# Experimental Study on the Characteristics of Granular Materials’ Flows and Fractures under Uniaxial Compression

Authors: Futian Zhao; Jun Liu; Zhimin Xiao; Mingqing Liu; Yue Wang; Chen Ou; Mengyang Zhen
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

The mechanical behaviors of granular materials have high complexity. Since the mechanical behaviors of granular materials are difficult to describe theoretically, in this paper, the flow and fracture characteristics of granular materials were discussed by the experimental method. An experimental method was firstly proposed to identify the mechanical behaviors of granular materials under extra loading. An experimental device, which can be used to monitor force and displacement between particles, was invented. The uniaxial compression experiments of granular particles with different materials and grades were carried out, and the overall and local force between particles was obtained and investigated. Due to the flow of particles, the overall force rises in a fluctuating manner and the local force is not distributed evenly. Then, the particle fragments were sieved layer by layer. It was confirmed that the particles and loading strength have great influences on fractures of granular materials.


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## Body

## 1. Introduction

Granular materials consist of discrete particles and surrounding voids. The mechanical behaviors of granular materials are involved in many engineering fields, such as mining engineering, mineral processing engineering, blasting engineering, hydraulic engineering, railway engineering, and so on. The flows and fractures of granular materials under external loading are very common and play important roles in these related engineering fields, such as ore crushing, mechanical behaviors of rockfill dam, the flows and fractures of railroad slag, and so on.The flows and fractures of granular materials are very complicated because the undisturbed granular materials resemble solid and the disturbed granular materials exhibit fluid characteristics. Therefore, the mechanical behaviors of granular materials are different from solids and fluids, which determines the complexity of its mechanical behaviors [1, 2]. During flow process, the collision between particles or particles and boundary would cause particle breakage, the broken particles would be incorporated into the particle system and continue to flow as part of the particle system, and further fractures would occur [3–11]. However, there are many factors [12–20] that affect the flows and fractures of granular materials, such as particles’ strength, size, shape, gradation, and loading rate. Due to the complexity of mechanical properties of granular materials, great efforts have been devoted to study the flows and fractures of granular materials in the past decades, and the main research methods are experiment and numerical simulation.Experimental research is divided into the single particle test and the particle system test. The purpose of single particle test is to establish the relationship between the strength, shape, and size of particle and the degree of particles’ fractures under different loading conditions and to identify the influencing factors and fracture mechanism. Gorham and Salman and Fu et al. [21, 22] analyzed the failure patterns under impact loading for single spherical particle made of glass, polymethyl methacrylate, and marble powder by impact tests. The results indicated that dynamic effects of particle under impact were clearly important, even at comparatively low-impact velocities. The high-velocity failure mode is not reproducible by any quasistatic test and is a consequence of the very high loading rate as the impact stresses reach very high values. Antonyuk et al. [23–25] studied the breakage behaviors of single γ-Al2O3 spherical particle by compression and impact tests. The breakage mechanisms of granule during elastic, elastic-plastic, and plastic deformation are explained. Chau et al. [26] proposed a new stress analysis method for isotropic elastic spheres compressed between two flat rigid platens. In this method, the size of the contact zone can be estimated quite accurately in terms of the granule size, the dynamic hardness, and the impact energy. The impact energy for fragmentation increases monotonically with the size and strength of the granules. By comparing the static and dynamic tests, an empirical formula is proposed to estimate the impact energy needed to break a granule if the static energy for fragmentation is known. Schubert et al. [27] studied the size distribution of fragments from a concrete granule failure under impact loading. A formula was proposed by Astrom and Herrmann [28] to describe the fragment size distribution by means of a statistic method. Olivier et al. [29] analyzed the size effects in single grain fragmentation by compression tests and two fracture modes were introduced, i.e., volume fracture and contact fracture. Jansen and Stoyan [30] verified the validity of the Weibull failure model for single brittle granule by compression tests.Compared to the single