Influences of True Triaxial Loading-Unloading Stress Paths on Mechanical Properties and Wave Velocity of Coal Samples subject to Risk of Rock Burst

Abstract

To study fracture evolution and peak stress in burst risk coal samples (BRCSs) under true triaxial loading and unloading conditions, experimental and numerical research was applied to BRCSs under true triaxial stress paths entailing “x-direction displacement fixed, y-direction loading, z-direction unloading.” Both the experimental and the numerical results demonstrated that the peak stress borne by the BRCSs was not only affected by the initial stress but also had a negative exponential relationship with the ratio of the unloading rate and the loading rate (RURLR); therefore, peak stress equations of BRCSs under true triaxial loading and unloading conditions were established. The triaxial stress-time curves obtained by experiments and simulations exhibited an “elasticity-yield-destruction” phase, and the characteristics of the yield phase were determined by the RURLR. A typical BRCS was selected for velocity tomographic imaging to analyze the fracture evolution characteristics under true triaxial loading and unloading. The results showed that when the BRCS was subjected to a triaxial state of stress, the high- and low-velocity regions existed alternately due to the presence of the crack; during the elastic phase, the crack closed during loading in the previous phase was reopened upon unloading, so that the velocity of the sample decreased and a wide range of low-velocity regions could be formed; when entering the yield phase, the original crack continued to expand into a hole-through crack, leading to wider extreme values and ranges of these low- and high-velocity regions; at the breaking phase, multiple microcracks were generated around the hole-through cracks, decreasing the overall velocity, and showing point distributions characteristics of high- and low-velocity regions. Overall, many low-velocity regions with similar normal directions to the unloading direction were formed; these correlated well with macrofractures (postfailure).

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

As the mining depth increases, rock burst becomes a serious mine disaster, which restricts the safety production of the coal mine [1–3]. The occurrence of rock burst is induced by many factors. According to statistics, the rock burst mainly occurs in the roadway (91%) during mining and driving. During the mining period, the production personnel are mainly located under the hydraulic of working face, and few personnel are in the roadway. So, personnel are less likely injured by the rock burst. On the contrary, the personnel are mainly located in the head and the rear of the roadway during the driving, which are just the rock burst prone area. So, it is easier to cause casualties during driving than during mining. From the perspective of coal seam properties, the difficulty of rock burst is affected by coal properties. For coal samples with a uniaxial compressive strength greater than 20 MPa, the critical stress value of rock burst is only 50 MPa, while the uniaxial compressive strength is less than 17 MPa, and the critical stress value of rock burst needs to reach 70 MPa [4]. By dividing the coal samples into different hazard levels, the scholar judges the difficulty of rock burst, and rock burst is most likely induced in the strong BRCSs [5–7]. Therefore, the roadway excavation in the strong BRCSs is more likely to cause casualties than the mining and is more likely to cause rock burst than the weak BRCSs; therefore, it has more research value.

With the driving disturbance [8], the initial rock stress state is broken, and the free surface radial stress of the surrounding rock instantaneously reduces to zero, which shows obvious radial unloading; the roof is continuously falling in the vertical direction of the surrounding rock, which shows apparent loading on the coal body; the trending direction of the surrounding rock is constrained by the adjacent coal body. The surrounding rock exhibits the triaxial stress path characteristic of “load-unload-displacement fixation.” According to numerous previous studies in the literature [9–11], the stress-strain paths have an important effect on the stress variation and fracture form of coal samples.

