J. Cent. South Univ. (2015) 22: 619−630
DOI: 10.1007/s11771-015-2563-1
Generation of 3D random meso-structure of soil−rock mixture and
its meso-structural mechanics based on numerical tests
XU Wen-jie(徐文杰), ZHANG Hai-yang(张海洋), JIE Yu-xin(介玉新), YU Yu-zhen(于玉贞)
State Key Laboratory of Hydroscience and Hydraulic Engineering
(Department of Hydraulic Engineering, Tsinghua University), Beijing 100084, China
© Central South University Press and Springer-Verlag Berlin Heidelberg 2015
Abstract: The mesoscopic failure mechanism and the macro-mechanical characteristics of soil−rock mixture (S-RM) under external
load are largely controlled by S-RM’s meso-structural features. The objective of this work is to improve the three-dimensional
technology for the generation of the random meso-structural models of S-RM, for randomly generating irregular rock blocks in
S-RM with different shapes, sizes, and distributions according to the characteristics of the rock blocks’ size distribution. Based on the
new improved technology, a software system named as R-SRM3D for generation and visualization of S-RM is developed. Using
R-SRM3D, a three-dimensional meso-structural model of S-RM is generated and used to study the meso-mechanical behavior through
a series of true-triaxial numerical tests. From the numerical tests, the following conclusions are obtained. The meso-stress field of
S-RM is influenced by the distribution of the internal rock blocks, and the macro-mechanical characteristics of S-RM are anisotropic
in 3D; the intermediate principal stress and the soil−rock interface properties have significant influence on the macro strength of
S-RM.
Key words: soil−rock mixture (S-RM); three dimensional meso-structure; meso-structural mechanics (M-SM); true-triaxial
numerical test; random simulation
1 Introduction
Soil−rock mixture (S-RM) is an extremely uneven
and loose geotechnical material that formed during the
Quaternary and consists of high-strength rock blocks of
different sizes, fine-grained soils, and pores. S-RM is
common in nature, and is often encountered in various
engineering constructions. However, the internal
structure of S-RM is complex and may differ widely
depending on the location, and even within a formation
in a study area. The meso-structural characteristics of
S-RM may greatly affect the meso-failure mechanism
and the macro mechanical characteristics under an
external load. Therefore, for a better understanding of the
mechanical systems of S-RM it is important to study its
meso-failure
mechanism,
macro
mechanical
characteristics and the deformation based on the mesostructure of S-RM.
The rapidly developing digital image processing
(DIP) technology has been widely applied in various
fields, including soil and rock mechanics, where it
achieved significant results in the field of meso-structure
and meso-structural mechanics of soil and rock materials
[1−3]. Using X-ray tomography images, MASAD et al
[4] studied the evolution of the internal structure of
asphalt concrete mixtures during compaction, and found
that the aggregate structure tends to have more random
orientation, and the void distribution in the specimens is
nonuniform. Using DIP technology based on the crosssectional images of the S-RM, XU et al [3, 5] rebuilt a
real meso-structural model of S-RM, and conducted a
series of numerical tests with the rebuilt model, and
found that the existence of “rock blocks” in S-RM will
greatly influence the distribution of the internal stress
field and the failure models. COLI et al [6−7] analyzed
outcrop images of the Shale−Limestone Chaotic
Complex bimrock using a geostatistical approach and
identified the parameters characterizing the content and
variability of rock inclusions in the images. However, the
meso-structural model of S-RM established through DIP
depends on the images of the sample for analysis, and it
is difficult to obtain complete set cross-sectional images
of S-RM in field (or digital images that describe the
meso-structure) by the present technology. Therefore, the
DIP method has some limitations in the study of the
Foundation item: Project(51109117) supported by the National Natural Science Foundation of China; Project(20111081125) supported by the Independent
Research Plan of Tsinghua University, China; Project(2013-KY-4) supported by the State Key Laboratory of Hydroscience and
Engineering Project, China
Received date: 2013−10−14; Accepted date: 2014−04−25
Corresponding author: XU Wen-jie, PhD; Tel: +86−10−62782301; Fax: +86−10−62785593; E-mail: [email protected]
J. Cent. South Univ. (2015) 22: 619−630
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meso-structural mechanics of S-RM.
The spatial distribution and size composition of
internal “rock blocks” of S-RM have good
self-organization characteristics on a statistical level [3].
