This is a repository copy of Modeling soil behaviors under principal stress rotations.

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1 This is eositoy coy of Modeling soil behvios unde incil stess ottions. White Rose Resech Online URL fo this e: htt://eints.whiteose.c.uk/15185/ Vesion: Acceted Vesion Poceedings Pe: Yng, Y, Wng, Z nd Yu, H-S (014) Modeling soil behvios unde incil stess ottions. In: Ok, F, Mukmi, A, Uzuok, R nd imoto, S, (eds.) Comute Methods nd Recent Advnces in Geomechnics. IACMAG 014: 14th Intentionl Confeence of the Intentionl Assocition fo Comute Methods nd Advnces in Geomechnics, -5 Se 014, yoto, n. CRC Pess, ISBN Tylo & Fncis Gou, London. This is n Acceted Mnuscit of book chte ublished by Routledge in Comute Methods nd Recent Advnces in Geomechnics on 04 Se 014, vilble online: htt:// Uloded in ccodnce with the ublishe's self-chiving olicy. Reuse Items deosited in White Rose Resech Online e otected by coyight, with ll ights eseved unless indicted othewise. They my be downloded nd/o inted fo ivte study, o othe cts s emitted by ntionl coyight lws. The ublishe o othe ights holdes my llow futhe eoduction nd e-use of the full tet vesion. This is indicted by the licence infomtion on the White Rose Resech Online ecod fo the item. Tkedown If you conside content in White Rose Resech Online to be in bech of U lw, lese notify us by emiling eints@whiteose.c.uk including the URL of the ecod nd the eson fo the withdwl equest. eints@whiteose.c.uk htts://eints.whiteose.c.uk/

2 Modeling Soil Behvios unde Pincil Stess Rottions Yunming Yng Detment of Civil Engineeing, Univesity of Nottinghm Ningbo Chin, Chin Zhe Wng Detment of Civil Engineeing, Univesity of Nottinghm Ningbo Chin, Chin Hi-Sui Yu Nottinghm Cente fo Geomechnics, Univesity of Nottinghm, U ABSTRACT: This e esents n elstolstic soil model consideing the incil stess ottion (PSR). The model is develoed on the bsis of well-estblished kinemtic hdening soil model using the bounding sufce concet. The imct of the stess te geneting the PSR is teted indeendently, nd is dded to the bse kinemtic hdening model. The significnce of indeendent tetment of the PSR stess te in the soil model is demonstted though coming the simultions of soil stess-stin esonses by using the bse soil model nd the modified model in the e. Vious test esults in diffeent snds unde both dined nd undined conditions e simulted, nd the new model gives bette simultions involving the PSR induced volumetic stin nd liquefction. The e lso discusses the simultions nd eeiments of snd esonses unde multile PSRs. 1 INTRODUCTION Mny tyes of lodings in geotechnicl engineeing cn genete the incil stess ottion (PSR) in soil, such s the ethquke, wve nd tffic loding (Ishih & Towht, 1983; Ishih, 1993; Gbe & Clyton, 009). Numeous eeimentl studies indicte tht chnge of incil stess diections, without chnge of incil stess mgnitudes, cn led to lstic defomtions in soil (Roscoe et l, 1967; Miu et l, 1986; Gutieez et l, 1991; Chen & utte, 009). Futhe, the incil stin incement diections e not coincident with the incil stess diections unde the PSR, nd this noncoincidence is clled the non-coility. Neglecting the PSR induced defomtions cn led to unsfe designs, such s in the study of snd liquefction. In conventionl elstolstic theoy, the stess te geneting the PSR nd the non-psr stess te e not distinguished, so tht the soil behvio cn not be oely simulted unde the loding including the PSR. A few elstolstic constitutive models hve been develoed to tet the PSR stess te nd non- PSR stess te setely (Gutieez et l, 1991; Tsutsumi & Hshiguchi, 005; Yng & Yu, 006; Li & Dflis, 006). Howeve, some of them cn only oely simulte t of sects involving the PSR, such s the non-coility. Some don t oely define nd sete the PSR stess te. Some cn only be used in monotonic loding. Some e comlicted nd not esy to be numeiclly imlemented. This e ims to develo soil model which cn oely eesent ll chcteistics of soil esonses induced by the PSR in eltively concise wy. Fo this uose, well-estblished kinemtic hdening soil model with the bounding sufce concet is used bse model (Dflis & Mnzi, 004). Model simultions with nd without the secil tetment of PSR stess te will be comed with test esults. Since thee e multile PSRs long diffeent diections in mny occsions in geotechnicl engineeing, ttemts e lso mde to study the imct of multile PSRs. Finlly, iece of testing equiment is intoduced, which cn imose shes nd coesonding PSRs in two othogonl diections. THE ORIGINAL BASE MODEL The totl stin te d cn be boken down into e the elstic d nd lstic comonent d, which is comosed of d m fom the stess te without the PSR d m, nmed s the monotonic loding fo simlicity, nd the d fom the PSR d. The subscit m nd eesent the monotonic loding nd e PSR loding heefte, esectively. d nd d m cn be obtined by using the conventionl elstolsticity theoy. A well-estblished soil model with the kinemtic hdening nd bounding sufce concet is used (Dflis & Mnzi, 004) s the bse model, which doesn t conside the PSR. Its fomultions e biefly esented in this section, nd the de-

