# Experimental and Numerical Analysis on the Damage and Failure Characteristics of Bituminous Coal under Multilevel Cyclic Loads

Authors: Shuang Gong; Chaofei Wang; Lei Zhou; Furui Xi; Shibin Yao; Xiaojun Li; Juan Liu; Wen Wang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The coal mining process is often accompanied by periodic disturbance of the surrounding rock mass around the coal mining face. Therefore, it is of great theoretical and engineering value to investigate the damage pattern of bituminous coal under cyclic loading and unloading conditions and analyze its damage precursors. The experiments of uniaxial multistage cyclic loading and unloading of bituminous coal were carried out, and the loading and unloading response ratios were extracted using the elastic modulus variation to describe the damage characteristics and damage precursors of bituminous coal. Based on the accumulated acoustic emission ringing counts, the response ratios were defined, and the internal damage evolution characteristics and damage laws during the damage of bituminous coal were analyzed. The CT scan images of the internal structure of the coal sample before and after the experiment were used to analyze the damage characteristics of the coal sample and the influence of the number of simulation units on the results using the inverse modeling simulation analysis method. The research shows that the response ratio of bituminous coal under uniaxial cyclic loading has three stages of variation, and it is characterized by periodic “W”-type variation at each level of stress. In addition, the inverse modeling and simulation can better characterize the damage evolution of the coal specimen.


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## Body

## 1. Introduction

In the field of mining engineering, roadway excavation and support, face mining, and overburden collapse lead to periodic loading and unloading of coal and rock mass around the stope. This makes the internal fractures of coal and rock mass evolve continuously, resulting in rock stratum damage and may induce catastrophic instability [1–3]. Therefore, the research and analysis of coal rock damage characteristics under unloading conditions will help to gain insight into the mechanism of damage, deterioration, and destabilization of engineered coal rock masses. For the perturbation characteristics of rock materials by the loading and unloading process, Yin et al. [4] put forward the concept of load/unload response ratio (LURR) in 1984. It was demonstrated that the LURR has the same physical mechanism as the accelerated energy release. And the prediction of mine seismicity was attempted using the LURR theory. Song et al. [5] studied the mechanical behaviour of different parts (top, middle, and bottom) of concrete exposed to monotonic and cyclic loading. Based on two different cyclic loading strategies, it is concluded that the maximum load level has more pronounced effect on energy dissipation than the minimum load level. JE Trotta et al. [6] investigated the sensitivity of LURR theory to specific parameters in predicting certain earthquakes. In terms of experimental research, Shi et al. [7, 8] adopted p-wave velocity and strain as response quantities in LURR theory and verified that the load-unload response ratio theory was applicable to capture precursor characteristics of sample failure. Miao et al. [9] demonstrated the feasibility of quantitatively analyzing the damage evolution process of rock specimens using uniaxial cyclic loading and unloading disturbance experiments with the loading and unloading response ratio theory. Yu et al. [10, 11] conducted triaxial cyclic unloading experiments for gneisses and found that the damage development process within the rock material is consistent with the evolution of the unloading response ratio. In terms of numerical simulations, Wang et al. [12] simulated the process of loading and unloading of solid materials when damage occurs and concluded that the more homogeneous or brittle the material is internally, the later the Y value rises and the steeper the Y curve. Liu [13] investigated the application of LURR in rock damage precursor characterization using REPA simulation software. Peter Mora [14] used Solid Lattice Model to demonstrate that the value of the load/unload response ratio increases with increasing load and then rises to a peak, with a sharp decrease in the value of the load/unload response ratio before the main rupture occurs. And the concept of maximum faulting orientation [15], that is, the maximum faulting orientation, was proposed to form a new method for calculating the load/unload response ratio.Although there are preliminary studies on loading and unloading response characteristics of solid materials, the knowledge for bituminous coal materials is still limited. Bituminous coal has a certain memory capacity [16], and the stress-strain curve forms a hysteresis loop under cyclic loading and unloading conditions. Its strength, elastic modulus, and damage characteristics all change with load. In addition, the deformation damage characteristics of coal rock are dependent on the loading and unloading speed and stress ratio [17–21]. Therefore, it is still important to carry out research on the damage characteristics of bituminous coal under cyclic loading. In this paper, experiments on the damage of bituminous coal under multistage cyclic loading were carried out, and the slope of the evolution curve of elastic modulus was used to define the load/unload response ratio [22–31]. The statistical law of acoustic emission ringing count was used to describe the load/unload response ratio in order to analyze the damage characteristics of bituminous coal. In addition, the internal structural damage evolution characteristics of the sample before damage were studied based on industrial CT scanning technology. The damage process of the sample was restored by applying numerical calculations by means of three-dimensional inversion. The results of the study have a positive effect on the analysis of the damage characteristics of coal rock materials, the mechanism of occurrence and evolutionary characteristics of coal rock impact dynamics hazard.


## 2. Experimental Results and Discussion

### 2.1. Experimental Samples

Bituminous coal is selected from the slope coal and rock mass of Yuanbaoshan open-pit mine in Chifeng City, Inner Mongolia (Figure1). It is of carboniferous age. The sample was machined as a standard cylindrical specimen of φ50 mm × 100 mm. The uniaxial compressive strength of the coal samples ranged from 6.11 to 20.5 MPa, uniaxial tensile strength of 2.33 to 8.09 MPa, modulus of elasticity from 0.307 to 1.06 GPa, and Poisson’s ratio from 0.15 to 0.35.Figure 1
Location of coal sample collection: (a) location of Chifeng City on the map of China, (b) location of Chifeng City in Inner Mongolia, (c) the mine range of Yuanbaoshan open-pit mine on Google Earth map, and (d) sampling location.