particle test, the loads and interaction between the particles in the particle system test are often complicated, considering not only compression and shear stress, but also the sliding friction and rolling friction between particles. Moreover, the particle breakage is still an important factor affecting the mechanical behavior of granular material.The uniaxial compression test of a sample consisting of the same particles shows that the yield strength of granular material is related to the average tensile strength of the particles [31]. Lade and Yamamuro [32, 33] pointed out that the high confining pressures cause large amounts of particle crushing, which in turn cause the development of large positive pore pressures. This led to the effective stress path to move rapidly toward the effective stress failure envelope. The Mohr–Coulomb strength, effective stress, and angle of secant friction are approximately the same in compression and tension. Vallejo et al. [34] conducted particle compression crushing tests using the same size glass beads and simulated the experimental process by the discrete element methods, the results show that the granular material forms a new system, and the particle size distribution in the new system presents a natural fractal feature. The above studies analyzed the mechanical behavior of granular material composed of the same size particles; however, the particle size distribution is one of the important parameters that describe the composition of granular material, which directly affects the constitutive relation of granular material [35]. Grine et al. [36] conducted shear fracture experiments of carbonate sand; as the proportion of silica sand and cement increases, the ability of the particles to resist crushing increases, and when the silica sand and cement are added to a certain proportion, the shear strength of particles reaches a maximum value. The compression experiments of three different granular materials under high stress condition were performed by Hagerty [37]; particle crushing is influenced by initial void ratio, particle size, particle angularity, and particle material composition. Three phases of compression behavior were identified: volume decrease as a result of particle rearrangement at low stresses; more intense compression as particles crush and are rearranged extensively under higher stresses; and pseudo elastic behavior characterized by very high values of constrained modulus, as the number of contacts between fractured particles increases greatly at very high stresses.Due to the large number and fluidity of particles, it is difficult to measure the contact force between particles by experimental methods; with the development of computers, numerical simulation methods have become an effective way to study the mechanical behavior of granular material. The discrete element method (DEM) was proposed by Cundall in 1971; DEM establishes an explicit equation group based on the motion equation of each unit; according to Newton’s second law and constitutive relation, the equation group can be solved by time-step iteration. DEM is suitable for dealing with large deformation, large displacement, and dynamic problems, as DEM does not necessarily need the particle motion to satisfy the continuous displacement [18, 38–46]. However, the contact force model in DEM simulation is based on assumptions and simplifications, and the calculation results are all approximate values. The parameters of contact force model are difficult to determine, such as stiffness, time-step, and so on. If the values of parameters are unreasonable, it may cause a large difference between the simulation results and experimental results.The mechanical properties of granular material have high complexity compared to the continuous material, and the existing experimental and numerical methods have some limitations. The current research studies are mainly focused on the influence of particle breakage on the overall mechanical behavior of granular material, lacking the analysis to the local mechanical behavior of granular material. Therefore, systematic experimental studies on granular materials with different sizes and gradations are important for identifying the flow and fragmentation mechanism of granular materials.In this paper, a systematic method was proposed to measure the mechanical behavior of granular material. A mold for making spherical particles was produced, which can produce different sized particles. The experimental fixture was improved, and through the fixture, the mechanical experiments of granular material can be performed on conventional pressers. Space for sensors was reserved on the fixture to monitor the local and overall loads of particles, and the stress-strain relationship of the particles can be obtained during loading. After loading, the particle size distribution can be counted by the layer-layer sieve test to analyze the damage characteristics of particles.In the following sections, the experimental method and equipment were first introduced. Then, the results and some phenomena were also illustrated. Finally, the main conclusions from the study are drawn.


