Developing a New Bursting Liability Index Based on Energy Evolution for Coal under Different Loading Rates

Abstract

The risk of a coal burst rises with the excavation depth and other mining-related activities. These devastating coal burst activities are a major concern during deep coal mining. During such activities, the loading rate is a major cause of damage. Different indexes, including the elastic strain modulus index (W_et), bursting energy index (K_e), dynamic failure time index (D_T), and compressive strength index (R_c), are used for coal bursting intensity; however, the loading rate and damage factors are not included in these indexes. In this study, a new coal bursting liability index called the elastic modulus damage index (EMDI) was developed using rock damage variables and the elastic strain modulus index, and is based on energy evolution characteristics under different loading rates. The results of this new index were compared with the existing indexes, and their range was proposed to evaluate coal bursting liability. The EDMI shows a positive polynomial second order degree relationship with W_et and K_e, having a determination factor of 0.99, while D_T shows a negative polynomial second order degree relationship with a determination factor of 0.94. The EDMI and R_c show a positive power relationship having a determination factor of 0.99. The relationships with other indexes revealed that the EDMI can be effectively used in evaluating the coal bursting liabilities in different stress environments.

1. Introduction

China is one of the leading countries globally both in the production and consumption of coal. According to statistics (for 2016), China produces and consumes approx. 3.41 and 2.70 billion tons of coal, respectively [1,2,3]. To fulfil this demand, mining has been switched to deep underground excavations in the country due to the depletion of shallow reserves [4,5,6,7,8]. These deep underground excavations cause different kinds of accidents, and coal burst type hazards are a major issue that not only threatens production and economic losses but also leads to injuries and even casualties [5,9,10,11,12,13].

To tackle this devastating and frequently occurring coal burst issue, research has been conducted to formulate effective measures for accident prevention and control [14,15,16]. However, the number of accidents in 2016 caused by coal bursts in China was almost 5.5 times that of 1985. This increase in the number of accidents is due to many factors, and an increase in coal mining depth is one of the major concerns. The chances of rock burst are increasing with excavation depth. With depth, the evolution of energy and mining-induced stresses has a substantial role in rock damage. In this process, the redistributed stresses due to excavation change the elastic and dissipated energies within the rocks [1,3,17,18,19,20,21,22,23,24,25,26,27,28,29]. When the elastic energy reaches the storage capability of rocks (coal), the rock burst (coal burst) occurs. The rock/coal burst intensity increases with depth due to the accumulation of high elastic strain energy and stresses within the rocks [30,31]. With mining depth, the coal stratum experiences different stress conditions (loading/stress rates) [32,33,34]. To capture the coal/rock burst phenomenon, research has been conducted in the last couple of decades.

The assessment of coal burst intensity, based on the measurement of stress-strain curve behaviors under loading, was extensively studied, and different indexes were defined. These indexes include the energy release rate index (ERRI) [35], burst energy index (K_e) [36], and burst energy release index (BERI) [37]. The aforementioned indexes are based on strain energy theory. Weng et al. [38] thoroughly investigated coal under loading. They studied the strain energy storage and released process and proposed a strain energy density index for coal bursts. Beck and Brady [39] and Jiang et al. [40] have investigated in detail the effects of energy evolution from pre to peak stage. They determined the energy release rate, called local energy release rate (LERR), by finding the differences between strain energies at the pre- and post-stage of brittle failure. Xu et al. [41] proposed a coal bursting liability index during coal failure, considering the LERR and limit energy storage rate (LESR) as a ratio. Lu et al. conducted research on coal samples under loading and proposed an elastic strain energy release rate (EESERR) index. This index is based on the energy evolution process during coal failure to assess coal bursting liability. Dai et al. [42] introduce a new index for coal burst (elastic modulus index (K_λ)), which is based on the stress-strain curve in uniaxial loading. K_λ is defined as the ratio of softening modulus (λ) after and elastic modulus (E) before peak stress in a coal stress-strain curve. The study revealed that the greater the softening modulus, the greater will be the intensity of a coal burst. Zhou et al. [43] thoroughly investigated the conversion of energy and rock damage under a dynamic uniaxial compression test. They suggested a rock damage equation considering the energy dissipation theory and also proposed a correlation between rock material damage and strain energy. The above indexes consider either energy liability or elastic modulus for the coal/rock burst intensity prediction. Based on the aforementioned indexes, the energy conversion and evaluation of rock damage in the failure process under different loading rates need further study to include both energy liability and elastic modulus and to fully understand the damage caused in rock under such conditions.