In order to better understand the stress characteristics and fracture mechanism of rocks under true triaxial loading and unloading conditions, many experimental and numerical investigations on rocks have been carried out. Based on the stress path of the underground engineering excavation, Du et al. [12] carried out true triaxial unloading compressive test and found the failure modes of the granite and red sandstone specimens changed from shear to slabbing with the increase of σ². Su et al. [13] carried out the experiments with a loading path that maintained one face free and applied loading along three axial directions on the other five faces and found that the tunnel axis stress has a significant influence on the strain burst characteristics. In the true triaxial loading-unloading test, Li et al. [14] found the total strain energy, elastic strain energy, and circumferential strain energy all increase as the initial confining pressure increases, whereas the dissipative strain energy does not. Chen et al. [15] carried out an experiment with one face kept free and the other five faces loaded and found that rock burst occurrence depends on several conditions, including specifically the tangential loading rate exceeding a certain threshold, the presence of considerable amounts of stored strain energy, the dissipation of energy through rock splitting on the free face, and the shear failure in the potential rock burst pit. Zhao et al. [16] found that the rock samples are prone to strain burst failure under a high unloading rate and the associated acoustic emission energy release in the strain burst process is dependent on the unloading rate. Yin et al. [17] studied the influence of true triaxial loading and unloading rate on energy characteristics of sandstone and found that the dissipated energy ratio increased first, then decreased, and finally increased with the increase of maximum principal strain. The dissipated energy ratio decreased with the increase of unloading rate at peak stress and increased with the increase of loading rate. Wang et al. [18] studied the effects of loading and unloading conditions on mechanical behaviors of sandstone and mudstone and found that the mechanical behaviors obtained from the unloading triaxial tests, such as the specimens’ failure surface, strain–stress curve, triaxial compressive strength, and triaxial shear strength, are different from ones obtained from the conventional triaxial tests. Feng et al. [19] found that the peak strength is nonsymmetrical with the increasing σ² and is closely related to the lode angle, and the strength variation exhibited a close relationship to the failure mechanism. Liu et al. [20] found that preexisting flow planes play significant roles in the strength levels, failure modes, and permeability levels under true triaxial stress paths. Zhu et al. [21] found that bursting failure occurs when the axial stress is more than three times the uniaxial compressive strength of the coal sample under a constant confining pressure. Zhao et al. [22] simulated the stress change of a rock mass in front of the working face during underground excavation and found that the total absorption energy, elastic strain energy, and dissipation energy increased with the loading rate increased. For a given loading rate, more cracks were formed by consuming less energy under a high unloading rate. Yang [23] found that higher initial unloading confining pressure is associated with earlier and more severe failure after peak stress. Faster unloading rates are also associated with earlier sample destruction after peak stress because the coal rapidly changes from a triaxial stress state to a uniaxial stress state with a higher unloading rate, crack propagation is insufficient, and more elastic energy is released. Zhang et al. [24] found that the test results show that the triaxial unloading strength of coal samples under different test conditions is lower than conventional triaxial tests, but the brittleness characteristics are more obvious. Si and Gong [25] found that under the same confining pressures, the variations in peak strength of granite specimens are in the following order: triaxial compression test biaxial compression test > triaxial unloading compression test under low unloading rate > triaxial unloading compression test under high unloading rate, which indicates that unloading induces an obvious strength-weakening effect on fine-grained granite.

In the experimental process, acoustic emission [26–28], photographic monitoring techniques [29, 30], tomography techniques [31, 32], and other methods [33, 34] have been used to monitor and analyze spatial distributions of microfractures in rocks. Tomography techniques have been used in the laboratory because of their many advantages including techniques penetration, relatively minor errors, and visualization [31, 32]. Cao et al. [31] used passive velocity tomography to study characteristics of mudstone during uniaxial deformation and found that high-velocity regions can be used for the prediction of large energy AE events in rocks. Goodfellow et al. [32] conducted a true triaxial test using attenuation tomography and found that attenuation properties could reflect the damage status in Fontainebleau sandstone at different loading phases.

The previous studies enrich the understanding of the mechanical characteristics and fracture characteristics under the condition of true triaxial loading and unloading. However, the effect of the RURLR is not considered in calculating the peak stress, and the study of the BRCS simulation under triaxial loading and unloading is not found. It is not found that the characteristics of the fracture evolution during the true triaxial loading and unloading process were analyzed by the velocity tomography. These are the research key contents of this paper. In this paper, the experimental and numerical methods are used to study the mechanical and fracture evolution characteristics of BRCSs under the triaxial loading and unloading, so as to provide a reference for the risk prediction of roadway driving in burst risk coal seams.