## 2. Experiment Method

In this experiment, a number of cement mortar particles of diameter 3, 4, and 5 cm were made by the designed mold, and a number of cement particles of diameter 0.6–2.2 cm were made by hand. Then, the particles were grouped, and the crushing experiments were carried out by groups. The experimental fixture was improved, and the mechanical experiments of granular material can be performed on conventional presses. During loading, the local and overall loads and displacement can be measured by the pressure sensors and electronic displacement meters. After loading, the fixture is divided into three layers according to the height, and the sieving experiments are performed on each layer to obtain the size distribution of particles.


### 2.1. Experimental Specimen

Experimental specimens are of two types: (1) cement mortar particles and (2) cement particles. Cement mortar particles are made of cement, sand, and water in a certain ratio (see Figure1). The cement used is Portland cement with strength of 32.5 MPa, and the fineness modulus of sand is between 2.3 and 3.0. The diameters of particles are 3, 4, and 5 cm, the shape of particles is regular, and size error is small. The shape of particles made by hand is similar to sphere, and the diameter ranges from 0.6 cm to 2.2 cm.Figure 1
Experimental specimen: (a) the mold; (b) the cement mortar particles; (c) the cement particles.
(a)(b)(c)


### 2.2. Experimental Setup

In this work, the loading was performed by the electrohydraulic servo machine, and the pressure sensor and electronic displacement meter are used to measure the local and overall loads and displacement. The monitored signal is saved by a computer through a dynamic resistance strain gauge (see Figure2).Figure 2
The experimental setup: (a) press machine; (b) pressure sensor; (c) electronic displacement meter; (d) dynamic resistance strain gauge.
(a)(b)(c)(d)An experimental device as a container for granular material was developed, and the device has four parts: fixture, upper bearing plate, lower bearing plate, and pin (see Figure3).Figure 3
The container for granular material: (a, b) the fixture; (c, d) lower bearing plate and pins; (e) upper bearing plate.
(a)(b)(c)(d)(e)The fixture is a cylindrical barrel, and the upper inner wall diameter is slightly larger than the lower. The pressure sensor can be placed inside the fixture, and the data line can be led through the hole in the lower part of the fixture. The lower bearing plate is a round steel plate with two holes, and the holes are symmetrical about the axis of the bearing plate. The pins are two solid steel cylinders, which are placed into the holes of the lower bearing plate. The surfaces of pins are in the same plane as the surface of the lower bearing plate, and the other sides of pins are connected to the pressure sensors. The upper bearing plate has two parts: a bolt and a round steel plate with a central threaded bore, and the two parts can be easily combined and split.


### 2.3. Experimental Process

Seven groups of experiments are performed (see Table1). For each group, the size and number of particles are the same, but the loading strength is different.Table 1
Experiment groups.
Experiment groupParticle size (cm)Particle numberLoading strength (kN)Experiment no.Cement mortar particle crushing experiments320301402503Cement mortar particle crushing experiments417304405506Cement mortar particle crushing experiments512307408509Mixed cement mortar particle crushing experiments383010484011——5012Mixed cement mortar particle crushing experiments4113013574014——5015Mixed cement mortar particle crushing experiments31030164104017555018Cement particle crushing experiments0.6∼0.810030191.0∼1.28040201.2∼1.66050211.6∼2.040The connection of the experimental instruments is shown in Figure4. The pressure sensors and the electronic displacement meters are connected with the dynamic resistance strain meter, the pressure sensor on the upper bearing plate is used to measure the overall load, and the electronic displacement meter is used to measure the overall displacement. During loading, the particles flow under the external load, and when the particles at the bottom of the fixture are in contact with the pins on the lower bearing plate, the local pressure can be monitored by the pressure sensors, which are connected with the pins. After loading, the height of the whole particles is measured; according to the height, the particles are divided into three layers, and the fragments in each layer are sieved separately; finally, the size distribution of particles could be obtained.Figure 4
Sketch of particle crushing experiment.


## 2.1. Experimental Specimen

Experimental specimens are of two types: (1) cement mortar particles and (2) cement particles. Cement mortar particles are made of cement, sand, and water in a certain ratio (see Figure1). The cement used is Portland cement with strength of 32.5 MPa, and the fineness modulus of sand is between 2.3 and 3.0. The diameters of particles are 3, 4, and 5 cm, the shape of particles is regular, and size error is small. The shape of particles made by hand is similar to sphere, and the diameter ranges from 0.6 cm to 2.2 cm.Figure 1
Experimental specimen: (a) the mold; (b) the cement mortar particles; (c) the cement particles.
(a)(b)(c)


## 2.2. Experimental Setup

In this work, the loading was performed by the electrohydraulic servo machine, and the pressure sensor and electronic displacement meter are used to measure the local and overall loads and displacement. The monitored signal is saved by a computer through a dynamic resistance strain gauge (see Figure2).Figure 2
The experimental setup: (a) press machine; (b) pressure sensor; (c) electronic displacement meter; (d) dynamic resistance strain gauge.
(a)(b)(c)(d)An experimental device as a container for granular material was developed, and the device has four parts: fixture, upper bearing plate, lower bearing plate, and pin (see Figure3).Figure 3
The container for granular material: (a, b) the fixture; (c, d) lower bearing plate and pins; (e) upper bearing plate.
(a)(b)(c)(d)(e)The fixture is a cylindrical barrel, and the upper inner wall diameter is slightly larger than the lower. The pressure sensor can be placed inside the fixture, and the data line can be led through the hole in the lower part of the fixture. The lower bearing plate is a round steel plate with two holes, and the holes are symmetrical about the axis of the bearing plate. The pins are two solid steel cylinders, which are placed into the holes of the lower bearing plate. The surfaces of pins are in the same plane as the surface of the lower bearing plate, and the other sides of pins are connected to the pressure sensors. The upper bearing plate has two parts: a bolt and a round steel plate with a central threaded bore, and the two parts can be easily combined and split.