It is significant for the study of meso-mechanics and
stability analysis of the S-RM slope to establish the
meso-structural model of S-RM based on the statistical
regularity of S-RM’s meso-structural characteristics.
As we know, computer random simulation has been
widely applied in many fields [8−11]. The material
meso-structural model based on computer random
simulation technology has provided a novel method for
the study of meso-structural mechanics, macro
mechanics and the deformation and failure mechanisms
of materials. Based on the Monte Carlo method, WANG
et al [12], and XU et al [13] proposed a series of
two-dimensional (2D) procedures for generating random
aggregate structures of concrete and used the generated
2D random meso-structural models in numerical tests to
study the meso-mechanics of concrete. By simplifying
the rock blocks as regular geometric bodies (such as
circular, triangulare, rectangular, hexagon-shaped, and
etc.), YOU et al [14] generated a random structural
model of S-RM and studied its failure mechanism under
external load. Further, XU et al [15] developed a 2D
random meso-structure generation system of S-RM
based on arbitrary polygonal and elliptic rock blocks
(R-SRM2D), and used this system to study the
meso-mechanics of S-RM. Although these studies based
on the 2D meso-structural models have obtained
significant researches on the meso-mechanics of
geotechnical materials, it is very difficult to reveal their
meso-mechanical characteristics in three dimension. To
study the 3D mechanics of concrete, DU et al [16] and
CHEN et al [17] generated 3D concrete aggregates with
irregular shapes. LIU et al [18] developed an algorithm
to randomly model the meso-structure of asphalt
concrete, where the coarse aggregates were represented
with irregular polyhedron particles. However, there is no
study on the meso-mechanics of S-RM based on its 3D
meso-structure. The algorithms mentioned above have
provided good methods for generating S-RM
meso-structure. However, the size distribution of
particles (such as, rock block size percentage) in these
methods is very simple, and the spatial orientation of
particles was not taken into consideration. So, there are
some limitations when using them to generate the
meso-structure of S-RM directly.
2 Objectives and scope
The aims of this work were to improve the 3D
random meso-structural modeling technology for
studying the physical and mechanical characteristics of
S-RM and develop generation and visualization software
system named R-SRM3D. Based on the random mesostructural models established by R-SRM3D, a series of
true-triaxial numerical tests were conducted to study the
mesoscopic failure mechanism of S-RM and the effect of
the meso-structure on its macro-mechanical behavior.
3 Key technology of random generation
The random number, the size distribution and the
spatial position and orientation of the rock blocks are
three main issues in the generation of meso-structural
model of S-RM. Among them, the random number is the
most basic element of random simulation. The following
two technologies determine the statistical similarity
between the obtained random meso-structural model of
S-RM and the studied sample.
3.1 Random number
The generation of the random number is an
important step in the random simulation using the Monte
Carlo method. The meso-structural characteristics are
generated on the basis of the random number during the
random structural modeling, including the space position,
space orientation and size distribution of rock blocks.
The most basic random number obeys uniform
distribution, which is a set of uniformly distributed
random variables on the interval [0, 1]. The random
variables in other distribution forms (such as normal
distribution, exponential distribution) can be obtained
through mathematical transformation on the basis of the
uniform distribution.
3.2 Size distribution of rock blocks
The size distribution of rock blocks of S-RM shows
a good linear correlation in the double logarithmic
coordinates [3, 8]. This provides the basis for the size
distribution of internal rock blocks in the meso-structure
generation of S-RM. XU et al [3, 8] showed that the
granularity fractal dimension characteristics of the rock
blocks of S-RM can be obtained based on the statistical
analysis of rock block content of soil-rock mixture
through digital image processing (DIP), in a laboratory
or by field screening. The particle size distribution
function of the rock blocks of S-RM can then be
established.
According to the granularity fractal dimension
characteristics of the rock blocks and the soil/rock
threshold (dS/RT) of the S-RM, the maximum grain size of
the rock block dmax can be obtained.
1
d max
 100  3 Dr

 dS/RT  
 100  Rp 


(1)
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where Dr is the granularity fractal dimension of the rock
block; Rp is the rock block content (%), and Rp=100−
P(dS/RT); P(dS/RT) is the cumulative percentage content of
all particle sizes smaller than dS/RT (%), and dS/RT is the
soil/rock threshold.
