Experimental Study on Coal Specimens Subjected to Uniaxial Cyclic Loading and Unloading

Abstract

The paper represents a test investigation of the mechanical properties and acoustic emission (AE) characteristics of low-strength coal specimens subjected to cyclic loading and unloading. From the lab tests, the following conclusions can be obtained: (1) The axial strain is very well linear with the loading–unloading cycle number, and the circumferential and volumetric strains are approximately quadratic functions with the loading–unloading cycle number; (2) Under the same loading stress interval, the elastic modulus firstly increases and then remains stable with the loading–unloading cycle number. In addition, the higher the maximum stress of a loading–unloading cycle, the more significant the plastic strengthening effect produced by this cycle; (3) The damage calculated by the cumulative AE hit count can better reflect the fact that the damage has been increasing in the loading phase and keeps basically unchanged in the unloading phase. So, the AE hit count, as a damage variable, can better describe the damage development of coal specimens. (4) The significant fluctuation of the AE b value can be used as the precursor of coal specimen failure. Additionally, the AE b value decreases rapidly at coal specimen failure. (5) The closer to the loading–unloading cycle of coal specimen failure, the more accurate the predicted “maximum magnitude” at coal specimen failure.

1. Introduction

Different types of coal barriers are inevitably set in an underground coal mine. Besides the static loads, these coal barriers are also affected by dynamic loads. Under the superposition of these two stresses, the coal barrier is prone to instability and failure, thus resulting in dynamic disaster accidents such as rockburst [1,2,3,4]. Only in the United States, according to incomplete statistics, more than fifty surface subsidence incidents were triggered by the collapse of coal barriers [5]. In South Africa, many coal barriers were suddenly destroyed decades later [6]. As we all know, as the mining range expands or mining goes deeper, the dynamic loads applied to the coal masses increase. That is, the coal masses are destroyed under the multilevel cyclic disturbing loads. So, it is very significant to study the damage and failure evolution characteristics of coal specimens subjected to graded uniaxial cyclic loading and unloading for coal mine production safety. Many studies have shown that the rock produces acoustic emission (AE) phenomenon under the loading [7,8,9,10]. Some studies have also shown there exist the Kaiser and Felicity effects in the AE phenomenon [11,12,13]. AE signals contain important information about the rock state; so, through extracting and analyzing these signals, the damaged state of loaded rock can be reliably assessed [14,15,16].

At present, the test research on high-strength rock subjected to cyclic loading and unloading has been extensively carried out. For example, Zhang et al. [17] studied the fracture properties of concrete under cyclic loading. Zhou et al. [18] studied the dynamic strength, strain rate, and damage of red sandstone, limestone, and sandstone under dynamic cyclic loading. Pu et al. [19] study the dynamic constitutive formula of rock subjected to cyclic loading. Wang et al. [20] studied the creep properties of salt rock subjected to long-period cyclic loading. Yang et al. [21] studied the mechanical properties of granite under static and dynamic cyclic loadings. In contrast, there are few studies of the low-strength coal specimens, their abundant internal joints and fissures, and the difficulty in processing them into standard specimens. Compared with the high-strength rock specimens, the low-strength coal specimens exhibit greater plasticity and poorer cementation. So, there are obvious differences in mechanical and physical properties between them. In this paper, the relevant research on low-strength coal specimens can make up for the shortcomings of the current research. In particular, the study of the AE b value has an important guiding significance for evaluating the stability of in situ engineering coal masses.

2. Experiment Design

2.1. Specimen

The coal chunks were taken from the Xuejiawan Coal Mine in Inner Mongolia Autonomous Region, China. In the processing room, they are processed into a large number of standard cylindrical specimens. Then, the coal specimens with no cracks and joints are selected, placed in a dry room for natural drying, and numbered.

Table 1. The basic parameters of tested coal specimens.

Specimen Number	Diameter/mm	Height/mm	Density/g·cm−3	Mass/g
1	50.3	101.2	1.157	232.6
2	49.5	99.1	1.158	220.8
3	49.4	98.2	1.161	218.4
4	49.5	99.6	1.158	221.8

lists the basic parameters of several tested coal specimens.

2.2. Experimental Devices

The cyclic loading–unloading tests were conducted using the ROCK600-50 mechanics test system (Top Industrie Corporation, Vaux-le-Penil, France). The characteristic parameters of AE signals were obtained using an AE21C AE system (Shenyang Computer Technology Research and Design Institute, Shenyang, China). The sampling frequency of 1.0 MHz AE signals was chosen; the preamplifier gain and threshold were set to 36.0 and 30.0 dB, respectively.

