# Research on Coal Mechanical Properties Based on True Triaxial Loading and Unloading Experiment

Authors: Yanyan Peng; Haoxiang Deng; Minghong Xing; Pengfei Guo; Chun Zhu
Journal: Advances in Civil Engineering
 (2021)

---

## Abstract

To study the safety issues caused by coal mine excavation, self-developed simulation of earth interior atmosphere and sound test system was used to perform true triaxial loading and unloading tests of coal. An acoustic emission detection system was used to record the damage evolution trend of coal under different intermediate principal stress states. The experimental results show that in the true triaxial unloading test, as the intermediate principal stress increases, the failure state of coal changes from shear failure to partial shear tension failure, finally leading to overall yield failure. In the stress-strain curves, with the increase in intermediate principal stress, the strain in the direction of intermediate principal stress gradually changes from compression to expansion, and typical expansion occurs. The Mogi–Coulomb strength criterion better reflects the strength failure characteristics of coal during unloading. The stress-acoustic emission diagrams show that the increase in intermediate principal stress causes the internal cracks of the coal to grow unsteadily and exponentially, and the increase in intermediate principal stress makes the coal lose its ability to continue to bear the load. Studying the influence of the intermediate principal stress on the mechanical properties of coal has practical significance for coal mine safety production.


---

## Body

## 1. Introduction

In coal mining engineering, the deep underground engineering rock mass is in a three-way stress state [1–4]. Excavation of slopes, tunnels, or mines causes strong expansion of rock mass in the area adjacent to excavation surface, accompanied by complex mechanical failures such as tension and shear. Therefore, to study the mechanical properties of deep underground engineering rock mass, it is not enough to rely on uniaxial compression, tensile tests, or conventional triaxial compression tests only. True triaxial tests are needed to simulate the real force of rock mass.In recent years, a large number of indoor true triaxial test studies have been conducted [5–12]. For example, He et al. [13, 14] carried out true triaxial unloading tests on limestone, sandstone, and granite samples in deep high in situ stress areas and obtained their rockburst induction mechanism and failure characteristics. Lü et al. [15] conducted a true triaxial unloading test on granite and derived a mechanical constitutive equation in the strain space considering the degradation effect of rock deformation parameters. Wang et al. [16] used a true triaxial testing machine to perform a series of loading and unloading tests on rock samples under compression and shear and obtained the variation trends of elastic shear modulus at different unloading stages. He et al. [17, 18] conducted a series of true triaxial simulation experiments and developed a new experimental method to simulate rockburst. Zhang et al. [19] conducted true triaxial loading and unloading confining pressure tests on marble and found that the energy dissipation of marble is related to the rate of unloading confining pressure. Li et al. [20] performed a true triaxial loading test of sandstone combined with CT scanning technology and systematically studied the characteristics of sandstone strength and deformation under different intermediate principal stress conditions. Xue and Liu [21] used a true triaxial testing machine to simulate the underground stress conditions of a mine and combined with acoustic emission equipment made an early warning of coal mass destruction. Xi et al. [22] used a true triaxial THMC coupling test machine to study the thermal deformation and expansion coefficient of granite. Xie et al. [23–25] used true triaxial tests to study the mechanical behavior of rocks during deep mining.At present, there are relatively few true triaxial test studies on the influence of intermediate principal stress on coal mechanical properties. Therefore, in this study, coal was taken as the research object; through true triaxial loading and unloading tests, the transient unloading failure of coal under the original rock stress state is simulated [26, 27], and acoustic emission detection technology was used to evaluate the effect of intermediate principal stress on coal strength and failure. The true triaxial test is used to study the influence of the intermediate principal stress on the mechanical properties of coal, which is of great significance to the safe mining of coal mines.


