arma-91-549_stress and behavior of material under direct shear

8/12/2019 ARMA-91-549_Stress and Behavior of Material Under Direct Shear

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Rock Mechanics s a Multidisctphnary cience, Roegiers ed ) 1991Balkema, Rotterdam ISBN906191 194X

Stress and behavior of material under direct shear

Anthony . annacchioneBureau of Mines, Pittsburgh esearch enter, a.

Luis E.VallejoUniversity f Pittsburgh, a.

ABSTRACT: Material shear strength is among the most impor-

tant geotechnical parameters used in the design process forengineers. For soils, soft rocks and rockfills the deter-mination of the shear strength properties is often accom-plished through the use of the direct shear test. Unfortu-nately, much controversy exists concerning the stress andstrain distributions, strength calculations and failureprocess within the direct shear test.

The objective of this study was to investigate the effectof material properties on material behavior under non-uni-form stress and strain conditions in the direct shear testusing the finite difference numerical technique. This re-search illustrated the effects of progressive failure withinelastic-plastic and strain softening materials on shearstrength. In particular, this paper describes the numericalsimulation of a well documented earth material within thedirect shear test. Within an individual material propertymodel, the effects of changes in stiffness, dilatancy, andstrain dependent yielding were identified and discussed.The analysis of these tasks allows for greater insight intothe behavior of materials in the direct shear test so thatmore realistic material properties can be determined.

1 THE DIRECT SHEAR TEST

The direct shear test is a procedure in which a specimen isconfined within rigid, fixed rotation frames and caused toshear on a plane. The specimen is generally elongated sothat the plane of shear is along the long axis. The con-finement within the specimen is produced by the applicationof a force normal to the plane of shearing and by the bound-aries of the frame (Figure 1). The shearing process isinduced by the displacement of the upper half of the solidframe with respect to the lower half. The normal stress(o.) and horizontal shear stress () acting along the fail-ure plane are calculated from the forces applied to thedirect shear box. This test is intended to force specimensto fail along a predetermined plane, the area of which isconstantly reduced as failure progresses.

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In this paper, the shear constantstrength of a material is horizontaldefined as the highest velocityaverage shear stress (?)across the plane of shear-ing. Stiff, dense oroverconsolidated materialhave a distinctive peakshear stress conditionwhich separates elasticfrom yield behavior.Yield occurs when there is

a departure from linearlyelastic behavior, i.e.when some of the defor-mation becomes irrecov-erable. Soft, loose, ornormally consolidated

materials experience agradual increase in shear

(7orous material

Itra[lingl I/ I I I I I I leadingedge ' ' ' ' edge

h}/ )/sher'g'ooel, ,/'/ /'/'1Figure . - Cross-sectional viewof the direct shear test showingthe rigid frame and shearingplane and the directions of dis-

placement and normal stress.

stress as deformation occurs until a residual shear strengthis achieved. When the residual shear strength is reached,the specimen undergoes ductile deformation. Ductile defor-mation defines the condition when materials can sustainfurther permanent deformation without increasing load-carrying capacity.

Once the shear strengths are known for a number of differ-ent normal stresses, a plot of shear versus normal stresscan be made. Drawing a straight line through these pointsallows for the evaluation of the strength parameters ( andC) used to define the linear Mohr-Coulomb failure criterion.

2 CONTROVERSY SURROUNDING THE DIRECT SHEAR TEST

The direct shear box was first utilized by Alexandre Callinin the 1840's to aid in the analysis of slope stabilityproblems (Skempton, 1949). Through the years, many modifi-cations and improvements have been made to the test withouteliminating its simplicity. Thus, it has become one of themore popular means of characterizing shear strengths of

earth materials. However, there has been a storm of contro-versy concerning the material strength at failure and modeof failure associated with the test.

