Mechanical Behaviors and Acoustic Emission Fractal Characteristics of Bump-Prone Coal under Different Loading Rates

Abstract

Coal and rock dynamic disasters occur frequently in deep coal mining. The loading rate affects the mechanical properties and behaviors. Uniaxial compression acoustic emission (AE) tests of bump-prone coal under various loading rates were carried out, and the mechanical properties, AE spatiotemporal evolution, and spatial fractal characteristics were analyzed. The experimental results indicate that the uniaxial compressive strength is positively related to the loading rate, and the elastic modulus increases before decreasing with the loading rate. The failure strain is positively related to the loading rate, and the percentage of the compaction phase relative to the pre-peak phase decreases with the loading rate. The hit rate, absolute energy, AE events, and amplitude evolution of coal samples under various loading rates are the same, and the maximum of AE absolute energy and hit rate is positively related to the loading rate. The spatial evolution of AE events of coal samples under various loading rates is the same, showing a “slow increase → slow increase → fast increase → rapid increase → slow increase” trend. The spatial fractal dimension ranges from 2.1 to 2.9, and the evolution of coal samples under various loading rates is the same, exhibiting a downward trend.

1. Introduction

Coal mine dynamic disasters, such as coal bumps and gas outbursts, occur increasingly frequently with increasing coal mining depth [1,2,3,4,5]. In particular, the stability and safety of coal pillars are of significance for safe and efficient mining. There is an urgent need to study the mechanical properties and behaviors of deep coal and rock. Their mechanical properties and behaviors are highly relevant to the loading rate [6,7,8,9]. Therefore, the mechanical properties and behaviors of coal with various loading rates are of importance in evaluating the stability and safety of coal pillars.

The mechanical properties and behaviors of rock materials are affected by the external loading rate, and many scholars have investigated the effect of the loading rate on the mechanical properties and behaviors of rock materials. Wu et al. [10] reported the mechanical responses of rock with various loading rates. The shear properties and behaviors of rock under cyclic loading conditions with various shear rates were investigated in [11]. Gong and Zhao [12] analyzed the mechanical properties and behaviors of sandstone under dynamic indirect tensile conditions with different loading rates. The combined effects of grain size and strain rate on the mechanical behaviors of sandstones were reported in [13]. Li et al. [9] studied the effect of the loading rate on the bursting characteristics of coal under uniaxial compression. Liu et al. [14] investigated the strength and mechanical behaviors of coal and rock under various strain rates. Cao et al. [8] reported on the damage evolution and AE characteristics under various loading rates. Hou et al. [15] analyzed the effect of loading rate on the mechanical properties and behavior of shale. Zou and Li [16] analyzed the failure modes of Carrara marble under various loading rates using numerical and experimental methods.

Acoustic emission (AE) signals are generated during the deformation and failure process of rock materials and are widely used to characterize the damage patterns in geotechnical engineering. Noam et al. [17] discussed the correlations between AE and stress drops under external load. Li et al. [18] investigated the mechanical properties and AE evolution of fractured coal during uniaxial compressive tests. Tan et al. [19] obtained the multifractal pattern for the AE energy dissipation of shale during uniaxial compression. Lou et al. [20] discussed the relations between AE and stress drops under external loads. Deng et al. [21] studied the AE fractal characteristics of flawed sandstone during uniaxial compression. Liu et al. [2] obtained the AE characteristics of weakly cemented sandstone collected from various buried depths in uniaxial compressive tests. Ge et al. [22] analyzed the AE evolution of gabbro after microwave heating. Zha et al. [23] obtained the mechanical and AE pattern of deep marble under creep conditions. Dou et al. [24] studied the mechanical behaviors and AE evolution of fractured sandstone. Zhao et al. [25] investigated the deformation field and AE evolution of weakly cemented rocks in an indirect tensile test. Zhao et al. [26,27] analyzed the strength, fracture patterns, and failure mechanism of bedding coal under mode I and II loading conditions based on the DIC and AE methods.