## 2.3. Experimental Process

Seven groups of experiments are performed (see Table1). For each group, the size and number of particles are the same, but the loading strength is different.Table 1
Experiment groups.
Experiment groupParticle size (cm)Particle numberLoading strength (kN)Experiment no.Cement mortar particle crushing experiments320301402503Cement mortar particle crushing experiments417304405506Cement mortar particle crushing experiments512307408509Mixed cement mortar particle crushing experiments383010484011——5012Mixed cement mortar particle crushing experiments4113013574014——5015Mixed cement mortar particle crushing experiments31030164104017555018Cement particle crushing experiments0.6∼0.810030191.0∼1.28040201.2∼1.66050211.6∼2.040The connection of the experimental instruments is shown in Figure4. The pressure sensors and the electronic displacement meters are connected with the dynamic resistance strain meter, the pressure sensor on the upper bearing plate is used to measure the overall load, and the electronic displacement meter is used to measure the overall displacement. During loading, the particles flow under the external load, and when the particles at the bottom of the fixture are in contact with the pins on the lower bearing plate, the local pressure can be monitored by the pressure sensors, which are connected with the pins. After loading, the height of the whole particles is measured; according to the height, the particles are divided into three layers, and the fragments in each layer are sieved separately; finally, the size distribution of particles could be obtained.Figure 4
Sketch of particle crushing experiment.


## 3. Experimental Result and Analysis

Results of the experimental study are given in this section; fragment distribution and layered fracture characteristics will be investigated.


### 3.1. Overall Load

For the particles with different sizes under the same loading, the overall load-time curves are shown in Figure5. The overall load change process of cement mortar particles can be divided into three stages. (1) Slow rising stage: in the initial stage of loading, the increase of overall load is relatively slow. Before the loading, the particles are in a state of natural accumulation and the porosity is large; as the applied load increases, the particles begin to flow and rearrange. (2) Fluctuating rising stage: with the increase of applied loading, the particle rearrangement is completed, and then the overall load change rate increases rapidly. When the applied load exceeds the particle crushing strength, the particles break and the broken particle fragments gradually fill into the voids of the particle system, resulting in a rapid increase of the overall displacement. At the same time, secondary flow and rearrangement occur in the new particle system formed by the broken particles. As the applied loading rate is less than the displacement increasing rate, an unloading process occurs. When the bearing plate is in close contact with the particles again, the overall load continues to increase. This loading-unloading-reloading process causes the overall load of the particles to rise in the form of fluctuation. (3) Rapid rising stage: as the particles continue to break, all the voids are filled, the particles become a system similar to the continuous medium, and the overall load no longer fluctuates and increases at a steady rate to the end.Figure 5
The overall load time-history curves of different particles under the same loading.For the cement particles, the overall load increase rate is relatively stable during the loading process and there is no obvious fluctuation in the force time-history curve. The main reason is that the particle system composed of small cement spheres has good gradation, high density, and low porosity.For the loading time from the beginning to end, the time for cement particles is shortest, 22 s. For different cement mortar particles, the time for 5 cm cement mortar particles is the longest, 62 s, the time for other particles is close, about 40–45 s, and the time for 3, 4, and 5 cm mixed particles is the shortest. In other words, when the material and loading condition are the same, the better the gradation of particle system is, the shorter the time to reach the steady state is.


### 3.2. Local Load

The local load time-history curves are shown in Figure6. In the initial stage of loading, the local load of cement mortar particles at the bottom is near zero. The reason is that there is no contact between the particle and the pin which is connected with the pressure sensor. As the particles break and flow, they come into contact with the pin, and the local load begins to rise. The fluctuations occur during the increase of local load, which is the same reason why the overall load has fluctuations. For the cement particle system, there is contact between the particle and the pin in the initial state. With the increase of the applied loading, the local load gradually increases. Although the local load has fluctuations in the loading process, the amplitude of fluctuations is significantly less than that of cement mortar particles.Figure 6
The local load time-history curves of different particles under the same loading.For the 3, 4, and 5 cm mixed cement mortar particles under 30 kN loading, the local load time-history curves are obtained from two monitoring points at the bottom of the fixture (see Figure7). There are great differences between the two curves in terms of trend and amplitude due to the differences of the gradation and arrangement of particles. In addition, the flow and rearrangement of the mixed particles during the loading process are random. Therefore, the load at the bottom is not uniformly distributed along the contact points, which is significantly different from the continuous medium.Figure 7
The two local load time-history curves in the same experiment.