## 2. Experimental

### 2.1. Testing Machine

The true triaxial loading and unloading test device is composed of a test system simulation of earth interior atmosphere and sound. The equipment uses six rigid independent loading modules in three directions to simulate the three-dimensional stress state of deep underground engineering. The equipment can be loaded in three directions and six sides to a certain stress state and then can be quickly unloaded on one side. The indenter quickly unloads within 20 ms, and the free fall time is 176 ms. The specimen can be exposed on one side in 196 ms. The maximum tensile and compression test force of the three-way six-sided loading actuator is 1000 kN, and the maximum range is 300 mm. The equipment is shown in Figure1(a).Figure 1
Test system simulation of earth interior atmosphere and sound. (a) Earth interior atmosphere and sound experiment host. (b) Schematic of acoustic emission detection system.
(a)(b)The acoustic emission system uses PCI equipment produced by American Physical Acoustics. The equipment is composed of six preprobes, six signal amplifiers, AE win system host, and corresponding pipelines. It can collect information such as impact count, amplitude, energy, and spatial positioning of coal during destruction. A schematic of acoustic emission detection system is shown in Figure1(b).


### 2.2. Sample Preparation

In this study, coal was selected as the research object. Coal was taken from the mining face in Shenshan Village, Tongchuan Town, Ordos City, Inner Mongolia Autonomous Region. To maintain the original stress state of sample, a large coal mass was selected from the mining face for processing. The coal sample was ground, so that the horizontal and vertical nonparallelism is less than 0.02 mm to form a coal sample of 100 mm × 100 mm × 100 mm, and wrapped with a plastic wrap. The average density of coal is 1578 kg/m3, Poisson’s ratio μ = 0.31, elastic modulus E = 1.75 GPa, average peak compressive strength σc = 14.6 MPa, cohesion c = 0.41, and internal friction angle φ = 41.3. A photograph of the rock sample is shown in Figure 2.Figure 2
Coal samples.


### 2.3. Experimental Scheme

To study the mechanical properties of coal under the effect of different intermediate principal stresses, the tests are divided into groups 1 to 4, corresponding to the intermediate principal stresses of 3, 6, 9, and 12 MPa. Two coal samples were taken from adjacent sampling positions as one group: one for true triaxial loading test and the other for true triaxial unloading test.In this test, the stress control method was used for loading, and each test system can automatically collect relevant data and draw the correlation curve of stress, impact count, energy count, and time. The test method is described below, and the relevant test data are shown in Table1. Sample 1-L represents the first sample of true triaxial loading experiment, and sample 1-U represents the first sample of true triaxial unloading experiment.(1)
True triaxial loading test: load coal to the hydrostatic pressure state (σ1 = σ2 = σ3) at a rate of 0.2 MPa/s; keep σ3 unchanged; continue to load σ1, σ2 to the set value (σ1 = σ2 > σ3) at a rate of 0.2 MPa/s; keep σ2 unchanged; and continue to load σ1 at a rate of 0.2 MPa/s until the coal is broken.(2)
True triaxial unloading test: the stress loading process is the same as above; when loadingσ1 at a rate of 0.2 MPa/s, load σ1 to 90% of the axial stress σ1 obtained when the coal is destroyed in the true triaxial loading test and keep σ1, σ2 constant. Then, unload σ3 at a rate of 0.5 MPa/s (transient unloading) and observe the damage of coal.Table 1
True triaxial loading and unloading test data.
True triaxial loading testTrue triaxial unloading testSpecimen number1-L2-L3-L4-L1-U2-U3-U4-Uσ1 (MPa)44.259.550.960.139.853.545.854.1σ2 (MPa)3691236912σ3 (MPa)22Loading rate (MPa·s−1)0.20.2Unloading rate (MPa·s−1)0.50.5During the test, the loading system and acoustic emission system should be kept synchronized in time. The acoustic emission system monitors the entire process of test coal failure and collects and analyzes relevant data.