The effect of loading rate on the strength and mechanical behaviors of rock has been investigated in previous studies, and the AE temporal characteristics of coal and rock materials have been reported. However, the effect of loading rate on the AE spatial characteristics of bump-prone coal has been ignored. In this paper, uniaxial compression tests of bump-prone coal with various loading rates were carried out, and the AE signals were obtained synchronously. The mechanical properties and the AE temporal and spatial characteristics of coal under various loading rates were analyzed, and the AE spatial fractal characteristics were discussed. The results provide a basis for the mechanism and prevention of deep dynamic disasters.

2. Materials and Methods

2.1. Specimen Preparation

Coal blocks were collected from the 3⁻¹ coal seam of Hongqinghe Coal Mine in southern Inner Mongolia Autonomous Region, China (Figure 1). The coal blocks were drilled, cut, and polished into cylindrical samples with a diameter of 50 mm and a height of 100 mm in a processing laboratory. According to previous research, coal is non-caking and is strongly bump-prone [28]. The test was divided into 4 groups, with 3 coal samples in each group. The physical properties of the samples are shown in

Table 1. Physical properties of coal samples.

Sample No.	Diameter (mm)	Height (mm)	Density (g/cm3)	Loading Rate (mm/min)
U1	49.50	100.40	1.25	0.20
U2	49.65	100.30	1.26
U3	49.60	100.65	1.23
U4	49.60	100.42	1.23	0.60
U5	49.50	100.40	1.31
U6	49.50	100.36	1.27
U7	49.41	100.30	1.26	1.00
U8	49.63	100.50	1.26
U9	49.52	100.60	1.24
U10	49.60	100.41	1.26	3.00
U11	49.73	99.88	1.27
U12	49.43	100.15	1.24

.

2.2. Experimental System

As shown in Figure 2, a materials testing machine, a multichannel AE instrument, and a multichannel strain acquisition instrument were used to monitor the mechanical behaviors and AE signals during the test. The load capacity of the material testing machine ranges from 0.005 to 300 kN, and the maximum loading rate is 254 mm/min. The maximum sampling frequency of the strain acquisition instrument is 1 MHz. The multichannel AE instrument is equipped with eight Nano 30 sensors and amplifiers.

2.3. Experimental Procedure

Before the test, the three monitoring systems of the test were wired for debugging, the system time of each monitoring system was adjusted to be consistent, and the three systems were started simultaneously. To monitor the internal damage and failure of the sample, a total of 6 AE sensors were selected for three-dimensional location. As shown in Figure 2, the AE sensors were laid on two planes 15 mm away from the end face, and Vaseline was used for coupling between the sensor and the sample. Vaseline was also used for coupling between the specimen and the load platen to reduce the friction and the end effect. A lead-breaking test was carried out before the main test to ensure sufficient contact of each channel and that sufficient effective data could be obtained. Strain gauges were attached to the middle of the back of the coal sample (Figure 2). Displacement-controlled loading was adopted; the loading rate of coal samples in each group was set to 0.2 mm/min, 0.6 mm/min, 1.0 mm/min, and 3.0 mm/min; and the corresponding strain rates were 3.34 × 10⁻⁵, 1.00 × 10⁻⁴, 1.67 × 10⁻⁴, and 5.00 × 10⁻⁴ s⁻¹, respectively. After the coal sample failed, the test data were stored and analyzed.

3. Results and Discussions

3.1. Mechanical Properties

According to the calculation formula of uniaxial compressive strength (UCS), the results are shown in

Table 2. Mechanical properties of coal samples.

Sample No.	Density (g/cm3)	Loading Rate (mm/min)	UCS (MPa)	Mean (MPa)	Elastic Modulus (GPa)	Mean (GPa)
U1	1.25	0.20	24.19	24.65	1.86	1.81
U2	1.26		21.07		1.81
U3	1.23		28.69		1.78
U4	1.23	0.60	26.21	26.48	1.75	1.89
U5	1.31		25.28		1.84
U6	1.27		27.95		2.09
U7	1.26	1.00	22.30	27.10	1.62	1.78
U8	1.26		29.64		1.93
U9	1.24		29.36		1.80
U10	1.26	3.00	35.73	30.04	1.85	1.76
U11	1.27		27.51		1.76
U12	1.24		29.88		1.65