### 3.3. Overall Deformation

The overall deformation curve is shown in Figure8. With the increase of applied load, the overall deformation gradually increases, but the increase rate gradually decreases. The deformable space of the particle system becomes smaller and smaller with the particles breaking and flowing, so the increase rate of overall deformation decreases gradually. Under the same loading, the deformation values of cement mortar particles are obviously higher than those of cement particles. For the cement mortar particles with different gradations, the deformation values for 3, 4, and 5 cm mixed particles are obviously lower than those for particles with other gradations; this indicates that the higher the compressive strength and the better gradation the particles, the better the ability to resist deformation.Figure 8
The overall deformation curve of different particles under the same loading.


### 3.4. Fragment Size Distribution

#### 3.4.1. Fragment Size Distribution for Same Particles under Different Loading

The breakage of cement particles and 3 and 4 cm mixed cement mortar particles under the loading of 30, 40, and 50 kN is shown in Figure9. Under the loading of 30 kN, the surface particles of cement particles contact with upper bearing plate, the contact particles have obvious plastic deformation, the particles have cracks, and a small number of particles are broken. With the increase of loading, the number of broken particles also increases. Under the loading of 30 kN, the surface particles of cement mortar particles are seriously damaged, most of the surface particles are broken, and only some surface particles are cracked. When the loading increases to 40 kN, the surface particles are all powdered.Figure 9
The breakage of particles under the loading of 30, 40, and 50 kN: (a–c) cement particles; (d–f) cement mortar particles.
(a)(b)(c)(d)(e)(f)The sieving curves of 3 and 4 cm mixed cement mortar particles and cement particles under the loading of 30, 40, and 50 kN are shown in Figure10. Under the loading of 30 kN, the mass of fragments less than 1 mm in diameter accounts for 22% of the total mass, and the mass of fragments less than 10 mm in diameter accounts for 43%. Under the loading of 50 kN, the mass of fragments less than 1 mm in diameter accounts for 37% of the total mass, and the mass of fragments less than 10 mm in diameter accounts for 61%. This indicates that with the increase of loading, the mass proportion of fragments whose diameter is smaller than a certain size increases significantly, and the degree of particle crushing increases accordingly. The cement particles also have the same phenomenon.Figure 10
The fragment sieving curves of particles under the loading of 30, 40, and 50 kN: (a) 3 and 4 cm mixed cement mortar particles; (b) cement particles.
(a)(b)


#### 3.4.2. Fragment Size Distribution for Different Particles under the Same Loading

The sieving curves for different particles under the same loading are shown in Figure11. The size distributions of cement mortar particles with different sizes are relatively close, which shows that in this experimental study, the size and gradation of particles have little influence on particle crushing.Figure 11
The size distribution for different particles under the same loading.Under the same loading, for the cement particles, the mass of fragments whose diameter is less than 1 mm accounts for 9% of the total mass; however, for the cement mortar particles, the mass of fragments whose diameter is less than 1 mm accounts for 21%∼25%. This indicates that the cement mortar particles with lower compressive strength are damaged severely, and the proportion of powdery fragments is higher than the proportion for cement particles with higher compressive strength. The compressive strength of particle has a great influence on the fragment size distribution.


### 3.5. Stratified Failure Characteristic

In this work, the particles are divided into three layers from top to bottom, and the sieving was performed layer by layer to determine the size distribution.For the 3 and 4 cm mixed cement mortar particles (see Figure12), under the loading of 30 kN, the particles in the surface layer are damaged seriously, most of them are powdered, and the rest are broken into small pieces. In the bottom layer, some of the particles are broken into large pieces, and some are only cracked and not broken. The particles in the medium layer are damaged lighter than the particles in the above layers, and most of them are only cracked. When the applied load increases, the degree of damage also increases. For the cement particles (see Figure 13), the damage of different layers is similar, and no obvious stratified damage occurs.Figure 12
The breakage of 3 and 4 cm mixed cement mortar particles under the loading of 30, 40, and 50 kN: (a–c) in the surface layer; (d–f) in the medium layer; (g–i) in the bottom layer.
(a)(b)(c)(d)(e)(f)(g)(h)(i)Figure 13
The breakage of cement particles under the loading of 30, 40, and 50 kN: (a–c) in the surface layer; (d–f) in the medium layer; (g–i) in the bottom layer.
(a)(b)(c)(d)(e)(f)(g)(h)(i)The stratified sieving curves of 3 and 4 cm mixed cement mortar particles and cement particles under the loading of 30 kN are shown in Figure14(a). For the mixed cement mortar particles, the curves have distinct differences, the mass of particles in surface and bottom layers whose diameter is less than 1 mm accounts for 40% of the total mass, and the mass whose diameter is less than 10 mm accounts for 72%; the maximum size of particles in the surface layer is less than 20 mm. The mass of particles in medium layers whose diameter is less than 1 mm accounts for 5% of the total mass, and the mass whose diameter is less than 10 mm accounts for 10%; the maximum size of particles in the surface layer is close to 40 mm. For the cement particles, the curves are very similar. From the above, it can be seen that the cement mortar particles with lower strength have obvious stratified failure characteristic.Figure 14
The stratified sieving curves: (a) 3 and 4 cm mixed cement mortar and cement particles under the loading of 30 kN; (b) 3 and 4 cm mixed cement mortar particles under the loading of 30 and 40 kN.
(a)(b)The stratified sieving curves of 3 and 4 cm mixed cement mortar particles under the loading of 30 and 40 kN are shown in Figure14(b). Under the loading of 40 kN, the curves gaps are small; as the applied load increases, the degree of particle crushing in the medium layer increases, and the stratified failure characteristic decreases.


