Frost,J. D. (1989): Shear moduius and cyclic undrained behavior ofHysteretic Damping RatioThe hysteretic damping ratio, h, is defined as shown inFig. 15. Like the equivalent shear modulus, the area ofthe hysteretic loop for the calculation of damping ratiosands, Soils and Foundations, 29 (4), 1051 19.'_) El-sohby, M. A. and Andrawes. K. Z. (197,-): Deformatiou characteristics of granular materia! under hydrostatic compression, Can.Geotech. J , 9 (9), 338350.3) Goto, S(1986): Strength and deformation characteristics ofincludes both the stiff side and soft side of the anisotropicgranular materials in triaxial tests, Drmaterial and therefore the anisotropy is averaged. Thedamping ratios are plotted in Fig. 16. The values fellTokyo.within the range given by Tatsuoka et al. (1978) based onresonant column and torsional shear tests on sand with awide range of density. Slight variations may be attributedto the test conditions and the number of cycles similar tothe equivalent shear modulus as the damping ratios byTatsuoka et al. (1978) were derived from the same testsreported by lwasaki et al. (1978). There was no significantdifference in values for the three methods of samplepreparation, or for the various directions of majorprincipal stress.Figure 17 shows the plot of damping ratio versus shearmodulus, which again indicates aimost no effect ofsample preparation methods and direction of shearing.Data points are very close to the dotted line suggested byTatsuoka et al. (1978).Engr*". Tllesis, University of4) Hardin, B. O_ and Richart, F. E., Jr. (1963): Elastic ¥vave velocitiesin _granular soils, J. Soi! Mech. Foi!nd. Engrg. Div , ASCE, 89(Slvll), 33-655) Hight, D. W., Gens. A. and S.vmes, M. J. (1983): The developmentof a new holio¥v cylinder apparatus for investigating the effects ofiprincipal stress rotation in soils, G otec/7niq:re, 33 (4), 355-3836) Ishibashi, ., Jenkins, J. T., Choi, J. W, and Parker IV, C_. L.(1996): The infiuence of boundaries on the volumetFic behaviour ofsolid and hollo v cyiindFical specimens of glass beads, Soi!,s airdi,Foundations, 36 (2), 45-55.7) Ishihara, K. (1983): Soil response in cyclic loading induced byearthquakes, traf c andvaves, Proc. 7th ARCSMFE, Haifa,Israel, 2, 42-66.!}8) Iwasaki, T., Tatsuoka, F, and Takagi, Y. (1978): Shear moduli ofsands under cyclic torsional shear loading. Soi!s and Foundations,18 (1), 39-56.9) Kallstenius, T. and Bergau, ¥V. (1961): Research on the texture ofgranular masses, Proc 5tll ICSMFE, 1, 165-170.lO) Kuerbis, R, and Vaid, Y. P. (1988): Sand sample preparation - theslurry deposition method, Soi!s and Foundations, 28 (4), 107-1 18.i}i:CONCl.USIONSStatic cyclic loading tests were conducted successfullyalong O' (90'), 22.5' (-67.5') and 45' (-45') onsamples prepared by air pluviation, ¥vater pluviation anddry rodding methods to study the effects of initial fabricand shearing direction on the stress-strain response, shearmodulus and damping ratio of medium dense Toyourasand over a wide range of strain. Anisotropy was observed in the stress-strain response and volumetric strainL11) Kuwano, J. and Ishihara, K. (1988): Analysis of permanentdeformation of earth dams due to earthquakes, Soi!s andFoundations, 28 (1), 41-) 5.!12) Ladd, R. S. (1974): Specimen preparation and liquefaction ofsands. J. Geotech. Engrg. Div.. ASCE, 100 (GTIO), 1 180=1 184.13) Ladd, R. S. (1976): Specimen preparation and cyclic stability ofsands, Liquefaction Proble,77s in Geotech. E,7grg. ASCE, National',;Convention, 199-226.,"'*14) Miura, S, and