AbstractParticle crushing plays an important role on the mechanical behavior of crushable granular soils. In this paper, the macro- and micro-mechanical behaviors of dense granular soils composed of crushable agglomerates in plane strain compression test are investigated using the Discrete Element Method (DEM). A detailed study on the effects of particle crushing on the soil behavior is facilitated by a comparison between the simulation results of crushable and uncrushable specimens. The DEM results show a strong dependency of particle crushing on the confining stress level. It is found that under low confining stresses, particle crushing is insignificant and does not affect the shear band formation, which is the primary failure mode in an uncrushable specimen. However, under high confining stresses, significant particle crushing occurs and leads to considerable volumetric compression and reduction of the peak shear stress ratio. More importantly, particle crushing interferes with the formation of shear band and results in massive contractive zones in the specimen, which essentially controls the shear strength behavior

Wang, J.F.

Yan, H.B.

Elsevier - Publisher Connector 

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The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction 
3D DEM Simulation of Crushable Granular Soils under Plane 
Strain Compression Condition 
J. F. WANGa and H. B. YANb
Department of Building and Construction, City University of Hong Kong, China 
Abstract 
Particle crushing plays an important role on the mechanical behavior of crushable granular soils. In this paper, the 
macro- and micro-mechanical behaviors of dense granular soils composed of crushable agglomerates in plane strain 
compression test are investigated using the Discrete Element Method (DEM). A detailed study on the effects of 
particle crushing on the soil behavior is facilitated by a comparison between the simulation results of crushable and 
uncrushable specimens. The DEM results show a strong dependency of particle crushing on the confining stress level. 
It is found that under low confining stresses, particle crushing is insignificant and does not affect the shear band 
formation, which is the primary failure mode in an uncrushable specimen. However, under high confining stresses, 
significant particle crushing occurs and leads to considerable volumetric compression and reduction of the peak shear 
stress ratio. More importantly, particle crushing interferes with the formation of shear band and results in massive 
contractive zones in the specimen, which essentially controls the shear strength behavior. 
© 2011 Published by Elsevier Ltd. 
Selection and/or peer-review under responsibility of [name organizer] 
Keywords: Crushable soil, Discrete Element Method, Plane strain, Shear band. 
1. Introduction
Particle crushing plays an important role on the mechanical behavior of crushable granular soils. A 
wealth of experimental and numerical research has been conducted on the single particle fracture and 
mechanical behavior of crushable soils (Nakata et al. 1999; McDowell & Bolton 1998; Cheng et al. 2003; 
a Corresponding author: E-mail address: jefwang@cityu.edu.hk 
b Presenter: E-mail address: haibiyan@cityu.edu.hk 
1877–7058 © 2011 Published by Elsevier Ltd.
doi:10.1016/j.proeng.2011.07.215
Procedia Engineering 14 (2011) 1713–1720
Open access under CC BY-NC-ND license.
Open access under CC BY-NC-ND license.
1714  J.F. WANG and H.B. YAN / Procedia Engineering 14 (2011) 1713–1720
Coop et al. 2004). It is found that grain crushing is most affected by the mineralogy type (e.g., siliceous or 
calcareous), mean effective stress level, initial relative density and stress path. However, the effects of 
particle crushing on the strength and deformation behavior of granular soils, as well as the underlying 
micromechanical mechanisms, are not fully understood.  