The stress and strain occurring within the specimen havelong been recognized as non-uniform (Terzaghi and Peck,1948; Hvorslev, 1937). The major causes of the non-uniformstress conditions are the moment force resulting from theapplication of load about the shearing plane and the effectsof the propagation of peak stress into the interior of thesample. Saada and Townsend (1981) stated that at everypoint inside the specimen and along the plane of relativemotion there is a different state of stress with different

orientations. Exact calculation of the principal stressesat points within the specimen have to be made based uponcertain assumptions, since only the measurements of thevertical load applied to the top and the horizontal load

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applied through the side of the direct shear box are known.Because the state of stress at the point of failure is un-known, a precise determination of the Mohr-Coulomb failureenvelope is not possible.

The second controversy surrounds the mode of failure ex-isting within the specimen. As stated earlier, the calcula-tions of the normal and shear stresses occurring within thedirect shear box specimen are based upon the corrected sur-face area of the shearing plane. Morgenstern and Tchalenko(1967) showed that by the time the peak strength for someclay material was reached, a very irregular failure zoneextended across the shearing zone. As the displacementscontinued, the cracks multiplied in a discrete sequence andat diminishing positive angles to the horizontal, forming acontinuous zone separating the two halves of the directshear box.

Another form of behavior during failure has been suggestedby Vallejo (1982). His model proposes that for brittle

materials, cracks propagate across specimens at angles con-trolled by the tensile strength properties in response tothe principal stresses at the tips of the cracks. Vallejo(1987) developed a mechanism of crack propagation understatic loads as support for his model. The results of thisresearch point to the importance of pre-existing cracks inthe development of the failure plane and, therefore, in thestrength of brittle materials.

3 MODELING THE DIRECT SHEAR TEST

In an attempt to address the controversial points of thedirect shear test, a numerical modeling exercise was initi-ated to investigate the influence of non-uniform stressdistributions on material property conditions and strengthcalculations. The validity of the modeling technique wasproven by reproducing the peak and residual strengths of awell documented Walton Wood Clay (Skempton, 1964). Numerousdirect shear tests over a wide range of effective normalstresses indicated the cohesion (C) of the Walton Wood Claydrops from a peak (Cp) of 0.0153 MPA (2.22 Psi) to a residu-al (Cr) of zero, while the angle of shear resistance ()

drops from a peak (p) of 21 to a residual (r) of 13 .A 5 cm (1.97 in) long by 3.4 cm (1.34 in) high discritizedFLAC model was constructed to simulate the horizontal dis-placement of the top half of the direct shear box over astationary bottom half. FLAC is a two-dimensional explicitfinite difference code which can simulate earth materialbehavior which undergo plastic deformation when their yieldlimit is reached (Itasca,1989). During the first 2000 time-steps, no horizontal displacement of the upper half of thedirect shear box was allowed. This caused the stress fieldwithin the model to come to equilibrium in response to theapplied vertical pressure along the top row of elements(Figure 2). A.constant horizontal velocity of 0.5e-6 m/swas applied to the grid nodes on the left and right outsideedges of the upper half of the box. Depending on the mate-rial properties utilized in the model, anywhere from 4,000

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to 24,000 time-steps wereneeded to fully evaluatethe peak and residualshear strength properties.

A number of differentmaterial models were uti-lized to determine whichmodel and properties al-lowed for the closestsimulation of shearstrength. In all, simula-tion with three elastic-plastic and twelve strainsoftening material modelswere completed. All ofthese models utilized a

peak cohesion (Cp) of0.015 MPa (2.22 Psi) and

an angle of shearing re-sistance of 21 . For thestrain softening models,once plastic strain oc-

P

\ % / \ \ / /

Constant velocityConstant stress

Fixed points

Figure Z. - Displacement of themodel grid during simulation ofthe direct shear test.

curred, these values drop to their residual levels listed intable 1. The linear softening characteristics were assignedin the program and are listed in column 6 of table 1.Poisson's Ratio for all simulations was 0.3.