### 2.2. Experimental System and Method

The experimental loading system adopts the EHF-EG200 KN-type fully digital hydraulic servo tester from the State Key Laboratory of Coal Resources and Safe Mining. The maximum load is ±200 KN dynamically and ±300 KN statically. The maximum stroke is ±50 mm. The load accuracy is within ±0.5% of the displayed value. SAEU2S acoustic emission system is adopted for acoustic emission monitoring, and four-channel sampling mode is adopted. The sampling frequency is 2500 kHz and the sampling length is 2048 points. The parameter interval is 2000μs. The locking time is 2000 μs. The waveform trigger mode is internal trigger, the waveform threshold is 30, the parameter threshold is 30, the front amplifier gain is 40 and the main amplifier gain is 0. The filter is 20 to 100 K, and the front and rear acquisition length is 51.2 μs. Figure 2 shows the installation of experimental equipment and samples.Figure 2
Experimental equipment and sample installation: (a) servo testing machine, (b) CT scanning equipment, and (c) acoustic emission.
(a)(b)(c)A displacement control method is used with a rate of 10μm/s and simultaneous acquisition of acoustic emission signals. Displacement loading is performed every 100 μm for one level. When the displacement loading level is reached, cyclic loading is applied by means of triangular perturbation. The perturbation size is ±50 μm, with 10 perturbations at each level of displacement. The displacement is unloaded to zero at the end of the perturbation and reloaded to the next level of displacement and perturbed again. Proceed as mentioned earlier until the specimen is destroyed. Figure 3 shows that the coal sample undergoes macroscopic damage at the fourth disturbance level. The coal samples undergo three stages of loading, disturbance and unloading under each level of displacement in turn. The total duration of the whole multistage loading and unloading process is 512.9 s. The ultimate load of 46.526 KN appears at 477.6 s after the start of loading.Figure 3
Variation curve of cyclic loading and unloading displacement with time.


### 2.3. Analysis of Cyclic Loading and Unloading Results

Figure4 shows the stress-strain curve under multistage cyclic loading and unloading. It is obvious that the stress-strain curve of bituminous coal under cyclic loading has a hysteresis loop. The strain increases from the initial value to 0.002617 when the sample completes the first level of cyclic perturbation. The strain reaches 0.004517 when the sample completes the second level of cyclic perturbation. The strain reaches 0.006395 when the sample completes the third level of cyclic perturbation. As the sample enters the fourth level of cyclic perturbation, the damage inside the coal sample increases continuously, and finally the specimen destabilization damage.Figure 4
Stress-strain relation curve of coal sample.The strain is used as the response quantity in the load/unload response ratio theory:(1)X=limΔP⟶0ΔRΔP=εσ=1E.Then the load/unload response ratio is as follows:(2)Y=X+X−=1/E+1/E−=E−E+,where E− and E+ denote the modulus of elasticity during unloading and loading, respectively. Considering that the stress-strain curve of coal rock-like materials will show hysteresis loops during cyclic loading and unloading, the slope of the curve changes more obviously during the unloading process, while it remains basically unchanged during the loading process. Therefore, the modulus of elasticity in the loading stage is taken as the slope of the straight-line segment of the stress-strain curve. The modulus of elasticity in the unloading stage is taken as the slope of the cut line of the unloading curve, that is, the slope of the peak and valley of the stress-strain curve. The data fluctuate a lot after loading to the first peak in the fourth stage of the cycle. As the unloading cycle proceeds, the overall E+ tends to increase, with large fluctuations in the intermediate values. The E+ value varies widely at the beginning of each cycle, and then suddenly becomes smaller after three or four cycles. At the end of the cycle, it increases again, basically in an “M” shape, as shown in Figure 5. E− has a large value at the beginning of each stage of the cycle. It gradually becomes smaller by the end of the cycle and suddenly rises before the destruction, as shown in Figure 5(b). Both of them vary greatly throughout the unloading and loading experiments near the damage. The loading and unloading response ratio basically fluctuate around 1. At the beginning, middle, and end of each cycle, the value is large, basically in “W” shape. It drops at the end of the third stage near the failure and at the beginning of the fourth stage, and suddenly rises before the failure, as shown in Figure 5(a). In the initial stage of loading, the value of E+ increases rapidly because the interior of the material is in the initial compaction stage. During unloading, the internal structure of the material has no obvious change, resulting in basically no change in E− value, so the loading and unloading response ratio is relatively large. With the increase of load, the coal rock material enters the elastic phase. The internal structure reaches the stable change phase, and the value of the response ratio Y for loading and unloading always fluctuates around 1. As the material approaches damage, the internal damage intensifies and the E+ decreases rapidly. The E− index also begins to decrease, but the rate of decrease is much less than the E+, so the Y value increases suddenly.Figure 5
Loading and unloading response ratio.The reason for the decreasing trend of Y value at the end stage of the third level in the experiment can be analyzed by using the critical sensitivity theory. A small disturbance will not induce damage before Y reaches the critical value and may induce damage when Y reaches the critical value, which indicates that the value of the load/unload response ratio Y is consistent with the critical sensitivity. When the load level is low, the damage degree of the material is smaller and the stability of its internal structure is higher. Thus, the critical sensitivity of the material is lower, and the value of the load/unload response ratio Y is smaller. A small disturbance will not lead to damage of the bituminous coal but cause microextension of the damage and microincrement of the deformation inside the bituminous coal material. With the increase of the load level, the internal damage and destruction of the bituminous coal material keeps intensifying, at which time the coal sample macroscopically shows a decrease in stiffness and a gradual decrease in internal structural stability. The load level is increasing while the resistance to destabilization damage is decreasing, so the possibility of destabilization damage is gradually increasing, leading to an increasing critical sensitivity of the material and an increase in Y value. When the load level is high, the internal damage of the bituminous coal material is larger before the unloading response ratio Y is about to reach the critical value. The ability to resist destabilization damage is greatly reduced, and its critical sensitivity increases rapidly, and any small disturbance will lead to material instability. After Y reaches the critical value, the bituminous coal material starts to enter the self-driven evolution process. The critical sensitivity will gradually decrease, and the Y value will also decrease significantly.