The Discrete Element Method (DEM) originally proposed by Cundall and Strack (1979) has been 
recognized as an effective tool for studying the micromechanical behavior of granular materials. Recently, 
DEM has been used to model particle fracture and crushable materials. Thornton et al. (1996; 1997) 
firstly used DEM to simulate the fragmentation of agglomerates which consist of adhesive balls 
considering surface energy. Then, Robertson (2000) simulated the crushable aggregates using PFC3D, 
with each particle modeled as an agglomerate which is composed of elementary balls bonded together by 
contact bonds in hexagonal close packing (HCP). He found that the random removal of some balls in the 
agglomerate could result in a Weibull’s distribution of fracture strength. By improving Robertson’s 
method, McDowell and Harireche (2002a; 2002b) reproduced the particle size effect on fracture strength 
and simulated the normal compression test on crushable sand. Cheng et al. (2003; 2004) adopted 
Robertson’s method to model the statistical strength of silica sand, and simulated isotropic compression 
and conventional triaxial compression on crushable sands. Bolton et al. (2008) investigated the micro- 
and macro-mechanical behavior of crushable materials based on the work of Cheng et al. (2003; 2004). 
In this paper, the macro- and micro-mechanical behavior of dense granular soils composed of crushable 
agglomerates in plane strain compression tests is investigated using the DEM simulation. A detailed study 
on the effects of particle crushing on the soil behavior is facilitated by a comparison between the 
simulation results of crushable and uncrushable specimens. 
2. Method 
2.1. Simulation of Single Particle Fracture 
To achieve a realistic simulation of the mechanical behavior of crushable soils in triaxial testing, it is 
our first step to simulate the fracture behavior of a single particle in a valid manner. Previous research 
(McDowell and Amon 2000; Nakata et al. 1999) has shown that the fracture strength of soil particles 
essentially obeys Weibull’s statistical distribution (Weibull 1951) given by: 
   > @ms dP 0exp VV  (1) 
where Ps is the survival probability of a particle with size d, ˢˢis the induced tensile stress, and ˢ0 is 
the characteristic tensile stress at which 1/e or 37% of tested particles survive, and m is the Weibull’s 
modulus. McDowell and Harireche (2002a; 2002b) showed that it was possible to model such a fracture 
strength behavior using PFC3D by randomly removing a portion of the elementary balls comprising the 
agglomerate. Such an approach is adopted in the current study. 
In this paper, all the agglomerates have a uniform diameter of 1 mm, with the composing elementary 
ball diameter being 0.2 mm. Each agglomerate is composed of 60~70 elementary balls, which are initially 
assigned a smaller diameter and filled randomly in a spherical container with a diameter of 1 mm. The 
balls are later allowed to expand gradually to the final size of 0.2 mm and consolidate until equilibrium is 
achieved. Then, parallel bonds are installed at all the contacts existing between balls to form the porous 
agglomerate. The advantage of the parallel bond against the contact bond is that it simulates a small piece 
of cement between two balls which provides a rotational resistance. Such a feature enables a more 
realistic simulation of real soil particles. The parameters of balls and parallel bond model used in this 
J.F. WANG and H.B. YAN / Procedia Engineering 14 (2011) 1713–1720 1715
study are listed in Table 1. To achieve the statistical variation of the fracture strength, 5%~10% of the 
elementary balls are randomly removed from each agglomerate generated. 
Table 1: Material Parameters Used in DEM Simulations 
Diameter of agglomerate: mm 1.0 
Diameter of elemental ball: mm 0.2 
Density of ball: kg/m3 2650 
Number of balls in an agglomerate 60~70 
Normal and shear stiffness of ball: N/m 2×106
Friction coefficient of ball 0.5 
Normal and shear parallel bond strength: N/m2 5×108
Normal and shear parallel bond stiffness: N/m3 5×1014
Figure 1 shows a typical result of an agglomerate fractured in a platen compression test. A major peak 
indicating the splitting of the particle is observed, which is preceded by a smaller subpeak suggesting the 
breakage of a local asperity. Figure 2 shows the relationship between the survival probability Ps of 30 
random agglomerates and their corresponding fracture stress V. The survival probability is calculated 
using the mean rank position proposed by Davidge (1979). If the number of tests is N, the survival 
probabilities under increasing stress are N/(N+1), (N-1)/(N+1), Ă1/(N+1). It is clear from Figure 2 that 
the relationship between Ps and Vagrees well with the Weibullÿs equation (1), which predicts the 
Weibullÿs modulus m = 5.4 and 37% fracture strength V0 = 18.9 MPa. 