Toki, S (1982): A sample preparation Inethod and itseffect on static and cyclic deformation-strength properties of sand,Soi!s and Foundations, 22 (1), 61-77.15) Mulilis, J. P., C_han, C. K. and Seed, H. B,, (1975): The effects ofdue to the shearing direction. Anisotropy was also ob-method of sample preparation on the cyclic stress-strain behaviorof sands, Report No. EERC 7 -18, Univ of California, Berkeley.served in the secant shear modulus both in cyclic tests, de-16) Nakamura, Y., Hashimoto, S. and Kuwano, J. (1998): Thefined separately for each direction of major principaldevelopment of a hollo¥ ' cylinder apparatus for a measurement iu aI*; CYCLIC DεFORMAnON CHARACT￡RISTICS OF SAND157 wide Strain rangeラPノ’oc．33rゴ∫αPσπN‘π10〃‘τ1Co11プ1．o〃Gθo∼εch， damp加g of sands under c｝℃1ic玉oadiag and 萎！s relat茎o鶏 to shear βη9／3、，Yamaguch圭，JapaneseGeotec熱。Soclety，1，519−520。17）Oda・M・（1972）：三nitialfabrlcsandtheirrelati・nst・mechanlcaI modulus，Soi’5αnゴFo姻ゴφon5，18（2），25−40、22）Tatsuoka，F．，Ochi，K，，Fujii，S．and Okamαo，M．（三986）：Cyclic、』as）d，lles難 propertiesofgranula罫material，So’Z5α”ゴFoμηゴαf’oη5，12（1）， undrained tr玉a』x玉al and tors玉onal shear streηgth of sands forost 17弓6 di貿erent sample preparation methods，So鉱∫αηゴFoμηゴαだ0133，26iUS18）Oda・M・・Koishika・va・La澱d磁9αch呈」・（1978〉：鷺xpe曲e繊allses「hem91rch）ro−sersY，7rOS乞，or of1arac−cα11．Gs ofミi［yof）citles五，89pm巳nt∋cts of垂383、C L「o田of 嚢r’∫α’τごきごed byHa1fa， 舞ui1・礁‘π’0η5，ture of）n一由e莚）7−118、ma蘇eロしlz5σηづ妻幾裟糞［ion of4184．董）趣ofねtiQna！iandltS）fsand，挿ec〔5σf、ehaviOferke互ey・8）1τilelent ipa23） Tatsuoka， F，， Shibuya， S。 and Teachavorasinskun， S． （1991）： So’Z∫01∼ゴEα〃1伽10115，18（1），2シ38． Dlscussion，So’なαπゴ召o雄磁！’o’15，31（2〉，202−209．lg）Shlbuya・S・a鷺d田ght・D・W・（1987）l A bounding surface for24）Vaid，Y。P，andNegussey，D、（1984）＝Acriticalassessmentof 郎anularmaterials，So’なα11ごFo醐ゴ頗oη5，27（4），123−i36， membranepenetrationin出etrlaxlahest，σeoごθごh．71ε5励9／，，720〕Sllver，M・L and Park・T・K・（1976）：Liquefaction potentlaI）r1C蓬妻嚢 （3），23−4董． study of aa玉sotropic she＆r strength Qf sand by plane strain test， （2），70−76． evaluaτed from cycllc strain−controi1燈d properties tests on sands，25）Vaid，Y．P，and Negussey，D．（1988）：Prepa影atlon Qf reconstlωted So115αηゴEo瑚吻ioπ5，16（3），51−66。 sand spec茎mens，／痩4y‘7ηα∼ゴ 7ン’i鳳Yノ‘71 71851iηg oゾSoi1 ‘7ηごRocκン21）IaIsuoka，E・Iwasak玉・τ・and Takagl・Y・（1978）＝｝｛ysteretic ASTM SτP977，405−417．
- ログイン
- タイトル
- stress Rate-Elastic Stretching Relations in Elastoplastic Constitutive Equations for Soils
- 著者
- I. Einav・A. M. Puzrin
- 出版
- soils and Foundations
- ページ
- 159〜160
- 発行
- 2002/02/15
- 文書ID
- 20447
- 内容
- SOILS AND FOUNDATIONSVol42, No, l, Feb. 2002Japanese Geotechnical SocietyIt would be interesting to assess what effect the missingDISCIJSSIONSterm would have on calculation of elastic strains duringplastic loading. The authors define the Gibbs free energyfunction (36) as:STRESS RATE-ELASTIC STRETCHINGRELATIONS IN ELASTOPLASTICG(crjj,F) y(p+ F) InP+ F 1po +CONSTITIJTIVE EQUATIONS FOR SOILS=)1+ 2 F tr((ri*Discussion by I. ElNAVi ) and A. M. PUZRINii)where y,The paper emphasizes the importance of the First Lawof Thermodynamics in description of elastic componentof elasto-plastic behaviour of soils. To ensure that theFirst La¥1' is satisfied, existence of energy potential shouldandare material constants, pto introduce thermomechanical principles into soil(7i*j = (Tij+pajj is the deviatoric stress tensor and F is theyield surface and is given by Eq. (28):-8 )F= Fo exp (9 1)ywhere 8 =8*Pi is the volumetric plastic strain, and p is amaterial constant. Differentiation of the Gibbs freeenergy function with respect to the stress tensor yields theelastic small strain tensor (38):modellin*', yet they seem to overlook this subtlety.In Eq. (1) the authors make an assumption with respectto decomposition of the stretching tensor D into elastic8i'J aG(aij,F)acfij(L +- -3 y6ijIno ++c_F F (Tstudied in the paper, this assumption reduces to convenjj =j'j +)1and plastic parts Djj =Dj*j + D ;Pj. In a case of small strains,tional decomposition of the strain rate tensor:(+ F8,'.