In this study, a new coal bursting liability index, called the elastic modulus damage index (EMDI), was developed under different loading rates based on energy evolution characteristics. The EMDI is based on the rock damage variable and elastic strain modulus index. The study not only proposes an effective coal bursting liability index but also presents a comprehensive understanding of the mechanism of coal bursts based on the evolution of energy under different loading rates.

2. Materials and Methods

2.1. Sample Preparation

In this research study, the coal samples were collected from a Lin Zhida coal mine situated in Shanxi Province, China (Figure 1a). The rectangular-shaped specimens with dimensions of 50 mm × 50 mm × 100 mm were prepared (Figure 1b) and subjected to uniaxial loading with different loading rates. The coal samples were prepared from the same coal block to maintain the uniformity and geometric integrity. The coal samples were kept/stored in a room at constant temperature for 30 days before testing, to avoid the effects of moisture content, humidity, and temperature. During storage, the samples were covered with a plastic coating. In order to avoid end non-parallelism, both the ends and sides of the coal specimens were carefully polished. Based on loading rates i.e., 0.1, 0.4, 0.7 and 1.0 mm/min, coal samples were categorized into four groups (each group contained four specimens) for clear understanding and processing.

2.2. Experimental Instrument

The c64.106 electro-hydraulic servo-controlled compressive testing machine with 1000 kN loading capacity was used for the experiment. A schematic diagram of the experimental work is shown in Figure 2. Before the compression process on the coal, the samples were covered by a plastic film on the upper and lower end to reduce and minimize the conduction of heat.

3. Strain Energy

In a closed system, the coal deforms under the action of an external load due to work performed on the coal under the action of external force. This phenomenon is based on the principle of the first law of thermodynamics, as defined in Equation (1).

$$\mathrm{W}=\mathrm{U}={\mathrm{U}}^{\mathrm{d}}+{\mathrm{U}}^{\mathrm{e}}$$

(1)

where W is the overall work performed by the external load, and U, U^d and U^e are the total strain, dissipated strain, and elastic strain energy in the stress-strain curve, respectively.

The total work and total strain energy (U) are terms that refer to the region under the stress-strain curve. The region is divided into two parts: U^d and U^e. In a uniaxial load, U^e is the releasable elastic strain energy and is defined in Equation (2) [44].

$${\mathrm{U}}^{\mathrm{e}}=\frac{{\mathsf{\sigma }}^2}{2{\mathrm{E}}_{\mathrm{u}}}$$

(2)

where, E_u is the elastic modulus during the unloading process. In this study, we adopted the Dong et al. [45] approach for the E_u calculation. In this approach, the elastic modulus of loading (E) is adopted instead of E_u. The average elastic modulus approach was used in this study to calculate E, as described in Equation (3).

$$\mathrm{E}=\frac{\mathrm{f}({\epsilon }_1)-\mathrm{f}({\epsilon }_0)}{{\epsilon }_1-{\epsilon }_0}$$

(3)

where, f(ε₁) refers to stress at the start point of the elastic stage, f(ε₀) refers to stress at the endpoint of the elastic stage, and ε represents strain.

4. Rock Burst Indexes

Generally, various types of rock burst indexes are used worldwide [46,47], but for coal bursts in particular, the most popular indexes are W_et, K_e, D_T, and R_c. Based on these indexes, coal burst proneness is classified into three classes (none, low and high), as shown in

Table 1. Standard coal burst proneness cataloguing [48].

