Some Aspects of Soil Mechanics Model Testing

7/22/2019 Some Aspects of Soil Mechanics Model Testing

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ASPECTS OF SOIL MECH NICSMODEL TESTING

byR. G. James *

CUED/C SOILS/TR 1971 No.6

* ss is tant Director of ResearchDepartment of EngineeringUnivers i ty of Cambridge.


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IN1ROOUC';rIqWDue tq the cOq\plex l l \ e c h a n ~ c p . ~ ~ e h a v z i , o l l r of r e ~ l s o i l there

are c o n s i d e r a b l ~ 4 f f i c u l t i ~ ~ in o b ~ a n i n 9 a c c ~ r a t e ~ q ~ u t i o n s to the boundary v a l ~ e p o b L e m ~ 9 f ~ o 1 1 m e q h ~ n ~ c s rhe majorityof present day methods of s o l u t i p ~ < h ~ l ? e n 9 , . ~ p p p m q , t h ~ m a t i c a l idea l i sa t ionsof toe. so i l stl:'ess ; ; t ~ a i n be1'l.avio\.u;to ei therperfectly plas t ic or perf( otily e las t ic . For the majority ofproblems botha f these i a . e a J . ; ~ s a t i o n s are unrea;j.ist:i,.c,and as aconsequence the p r e d i c t i o ~ s made by cQnvemtiq:p.al m(i!tllo4l:i of analysisare prone to error . Ip ~ 4 0 i t i o n t o the 4 i f f i c ~ l t i e 8 of ideal is ingthe mechanical behav;l.our of the o , i . ~ , t h . ~ p r o ~ l ~ ~ themselves areusually of a complex nature, e . g t h e p ~ o b l e m o f a pier foundationrota t ing aQ0ut i t s upper surfq.ce as pQ;,tf'ayed in Fig.J. and dis-cussed by Roscoe :+970) in tn.e Tenth llankine ~ e c t u : l : 7 e .

C o n 5 e g ~ e n t l y experimental i n v e s ~ i g a t i Q ~ 01 the l o a ~ displace-ment re la t ionships for tne1;>q\,1ndary vatl,ie ~ r o b l ~ I l l s 9 ; sqi l mechanicsis essent ia l . Testing 9f fu l l ~ e a l e prototype s t ~ u c ; l t ; . l 1 ~ e s , althoughvery necessary, is e x p ~ n E ? i v e a ~ d t m ~ con.suming, ~ n d t ~ e r e f o r e the incentive and need to perform representat ive model te s ts isgreat. One may broadly classify mqdel tes t ing depencent upon theprime objectives, in to three diE?tinct, but. in te r re la ted categor ies .These categories will be referred to as category I 11 and Ill

C L A S S l F I C A ~ J ; O N OF MOPELfi'EpTINGCategory I model tes ts are defiped as being concerned only

with predicting the behaviour of a specif ic prototype structurefrom tha t of the model. Any s p e c i ~ l g ~ o u n d conditions, i . e . soi ls t ra ta water conditions etc" s u c ~ as i l lus t ra ted in Fig.2a for apad foundation ~ r o b l e m must be ~ ~ i t a ~ ~ s i m ~ l a t e d in the model,


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and so the r e su l t s opta ined do :pot have genera l p p l i ~ b i l i t yIn t h i s type of model t ,est t h e p r i n o i p l e s o f s i mi l , a r i t y mq s t besa t i s f i e d before the r e su l t s cq,n be t p r a c t i c a l use (e .g .Suther land 1965)) . However, the g e n e r ~ p r i n c i p l e s qiscQssedby Rocha 1957) and Roscoe 1968) s h o q l e n s u ~ e wider app l i ca t ion .of t h i s type of model t e s t , es p ec i a l l y in the a rea of cen t r i fuga lmodel t e s t ing which al lows the use of p ro t o t y p e s o i l a t Pro to-type s t r e s s l eve l s and under approXimately c o r r e c t Condi t ions ofs t r e s s and s t r a i n paths . Poss ib ly one of the major ~ v n t g e s ofcen t r i fuga l model t e s t i n g i s t h a t processes such 9s primary con-so l ida t ion occur very much f as te r in the model t h ~ n in t he prQto-type , i . e . t i m e i s m o d e l i e d N2 where N i s the model sca l e .Thus for a s ca l e model 2 t hou;t:"s i n . t h e mOdel equivi;l.;Lentto 1 year in the profo type .

The eecond approach to model l ing, def ined as C ateg o r y I I ,i s to c o n s i d e r t h t t h e m o d ~ l i s a smal l prb to type s t ruc tu rei t s e l f and to compare ts behaviour wi th t h a t pred ic ted by somemethod of ana lys i s . For t h i s approach to be u s e fu l t i s ofutmost importance t h a t the model conforms with the assumptionsinheren t in the method o f an a ly s i s adopted . Typica l requirementswould be t ha t the s o i l i s in a uniform s t a t e and t h a t the in f luenceof t he boundar ies of the con ta iner o f t p e model may be ignored,e .g . as i l l u s t r a t e d in Fig .2b fo r the bear ing cap ac i ty problem.From the r esu l t s of such t e s t s t should be p o s s i b l e t o assesst he accuracy of var ious methods of an a ly s i s and a l s o to confirmt h a t the so i l co n s t an t s es tab l i shed from fundamental t e s t i n gappara tus re levan t to the s t r e s s condi t ions in the model can beused to p red ic t the performance of the model. The r e s u l t s obta ined


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3.