## 2.1. Testing Machine

The true triaxial loading and unloading test device is composed of a test system simulation of earth interior atmosphere and sound. The equipment uses six rigid independent loading modules in three directions to simulate the three-dimensional stress state of deep underground engineering. The equipment can be loaded in three directions and six sides to a certain stress state and then can be quickly unloaded on one side. The indenter quickly unloads within 20 ms, and the free fall time is 176 ms. The specimen can be exposed on one side in 196 ms. The maximum tensile and compression test force of the three-way six-sided loading actuator is 1000 kN, and the maximum range is 300 mm. The equipment is shown in Figure1(a).Figure 1
Test system simulation of earth interior atmosphere and sound. (a) Earth interior atmosphere and sound experiment host. (b) Schematic of acoustic emission detection system.
(a)(b)The acoustic emission system uses PCI equipment produced by American Physical Acoustics. The equipment is composed of six preprobes, six signal amplifiers, AE win system host, and corresponding pipelines. It can collect information such as impact count, amplitude, energy, and spatial positioning of coal during destruction. A schematic of acoustic emission detection system is shown in Figure1(b).


## 2.2. Sample Preparation

In this study, coal was selected as the research object. Coal was taken from the mining face in Shenshan Village, Tongchuan Town, Ordos City, Inner Mongolia Autonomous Region. To maintain the original stress state of sample, a large coal mass was selected from the mining face for processing. The coal sample was ground, so that the horizontal and vertical nonparallelism is less than 0.02 mm to form a coal sample of 100 mm × 100 mm × 100 mm, and wrapped with a plastic wrap. The average density of coal is 1578 kg/m3, Poisson’s ratio μ = 0.31, elastic modulus E = 1.75 GPa, average peak compressive strength σc = 14.6 MPa, cohesion c = 0.41, and internal friction angle φ = 41.3. A photograph of the rock sample is shown in Figure 2.Figure 2
Coal samples.


## 2.3. Experimental Scheme

To study the mechanical properties of coal under the effect of different intermediate principal stresses, the tests are divided into groups 1 to 4, corresponding to the intermediate principal stresses of 3, 6, 9, and 12 MPa. Two coal samples were taken from adjacent sampling positions as one group: one for true triaxial loading test and the other for true triaxial unloading test.In this test, the stress control method was used for loading, and each test system can automatically collect relevant data and draw the correlation curve of stress, impact count, energy count, and time. The test method is described below, and the relevant test data are shown in Table1. Sample 1-L represents the first sample of true triaxial loading experiment, and sample 1-U represents the first sample of true triaxial unloading experiment.(1)
True triaxial loading test: load coal to the hydrostatic pressure state (σ1 = σ2 = σ3) at a rate of 0.2 MPa/s; keep σ3 unchanged; continue to load σ1, σ2 to the set value (σ1 = σ2 > σ3) at a rate of 0.2 MPa/s; keep σ2 unchanged; and continue to load σ1 at a rate of 0.2 MPa/s until the coal is broken.(2)
True triaxial unloading test: the stress loading process is the same as above; when loadingσ1 at a rate of 0.2 MPa/s, load σ1 to 90% of the axial stress σ1 obtained when the coal is destroyed in the true triaxial loading test and keep σ1, σ2 constant. Then, unload σ3 at a rate of 0.5 MPa/s (transient unloading) and observe the damage of coal.Table 1
True triaxial loading and unloading test data.
True triaxial loading testTrue triaxial unloading testSpecimen number1-L2-L3-L4-L1-U2-U3-U4-Uσ1 (MPa)44.259.550.960.139.853.545.854.1σ2 (MPa)3691236912σ3 (MPa)22Loading rate (MPa·s−1)0.20.2Unloading rate (MPa·s−1)0.50.5During the test, the loading system and acoustic emission system should be kept synchronized in time. The acoustic emission system monitors the entire process of test coal failure and collects and analyzes relevant data.