Index	Wet	DT (ms)	Rc	Ke
None	<2	>500	<7	<1.5
Low	2 ≤ Wet < 5	50 < DT ≤ 500	7 ≤ Rc < 14	1.5 ≤ Ke < 5
High	≥5	≤50	≥14	≥5

.

4.1. Elastic Strain Energy Index

The elastic strain energy index (W_et) is usually used for coal burst liability. This index was proposed by Kidybiński [49] for coal burst assessment, as shown in Figure 3a. This index is defined as the ratio of U^d and U^e at the point of 0.80–0.90 ultimate strength. At this point, the input energy will be the sum of U^d and U^e. The index definition reveals that the higher the U^e, the higher the tendency of coal burst. In other words, the higher the U^e, the lower U^d will be, resulting in a higher ratio. A lower U^d means fewer cracks are generated and propagated or less deformation occurs, as dissipation energy is a function of deformation and failure [50]. Therefore, W_et might show the hazard of coal burst before ultimate strength from the U^e proportion aspect [50]. The expression plastic strain energy is an analogy to U^d.

4.2. Bursting Energy Index

The bursting energy index (K_e) is calculated from the stress-strain curve by drawing a vertical line from the peak strength point and dividing the curve into two parts, as shown in Figure 3b. It is also called the burst energy coefficient [51]. In Figure 3b, the K_e can be defined as the ratio of elastic energy (E_a) to dissipation energy (E_b) before the peak strength [48]. The K_e emphasizes the dissipation of energy after failure, while W_et focuses on energy storage before failure. The literature reflects that a lower value of K_e means that the rock will fail abruptly, and more energy will be dissipated in the deformation [50].

4.3. Dynamic Failure Time

During the coal failure process, the amount of released dissipation energy indicates the proneness of coal burst [52]. When the coal samples are subject to uniaxial compressive loading, the time taken by the samples from failure point to rupture point is called dynamic failure time (D_T), as shown in Figure 3c. The magnitude of dissipated energy is proportional to time duration during the coal failure process. Zhang, Wang, Wu and Qu [52], during their research study, selected 11 different coal seams from China and Poland and conducted a series of tests on coal samples at 0.5 and 1 MPa/min loading rates. Zhang, Wang, Wu and Qu [52] suggested a quick and effective index to determine the coal explosion tendency. This tendency shows that a coal seam having less dynamic time is likely to burst with more intensity.

4.4. Uniaxial Compressive Strength Index (Rc)

This index was used for the first time in Poland for coal burst [53]. The strength at the time of failure reflects the potential for rock burst. The literature revealed a positive relationship between R_c and other coal burst indexes [54].

5. Experimental Results

5.1. Mechanical Properties

In this study, when coal specimens were subjected to different loading (0.1, 0.4, 0.7 and 1.0 mm/min), the stress-strain behavior changed from ductile to brittle, as shown in Figure 4a. The coal specimens during loading showed that some mechanical properties increased, and some decreased with the loading rate. The ‘‘axial stress method’’ was used in this paper to assess the compaction stage of coal at different loading rates in stress-strain curves. Several points were selected in the elastic deformation stage in the stress-strain curve to draw a straight line. The junction point before the fitting straight line on the stress-strain curve is known as the endpoint of the compaction stage. This compaction endpoint differentiates compaction and elastic stage based on the line slope [55]. The compaction stage stress and peak stress increase with an increase in loading rate, while the compaction stage proportion decreases, as shown in Figure 4a. In this study, Gao and Kang [56] procedure was adopted for calculation of residual strength. The residual strength increased with loading rate, i.e., at loading rates 0.1, 0.4, 0.7 and 1 mm/min, the corresponding residual strengths were 1.80, 1.99, 2.24 and 2.50 MPa, respectively (Figure 4b). For these loading rates, the corresponding strains were 0.017, 0.015, 0.013 and 0.011, respectively (Figure 4b). We considered the 0.1 mm/min loading rate as a standard load and compared it with others. For the loading rates 0.4, 0.7 and 1 mm/min, the residual strength increased 10.88, 24.44 and 38.8 fold, while the corresponding strain decreased 11.76, 23.52 and 35.29 fold, respectively. Moreover, the peak strength increased with a predetermined loading rate, and its values were 2.8, 5.4, 5.9 and 6.3 MPa, while the decrease in corresponding strain was 0.017, 0.013, 0.011 and 0.0098, respectively (Figure 4b,c). Furthermore, the elastic modulus also increased with the loading rate, as shown in Figure 4d.