The rock block size is divided into several groups
according to the soil/rock threshold (dS/RT) and the
obtained maximum rock block size (dmax). The lower
limit of each group interval is set to the particle size of
this block group, and the rock block group order is in a
descending order. Therefore, the percentage content of
the ith rock block group in the total sample is described
as
 d (1)  (3 Dr )
Rp (i )  100   r 
 d r (i) 

 d (1) 

  r
 d r (i  1) 
 (3 Dr ) 



spherical surface, with the two points distributed on both
sides of the circle plane. As a result, a hexahedron is
generated by the equilateral triangle (ABC) and the two
points (D, E). In order to facilitate further generation of
the irregular polyhedral blocks, the distances between the
points (D, E) and the plane formed by the triangle ABC
are controlled to be more than 0.2 times the random
sphere’s radius so that the surfaces of the generated
hexahedron will not be too small. The generated
hexahedron is ensured to be a convex polyhedron.
(2)
where dr(i) is the lower limit of the ith rock block group,
dr(i)> dr(i+1), and ΔRp(i) is the percentage content of the
ith rock block group in the total sample.
3.3 Spatial position and orientation of rock blocks
When a single rock block is generated, the spatial
position and orientation of the rock block needs to be
determined as follows.
1) Position of the rock block. The position of the
rock block in S-RM is very complicated, and it is
difficult to express the coordinates of the rock block
centroids with a corresponding mathematical function
because of the great randomness. Therefore, the centroid
coordinates of the rock block are simplified to conform
with the uniform distribution in the generation space.
2) Rock occurrence. This describes the orientation
and inclination of the main axle of the rock block. Rock
blocks in S-RM usually distributed in a main direction
[3]. The main axles of the rock blocks are assumed to
have normal distribution or uniform distribution within a
certain range of angles which can be chosen by the users.
4 Algorithm for random generation of 3D
meso-structure of S-RM
4.1 Random generation of single block
The 3D rock block, which is represented by an
irregular polyhedron, is randomly generated in
accordance with certain rules based on a simple block
(tetrahedron, hexahedron, and etc.).
1) Basic block of random hexahedron.
The tetrahedron or hexahedron is generated based
on a random sphere with a diameter that equals the rock
block size (Fig. 1) following these three steps. First,
randomly generate an equilateral triangle (ABC)
inscribed in a circle through the center of the random
sphere. Then, generate points D and E randomly on the
Fig. 1 Inscribed hexahedron of a sphere generated randomly
2) Random generation algorithm of 3D block.
The principle of the random generation of the 3D
block is that the triangle surface is extended if its area is
larger than the area Smin, which is set as
S min   
3 3R 2
4
(3)
where R is the radius of the random sphere (the grain size
of the block) and ξ is a coefficient that can be set to a
value in the range of 0.1−0.3.
The three spatial points A1, A2, and A3 have
coordinates (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3),
respectively, as shown in Fig. 2. According to the Heron
formula, the area of the triangle can be expressed as
Δ  s  (s  d1 )  (s  d 2 )  (s  d 3 )
(4)
where d1, d2 and d3 are the lengths of the three sides of
the spatial triangle.
d1  ( x1  x 2 ) 2  ( y1  y 2 ) 2  ( z1  z 2 ) 2
d 2  ( x1  x3 ) 2  ( y1  y3 ) 2  ( z1  z3 ) 2
d 3  ( x2  x3 ) 2  ( y 2  y3 ) 2  ( z 2  z3 ) 2
s  (d1  d 2  d3 ) / 2
Based on the above calculation, the center of gravity
O of the selected extension surface can be calculated. A
new sphere can now be generated with its center at point
O and a radius equals the maximum distance L ma x
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Fig. 2 Generated point P extending from triangular surface
A1A2A3
between the center of gravity and the vertex on the
surface. According to this new sphere, a new vertex P
can be obtained [16].
x P  ( x1  x2  x3 ) / 3    Lmax cos( r1  360)  sin( r2 180)
(5)
y P  ( y1  y 2  y3 ) / 3    Lmax sin( r1  360)  sin( r2 180)
(6)
z P  ( z1  z 2  z3 ) / 3    Lmax cos(r2 180)
(7)
where (xP, yp, zp) are the coordinates of point P; r1 and r2
are two random numbers in the interval [0, 1]; and χ is a
coefficient in the range of 0−1 that controls the
generation of the rock block. Figure 3 shows the
influence of χ on the shape of the rock block. In the
simulation, the value of χ can be set to determine the
shape of the generated rock block between 0 and 1 as
random number.