### 2.4. Analysis of Acoustic Emission Results

Figure6 shows the results of acoustic emission ringing counts during the destruction of coal samples. The cumulative ringing counts increased abruptly when the axial strain reached 0.002617, 0.004517, and 0.006395, respectively. The coal sample was at the moment of starting unloading, and more obvious fracture development occurred inside the sample. As the load continued to increase, the cumulative ringing counts reached maximum value when the strain reached 0.00704, which predicted the sample is about to undergo the overall instability damage.Figure 6
Relationship curve between cumulative ring count and strain.There are various methods for defining the damage variableD. One of the simpler ones is to choose the modulus of elasticity E of the material. According to the principle of equivalent effect variation, the expression of the damage variable D takes the form:(3)D=1−EE0,where E0 is the value of elastic modulus of the material without damage and E is the value of elastic modulus of the damaged material. There is a relationship between the damage variable and the number of acoustic emission ringing as follows:(4)D=NNm,where N is the number of acoustic emission ringing after the material is subjected to internal damage and Nm is the cumulative acoustic emission ringing count when the material is completely damaged.Note that the rate of change of the damage variableD during loading and unloading are ΔD+ and ΔD−, respectively. The number of acoustic emission ringing generated during loading and unloading are N+ and N−, respectively. Then the following relationship is obtained:(5)ΔD+=N+Nm,ΔD−=N−Nm,ΔD+ΔD−=N+N−.According to the definition in seismology, the load/unload response ratioY can be defined as follows:(6)Y=N+N−.The relationship between acoustic emission ring count and loading/unloading response ratio can be obtained:(7)Y=E−E+=ΔD+ΔD−=N+N−.By processing the acoustic emission ring count in equation (7), the loading and unloading response ratio characterized by the ring count can be calculated.It can be seen from Figure7 that the loading and unloading response ratio Y calculated according to the ringing times is larger when the load level is low. The Y value decreases gradually with the increase of load. In the near failure stage, the Y value is the smallest and fluctuates around 1. This is mainly due to the fact that acoustic emission is generally generated at the stage of internal microstructural adjustment of the material and is mostly in advance of the stress-strain changes. Therefore, the acoustic emission signal at low experimental load level is mostly concentrated in the loading phase, when the Y value is larger. When the load level is higher, especially near the damage, the unloading phase will produce residual tensile stress. While the residual tensile stress exceeds the tensile strength of the coal sample, damage will also occur. The unloading phase acoustic emission signal may also increase to the same level as the loading phase, so the Y value calculated by the number of acoustic emission ringing will tend to 1 when the material is close to the damage phase.Figure 7
Y value of acoustic emission ringing number.


## 2.1. Experimental Samples

Bituminous coal is selected from the slope coal and rock mass of Yuanbaoshan open-pit mine in Chifeng City, Inner Mongolia (Figure1). It is of carboniferous age. The sample was machined as a standard cylindrical specimen of φ50 mm × 100 mm. The uniaxial compressive strength of the coal samples ranged from 6.11 to 20.5 MPa, uniaxial tensile strength of 2.33 to 8.09 MPa, modulus of elasticity from 0.307 to 1.06 GPa, and Poisson’s ratio from 0.15 to 0.35.Figure 1
Location of coal sample collection: (a) location of Chifeng City on the map of China, (b) location of Chifeng City in Inner Mongolia, (c) the mine range of Yuanbaoshan open-pit mine on Google Earth map, and (d) sampling location.


## 2.2. Experimental System and Method

The experimental loading system adopts the EHF-EG200 KN-type fully digital hydraulic servo tester from the State Key Laboratory of Coal Resources and Safe Mining. The maximum load is ±200 KN dynamically and ±300 KN statically. The maximum stroke is ±50 mm. The load accuracy is within ±0.5% of the displayed value. SAEU2S acoustic emission system is adopted for acoustic emission monitoring, and four-channel sampling mode is adopted. The sampling frequency is 2500 kHz and the sampling length is 2048 points. The parameter interval is 2000μs. The locking time is 2000 μs. The waveform trigger mode is internal trigger, the waveform threshold is 30, the parameter threshold is 30, the front amplifier gain is 40 and the main amplifier gain is 0. The filter is 20 to 100 K, and the front and rear acquisition length is 51.2 μs. Figure 2 shows the installation of experimental equipment and samples.Figure 2
Experimental equipment and sample installation: (a) servo testing machine, (b) CT scanning equipment, and (c) acoustic emission.
(a)(b)(c)A displacement control method is used with a rate of 10μm/s and simultaneous acquisition of acoustic emission signals. Displacement loading is performed every 100 μm for one level. When the displacement loading level is reached, cyclic loading is applied by means of triangular perturbation. The perturbation size is ±50 μm, with 10 perturbations at each level of displacement. The displacement is unloaded to zero at the end of the perturbation and reloaded to the next level of displacement and perturbed again. Proceed as mentioned earlier until the specimen is destroyed. Figure 3 shows that the coal sample undergoes macroscopic damage at the fourth disturbance level. The coal samples undergo three stages of loading, disturbance and unloading under each level of displacement in turn. The total duration of the whole multistage loading and unloading process is 512.9 s. The ultimate load of 46.526 KN appears at 477.6 s after the start of loading.Figure 3
Variation curve of cyclic loading and unloading displacement with time.