= e i y In,P is defined by Eq. (68) using associated fiow rule(60) and extended consistency condition (59), while theelastic component (Eqs. (2) and (5)) is given by the ex-F I (92)Then the volumetric elastic strain is given byiP ･ In the model proposed in the paper, the plastic component- (Ti /3 is theisotropic hardening function related to the size of therelationship is easily derived by double differentiation ofalso made dependent on plastic strains, derivation of incremental elastic stress-strain relationship becomes subtler. The authors are to be congratulated on their attemptCTk J ) (90)mean effective stress, po is the initial mean effective stress,be assumed. Then the incremental elastic stress-strainthis potential. However, when this energy potential isF0+F (93)and its correct rate of change bypression:'.* aG(cr;j, iPj) .a(Tija(Tkl akl- yp +y( p - po) 'FF)( po + F)F ( p +while the rate of chan*"e calculated using Eqs. (2) and (5),i:';'where ((Tij, 8,Pj) is the Gibbs free energy potential func-as suggested by the authors, is simplytion.( ,')A-y -. p + F P (95)Unfortunately, Eq. (87) represents only a part of the"elastic" strain rate tensor. In fact, following Eq. (38),from definition of the CJibbs free energy potential we ob*,,tain:tic component of volumetric strain. Expression (95), on8i=j = aG((Tij, e iPj)I(88)acr *;**i;,,", a (orij, eiPj) aG((T ;, eiPj) .='jaai -j a (cTk klla(7i +j a 8lthe contrary, is not a full differential and its integrationwill depend on the integration path. The simplest example to consider would be isotropic consolidation, when F=p and F0=po, so that integration of expression (95)and the full differential of this equation is *'iven byi{Obviously, because Eq. (94) is a full differential, when in-tegrated it wiil produce a correct expression (93) for elas-(89)yields:(e, I)Ay In P (96)+ powhich reduces to Eq. (87) only for a case of non-plasticfoading. Therefore, for a general case of plastic loading(Eq. (69)), the authors have missed the term (a( !((Tij, e iPj) /while the correct expression for volumetric elastic strain isaaija 1) l' reflecting changes in elastic strains dueobtained by substituting F=p into expression (93):toges in plastic strains.By Koichi Hashi_ uchi and lan- F. CoHins., Vol. 41, No 2, April 2001, pp. 77-87Doctoral Studen and Associate Professor respectively at the Technion, Israel Institute of Technology, Haifal 59 DISC_tJSSIONS16050[200a [i40- 301500 [eo 20-ce- f' : e* Iooo r*'50a [Correctedplastic[Eq. (4110the ela:oof e' ir500 1000 20001500op [kPa]Authorsrowhere i*o oa8o o 002 o 004 o 006o olwhereFig. 7. The relative error in elastic strainssYFig. 6. Comparison betll'een the non-plastic volumetric-strain fornormally consolidated clay in isotropic consoiidationsiderable step forward as compared to models where;!neither elastic nor plastic behaviour satisfies the FirstLaw. However, as we have seen, an attempt to model thedependency of eiastic properties on plastic strains withinthis mixed frame¥vork may lead to inconsistencies.