uniﬁed soil behavior of interface shear test and direct...

Granular MatterDOI 10.1007/s10035-011-0275-2

ORIGINAL PAPER

Unified soil behavior of interface shear test and direct shear testunder the influence of lower moving boundaries

Jianfeng Wang · Mingjing Jiang

Received: 11 February 2011© Springer-Verlag 2011

Abstract Based on a detailed analysis of DEM simulationdata,this paper provides new insights into the effects ofboundary surface topography on the mobilized stress ratioand stress-displacement behavior in the interface shear testand the direct shear test. The soil mechanics observed in thetwo types of tests are unified under a novel perspective ofboundary-induced soil behavior. It is shown that the prin-cipal direction of the contact force anisotropy developed atthe soil-surface boundary has an exclusive control over thepeak stress ratio measured both at the boundary and insidethe sampling window. However, a subtle change in the rolesof the principal direction and the magnitude of contact forceanisotropy is found as the contact force chains extend fromthe surface into the interphase soil.

Keywords Discrete element method · Boundary-inducedsoil behavior · Direct shear test · Interface shear test ·Contact force anisotropy

1 Introduction

The interface shear test (IST) and the direct shear test (DST)are two important standard laboratory tests widely used inthe geotechnical community for totally different purposes.The IST is intended for the determination of the shear resis-tance developed at the interface between a soil and a rough,

J. Wang (B)Department of Building and Construction, City Universityof Hong Kong, Kowloon, Hong Konge-mail: [email protected]

M. JiangDepartment of Geotechnical Engineering, College of Civil Engineering,Tongji University, Shanghai, China

continuous manufactured or natural material surface whenshear displacement occurs between the two entities [1]. In anIST, the interphase refers to a region which consists of thesurface with its asperities, and a variety thickness of granularsoil directly adjacent to the surface. The interphase governsthe overall behavior of a geotechnical composite system. TheDST is the conventional shear box test intended for the deter-mination of the drained shear strength of a soil material underthe direct shear condition [2]. No linkage has been madebetween the two tests in the literature except that the shearstrength parameters of granular soils determined in the directshear test are often taken to be the basis to which the interfaceshear strength parameters are normalized to obtain the effi-ciency parameter an index indicating how much percentageof the full shear strength of the granular soil is mobilized bythe construction material surface.

A rich body of research has been dedicated to the determi-nation and quantification of effects of surface topography onthe interphase strength behavior (e.g., [5,4,9,14,15,17,18]).The primary mechanism by which the rough surface controlsthe peak interphase strength behavior was previously shownby the first author to be rooted in the anisotropies of fabric andcontact forces developed at the soil-surface boundary [17].Based on this mechanism, a semi-empirical failure criterionwhich relates the peak interphase strength to the principaldirection of surface normal distribution was proposed [18].

The direct shear test, on the other hand, has also receivedextensive experimental and numerical studies due to itssimplicity and relatively low testing cost. Significant ad-vances have been achieved in understanding the develop-ment of internal stress and strain localization conditionsduring the shearing process, and their relationship with theexternal stress measurements at the lateral boundaries (e.g.,[7,10,12,19]), as well as the variation of these behavior underthe influence of varying shear box size/scale (e.g., [6,22]).

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However, no effort is known to the authors that has beenmade to link the soil mechanics occurring in the two typesof tests. The goal of this paper is to provide a new perspec-tive which unifies the soil behavior observed in the interfaceshear test and the direct shear test, and to promote a coherentunderstanding of the soil mechanics under the influence ofgeometric boundaries.

2 Background

The first author has made comprehensive investigations intoboth types of tests using the DEM approach [16–22]. Thecontent of the current paper is built upon these previous stud-ies but the idea and results presented are novel and significantenough to make themselves stand alone.

In an interface shear test, while the shear stress ratio mea-sured along the surface is directly determined by the inter-action between the surface and the first layer of particlesthat touch the surface, the source of this shear resistancelies in the internal shear strength of the interphase soil adja-cent to the surface that is mobilized. The degree of mobili-zation of internal shear strength depends on the maximumanisotropies of fabric and contact force that can be sup-ported by the rough surface. It was shown that the averageshear stress ratio based on the homogenization of granularcontact quantities within a small sampling window abovethe surface represents a downscaled boundary measurement[17,18].