5.2. Strain Energy

Figure 5 shows the strain energy evolution in the stress-strain curve at different loading rates during the uniaxial compression test. According to Xiao et al. [39], the coal samples pass through four stages under loading i.e., compaction, elastic, plastic, and failure stages. In the first stage (compaction), the samples show a slow increase in strain energy with loading rate. In this stage, the U^e is more than the U^d; however, the U^d rate is greater than the U^e rate. This increase in the rate of U^d is caused due to the consumption of energy in the primary pore and closure of microcracks. In the elastic deformation stage, the external energy is mainly converted into U^e and slightly converted into U^d or unchanged. Here, the U^e storage is higher due to no crack generation or propagation, as crack generation and propagation result in energy dissipation. As a result, the external energy is mostly accumulated as U^e, and a minute magnitude of energy is dissipated. In the plastic stage, the external input energy of some parts is accumulated as U^e and some parts as U^d. This U^d occurs due to new meso-crack generation in the coal sample. Although U^e accumulation is higher than that of U^d, the U^d increases substantially in the plastic stage of the stress-strain curve. In the final stage (failure stage), the U^e curve tends to be steep when achieving the peak stress level, while the U^d increases rapidly. The U^e curve decreases quickly to the minimal level after reaching the maximum stress stage. At this stage, the U^d curve increases and reaches its highest magnitude. As U^d exceeds the highest stress stage, macro crack expansion and breakage increase further. After exceeding the peak stress, the U^e reduces rapidly, and the U^d curve rises quickly. This indicates that the deformation and failure of coal samples are the mechanisms of continuous energy absorption and release. Moreover, the change in the loading rate will predictably lead to an obvious difference in the value of strain energy at peak stress. Figure 6 represents the variation trends in the total, elastic, and dissipated strain energy with different loading rates at the peak stress point. These energies show a positive exponential correlation with loading rates. Moreover, the total strain energies increase with loading rate and are 0.028, 0.0342, 0.0417 and 0.054 J.cm⁻³ for loading rates of 0.1, 0.4, 0.7 and 1.0 mm/min, respectively.

The rate of U^d (∆U^d) reflects the crack generation/propagation in coal specimens. The crack generation and propagation are directly proportional to ∆U^d, which can be calculated using Equation (4).

$$∆{\mathrm{U}}^{\mathrm{d}}=\frac{{\mathrm{U}}^{\mathrm{d}}(\mathrm{t}+∆\mathrm{t})-{\mathrm{U}}^{\mathrm{d}}(\mathrm{t})}{∆\mathrm{t}}$$

(4)

The ∆U^d in the stress-strain curve shows different trends with loading rates, as shown in Figure 7. The results revealed that ∆U^d increased at the crack generation or propagation point. At the failure point, the stress drops and ∆U^d increases, which can be used as a failure indicator. After the failure, more cracks are generated and propagated, which shows a maximum ∆U^d.

5.3. Energy Modulus and Damage Variable Index for Coal Burst

Coal bursts are triggered by the rapid release of elastic strain energy from the deep excavation. This bursting intensity imitates the surrounding rock mechanical characteristics during the event. The release of U^e during coal burst occurs when the load exceeds the bearing strength of the coal. The bursting liability index reflects the accumulation and release of a coal sample’s U^e during the fracture process [57,58].