(1 +pe = - y In p0+p (97)The error resulting from the missing term can be quantified by considering a particular parametric case suggestedby the authors: = O.1, y =0.004 and p0= 100 kPa. Elastic stress-strain curves obtained in isotropic consolidationare compared in Fig. 6, while the relative error 6 = { [(e,'.)A-8,*,]/e,*,} >< 1000/0 is plotted versus the mean effectivestress in Fig. 7. In conclusion, it is worth mentioning thatin the writers' vie¥v this mistake could have been avoided.Necessity to satisfy the la¥vs of Thermodynamics whenmodeling behaviour of materials has been reco*"nized bymany researchers. Unfortunately, some of them limit;;IThis problem can be easily avoided by applying a moreconsistent thermomechanical framework to modeling of Ielasto-plastic behaviour, (e.*'. Collins and Houlsby,1997). Important feature of this framework is that theand thlGibbs free energy represents a potential for total strainsand not just elastic ones. In this case, assumption of dependency of elastic properties on plastic strains would automatically lead to appearance of additional strain termscoupling between elastic and plastic strains. As a resultboth elastic and plastic behaviour ¥vill be consistent ¥vithThethe First and the Second Laws of Thermodynamics andno terms will be missed.TheEqs. (1their efforts to satisfy the First L,aw only by elastic com-REFERENCE,ponent of this behaviour, while the plastic component isfound from more or less conventional frame¥vork, ¥vhichhas nothing to do vith Thermodynamics. Still it is a con-36) Col ins, I. F. and Houlsby, G. T_ (1997): Application of thermomechanical principles to the modeling of geomaterials. Proc.jRoya! Societ_v of I,0,Idon. Series A, 453, 1975-2001 .fSTRESS RATE-ELASTIC STRETCHINGRELATIONS IN ELASTOPLASTICCONSTITUTIVE EQIJATIONS FOR SOIL,S*)Closure by KOICHI HASHIGUCHlii)and IAN F. ColuNsiii)tegration of Eq. (32) or (33) under the condition F=const.whereOn this circumstance the discussers derived the elasticvolumetric stretching Eq. (94) inversely from the com-a :O a'The telplementary energy function (36) ¥vithout fixing F. In ¥vhatfollows let the novel elastoplastic constitutive equation be(35), the complementary energy function (36) and thestress-elastic strain relation (37) or (38) ¥vas sho¥vn as aForderived by the first author formulating the complete setconstitthe halof strain energy function, complementary energy function, stress-elastic strain relation and stress rate-elasticstretching relation, whilst the Hooke's type elastic laThe stress rate-elastic stretching relation (32) or (33)¥vas formulated based on the physical considerations. Onthe other hand, the novel set of the strain energy functionelastic;'lp(8e,does not hold any more, and further the complexity is**"caused by the elastic-plastic coupling in not only elasticibut also elastoplastic constitutive equations.Assume the following complementary energy function'G (a,G for infinitesimal elastic strain 8*.supplement, ¥¥'hich is derived formally by the time-in,;i) Voi. 41, No. -?, April 200i, pp^ 77-87. (Previous discussion by I_ Einav and A. M. Puzrin, Vol 42, N0. l, February 2002, pp 159- 60.)i professor. CJraduate School of Bioresources and Environmemal Sciences, Kyushu University, Hakozaki 6-l0-1 . Hi_gashi-ku, Fukuoka 812i)'*i"':from8581. Japan{ii) pFofessor. Department of En*aineering Science, School of Engineering, University of Auckland, Auckland. Ne¥v Zeaiand.#
- ログイン
- タイトル
- stress Rate-Elastic Stretching Relations in Elastoplastic Constitutive Equations for Soils(closure)