In a direct shear test, the boundary measurement is usu-ally taken to be the full shear strength of the granular soil.This is based on the assumption that the stress and shearstrain distributions are uniform inside the direct shear appa-ratus (DSA). However, the detailed DEM studies by the firstauthor [19] show that the boundary-induced strain localiza-tion propagates gradually from the two lateral boundariestowards the middle of the DSA, and the final configura-tion of the shear band depends on the initial density, nor-mal stress, and specimen size/scale, etc. More importantly,it was shown that the specimen size and aspect ratio (i.e.,box length/box height) have considerable effects on theboundary measurement. The underlying mechanism of thisgeometric effect is the different failure modes of the spec-imen: when the specimen aspect ratio is small, the globalfailure will control the macroscopic strength behavior; andwhen the specimen aspect ratio is large, progressive failurebecomes a more likely option. The global vs. progressivefailure modes refer to the different degrees and extents of thefabric change, strain localization and shearing banding inthe DSA as the peak stress ratio is reached. Specifically, theglobal failure implies the formation of a uniform and coher-ent shear band at the mid-height plane of the DSA at the peakstress state and the full mobilization of the shear strength of

the granular specimen inside the shear band; whereas theprogressive failure implies the propagation of the bound-ary-induced shear localization from the lateral boundariestowards the middle of the box and the partial mobilization ofthe shear strength of the granular specimen at the peak stressstate [22].

3 Unified soil behavior of interface shear test and directshear test

With the previous knowledge, it is now possible to unify thesoil mechanics in an interface shear test and a direct sheartest under the concept of “boundary-induced” soil behavior.In a generic sense, the study of soil behavior in any fieldor laboratory testing condition is the study of the effectsof certain kinds of external boundary condition on the soil.Following this idea, an analogy between the two types oftests can be made by treating the moving boundaries of theDSA as a special type of “U-shaped asperity” which engagesand displaces a much greater amount of matrix soil than thesurface asperities in an interface shear test. Under such aperspective, the soil mechanics occurring in an IST and aDST can be treated, in a unified way, as a consequence ofthe movement of lower boundaries. Despite the drasticallydifferent amount of the matrix soil displaced in the two typesof the tests, the mobilized shear strength measured either atthe testing device boundaries or inside the sampling windowdepends totally on the degree and extent of the strain local-ization and shear banding inside the specimen, as will bedemonstrated below. With such a common basis, it is easierto achieve a coherent understanding of the shear behavior inthe two types of the tests.

3.1 Numerical simulation program

The parametric numerical study on the IST and the DST wasconducted using the two-dimensional discrete element pro-gram PFC2D, Version 3.0 (Itasca Consultants, Inc.). DEMmodels of the IST and the DST were developed [16] andvalidated against the laboratory data [4,8]. The model setupis briefly described as follows. The IST device is a 128 mm-long, 28 mm-high shear box formed by two fixed, rigid lateralboundaries, a bottom rough boundary and a top boundarythat applies a constant normal stress using a servo mecha-nism. The bottom boundary consists of a 88 mm-long roughmaterial surface to be tested and two 20 mm-long, friction-less and flat zones located adjacent to each lateral boundary.Quasistatic horizontal shear displacement is applied to theentire bottom boundary at a constant velocity of 1 mm/ min.The granular material is poly-dispersed (well-graded) withan almost linear size distribution between the maximum andminimum particle diameters (Dmax , Dmin) of 1.05 mm and

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Unified soil behavior of interface shear test and direct shear test

Fig. 1 Dimensions of twoDSTs and surface profiles offour ISTs: a IST1—regularsawtooth surface; bIST2—irregular asperitysurface; c IST3—coextrudedgeomembrane surface; dIST4—concrete surface; eDST1—L = 88 mm andH = 56 mm; fDST2—L = 88 mm andH = 14 mm

X Coordinate (mm)

Y C

oo

rdin

ate

(mm

)