During coal burst, the rapid release of the U^e contributes to the displacement of coal pieces. Hence, the amount of stored U^e to total strain energy plays a significant role in coal burst potential. In previous research, Dai, Wang, Pan and Liu [42] introduced a new coal burst index known as the elastic modulus index (K_λ). As discussed in the introduction, this index is a function of softening modulus (λ) and E. According to this index, the greater the λ, the stronger the intensity of a coal burst. If we compare K_λ with D_T, the less the difference between peak stress and residual stress time, the intensity of the coal burst will be stronger. Lu, Ju, Gao, Feng, Sun, Wang and Yi [10] proposed the EESERR index for coal burst liability. This index depends on the storage of U^e in the pre-peak stage and D_T. A higher pre-peak U^e and lower D_T will result in an intense coal burst.

Research by Xiao et al. showed that the U^e curve tends to be steep when reaching the peak stress level, while the U^d curve increases rapidly. The U^e curve decreases rapidly to a minimum after achieving the peak stress level. By contrast, the energy curve that is dissipated increases rapidly to the highest limit. The above findings demonstrate that internal coal damage increases rapidly near peak stress, and much of the energy (i.e., U^d) is absorbed by the extension of damage cracks, friction, and dislocation between coal particles. The U^d and the expansion of macro-cracks and breakage increase further after reaching the peak stress level. The damage is related to U^d; the more U^d released, the greater the damage will be. There is no coal burst index available that can consider a damage variable in the coal burst index. Bearing in mind the damage factor, in this study, we proposed a new bursting liability index called the elastic modulus damage index (EMDI), as defined in Equation (5).

$$\mathrm{EDMI}=\frac{\mathsf{\lambda }}{\mathrm{E}}\ast \frac{{\mathrm{U}}_{\mathrm{d}}}{\mathrm{U}}\ast \frac{{\mathsf{\sigma }}_{\mathrm{r}}}{{\mathsf{\sigma }}_{\mathrm{p}}}$$

(5)

where λ is elastic modulus after peak stress, E is elastic modulus, U_d is dissipated energy at peak stress, U is the total strain energy at peak stress, σ_r is residual strength and σ_p is peak strength.

Equation (5) is the combination of two previous equations; λ/E is the elastic modulus index proposed for coal burst by Dai, Wang, Pan and Liu [42], and (U^d/U) * (σ_r/σ_p) is the damage variable proposed by Dai, Wang, Pan and Liu [42] for material damage. These two-equation combinations yield a reliable coal burst index. The EDMI relationship with previous indexes was evaluated, and the performance of the EDMI was analyzed using root mean square error (RMSE) and coefficient of determination (R²). The RMSE is defined in Equation (6).

$$\mathrm{RMSE}=\sqrt{\frac{{\displaystyle \sum _{i=0}^n{(Predicte{d}_i-Actua{l}_i)}^2}}{n}}$$

(6)

5.4. Index Comparison

Figure 8 shows the relationship of EMDI with W_et, K_e, D_T, and R_c. The EDMI shows a good positive polynomial second-order degree relationship with W_et and K_e having RMSE and determination factor (0.0003, 0.99) and (0.0031, 0.99), respectively, as shown in Figure 8a,b. The relationship between EDMI and D_T shows a negative polynomial second order degree relationship with RMSE and determination factor 0.0730 and 0.94, as shown in Figure 8c. Similarly, the R_c shows a positive power relationship with EDMI having RMSE and determination factor 0.0741 and 0.99, as shown in Figure 8d. These relationships revealed a good determining factor. The current experimental work was based on different loading conditions (0.1, 0.4, 0.7 and 1.0 mm/min); therefore, it was concluded that the new index can be utilized to obtain reliable results for coal bursts in different stress environments.

Based on the relationships, the coal burst classification value and limits were calculated for EDMI as described in

Table 2. The threshold values for previous coal bursting liability and EMDI (16 samples).