- 著者
- Koichi Hashiguchi
- 出版
- soils and Foundations
- ページ
- 160〜164
- 発行
- 2002/02/15
- 文書ID
- 20448
- 内容
- DISC_tJSSIONS16050[200a [i40- 301500 [eo 20-ce- f' : e* Iooo r*'50a [Correctedplastic[Eq. (4110the ela:oof e' ir500 1000 20001500op [kPa]Authorsrowhere i*o oa8o o 002 o 004 o 006o olwhereFig. 7. The relative error in elastic strainssYFig. 6. Comparison betll'een the non-plastic volumetric-strain fornormally consolidated clay in isotropic consoiidationsiderable step forward as compared to models where;!neither elastic nor plastic behaviour satisfies the FirstLaw. However, as we have seen, an attempt to model thedependency of eiastic properties on plastic strains withinthis mixed frame¥vork may lead to inconsistencies.(1 +pe = - y In p0+p (97)The error resulting from the missing term can be quantified by considering a particular parametric case suggestedby the authors: = O.1, y =0.004 and p0= 100 kPa. Elastic stress-strain curves obtained in isotropic consolidationare compared in Fig. 6, while the relative error 6 = { [(e,'.)A-8,*,]/e,*,} >< 1000/0 is plotted versus the mean effectivestress in Fig. 7. In conclusion, it is worth mentioning thatin the writers' vie¥v this mistake could have been avoided.Necessity to satisfy the la¥vs of Thermodynamics whenmodeling behaviour of materials has been reco*"nized bymany researchers. Unfortunately, some of them limit;;IThis problem can be easily avoided by applying a moreconsistent thermomechanical framework to modeling of Ielasto-plastic behaviour, (e.*'. Collins and Houlsby,1997). Important feature of this framework is that theand thlGibbs free energy represents a potential for total strainsand not just elastic ones. In this case, assumption of dependency of elastic properties on plastic strains would automatically lead to appearance of additional strain termscoupling between elastic and plastic strains. As a resultboth elastic and plastic behaviour ¥vill be consistent ¥vithThethe First and the Second Laws of Thermodynamics andno terms will be missed.TheEqs. (1their efforts to satisfy the First L,aw only by elastic com-REFERENCE,ponent of this behaviour, while the plastic component isfound from more or less conventional frame¥vork, ¥vhichhas nothing to do vith Thermodynamics. Still it is a con-36) Col ins, I. F. and Houlsby, G. T_ (1997): Application of thermomechanical principles to the modeling of geomaterials. Proc.jRoya! Societ_v of I,0,Idon. Series A, 453, 1975-2001 .fSTRESS RATE-ELASTIC STRETCHINGRELATIONS IN ELASTOPLASTICCONSTITUTIVE EQIJATIONS FOR SOIL,S*)Closure by KOICHI HASHIGUCHlii)and IAN F. ColuNsiii)tegration of Eq. (32) or (33) under the condition F=const.whereOn this circumstance the discussers derived the elasticvolumetric stretching Eq. (94) inversely from the com-a :O a'The telplementary energy function (36) ¥vithout fixing F. In ¥vhatfollows let the novel elastoplastic constitutive equation be(35), the complementary energy function (36) and thestress-elastic strain relation (37) or (38) ¥vas sho¥vn as aForderived by the first author formulating the complete setconstitthe halof strain energy function, complementary energy function, stress-elastic strain relation and stress rate-elasticstretching relation, whilst the Hooke's type elastic laThe stress rate-elastic stretching relation (32) or (33)¥vas formulated based on the physical considerations. Onthe other hand, the novel set of the strain energy functionelastic;'lp(8e,does not hold any more, and further the complexity