08844220 66

1.6(b) IST2

0.7

074.22.80 5.61.4

(a) IST1

8844220 660

0.9 (c) IST3

8844220 660

0.3 (d) IST4

Shear direction

88 mm

28 mm

28 mm

Normal pressure(e) DST1

Shear direction

88 mm

7 mm

7 mm

Normal pressure

(f) DST2

0.35 mm, respectively, and a median particle diameter (D50)

of 0.7 mm. The interparticle and particle-boundary frictioncoefficients are 0.5 and 0.9, respectively. Five groups of DEMsimulations of the IST on three types of representative sur-faces, namely, idealized regular sawtooth surfaces, randomirregular asperity surfaces and real manufactured materialsurfaces, were conducted under a normal stress of 100 kPa.The main difference between the three types of surfaces isthat the first two types are numerically generated, artificialsurfaces whereas the third type is real material surfaces whichare obtained by scanning the surfaces using a stylus profilom-eter at a 1 μm data point spacing. Four examples of the threetypes of surfaces are given in Figs. 1a-d. Three values of theparticle to surface friction coefficient (tan ϕμ), i.e., 0.05, 0.2and 0.5 were employed in the previous studies [17,18]. Fulldetails of the IST model setup and simulation program canbe found in these papers.

The previous DEM study on the DST focused on theeffects of specimen size/scale by varying the box length scale

L/D50, the box height scale H/D50 and the box aspect ratio(L/H) [22]. Two typical examples of the direct shear boxwith different aspect ratios are shown in Figs. 1e and f. A uni-form particle to boundary friction coefficient of 0.9 is usedto ensure a rough boundary condition in all the simulations.In the current study, in order to facilitate a strict compari-son between the IST and the DST under the perspective of“boundary-induced soil behavior”, all the DST simulationsusing the poly-dispersed materials under a constant normalstress of 100 kPa are rerun by employing three different val-ues of the particle to lower moving boundary friction coeffi-cient (tan ϕμ), i.e., 0.05, 0.2 and 0.5, which are the same asthe tan ϕμ values used in the IST simulations. The particle toupper fixed boundary friction coefficient remains 0.9 in theDST simulations. Furthermore, the stress ratio measured atthe boundaries is calculated based on the total lateral and ver-tical forces measured on the lower moving boundaries. Thisis made also to be consistent with the stress ratio calculationin the IST simulations.

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Horizontal Displacement (mm)

(τ/σ

) bou

ndar

yDST1

DST2IST1

IST2

IST3

IST4

20 64 108

0

0.1

0.2

0.3

0.4

0.5

0.6

(τ/σ

) ave

DST1

DST2

IST1

IST2

IST3

IST4

Horizontal Displacement (mm)20 64 108

(a)

(b)

`

Fig. 2 Evolutions of stress ratios measured at the testing device bound-ary and inside the sampling window against shear displacement fortwo DSTs and four ISTs, a boundary-measured stress ratio; b window-measured stress ratio

3.2 Stress-displacement behavior and shear strainlocalization

Figure 2 compares the stress ratio-displacement relationsfrom two DST simulations and four IST simulations, whoseconfigurations of the shear box or surface profile are shownin Fig. 1. The tan ϕμ value is 0.05 in these simulations.The stress ratios measured on the lower moving boundariesand in the sampling windows are compared respectively. Forthe average stress ratio calculated in the sampling window,a 7 mm high sampling window sitting over the rough surfaceis used in the ISTs, and a 14 mm high sampling window sym-metric about the middle plane of the box (i.e., 7 mm aboveand 7 mm below the middle plane) is used in the DSTs.

In Fig. 2a, it is seen that the boundary-measured peakstress ratios and steady state stress ratios in the ISTs are veryclose to those measured in the DSTs if the surface is roughenough, but they drop remarkably as the surface roughnessdecreases, particularly for the coextruded geomembrane sur-face and the concrete surface. In a unified sense, the aboveresults illustrate the varying capabilities of different kinds ofgeometric boundary in engaging granular soils in shearingand mobilizing varying portions of the full shear strength ofthe matrix soil. The degree of shear strength mobilizationis associated with the development of anisotropy and shearstrain localization.