Table 1. - Model material properties (values in MPa)

No. E ,0 ,o C, E,% o. Time-step ? 7, 7,A .138 3500 .056 .032B 172 13 10 0 2 .207 3600 .079 .048C .276 4000 .100 .064

D .138 10000 .041 .031E 17.2 13 10 0 2 .207 14000 .056 .047F .276 18200 .073 .062

G .138 2700 .063 .063H 172 21 0 .015 NA .207 3100 .087 .087I .276 3500 .112 .112

J .138 2900 .040 .031K 172 13 10 0 .1 .207 3200 .056 .047L .276 3500 .070 .062

M .138 3200 .060 .031N 172 13 0 0 2 .207 3600 .082 .047O .276 4000 .103 .062

Note - f, Number f FLAC ime-steps at p and C,; $ NA, Does not apply

4 FAILURE OF MODELED MATERIALS UNDER DIRECT SHEAR

In this analysis, failure propagation is evaluated through

the development of zones of intense deformation. Tensilefailure and corresponding crack propagation may also be im-portant in brittle materials under direct shear, but werenot addressed in this study. However, dilation (changes in

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volume) of the failed material can be evaluated. The dilat-ancy of the specimen in response to either shear or tensilefailure is needed to simulate the behavior of broken materi-al along the failure zone.

Shear failure is assumed to be initiated when the deforma-tion patterns within the model suddenly focus along a narrowzone. Therefore, the alignment of predicted rapid deforma-tion zones with the observed shearing zones would help toverify test results. This verification was accomplished byanalyzing the magnitude and distribution of plastic strainat different failure stages.

Prior to the specimen in

Testachievingeak ii ---trength, the horizontalshear stress was concen-tratedlongherailing

edgef he hearox.Howeverueo he oarse- . . ........asa of the grid, contoursof shear stress could notbe sedo dentifyhe ' -- ....... I 'ocations of shear bandpatterns. Failure zoneswere best identified bycontouring the percentageof plastic strain (Figure Figure 3. - Percent plastic3). This figure indicates strain contour iccpache prior tothat failure zones would peak strength conditions fordevelop from either end of Test B.the direct shear box priorto reaching peak strength. At peak strength conditions, thehorizontal shear stress was concentrated closer to the lead-

ing edge of the direct shear box. At this point, deforma-tion propagated across the entire shearing plane (Figure 4).The location and orientation of these plastic strain con-tours corresponds well with laboratory observations of shearplane development (Morgenstern and Tchalenko, 1967).

Another important behavior exhibited during failure in thedirect shear test is dilation. Unlike linearly elasticmaterial, a non-linear material does not preserve specimenvolume. This process was

firstotedorranularaterialyReynolds i i i i --- i- i . . -,.................. .... ... ....(1885) as shear dilatancy.He eferred o dilatancyas the change n volumeassociated ith shear i ... ----+---*5-i---]distortionfzones ithinspecimen. entHansen(1958) extended his theo-ry by developing a parame-ter for characterizing adilatant material. He

referred to this parameter L ...Las the dilatancy angle Figure 4. - Percent plastic(), which is the ratio of strain contour iccpache at peakplastic volume change over strength conditions for Test B.

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plastic shear strain. For many soils, concretes and rocks,the dilatancy angle is thought to be considerably smallerthan the angle of shearing resistance (Vermeer and de Borst,1984). Therefore, a dilatancy angle of =10 was used inTest B, C and D (Table 1).

The above theory suggests that when shearing is initiated,most materials will show signs of dilation. However asshearing intensifies, the material volume changes shoulddiminish with a corresponding decrease in the dilatancyangle. Therefore, a second evaluation was performed todetermine the effect of dilatancy angle decrease (r=0 ,r=13 ) on strength (tests M, N and O, Table 1). It shouldbe noted that a decrease in dilatancy angle did not signifi-cantly influence shear strength.