2. Experiments and Simulations of BRCSs

According to the introduction, our predecessors have used experimental and numerical methods to study the stress equation and fracture characteristics under the condition of true triaxial loading and unloading. The two methods have their own advantages and disadvantages: the coal samples naturally contain multiple fracture units, which results in a certain dispersion of their mechanical characteristics, but the experimental method can better reflect the evolution of the natural coal samples. The results obtained by the numerical simulation method can reflect the mechanical characteristics of the sample with certain physicomechanical parameters, but its description of the fracture evolution of the natural coal samples is poor, especially when using finite element analysis. Therefore, in the present work, experiments and simulations are both used to study the mechanical and fracture evolution characteristics under true triaxial loading and unloading.

2.1. Experimental Methods and Procedures

The stress paths applied in the experiments entail “x-direction displacement constant, y-direction loading, z-direction unloading.” The specimens are cubes with a side length of 70.7 mm.

Two schemes were adopted. (1) The effect of RURLR: the samples are loaded to initial stress of 25 MPa, and then the Y-axis is loaded at a certain rate; the ratio of the Z-direction unloading rate to the Y-direction loading rate is shown in Table 1; the X-direction displacement is kept constant until the sample is destroyed. (2) The effect of initial stress: the samples are loaded to different initial stresses (see Table 1); then the ratio of the unloading rate in the Z-direction to the loading rate in the Y-direction is set to 1.5 for true triaxial loading and unloading tests. The displacement in the X-direction is kept constant until the sample is destroyed.

Table 1

The effect test of RURLR and initial stress.

Test content	Initial stress (MPa)	Loading rate (Y-axis) (mm/min)	Unloading rate (Z-axis) (mm/min)	RURLR
RURLR	25	1	0.5	0.5
			1	1
			1.5	1.5
			2	2
			2.5	2.5
Initial stress	6.25	1	1.5	1.5
	12.5
	18.75
	25
	31.25

During each experiment, the acoustic emission events were monitored by using a PCI-2 acoustic emission acquisition system equipped with eight Micro-80S miniature AE probes. The acoustic emission probes are embedded in an iron block, and the surfaces of the probes are coated with Vaseline® to couple them to the coal samples (as shown in Figure 1); a layer of rubber is placed between the iron block and the coal to prevent the wave propagating through the iron block to the probes, thereby improving the accuracy of waveform signal monitoring.

[figure omitted; refer to PDF]

(4) Application of the Equations. Equations (8) and (9) show that the loading axial stress and unloading axial stress of coal mass at peak stress under true triaxial loading and unloading regimes can be obtained from the initial triaxial stresses and the ratio of unloading rate to loading rate. Specifically, for roadway excavation operations, by measuring the initial triaxial stress of the stratum, knowing the rates of axial and radial deformation of the roadway, the triaxial stress when the surrounding rock of the roadway reaches the peak can be estimated.

3.3. Velocity Tomography Images

3.3.1. Theory of Velocity Tomography [36, 37]

Tomography requires dividing the body into cubes called voxels in the three-dimensional situation to estimate the body characteristics in all voxels. Suppose that the ray path of the ith acoustic wave is L_i and the travel time is T_i; thus, the time is the integral of the inverse velocity, as described in equations (10) and (11). As an acoustic wave will propagate along a curved path in a heterogeneous medium, ray bending must be taken into consideration for accurate velocity calculation. Thus, the inversion area should be divided into m voxels, and the travel time of the ith ray can be presented as equation (12):$$\begin{array}{}\text{(10)}& V=\frac{L}{T}⟶VT=L,\text{(11)}& T_i={\displaystyle {\int }_{L_i}\frac{\text{d}L}{Vx,y,z}}={\displaystyle {\int }_{L_i}Sx,y,z\text{d}L},\text{(12)}& T_i={\displaystyle \sum _{j=1}^m{d}_{ij}{S}_j}\hspace{1em}i=1,\dots ,n,\end{array}$$where V (x, y, z) is the velocity (m/s), L_i is the ray path of the ith wave (m), T_i represents the travel time (s), and S (x, y, z) is the slowness (s/m). d_ij is the distance of the ith ray in the jth voxel, n is the total number of rays, and m is the number of voxels.