Index	Wet	DT (ms)	Rc	Ke	EMDI
None	<2	>500	<7	<1.5	<0.91
Low	2 ≤ Wet < 5	50 < DT ≤ 500	7 ≤ Rc < 14	1.5 ≤ Ke < 5	0.91 ≤ EMDI < 1.93
High	≥5	≤50	≥14	≥5	>1.93

. The bursting liabilities of the proposed and other coal burst indexes were determined at different loading rates, as shown in

Table 3. Evaluation of bursting liability indexes with different loading rates.

Indexes	Loading Rate (mm/min)				Bursting Liability Evaluation with Different Loading Rate
	0.1	0.4	0.7	1	0.1	0.4	0.7	1
Wet	0.070	1.730	3.100	4.700	None	None	Weak	Weak
DT (ms)	30813	23781	11328	9012	None	None	None	None
Rc	2.837	5.4492	5.7876	6.314	None	None	None	None
Ke	1.300	2.650	3.970	4.970	None	Weak	Weak	Weak
EDMI	0.003	0.820	1.310	1.860	None	None	Weak	Weak

. The table indicates that with a given loading rate, all indexes’ intensity values will increase, including that of EDMI, but D_T will decrease. This decrease in D_T with loading rate is due to the coal samples’ transition from the ductile to brittle behavior. This transition highly depends on the sample properties under loading. Further, the coal burst intensity will be reflected in the burst tendency values; the higher the value, the higher the intensity, and vice versa. This statement is valid for all indexes except D_T. For the D_T index, the coal burst intensity is inversely correlated to the burst tendency value. The higher the burst intensity, the lower the tendency value will be.

When comparing the established bursting liability indexes for coal, it is clear that the various indexes have very reasonable interpretations regarding the bursting liability of the same coal sample at different loading rates. Some liability indicates burst irrespective of tendency (weak or high), but some do not reflect the coal burst occurrence, such as R_c and D_T, as shown in Table 3. The W_et shows coal burst liability as the loading increases. At 0.1 and 0.4 mm/min, the coal samples have no bursting, whereas at 0.7 and 1 mm/min, the samples have a weak burst. In K_e, weak burst liability exists at all loading rates except at 0.1 mm/min. The EDMI index was used for coal samples at different loading rates, and the results were evaluated and listed in Table 3. Table 3 shows that the coal samples at 0.1 and 0.4 mm/min loading rate had no bursting liabilities, whereas at 0.7 and 1 mm/min, they had weak bursting liabilities (similarly to W_et). In this new index, all the factors considered by the previous indexes are incorporated, thus covering the limitations of individual indexes. Furthermore, these index threshold values were based on limited samples (16 coal samples). This threshold value range may change if more samples are tested.

6. Discussion

Coal is a substance with prominent structures (pores and cracks), and in the initial loading process, compaction occurs in these structures. In the compaction stage, most of the U is converted into U^d because more energy is used in closure of the cracks and micro-pores, and less U^e is accumulated in this stage. After the specimens reach the elastic deformation stage, the climb in the stress-strain curves is nearly linear (as shown in Figure 4a). In this stage, the accumulation of U^e is higher than that of U^d; therefore, it can be considered the primary stage of U^e accumulation. After this primary stage, the specimen shows damage and experiences the plastic behavior/stage. Here, the first drop in stress occurs due to the movement along microstructural planes within the sample. This drop-in stress reveals that the internal integrity of the coal sample has been disrupted, and the energy release occurs; ultimately, the concentration is reduced [10,59]. When the stress-strain curve approaches peak stress level, maximum U^e accumulates. However, at the failure point and after failure, the U^e drops while U^d increases abruptly. This shows that at the failure point, the rock damage accelerates and leads toward rupture. The magnitude of damage is directly proportional to U^d.

The coal sample under loading is a continuous phenomenon of energy absorption and release. Simultaneously, the energy parameter curves of the coal display a standard evolutionary law under different loading rates. This indicates that the energy conversion rate of coal sample deformation will not influence the energy conversion pattern and failure phase. As the loading rates rise, the peak stress increases, which results in a small increase in U absorption. However, this rise in loading rate significantly increases U^e and U^d. At peak stress, the U^e decreases while U^d increases with the loading rate. Therefore, the higher loading rate will turn more energy into dissipated energy, which causes more damage and the ejection of coal pieces at the point of failure as compared with the lower loading rate.