The effect of dilatantbehavior was found to be

important in reproducingobserved behavior of mate-

rials under direct shear.Prior to peak strength,only the edges of the spec-imen fail, causing verysmall amounts of volumet-ric increase within theleading and trailing edgeelements. At peakstrength, the materialshowed a much greater Figure 5. - Displacement vectorsvolumetric increase, corre- at residual strength conditionssponding to the expansion for Test B.of the shear plane. Ifthe volumetric increase within the failed zones was pre-served after the residual strength of the material wasreached, almost all of the specimen rotation, discussed infollowing section, was overshadowed by the increased volumeof the sheared zones (Figure 5). However, if the dilatancyangle was allowed to decrease to zero (test M, N and 0), thedisplacement vectors eventually lost most of their verticalcomponents. This process would accurately simulate the lossof material volume changes associated with the intenseshearing of the specimen.

5 STRESS PROFILE ANALYSIS FOR MATERIALS UNDER DIRECT SHEAR

Horizontal load, applied at some distance above the plane ofshearing, rotate the material Within the direct shear box,causing a non-uniform stress profile. This non-uniformstress distribution is further complicated by the progres-sive failure patterns produced by the elastic-plastic andstrain softening material models.

The non-uniform vertical and horizontal stresses producednon-uniform shear stress profiles at peak strength condi-

tions for both the elastic-plastic (Test H) and strainsoftening (Test B and N) material models (Figure 6) [Note:Test E and K show effects of lower Elastic Modulus and willbe discussed later]. In both of these material models,

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maximum values of thehorizontal shear stress

occurred in conjunctionwith the trailing por-tion of the shearingzone prior to reachingpeak shear strengthcondition and closer tothe leading portionbeyond peak shearstrength conditions.An example of thechanges in the horizon-tal shear stress pro-files prior to (time-steps 3000 to 3400) andat peak stress (time-step 3600) conditions

are shown in figure 7(Test B). This processshows the destructionof the elastic core.

Once peak strength wasachieved, the stressprofile undergoes verylittle change. Onlythe magnitudes of theshear stress change,decreasing in thestrain softening mate-rial models. The ef-fects of shear strength

Distance along shearing plane, in0..5 1 1 .5 'G

..........'' KEY "% 50--B --HN .....E - - -K 0 N1 2 3 4 5 O

Distance long shearing lane, cm

Figure 6. - Shear stress profilesat peak strength for one elastic-plastic and four strain softeningmaterial models (0,=0.207 MPa).

o1.25

1.7,5

.5

.250

0

Distance along shearing plane, in0.5 1 1.5

--'_.-_--.'........ ,- -,,,


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specimen as opposed tothe leading edge for u .10the higher elastic mod-ulus material.

The average peakshear strength was dra-

matically affected bylowering the elastic 2.04modulus (Figure 8).The magnitudes of theaverage peak stresses /were much lower and the < 0

0amounts of horizontaldisplacement requiredto achieve peak

Horizontal displacement, in.01 .02 .03

/r ...........................

...... .._--_--3'_--2--_'........'"'" KEY....-'"'"' -- $ --- K

.-' ...... E N

Horizontal displacement, mm

Figure $. - Average shear stress atstrength were increased different horizontal displacementsby a factor equivalent for one elastic-plastic and fourto the change in modu- strain softening material models

lus (Table 1). (o.=0.207 MPa).The strain at whichmaterial properties change from peak to residual values onan element by element basis has a considerable effect onshear strength. Three different strain softening materialmodels were evaluated to examine this effect (test J, K andL, table 1). These tests allowed the material properties todrop from peak conditions (Cp=0.015 MPa and p=21 ) toresidual conditions (Cr=0 and r=13 ) after just 0.1% ofplastic strain had been achieved. This material modelexhibited a considerably different shear stress profilealong the shearing plane very similar to those associatedwith the lower modulus material (Figure 6). The rapid dropin material properties caused a considerable decrease in theaverage peak shear strengths and a swift fall to residualstrength conditions (Figure 8).

7 COMPARISON OF MODEL AND LABORATORY SHEAR STRENGTHS

Evaluation of the accuracy of the elastic-plastic and strainsoftening material models in simulating the behavior of theWalton Wood Clay was possible by comparing the shear

strengths from the various models with the laboratory re-sults. If these results compare well, then the predictedbehaviors, and hence stress profiles, discussed above may beconsidered reasonable.