## 3. Analysis of Experimental Results of Coal Samples

### 3.1. Failure Analysis

Figure3 shows the characteristics of coal failure sections in true triaxial unloading tests under different intermediate principal stresses. Along the unloading direction, the coal has lateral expansion, and tensile fragments appear near the unloading surface.Figure 3
Failure section of coal in true triaxial unloading test. (a) Intermediate principal stress is 3 MPa. (b) Intermediate principal stress is 6 MPa. (c) Intermediate principal stress is 9 MPa. (d) Intermediate principal stress is 12 MPa.
(a)(b)(c)(d)When the intermediate principal stress is 3 MPa, small cracks appear on the unloading surface, and the crack direction and unloading direction have a certain angle between them. They expand along the unloading surface, showing obvious signs of shear friction. The failure mode of coal appears as shear failure, as shown in Figure3(a).When the intermediate principal stress is 6 MPa, vertical rough tension cracks appear near the unloading surface, locally accompanied by shear cracks. The failure mode of coal appears as a partial shear tension failure, as shown in Figure3(b).When the intermediate principal stresses are 9 MPa and 12 MPa, not only partial shear tension failure cracks appear in the coal near the unloading surface but also shear cracks penetrate the entire coal, resulting in yield failure, as shown in Figures3(c) and 3(d).The failure mode of entire coal shows that with the increase in intermediate principal stress, the fracture surface of coal specimens and the number of crushed coal pieces also gradually increase, and the overall coal gradually develops a higher degree of fracture. Compared with Figure3(a), the axial stress and lateral stress in Figure 3(d) have a greater impact on the coal sample. The internal microcracks are affected by transverse expansion tensile stress. When the stress at the ends of microcracks exceeds the shear strength of material at any time, the tension cracks on the outer surface of coal have a higher degree of development, and they have a clear positive correlation with the intermediate principal stress. At the same time, the number of cracks on the outer surface of coal specimens gradually increased. The cracks along the unloading direction divide the coal into several independent blocks, with the main fracture surface consistent with the direction of intermediate principal stress, indicating that the intermediate principal stress increased. In this case, the damage of specimen is mainly tensile and yield failure.


### 3.2. Deformation Analysis

Figure4 shows the stress-strain relationship curves of true triaxial unloading tests under different intermediate principal stresses. ε1 is the axial strain; ε2 is the strain in the intermediate principal stress direction; ε3 is the strain in the minimum principal stress direction; and εv is the volumetric strain, as shown in Figure 4.(1)
When the values of intermediate principal stressσ2, σ3 are relatively close, the stress-strain curve in the loading stage is similar to the conventional triaxial loading test. Coal underwent a development process from the compaction of original fissures to the initiation of new fissures and then to the interpenetration of fissures. Coal accumulates a certain amount of elastic potential energy during the loading stage. The curve tends to be horizontal after unloading, and brittle failures such as tension and shear occur [28–30].(2)
With the increase in intermediate principal stressσ2, the deformation range of curve ε3 in the loading stage also continues to widen. This is because the deformation in the ε2 direction is constrained, and the Poisson effect causes lateral expansion in the ε3 direction, resulting in increased deformation.(3)
With the increase in intermediate principal stressσ2, curve ε2 has an obvious inflection point, indicating that strain b is first compressed and then expanded. Curve εv has a significant slowdown or even rotation, indicating that the volumetric strain tends to expand.Figure 4
True triaxial unloading test stress-strain curve. (a) Intermediate principal stress is 3 MPa. (b) Intermediate principal stress is 6 MPa. (c) Intermediate principal stress is 9 MPa. (d) Intermediate principal stress is 12 MPa.
(a)(b)(c)(d)