from such t e s t s are not necessar i l Of i m m e d ~ a t ~ ~ e thedesign of a complex fu l l sca le proto type , but a ~ e o ~ ~ r e a t va luein es tab l i sh ing cer ta in design p r i n c i p l e s ~ x p e ~ m e n t s of theabove two types are inherent lY r e s t r i 9 t ed by the n e e ~ t o s imula terea l problems. This automat ica l ly l eaqs to t h i F ~ ty?e t modelt e s t , def ined as Category I l l , of which the f u l ~ ~ c ~ ~ e n ~ e d neverex i s t , but which i s designed s p e c i f i c ~ l ~ y to r eve , l d e t a i l eds t re ss and deformation informat ion about a p ~ o 9 ~ e ~ Tne primeobjec t ives of t h i s type of t e s t are to i n c r e a ~ e the unders tanding

andof the so i l b e h a v i o u ~ / t h e so i l s t ~ u c t u ~ e i n t e rac t i cn , suer t ha tnew methods of ana lys i s may be developed which in tUrn w i ~ l l eadto be t te r design ru les for use in the f u t u r e . Su cn a ~ o ~ e l experiment, a narrow wall ro t a t ing about ;i t s into sand, i s '-- s si l l u s t r a t ed in Fig .2c . 8y employing suCh a t h i n plane s t r a i nmodel it i s poss ib le by radiography to obta in d ~ t a i l e d informat ionon the so i l s t r a i n behaviour not poss ib l e on wider plane s t r a i nor th ree dimensional ' models.

In the pas t numerous workers have performed q var i e ty ofexperiments fa l l ing in to the above mentioned categOries. t i snot poss ib le to mention a l l here , but a few examples wi l l begiven to i l l u s t r a t e the ca tegor ies fur ther . Good examples ofCategory I type t e s t s are to be found in the f i e ld ~ a t h e r thanthe l abora tory and ex i s t in the form pf inst rumented t r i a l ea r ths t r u c t u r e s , i e . t e s t embankments. In ce r t a in cases nature hasalready car r i ed out fu l l sca le t e s t s in the form of natura l s lopefa i lu res , and in cases where care fu l s i t e inves t igat ion es t ab l i shesthe r e levan t so i l parameters and ground water c o n d ~ t i o p s tneset e s t s produce valuab le compaJ;: isons between theOrY and "exl?eriment ,(e.g. Skempton and Hutchinson (1969.


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Without a cen t r i fuge it i s in genera l extremely d i f f i c u l tto perform r ep resen t a t i ve smal l sca l e Category I type t e s t s ,due to t he d i f f i c u l t y of model l ing the s o i l . Witb t ~ ~ c e n t r i f u g e ,however, t h i s major d i f f i c u l t y may be overcome, s ince prov id ingthe s o i l gra in s i z e s are s u f f i c i e n t l y smal l the p ro to type s o i l smay be used in the model. ~ m p l e s of such t e s t s are given bySchofie ld and Lyndon (1970) on the shor t term s t a b i l i t y of s lopesin overconso l ida ted c lay , and by Endico t t (1971) on the se t t l em en t sof a granula r ill embankment s i t e d on a subs t ra t a of s o f t c l ayand pea t . Fig .3 shows the s o i l s t r a t a beneath the embankment andFig .4 the displacements c o r r e s ~ o n d i n g to ' end of cons t ruc t ion anda t a t ime cor responding to 1 .3 years l a t e r . In the main the abovement ioned t e s t s were des igned s pe c i f i c a l l y to s imulate r e a l pro to -type behaviour and thus may be considered to f u l f i l the r equ i r e -ments of Category I t e s t s .

There are numerous examples of Category 11 type t e s t s ,s ince in genera l the majo r i ty o f s o i l mechanics model t e s t i n g f a l l si n to t h i s ca tegory . One good example in Europe i s the l a r g esca le foot ing t e s t s Performed a t Kar l s ruhe Univers i ty repor tedby Leuss ink, Bl inde and Abel. They t e s t e d ins t rum ented founqat ionsup to 1.5 met res square , in a 9 x 9 x metre p i t f i l l e d withuniformly compacted sand (see Fig .S) . Due to the la rge s i z e o ft he i r model t hey were ab le to determine the normal pressu red i s t r i bu t i on beneath t he i r foo t ing in .g redt de t a i l .

The work on pass ive wal l s repor ted by Rowe and Peaker (1965)represents a c l a s s i c example of Category 11 type t e s t s . Theyt r ans l a t ed a ve r t i c a l wal l a t various angles to the hor izonta l i n tosand, observing the mobil ised angle of wal l f r i c t i on (0) , thenormal pre ssu re d i s t r i b u t i o n , load displacement r e l a t i onsh ips and


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? modes of f a i l u r e . Typical re su l t s fo r two d i rep t ions of w ~ l l movement i n to dense sand are reproduced in F igs .6(a ) and Cb).Some of the s t r e s s s t r a i n proper t ies of the sand ~ ~ p l o ~ d area l so shown in Fig .6 (c ) . Study of these f igures r evea l s th r eeimportant fea tures : (i) the importance of the diJ; eotion ofwal l movement, i . e . the wall which was t r an s l a t ed upwards ~ t 45to the hor izon ta l has a peak pass ive ear th pressure co e f f i c i en t K. Pof only 3.0 whereas the wal l t r ans la ted p p r o ~ i m t e l y h o r i ~ o n t l l y genera ted a peak K o f approximate ly 7.4 .

( i i ) the qu i t e d i f f e r e n t load displacement r e l ~ t i o n s h i p s fo r the two d i rec t ions of movement, and

( i i i ) the peak value of mobi l i sed obta ined by backana lys i s employing convent ional theory i s cons iderab ly l e s s thanthe peak observed in the plane s t r a in t e s t s , i . e . ~ m observedin wall experiments o f between ~ and 37 whereas peak measuredin fundamental plane s t r a i n t e s t i s approximate ly 43 9

Rowe and Peaker exp la in t h i s l a t t e r fea tu re qua l i t a t ive lyy pos tu l a t ing the mechanism of progress ive f a i l v re . r have

mentioned Rowe and Peake r s observat ions in some de t a i l , s incec l ea r l y in order to descr ibe quan t i t a t i ve ly the m ~ c h a n i s m ofprogress ive f a i l u r e appropr ia te Category I I I experiments need tobe performed.