## 2.3. Analysis of Cyclic Loading and Unloading Results

Figure4 shows the stress-strain curve under multistage cyclic loading and unloading. It is obvious that the stress-strain curve of bituminous coal under cyclic loading has a hysteresis loop. The strain increases from the initial value to 0.002617 when the sample completes the first level of cyclic perturbation. The strain reaches 0.004517 when the sample completes the second level of cyclic perturbation. The strain reaches 0.006395 when the sample completes the third level of cyclic perturbation. As the sample enters the fourth level of cyclic perturbation, the damage inside the coal sample increases continuously, and finally the specimen destabilization damage.Figure 4
Stress-strain relation curve of coal sample.The strain is used as the response quantity in the load/unload response ratio theory:(1)X=limΔP⟶0ΔRΔP=εσ=1E.Then the load/unload response ratio is as follows:(2)Y=X+X−=1/E+1/E−=E−E+,where E− and E+ denote the modulus of elasticity during unloading and loading, respectively. Considering that the stress-strain curve of coal rock-like materials will show hysteresis loops during cyclic loading and unloading, the slope of the curve changes more obviously during the unloading process, while it remains basically unchanged during the loading process. Therefore, the modulus of elasticity in the loading stage is taken as the slope of the straight-line segment of the stress-strain curve. The modulus of elasticity in the unloading stage is taken as the slope of the cut line of the unloading curve, that is, the slope of the peak and valley of the stress-strain curve. The data fluctuate a lot after loading to the first peak in the fourth stage of the cycle. As the unloading cycle proceeds, the overall E+ tends to increase, with large fluctuations in the intermediate values. The E+ value varies widely at the beginning of each cycle, and then suddenly becomes smaller after three or four cycles. At the end of the cycle, it increases again, basically in an “M” shape, as shown in Figure 5. E− has a large value at the beginning of each stage of the cycle. It gradually becomes smaller by the end of the cycle and suddenly rises before the destruction, as shown in Figure 5(b). Both of them vary greatly throughout the unloading and loading experiments near the damage. The loading and unloading response ratio basically fluctuate around 1. At the beginning, middle, and end of each cycle, the value is large, basically in “W” shape. It drops at the end of the third stage near the failure and at the beginning of the fourth stage, and suddenly rises before the failure, as shown in Figure 5(a). In the initial stage of loading, the value of E+ increases rapidly because the interior of the material is in the initial compaction stage. During unloading, the internal structure of the material has no obvious change, resulting in basically no change in E− value, so the loading and unloading response ratio is relatively large. With the increase of load, the coal rock material enters the elastic phase. The internal structure reaches the stable change phase, and the value of the response ratio Y for loading and unloading always fluctuates around 1. As the material approaches damage, the internal damage intensifies and the E+ decreases rapidly. The E− index also begins to decrease, but the rate of decrease is much less than the E+, so the Y value increases suddenly.Figure 5
Loading and unloading response ratio.The reason for the decreasing trend of Y value at the end stage of the third level in the experiment can be analyzed by using the critical sensitivity theory. A small disturbance will not induce damage before Y reaches the critical value and may induce damage when Y reaches the critical value, which indicates that the value of the load/unload response ratio Y is consistent with the critical sensitivity. When the load level is low, the damage degree of the material is smaller and the stability of its internal structure is higher. Thus, the critical sensitivity of the material is lower, and the value of the load/unload response ratio Y is smaller. A small disturbance will not lead to damage of the bituminous coal but cause microextension of the damage and microincrement of the deformation inside the bituminous coal material. With the increase of the load level, the internal damage and destruction of the bituminous coal material keeps intensifying, at which time the coal sample macroscopically shows a decrease in stiffness and a gradual decrease in internal structural stability. The load level is increasing while the resistance to destabilization damage is decreasing, so the possibility of destabilization damage is gradually increasing, leading to an increasing critical sensitivity of the material and an increase in Y value. When the load level is high, the internal damage of the bituminous coal material is larger before the unloading response ratio Y is about to reach the critical value. The ability to resist destabilization damage is greatly reduced, and its critical sensitivity increases rapidly, and any small disturbance will lead to material instability. After Y reaches the critical value, the bituminous coal material starts to enter the self-driven evolution process. The critical sensitivity will gradually decrease, and the Y value will also decrease significantly.