## 3.1. Overall Load

For the particles with different sizes under the same loading, the overall load-time curves are shown in Figure5. The overall load change process of cement mortar particles can be divided into three stages. (1) Slow rising stage: in the initial stage of loading, the increase of overall load is relatively slow. Before the loading, the particles are in a state of natural accumulation and the porosity is large; as the applied load increases, the particles begin to flow and rearrange. (2) Fluctuating rising stage: with the increase of applied loading, the particle rearrangement is completed, and then the overall load change rate increases rapidly. When the applied load exceeds the particle crushing strength, the particles break and the broken particle fragments gradually fill into the voids of the particle system, resulting in a rapid increase of the overall displacement. At the same time, secondary flow and rearrangement occur in the new particle system formed by the broken particles. As the applied loading rate is less than the displacement increasing rate, an unloading process occurs. When the bearing plate is in close contact with the particles again, the overall load continues to increase. This loading-unloading-reloading process causes the overall load of the particles to rise in the form of fluctuation. (3) Rapid rising stage: as the particles continue to break, all the voids are filled, the particles become a system similar to the continuous medium, and the overall load no longer fluctuates and increases at a steady rate to the end.Figure 5
The overall load time-history curves of different particles under the same loading.For the cement particles, the overall load increase rate is relatively stable during the loading process and there is no obvious fluctuation in the force time-history curve. The main reason is that the particle system composed of small cement spheres has good gradation, high density, and low porosity.For the loading time from the beginning to end, the time for cement particles is shortest, 22 s. For different cement mortar particles, the time for 5 cm cement mortar particles is the longest, 62 s, the time for other particles is close, about 40–45 s, and the time for 3, 4, and 5 cm mixed particles is the shortest. In other words, when the material and loading condition are the same, the better the gradation of particle system is, the shorter the time to reach the steady state is.


## 3.2. Local Load

The local load time-history curves are shown in Figure6. In the initial stage of loading, the local load of cement mortar particles at the bottom is near zero. The reason is that there is no contact between the particle and the pin which is connected with the pressure sensor. As the particles break and flow, they come into contact with the pin, and the local load begins to rise. The fluctuations occur during the increase of local load, which is the same reason why the overall load has fluctuations. For the cement particle system, there is contact between the particle and the pin in the initial state. With the increase of the applied loading, the local load gradually increases. Although the local load has fluctuations in the loading process, the amplitude of fluctuations is significantly less than that of cement mortar particles.Figure 6
The local load time-history curves of different particles under the same loading.For the 3, 4, and 5 cm mixed cement mortar particles under 30 kN loading, the local load time-history curves are obtained from two monitoring points at the bottom of the fixture (see Figure7). There are great differences between the two curves in terms of trend and amplitude due to the differences of the gradation and arrangement of particles. In addition, the flow and rearrangement of the mixed particles during the loading process are random. Therefore, the load at the bottom is not uniformly distributed along the contact points, which is significantly different from the continuous medium.Figure 7
The two local load time-history curves in the same experiment.


## 3.3. Overall Deformation

The overall deformation curve is shown in Figure8. With the increase of applied load, the overall deformation gradually increases, but the increase rate gradually decreases. The deformable space of the particle system becomes smaller and smaller with the particles breaking and flowing, so the increase rate of overall deformation decreases gradually. Under the same loading, the deformation values of cement mortar particles are obviously higher than those of cement particles. For the cement mortar particles with different gradations, the deformation values for 3, 4, and 5 cm mixed particles are obviously lower than those for particles with other gradations; this indicates that the higher the compressive strength and the better gradation the particles, the better the ability to resist deformation.Figure 8
The overall deformation curve of different particles under the same loading.