Examples of Category I I I type exper iments , wi th c o h ~ i a n l e s s s o i l s , are shown in the work of ar inch Hansen (1953) who observed

r ~ l p t u r e modes for a wide va r i e ty of idea l i sed wal l p r o ~ l e m s andmDre recent ly in the work of But t e r f i e ld , Harkness and Andrawes(1970) who have observed the de ta i l ed displacement f i e l d s assoc ia tedwith the problem of the pene t r a t ion of a sand mass by a r ig id wedge.


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So-il mec;:hanics has now reaoh,ed a s tage in i tE ideve lopmentwhere the fundamental st:l:"E;lSS st:r;ain laws of engineer;i .ng SiQilsa re beginning to e under s tood . At the same t ime e n g i n ~ e r a reunder pressure to produce more econom-ic des igns and b e t t . r p re -d i c t i o n s of so i l s t r u c tu r e per formance , A p red i c t i o n of w h e t l l ~ ~

s t ruc tu re w i l l s t and up o r f a l l down, a l though v i t a l , i s nolonger adequate . There i s t h e re fo re g rea t need fo r experimeri tsJ the Category I I r t y p e which snould prove of g re a t as s i s t an ce

in the development of more so p h i s t i o a t ed methods o f ana lys i swhich may then pe brought i n to genera l use v ia C9tegory 1 1 a n dexper iments .

SOME TYPICAL RESULTS GF A CATEGORY I I IEXPERrMENT AT CAMBRIDGE

I bel ieve t h a t the major i ty of the model work performeda t Cambridge in the p as t decade under t he l ead e r sh ip of ProfessorRoscoe would be c l a s sed as Category Ill Roscoe 's objec t iveswere always to develop new and b e t t e r t h eo r i e s v i a new exper imentu lobserva t ions . Poss ib ly the most -important aspec t of Category I I Imodel exper iments of ~ o d a y i s t he d e t a i l ed observa t ion of s t r a i nphenomena. In order t h a t such obse rva t ions may be achieved iti s necessa ry to work wi th r e l a t i v e ly th in (6" 9" t h i ck) plilnt:s t r a i n models cmp loy ing t ~ s t tanks with LranSpdrent ' s i d es . Suchmodels alloVl the d e t a i l e d obse rva t ion of s o i l disp lacements byphotography or rad iography , however only a t the expense of i n t ro -ducing s ide f r i c t i o n e f f e c t s . These e f f e c t s may be minimised y

i t 'Illlc choice of mat e r i a l s and l u b r i can t s , but t hey may neverLe.: c,);;1plctely removed. A t y p i ca l t e s t f a c i l it y i s shown in Fig. 7


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which i s a photograph of a model wal l appa;t at1,.l'f? T h ~ wal l i s LJhigh apd the t e s t tank a.imensions 96 ~ 60 x 7 ~ With t h i sapparatus it i s p o s s i b l ~ with v a ~ i o u s modes of wal l movement,to o b ~ e r v e wal l p ressu re d i ~ t r ~ b u t i Q n s (both normal ~ n 4 shear) andthe detaiLed, s o i l displacement and s t r a i n b e h ~ v i o u r Typicals t r a in r e s u l t s for the case o f wal l r o t a t ~ o n qP01 .lt the top i n todense Leighton Buzzard sand are shown in Fig.S fo r t h r ee s t agesof ro t a t i on , i . e . e = 0 .5 , 0.95 and 1 ~ 4 ~ o ~ t ~ s p o p ~ i n g to S8, 83and 97 o f the peak load m e a ~ u r e d on the wal l . T ~ ~ f u l l l i necontours r ep re sen t values o f maximum shear s t r ~ i n and the brokenl i nes t r a j ec to r i e s of pr inc ipa l compressive s t r a in . Cons ider ingFig .8c it i s qu i t e c lea r t ha t t he re i s a ~ a r g e concent ra t ion ofs t r a i n a t the toe o f the w ~ l l and t ha t a sups tap t i a l t r a n s i t i o nzone of deformat ion or ig tna t es from t h i s p p i ~ t Fig.9 shows thecorrespondipg observed t r a j ec to r i e s of zero ex tens ion , i . e . s l i pl i ne s i nd i ca t i ng a wel l d e f i n ~ d ~ o n e of p l a s t i c deformat ion .t i s c lea r from these f igures t ha t the mode of f a i l u r e , termed

progress ive , occurs in t h i s exper iment . F i g s ~ l O and 11 show s imi la rdata for loose sand.

Typical s t r e s s r a t i o s t r a i n laws pb ta ined from the s impleshear appara tus fo r dense and loose Leighton B u ~ z a r d sand areshown in Fig .12 . Osing these r e l a t ionsh ips in conjunct ion withthe s t r a i n da ta shown in Figs .8 and 10 it w o u ~ d be poss ib le todef ine t he mobi l i sed shear , s t r eng th throughout the deforming zonesa t any s t age of defor rn-a t ion. Res t r i c t ing such an exe rc i se tothe cen t re l i ne of the t r a ns i t i on zone, i . e . taa l i n e pass ingthrough the peaks of the shear s t r a i n con tours , it i s poss ib l e t odeduce the mobi l i sed shear s t r eng th along the cent:t:'e s l i p l i n e .This exerc i se has been car r i ed ou t fo r the da ta on dense sandpresen ted in Fig .8 and the r e s u l t s are presen ted in F ig .13 . In