3 tils cn be found in Dflis & Mnzi (004). The yield function of model is, f [( s ) : ( s )] 1/ /3m 0 (1) whee s nd e devitoic stess tenso nd confining essue, esectively. is the bck-stess tio eesenting the cente of yield sufce, nd m is the dius of yield sufce on the devitoic lne with vey smll constnt. d m is given s, 1 f d m Lm Rm ( dm) Rm () m whee L m eesents the loding inde, m is the lstic modulus nd R m eesents the flow diection. m is defined s, 1/ m G0h0(1c he) 3 t ( in ) (3) whee b is the distnce between the cuent bckstess tio tenso nd bounding bck-stess tio tenso on the bounding sufce. G 0, h 0 nd c h e the lstic modulus model metes. R m is defined s, 1 1 R m n DmI n A d ( ) I (4) 3 3 whee n eesents the noml to the yield sufce on the devitoic lne, nd D m is the diltncy tio. d is the distnce between the cuent bck-stess tio tenso nd diltncy bck-stess tio tenso, nd A d is diltncy model mete. The model is fist used to edict stess-stin esonses of Toyou snd unde dined conditions, in which sevel tyicl stess ths e studied. One is the monotonic loding ths (F ths) in which monotonic lodings e lied t diffeent ngles with the hoizontl bedding lne (Miu et l, 1986). This is lso used to clibte model metes. Anothe loding th is the ue PSR th (R ths), in which the stess tio ( t )/( t ) is chosen to be 0.5 (R1) nd 0.6 (R), esectively (Miu et l, 1986). The thid loding tests e efomed by Gutieez et l (1991), in which the noncoility is mesued t diffeent mobilized fictionl ngles. In ll those tests, the confining essue emins constnt t 98 kp, nd b emins constnt t 0.5. Figue 1 shows the tests esults nd model edictions fo the monotonic tests, nd esonbly good geement is chieved. It is noted tht this model doesn t conside the ole of fbic nisotoy, nd its simultions e intended to fit the vege of ll tests esults long diffeent loding diections. Tble 1 shows the model metes clibted in the monotonic loding test. Figue shows the evolutions of vious stin comonents including the volumetic stin with ottionl ngles of incil stess in tests esults nd edictions fo the PSR th R1. Figue 3 shows the tests esults nd edictions fo the PSR th R, stting t = Figue shows esonbly good geement between the test esults nd edictions in the PSR th R1, ecet fo the dil stin, which is much smlle thn othe stin comonents nd cn be neglected. Howeve, Figue 3 shows the discency between the edicted nd mesued esults is much lge in R thn in R1, esecilly fo the she stin nd volumetic stin. The edicted volumetic stin is much smlle thn tht mesued in the test. Tble 1. Model metes in the oiginl nd modified models fo Toyou snd (the fist line) nd Nevd snd (the second line) oiginl model elsticity citicl stte Y.S. e 0 m G 0 v M c c lsticity diltncy modified model h 0 c h n b A 0 n d h 0 A Figue 1. Test esults nd model edictions of the monotonic lodings in Miu et l (1986) fo Toyou snd (F denotes the ngle of loding). It is becuse the stess tio in R is close to diltncy sufce o the hse tnsfomtion line, which esults in smlle edicted volumetic contction. If the PSR occus t stess tio little highe thn