## 2.4. Analysis of Acoustic Emission Results

Figure6 shows the results of acoustic emission ringing counts during the destruction of coal samples. The cumulative ringing counts increased abruptly when the axial strain reached 0.002617, 0.004517, and 0.006395, respectively. The coal sample was at the moment of starting unloading, and more obvious fracture development occurred inside the sample. As the load continued to increase, the cumulative ringing counts reached maximum value when the strain reached 0.00704, which predicted the sample is about to undergo the overall instability damage.Figure 6
Relationship curve between cumulative ring count and strain.There are various methods for defining the damage variableD. One of the simpler ones is to choose the modulus of elasticity E of the material. According to the principle of equivalent effect variation, the expression of the damage variable D takes the form:(3)D=1−EE0,where E0 is the value of elastic modulus of the material without damage and E is the value of elastic modulus of the damaged material. There is a relationship between the damage variable and the number of acoustic emission ringing as follows:(4)D=NNm,where N is the number of acoustic emission ringing after the material is subjected to internal damage and Nm is the cumulative acoustic emission ringing count when the material is completely damaged.Note that the rate of change of the damage variableD during loading and unloading are ΔD+ and ΔD−, respectively. The number of acoustic emission ringing generated during loading and unloading are N+ and N−, respectively. Then the following relationship is obtained:(5)ΔD+=N+Nm,ΔD−=N−Nm,ΔD+ΔD−=N+N−.According to the definition in seismology, the load/unload response ratioY can be defined as follows:(6)Y=N+N−.The relationship between acoustic emission ring count and loading/unloading response ratio can be obtained:(7)Y=E−E+=ΔD+ΔD−=N+N−.By processing the acoustic emission ring count in equation (7), the loading and unloading response ratio characterized by the ring count can be calculated.It can be seen from Figure7 that the loading and unloading response ratio Y calculated according to the ringing times is larger when the load level is low. The Y value decreases gradually with the increase of load. In the near failure stage, the Y value is the smallest and fluctuates around 1. This is mainly due to the fact that acoustic emission is generally generated at the stage of internal microstructural adjustment of the material and is mostly in advance of the stress-strain changes. Therefore, the acoustic emission signal at low experimental load level is mostly concentrated in the loading phase, when the Y value is larger. When the load level is higher, especially near the damage, the unloading phase will produce residual tensile stress. While the residual tensile stress exceeds the tensile strength of the coal sample, damage will also occur. The unloading phase acoustic emission signal may also increase to the same level as the loading phase, so the Y value calculated by the number of acoustic emission ringing will tend to 1 when the material is close to the damage phase.Figure 7
Y value of acoustic emission ringing number.


## 3. Three-Dimensional Reconstruction Model Construction

### 3.1. CT Scan and Reconstruction of Coal Samples

The ACTIS300-320/225 industrial CT inspection system from the State Key Laboratory of Deep Coal Resources Mining, China University of Mining and Technology (Beijing) was used to scan the internal structure of typical coal samples before and after the experiment. For testing coal samples with a resolution of about 80µm, the equipment is shown in Figure 2(b). In the CT scan image, the different grayscale represents the different degree of X-ray absorption of the internal material of the sample. The black area in the figure shows the lower X-ray absorption area, representing the low-density material, such as pores and fissures. The bright white area is the higher X-ray absorption area, representing the high-density material, such as hard inclusions, as shown in Figure 8(a). Three-dimensional reconstruction is to segment the existing two-dimensional image sequence, such as boundary recognition. Then, the three-dimensional reconstruction of coal samples is carried out by using mimics, and the reconstruction results are shown in Figure 8.Figure 8
Reconstruction model of coal sample: (a) internal characteristic cross section of the sample and (b) component model of sample.
(a)(b)


### 3.2. Model Building and Parameter Setting

The 3D model was meshed and imported into the discrete element software for the numerical simulation study of the load/unload response ratio. The numerical model is shown in Figure9. The model size is a cylinder of φ50 mm × 100 mm with 6997 particle units.Figure 9
Different types of numerical models of coal samples: (a) finite-element mesh model of sample and (b) discrete element model of sample.
(a)(b)The first group is high-density inclusions, which contains 101 particle units, accounting for about 1.44% of the total number of particle units. The other group is coal matrix, accounting for about 98.56% of the total number of particle units. Loading is performed by displacement control, and the speed increases slowly at the beginning of loading. The speed gradually decreases to zero near the transition point, and the speed increases slowly in the reverse direction at the beginning of unloading. Table1 lists the main parameters of the material components used in the numerical simulations.Table 1
Calculation parameters for numerical simulation.
GroupNormal stiffness (N/m)Tangential stiffness (N/m)Normal strength (Pa)Tangential strength (Pa)Friction coefficientContent (%)Group12E + 102E + 103E + 73E + 70.21.44Group23.2E + 93.2E + 90.78E + 60.78E + 60.3898.56