Figure 3 show the shear strain localizations in these sim-ulations at their peak stress states. The dimensions of theDST and IST boxes are drawn in scale so that the strainlocalizations can be compared directly. The shear strain dis-tributions are calculated using the mesh-free strain calcula-tion method previously developed by the first author [20].It can be seen that the primary zone of strain localizationreduces significantly with the reduction of the surface rough-ness (Fig. 3c-f). However, for a highly rough surface (e.g.,IST1), the zone of strain localization (marked by the bluecurve) could be comparable to that in a direct shear test (e.g.,DST1) (Fig. 3b and c). On the other hand, the degree of shearstrength mobilization in a DST depends on the box aspectratio. It is seen in Fig. 2a that a higher peak stress ratio isobtained at a larger displacement in DST1 due to its smalleraspect ratio, which allows the contact force chains stemmingfrom the lateral boundaries to extend farther into the innerpart of the specimen. As a result, a global failure featuredwith a primary zone of localization around the mid-height ofthe box dominates the peak stress state (Fig. 3b). The shearband, however, appears less uniform and concentrated thanthat shown in [22], because the tan ϕμ value is much lowerthan the one (i.e., 0.9) used in that study. This reconfirms theimportance of adopting rough boundaries in a DST. Whenthe box aspect ratio becomes larger (e.g., DST2), a lowerstress ratio is obtained at a smaller displacement at the peakstate (Fig. 2a). This is caused by the inability of the DSA toengage the main portion of the material at the middle of thebox into shearing at the peak state due to the severe interfer-ence of the upper and lower boundaries upon the formation oflong-range force chains [13,11]. Consequently, the primaryzone of localization is forced to develop along the bottom ofthe box, deviating from the mid-height (Fig. 3a). Based onthe above information, it is justified to conclude that a DSTdoes not necessarily provide the “standard” shear strengthparameter while an IST may yield the fully mobilized shearstrength as well.

A better way to study the boundary-induced macroscopicstrength behavior is to look into the homogenized, averagestress ratio calculated within the sampling window whichencompasses the primary zone of strain localization in bothtypes of tests. It is clear that the average stress ratio curvesin Fig. 2b resemble their corresponding boundary-measuredcurves in Fig. 2a for each simulation but have overalllower magnitudes and higher smoothness. The average stressratio has been shown to be closely related to the height of thesampling window, and will be equal to the boundary mea-surement when the sampling window is narrow enough [19].The steady-state portions of the curves of DST1, DST2 andIST1 are very similar, although some differences are found intheir peak stress ratios. This observation indicates that similarmicromechanical conditions are established at the large-deformation stage within the primary zone of strain

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Fig. 3 Shear straindistributions of the two DSTsand four ISTs at their peak states(tan ϕμ = 0.05 for all thesimulations): a DST2; b DST1;c IST1; d IST2; e IST3; f IST4

(a)

(b)

(c)0 44 88

0 128

-0.1 ~ -0.06 -0.06 ~ -0.02 -0.02 ~ 0.02 0.02 ~ 0.06

-28

0

28

20 64 108

0 12820 64 108

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0

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-7

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J. Wang, M. Jiang

0

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0 10 20 30 40 50 60 70 80 90

θr (degrees)

IST, regular sawtooth surfaceIST, irregular asperity surface

IST, real material surfaceDST

(τ/σ

)bou

ndar

y

tanφμ = 0.05

DST with L = 35 mm and H = 14 mm

0

0.1

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0.3

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0.5

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0.8

0 10 20 30 40 50 60 70 80 90

θr (degrees)

(τ/σ

)bou

ndar

y

tanφμ = 0.2


0

0.1

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0 10 20 30 40 50 60 70 80 90

θr (degrees)

(τ/σ

)bou

ndar

y

tanφμ = 0.5


(c)

(b)

(a)

Fig. 4 Relationships between the peak stress ratio measured at thelower moving boundaries and θr from all the ISTs and DSTs: a tan ϕμ =0.05; b tan ϕμ = 0.2; c tan ϕμ = 0.5

localization when the boundaries are rough enough to fullymobilize the shear strength of the material, regardless of thetype of the testing device boundary.