4 tht in R o bove the hse tnsfomtion line ( ( t )/( t ) =0.65), the volumetic ension is even geneted in simultions, which is shown in Figue 3. The oo ediction of volumetic stin hs seious consequence in the study of undined soil behvios in which the lstic volumetic stin diectly contols the genetion of oe wte essues. The discency is undestndble s the model doesn t distinguish the PSR nd non-psr stess te, nd ll the model metes e clibted in the monotonic lodings. Figue 4 shows the edicted nd mesued non-coility t vious mobilized fiction ngles, nd they e in vey good geement. The lge the mobilized fiction ngle is, the smlle the non-coility becomes. This is becuse, ccoding to the ojection ule of the bounding sufce concet used in this model nd mny othe kinemtic models, the diection of lstic flow on the devitoic lne gets close to tht fo the incil stesses t highe stess tio when it oches the bounding sufce. The model is lso used to eoduce stess-stin esonses of Nevd snd with thee stess ths in hollow cylinde tests. The fist one is the dined tiil comession with vious initil confining essues nd eltive densities. In the second th clled the tosionl she, the soil secimen is fist subjected to dined tiil etension loding with 0 =1.38, followed by cyclic loding of she stess unde undined conditions until liquefction occus. Becuse the loding stts with the initil nisotoic condition nd the effective confining essue cn t ech zeo, nd the liquefctions mnifest themselves though lge defomtions. In the thid th clled the ottionl she, the soil is subjected to continuous incil stess ottions unde undined conditions. Figue 5 shows tyicl test esults nd simultions unde tiil comessions, nd they e used to clibte model metes, shown in Tble 1. Figue 6 nd 7 show the test esults nd model simultions unde the second nd thid stess ths. These two figues indicte tht the model edictions e unble to bing the soil to liquefctions. Figue. Test esults nd edictions of PSR lodings R1 in Miu et l (1986) with the oiginl bse model nd the modified new model (es-: il stin; es-t: cicumfeentil stin; es-: dil stin; es-t: she stin; es-v: volumetic stin). Figue 3. Test esults nd edictions of PSR lodings R in Miu et l (1986) nd the volumetic stin fo the dditionl stess tio (0.65) with the oiginl bse model nd the modified new model 3 THE MODIFIED MODEL WITH THE PSR In the modified model, the stess te comonent geneting the PSR is teted indeendently. One cn

5 efe to Yng & Yu (01) fo detiled descitions, nd bief descition is esented in this section. d geneted fom d is given s, 1 f d L R ( d ) R (5) 1/ b : n G h che 0 0 (1 ) (6) 3 t in ( ) : n whee L is the loding inde, lstic modulus nd R flow diection fom the PSR. h 0 nd e new model metes fo the PSR lstic modulus. The PSR lstic modulus is simil to tht fo the monotonic loding ecet the ddition of. is genelly lge thn unity, which mkes moe sensitive to the stess tio. y d 1 ( ) 8t y d 1 ( ) y 8t ( ) y y d y 4t 1 ( ) y 8t 1 ( ) y 8t ( ) 4t y y ( ) y y d t ( ) d y y y t d y y 1 t (8) whee t ( y) / 4 y. Similly, in the sce (y, z) denoted with nd (z, ) with, they cn be eessed s d N d nd d N d. Combining d, d nd d, letting d d d, d d d nd d d d, one cn obtin y y y z d in the genel stess sce, d Nd (9) z z Figue 4. Mesued nd edicted non-coility fo the PSR lodings t vious stess tios in Gutieez et l (1991) R is defined s, 1 1 R I 1- n D n A I b (7) 3 3 whee D is the diltncy tio, nd A is the diltncy model mete fo the PSR loding. nd b e the mlitudes of bck-stess tio nd bounding bck-stess tio. n cn be oimted to be n in mny cses. The detemintion of D uses the ostulte fo the PSR diltncy ule by Gutieez et l (1991). Thus, thee new PSR elted model metes e used in the modified model. They e indeendent of the monotonic loding, nd cn be esily obtined though ue PSR loding ths t diffeent stess tio levels. The finl tsk is to detemine d. It is fist detemined in two dimension (, y), denoted with. It cn be eessed s d N d, witten in mti fom s, Figue 5. Test esults nd model edictions of the monotonic lodings in Chen & utte (009) fo Nevd snd The totl stess incement cn be eessed s, d E( dd ) E( ddmd) (10) whee E eesents the elstic stiffness tenso. Using mthemticl mniultions nd the eltionshi EN GN (11) One cn obtin, d E e d (1) E e ( ER)( ln ) E B1 lnr ( ER)( le) ( ER )( ln ) ( ER )( le) B ler lnr ler (13)

6 N GN (14) B 1 lnr lnr ler ler ler ler 1 (15) 1 lnr B (16) lnr These equtions indicte tht the stiffness tenso is indeendent of stess incements, nd the stess nd stin incements hve line eltionshi. In these equtions, if is set to be nd R to be R, they will be downgded to the fomultions in the clssicl lsticity. Figue 7. Test esults nd model edictions of the ottionl she tests in Chen & utte (009) Figue 6. Test esults nd model edictions of the tosionl she tests in Chen & utte (009) Figues nd 3 show the dined edictions using the modified model fo the tests in Miu et l (1986). These figues indicte tht the new edictions hve ovell bette geements with the test esults thn the oiginl edictions, esecilly fo the she nd volumetic stins. Figues 6 nd 7 show the new undined edictions fo Nevd snd, nd they e ble to eoduce the liquefction, eflected by the lge dislcements. The model efomnces with two PSRs long diffeent diections e lso studied. The tests by Miu et l (1986) e used s efeence. Its initil isotoic confining essue is 98 kp, nd is Figue 8. Pedicted oe wte essue nd il stin with diffeent tios of she mlitudes in two PSRs incesed to 196 kp unde the dined condition. The cyclic she stesses y nd z with diffeent mlitudes e then lied unde undined conditions. z is one qute of cycle lte thn y. The mlitude of mjo she y is lwys 10 kp, nd thee cses of mino she z e consideed with thei mlitudes of 0, 5 nd 10 kp, giving the tio of she mlitudes of 1:0, :1, 1:1, esectively. Figue 8 shows the edictions of oe wte