Furthermore, for point P to satisfy the requirements
of the 3D block generation, the program needs to execute
the following judgments:
1) Whether point P is at the outside of the generated
3D block, that is whether the point P invades the space
inside the convex polyhedron;
2) Whether the distance between point P and point
O is less than the upper size limit of the particle group of
the generating block, and the size of the generated rock
block is within the specified group.
3) Whether the position of point P ensures that the
newly generated polyhedron is still a convex polyhedron,
namely, does it satisfy the criterion of the spatial
polyhedron’s convexity?.
Point P is a newly extended point of the block if the
above three conditions are satisfied. The corresponding
triangular surfaces are generated, and the vertexes of
each triangle surface are sorted in a counterclockwise
direction from the outside toward the inside of the block.
The volume of the tetrahedron PA1A2A3 (Fig. 2) can be
expressed as
Fig. 3 Examples showing influence of χ on rock block shape: (a)
χ= 0.4; (b) χ= 0.6; (c) χ= 0.8
V 
xP
yP
zP 1
1 x1
6 x2
x3
y1
y2
y3
z1
z2
z3
1
1
1
(8)
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The calculated volume according to Eq. (8) is less
than zero if point P is inside the boundaries of the
convex polyhedron, and is bigger than zero if point P is
outside the convex polyhedron. Therefore, the criterion
that determines whether point P is in or out of the convex
polyhedron Ω can be described as
 P  Ω , V >0

 P is on the boundary of  , V =0
 P   , V <0

(9)
4) Judging spatial polyhedron’s convexity.
To ensure that the shape of the rock block conforms
to the requirements, a convexity test for the generated
polyhedron is needed at each step. According to the
abovementioned arrangement of the triangle vertexes of
the polyhedron, if the generated block is still a convex
polyhedron, then the volume of the block (obtained by
Eq. (8)) that is formed by all the triangular surfaces except
the generating triangle and point P is less than zero.
Based on the algorithm that generates the single
convex polyhedron, the process of generating the 3D
block by randomly extending the basic convex
hexahedral block is shown in Fig. 4.
4.2 Determining intersection of blocks
There are many technical problems during the
establishment of the random meso-structural model of
S-RM such as the algorithm for the random generation of
block, the size composition, and the block’s spatial
orientation. Furthermore, when the new block is put into
the sample space, the position of the generated 3D block
relative to the existing blocks needs to be determined, ie.,
whether it invades the space of any existing blocks. That
is the criterion of block intersection.
If the newly generated block is put into a location
where it intersects with an existing block, the process
fails, and continues into the next step, where it puts the
block into another location of the sample, until it does
not intersect with any existing blocks. The space
geometry algorithm and the graphics interfering method
are applied to determining whether the new and existing
block intersect, as described below.
4.2.1 Space geometry algorithm
There are two kinds of situations where adjacent
blocks intersect: one is when the vertex of one block is in
the internal of another block; the other is shown in Fig. 5.
For the first case, Eq. (13) can be employed as the
Fig. 4 Illustration of growth process
of a block: (a) Original hexahedron;
(b) First growth of block; (c) Second
growth of block; (d) Third growth of
block; (e) Fourth growth of block
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Fig. 5 Special situation of intersection between two convex
polyhedrons
judgment criterion. For the second case, the edges of the
new block should be detected if they intersect with the
surfaces of the existing block.
The coordinates of the three points A1, A2, and A3
are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3), respectively.
The vector n normal to the surface A1A2A3 is defined as
i
n  x1  x2
j
y1  y2
k
z1  z2
x1  x3
y1  y3
z1  z3
(10)
Thus, n=ai+bj+ck, where a=(y1−y2)(z1−z3)−(y1−y3)
(z1−z2); b=(x1−x3)(z1−z2)−(x1−x2)(z1−z3); c=(x1−x2)(y1−
y3)−(x1−x3)(y1−y2); i, j and k are unit vectors.