3.3 Control of the contact total force anisotropyon the shear strength behavior

It has been shown previously that the principal directionof the contact total force anisotropy developed at the par-ticle-surface boundary in an IST has a dominant control overthe peak interphase strength behavior [17]. The anisotropiesof the average contact normal force, average contact shearforce and average contact total force are described by thetwo-dimensional, second-order density distribution tensors

Ni j , Si j and Ri j , respectively as [3,17]

Ni j = 1

2π

2π∫

0

f̄n (θ)

f̄0ni n j dθ = 1

Nc

Nc∑k=1

f kn

f̄0nk

i nkj , (1)

Si j = 1

2π

2π∫

0

f̄s (θ)

f̄0ti n j dθ = 1

Nc

Nc∑k=1

f ks

f̄0tki nk

j (2)

and

Ri j = 1

2π

2π∫

0

f̄r (θ)

f̄r0mi m j dθ = 1

Nc

Nc∑k=1

f̄ kr

f̄r0mk

i mkj , (3)

where, f̄n (θ) , f̄s (θ) and f̄r (θ) are the correspondingdensity distribution functions; fn, fs and fr are the con-tact normal force, contact shear force and contact total force,respectively; Nc is the total number of contacts within thegranular volume; n = (cos θ, sin θ) is the unit contact nor-mal vector, t = (− sin θ, cos θ) is the vector perpendicularto n; m = (cos α, sin α) is the unit vector in the direction ofcontact total force; and f̄0 and f̄r0 are the average contactnormal forcer and total force calculated by:

f̄0 = 1

2π

2π∫

0

f̄n (θ) dθ = 1

Nc

Nc∑k=1

f kn (4)

and

f̄r0 = 1

2π

2π∫

0

f̄r (θ) dθ = 1

Nc

Nc∑k=1

f kr . (5)

The Fourier series approximations for f̄n (θ) , f̄s (θ) andf̄r (θ) are written as:

f̄n (θ) = f̄0 [1 + an cos 2 (θ − θn)] , (6)

f̄s (θ) = f̄0 [−as sin 2 (θ − θs)] (7)

and

f̄r (θ) = f̄r0 [1 + ar cos 2 (θ − θr )] , (8)

where an, as and ar are the magnitudes of the correspondinganisotropies; and θn, θs and θr are the principal directions(all measured from the vertical) of the corresponding aniso-tropies.

Based on the previous result, it is now interesting tosee whether the methodology can be extended to the DST.Figure 4 shows the peak stress ratios (τ/σ )boundary measuredat the lower moving boundaries in all the IST and DST sim-ulations. The data from the IST simulations are identical tothose shown in [17,18] but the data from the DST simulationsare newly included to see whether a consistent correlationpattern could be obtained by treating the DST as a specialtype of the IST. It is clear in Fig. 4 that for any tan ϕμ value,

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Table 1 Peak stress ratios measured at the lower moving boundaries using two methods from all DST simulations

tan ϕμ L ( mm) H ( mm) L/H N (τ/σ )boundary−asp (τ/σ )boundary−con(τ/σ )boundary−con−(τ/σ )boundary−asp

(τ/σ )boundary−asp(%)

0.05 88 56 1.57 11239 0.634 0.708 11.7

88 28 3.14 5669 0.57 0.639 12.1

88 14 6.28 2884 0.52 0.575 10.6

63 28 2.25 4087 0.637 0.731 14.8

63 14 4.5 2093 0.6 0.689 14.8

35 14 2.5 1186 0.711 0.845 18.8

0.2 88 56 1.57 11239 0.65 0.791 21.7

88 28 3.14 5669 0.582 0.654 12.4

88 14 6.28 2884 0.531 0.588 10.7

63 28 2.25 4087 0.63 0.741 17.6

63 14 4.5 2093 0.603 0.693 14.9

35 14 2.5 1186 0.724 0.88 21.5

0.5 88 56 1.57 11239 0.665 0.807 21.4

88 28 3.14 5669 0.572 0.636 11.2

88 14 6.28 2884 0.52 0.57 9.6

63 28 2.25 4087 0.63 0.738 17.1

63 14 4.5 2093 0.606 0.697 15.0

35 14 2.5 1186 0.724 0.89 22.9

N the total number of particles in the simulation

the DST data fall within the horizontal portion of the correla-tion, which approximately starts when θr is greater than 30◦.In this region, the amplitude of variation of (τ/σ )boundary