. The minimum UCS is 24.65 MPa when the loading rate is 0.2 mm/min, and the maximum UCS is 30.04 MPa at 3.0 mm/min, which is 1.22 times that under 0.2 mm/min. On the whole, the UCS of coal samples increases with increased loading rate and is positively related to the loading rate, which is in agreement with previous research results [9,10,12,29]. Generally, the correlations between the UCS and loading rate can be described by linear, exponential, logarithmic, and power functions. Figure 3 shows that the correlations between the UCS and loading rate can be expressed by the above functions, among which the fitting degree is highest for the logarithmic function and lowest for linear functions. It should be pointed out that the UCS of the coal samples is relatively discrete as a result of the complexity and heterogeneity of the coal structure.

Elastic modulus is defined as the slope of the line in the stress–strain curve of the elastic phase; the elastic modulus results are listed in Table 2. As shown in Figure 4, the maximum mean elastic modulus is 1.89 GPa when the loading rate is 0.6 mm/min, and the minimum elastic modulus is 1.76 GPa at 3.0 mm/min, which is 93.12% that under 0.6 mm/min. As a whole, the elastic modulus of the coal sample increases before decreasing with increased loading rate, which is consistent with the previously reported research results [14]. It should be pointed out that the elastic modulus of some coal samples shows large dispersion due to the complexity and heterogeneity of the coal structure.

As shown in Table 1 and Table 2, the physical and mechanical properties are similar for each group, and the deformation behaviors of each group are consistent. Only one representative specimen was selected for each loading rate for analysis due to the large number of coal specimens. Figure 5 shows the stress–strain curves of representative coal samples under various loading rates; the deformation and failure patterns of coal samples under various loading rates are coincident. During the initial loading phase, the curve is concave, with compaction and closing of internal fissures and pores during the compaction phase, showing obvious nonlinear characteristics. With increased load, the stress–strain curve becomes nearly linear, with a few microcracks during the linear elastic phase. As the load continues to increase, the curve deviates from the straight line, becoming convex, with a large number of internal microcracks initiated and few microcracks coalescing during the yield phase. When the load approaches the peak value, it drops suddenly with microcrack coalescence and macrocrack initiation, and the sample bursts.

However, the percentage of the compaction phase relative to the pre-peak phase gradually decreases with increased loading rate. This phenomenon indicates that the input energy rate of coal samples increases with the loading rate, and the closing rate of internal fissures and pores increases, leading to the shortening of the compaction phase. There are great distinctions in the failure strain of coal samples under various loading rates. The maximum failure strain is 0.0275 when the loading rate is 3.0 mm/min, and the minimum failure strain is 0.020 at 0.2 mm/min, which is approximately 72.73% of that under 3.0 mm/min. Thus, the failure strain of the coal sample is positively related to the loading rate. However, the failure strain of some coal samples is dispersive due to the complexity and heterogeneity of the inner coal structure.

3.2. AE Temporal Characteristics

AE signals are produced during the deformation and failure process of rock materials, which can be used to quantitatively investigate the deformation and failure characteristics [6,28,30]. In this section, the AE temporal characteristics of coal samples under various loading rates are investigated.

Figure 6 shows the evolution characteristics of stress, the AE hit rate, and the AE absolute energy of coal samples under various loading rates. The AE hit rate and absolute energy evolution of coal samples under various loading rates are coincident and can be divided into five phases. The primary defects, such as pores and fissures within the coal sample, are compacted and closed under external load during the crack compaction phase, only a small amount of AE signals is detected, and the absolute energy increases slowly with a low hit rate. With increased load, a small number of microcracks is detected during the crack initiation phase, with a small amount of AE signals. The AE absolute energy increases slowly, and the AE hit rate is low. As the load continues to increase, internal microcracks are rapidly generated during the stable crack growth phase with large numbers of AE signals, the absolute energy increases rapidly, and the hit rate is high. Then, large numbers of AE signals are detected during the unstable crack growth phase, with a large number of internal microcracks, a rapid increase in AE absolute energy, and a rapid increase in the hit rate. When the load exceeds the peak value, a small number of AE signals is detected, the AE absolute energy increases slowly, and the AE hit rate decreases slightly during the post-peak failure phase as a result of some AE sensors falling off.