is**"caused by the elastic-plastic coupling in not only elasticibut also elastoplastic constitutive equations.Assume the following complementary energy function'G (a,G for infinitesimal elastic strain 8*.supplement, ¥¥'hich is derived formally by the time-in,;i) Voi. 41, No. -?, April 200i, pp^ 77-87. (Previous discussion by I_ Einav and A. M. Puzrin, Vol 42, N0. l, February 2002, pp 159- 60.)i professor. CJraduate School of Bioresources and Environmemal Sciences, Kyushu University, Hakozaki 6-l0-1 . Hi_gashi-ku, Fukuoka 812i)'*i"':from8581. Japan{ii) pFofessor. Department of En*aineering Science, School of Engineering, University of Auckland, Auckland. Ne¥v Zeaiand.# 161DISCUSSIONSNote that the Hooke's type elastic law does not hold by8' aG((T, H. H) (98)the appearance of the second and third terms in the righthand side of Eq. (99) due to the elastic-plastic coupling.The substitution of the flow rule (60) into Eq. (99) Ieadsa(7-/where H and H are the second-order and the scalar valuedplastic internal variables, respectively, as described forEq. (41) of the yield condition. Further, if we assume thatthe elastic stretching is given by the time-differentiationtotr (N ) ( a2G a2G )+ Mp_ acraHh+aaaHof 8' in Eq. (98), it holds that. a2G . a2G2000D'=E (T+aaaH H+ aaaH HThe stretching D is obtained from Eqs. (1), (60), (61)and (101) as follows:(99)' (N'+ ( I 02)M p aaaH aaaHD E-la+tr(N ) a2G h+ a2G- )hwhereElwherea2Gfrom Eq. (102) as follows:e Firstdel the_M +tr(NEN)+trtr (NED)NE aG¥vithina moreiia( aH:ling ofDulsby,(NE-h) +h tr)a2Ga(1 aHand thus the plastic stretching is described ashat theDP_ __ (___N(104)(NE- 2_)M +tr(NEN)+tr NE aGaaaHtr (NED)strainsl of de-a(TaH,uld au-n termsh) +h tra2GThe loading criterion is given as follows (Hashiguchi, 2000):a resultntThe positive proportionality factor in the flow rule (60)is expressed in terms of the stretching D, rewritingas A ,(1 OO)acFaoFDPvith.*;0:A > O,D P = O:)i:ics andThe inverse expression of Eq. (102), i.e. the expression of the stress rateEqs. (1), (l02), (103) and (105) asO. (105)in terms of the stretching D is given froma 'h+h/ (N+_ tr(N'D) (-2d2Ga2G() IaG-p - --E (-acFaHaaaHof ther-=EDls, ProcM +tr(NEN)+tr NE aoraH*)06)h) + h tr NE a(7aH:'=const.where < > is the McCauley's bracket, i,e. <a>=a forelasticle com"a :O and <a> = O for a<0 for arbitrary scalar variable.The terms containing in Eq. (106) are induced by theIn ¥vhatelastic-plastic coupling.ation bcFor the present soil modei the complete set of elasticconstitutive equations taken account of the variation inthe hardening function F can be given as follows:)lete sety func'* ;e-elasticV/(8',F)=y(p0+ Fo)exp -tr8' + Ftr8'stic lal ',lexity isyv elastic+1Ftr s'*2+ - Ftr (a 8'*)2FoG(a, F) = y(p+ F) Jlln ( p+ F ) _ IIJi'unctiono +oka S12,{I,ifrom which it holds that+e_8F + - aF8e*Fo(109)e aG((5f'F)8-aa)yln/P+ F )I++('-(7-Foo +FO' p0+ Fo(trD )1+ FDe + FI+F(107)a=(110)8e*+(To. (111)_Fo+ I tra* ' l2 FFO tr (a'a'); 59- 1 60.)(F) tr(1aW(8e,= - (p0+ Fo)exp(l08)_p + yF) F*-3( FI_D*3(d.1+py+ F)F2CF'(1 12) 王62DISCUSS三〇NS2，000’鞭■！1，500 P（kPa）EinavandP面nl ， （1＋9）P ゆ！1，000Eq（97）1εソ鳶ザ｝n跳仰1■5001 ’ ’ ’ ○ ε PE“（118）1εv甑｝71nπ‘一● ，E“（119）・阜1柔9暢 ’00一〇〇〇2a一〇〇〇6 −0008 −0010一〇〇〇485韮Fig．8．Co即朗so獄ofe隻as窒董cvo夏ume皇ricstrainsca匪cu藍atedbythreee簾asl鑑ceoロs舳tiverelat董onsin伽e簸ormaトcoロso蓋ida重ionprocess一〇〇30．5y一〇．02石6v0．25一〇〇1罰000 1，000 2，000 3，000ヂ P（kpa）eIsoPセopic consolidatio且霧O605 0、677 9一，碕い嘘，一’匿甲 n 騨 ■ ” P 囎 一 孕 ’ ゆ■甲’ 』 甲一一？，酔，囎圏脚 ’ひ7一’ ●狩1’■，’一’”一 騨 一 〆．牢1﹃8置﹂8 掃r 趣『 ヌεγ O。3025，！ 3P ’1r1門 齢鼎0．