Figure 1: Typical result of platen compression test on an agglomerate: (a) stress-compression relation; (b) particle fractures 
(b) (a) 
0
2
4
6
8
10
12
14
16
18
0 0.02 0.04 0.06 0.08 0.1 0.12
S
tr
es
s 
: M
P
a
Displacement: 10-3mm
1716  J.F. WANG and H.B. YAN / Procedia Engineering 14 (2011) 1713–1720
y = 5.435x - 15.974
R² = 0.9663
m = 5.4; ı = 18.9 MPa 
-4
-3
-2
-1
0
1
2
0 0.5 1 1.5 2 2.5 3 3.5 4
L
n
[L
n
(1
/P
s)
]
Lnı
Figure 2: Weibull probability plot of agglomerates in platen compression 
tests.
Figure 3: Typical DEM specimen of 1000 crushable 
agglomerates.
2.2. Simulation of Plane Strain Compression Test 
A series of plane strain compression simulations are performed on cuboid dense specimens with a 
dimension of 8 mm × 6 mm × 17.5 mm. The specimen contains 1000 uniform random agglomerates 
created following the procedure described above. In order to obtain a dense homogeneous specimen, the 
1000 agglomerates are deposited in four layers, with each layer containing 250 agglomerates and 
compacted under a normal pressure of 100 kPa to achieve a target void ratio of 0.7.  A low ball friction 
coefficient of 0.1 is adopted in this process to achieve this dense packing. Figure 3 shows a typical DEM 
specimen of crushable agglomerates. 
After the specimen is generated, it is subjected to an isotropic compression with the isotropic confining 
stress (V3) being 500 kPa, 800 kPa, 1000 kPa and 1500 kPa, respectively, until complete equilibrium is 
achieved. During the subsequent plane strain compression test, the specimen is sheared by moving the top 
and the bottom walls towards each other at a constant velocity of 7×10-4 mm/s but maintaining the 
confining stress on the two lateral walls normal to the X-direction and fixing the other two lateral walls 
normal to the Y-direction. To better study the effects of particle crushing on the behavior of crushable 
specimens, the same simulations are also carried out on the uncrushable specimens by raising the parallel 
bond strength parameters by 100 times. 
3. Results 
The stress ratio and volumetric strain vs. axial strain relationships from the simulations on both 
crushable and uncrushable specimens are shown in Figure 4.  It is seen that the effects of particle crushing 
on the stress-strain behavior are not appreciable under confining stresses lower than 1000 kPa although a 
slightly lower peak stress ratio is observed for the crushable specimen with V3 = 800 kPa. But a 
significant reduction of peak stress ratio is found in the crushable specimen with V3 = 1500 kPa. This is 
an obvious result of significant particle crushing occurring under the high confining stress level. 
J.F. WANG and H.B. YAN / Procedia Engineering 14 (2011) 1713–1720 1717
Figure 4: Stress ratio and volumetric strain vs. axial strain relationships: 
(a) and (b) uncrushable specimens; (c) and (d) crushable specimens.  