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t h i s f i g u ~ e t he ~ o b i l i s e d s t r e s s r a t i o % s t n ~ m o i s p l o t t e da g a i n s t t h e n o n ~ d i ~ e n s ~ Q n a l d t s t an ce a l6ng the c e n t r e $ l i p l i n eS The major p o in t pf i n t e r e s t in t h i s f i g u re i s t he c ~ r v e P Qf-I~ o r r e ~ p o n d i n g t o e 1 .4 , i e a t a p p ~ o x i m a t e 1 y p ~ k l o ~ d ontile wal l . Only t he sand a t p o iq t P h ~ s t h e f u ~ ~ y W o ~ ~ l i s e d peak

~ . t r e s s t a t i o . The sand to t h e ~ i g h t o f P, i . ~ curve PQ has y e tto m o b i l i s ~ ~ t s peak s t r e s s ~ a t i o w h e r e a s t he s ~ r t d t o t h e l e f t o fi i . e . curve OP, has passed beyond its peak s t r e n g t h and i s

c r i t i c a l s t a t e i p ~ i c a t epproaching t ~ e . s t r e n g t h . These c u ~ v e s t he danger i n h e r ~ n t i n c o n s t a n t ana lyses ~ n d ~ h e duqious n a tu reof ever assuJ; t l inga ; ful ly mobi l i sed lnsoils ~ r o b l e ; l l S

In o rd e r t o throw more l i g h t on t h e s t r a i n ~ e h ~ v i o q ~ int h i s problem it i s u se f u l t o r e p l o t t h e d a t a Sh wn in Figs.8aJ1 j 10 as t h e r e c i p r o c a l of shea r s t r a i n , i e ~ ag a in s t t he noo-MdiGlensional d i s t a n c e a long t he c e n t r e l i n e of the t r a n s i t i o n zone..M fo r each s t ag e of r o t a t i o n . The r e s u l t s a re shown in Figs .143nd 15 fo r dense and loose sand r e s p e c t i v e l y . These f i g u r e s a re

s u r p r i s ~ n g in view o f t he appa ren t ly complex s t r a i n behaviour~ c c u r r i n g in t h i s problem. It would appear t h a t t he s t r a i nl cnav iour i s adequa te ly desc r ibed a t each s t a g e o f wal l r o t a t i o nLy s imple l i n e a r r e l a t i o n s h i p s . ay p l o t t i n g t he wal l r o t a t i o n 8div ided by t he shea r s t r a i n , i e ~ a g a i n s t ~ it i s p o ss i b l e t oMo b t a i n s i n g l e apprOXimately unique r e l a t i o n s h i p s which a re shownin Figs .16 and 17 fo r dense and loose sand r e spec t ive ly ,

I f one could apply a s imple kinemat ic theory to the: ~ r G b l e m under co n s id e ra t i o n and could p r e d i c t r e l a t i o n s h i p s s i m i l a rto those o ~ s e r v e d then in c on junc t i on w i th an appropr i a t e s t r e s sr a t i o s t r a i n law one would a l so be a b l e to es t ima te the load-

~ ~ l l ct i sp lacement r e l a t i o n s h i p s . With t h i s aim in mind a s i m p l i f i e d


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approach t o p red ic t ing the l o ~ d ~ d i s p ~ a c e m e n t r e l a t i o n s h ip fort h i s problem w i l l be made in the next sec t ion . However, theobserved s t r a in d i s t r i ~ t i o n laws o f f igs .16 and 17 w i l l beemployed ra the r than p o s s i b ~ e pred ic t ions .

~ ~ I W E M A T I C PPRO CH TO THE SOLUTlONOF A PASSIVE E RTH PRESSURE PROBLEM

James ~ d arapsby (1971) postu la ted a s l i p l i n e f i e ld fora cons tan t d i l a t a t i o n r a t e mater ia l which with s u i t ab l e boundarycond i t ions al lows pred ic t ions of s t r a in d i s t r ibu t ions throughoutdetorming +egions of a sand mass. The essen t i a l fea ture of thes l i p l i ne f i e ld WaS t h a t the b o ~ n d i n g s l i p l i ne i . e . the s l i pl i ne beyond which t he re was no movement, was a log sp i r a lor ig ina t ing a t the toe o f the wall with i t s cen t re a t the topof the wal l as i l l u s t r a t e d in F i g . ~ 8 . The equat ion o f the sp i ra li s r = r o ~ t n v where r i s the radius from the top of the wal lto a poin t on the s p i r a l the angle of t h i s rad ius to theve r t iCa l and v the angle o f d i ~ a t a t i o n L e . v = s in 1 -; where~ and YM are the ins tantaneous volumetric and shear YMs t r a in r a tes re spec t ive ly . The sp i ra l por t ion cont inues as f a ras ~ = 45 ~ and the upper por t ion of the bounding s l i p l inei s assumed to cont inue as a s t r a i g h t l i n e inc l ined a t 45 - ~ to the h o r i ~ o n t a l su r face .

I t wil l now be assumed t ha t such a s p i r a l and s t r a i g h t l inedef ines the cent re s l i p l i ne o f the t rans i t ion zone, i . e . the s l i pl i n e along which the exper imenta l data i nd ica t e t h a t the shears t ra ins are a maximum for the problem of pass ive ro ta t ion of awal l about i t s upper edge. This assumption may be consideredreasonable s ince for the given mode of wall movement such a s l i p