## 3.4. Fragment Size Distribution

### 3.4.1. Fragment Size Distribution for Same Particles under Different Loading

The breakage of cement particles and 3 and 4 cm mixed cement mortar particles under the loading of 30, 40, and 50 kN is shown in Figure9. Under the loading of 30 kN, the surface particles of cement particles contact with upper bearing plate, the contact particles have obvious plastic deformation, the particles have cracks, and a small number of particles are broken. With the increase of loading, the number of broken particles also increases. Under the loading of 30 kN, the surface particles of cement mortar particles are seriously damaged, most of the surface particles are broken, and only some surface particles are cracked. When the loading increases to 40 kN, the surface particles are all powdered.Figure 9
The breakage of particles under the loading of 30, 40, and 50 kN: (a–c) cement particles; (d–f) cement mortar particles.
(a)(b)(c)(d)(e)(f)The sieving curves of 3 and 4 cm mixed cement mortar particles and cement particles under the loading of 30, 40, and 50 kN are shown in Figure10. Under the loading of 30 kN, the mass of fragments less than 1 mm in diameter accounts for 22% of the total mass, and the mass of fragments less than 10 mm in diameter accounts for 43%. Under the loading of 50 kN, the mass of fragments less than 1 mm in diameter accounts for 37% of the total mass, and the mass of fragments less than 10 mm in diameter accounts for 61%. This indicates that with the increase of loading, the mass proportion of fragments whose diameter is smaller than a certain size increases significantly, and the degree of particle crushing increases accordingly. The cement particles also have the same phenomenon.Figure 10
The fragment sieving curves of particles under the loading of 30, 40, and 50 kN: (a) 3 and 4 cm mixed cement mortar particles; (b) cement particles.
(a)(b)


### 3.4.2. Fragment Size Distribution for Different Particles under the Same Loading

The sieving curves for different particles under the same loading are shown in Figure11. The size distributions of cement mortar particles with different sizes are relatively close, which shows that in this experimental study, the size and gradation of particles have little influence on particle crushing.Figure 11
The size distribution for different particles under the same loading.Under the same loading, for the cement particles, the mass of fragments whose diameter is less than 1 mm accounts for 9% of the total mass; however, for the cement mortar particles, the mass of fragments whose diameter is less than 1 mm accounts for 21%∼25%. This indicates that the cement mortar particles with lower compressive strength are damaged severely, and the proportion of powdery fragments is higher than the proportion for cement particles with higher compressive strength. The compressive strength of particle has a great influence on the fragment size distribution.


## 3.4.1. Fragment Size Distribution for Same Particles under Different Loading

The breakage of cement particles and 3 and 4 cm mixed cement mortar particles under the loading of 30, 40, and 50 kN is shown in Figure9. Under the loading of 30 kN, the surface particles of cement particles contact with upper bearing plate, the contact particles have obvious plastic deformation, the particles have cracks, and a small number of particles are broken. With the increase of loading, the number of broken particles also increases. Under the loading of 30 kN, the surface particles of cement mortar particles are seriously damaged, most of the surface particles are broken, and only some surface particles are cracked. When the loading increases to 40 kN, the surface particles are all powdered.Figure 9
The breakage of particles under the loading of 30, 40, and 50 kN: (a–c) cement particles; (d–f) cement mortar particles.
(a)(b)(c)(d)(e)(f)The sieving curves of 3 and 4 cm mixed cement mortar particles and cement particles under the loading of 30, 40, and 50 kN are shown in Figure10. Under the loading of 30 kN, the mass of fragments less than 1 mm in diameter accounts for 22% of the total mass, and the mass of fragments less than 10 mm in diameter accounts for 43%. Under the loading of 50 kN, the mass of fragments less than 1 mm in diameter accounts for 37% of the total mass, and the mass of fragments less than 10 mm in diameter accounts for 61%. This indicates that with the increase of loading, the mass proportion of fragments whose diameter is smaller than a certain size increases significantly, and the degree of particle crushing increases accordingly. The cement particles also have the same phenomenon.Figure 10
The fragment sieving curves of particles under the loading of 30, 40, and 50 kN: (a) 3 and 4 cm mixed cement mortar particles; (b) cement particles.
(a)(b)