from the DST simulations agrees well with that from theIST simulations, except one higher value from the DST withL = 35 mm and H = 14 mm. Its higher (τ/σ )boundary valueis attributed to the insufficient number of particles containedin that simulation. The consistent correlation pattern ob-tained in Fig. 4 suggests that the (τ/σ )boundary values in ISTsand DSTs can be quantified in a unified way by means ofθr measured along the same boundary, despite the large dif-ference between the two types of the testing device bound-aries. None of the DST data points lies in the inclined portionof the correlation with θr < 30◦, which reflects a remark-able control of θr on (τ/σ )boundary for those surfaces withinadequate roughness to fully mobilize the shear strength ofthe material. When the boundary roughness is high enough,the mobilized shear strength is nearly a constant and equal orclose to the maximum shear strength of the material. The datascatter in the region of θr > 30◦ indicates the insufficiency ofθr alone to accurately quantify the mobilized shear strength.

It is worth pointing out that the (τ/σ )boundary values fromthe DST simulations deviate considerably from the valuescalculated in the conventional way. In the conventional way,(τ/σ )boundary is calculated by dividing the horizontal stresswhich presumably acts on the mid-height shearing planeby the constant normal stress (i.e., 100 kPa in this study),and the horizontal stress is obtained by dividing the total

horizontal force measured on the lower moving boundariesby the effective area of the shearing plane. Table 1 lists thevalues from all DST simulations calculated in both ways,with (τ/σ )boundary−asp denoting the values calculated in thecurrent way and (τ/σ )boundary−con denoting those calculatedin the conventional way. It is seen that the (τ/σ )boundary−asp

values are about 10-20% lower than the (τ/σ )boundary−con

values, indicating an overestimation of the actual peak stressratio in the laboratory. Apparently, the consistent bilinearcorrelation would not be obtained if the (τ/σ )boundary−con

values are plotted in Fig. 4. In Fig. 5, the difference betweenthe two values is plotted as a function of the box aspect ratio,and the trends of variation against the box length scale andthe box height scale are marked by two groups of arrows.Obviously, in all the tan ϕμ cases, the difference between thetwo values increases with the decreasing aspect ratio in bothdirections but the rate of change is much higher in the direc-tion of constant box height scale and decreasing box lengthscale. This observation indicates that an overestimation ofthe actual peak stress ratio can be minimized when a sameaspect ratio but a greater box length is used.

Figure 6 shows the correlations between the average peakstress ratios (τ/σ )ave measured inside the sampling win-dows and θr measured at the lower moving boundaries. The(τ/σ )ave values from the IST simulations are different fromthose shown in [17,18] due to a smaller sampling windowused in the current study. An equally well-defined bilin-ear profile with an even less amount of data scatter in the

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J. Wang, M. Jiang

(a)

(b)

(c)

0

10

20

0 2 4 6 8

Box aspect ratio

constant length scaledecreasing height scale

constant height scaledecreasing length scale

(τ/σ

)bou

ndar

y-co

n -

(τ/σ

)bou

ndar

y-as

p

(τ/σ

)bou

ndar

y-as

p

(%)

tanφμ = 0.05

tanφμ = 0.2

tanφμ = 0.5

0

10

20

0 2 4 6 8

Box aspect ratio

(τ/σ

)bou

ndar

y-co

n -

(τ/σ

)bou

ndar

y-as

p

(τ/σ

)bou

ndar

y-as

p

(%) 30

0

10

20

0 2 4 6 8

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(τ/σ

)bou

ndar

y-co

n -

(τ/σ

)bou

ndar

y-as

p

(τ/σ

)bou

ndar

y-as

p

(%) 30

Fig. 5 Effects of the box aspect ratio (L/H) on the difference betweenthe peak stress ratios measured at the lower moving boundaries usingthe two methods: a tan ϕμ = 0.05; b tan ϕμ = 0.2; c tan ϕμ = 0.5

horizontal portion is found in each tan ϕμ case. Interestingly,the abnormally high value of (τ/σ )boundary in the DST withL = 35 mm and H = 14 mm is found to be replaced witha lower (τ/σ )ave value that conforms well to the horizontalportion of the profile. This observation reconfirms the unifiedshear strength behavior of the DST and IST inside the matrixsoil under the influence of lower moving boundaries.