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10.l i ne r ep re sen t s the poss ib l e l oca t ion of a k i n e m t i c ~ l y admiss ib le '*s t rong displacement d iscon t inu i ty , and hence a l so the l oca t ionof the l a rges t s t r a i n s . Since the s t ra ins are l a rge , s i gn i f i c a n tmobil ised shear s t rengths ~ e a l so impl ied and hence, in ordert ha t s t r e s s equ i l ib r ium be mainta ined, the mater ia l e i t he r s ideof such a s l i p l i n e mllst a l so su f fe r l a rge s t ra ins in order todevelop s u f f i c i e n t s t reng th . Thus the s l i p l i n e can be taken torep resen t the cent re l i n e f a subs tan t i a l t r a ns i t i on zone. Theprec i se boundaries of the t r ans i t i on zone are not e a s i l y def ineds ince they are dependent not only on the kinemat ics of the problembut a l so upon the s t r e s s - s t r a in proper t i e s of the so i l . However,it i s c lea r tha t the s t r a in s in the t r a ns i t i on zone must be sucht ha t s t r e s s equi l ibr ium i s maintained along any s l i p l i ne wi th in itFor s impl i c i t y it wi l l be assumed t h a t a fan of s l i p l i nes or ig ina tesa t the toe Of the wal l , with an inc luded angle .of 45 andt h a t the fan be i nc l ined syme t r i ca l ly with r e spec t to the cen t res l i p l i ne . The oute r s l i p l ines of t h i s fan are con$idered to bethe bounding s l i p l i nes of the t r a ns i t i on zone, i . e . as por t rayedin Fig .19 . Thus the upper bounding s l i p l ine i s def ined by a vlog s p i r a l with cent re 02 ' the cent re s l i p l ine of the t r a ns i t i onzone by a v log sp i ra l with cen t re 1 and the iower bounding s l i pl i ne by a v log sp i ra l with cen t re 03. The above method o fdef in ing the t r ans i t i on zone and the l ip l ines with in it i ssomewhat a rb i t r a ry ; however, fo r the problem under cons idera t ionit produces a zone of s l i p l i nes s imi l a r to those observedexper imenta l ly .

The s o i l with in the t r ans i t i on zone may be a r b i t r a r i l ydivided in to t r i angu la r elements as shown in Fig.20. I f theangles of the r e su l t an t s t r e s s vec tors on the three s ides of each* Both t he log sp i ra l and s t r a i g h t l i ne por t ions of t h i s s l i p l ine

are ind iv idual ly kinemat ica l ly admiss ible for a constant v mater i a l ,however for the combination to be so the mater ia l above t he s l i pl ine must su f fe r some deformat ion.


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11.

t r i angu la r element are known, then by cons ider ing the fo rceequ i l ib r ium of each element and commencing the ca lcu la t ions fromthe uppermost t r i angu la r element , i . e . element 1 l abe l l ed HDJin Fig.20(a) t i s poss ib le to e s t a b l i sh the magnitudes o f ther e s u l t an t fo rces ac t ing on every p o r t i o n of the s l i p l i n e s T BCDand TEFGHJ. Subsequently the r e su l t a n t fo rces ac t ing on ap a r t i cu l a r s l i p l i n e may be summed v ec to r i l y and by co n s i d e ra t i o nof the fo rce equ i l ib r ium of the b l o c k of mater ia l above t h a ts l i p l i n e the m ~ g n i t u e and d i r e c t i o n of the r e s u l t an t force onthe wall may be determined , i . e . as shown in Fig .20(b) .

The advantages o f such a method of ca lcu la t ion are ( i) t h a tboth magnitude and di rec t ion of the r e su l t a n t wall force aredefined, whereas in most convent ional methods the angle 0 has tobe assumed, and ( i i ) th a t d i f f e re n t mater ia l proper t ies may beassumed fo r each t r i angu la r element spec i f i ed in the t r a ns i t i onzone. In a convent ional ca lcu la t ion method t i s usual ly assumedt h a t l ines of s l i p are a l so planes of maximum s t r es s ob l iqu i ty ,and thus the angles of the s t r e s s vec to rs along such a l i n e a reusual ly assumed to be a t to the .normals . In the presen t c a l -cu la t ion s ince the s l i p l i ne s are l ines o f zero ex tens ion t hes t r e s s vec to r wi l l be inc l ined a t t to the nOrmal as shown inFig .20(b) . The re l a t ionsh ip between s i n ~ the mobi l i sed shear ing.re s i s t ance , v the d i l a t a t ion r a t e ( i . e . sinv = land t i s given

~ by equat ion 1 .s i n ~ cosvmt an t = 1 s i n ~ m s i n v

which i s obta ined d i r ec t l y from Mohr s c i r c l e s of s t r e s s ands t r a i n r a t e by assuming t ha t axes of s t r e s s and of s t r a i n r a t eare co inc iden t .


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12.

Employing the empir ica l r e la t ionsh ip YM = 1.47in the case of dense sand, t i s poss ib le to assess an averagemagnitude of the shear s t r a i n appropr ia te to each t r i a n g u l a relement . Using these magnitudes in con junct ion with a s t r e s sr a t i o shea r s t r a in law, a value of mobil ised shearing re s i s t ancemay be def ined . Thus S fo r each e lement may be def ined fo r anyspec i f i c angle of wal l r o t a t i o n by i n s e r t i n g the appropr ia tev i svalues of and v (/assumed cons tan t and equal to 20 for densemLeighton Buzzard sand) i n to Equat ion 1 . In the case of loosesand the empir ica l re l a t ionsh ip YM = 1.16 and v = 0 have beenemployed. The angle of the s t r e s s vec to r on those s ides of at r i angu la r element which are common to two elements , such ass ide OH (Fig.20(a i s def ined from the Mohr s c i r c l e of s t r e s sappropr ia te to the r i g h t hand element fo r the elements as drawnin Fig.20. The r e su l t s o f a se r ies of ca lcu la t ions using themethod out l ined b r i e f l y above are given in Figs .21 and 22toge ther with exper imenta l observa t ions .

Fig.21 presen t s a plo t of passive ea r th pressure co e f f i c i en tK mul t ip l i ed by sec 6 versus angle of wall ro tn t ion e. Fig.22ppresen ts mobi l i sed angle of wal l f r i c t i on versus B

In both diagrams the fu l l l ines r e l a t e to the theore t i ca lca lcu la t ions and the broken l i ne s to the oLservat ions .