The shear strengths for the three elastic-plastic (G, Hand I) and strain softening (A, B and C) tests were plottedin figure 9. The Mohr-Coulomb failure envelope for theelastic-plastic material model (C=0.015 MPa =20 ) was foundto be slightly less than the laboratory value (C=0.0153 MPa=21). The strain softening simulations produced a Mohr-Coulomb failure envelope (C=0.01 MPa =18 ) that was slight-ly less than the elastic-plastic material model. The resid-ual stresses for the strain softening material model wereexactly the same as the laboratory values (C=0 MPa

The lower peak stress values may be a direct result of theelement by element failure propagation across the specimen.556


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rotation of the specimen occurred in response to the appli-cation of horizontal stress above the shearing plane, 2)dilatant behavior of failed zones aids in the reproductionof deformation patterns during tensile and shear failure, 3)zones of rapid plastic deformation characterize zones ofshear failure, 4) modulus variations significantly effect

stress profiles, peak stress values and deformation pat-terns, and 5) the rate at which material properties changefrom peak to residual values on an element by element basishad a considerable effect on shear strength.

The Conclusions drawn from this investigation are summa-rized in the following statements. Because of the non-uni-form stress and strain conditions across the shearing zone,material properties of the intact specimen take on a rangeof values. Since the maximum material properties (Cp and p)mobilize within relatively narrow bands, the Mohr-Coulombfailure envelopes constructed from laboratory direct sheartests produce lower material properties at peak stress con-ditions than what may actually exist at the point of fail-ure. Therefore, numerical simulations of slope or founda-tion failures produce conservative results when using peakstrength material properties data from the direct sheartest.

REFERENCES

Hansen, C.E. Bent 1958. Line Ruptures Regarded as NarrowRupture Zones - Basic Equations Based on KinematicConsiderations. Proc. of the Conf. on Earth PressureProblems, Vol.l, Brussels, pp. 39-48.

Hvorslev, M.J. 1937. Physical Properties of RemouldedCohesive Soils. PhD Thesis, Vienna Inst. of Tech.,(English translation by U.S. Army Waterways ExperimentStation, Vicksburg, No. 69-5, 1969), 165 p.

Itasca, Fast Lagrangian Analysis of Continua (Version 2.2),Itasca Consulting Group, Inc., Minneapolis, MN, June 1989.

Morgenstern, N.R. and J.S. Tchalenko 1967. MicroscopicStructures in Kaolin Subjected to Direct Shear.Geotechnique 17(4):309-328.

Reynolds, O. 1885. On the Dilatancy of Media Composed ofRigid Particles in Contact. Phil. Mag., 5th, Ser.20.

Saada, A.S. and F.C. Townsend 1981. State of the Art:Laboratory Strength Testing of Soils. Laboratory ShearStrength of Soil, ASTM Special Tech. Publ. 740, pp. 7-77.

Skempton, A.W. 1949. Alexandre Collin: A Note on His PioneerWork in Soil Mechanics. Geotechnique 1(4):216-221.

Skempton. A.W. 1964. Long-Term Stability of Clay Slopes.Geotechnique 14(1):77-102.

Terzaghi K. and R.B. Peck 1948. Soil Mechanics inEngineering Practice. New York: John Wiley.

Vermeer, P.A. and R. de Borst 1984. Non-associatedPlasticity for Soils, Concrete and Rocks. Heron 29(3):64.

Vallejo, L.E. 1982. Development of a Shear Zone Structure inStiff Clays. Proc. of the 4th Intern. Conf. on NumericalMethods in Geom., Edmonton, May 31 - June 4, pp. 255-262.

Vallejo, L.E. 1987. The Influence of Fissures in a StiffClay Subjected to Direct Shear. Geotechnique 37(1):69-82.

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arma-91-549_stress and behavior of material under direct shear

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