7 essues nd il stins by using the modified nd oiginl model. Thee is not sudden incese of stins in ll these thee loding cses, nd theefoe the liquefction doesn t occu by using the oiginl model. In contst, the liquefction tkes lce in ll the cses by using the modified model. As discussed befoe, this is becuse the oiginl model edicts smlle lstic volumetic contction (o even volumetic ension) t highe stess tio fo the PSR. Figue 8 lso indictes tht multile PSRs mke soil ech liquefction fste thn one PSR. The ctul tests e being conducted by using the Vible Diection Dynmic Cyclic Simle She (VDDCSS). The VDDCSS is new oduct mnufctued by GDS, which llows simle she to be efomed in two diections. This is chieved by hving secondy she ctuto tht cts t 90 degees to the imy she ctuto. The secondy she is nd be used indeendently of the othe she is o in conjunction with it, leding to indeendent contol of two PSRs. The VDDCSS ws mnufctued nd instlled t the Univesity of Nottinghm Ningbo Chin (UNNC) in 013. Test esults will be used to veify the model edictions. 4 CONCLUSION The e fist discusses the cbility of wellestblished kinemtic hdening soil model in edicting stess-stin esonses of soil unde the PSR. It cn edict the non-coility vey well, but its ediction of volumetic nd she stins is the ooest. The model is modified to indeendently tet the stess te comonent geneting the PSR. An dditionl flow ule nd lstic modulus fo the PSR stess te e used, nd the edictions e imoved, esecilly fo the she stin comonent nd volumetic stin. One imotnt fetue of the model is tht it is develoed in the genel stess sce with si stess vibles, nd it cn tke into ccount multile PSRs. Anothe fetue is tht it etins the line stess te-stin te eltionshi. Soil esonses unde multile PSRs e lso studied, nd they cn bing soil to filue fste thn one PSR. Chen, Y.R., utte, B.L. (009), Contction, diltion, nd filue of snd in tiil, tosionl, nd ottionl she tests, ounl of engineeing mechnics, 135(10), Dflis, Y.F. & Mnzi, M.T. (004), Simle lsticity snd model ccounting fo fbic chnge effects, ounl of Engineeing Mechnics, ASCE, 130(6), Gbe, P.. & Clyton, C.R.I. (009), Effects of incil stess ottion on emnent defomtion in il tck foundtions, ounl of Geotechnicl nd Geoenvionmentl Engineeing, ASCE, Gutieez, M., Ishih,. & Towht, I. (1991), Flow theoy fo snd duing ottion of incil stess diection, Soils nd foundtions, 31(4), Ishih,. & Towht, I. (1983), Snd esonse to cyclic ottion of incil stess diections s induced by wve lods, Soils nd Foundtions, 3(4), 11-6 Ishih,. (1993), Liquefction nd flow filue duing ethqukes, Geotechnique, 43(3), Li, X.S. & Dflis, Y.F. (004), A constitutive fmewok fo nisotoic snd including non-ootionl loding, Geotechnique, 54(1), Miu,., Miu, S. & Toki, S. (1986), Defomtion behvio of nisotoic dense snd unde incil stess es ottion, Soils nd Foundtions, 6(1), 36-5 Roscoe,.H., Bssett, R.H. & Cole, E.R.L. (1967), Pincil es obseved duing simle she of snd, Poceedings of the Geotechnicl Confeence, Oslo, Tsutsumi, S. & Hshiguchi,. (005), Genel nonootionl loding behvio of soils, Intentionl ounl of Plsticity, 1, Yng, Y. & Yu, H.S. (006), A non-coil citicl stte model nd its liction to simle she simultions, Intentionl ounl fo Numeicl nd Anlyticl Methods in Geomechnics, 30, Yng, Y. & Yu, H.S. (01), A kinemtic hdening soil model consideing the incil stess ottion, Intentionl ounl fo Numeicl nd Anlyticl Methods in Geomechnics, DOI:10.100/ng PREFERENCES