Consider ing dense sand f i r s t the degree of cor re l a t ionup to peak between observed and pred ic ted mobi l i sed ear th pressurecoef f ic ien t i s good. The cor re l a t ion beyond peak i s poor, i . e .por t ions of the curves PQ and PR are qui te unrelated; however,t h i s may have been ant ic ipa ted s ince beoyond peak t i s knownt h a t s t rong d i s co n t in u i t i e s form within the sand mass and hence


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13.

the empir ica l s t r a i n r e l a t i o n s h ip YM ; 1.47 employed fo rdense sand i s no longer appl icable . When such s t rong d i s co n t in u i t i e sform the s t ra ins become very l a rge and the mobi l i sed ~ h e r i n g r es i s tance wi l l quickly drop to the c r i t i c a l s t a t e value .

To some ex ten t the good agreement between tne theory andexperiment over curve por t ions P must be considered fo r tu i touss ince it i s known t h a t the exper imenta l ly determined pass iveea r th pressure coef f ic ien t s inc lude the ef fec t s of t ~ n k s idef r i c t i on . Nevertheless , in view of the magnitude of the assumpt ionsmade and the s impl ic i ty of the ca lcu la t ion procedure the degreeo f cor re l a t ion i s encouraging .

Considering the r e su l t s fo r loose sand the degree ofco r r e l a t i o n a t l a rge angles of wall ro t a t ion i s good but d e t e r i o r a t e sin the ear ly s tages o f wall movement. In t h i s case one wouldexpect good o r r e l ~ i o n a t peak s ince s t rong d i s co n t in u i t i e s donot form a t large wall r o t a t i o n s . However, poorer co r r e l a t i o nwould be expected a t the smal le r angles of wal l movement s ince iti s known t ha t the loose sand su f fe r s subs t an t i a l con t rac t ionduring the ear ly s tages of shear deformation i . e . < 0) , whereasfo r s impl i c i ty in the loose ca lcu la t ions was assumed equal tozero . The corresponding mobil ised angle o f wall f r i c t i o n datapresen ted in Fig.22 indica te a good cor re l a t ion for the loose sandand a much l e s s sa t i s f ac to ry cor re l a t ion fo r the dense sand.

CONCLUDING REMARKS

My primary objec t ives in t h i s paper have been to c l a s s i fymodel t e s t ing dependent upon the immediate goals of the t e s t s , andto i nd ica t e the value of the more academic Category I I I t e s t . t


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14.

was s t a t ed t h a t Category t e s t s in genera l a re d i f f i c u l t toperform with in the l ab o ra to ry due to problems assoc ia ted wi thmodel l ing the s o i l . H o w ev er cen t r ifu g a l mo d e l t e s t i n g i sexpected to increase the a t t r a c t i o n o f ~ type of t e s t s ince tal lows the use of pro to type so i l s a t pro to type s t r e s s l ev e l s .

From the po in t of view o f advancing our knowledge anddeve loping new and b e t t e r methods o f ana lys i s Category 11 andCategory I I I t e s t s of fe r the most p r o f i t ab l e approach. In thelong te rm t i s an t i c ipa t ed t h a t f i n i t e element ana lys i s employingl ab o ra to ry determined so i l parameters w i l l be ab le to give accura tepred ic t ions of the behaviour o f complex fu l l s ca l e pro to types t ruc tu res ; however before t h a t day can a r r ive model t e s t i n g hasa v i t a l ro l e to perform by providing data fo r de ta i l ed comparison jibetween pred ic t ion and r e a l i t y .

In the l a t t e r par t of the paper t was shown how aCategory I I I type experiment could shed l i gh t on the phenomenaof p ro g res s iv e f a i l u r e . Subsequent ly an empir ica l approach top red i c t the load displacement r e la t ionsh ip fo r the problem cons ideredwas made. The r e s u l t s i l l u s t r a t e the l imi t a t ions o f the s impleapproach; however they a l so i l l u s t r a t e the importance of t ak ings t r a i n s i n to cons idera t ion . There i s a ser ious gap in ourt h eo r e t i c a l and exper imental knowledge of t he kinematic behaviourin so i l s problems which urgen t ly needs to be f i l l e d . There a renumerous s t a t i c s t r es s f i e ld so lu t ions to s o i l s problems whichemploy a cons tan t i d ea l i s a t i o n but such so lu t ions usual ly takeno account of the kinematics o r the ef fec t s of s t r a ins (seeDavis (1968)) . There are prec ious few complete kinematic so lu t ions and so lu t ions which sa t i s fy kinemat ic cons idera t ions s t a t i c s t r e s s


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15.

f i e l d requi rements and t h e r e a l s t r e s s s t r a i n laws o f s o i lare a lmost unknown. Only when a l l t h r e e requi rements a res a t i s f i e d s imul t aneous ly wi l l s a t i s f a c t o r y load d isplacementp re d i c t i o n s be pos s ib l e .

Thus a more de t a i l ed t heo re t i ca l and exper imenta l s tudyo f s o i l kinema t i c s v i a Category I I I t ype expe r imenta t ion i sl i ke l y to prove a reward ing and va luab le exerc i se .

CKNOWLEDGEMENTS

The au thor wishes to acknowledge a deb t o f g r a t i t u d eto the l a t e Profes so r Roscoe fo r h i s con t inuous i n sp i ra t i onand encouragement over the l a s t decade. t was both a p leasu reand a p r i v i l e g e to work as a member o f h i s r esea rch team. amsure t ha t by con t inued perseverance we may u l t ima te ly achievethe goa ls t h a t Ken Roscoe pursued in such a ded ica ted f ash ion .

a l so wish to ex tend my thanks to a l l t he members o f t h eCambridge Soi l Mechanics group and Engineer ing Department whohave a s s i s t e d me in prepara t ion o f t h i s paper .