According to space geometry, the equation of the
space plane that contains the three points A1, A2 and A3
can be expressed as
a ( x  x1 )  b( y  y1 )  c( z  z1 )  0
(11)
Furthermore, the parametric equation of the straight
line that contains points A4 (x4, y4, z4) and A5 (x5, y5, z5)
can be expressed as
 x  x 4  ( x5  x4 )t

 y  y 4  ( y5  y 4 )t
 z  z  ( z  z )t
4
5
4

(12)
The parameter t can be obtained by substituting
Eq. (12) into Eq. (11). The coordinates of point P, the
intersection of the straight line A4A5 and the space plane
A1A2A3, can also be calculated (Fig. 5). The following
criteria can be applied to determining if point P is in the
triangle A1A2A3.
 S p  SΩ , P  Ω

or P is at the boundary of Ω

  S p  SΩ , p  Ω
(13)
where Ω is the space plane domain formed by A1A2A3, SΩ
is the area of the spatial triangle A1A2A3 (Eq. (4)), and
ΣSP is the total area of the triangles formed by point P
and the edges of triangle A1A2A3.
4.2.2 Graphics interfering method
Existing graphics softwares, such as AutoCAD,
Open Inventor, and CATIA, have powerful graphics
operation functions (such as Boolean operation) and have
powerful functions in secondary development. We use
the graphics interfering method with the scripting
language of these software products to conduct the
Boolean intersection operation between a newly
generated block and an existing block. If the volume of
the obtained block is larger than zero then the two blocks
intersect; otherwise, the two blocks do not intersect.
Hence, when developing a 3D meso-structure modeling
system based on these graphics software (such as
AutoCAD), we can use the graphics interfering method
of the software to judge if the new rock block intersects
with existing block.
4.3 Development of 3D meso-structure modeling
system of S-RM
The random meso-structure modeling system of
S-RM — R-SRM3D, based on the convex polyhedron
block, is developed based on the abovementioned
algorithm. The structural model of R-SRM3D can be
easily imported into finite element softwares (such as
ABAQUS or ANSYS) for numerical tests that provide a
powerful technical support for studying of the
meso-structural mechanics of S-RM. The basic flow
chart of the development of the R-SRM3D system is
shown in Fig. 6.
The 3D random meso-structure models of S-RM
with different rock block contents are established
through the R-SRM3D system, as shown in Fig. 7.
5 True-triaxial numerical tests of S-RM
5.1 Test case
The physical and mechanical properties of S-RM
show a high degree of anisotropy characteristics in 3-D
space due to the irregularity of the rock block shape and
the non-uniformity of the spatial distribution. To study
the deformation and strength features of S-RM under
various stress conditions, some true-triaxial numerical
tests are conducted based on the 3-D S-RM samples
generated by R-SRM3D. The results confirmed the
feasibility of the developed system in this work.
The selected sample area was 1 m×1 m×2 m, the
rock block content was 40%, the soil/rock threshold
(dS/RT) was 0.07 m, and the rock block size distribution
fractal dimension was 2.78. The 3-D sample of S-RM
generated by R-SRM3D is shown in Fig. 8.
The material parameters of the soil and rock in the
simulated sample are listed in Table 1. The soil was
modeled as Mohr-Coulomb material, and the rock blocks
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Fig. 6 Flow chart of R-SRM3D process
were assumed to be elastic material where any failure of
the rock block was ignored. Coulomb friction contact
was used to simulate the interaction between the soil and
rock, and the friction coefficient was 0.5 unless
otherwise noted.
The numerical tests were conducted using the finite
element software ABAQUS. The soil and rock were
meshed with four-node tetrahedral elements (Fig. 9).The
total number of nodes was 91787 and the total number of
elements was 406173. The axial stress was applied
separately through the two rigid plates at the top and the
bottom of the sample (Fig. 9(a)). Coulomb friction
contact was used to simulate the interaction between the
rigid plate and the sample, with a friction coefficient of
0.5.