### 3.3. Analysis of Simulation Results

The strain is used as the response in the loading and unloading response ratio theory to analyze the simulation results:(8)X=limΔP⟶0ΔRΔP=εσ=1E.The load/unload response ratio is as follows:(9)Y=X+X−=1/E+1/E−=E−E+.From Figures10 and 11, it can be concluded that the coal samples underwent a total of three complete levels of cyclic loading and unloading process. At the fourth cyclic load level, the samples suffered macroscopic damage, in which, the first and second stage cyclic loading and unloading are carried out in the elastic phase of the material and the hysteresis phenomenon is not significant. As the load continues to increase, the loading process exhibits obvious nonlinear characteristics. Near the peak load 24.23 MPa, the third stage of cyclic loading and unloading was carried out, and a more obvious hysteresis phenomenon appeared. When the stress drops to 22.17 MPa, the fourth cycle of unloading is carried out. With the unloading, the stress decreases sharply and macroscopic damage occurs in the specimen.Figure 10
Displacement control in numerical simulation.Figure 11
Stress-strain curve of numerical simulation.Figure12 shows the displacement vectors at different cyclic loading levels. The displacement vectors of the specimen mostly point from the ends of the specimen to the middle of the specimen until the peak load is reached. After the peak, there is a more obvious transformation of the displacement vector, as shown in Figure 12(d). The specimen eventually forms a tensile-shear damage. Figure 13 shows the failure morphology of coal samples at different cycle stages. Figure 14 shows the CT scans of the final damaged specimens and the internal damage features. The destruction of the coal sample produced a fracture zone (white stripes) running through the interior of the specimen. As shown in Figure 14(a) and 14(c), the fracture from the upper edge of the specimen points obliquely downward to the middle of the specimen for the form of shear damage. Part of the fracture straight down through the entire specimen for the form of splitting damage. From the location and direction of the fractures, it can be judged that the coal sample is finally splitting damage mainly.Figure 12
Displacement vectors of different load/unload state: (a) first cycle step, (b) second cycle step, (c) third cycle step, and (d) final damage.
(a)(b)(c)(d)Figure 13
Failure morphology of coal samples at different cycle stages: (a) first cycle step, (b) second cycle step, (c) third cycle step, and (d) final damage.
(a)(b)(c)(d)Figure 14
CT scanning pictures of failure coal sample: (a) left view, (b) rear view, (c) right view, and (d) final damage specimen.
(a)(b)To compare the experimental results, the variation curve of the response ratio with loading obtained from the numerical simulation was analyzed and obtained, as shown in Figure15. During the first two stages of cyclic loading, E+ remained basically unchanged. The indicator E− tends to increase, but the change is not obvious, and it is always maintained around 3 GPa. The loading and unloading response ratio Y fluctuate around 1. At the third cyclic loading stage, E− suddenly increases to 4.07 GPa. While E+ decreases to 2.96 GPa, and the Y value fluctuates. Finally, the specimen was damaged in the fourth cyclic step. The indicator E− increased sharply to 9.78 GPa, while E+ suddenly decreased to a negative value. Subsequently, the response ratio Y also fluctuates, which is consistent with the experimental results.Figure 15
Load/unload response ratio.The E+, E−, and Y values did not show the fluctuation phenomenon in the experimental process at the early stage of cyclic loading. The main reason may be the fluctuation of elastic modulus caused by the continuous opening and closing of cracks inside the sample with cyclic loading and unloading. The influence of the fissures is not considered in the numerical simulation, so the elastic modulus does not change much. In summary, the modulus of elasticity E+ and E− and the response ratio Y of unloading and loading appear to change more obviously when the sample is close to damage, so it can be used as a basis for damage precursors.


### 3.4. Influence of the Number of Model Cells on the Response Ratio

The 3D models with different number of units were obtained by varying the particle radius. The simulations are analyzed under the same material parameters with the same loading method as described in the previous subsection. Figure16 shows the relationship between the number of units and the computation time consumed. When the number of cells is below 24,000, the computation time increases slowly to 1063 minutes as the number of cells increases. However, when the number of cells increases to 45,000, the computation time increases abruptly to 11,662 minutes, which seriously reduces the computation efficiency.Figure 16
Calculation time of coal sample with different particle numbers.Figure17 shows the stress-strain curves for four models containing different number of units. The loading process uses the same displacement control method and undergoes a total of seven stages of cyclic loading and unloading of the process. The model with different number of cells reaches the peak stress at different cycle levels. As shown in Figure 17, the macroscopic modulus of elasticity of the model increases with the increase in the number of cells. The peak stress tends to increase significantly with the increase in the number of cells. This may be due to the fact that the porosity of the reconstructed model decreases with the increase in the number of cells. Figures 18 and 19 show the loading and unloading response elastic modes E+ and E− at different cyclic levels for different unit number models, respectively. Figure 20 shows the load/unload response ratio of coal sample with different particle numbers.Figure 17
Stress-strain curves of coal sample with different particle numbers.Figure 18
Load response (E+) of coal sample with different particle numbers.Figure 19
Unload response (E–) of coal sample with different particle numbers.Figure 20
Load/unload response ratio of coal sample with different particle numbers.Figure18 shows the different models reaching peak stress at different cycle levels. At the preload cycle level, E+ increases first and then level off, as in models b, c, and d. At the midloading cycle level, the E+ in model b continues to increase and then level off. The E+ in both models c and d rises to a relatively large value and then begins to decrease. Although the response characteristics of E+ differed, the trend of E+ variation was relatively simple with a small fluctuation range. The E+ exhibits “M”-shaped fluctuations in one cycle before the specimen is damaged, as shown in model a first level, model b third level, model c fifth level, and model d sixth level. As the stress approaches or reaches a peak cyclic level, E+ suddenly drops to a minimum value.Figure19 indicates that E− increases first and then levels off during the preloading and midloading periods, as shown in the calculated results of models c and d. At the beginning of each cycle level, there is a more pronounced tendency for E− to increase, followed by a gradual decrease. E− increases to a maximum value during the first unloading when the stress is close to or at the peak cycle level. Comparing Figures 18 and 19, it can be seen that at the beginning of each cycle phase, the fluctuation of E− is greater than the amount of change of E+ at the corresponding position.The E+ and E− variations accordingly cause fluctuations in the value of the load/unload response ratio Y, as shown in Figure 20. In the preload period, the load/unload response ratio Y is always maintained at about 1. As the stress approaches its peak, the Y value increases abruptly, as shown by the response at the last cycle level of models a and d in Figure 20. The Y value fluctuates more at the peak and even becomes negative.The E+, E−, and Y values remain at a more stable value throughout the preload and midload periods. As the stress approaches or reaches its peak, the E+, E–, and Y values change abruptly. In comparison, E– and Y values change more obviously and are more suitable as precursors of specimen damage to judge or predict specimen damage. However, since both matrix and inclusions are homogeneous in the reconstructed coal sample model, the abrupt change point of the loading and unloading response ratio is very close to the peak. This poses a challenge to predict specimen damage in advance.