2.3. Test Scheme

As is known to all, the strain rate is an important factor affecting the mechanical properties of rock. The higher the strain rate, the higher the rock strength. If the loading rate is slow enough, creep failure occurs in the rock. If the strain rate is very high, the impact failure occurs in the rock. In this paper, only the mechanical properties of coal specimens under static loading–unloading conditions are studied.

To determine a reasonable cyclic loading–unloading path, the conventional uniaxial compression test was first conducted on three coal specimens. Before each test, a contact force of 0.2 kN was applied to the coal specimen. In the tests, the loading rate is 0.04 MPa/s. Their strengths are 4.74, 5.46, and 4.18 MPa, respectively. In the cyclic loading–unloading tests, the loading rate and unloading rate are set to 0.04 MPa/s, and the minimum stress of each loading–unloading cycle is designed as 3.0 MPa to simulate the static loads that are imposed on the in situ coal masses. The coal specimen is first linearly loaded from 0.0 to 3.0 MPa, and then the cyclic loading and unloading is carried out. The maximum stress of the first loading–unloading cycle is set to 3.5 MPa, and the maximum stress increment of each subsequent loading–unloading cycle is chosen as 0.5 MPa. Figure 1 shows the cyclic loading–unloading path.

3. Testing Results

3.1. Deformation and Elastic Modulus

3.1.1. Stress versus Strain Curves

Figure 2 shows the relation curves between axial, circumferential, and volumetric strains and axial stress of the No. 4 coal specimen subjected to cyclic loading and unloading. In Figure 2, the symbol “ε” represents the strain, and the “σ₁” represents the axial stress. From Figure 2, the three curves of the coal specimen in each loading–unloading cycle do not form the enclosed hysteresis loops. These show that there are many microcracks, microdefects, and holes inside the coal specimen. The coal specimen has a loose texture and poor resistance to deformation.

3.1.2. Relation between Strain and Loading–Unloading Cycle Number

Figure 3 shows the evolution characteristics of axial, circumferential, and volumetric strains of the No. 4 coal specimen as the cycle number increases. In Figure 3, the symbol “N” represents the loading–unloading cycle number, “ε₁” represents the axial strain, “ε₃” represents the circumferential strain, and “ε_v” represents the volumetric strain. Additionally, in Figure 3, the “cyclic initial axial strain” refers to the axial strain value at the beginning of a cycle, the “cyclic maximum axial strain” refers to the axial strain value at the maximum stress point of a cycle, and the definitions of circumferential and volumetric strains are the same as those of axial strain. From Figure 3, the axial strain is very well linear with the cycle number, and the circumferential and volumetric strains are approximately quadratic functions with the cycle number. The determination coefficient “R” of the axial strain versus cycle number fitting curve is higher than those of the circumferential and volumetric strains. So, under cyclic loading and unloading, the axial strain evolution of coal specimens can be better predicted. However, the change in circumferential strain with cycle number is more obvious and sensitive. Therefore, if the variation characteristics of axial and circumferential strains are considered together, it can improve the prediction reliability of coal specimen failure under cyclic loading and unloading.

3.1.3. Elastic Modulus

Figure 4 shows the relation curve between elastic modulus and cycle number of the No. 4 coal specimen in different loading stress intervals. Here, the elastic modulus refers to the secant modulus between the beginning point and some stress point in the cyclic loading phase. When the loading stress interval is between 3.0 and 3.5 MPa in the initial three loading–unloading cycles, the elastic modulus increases significantly with the cycle number; that is, the plastic strengthening effect occurs in coal specimens. However, the elastic modulus is basically stable in the subsequent loading–unloading cycles, indicating that the plastic strengthening effect is no longer obvious. When the loading stress interval is between 3.0 and 4.0 MPa in the initial three loading–unloading cycles, the elastic modulus increases gradually, and the plastic strengthening effect of the coal specimen is very significant. However, in the subsequent loading–unloading cycles, the elastic modulus keeps basically stable, and the plastic strengthening effect of the coal specimen is not obvious. When the loading stress interval is between 3.0 and 4.5 MPa in the initial two loading–unloading cycles, the elastic modulus increases, and the plastic strengthening effect of the coal specimen is very significant. However, in the subsequent loading–unloading cycles, the elastic modulus keeps basically stable, and the plastic strengthening effect is no longer obvious. When the loading stress interval is between 3.0 and 5.0 MPa in the initial two loading–unloading cycles, the elastic modulus increases, and the plastic strengthening effect is very significant. However, in the subsequent loading cycles, the elastic modulus keeps basically stable, and the plastic strengthening effect is no longer obvious. When the loading stress interval is between 3.0 to 5.5 MPa, although only two loading cycles are carried out, it can also be concluded that the plastic strengthening effect of the coal specimen is very significant after one loading–unloading cycle. The above results show that within the same loading–unloading stress interval, the elastic modulus first increases and then keeps basically stable as the loading–unloading cycle number increases; in addition, the higher the maximum stress of a loading–unloading cycle, the more significant the plastic strengthening effect produced by this cycle.