### 3.3. Strength Analysis

Based on the Mises criterion theory, Mogi [31] found that intermediate principal stress has a significant effect on the strength of rock through true triaxial loading and unloading tests of various rocks. Therefore, an octahedral strength criterion considering the intermediate principal stress is proposed, the essence of which is still the shear failure criterion. The strength relationship between octahedral shear stress τoct and effective intermediate principal stress σm,2 at the time of failure can be expressed using equations (1) and (2):(1)τoct=13σ1−σ32+σ1−σ22+σ2−σ32,(2)σm,2=σ1+σ32.Al-Ajmi and Zimmerman [32, 33] compiled a large number of true triaxial test data and found that after combining the Mogi empirical strength criterion with the Coulomb strength criterion, the f (σm,2) line-shape fit is ideal, namely, the Mogi–Coulomb strength criterion, which can be expressed using equations (3)–(6):(3)τoct=α+βσm,2,(4)α=233c⋅cosφ,(5)β=233sinφ,(6)τ¯=∑ABSτoct−τoctTN,where c is the cohesive force; φ is the angle of internal friction; α is the intercept between Mogi–Coulomb strength criterion fitting through a straight line and the τoct-axis; β is the slope of fitting straight line; τ¯ is the average deviation of octahedral shear stress intensity; τoct and τoctT are the calculated and tested values; and N is the number of test groups.To better reflect the strength failure characteristics of coal during unloading under high in situ stress conditions, a scatter plot was drawn using the transient unloading stress data of true triaxial unloading test, and the relationship curve betweenτoct and σm,2 was obtained by quadratic polynomial linear fitting, as shown in Figure 5.Figure 5
τoct-σm,2 relationship of true triaxial unloading test.According to the fitted quadratic polynomial curve,α = 0.4013, β = 0.7870, R2 = 0.9688, calculated cohesion c = 0.47, internal friction angle φ = 42.9°, and the average deviation of the octahedral shear stress intensity τ¯  = 0.11.The calculated values ofc and φ are relatively close to the test values measured by conventional triaxial loading test. Therefore, the Mogi–Coulomb strength criterion can better describe the strength failure characteristics of coal during unloading.


## 3.1. Failure Analysis

Figure3 shows the characteristics of coal failure sections in true triaxial unloading tests under different intermediate principal stresses. Along the unloading direction, the coal has lateral expansion, and tensile fragments appear near the unloading surface.Figure 3
Failure section of coal in true triaxial unloading test. (a) Intermediate principal stress is 3 MPa. (b) Intermediate principal stress is 6 MPa. (c) Intermediate principal stress is 9 MPa. (d) Intermediate principal stress is 12 MPa.
(a)(b)(c)(d)When the intermediate principal stress is 3 MPa, small cracks appear on the unloading surface, and the crack direction and unloading direction have a certain angle between them. They expand along the unloading surface, showing obvious signs of shear friction. The failure mode of coal appears as shear failure, as shown in Figure3(a).When the intermediate principal stress is 6 MPa, vertical rough tension cracks appear near the unloading surface, locally accompanied by shear cracks. The failure mode of coal appears as a partial shear tension failure, as shown in Figure3(b).When the intermediate principal stresses are 9 MPa and 12 MPa, not only partial shear tension failure cracks appear in the coal near the unloading surface but also shear cracks penetrate the entire coal, resulting in yield failure, as shown in Figures3(c) and 3(d).The failure mode of entire coal shows that with the increase in intermediate principal stress, the fracture surface of coal specimens and the number of crushed coal pieces also gradually increase, and the overall coal gradually develops a higher degree of fracture. Compared with Figure3(a), the axial stress and lateral stress in Figure 3(d) have a greater impact on the coal sample. The internal microcracks are affected by transverse expansion tensile stress. When the stress at the ends of microcracks exceeds the shear strength of material at any time, the tension cracks on the outer surface of coal have a higher degree of development, and they have a clear positive correlation with the intermediate principal stress. At the same time, the number of cracks on the outer surface of coal specimens gradually increased. The cracks along the unloading direction divide the coal into several independent blocks, with the main fracture surface consistent with the direction of intermediate principal stress, indicating that the intermediate principal stress increased. In this case, the damage of specimen is mainly tensile and yield failure.