## 3.1. CT Scan and Reconstruction of Coal Samples

The ACTIS300-320/225 industrial CT inspection system from the State Key Laboratory of Deep Coal Resources Mining, China University of Mining and Technology (Beijing) was used to scan the internal structure of typical coal samples before and after the experiment. For testing coal samples with a resolution of about 80µm, the equipment is shown in Figure 2(b). In the CT scan image, the different grayscale represents the different degree of X-ray absorption of the internal material of the sample. The black area in the figure shows the lower X-ray absorption area, representing the low-density material, such as pores and fissures. The bright white area is the higher X-ray absorption area, representing the high-density material, such as hard inclusions, as shown in Figure 8(a). Three-dimensional reconstruction is to segment the existing two-dimensional image sequence, such as boundary recognition. Then, the three-dimensional reconstruction of coal samples is carried out by using mimics, and the reconstruction results are shown in Figure 8.Figure 8
Reconstruction model of coal sample: (a) internal characteristic cross section of the sample and (b) component model of sample.
(a)(b)


## 3.2. Model Building and Parameter Setting

The 3D model was meshed and imported into the discrete element software for the numerical simulation study of the load/unload response ratio. The numerical model is shown in Figure9. The model size is a cylinder of φ50 mm × 100 mm with 6997 particle units.Figure 9
Different types of numerical models of coal samples: (a) finite-element mesh model of sample and (b) discrete element model of sample.
(a)(b)The first group is high-density inclusions, which contains 101 particle units, accounting for about 1.44% of the total number of particle units. The other group is coal matrix, accounting for about 98.56% of the total number of particle units. Loading is performed by displacement control, and the speed increases slowly at the beginning of loading. The speed gradually decreases to zero near the transition point, and the speed increases slowly in the reverse direction at the beginning of unloading. Table1 lists the main parameters of the material components used in the numerical simulations.Table 1
Calculation parameters for numerical simulation.
GroupNormal stiffness (N/m)Tangential stiffness (N/m)Normal strength (Pa)Tangential strength (Pa)Friction coefficientContent (%)Group12E + 102E + 103E + 73E + 70.21.44Group23.2E + 93.2E + 90.78E + 60.78E + 60.3898.56


## 3.3. Analysis of Simulation Results

The strain is used as the response in the loading and unloading response ratio theory to analyze the simulation results:(8)X=limΔP⟶0ΔRΔP=εσ=1E.The load/unload response ratio is as follows:(9)Y=X+X−=1/E+1/E−=E−E+.From Figures10 and 11, it can be concluded that the coal samples underwent a total of three complete levels of cyclic loading and unloading process. At the fourth cyclic load level, the samples suffered macroscopic damage, in which, the first and second stage cyclic loading and unloading are carried out in the elastic phase of the material and the hysteresis phenomenon is not significant. As the load continues to increase, the loading process exhibits obvious nonlinear characteristics. Near the peak load 24.23 MPa, the third stage of cyclic loading and unloading was carried out, and a more obvious hysteresis phenomenon appeared. When the stress drops to 22.17 MPa, the fourth cycle of unloading is carried out. With the unloading, the stress decreases sharply and macroscopic damage occurs in the specimen.Figure 10
Displacement control in numerical simulation.Figure 11
Stress-strain curve of numerical simulation.Figure12 shows the displacement vectors at different cyclic loading levels. The displacement vectors of the specimen mostly point from the ends of the specimen to the middle of the specimen until the peak load is reached. After the peak, there is a more obvious transformation of the displacement vector, as shown in Figure 12(d). The specimen eventually forms a tensile-shear damage. Figure 13 shows the failure morphology of coal samples at different cycle stages. Figure 14 shows the CT scans of the final damaged specimens and the internal damage features. The destruction of the coal sample produced a fracture zone (white stripes) running through the interior of the specimen. As shown in Figure 14(a) and 14(c), the fracture from the upper edge of the specimen points obliquely downward to the middle of the specimen for the form of shear damage. Part of the fracture straight down through the entire specimen for the form of splitting damage. From the location and direction of the fractures, it can be judged that the coal sample is finally splitting damage mainly.Figure 12
Displacement vectors of different load/unload state: (a) first cycle step, (b) second cycle step, (c) third cycle step, and (d) final damage.
(a)(b)(c)(d)Figure 13
Failure morphology of coal samples at different cycle stages: (a) first cycle step, (b) second cycle step, (c) third cycle step, and (d) final damage.
(a)(b)(c)(d)Figure 14
CT scanning pictures of failure coal sample: (a) left view, (b) rear view, (c) right view, and (d) final damage specimen.
(a)(b)To compare the experimental results, the variation curve of the response ratio with loading obtained from the numerical simulation was analyzed and obtained, as shown in Figure15. During the first two stages of cyclic loading, E+ remained basically unchanged. The indicator E− tends to increase, but the change is not obvious, and it is always maintained around 3 GPa. The loading and unloading response ratio Y fluctuate around 1. At the third cyclic loading stage, E− suddenly increases to 4.07 GPa. While E+ decreases to 2.96 GPa, and the Y value fluctuates. Finally, the specimen was damaged in the fourth cyclic step. The indicator E− increased sharply to 9.78 GPa, while E+ suddenly decreased to a negative value. Subsequently, the response ratio Y also fluctuates, which is consistent with the experimental results.Figure 15
Load/unload response ratio.The E+, E−, and Y values did not show the fluctuation phenomenon in the experimental process at the early stage of cyclic loading. The main reason may be the fluctuation of elastic modulus caused by the continuous opening and closing of cracks inside the sample with cyclic loading and unloading. The influence of the fissures is not considered in the numerical simulation, so the elastic modulus does not change much. In summary, the modulus of elasticity E+ and E− and the response ratio Y of unloading and loading appear to change more obviously when the sample is close to damage, so it can be used as a basis for damage precursors.