3.2. AE Characteristics

3.2.1. AE Ring Count

Figure 5 shows the results of the AE ring count of the No. 4 coal specimen. AE ring count presents the following evolution laws: As the axial stress was linearly loaded from 0.0 to 3.0 MPa, the coal specimen is in the compaction and elastic deformation phases, and there occur basically no new cracks, so the AE ring count is very low. In the initial two loading–unloading cycles, a small number of new cracks began to appear in the coal specimen, but the AE ring count is still low. In the subsequent loading–unloading cycles, with the continuous improvement of cyclic loading and unloading maximum stress, the coal specimen falls into the crack propagation and penetration phases. The AE ring count keeps increasing and goes up to a maximum value at coal specimen failure. However, it should be noted that during the 1505–1506 s, the maximum value of the AE ring count is greater than that of the next cycle but less than that of coal specimen failure. This shows that a small-scale local failure emerged in the coal specimen at that time, and the internal structure of the coal specimen quickly reached a new stable state after readjustment. In addition, before the failure cycle of the coal specimen, the AE ring count is very high in the loading phase of each cycle but very small in the unloading phase of each cycle. This shows that when the loading and unloading do not cause the failure of the coal specimen, the AE activities mainly occur in the loading phase, and there exist basically no AE activities in the unloading phase. More importantly, it is worth noting that except for the failure cycle, the maximum AE ring count of other cycles appears before the maximum stress of the loading phase.

3.2.2. AE Energy Count

Figure 6 shows the results of the AE energy count of the No. 4 coal specimen. The evolution characteristics of AE energy count are the same as that of AE ring count; just in the unloading phase, the AE energy count is very lower and close to 0. Further, the evolution laws of cumulative ring count are different from the cumulative energy count. The cumulative AE ring count basically increases linearly. The cumulative AE energy count increases in the loading phase of each cycle and keeps stable in the unloading phase of each cycle; it presents a stepped increase with the cycle number.

3.2.3. AE Hit Count

Figure 7 shows the results of the AE hit count of the No. 4 coal specimen. The AE hit count of the coal specimen presents the following evolution laws: In the linear loading phase and the initial two loading–unloading cycles, the AE hit count is very low. This shows that the coal specimen is mainly compacted, and there occur almost no new cracks. From the third loading–unloading cycle on, the AE hit count began to increase with the improvement of cyclic loading–unloading maximum stress. It shows that the cracks in the coal specimen begin to initiate, expand, and penetrate. When the coal specimen failed, the AE hit count reached the maximum. However, it should be noted that during the 1505–1506 s, the maximum value of the AE hit count is greater than that of the next cycle but less than that of the coal specimen failure. This shows that a small-scale local failure emerged in the coal specimen at that time, and the internal structure of the coal specimen quickly reached a new stable state after readjustment. In addition, before the coal specimen failure, the AE hit count is very high in the loading phase of each cycle but very small in the unloading phase of each cycle. This shows that when the loading and unloading do not cause the failure of the coal specimen, the AE activities mainly occur in the loading phase, and there exist basically no AE activities in the unloading phase.

The above results show that the evolution law of cumulative AE hit count is the same as the cumulative AE energy count, also increasing in a stepped shape with the cycle number. That is, the cumulative AE hit count increases in the cyclic loading phase and keeps stable in the cyclic unloading phase.

AE hit count reflects the crack propagation rate and can better indicate the active degree of the AE phenomenon. In a loading–unloading cycle, it is inaccurate to use the maximum hit count to reflect the AE activities because the maximum hit count only reflects the AE active degree and crack growth rate at a certain time point. The AE active degree of loading–unloading cycle should be characterized by the cumulative AE hit count in this cycle. Figure 8 shows the cumulative AE hit count of different cycles in loading, unloading, and the whole loading–unloading phases.