Generally, the AE event location and subsequent ray paths are calculated using an initial velocity model. However, the velocity, distance, and time in an individual voxel are unknown. Thus, arranging the slowness, distance, and time for each voxel into matrices, the velocity can be determined in matrix form as$$\begin{array}{}\text{(13)}& T=DS⟶S=D^{-1}T,\end{array}$$where T is the travel time per ray matrix (1 × n), D is the distance per ray per voxel matrix (n × m), and S is the slowness per grid cell matrix (1 × m).

Many studies show that the high-velocity zone corresponds to the high-stress zone, and the low-velocity zone corresponds to the low-stress zone and the fissure zone. Based on this, the stress and fissure distribution law of the sample can be obtained.

3.3.2. Evolution Characteristics of Velocity

The number of samples subjected to true triaxial loading-unloading experiments is large, and the velocity evolution characteristics of samples are roughly the same, so a typical sample was selected for analysis. Figure 8 shows the triaxial stress and acoustic emission energies over the whole experimental period. The tomography can be divided into five phases: phase A is the triaxial stress loading phase, phase B is the elastic phase of the loading and unloading experiment, phase C is the yielding phase of the loading and unloading experiment, and phase D is the failure phase of the loading and unloading experiment. Due to the large number of acoustic emission events in phase C, it is subdivided into two phases, C1 and C2. Photographs of specimens before and after testing are shown in Figure 9. The acoustic emission monitoring sites used in each phase are illustrated in Figure 10, and the velocity tomographic images of each phase are shown in Figure 11.

[figure omitted; refer to PDF]

[figures omitted; refer to PDF]

It can be found from the tomographic phase (phase A, Figure 11(a)) that the continuity of the distribution of low- and high-wave velocity zones is poor on each section of the sample, showing the characteristics of a point-like cross-distribution. The wave velocity range is 0.65 km/s to 1.70 km/s. Figure 9 shows that there are some macrocracks in the sample before the test. The velocity of wave propagation in the fracture region is low, and the bearing capacity is weak. The stress is carried by the intact coal body around the cracked region, which leads to a high velocity in the intact region. Due to the presence of the original cracks, the cross-distribution of high and low velocities is formed in the coal body. As shown in Figure 10, the acoustic emission events are mainly concentrated in the area where there are no obvious cracks (0 ≤ x ≤ 35, 0 ≤ y ≤ 35, 35 ≤ z ≤ 70) in the sample, which proves that the coal body in intact areas is the main load-bearing area.

From the velocity distribution map of phase B, it can be found that the extent of the high-velocity region decreases, while that with a low velocity enlarges, and the maximum and minimum wave velocities (ranging from 0.55 km/s to 1.50 km/s) are lower than those in phase A (Figure 11(b)). This is due to the unloading effect manifested in phase B, the density of the sample decreases, and the original cracks closed under compression in phase A reopen, resulting in an enlargement of the low-velocity region and a decrease in the overall wave velocity.

As the test progresses, the sample enters the yield failure state of phase C, wherein new cracks are generated continuously, and the opening of the original cracks also increases, which results in the number of acoustic emission events in phase C being greater than that in phase B, and the range and the extreme values of low wave velocity (the lowest wave velocity was 0.50 km/s) being greater than those in phases A and B. The formation of new cracks results in the transfer of stress to the surrounding, more intact, coal body, resulting in the increase of stress and extent of the high-stress region. Therefore, the range and extreme values of the high-velocity region (the maximum velocity was 2.00 km/s) in the coal sample are also greater than those in phases A and B. Under the action of new crack formation and increased crack opening, penetrating cracks develop, resulting in vertical low-velocity regions with approximate penetration appearing in coal samples (as evinced by the x-direction tomographic slices).