3.4 Control of the contact force anisotropyon the stress-displacement behavior

Besides the control of θr on the peak strength behavior, it isinteresting to further examine the relationships between the

0 10 20 30 40 50 60 70 80 90

θr (degrees)

IST, regular sawtooth surfaceIST, irregular asperity surface

IST, real material surfaceDST

(τ/σ

)ave

tanφμ = 0.05

(a)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70 80 90

θr (degrees)

(τ/σ

)ave

tanφμ = 0.2

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70 80 90

θr (degrees)

(τ/σ

)ave

tanφμ = 0.5

(c)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fig. 6 Relationships between the average peak stress ratio measuredinside the sampling window and θr from all the ISTs and DSTs: atan ϕμ = 0.05; b tan ϕμ = 0.2; c tan ϕμ = 0.5

contact force anisotropies and the entire stress-displacementbehavior both at the boundaries and inside the sampling win-dows. Figure 7 shows the typical simulation results fromIST1, IST2 and IST4 with tan ϕμ equal to 0.05. To clearlydemonstrate the influences of the contact total force anisot-ropy measured at the lower boundaries on the stress ratio-displacement behavior, the scales of ar, θr and (τ/σ )boundary

are adjusted appropriately in the same plot to facilitate a bet-ter examination on their relationships.

It is seen in Fig. 7 that ar and θr play different roles in theevolution of stress ratio-displacement behavior for differenttypes of surfaces. Clearly, for a random, irregular surface,the stress ratio evolution is mainly controlled by θr (Figs. 7band c); while for a regular sawtooth surface, the role of

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(τ/σ)boundary ar

θr

θr (degree)

IST1

0

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0 2 4 6 8 10

ar

θr

IST2

ar θr (degree)


1.0

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10

20

30

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25

30

35

40

0.0 20

ar

0

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IST4

ar θr (degree)


1.6

1.8

1.9

0

10

20ar

2.0


(c)

(a)

(b)

(τ/σ)boundary

(τ/σ)boundary

(τ/σ)boundary

(τ/σ)boundary

(τ/σ)boundary

Fig. 7 Evolutions of the stress ratio, magnitude and principal direc-tion of contact total force anisotropy developed at the particle-surfaceboundary against shear displacement in ISTs (tan ϕμ = 0.05): a IST1;b IST2; c IST4

ar becomes more dominant (Fig. 7a). The former result isconsistent with the critical role of θr on the peak stressratio and indicates further that θr is a great predictor for theentire stress-displacement behavior. The latter result is inter-esting and a bit surprising too at a first glance because thedominant role of ar seems to be contradictory with the pre-vious results. However, an understanding of this behavior isachieved quickly by noting that the variation of θr is muchsmaller during the shear process as compared to the case of

(τ/σ)boundary ar

θr

θr (degree)

DST1

ar

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10

85

75


(a)

0.7 70

80

90

(τ/σ)boundary

0.4

0.5

0.6

0.7

(τ/σ)boundary ar

θr

θr (degree)

DST2

ar

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10

60

50


(b)

0.7 40

70

(τ/σ)boundary

0.2

0.4

0.6

0.8

1.0

0.0

Fig. 8 Evolutions of the stress ratio, magnitude and principal directionof contact total force anisotropy developed at the lower moving bound-aries against shear displacement in DSTs (tan ϕμ = 0.05): a DST1;b DST2

irregular surfaces. The fact is that a large rotation of the prin-cipal stress or major contact force chains takes place in anirregular asperity surface, due to the initial wider distributionof the particle-surface contact normals; whereas only a lim-ited rotation of the principal stress, especially after the peakstate, occurs in a regular sawtooth surface due to the constantasperity slope during shear. When the direction of the majorcontact force chains is relatively stable, the accumulation orloss of contact normal and contact force magnitude in thatdirection, i.e., the magnitude of anisotropy, ar, becomes adecisive factor. Based on the above analysis, it is not hardto conclude that the effect of θr is a first-order, decisive onein controlling the stress-displacement behavior of the inter-phase system, and the effect of ar is a second-order one whichwill only rise to play a major role when θr is relatively fixed.