The U^d plays an important role in the deformation and failure of material [60,61]. The U^d is related to coal damage that ultimately weakens the strength properties of the material. This study proposed quantitative determination of ∆U^d, which can be used as a crack indicator for coal samples. Experimental results showed that the corresponding U^d increases as stress suddenly drops in the stress-strain curve. This increase is maximum at violent failure. This change in ∆U^d is due to U^d release in crack development or propagation in the coal sample under loading. The relationship between ∆U^d peaks and stress drops within coal was calculated by Feng, Wang, Chen and Ding [1]. During their experimental study, coal sample deformation under quasi-static and dynamic loading was studied. In their study, the mechanism of loading was captured by a high-speed camera. As a result, crack propagation was typically caused by a tensile crack opening at the crack edge, followed by an immediate shearing along the crack surfaces, which simultaneously resulted in a stress drop. Consequently, the peak energy dissipation rate in quasi-static experiments is naturally correlated with crack propagation. This propagation is due to the shear slip along the crack surfaces. The experiments revealed that the crack opened in the load direction and the displacement of the crack opening continuously increased. The energy dissipation rate increases at the beginning of the tensile crack opening, and then the stress drop occurs gradually. As a result, the peak dissipation energy rate in dynamic experiments was related with crack propagation, which was the same as in quasi-static tests.

The previous bursting indexes reflect only the bursting liability attribute and are thus constrained in their predictive capacity [10]. The R_c reflects the energy accumulation potential of the specimen, but R_c is not necessarily related to bursting liability. At the pre-peak point of the compression test, all the work done by the hydraulic press machine is not stored in the form of U^e in the sample. The K_c is estimated by the ratio of pre-peak to post-peak energy. During loading, the U^e that accrued during the pre-peak period is not measured separately, and hence, this index for the bursting liability is typically very high. The W_et coal burst index predicts the U^e and U^d before failure. This index is limited to the U^d before failure and gives no information related to U^d after failure.

However, the coal/rock burst intensity highly depends on the energy release after peak point in the stress-strain curve (after failure). The D_T is based on the time between failure strength and residual strength; however, the index reflects no mechanical characteristics of the stress-strain curve. The discussion above concerns the individual index limitations. These indexes are either based on energy liability or elastic modulus for the coal/rock burst intensity prediction. In this article, we proposed a new index, the EDMI, which considers both elastic modulus (damage factor) and energy liability for the promising result. The proposed index shows good agreement with the previous coal burst index as mentioned in Section 4. The proposed index is based on the specific dimensions of the coal sample and four loading rates. To extend EDMI to a generalized form, it is recommended to consider different standard sample dimensions, loading rates, and types of loading. To capture the real cracking and ejection of coal from the sample, the recommended conditions will be studied using infrared radiation and acoustic emission technologies.

7. Conclusions

The findings derived from the research study are below:

• The stress-strain curve moves from ductile to brittle under different loading rates. Additionally, the elastic modulus, peak, and residual strength increase, while peak and residual strain decrease.
• The total strain energy, elastic strain energy, and dissipated strain energy at ultimate strength have a positive correlation with loading rates. The ∆U^d was used and suggested as an indicator for crack development and propagation during stress-strain curves based on the energy mechanism. Furthermore, the experimental results indicated that the ∆U^d increased with the loading rate.
• A new elastic modulus damage index (EDMI) was proposed and is based on the elastic modulus (damage factor) and energy liability. The EMDI was compared with available coal burst indexes (W_et, K_e, D_T, and R_c), and the results show a good correlation determination factor.
• Based on the comparative analysis, it was proposed that the EMDI can be effectively used in monitoring coal bursting liability for the safe mining of deep coal deposits.