The process of the numerical testing can be divided
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Fig. 7 Three-dimensional random meso-structure models of
S-RM with different rock block contents generated by
R-SRM3D (sample dimensions of 1 m×1 m×2 m): (a) Rock
block content 30%; (b) Rock block content 50%
Fig. 9 Whole model and finite element mesh of numerical test
model of S-RM: (a) Whole model of sample and its 3D profile;
(b) Finite element mesh of rock blocks
Fig. 8 Three-dimensional meso-structural model of S-RM (rock
block content 40%): (a) Spatial distribution of block stone; (b)
3D profile of generated sample
Table 1 Soil and rock block parameters of S-RM used in
numerical test
Material
Elastic
Poisson Density/ Friction Cohesion/
modulus/MPa ratio (kg·m−3) angle/(°)
kPa
Soil
50
0.3
1800
30
50
Rock
block
2.4×104
0.2
2500
—
—
into three steps. 1) The 3D consolidation of the sample is
conducted under a given consolidation pressure (the
minimum principal stress). 2) The side pressure in one
direction (x or y) increases to the intermediate principal
stress of the test. 3) To slowly apply the axial stress to
the sample, a velocity load (0.05 mm/s) is applied to the
rigid plates at the top and bottom of the sample until the
axial strain reaches 15%.
5.2 Analysis of numerical test results
5.2.1 Effect of intermediate principal stress
To study the effect of the intermediate principal
stress on the stress strain relationship of S-RM,
true-triaxial numerical tests were conducted under
different stress conditions. The minimum principal stress
applied to the specimen surface that is perpendicular to
the x axis was 400 kPa, and the intermediate principal
stresses applied to the specimen surface which is
perpendicular to y axis were 400 kPa, 800 kPa and
1.2 MPa.
Figure 10 shows the internal stress distribution of
S-RM obtained from the true-triaxial tests. Here, the
minimum principal stress σ3 was 400 kPa (applied on the
side surfaces of the sample perpendicular to the x axis, or
σ3 parallel to the x axis, σ3//x), and the intermediate
principal stresses were 400 kPa and 800 kPa (applied on
the side surfaces of the sample perpendicular to the y
axis, or σ2 parallel to the y axis, σ2 //y). Because of the
extreme difference between the mechanical properties of
soil and rock, the meso-stress field is non-uniform, the
deformation appears incompatibility and high stress
concentrations appear at the soil−rock interface.
Generally, the strength of the soil−rock interface is lower
than that of naturally-occurring soil and rock blocks.
Therefore, the soil−rock interface is the weakest zone in
the S-RM. During the shear failure process, a plastic
shear band first appears around the rocks in the middle of
the sample, then gradually expands around the whole
rock block as the shear load increases as shown in Fig. 11.
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Fig. 10 Internal stress distribution in S-RM sample (arrow
shows principal stress direction, with σ2 parallel to y axis): (a)
σ2=400 kPa; (b) σ2=800 kPa
Fig. 11 Evolution of damage process of S-RM during
true-triaxial test
Figure 12 shows the final shear band obtained from
the true-triaxial test. The shape of the shear band is
closely related to the distribution of the rock blocks, and
is also affected by the external load. The main shear band
of the sample appeared in the form of an “X” in the plane
perpendicular to the intermediate principal stress when
the intermediate principal stress was much larger than the
minimum principal stress (Fig. 12(b)). However, the
shear band form was not obvious when the intermediate
principal stress was equal to the minimum principal
stress (Fig. 12(a)).
627
Fig. 12 Shear band obtained by true-triaxial test of S-RM
sample (σ2//y): (a) σ2=400 kPa; (b) σ2=800 kPa
Figure 13 shows the relationship between the stress
deviation (σ1−σ3) and strain obtained in the true-triaxial
numerical tests. The minimum principal stress σ3 was
applied on the side surface of the sample perpendicular
to the x axis (σ3 parallel to the x axis, σ3//x) with σ3=
400 kPa. The intermediate principal stress σ2 were
applied on the side surfaces of the sample perpendicular
to the y axis (σ2 parallel to the y axis, σ2//y), with σ2=
400 kPa, 800 kPa and 1.2 MPa. The relationship curves
change with the variation of intermediate principal stress
σ2 while the consolidation pressure σ3 remained constant.
With the increment of the intermediate principle stress
the limitation of the rock blocks in 3D space will
increase too, which will improve the resistance of the
rock blocks to the external load. As a result, the shear
strength of the sample increases with the increment of
the intermediate principal stress. When the sample
entered into the plastic stage, the slope of the curve
increased as the intermediate principal stress rose,
indicating that the strain hardening became more obvious
with the rise in intermediate principal stress. Therefore,
the intermediate principal stress has a significant effect
on the stress−strain relationship of S-RM, especially in
the plastic stage.