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REFERENCES

BVTTERFIELD R. , HARKNESS R.M., &ANDRAWES K.Z. (1970)"A ~ t e r e o p h o t o g r a ~ ~ e t r i c m ~ t h o d for measuring disp lacementf i e ld s . " G ~ o t e c h n i q u e 20:3:308-314.DAVIS E.R. (1968) "Theories of p l a s t i c i t y ~ n q the f a i l u r e o f

s o i l masses ." Soi l Mechanics Selec ted Topics , Ed.K.I .Lee ,But terworths .ENOICQTT L.J . ( l971) "Cent r i fuga l t e s t ing of s o i l models ."Ph.D.Thesis , Cambridge Univers i ty .HANSEN, J .Br inch (1953) "Earth pressure ca lcu la t icms ."Danish Technical Press . pp 271.

JAMES R.G. ( l965) "St ress and s t r a i n f ~ e l d s in sand."Ph.D.Thesis , Cambridge Univers i ty .JAMBS R.G. &BRANSBY P.L. (1971) "A ve l oc i t y f i e l d for some

pass ive ear th pressure problems." G ~ o t e c h n i q u e 21:LEUSSINK H., BLINDE A., &ABEL P. (1966) "Versuche llber d ie. s o h l d r u c k v ~ r t e i l u n g unte r s ta r ren G r ~ n d u n g s K ~ p p e r n auf KohArsionlosens Sand." V e r ~ f f e n t l i c h u n g e n des I n s t i t u t e s fUr Bodenmechanik und Felsmechanik derTechnischen Hochschule Fr ider ic iana U n i v e r s i t ~ t Kar ls ruhe .LORD J .A. 1 9 6 ~ "Stresses and s t r a i n s in an ea r t h 9 re ssu reproblem." Ph.D.Thesis , Cambridge U n i v e r s ~ t yLYNDON A. & SCHOFIELD A ~ N (1970) "Centr i fugal ~ o d e l t e s t o fa sho r t - t e rn fa i lu re in London c l ay . " Technical ~ o t e Geotechnique 20:4:440-442.ROCHA M. (1957) "The p o s s ib i l i t y of so lv ing s o i l mechanicsproblems by the use of models. Proc .4 th rnt .Conf .Soi l Mech., London, 1:183.ROSCOE K.H. (1968) "Soi ls and model t e s t s . " Journal of S t r a inAnalysis Vol .3:1:57-64.ROSCOE K.H. (1970) "The in f luence of s t r a ins in so i l mechanics ."10 th Rankine Lecture , G ~ o t e c h n i q u e 20:2:129-170.ROWE P.W. PEAKER K. (1965) "Pass ive ear th pressure measurementsGeotechnique 15:1:57.78.SKEMPTON A.W. &HUTCHINSON J . (1969) "S tab i l i ty of natura l s lopesand embankment foundat ions ." St a t e of the Art Vo;l.ume, P::::::.

7th In t .Conf .Soi l Mech & Found.Eng. , Mexico, 2 9 l ~ 3 4 0 . SUTHERLAND H.B. (1965) "Hodel s tud ie s for sha f t r a i s ing through

cohes ionless s o i l s . " Proc. 6 th In t . Conf. Soi l Hech. ,Montreal , 11:410-413.


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'WdNGg

H"1


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~ ~ - - - - - : ~ ~ - ~ ~ ~ -- "OP 501 L~ SI LT

, . ,i \ , :, 1\

' i / 0 / ~ / / / 2 / FIRM CLAY= ; : . = ~ ~ ~ ~ _ : -==-==:::-c-. .. ': _ -' _ -- -: _

, \ I ~ 1/_,\1/... ~ \ J / ; . -= - - PEAT~ y u ~ ~ 5 I T Y CLAYla C TEGORY TEST SIMULATI NG REAL PROTOTYPEw

. .. ". . . ..

.UNIFORM

. ,SAND. . .

Cb C TEGORY II TEST IDEAL\ZED SM LL PROTOTYPE

c - ..

......................I 0 0 . / JXIS OF . ' I , UN I FORM ' . .77 /ROTATION . WALL. 1 'SAND' : . " / /I . / / .I . " ~ / ' .. ' I ' ' / ~ ,

I I ' ' I . " ,__::--:;:7/ :,__ __ :;;7 ~ C E . ~ /. , . . f P . . \ \ . . . I J I ~ S ~ ~ - - - - - ' ')1/ - - ' : ' ; : ' - - : : : : - - . ' . .

Ile) CATEGORY ill TEST IDEALISED RTIFICI L PROTOTYPEFIG 2 MODEL TEST CATEGORI ES.


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Scale.5rn

\ A,' ' 'c ;-- ----

- .. ----- - - - - - - - - - - - - ~ ~ ~ ~ : = ~ ~ ~ ~ i ~ ~ T -. . ~

Key to soilslembankment f i l l

,.", topsoil'1 firm brown clayC sof t brown clay_ Section of modelsoft grey s i l ty clay.- s t i f f u s t ~

- peat /sof t blue s i l ty clay soft s i l ty ' ~clay r=---of t dark s i l ty clay .e.. peat 't '... blue sand soft s11 ty... firm blue clay clay

"-:/,,, weathered Kimmeridge Clay

,Figure 3 Soil strata beneath triol embankmlZnt at King's Lynn


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Outline i s p l ~ e r n e n t s Prototype scale

5rn. lm.

10cm.Moriel scale

2cm.

, , . ,/J11\ \ \.. , 4 " . ..... o , /IJ \\ .. , ..

.. .. -I ( .. -- .11 .. .. .

displacements at 'end of construction'

/ / / / / \ \ \ \ - "- ' .,


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sc )

I

Eoto..DHYDRAULIC JACKPRESSURE

T R A N 5 D L J C ~ R FOUND TION

.i \ .

I_ . . E.. ' " ' ' _ S ND . . - 0............. : ......................................: g.