However, there are some distinctions in the maximum AE hit rate of coal samples under various loading rates. The maximum AE hit rate is 5773 when the loading rate is 3.0 mm/min, whereas the maximum hit rate is only 1267 at 0.2 mm/min, which is approximately 21.95% of that at 3.0 mm/min. Thus, there are positive correlations between the maximum AE hit rates with the loading rate on the whole. Furthermore, there are some distinctions in AE absolute energy under various loading rates. The AE absolute energy is 11.40 × 10⁹ aJ when the loading rate is 3.0 mm/min and 2.73 × 10⁹ aJ at 0.2 mm/min, which is approximately 23.95% of that at 3.0 mm/min. Thus, the AE absolute energy of the coal sample is positively correlated with the loading rate. This phenomenon indicates that the higher the loading rate, the faster the input energy rate and that the faster the energy storage rate, the more severe the damage and the more energy released.

Figure 7 shows the evolution of stress, AE events, and amplitudes of coal samples under various loading rates over time. The AE events and amplitudes of coal samples at various loading rates are consistent. During the initial phase of loading, only a few AE events are detected, mainly due to the primary pores and fissures inner the coal sample being closed and compacted under external load, and the amplitude is concentrated at 40–80 dB. Then, many AE events occur with an amplitude of 40–100 dB during the crack initiation phase. During the stable crack growth phase, large numbers of AE events are detected, with the amplitude ranging from 40 dB to 100 dB. AE events are generated quickly, and the range of amplitude is 40–100 dB during the unstable crack growth phase. Only a few AE events are detected in the post-peak failure phase, and the corresponding amplitudes are distributed in the range of 40–100 dB.

However, there are some distinctions in the distribution of AE amplitude. AE events with high amplitude (>90 dB) only occur during the crack initiation phase at a loading rate of 0.2 mm/min, whereas they occur during the crack initiation phase, the stable crack growth phase, and the unstable crack growth phase at 0.6 mm/min. AE events with high amplitude occur during the crack initiation phase, stable crack growth phase, and non-stable crack growth phase at 1.0 mm/min, whereas they only occur during the stable crack growth stage at 3.0 mm/min.

3.3. AE Spatial Characteristics

The spatial evolution of AE events reflects the crack initiation, propagation, and coalescence progress within the sample [31]. The AE event sources reflect the occurrence location of internal microcracks. To obtain the occurrence location of microcracks inside the sample, AE sensors were attached to the sample surface according to a certain geometric relationship; then, AE event sources were determined based on the signal parameters monitored by different AE sensors, in combination with a positioning algorithm. The Simplex location algorithm and Geiger location algorithm are the two most commonly used time difference location algorithms. The principle of these algorithms is to retrieve the AE event source by collecting the arrival time difference of P-wave from AE sensors at different locations. The Geiger location algorithm applies to AE (microseismic) and seismic events in small areas.

AE event sources were obtained according to the Geiger location algorithm. Figure 8, Figure 9, Figure 10, Figure 11 show that the spatial evolution of AE events of coal samples under various loading rates is consistent. During the initial phase of loading, only a small number of AE events is detected in the middle of the coal sample, and the amplitude is concentrated in the range of 40–80 dB. With increased load, many AE events are generated in the middle of the coal sample during the crack initiation phase, and the amplitude is concentrated in the range of 40–100 dB. Then, it enters the stable crack growth phase, and large numbers of AE events are detected in the middle of the coal sample, with the amplitude concentrated in the range of 40–100 dB. AE events continue to occur rapidly in the middle of the coal sample during the unstable crack growth phase, and the amplitude is concentrated in the range of 40–100 dB. Finally, only a few AE events are detected in the post-peak failure phase, with some AE sensors falling off and receiving fewer AE signals. AE events mainly occur in the middle of the coal sample during the whole loading process, with fewer at both ends, showing that the failure of the coal sample is concentrated in the middle of the sample.

3.4. Column-Covering Fractal Model of AE Events

Fractal theory has been widely adopted in many research fields, such as civil engineering, material science, and computer science [31,32,33]. Many studies have shown that the AE sequences generated during the damage process of rock materials have certain fractal characteristics both in time and space [34,35,36,37]. Common methods used to determine the spatial fractal dimension of AE events are the spherical covering method, the column-covering method, and the projected-circle covering method. The column-covering method is more accurate for cylindrical specimens.