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J. Cent. South Univ. (2015) 22: 619−630
were conducted where the direction of the minimum
principal stress (400 kPa) and intermediate principal
stress (800 kPa) was interchanged. Figure 15 shows the
shear zone obtained from the triaxial shear test with the
intermediate principal stress applied on the side surfaces
of the sample perpendicular to the x axis (σ2 parallel to
the x axis, σ2//x)
Fig. 13 Stress−strain relations of S-RM from true-triaxial shear
tests under different stresses
Furthermore, uniaxial compression tests (σ2=σ3=
0 kPa) of S-RM were conducted, as shown in Fig. 13.
The strength of S-RM under unconfined uniaxial load is
far below the strength under confined conditions. In the
uniaxial compression test, the normal stress at the
soil−rock interface was low; therefore, the resistance at
the soil−rock interface was small, resulting in a sharp
decrease in the macro strength of the sample. Figure 14
shows the failure process of the sample under uniaxial
compression condition. The soil−rock interface gradually
expanded and separated at various positions as the
deformation developed, leading to obvious dilatancy
features in the sample. The macro strength of the S-RM
sample decreased because of the separation of the soil
and rock block, which decreased the interaction between
the soil and the rock block. The shearing strength of the
soil−rock interface increased as the confining pressure
was raised, and the macro mechanical strength of the
S-RM sample sharply improved.
Fig. 15 Shear band obtained by true-triaxial test with
intermediate principal stress (800 kPa) parallel to x axis (σ2//x)
Figure 16 shows the relationship between the stress
deviation (σ1−σ3) and strain under different stress
directions. A significant difference exists between the
curves when the direction of intermediate principal stress
is different from that of the minimum principal stress.
The position and form of the sample’s shear band clearly
changes because of the change in direction of the
intermediate principal stress and the minimum principal
stress (Fig. 12(b), Fig. 16). The macro strength of S-RM
is sensitive to the direction of the external load because
of the difference in the internal rock block shapes and
rock block spatial distribution. Therefore, the mechanical
properties of S-RM have anisotropic characteristics
because of the different meso-structural characteristics
such as rock block shape, and spatial distribution.
Fig. 14 Evolution of damage process of S-RM during uniaxial
compression test
5.2.2 Mechanical anisotropic characteristics of soil−rock
mixture
In order to study the anisotropic characteristics of
S-RM in 3D space, the simulated true-triaxial shear tests
Fig. 16 Effect of stress direction on macro mechanical property
of S-RM
J. Cent. South Univ. (2015) 22: 619−630
5.2.3 Effect of soil−rock interface characteristics
Because of the extreme difference between the
physical and mechanical properties of the soil and rock
on both sides of the soil−rock interface, the stress and
deformation of S-RM in the two sides of the soil−rock
interface appear incompatible (Fig. 17), which leads to
stress concentration on the soil−rock interface. As we
know, the origins of S-RM are different in nature, the
soil−rock interfaces are also different. In order to study
the effect of the soil−rock interface on the mechanical
properties of S-RM, triaxial numerical tests with a
friction coefficient (fc) of soil−rock interface of 0.5, 0.2,
and 1.0 (σ2=σ3=400 kPa) were conducted in this work.
The relationship between stress deviation (σ1−σ3) and
strain (Fig. 18) shows that the soil−rock interface
characteristics have a significant influence on the macro
mechanical properties of the S-RM: the macro shear
strength of the S-RM increases as the shear strength of
the soil−rock interface increases.
629
soil−rock mixture is improved. Based on this technology,
a generation and visualization software system named
R-SRM3D is developed.
2) Using R-SRM3D, the meso-structural model of
S-RM containing irregular rock blocks with different
shapes, sizes and distribution can be generated randomly
according to the characteristics of the rock block size
distribution, which confirmed that it is an effective tool
for the research of meso-structure and mechanical
properties of S-RM.
3) Based on the structural model randomly
generated by the R-SRM3D, the strength characteristics of
S-RM are studied using true-triaxial numerical tests. The
results show that the meso-structural characteristics have
a great effect on the internal stress distribution, the
deformation failure mechanism and the macro
mechanical properties of S-RM. The mechanical
properties of S-RM have anisotropic characteristics due
to differences in the internal meso-structural properties
such as rock morphology and spatial distribution.
Furthermore, the mechanical properties of the soil−rock
interface have a direct influence on the macro
mechanical properties of S-RM.
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