## 3.4. Influence of the Number of Model Cells on the Response Ratio

The 3D models with different number of units were obtained by varying the particle radius. The simulations are analyzed under the same material parameters with the same loading method as described in the previous subsection. Figure16 shows the relationship between the number of units and the computation time consumed. When the number of cells is below 24,000, the computation time increases slowly to 1063 minutes as the number of cells increases. However, when the number of cells increases to 45,000, the computation time increases abruptly to 11,662 minutes, which seriously reduces the computation efficiency.Figure 16
Calculation time of coal sample with different particle numbers.Figure17 shows the stress-strain curves for four models containing different number of units. The loading process uses the same displacement control method and undergoes a total of seven stages of cyclic loading and unloading of the process. The model with different number of cells reaches the peak stress at different cycle levels. As shown in Figure 17, the macroscopic modulus of elasticity of the model increases with the increase in the number of cells. The peak stress tends to increase significantly with the increase in the number of cells. This may be due to the fact that the porosity of the reconstructed model decreases with the increase in the number of cells. Figures 18 and 19 show the loading and unloading response elastic modes E+ and E− at different cyclic levels for different unit number models, respectively. Figure 20 shows the load/unload response ratio of coal sample with different particle numbers.Figure 17
Stress-strain curves of coal sample with different particle numbers.Figure 18
Load response (E+) of coal sample with different particle numbers.Figure 19
Unload response (E–) of coal sample with different particle numbers.Figure 20
Load/unload response ratio of coal sample with different particle numbers.Figure18 shows the different models reaching peak stress at different cycle levels. At the preload cycle level, E+ increases first and then level off, as in models b, c, and d. At the midloading cycle level, the E+ in model b continues to increase and then level off. The E+ in both models c and d rises to a relatively large value and then begins to decrease. Although the response characteristics of E+ differed, the trend of E+ variation was relatively simple with a small fluctuation range. The E+ exhibits “M”-shaped fluctuations in one cycle before the specimen is damaged, as shown in model a first level, model b third level, model c fifth level, and model d sixth level. As the stress approaches or reaches a peak cyclic level, E+ suddenly drops to a minimum value.Figure19 indicates that E− increases first and then levels off during the preloading and midloading periods, as shown in the calculated results of models c and d. At the beginning of each cycle level, there is a more pronounced tendency for E− to increase, followed by a gradual decrease. E− increases to a maximum value during the first unloading when the stress is close to or at the peak cycle level. Comparing Figures 18 and 19, it can be seen that at the beginning of each cycle phase, the fluctuation of E− is greater than the amount of change of E+ at the corresponding position.The E+ and E− variations accordingly cause fluctuations in the value of the load/unload response ratio Y, as shown in Figure 20. In the preload period, the load/unload response ratio Y is always maintained at about 1. As the stress approaches its peak, the Y value increases abruptly, as shown by the response at the last cycle level of models a and d in Figure 20. The Y value fluctuates more at the peak and even becomes negative.The E+, E−, and Y values remain at a more stable value throughout the preload and midload periods. As the stress approaches or reaches its peak, the E+, E–, and Y values change abruptly. In comparison, E– and Y values change more obviously and are more suitable as precursors of specimen damage to judge or predict specimen damage. However, since both matrix and inclusions are homogeneous in the reconstructed coal sample model, the abrupt change point of the loading and unloading response ratio is very close to the peak. This poses a challenge to predict specimen damage in advance.


## 4. Conclusion

The uniaxial cyclic loading and unloading experiments of bituminous coal were carried out, and damage monitoring was performed by means of acoustic emission. The damage and breakage characteristics of the bituminous coal were further investigated by reverting the experimental process with a three-dimensional inversion technique. The following conclusions were drawn:(a)
At the beginning of the loading phase, the modulus of elasticity shows an increasing trend. In the unloading stage, the modulus of elasticity exhibits a decreasing trend. Near the damage, it appears to change sharply. In the initial loading phase, the elastic modulus plus the unloading response ratio Y increases. With continued loading, the sample enters the elastic stabilization stage with the Y value fluctuating around 1. The Y value increases sharply and the sample is finally destroyed.(b)
The cumulative acoustic emission ringing counts can better reflect the internal damage evolution of the sample during loading and unloading. When the loading stress exceeds the last unloading stress, the cumulative ringing count changes abruptly. The rest of the time, there is no significant change and the signal suddenly increases before the sample is damaged. The response ratio of acoustic emission for loading and unloading gradually decreases with the increase of loading, and finally tends to 1.(c)
The CT scan experiment of the specimen can acquire the internal structural characteristics of the sample. The internal structure of the sample can be restored more realistically by 3D reconstruction. The numerical simulation based on 3D inverse modeling can predict the damage characteristics of the specimen before the experiment.



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*Source: 7455508-2022-04-07.xml*