Microscopic Geometrical Characteristics of the
Granular System and the Evolution Rules under
Complex Loads
Hou Ming-xun, Tang Meng-xiong, Hu He-song Guangzhou Institute of Building Science Co., Ltd., Guangzhou, 510641, China
Mo Hai-hong State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, 510641,
China
Chen Qiao-song Guangzhou Metro Corporation, Guangzhou, 510641, China
Abstract—An accurate quantification of the grains ’
arrangement and structure is the key to establish the
relationship between microscopic and macroscopic
properties for granular media, which is also of vital
importance for precisely predicting macro-deformation and
mechanical behavior using the system ’ s microscopic
properties. In order to further reveal the structural
characteristics of the granular media, a special loading
device was designed and developed; then, the polycarbonate
disk grains with the diameters of 3 mm and 5 mm were
prepared for photo-elastic tests under complex loads. The
relationship of the distribution frequency of the contact
angle between grains with grain scale, grain combination as
well as the magnitude and direction of the external load was
explored. Results reveal that: (1) for granular media
consisting of a single component, the geometrical structure
shows obvious initial anisotropy without the application of
load, the initial structure determines the transfer of force in
the granular system; during the shearing process, the
frequency distribution of the contact angle increased
significantly along the directions of great main stresses but
decreased along the directions of small main stresses. (2) for
the mixed granular system consisting of grains with two
different diameters, the anisotropy was not obvious,
whether under initial conditions or under compression and
shearing loads.
Index Terms—granular medium; geometrical
characteristics; contact angle; photo-elastic test
I. INTRODUCTION
Granular matter mechanics is a science that focuses on
the equilibrium and motion laws of the complex system
consisting of a great number of discrete solid particles
and the related applications. In this complex system, the
particles, with the diameter over 1 μm (d>1μm),
Manuscript received August 25, 2017; revised March 20, 2018.
interact with each other and the interstitial fluid and show
low viscosity and saturation (the saturationis generally
smaller than 1, i.e., S<1); additionally, the strongly
dissipative contact friction dominates the interaction
among these particles, while the thermal motion can be
neglected [1], [2]. For last two decades, researchers
began to notice the fine mechanical behavior in the
granular matter system and focused on the physical
mechanisms behind them [3], [4]. In the granular
system’s multi-scale structural framework, both the
theoretic studies based on the contact mechanics of solid
particles and the numerical simulation methods based on
discrete element method have achieved great progress
[5]-[8]. The researchers have made breakthroughs in
dissipative particle gas, granular discrete element, mixing
& grading, vibration and shear dynamic mechanisms
[9]-[11]. However, it was also realized that solid
mechanics based on continuum hypothesis falls short in
explaining the granular matter’s mechanical behavior,
and the phenomenological relations based on
macroscopic prototype tests cannot take into account the
effects of a single grain’s physical properties [10], [12].
The test methods and techniques of the granular
matter’s internal stress and strain are particularly
important in validating theoretical and numerical
calculation results and exploring the interaction
mechanisms in the granular matter. Photo-elastic testing
may be the only one experimental measure so far that can
visually reveal the internal force distribution in granular
matter [6], [13]-[15].
In 1957, Dantu first used photo-elastic technique to
observe force propagation model in the granular matter.
Oda et al. focused on the two-dimensional (2D) pillared
photo-elastic materials and investigated the contact force
distribution, fabric change and anisotropy in 2D granular
materials [16]. Nagel, S R and Majumdar, S [17]
simulated the non-uniform distribution of force in a
granular pile and found the load’s exponential decay
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© 2018 Int. J. Struct. Civ. Eng. Res.doi: 10.18178/ijscer.7.2.125-129
law when the internal force between the grains exceeded
the average contact force. R. R. Hartley and R. P.
Behringer [18] constructed a 2D shearing system using a
photo-elastic disk and then conducted slow shear tests on
the granular material to examine the correlation between
stress and shearing rate. They found that the average
stress showed a logarithmic relationship with the
shearing rate in plastic deformation, and the increase of
shearing rate would lead to the increase of the strength of
force chain network and the fluctuating amplitude of
stress, and simultaneously change the distribution rules
of stress concentration and relaxation. Through
photo-elastic disk tests on the granular system, T. S.
Majmudar1and M. Sperl [19] verified that the average
coordination number increased rapidly when the model’
s volume fraction reached the critical value; as the model’s volume fraction exceeded the critical value, the average
distribution number and uniform load increased
exponentially with the volume fraction. R. W. Yang and
X. H. Cheng [20] focused on a mixed granular system
that was composed of two kinds of grains with different
diameters and also used photo-elastic tests for
preliminary research of the system ’ s force chain
distribution and the geological structure change under 2D
direct shear tests; then, they processed the photo-elastic
experimental results using digital image technology,
attempted to characterize the bearing force on the
granular materials using color gradient algorithm and
acquired the force chain with average strength .