The principle of the column-covering method is as follows. Assuming that the location of AE events meets the volume distribution, one cylinder with radius r and height h is used for coverage (Figure 12). The correlation between the counts of AE events (M_(r)) contained in the cylinder with the radius (r) and height (h) is as follows:

$$M_{(r)}={\mathrm{C}}_1{r}^{2}h$$

(1)

Because the height–radius ratio of the sample is a constant C₂, Equation (1) can be expressed as:

$$M_{(r)}={\mathrm{C}}_1{\mathrm{C}}_2{r}^3$$

(2)

The correlation between the counts of AE events (M_(r)) and the radius (r) based on basic fractal theory can be expressed as:

$$M_{(r)}\propto \mathrm{C}{r}^D$$

(3)

where C is a material constant.

Therefore, the AE spatial fractal dimension (D) based on the column-covering method can be expressed as:

$$\log M_{(r)}=\log \mathrm{C}+\mathrm{Dlog} r$$

(4)

For any radius (r_i), M_(r) can be obtained. Multiple points (log r, M_(r)) are drawn in a double logarithmic coordinate system; then, the least-square method is used to linearly fit these points. The slope of the corresponding fitting line is the AE spatial fractal dimension (D) (Figure 12).

3.5. Spatial Fractal Characteristics

According to the above basic principles, the AE spatial fractal dimension values of different stress levels of coal samples under various loading rates were calculated. Figure 13 shows that the evolution characteristics of spatial fractal dimension of coal samples under various loading rates are consistent, with an overall downward trend. The fractal dimension during the crack compaction phase (0–0.2 σ_c (peak stress)) is high, mainly concentrated in the range of 2.7–2.9, indicating that the distribution of primary fractures in the coal sample is uniform, and the AE events are uniformly distributed. With increased load (0.2–0.8 σ_c), the fractal dimension decreases slowly, mainly due to the initiation and propagation of microcracks during this stage, leading to the slow clustering of AE events. Near the peak load (0.8–1.0 σ_c), a large number of microcrack propagations and coalescences forms a macrofracture surface, and the fractal dimension decreases rapidly to the minimum value, which is distributed in the range of 2.1–2.3. These results are consistent with those obtained by Pei et al. [38] in granite experiments.

However, there exist some differences in fractal dimension evolution at various loading rates. When the loading rate is 0.6 mm/min, the fractal dimension is stable during the initial loading phase and decreases rapidly when the fractal dimension is close to 0.8 σ_c. At a loading rate of 0.2 mm/min, the fractal dimension cannot be calculated due a lack of AE events during the compaction stage. Due to the high anisotropy of coal samples, there are large distinctions in the primary fractures and pores within the coal samples, leading to large differences in the count and spatial evolution of AE events during the compaction phase, so the corresponding AE fractal dimensions differ.

4. Conclusions

In this study, the mechanical properties, AE spatiotemporal evolution, and spatial fractal characteristics of coal samples were analyzed in a uniaxial compression test with various loading rates. The main conclusions are as follows.

(1)

The UCS is positively related to the loading rate, and the elastic modulus increases before decreasing with the loading rate. The failure strain is positively related to the loading rate, and the percentage of the compaction phase relative to the pre-peak phase decreases with the loading rate.

(2)

The hit rate, absolute energy, AE events, and amplitude evolution of coal samples under various loading rates are consistent. The maximum hit rate and absolute energy of coal samples are positively related to the loading rate, and there are some differences in the distribution of AE amplitude.

(3)

The spatial evolution of AE events of coal samples under various loading rates is consistent, showing a “slow increase → slow increase → fast increase → rapid increase → slow increase” trend. AE events mainly occur in the middle of the coal sample during the whole loading process, with fewer events at both ends.

(4)

The AE spatial fractal dimension ranges from 2.1 to 2.9, and the evolution of coal samples with various loading rates is consistent, showing a downward trend. There exist some differences in fractal dimension evolution at various loading rates.