Drastic distinctions, however, are found in the volumetric strain behavior of crushable and uncrushable 
specimens under all the confining stress levels (Figs 4b and 4d). For uncrushable dense specimens, a 
typical pattern of initial slight contraction-severe dilation-steady state constant volume is observed. The 
failure of the specimen is characterized by the strain localization and formation of a clear shear band 
which is inclined at about 30 degrees from the vertical. Figure 5 shows two examples of deformed 
specimens and their displacement fields at 15% strain. For crushable dense specimens, the confining 
stress plays a critical role on the volumetric strain behavior. Under the low 
(d) 
0 5 10 15 20 25
-12
-10
-8
-6
-4
-2
0
2
4
Confining stress
 500KPa
 800KPa
 1000KPa
 1500KPa
Axial strain: %
 V
ol
um
et
ric
 s
tr
ai
n:
 %
(a) 
0 5 10 15 20 25
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Confining stress
 500KPa
 800KPa
 1000KPa
 1500KPa
St
re
ss
 ra
tio
Axial strain: %
(c) 
0 5 10 15 20 25
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Confining stress
 500KPa
 800KPa
 1000KPa
 1500KPa
 S
tr
es
s 
ra
tio
Axial strain: %
(b) 
0 5 10 15 20 25
-2
-1
0
1
2
3
4
Confining stress
 500KPa
 800KPa
 1000KPa
 1500KPa
Axial strain: %
 V
ol
um
et
ric
 s
tr
ai
n:
 %
1718  J.F. WANG and H.B. YAN / Procedia Engineering 14 (2011) 1713–1720
Figure 5: Deformation and displacement field of uncrushable specimens: 
 (a) and (b) ˢ3= 500 kPa; (c) and (d) ˢ3= 1500 kPa. 
Figure 6: Deformation, displacement field and distribution of particle crushing of crushable specimens: (a), (b) and (c) ˢ3 = 500 
kPa; (d), (e) and (f) ˢ3 = 1500 kPa. 
(a) (b) (c) (d) 
(a) (b) (d) (e) 
(c) (f) 
J.F. WANG and H.B. YAN / Procedia Engineering 14 (2011) 1713–1720 1719
confining stress (i.e. V3 = 500 kPa), overall dilation is still observed but is much less than that of the 
uncrushable specimen. This reduced dilation is mainly attributed to the particle crushing, whose 
distribution is shown in Figure 6. It can be seen that the amount of particle crushing is moderate and a 
shear band can still be visualized due to the low level of confining stress (Figures 6b and 6c). It can be 
readily inferred that the degree of particle crushing will increase vastly with the increasing confining 
stress, as evident in Figure 6f. The specimen shows an overall contraction behavior at larger strains for V3
= 800 kPa and V3 = 1000 kPa. Under the highest confining stress of 1500 kPa, the specimen fails to dilate 
but keeps contracting linearly at a high rate until the simulation is stopped at an axial strain of 20%. As 
shown in Figure 6f, the amount of particle crushing is excessive, which explains the severe volumetric 
compression of the specimen. It is interesting to note that the crushing zone is mainly concentrated on 
both ends of the specimen, and an absence of a distinct, identifiable shear band is apparent. This 
observation suggests that the strength and failure of the specimen is mainly controlled by the massive 
crushing-induced volume compression, which prevails over the dilation caused by particle rearrangement 
and interferes with the formation of shear band. 
4. Conclusions 
This paper presents a 3D DEM study on the mechanical behavior of crushable granular soils subjected 
to plane strain compression conditions. The parallel bond model is adopted to form porous agglomerates 
and statistical variation of the particle fracture strength is achieved by randomly removing 5~10% of 
elementary balls comprising the agglomerates, which is demonstrated by the good agreement between the 
simulation data and Weibull’s distribution equation (1). By comparing the simulation results from 
crushable and uncrushable specimens under different levels of confining stresses, we find that the strength 
and failure behavior of the granular soils is governed by two types of competing deformation mechanisms: 
shear banding and crushing-induced volumetric compression. Under the relatively low confining stresses, 
the particle crushing is insignificant, so the strength and failure of the material is controlled by particle 
rearrangement-induced dilation and shear band formation. However, when the confining stress is high 
enough to cause significant particle crushing, the strength and failure of the material is then dominated by 
severe and continuous volumetric compression, which prevails over the dilation and interferes with the 
formation of shear band. 
5. Acknowledgments 
This study is supported by the Strategic Research Grant of City University of Hong Kong under 
Project No. 7008030.  This support is gratefully acknowledged. 
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3D DEM Simulation of Crushable Granular Soils under Plane Strain Compression Condition 

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3D DEM Simulation of Crushable Granular Soils under Plane Strain Compression Condition

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