As stated above, these studies regarding granular
materials based on photo-elastic tests have greatly
advanced the development of granular dynamics in both
theory and numerical calculations [14], [21], [22]. For
gaining a better understanding of the granular system’s
geometrical features, this study designed and developed a
compressive/direct-shearing loading device for
photo-elastic granular materials. Two kinds of
polycarbonate disk grains with two diameters—3 mm
and 5 mm, were processed, and the photo-elastic tests
were performed on these granular media. The granular
medium’s geometrical characteristics and evolution
patterns under complex loads were investigated by
statistically analyzing the relationships of contact angle
with grain size, grain configuration, external load’s
magnitude and direction.
II. EXPERIMENTS
A. Experimental Model
(1) In order to study the photo-elastic grains with
high-transparency, small size and excellent
photosensitivity, this study used apolycarbonate sheet
with a thickness of 5 mm produced in Japan; then, using
the numerical-control (NC) carving machine for plastics,
the disks with the diameter of 3 mm and 5 mm were cut
out. Since the cutting face is parallel to the light direction,
the propagation of light is not affected by the processing
and the processed disks were characterized by high
transparency. High machine stress was produced at the
edge of grains during the cutting process, and therefore,
annealing should be performed on the polycarbonate
disks for eliminating the machine stress.
(2) In order to overcome the shortcomings of the
existing photo-elastic experimental system, this study
made use of the advantages of a digital photo-elastic
device, as well as designed and developed a special
loading device suitable for this work. As shown in Fig. 1,
the device is light and convenient so that small grains can
be easily placed in it; moreover, the planar photoelasitic
compression tests, shearing tests and the related
simulations of engineering structures can be conducted
using this device.
Figure 1. Illustration of the developed loading device
1-Shell frame; 2-Base; 3-Digital display instrument;
4-Upper shell of the container;
5-Lower shell of the container; 6-Axial loading system;
7-Shearing loading system;
8-Axial loading screw; 9-Shearing loading screw;
10-Cover plate for loading; 11-Screw
for lateral fixing; 12-Sliding rail board; 13-Rolling block;
14-Wire for data transmission;
15-Pin; 16-Photo-elastic granular medium
Figure 2. Schematic diagram of the test device
B. Experimental Setupand Procedures
(1) Experimental setup The granular materials are with a diameter of 5 mm
and 3 mm, respectively; and amixof these two disk grains
wasselected for this study. The materials were put into
the above-described experimental device; then,
compression and shearing were applied for investigating
the materials’ photo-elastic properties under complex
loads. The acquired photo-elastic pictures were then
processed using mean square grayscale (color) gradient
method and image digitalization technique.
(2) Experimental procedures
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© 2018 Int. J. Struct. Civ. Eng. Res.
①Firstly, after annealing, the disk grains with a
diameter of 3 mm were manually placed in the container
in a random way, during which the smooth surface of the
granular material should be parallel to the loading box’s
glass plate. Then, the container was placed in the loading
device, with
the loading device and the loading box parallel to the
photo-elastic device’s lens, and the loading box located at
the center of the photo-elastic device’s optical source.
Next, the axial loading screw was rotated so that the
loading cover plate was exactly touching the disk grains.
At that moment, the test started and the digital display
instrument was reset.
②The positive loading was applied by slowly rotating
the screw at a speed of 2 mm/min. The positive load and
displacement were recorded once after each advance for
a certain distance; meanwhile, two pictures were taken, a
photo-elastic picture of the granular materials under dark
conditions and another showing the geometrical
positioning of the disk grains under bright conditions.
③Similarly, the photo-elastic tests under shearing
action were then performed.
④For the disk grains with a diameter of 5 mm, the
above steps were repeated in order to investigate their
microscopic structural properties.
⑤Finally, for the mixed disk grains, the same steps
were performed.
(a) (b)
Figure 3. Illustration of the experimental results
III. RESULTS AND DISCUSSION
The pictures of the granular media after the removal of
rotationally polarized lens were then processed using
image processing software, and the distribution
frequencies of the grain’s contact angle for different grain
sizes, grain configuration sand load under compression as
well as the combined action of compression and loading
were investigated.
A. Evaluation Laws of the Contact Angle between
Grains under Different Compression Loads
(1) Results for the disk grains with a diameter of 3
mm As stated above, the disk grains with a diameter of 3
mm were put into the container, and the positive loads
were applied by rotating the axial loading screw. The
pictures under the positive load of 0 N, 30 N, 50 N and
70 N were selected for statistical analysis of the contact
angle, as the results is shown in Fig. 5. Since the contact
angles were symmetrical, the contact angles within the
range of 0~180° were selected and 9°intervals were set
as theanalysis range. The angles with the frequencies no
smaller than 0.018 were defined as the polarized angles,
and the polarized angles under the initial state were
defined as the initial polarized angles.
(a) under a positive load of 0 N
(b) under a positive load of 30 N
(c) under a positive load of 50 N
(d) under a positive load of 70 N
Figure 4. Frequency distributions of the contact angles in compression
tests
Due to the effects of boundary and sample loading, the
frequency distribution of the contact angle between
grains in each angle range shows strong randomness.