_ . . ' " " I ... ' " . , . ' . . . . I - - 4- _ ~ .... ~ j. ,_._I -. . . i m ,OmJ

FIG 5 KARLSRUHE UNIVERSITY LARGE FOOTINGAPPARATUS
http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80http:///reader/full/%E5%AE%AE..%E5%AE%AE..%E5%AE%AE......................%E5%80%80


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I


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Fig 7 odel ea r th pressure appara tus and recordingequipment showing instrumented wall OB


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1

sI

lO

O


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SAND SURF CE. - . . . . . . . . ~ -----0AXIS OF WALL .-1' ZERO EXTENSION TRAJECTORIESROTATION PRINCIPAL COMPRESSJVE STRAIN TRAJECTORIES

(0)5

P1 ;.-058 /8

/

(b)9 - 9sDP~ 8 3

.

I(C) I I_ .4 Ip. IP r n ~ 097

11I II I l ~ ~~

-

FIG. 9. T?A,iECTOPIFS OF ZER() ~ } T F . N : : ; l Q N A N ~ t B ~ N C l PAL. COMPRESSIVE STRAIN FOR TEST LE (eo O 0550) -JAMES /965.


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SAND SURFACEo

00

MAX SHEAR STRAIN 0.159a) IH RHiEIlT ~ 1 B=0_1 0

Or-I ~ ~

ii2


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Oj

MAX SHEAR STRAlU 0 573C) CUMULATIYE STRAINS AT 8=3 .. . , ...

0,...-, : . . . . . -

MAX SHEAR STRAIN 1 1B3(d) CUMULATIVE STRAINS

FIG. 10 CUMUl.ATIVEAT B=5 .SHEAR ST.RA1N5 .FOR TeST .

eo : 0 70 1..0RD i9G9 ..


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O ~

) \II I/ - - - TRAJECTOQIES/ . / I . 1 / I I I I / / O ZERO EXTENSION/

T ~ J E C T O R I E S O COMPQESS\\'E T ~ ~ '

B .. .-a) BASED ON CUMULATIVE STRAINS AT e=2

0,.... ~ . . . . . .t

III

II

I.//r/. /

I7

--11 b) BASED CUMULATIVE STRAlHS AT 8

TRAJECTORIES OF ZER.O EXTENSiON AND PRINCIPALCOMPR-ESSIVE STRAIN. TEST M.D;(eo =o70) LORD 1969


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4 I I

5

6

'8.D0E'E)... 7 / DENse SAND.- /)0

I / LOOSE SAND

, I I I

J 3 4SHEAR STRAINFIG. 12. TVPICAL STRESS RATIO STRAIN RELATIONSHIPS FOR SAND FROM

THE S\MPLE SHEAR APPARATUS- ~ = = - ; = ; - - - - - ~ ~ - ~ - ~ - - - - - - - - - - - - - - - - ~ - - - - - - - - - -


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-8

p

7

t55i.n 'fmOb )

6 Q

5 1

1 I4 0

FIG. 3 MOBILIZED SHEAR STRENGTHLINE OF TRANSITION LAYER

I20SH

DISTRIBUTIONS LONG CENTR:FOR TEST. LE to =-55


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180

160

DENSE SAND V -a- 20 .4

120 tHt110

r80

60

40

20 f-

---- -I _/ 0 5

HFIG. 14 SHEAR T F \ ~ I N RELATIONSHIPS ON THE CENTf\E LINEOF THE TRANSITION LAYER FOF TEST.LG -eo = 53)

2-0


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tHj120

LOOSE SAND v: : 0 01I

l M8

6

4

2

FIG_ 5

-a S 2 0H

SHEAR STRAIN RELATIONSHIPS ON CENTRE LINEOF TRANSiTION LAVER FOR TEST tvi D (.fo 0-70


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2-0

- i M l = 68 ~ olVi e YJI 1 = 47 He5

'-ao o V

VI

'0 SH

FIG 16 SHEAR STRAIN RELATIONSHIP ON CENTRE LINEOF TRANSITION LAYER FOR TEST LE to =-55)

2'0


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(

o A

/

= 0 86J' .

Le. I M = 1-16A

LOOSE SAND

i:8-)/, /0

1M

5

/0 SH

FlG 7 SHEAR STRAIN RELATIONSHIP ON CENTRE LINE OFTRANSITION LAYER TEST. MD eo = 0-70)


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as O 45 ~ 55 (45 ~

vFIG. 18 PREDICTED RUPTURE SURFACE M E C H A N I S ~

ND N OBSERVED RUPTURE MECHANISMJAMES 1965) IN DENSE St-\ND FOR W LLROTf\TION BOUT THE TOP,


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.s

RIGID

V45-

x . 4Y2_ \ . ~

o v O ~ 3 _ ~ - s \ t : : J~ Q - ~/

1/AXI5 OF RO",ATlON\ OF WALL

0 . SAND SURFACE

\IT45 ~ )

FIG 19 GEOMETR C CONSTRUCT10N OF THE TRANSITIONZONE FOR A CONSTANT V MATERIAL,


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A~ Wtan b = in ~ o s "I - Slrt ~ n V

R,

R2w

,R8

OK


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-------

12

18 I 0IG

14

(410UJ

:0

86

4

CALCUL,4,TED P O N ~ THEORY DENse

Q

fp

/; \ TH1

K _P Cosp - L Y ~

\ p / 5 (SOil. DENSITY)\ \OBSERVED DENSE TEST LE)

\ .~ .~ _, THEORV LOOSE

L.OOSE TEST M D)

I I I0 : 2 3 4 5FIG.21. PASSIVE EARTH PRESSURE - VVALL

ROTATION. RELATIONSHIPS.


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30THEORV DENse

LOOg ~ ~ R V LOOSE

2 5

10FIG 22 MOBILIZED ANGLE OF W LL FRICTION-

W LL ROT TION REL TIOf\lSH tPS .

Documents

Some Aspects of Soil Mechanics Model Testing