From Figure 8, both the cumulative AE hit count, and the AE hit count in the cyclic loading phase increase gradually with the cycle number. However, the AE hit count in the cyclic unloading phase basically keeps stable except for the failure cycle.

To investigate the loading history effect on AE activities, the cumulative AE hit count at several key stress points in different loading–unloading cycles is recorded and analyzed, as shown in

Table 2. The cumulative AE hit count of coal specimens at key stress points in different loading–unloading cycles.

Cycle Number	Cumulative AE Hit Count in Several Key Stress Points
	3.5 MPa	4.0 MPa	4.5 MPa	5.0 MPa	5.5 MPa	5.826 MPa
1	104	—	—	—	—	—
2	9	164	—	—	—	—
3	2	49	423	—	—	—
4	0	0	267	774	—	—
5	0	0	1	35	785	—
6	0	0	0	2	27	1277

. From Table 2, in the cyclic loading phases with the equivalent stress amplitude, the AE activities of the coal specimen decrease gradually with the loading–unloading cycle number.

3.2.4. AE Kaiser Effect

Many studies have shown that rock AE activities have the Kaiser and Felicity effects under cyclic loading and unloading. When the Felicity ratio is less than 1, there exists the Felicity effect; in contrast, if the Kaiser effect occurs, then the Felicity ratio is greater than 1. The Felicity ratio is calculated as follows:

$$F_r=\frac{P_{\mathrm{AE}}}{P_{\max }}$$

(1)

where P_AE is the initial stress at which the specimen exhibits active AE activities during repeated loading and unloading; P_max is the maximum stress applied to the specimen before a certain loading–unloading cycle.

In this paper, the cumulative AE hit count of the prior loading–unloading cycle is taken as the criterion of “significant increase” in the Kaiser effect of this cycle.

Table 3. The Kaiser effect point and the corresponding Felicity ratio.

Cycle Number	1	2	3	4	5	6
Cyclic loading maximum stress/MPa	3.5	4	4.5	5	5.5	5.826
Kaiser point/MPa	—	3.886	4.166	4.708	5.501	5.819
Fr	—	1.110	1.042	1.046	1.100	1.058

and Figure 9 list the Kaiser effect points and the corresponding Felicity ratio.

From Figure 9, in the whole cyclic loading–unloading process, the Felicity ratios are all greater than 1, indicating that the coal specimen has the obvious Kaiser effect. However, the Felicity ratio fluctuates irregularly.

3.3. Damage Evolution Characteristics

Damage reflects the deterioration degree of specimen mechanical properties under different loadings [22]. The elastic modulus, residual strain, dissipated energy, ultrasonic velocity, and cumulative AE counting can all be defined as damage variables for quantification calculation. The disadvantage of the elastic modulus method is that it can not determine the initial elastic modulus of the specimen. The residual strain method and the dissipated energy method can only calculate the damage according to the cycle number, thus resulting in the discontinuity of the damage process. The disadvantage of the ultrasonic velocity method is that the damage increases in fluctuation in the process of cyclic loading and unloading, which is inconsistent with the fact that the damage has been increasing. Instead, the cumulative AE counting method does not have the above defects. So, this method is adopted for damage calculation. The calculation equations are as follows:

$$D_1=\frac{N_{1i}}{N_{1E}}$$

(2)

where D₁ is the damage calculated by the AE ring counting method, N_1i is the cumulative AE ring count at some time point, and N_1E is the cumulative AE ring count at failure.

$$D_2=\frac{N_{2i}}{N_{2E}}$$

(3)

where D₂ is the damage calculated by the AE hit counting method, N_2i is the cumulative AE hit count at some time point, and N_2E is the cumulative AE hit count at failure.

The damage evolution curves are shown in Figure 10. The damage calculated by the cumulative AE ring count basically increases according to the linear law, which can not reflect the fact that the damage is basically unchanged in the unloading phase. Instead, the damage calculated by the cumulative AE hit count can better represent the fact that the damage has been increasing in the loading phase and kept basically unchanged in the unloading phase. Therefore, the AE hit count as a damage variable can better describe the damage development of coal specimens subjected to cyclic loading and unloading.