Therefore, in this study, we neglected the specific values
of frequency but focused on the overall evolution
patterns of the frequency distributions of the contact
angle, as the results shown in Fig. 6.
(a) (b)
(c)
Figure 5. Overall variation tendency of the frequency distribution of the contact angle between the grains with a diameter of 3 mm
(2) As shown in Fig. 6 (a), without the application of
initial load, six polarized angle ranges can be observed at
six angles--30 ° , 60 ° , 150 ° , 210° , 270 ° and 330 ° ,
respectively; the contact angle shows a
symmetricdistribution along these six directions, and the
distribution appears to be a six-pointed star. The
frequency distributions along these six directions differ
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© 2018 Int. J. Struct. Civ. Eng. Res.
greatly from the distributions along the other directions,
suggesting that the grains show obvious initial anisotropy
in the overall geometrical structure.
(3) As shown in Fig. 6 (b), with the increase of
positive compression load, the frequency of the contact
angle along the vertical distribution increased rapidly
while decreasing to varying degrees along the other
directions, suggesting an enhanced anisotropy in granular
medium’s geometrical structure. However, as shown in
Fig. 5(c), the frequency distribution of contact angle
shows a different tendency with the increase of applied
load. The deformation of grains and slippage and
dislocation between the grains can be observed under a
large load, which further caused the compaction and
recombination of grains and thereby changed the
variation tendency of geometrical structure.
B. Results for the Disk Grains with a Diameter of 5 mm
The pictures under the applied loads of 0 N, 50 N, 100
N and 150 N were selected for analyzing the variation
tendency of the distribution frequency of the contact
angle, withthe results shown in Fig. 6.
(a) (b)
Figure 6. Overall variation tendency of the frequency distribution of the
contact angle between the grains with a diameter of 5 mm
(1) It can be observed that, for the grains with a
diameter of 5 mm, their geometrical structure shows
obvious initial anisotropy; however, the polarized angle
ranges increased and the distribution appeared to be an
eight-pointed star. The grains with a diameter of 5 mm
differ greatly from those with a diameter of 3 mm in the
contact angles with higherfrequencies.
(2) With the increase of load along the vertical
direction, the frequency of contact angle increased
significantly along the vertical direction or in the
polarized angle range near the vertical direction, but
decreased significantly along the horizontal direction.
With increasing load, the frequency distribution of
contact angle almost remained unchanged, which is
unlike the variation tendency of the grains with a
diameter of 3 mm. This is due to the fact that, as the grain
diameter increased, slippage and dislocation between the
grains occurred was reducedduetothe limitations of
model size, and accordingly, the entiregrain system was
difficult to be recombined. 3. Results for the mixed
grains at a ratio of 3-mm grains to 5-mm grains of 2:3 The grains with the diameters of 3 mm and 5 mm were
mixed at a ratio of 2:3, and then randomly placed in the
container. The positive load was applied by rotating the
axial loading screw, and the pictures under the positive
loads of 0 N, 50 N, 100 N and 150 N were selected for
statistical analysis of the contact angle, with the results
shown in Fig. 7.
(a) (b)
Figure 7. Overall variation tendency of the frequency distribution of the contact angle between the mixed grains
(3) As shown in Fig. 8, for the mixed grains, the
contact angles show quite a different frequency
distribution with respect tothe results for the grains with a
single component. Specifically, the polarized angle
ranges decreased in number, and the difference of the
distribution frequency between the polarized angle
ranges and the non-polarized angle ranges decreased. The
overall distribution pattern falls in between a six-pointed
star and an eight-pointed star; overall, the grains show no
obvious anisotropy in geometrical structure.
(4) With the increase of load, the distribution
frequency of the contact angle within the polarized angle
range decreased gradually rather than increased; the
number of polarized angles also decreased. Finally, as
reflected by the contact results, the grains show
approximate isotropy in geometrical structure. Through
experimental observations, for the mixed granular media
consisting of two grains with different diameters, the
slippage and dislocation between the grains more easily
occurred, i.e., the smaller grains more easily moved to
the gap between larger grains.
IV. CONCLUSIONS
(1) For the granular media consisting of a single
component (i.e., the grains with an identical diameter),
the contact angle distribution implies that the internal
structural characteristics are uniform and symmetrical
and appears to be a six-pointed star along several
directions. This suggests that the granular system ’ s
overall geometrical structure shows an obvious initial
anisotropy. This anisotropy was increasedgradually after
the application of compression loads, withthe initial
anisotropy important for determining the evolution of the
system’s geometrical structure after the application of
load (the contact angle distribution remained unchanged
in pattern, but the frequency distribution in the initial
polarized angle ranges increased).
(2) For the granular media consisting of a single
component, under the application of shearing load,
translation, rolling-over and climbing can be observed,
The geometrical structures show significant changes, the
frequency distributions of the contact angles increased
remarkably along the large main stress directions but
decreased steadily along the small main stress directions,
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and the outer contour changed from approximate circles
to ovals.
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