## 3.4.2. Fragment Size Distribution for Different Particles under the Same Loading

The sieving curves for different particles under the same loading are shown in Figure11. The size distributions of cement mortar particles with different sizes are relatively close, which shows that in this experimental study, the size and gradation of particles have little influence on particle crushing.Figure 11
The size distribution for different particles under the same loading.Under the same loading, for the cement particles, the mass of fragments whose diameter is less than 1 mm accounts for 9% of the total mass; however, for the cement mortar particles, the mass of fragments whose diameter is less than 1 mm accounts for 21%∼25%. This indicates that the cement mortar particles with lower compressive strength are damaged severely, and the proportion of powdery fragments is higher than the proportion for cement particles with higher compressive strength. The compressive strength of particle has a great influence on the fragment size distribution.


## 3.5. Stratified Failure Characteristic

In this work, the particles are divided into three layers from top to bottom, and the sieving was performed layer by layer to determine the size distribution.For the 3 and 4 cm mixed cement mortar particles (see Figure12), under the loading of 30 kN, the particles in the surface layer are damaged seriously, most of them are powdered, and the rest are broken into small pieces. In the bottom layer, some of the particles are broken into large pieces, and some are only cracked and not broken. The particles in the medium layer are damaged lighter than the particles in the above layers, and most of them are only cracked. When the applied load increases, the degree of damage also increases. For the cement particles (see Figure 13), the damage of different layers is similar, and no obvious stratified damage occurs.Figure 12
The breakage of 3 and 4 cm mixed cement mortar particles under the loading of 30, 40, and 50 kN: (a–c) in the surface layer; (d–f) in the medium layer; (g–i) in the bottom layer.
(a)(b)(c)(d)(e)(f)(g)(h)(i)Figure 13
The breakage of cement particles under the loading of 30, 40, and 50 kN: (a–c) in the surface layer; (d–f) in the medium layer; (g–i) in the bottom layer.
(a)(b)(c)(d)(e)(f)(g)(h)(i)The stratified sieving curves of 3 and 4 cm mixed cement mortar particles and cement particles under the loading of 30 kN are shown in Figure14(a). For the mixed cement mortar particles, the curves have distinct differences, the mass of particles in surface and bottom layers whose diameter is less than 1 mm accounts for 40% of the total mass, and the mass whose diameter is less than 10 mm accounts for 72%; the maximum size of particles in the surface layer is less than 20 mm. The mass of particles in medium layers whose diameter is less than 1 mm accounts for 5% of the total mass, and the mass whose diameter is less than 10 mm accounts for 10%; the maximum size of particles in the surface layer is close to 40 mm. For the cement particles, the curves are very similar. From the above, it can be seen that the cement mortar particles with lower strength have obvious stratified failure characteristic.Figure 14
The stratified sieving curves: (a) 3 and 4 cm mixed cement mortar and cement particles under the loading of 30 kN; (b) 3 and 4 cm mixed cement mortar particles under the loading of 30 and 40 kN.
(a)(b)The stratified sieving curves of 3 and 4 cm mixed cement mortar particles under the loading of 30 and 40 kN are shown in Figure14(b). Under the loading of 40 kN, the curves gaps are small; as the applied load increases, the degree of particle crushing in the medium layer increases, and the stratified failure characteristic decreases.


## 4. Conclusions

In this paper, a systematic method was proposed to measure the mechanical behavior of granular material, and the experiments were performed with different sizes and gradation particles. The overall load, local load, overall displacement, and fragment size distribution were analyzed and compared, and the main conclusions are shown below:(1)
During the loading, the fracture and flow of the particles lead to repeated loading-unloading-reloading phenomenon, and the overall load rises in a fluctuating manner. When all the voids are filled, the overall load increases to the end at a steady rate.(2)
During the loading, as the force chain with different strength is formed inside the granular particles, the force distribution in the bottom of granular particles is not uniform according to the contact points, which is significantly different from the load distribution in the continuous medium method.(3)
During the loading, the increase rate of the overall displacement gradually decreases. The magnitude of the displacement depends on the compressive strength and gradation of particles.(4)
The cement mortar particles have obvious stratified failure characteristic in the low loading, and as the loading increases, the stratified failure characteristic will be weakened. For the cement particles whose compressive strength is higher than cement mortar particles, there was no obvious stratified failure characteristic. So, the compressive strength and loading strength have a great influence on the fragment size distribution of particles.



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*Source: 8846684-2020-12-07.xml*