## 3.2. Deformation Analysis

Figure4 shows the stress-strain relationship curves of true triaxial unloading tests under different intermediate principal stresses. ε1 is the axial strain; ε2 is the strain in the intermediate principal stress direction; ε3 is the strain in the minimum principal stress direction; and εv is the volumetric strain, as shown in Figure 4.(1)
When the values of intermediate principal stressσ2, σ3 are relatively close, the stress-strain curve in the loading stage is similar to the conventional triaxial loading test. Coal underwent a development process from the compaction of original fissures to the initiation of new fissures and then to the interpenetration of fissures. Coal accumulates a certain amount of elastic potential energy during the loading stage. The curve tends to be horizontal after unloading, and brittle failures such as tension and shear occur [28–30].(2)
With the increase in intermediate principal stressσ2, the deformation range of curve ε3 in the loading stage also continues to widen. This is because the deformation in the ε2 direction is constrained, and the Poisson effect causes lateral expansion in the ε3 direction, resulting in increased deformation.(3)
With the increase in intermediate principal stressσ2, curve ε2 has an obvious inflection point, indicating that strain b is first compressed and then expanded. Curve εv has a significant slowdown or even rotation, indicating that the volumetric strain tends to expand.Figure 4
True triaxial unloading test stress-strain curve. (a) Intermediate principal stress is 3 MPa. (b) Intermediate principal stress is 6 MPa. (c) Intermediate principal stress is 9 MPa. (d) Intermediate principal stress is 12 MPa.
(a)(b)(c)(d)


## 3.3. Strength Analysis

Based on the Mises criterion theory, Mogi [31] found that intermediate principal stress has a significant effect on the strength of rock through true triaxial loading and unloading tests of various rocks. Therefore, an octahedral strength criterion considering the intermediate principal stress is proposed, the essence of which is still the shear failure criterion. The strength relationship between octahedral shear stress τoct and effective intermediate principal stress σm,2 at the time of failure can be expressed using equations (1) and (2):(1)τoct=13σ1−σ32+σ1−σ22+σ2−σ32,(2)σm,2=σ1+σ32.Al-Ajmi and Zimmerman [32, 33] compiled a large number of true triaxial test data and found that after combining the Mogi empirical strength criterion with the Coulomb strength criterion, the f (σm,2) line-shape fit is ideal, namely, the Mogi–Coulomb strength criterion, which can be expressed using equations (3)–(6):(3)τoct=α+βσm,2,(4)α=233c⋅cosφ,(5)β=233sinφ,(6)τ¯=∑ABSτoct−τoctTN,where c is the cohesive force; φ is the angle of internal friction; α is the intercept between Mogi–Coulomb strength criterion fitting through a straight line and the τoct-axis; β is the slope of fitting straight line; τ¯ is the average deviation of octahedral shear stress intensity; τoct and τoctT are the calculated and tested values; and N is the number of test groups.To better reflect the strength failure characteristics of coal during unloading under high in situ stress conditions, a scatter plot was drawn using the transient unloading stress data of true triaxial unloading test, and the relationship curve betweenτoct and σm,2 was obtained by quadratic polynomial linear fitting, as shown in Figure 5.Figure 5
τoct-σm,2 relationship of true triaxial unloading test.According to the fitted quadratic polynomial curve,α = 0.4013, β = 0.7870, R2 = 0.9688, calculated cohesion c = 0.47, internal friction angle φ = 42.9°, and the average deviation of the octahedral shear stress intensity τ¯  = 0.11.The calculated values ofc and φ are relatively close to the test values measured by conventional triaxial loading test. Therefore, the Mogi–Coulomb strength criterion can better describe the strength failure characteristics of coal during unloading.