A similar examination into the results from two DST sim-ulations shown in Fig. 8 indicates that the amplitudes of vari-ations of ar and θr allowed in a DST are significantly affectedby the box aspect ratio. A much larger variation of ar and asmaller variation of θr is found when the box aspect ratiois larger. However, the variations of the two quantities areoverall more consistent than those in the ISTs, indicating themeasured (τ/σ )boundary reflects more a combined effect of θr

and ar. However, a more prevailing role of θr in the evolution

123

J. Wang, M. Jiang

(a)DST1 DST2

IST1

IST2 IST3 IST4


20 64 108

θn (

degr

ee)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 DST1

DST2

IST1

IST2

IST3

IST4


20 64 108

an

(b)

0

20

40

60

80(c)

θs (

degr

ee)

DST1

DST2

IST2IST1

IST3

IST4


20 64 108

0

0.1

0.2

0.3 DST1

DST2

IST1

IST2IST3

IST4


20 64 108

as

(d)

0

10

20

3040

50

60

70

8090

`

Fig. 9 Evolutions of anisotropies of contact normal force and contact shear force within the sampling window against shear displacement fortwo DSTs and four ISTs: a θn vs. horizontal displacement; b an vs. horizontal displacement; c θs vs. horizontal displacement; d as vs. horizontaldisplacement

of the stress ratio-displacement behavior can be discerned inboth DSTs.

Further insights of the micromechanics inside the sam-pling window are given by the evolutions of anisotropies ofcontact normal force and contact shear force with shear dis-placement shown in Fig. 9. It is interesting to examine theroles of θn, θs, an and as on the average stress ratio insidethe sampling window, and compare them with the roles ofθr and ar on the boundary-measured stress ratio discussedbefore. Apparently, the value of θn becomes relatively stableand lies between about 30◦ ∼ 60◦ after a significant rotationat the early stage for almost all the simulations. The onlyexception is IST4 (i.e., the concrete surface) whose θn valuekeeps fluctuating and stays below 20◦ throughout the wholeshearing process, as shown in Fig. 9a. A complete oppositescenario is found in the an evolutions in Fig. 9b. It is seen thatall the simulations have overall an profiles resembling theircorresponding average stress ratio curves except IST4, whosean value is fairly stable and much lower than the other sim-ulations. Obviously, inside the sampling window, the effectof an is a first-order, decisive one in controlling the averagestress ratio-displacement behavior of the interphase soil forall the rough boundaries that are capable of supporting sta-ble contact force chains oriented within 30◦ ∼ 60◦. However,the effect of θn becomes dominant for those smooth bound-aries, like the concrete surface which has limited capabilityof altering the contact force network away from the surface.For the latter case, the variation of θn is caused by the lim-ited change of contact force direction at the particle-surface

boundary, and the value of an can gain very little change. Asa result, the mobilized shear strength must be low.

As compared to the contact normal force anisotropy, theeffects of contact shear force anisotropy are secondary. Thisis evidenced by the overall much lower values of as for allthe simulations (Fig. 9d). However, the responses seem to bemore consistent for all the testing device boundaries, with as

showing more influences than θs. Furthermore, θs also exhib-its less disparities for different testing device boundaries thanθn (Fig. 9c).

4 Conclusions

This paper provides a new perspective which unifies thesoil mechanics observed in an interface shear test and adirect shear test under the concept of “boundary-induced”soil behavior. Based on the detailed analysis of microme-chanical data from DEM simulations, a complete understand-ing of the mechanisms by which the different types of test-ing device boundaries control the shear strength and stressratio-displacement behavior of granular soils is achieved. Itis shown that the mobilized shear strength measured either atthe testing device boundaries or inside the sampling windowdepends on the degree and extent of the strain localizationand shear banding developed inside the specimen. The peakstress ratios measured in ISTs and DSTs can be well quan-tified using the principal direction of the contact total forceanisotropy. However, a subtle distinction is found in the roles

123


of the principal direction and the magnitude of contact forceanisotropy in controlling the stress ratio-displacement behav-ior as the contact force chains extend from the boundary intothe interphase soil. The origin of this distinction is the puregeometric factor, i.e., the rigid boundary surface geometryvs. the adjustable interphase soil fabric.

Acknowledgments The study presented in this article was jointly sup-ported by the Strategic Research Grant from City University of HongKong under Grant No. 7008083 and the China National Funds for Dis-tinguished Young Scientists with Grant No. 51025932. These supportsare gratefully acknowledged.

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