25’ミ’’ノli卜’ 警 ’！i’ i 000、2llε＊1001一〇〇2一〇〇5 き薫嚢8v O005εv O0、02讐嚢0，1 O、04 0．1 0、2 0 005 0．10 1ε＊l l蕊＊l T船頭alc・mpress孟on T打a滋alextensio簸wi出c・nstandateralpress町e wi血const瓢1ateralpress肛eFig。9。（114）Meas級red cu罫マe（・セt刃’’’81 ’＝ri1ε＊ll1一’’『0，夏嚢 1σ州P 『i3ρ！華弄（！陛謬﹃iI lfI i，1σ＊llγ’’膠1 ， ’置 ’00．5■鱈 − ’ 一甲叫’，0、3tlうa獄dpredictedcurve（ （一一一P。蚤ss。n・srat量。））by重hee蓋as童卿sticc。。stit櫨iveEq。（106）wi撫Eqs，（113）臼・δ藝 __ yI+ I a*1J F'i{163DISC_USSIONSE,jkl(p+y F 32 ii6kl+ F(6ik6i +6il6jk)The maximum relative difference due to f is(113)( -1) i f y I IJ 6ijakk :_3 3(p+ F) 2 Fi jkl1+ 4 F (a k6, + 6* 6Jk)(113)'anda2G{acFaH3( P +F)F2(1 14)noting the relationsp + = Fex tr )8p( e(1 1 5)po + FO yof* a _F Fo8e*(1 1 6)/(1 +atmost as known by comparing Eqs. (1 18) and (1 19). Thus,the relative difference is 9.090/0 constantly in the monotonic isotropic normal-consolidation process with = O. 1used in Fig. 4 as shown in Fig. 8, although it increases upto 400/0 in Figs. 6 and 7 calculated by the discussers usingtheir Eq. (97) which involves the inappropriate replacement of the initial pressure to the current pressure asknown by comparing it with Eq. (1 18).Further, the prediction by Eq. (106) with Eqs. (113)and (1 14) with the full elastic-plastic coupling shown inFig. 9 is almost same as the prediction by Eq. (71) withEqs. (34) and (72) shown in Fig. 4, whilst same values ofmaterial parameters are used for these figures. Eventually, the difference of the prediction due to p would not beso large as examined for the monotonic normal-consolidation process in which the difference exhibits maximum,whilst not only the elastic but also the elastoplastic con-The elastic volumetric strain eis given exactly fromEq. (110) asP/i!^'I8/p+ Ftr 8'= y In 0+ FO (1 17)vhich reduces toe = ylnP (118)po{;for the monotonic isotropic normal-consolidation process (F=p) studied by the discussers, in which the ratio ofthe increment of hardening function F to that of pressureI,p is maximum, i.e, the maximum elastic-plastic coupling(fr/p = max.) is realized, the elastic volumetric strain*i.being independent of the material constantprescribingthe elastic-plastic coupling. On the other hand, the elasticIvolumetric strain due to the stress rate-elastic stretchingrelation (32) is given by{=_ y In Po (1'8'1 9)' (1(-)+p{**'{i;'!;.*artd;"'*I;*;'stitutive equations becomes complex by incorporating therate-type elastic constitutive equation with the term of frbringing about the full elastic-plastic coupling.The therrnomechanical approach at the present stagewould not play an inevitable role for modeling concreteforms of constitutive equations as was indicated againstthe conclusion of Collins and Houlsby (1997) by the firstauthor (Hashiguchi, 2001). The elastic constitutive equation formulated in the article would give sufficiently exactprediction for practical use, whilst a more elaborateelastoplastic constitutive equation taken account of thefull elastic-plastic coupling is given in this closure.REFERENCE37) Hashiguchi. K. (2001): On the thermomechanical approach to theformulation of constitutive equations, Soi!s and Foundations, 41(4), 89 94.
- ログイン
- タイトル
- scale-Modelling of Fluid Flow in Geotechnical Centrifuges(closure)
- 著者
- 出版
- soils and Foundations
- ページ
- 164〜164
- 発行
- 2002/02/15
- 文書ID
- 20449
- 内容
- ログイン
- タイトル
- Announcements
- 著者
- 出版
- soils and Foundations
- ページ
- 165〜165
- 発行
- 2002/02/15
- 文書ID
- 20450
- 内容
- ログイン
- タイトル
- JGS NEWS
- 著者
- 出版
- soils and Foundations
- ページ
- I〜II
- 発行
- 2002/02/15
- 文書ID
- 20451
- 内容
- ログイン