3.4. AE b Value

3.4.1. Calculation of AE b Value

The b value originates from seismology. By analyzing the global seismicity, the relation between seismic magnitude and the number is obtained as follows [16]:

$$\lg N=a-bM$$

(4)

where M is the seismic magnitude, N is the number of seisms with a magnitude greater than or equal to M, and a and b are constants.

In the lab test, the AE activity is similar to seismicity. However, they are different in the expression of magnitude. The transformation relation between them is as follows:

$$M_L=\frac{M_s}{20}$$

(5)

where M_s is the AE amplitude, and M_L is the equivalent seism magnitude.

So, in the lab AE test, the following equation is established.

$$\lg N=a-b{M}_L$$

(6)

In this paper, the AE amplitude in the loading–unloading process of each cycle is firstly converted to the equivalent seism magnitude by Equation (5). Secondly, these data are calculated and analyzed at the interval of 0.05 dB to acquire the equivalent seism frequency. In the end, the AE b value in the loading–unloading process of each cycle is obtained by Equation (6).

3.4.2. Evolution of AE b Value

The relation curve between the AE b value and the loading–unloading cycle number is shown in Figure 11. In the initial three cycles, the AE b value increases continuously, indicating that the AE activities in this phase mainly come from the compaction and closure of primary fractures and the initiation of microcracks in the coal specimen. The released energy by AE activities is very low, and the amplitude is very small. The maximum stress of the fourth loading–unloading cycle accounts for 85.76% of coal specimen peak strength. Under this loading–unloading cycle, the microcracks in the coal specimen further initiate, nucleate and expand, and the size of new cracks, the released energy by the AE activities, and the AE amplitude are all very larger, but the AE b value is reduced. The maximum stress of the fifth loading–unloading cycle accounts for 94.34% of coal specimen peak strength. Under this loading–unloading cycle, the AE b value increases because the coal specimen produced plastic strengthening under the fourth loading–unloading cycle. However, it should be noted that if the loading–unloading process is repeated many times according to the stress level of the fifth loading–unloading cycle, the effect of plastic strengthening will gradually decrease and even turn into plastic softening. In the sixth loading–unloading cycle, the abundant microcracks in the coal specimen began to penetrate and form the macrocracks. The released energy by AE activities was very high, and the amplitude was also large. The coal specimen finally failed, and the AE b value decreased rapidly.

The above analysis shows that the AE b value fluctuates as the loading–unloading cycle number, and its significant fluctuation can be used as the precursor of coal specimen failure. In addition, the AE b value decreases rapidly at coal specimen failure.

3.4.3. Prediction of AE Maximum Magnitude

Assuming that the AE equivalent magnitude meets the past law, by taking the parameter “N” as 1 in Equation (5), the “maximum magnitude” at coal specimen failure can be predicted according to the following equation:

$$M_{\max }=\frac{a}{b}$$

(7)

where M_max is the predicted “maximum magnitude” at the coal specimen failure.

Figure 12 shows the predicted “maximum magnitude” at coal specimen failure. According to the test results, the equivalent magnitude of coal specimen failure in the sixth loading–unloading cycle is 3.35 dB. From Figure 12, the “maximum magnitude” predicted by the fifth loading–unloading cycle is 3.30 dB, which is the closest to the real magnitude of coal specimen failure. So, the closer to the loading–unloading cycle of coal specimen failure, the more accurate the predicted “maximum magnitude” at coal specimen failure.

4. Conclusions

At present, limited research findings on the low-strength coal specimen subjected to cyclic loading and unloading exist because this type of specimen is difficult to process according to the test standard. In this paper, this topic is studied. The main innovative achievements are as follows:

(1)

The axial strain is very well linear with the loading–unloading cycle number, and the circumferential and volumetric strains are approximately quadratic functions with the loading–unloading cycle number;

(2)

Under the same loading stress interval, the elastic modulus firstly increases and then keeps basically stable with the loading–unloading cycle number. In addition, the higher the maximum stress of a loading–unloading cycle, the more significant the plastic strengthening effect produced by this cycle;

(3)

The damage calculated by the cumulative AE hit count can better reflect the fact that the damage has been increasing in the loading phase and keeps basically unchanged in the unloading phase. So, the AE hit count as a damage variable can better describe the damage development of coal specimens;

(4)

The significant fluctuation of the AE b value can be used as the precursor of coal specimen failure. In addition, it decreases rapidly at coal specimen failure;

(5)

The closer to the loading–unloading cycle of coal specimen failure, the more accurate the predicted “maximum magnitude” at coal specimen failure.