## 4. Analysis of Characteristics of Acoustic Emission Damage Evolution

Figure6 shows the results of true triaxial unloading test (stress difference-acoustic emission) under different intermediate principal stresses.Figure 6
True triaxial unloading test of stress difference-AE curve. (a) Intermediate principal stress is 3 MPa. (b) Intermediate principal stress is 6 MPa. (c) Intermediate principal stress is 9 MPa.
(a)(b)(c)Figure6 shows that the characteristics of unloading acoustic emission under the condition of intermediate principal stress of coal have the following trends (because the failure of 9 MPa and 12 MPa of intermediate principal stress is similar, only 9 MPa is listed for explanation):(1)
Loading (stage I): within a few seconds before the start of this stage, the acoustic emission energy count increases, and the stress difference is 0. This is because coal is deposited in a certain amount of original fissures in their natural state. As the test progresses, the fissures are continuously compacted [34]. Then, it enters the load. By fitting the impact count curve of stage I, the curve was found to be linearly distributed, and the energy count did not increase sharply, indicating that with the increase of load, the microcracks inside the coal begin to initiate and expand, and the elastic energy continues to accumulate. Thus, a steady growth trend was observed [35]. However, as a whole, the internal crack expansion is generated in a small area only, a linear elastic section [36], as shown in Figures 6(a) and 6(b) (stage I).In addition, a longitudinal comparison showed that with the increase in intermediate principal stress, the crack propagation in coal rapidly developed from a stable linear growth to an exponentially unsteady exponential growth, as shown in Figure6(c) ((i) and (ii) of stage I).(2)
Confining pressure maintenance (stage II): to simulate the original stress state of coal so that it can more truly reflect the force of underground stress, this stage was set to maintain a stable time of 100 s to 150 s after maintaining linear loading. Loading was stopped at this stage. The stress difference and impact count curve are both horizontal, and the energy count has no major fluctuations.(3)
Unloading (stage III): in this stage, the minimum principal stress is unloaded. The two stress difference curves in the figure are separated, and the acoustic emission energy count sharply increases. After the impact count curve is fitted, it shows an exponential increase. This indicates that the internal pressure of coal after unloading the stored elastic energy is suddenly released, and the cracks formed inside penetrate each other, forming macroscopic cracks.(4)
Unloading completion (stage IV): at this stage, the coal has been destroyed, and the cracks have penetrated the entire coal. However, the impact count curve has not increased, and the energy count has not fluctuated, indicating that the rock mass still has a certain bearing capacity after failure [37–42], as shown in Figures 6(a) and 6(b) (stage IV). In addition, with the increase in intermediate principal stress, the coal has shown yield failure when entering stage IV, and the stress difference curve has a significant decline section, indicating that the intermediate principal stress makes the coal no longer able to continue to bear the load, as shown in Figure 6(c) (stage IV).


## 5. Conclusions

Through scientific experiments, the effect of intermediate principal stress on coal mechanical properties was evaluated. According to the effect of coal stability under different intermediate principal stresses, a prepeak unloading test was performed. Combining with the acoustic emission detection technology, obtain the coal failure law under the true triaxial unloading experiment. This research is of great significance to the study of the failure mechanism of coal mining:(1)
In the true triaxial unloading test, the deformation and failure characteristics of coal become severe with the increase in intermediate principal stress. The failure state develops from shear failure to partial shear tension failure, finally reaching yield failure. As the intermediate principal stress increases, the deformation in the direction of intermediate principal stress changes from compression to expansion, and capacity expansion occurs.(2)
The shear strength parameters calculated using the Mogi–Coulomb strength criterion are similar to those obtained experimentally. The Mogi–Coulomb strength criterion can better fit the true triaxial unloading strength of coal. This strength criterion accurately reflects the strength failure characteristics of coal during unloading when the intermediate principal stress changes.(3)
An increase in intermediate principal stress can cause unstable growth of cracks in the loading stage. During the unloading stage, the acoustic emission energy count increases significantly with the increase in intermediate principal stress, indicating that it has a certain effect on the accumulation of elastic energy in coal. In the unloading stage, when the intermediate principal stress is slight, the coal still has the bearing capacity, but with the increase in intermediate principal stress, the bearing capacity of coal decreases.



---

*Source: 6675222-2021-03-16.xml*