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

125

International Journal of Structural and Civil Engineering Research Vol. 7, No. 2, May 2018

© 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

126

International Journal of Structural and Civil Engineering Research Vol. 7, No. 2, May 2018

© 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

127

International Journal of Structural and Civil Engineering Research Vol. 7, No. 2, May 2018

© 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,

128

International Journal of Structural and Civil Engineering Research Vol. 7, No. 2, May 2018

© 2018 Int. J. Struct. Civ. Eng. Res.

and the outer contour changed from approximate circles

to ovals.

REFERENCE

[1] N. Menon and D. J. Durian, “Diffusing-wave spectroscopy of

dynamics in a three-dimensional granular flow,” Science, vol.

275, no. 5308, pp. 1920-1922, 1997. [2] M. D. Silva and J. Rajchenbach, “Stress transmission through a

model system of cohesionless elastic grains,” Nature, vol. 406,

no. 6797, pp. 708-710, 2000. [3] P. Sipos, V. Kovács Kis, T. Németh, et al, “TEM-EDS study of

metals' partition at particle level after their sorption in soil: EGU

General Assembly Conference,” 2016 [C]. [4] Y. H. Jung, T. G. Kim, and S. Y. Shin, “A hierarchical approach

to soil arching problem via physical model test with photoelastic measurement and discrete element simulations,” Japanese

Geotechnical Society Special Publication, vol. 2, no. 17, pp.

654-659, 2016. [5] Q. C. Sun and G. Q. Wang, “Force distribution in static granular

matter in two dimensions,” Acta Physica Sinica, vol. 57, no. 8,

pp. 4667-4674, 2008. [6] Z. Zhang and R. Yang, “Development and application of direct

shear apparatus of photo-elastic granular materials,”

Experimental Technology & Management, 2011. [7] Y. G. Fang, “Shear test and physical mechanism analysis on size

effect of granular media,” Acta Physica Sinica, vol. 63, no. 3,

pp. 34502-34572, 2014. [8] Y. G. Fang and M. X. Hou, “Visual analysis of initiation of soil

arching effect in piled embankments,” Chinese Journal of

Geotechnical Engineering, no. 09, pp. 1678-1684, 2015. [9] I. Vazaios, K. Farahmand, N. Vlachopoulos, et al. “A study of

the geometrical and the mechanical scale-dependency of

fractured rockmasses using a micro/meso mechanical approach:

Canadian Geotechnical Conference,“ 2016 [C].

[10] M. Cox, D. Wang, J. Barés, et al. “Self-organized magnetic

particles to tune the mechanical behavior of a granular system,” Physics, pp. 296-297, 2015.

[11] L. Monforte, J. M. Carbonell, M. Arroyo, et al. “Performance of

mixed formulations for the particle finite element method in soil

mechanics problems,” Computational Particle Mechanics, pp.

1-16, 2016.

[12] O. Durán, N. P. Kruyt, and S. Luding, “Analysis of

three-dimensional micro-mechanical strain formulations for granular materials: Evaluation of accuracy,” International

Journal of Solids & Structures, vol. 47, no. 47, pp. 251-260,

2010. [13] Y. H. Jung and J. W. Jung, “Visualizing force-chain buckling in

stress and displacement fields of granular assembly using

photoelastic measurement,” Geotechnical Special Publication, vol. 27, no. 234, pp. 751-760, 2014.

[14] N. Sepúlveda and R. P. Behringer, “Measuring creep and

stick-slip behavior in 2-dimensional photoelastic granular medium,” 2013.

[15] S. Y. Shin, Y. H. Jung, and T. Kim, “Investigation of the change

of soil arch structure in model particle assembly subjected to displacing trapdoor via photoelastic measurement technique,” vol.

32, no. 10, pp. 31-40, 2016.

[16] M. Oda, J. Konishi, and S. Nemat-Nasser, “Experimental micromechanical evaluation of strength of granular materials:

Effects of particle rolling,” Mechanics of Materials, vol. 1, no. 4,

pp. 269-283, 1982. [17] S. R. Nagel, D. A. Schecter, S. N. Coppersmith, et al. “Force

fluctuations in bead packs,” Science, vol. 269, no. 5223, pp.

513-515, 1995. [18] R. R. Hartley and R. P. Behringer, “Logarithmic rate dependence

of force networks in sheared granular materials,” Nature, vol.

421, no. 421, pp. 928-931, 2003. [19] T. S. Majmudar, M. Sperl, S. Luding, et al. “Jamming transition

in granular systems,” Physical Review Letters, vol. 98, no. 5,

58001, 2006. [20] R. W. Yang and X. H. Cheng, “Direct shear experiments of

photoelastic granular materials,” Rock & Soil Mechanics, 2009.

[21] R. Hurley, E. Marteau, G. Ravichandran, et al. “Extracting inter-particle forces in opaque granular materials: Beyond

photoelasticity,” Journal of the Mechanics & Physics of Solids,

vol. 63, no. 1, pp. 154-166, 2014. [22] A. Tordesillas, D. Carey, A. B. Croll, et al. “Micromechanics of

elastic buckling of a colloidal polymer layer on a soft substrate: experiment and theory,” Granular Matter, vol. 16, no. 2, pp.

249-258, 2014.

129

International Journal of Structural and Civil Engineering Research Vol. 7, No. 2, May 2018

© 2018 Int. J. Struct. Civ. Eng. Res.