In phase C1, the low-wave-velocity region is mainly distributed within 0 ≤ Z ≤ 35 m near the unloading face, and the high-wave-velocity region is mainly distributed within 35 ≤ Z ≤ 70 m, suggesting that cracks are formed near the unloading face, and the main load-bearing stress zone is far from the unloading surface. In phase C2, the region with 35 ≤ Z ≤ 70 m changes from being a high-velocity region to a low-velocity region, and it also accounts for most acoustic emission events (Figure 10), reflecting the fact that cracks have propagated from a position near the unloading surface to throughout the specimen.

It can be seen from the range of velocity distributions in phase D that the penetrating low-velocity zones gradually disappear, and the range and extreme value of the high- and low-wave-velocity zones (ranging from 0.63 km/s to 1.50 km/s) also decreased. This is due to the expansion of the coal body, which decreases the opening displacement of large through cracks and forms many microcracks, resulting in poorer continuity of high- and low-velocity regions than in phase C.

Throughout the experimental process, many low-velocity zones with their normal direction approximately parallel to the unloading direction are formed; this is in good agreement with the many cracks, approximately parallel to the unloading surface, formed in the experiment (Figure 9).

4. Conclusions

(1) The stress-strain curves and failure characteristics of BRCSs under uniaxial compression could be simulated by dividing the sample unit grids into elements measuring more than 5 mm and controlling the loading rate to within 0.001 mm/step

(2) Both experiments and simulations show that the stress-time curve of the BRCSs under true triaxial loading and unloading can be divided into three distinct phases of “elasticity-yield-failure”: in the elastic phase, the unloading lateral stress decreases gradually, and the loading lateral stress increases with a certain slope. In the yield phase, due to the fracture and expansion of the coal body, the rate of increase of the applied lateral stress and the rate of reduction of the unloading of lateral stress decrease, resulting in a well-defined yield point; in the failure phase, the applied lateral stress decreases, and stress changes in other directions are small

(3) Both experiments and simulations show that the peak stress of the BRCSs increases linearly with the increase of the initial stress and has a negative exponential relationship with the RURLRs under true triaxial loading and unloading conditions; thus, the peak stress equations of the BRCSs under true triaxial loading and unloading can be established

(4) Velocity tomographic imaging can reveal the fracture evolution in BRCSs under true triaxial loading and unloading conditions: when the BRCS is subjected to a triaxial stress regime, the high- and low-velocity regions exist alternately due to the presence of the crack; during the elastic phase, the crack closes under load in the previous phase reopened upon unloading, so that the wave velocity through the specimen decreases and a wide range of low-velocity regions can be formed; when entering the yield phase, the original crack continues to expand into a hole-through crack, leading to a wider range between extreme values and that between the low and high-velocity regions; in the breaking phase, many microcracks are generated again around the hole-through cracks, thereby decreasing the overall wave velocity, and showing the point distribution characteristics of high- and low-velocity regions. Throughout the tests, many low-velocity regions with a similar normal direction to the direction of stress-unloading are formed, which are found to correlate well with macrofractures in postfailure specimens.

Acknowledgments

The authors extend special thanks to the team at Hua-ting coal mine, who provided the coal body. The authors gratefully acknowledge support by the Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province (Grant No. ZJRMG-2019-06), the Science and Technology Projects of Jiangsu Construction System (Grant No. 2019ZD001159), the Research Fund of the Jiangsu Engineering Laboratory of Mine Earthquake Monitoring and Prevention, CUMT, and the National Natural Science Foundation of China (Grant No. 51974302).

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