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A Modified Bursting Energy Index for Evaluating Coal Burst Proneness and Its Application in Ordos Coalfield, China

: Coal burst is a type of dynamic geological hazard in coal mine. In this study, a modified bursting energy index, which is defined as the ratio of elastic strain energy at the peak strength to the released strain energy density at the post-peak stage, was proposed to evaluate the coal burst proneness. The calculation method for this index was also introduced. Two coal mines (PJ and TJH coal mines) located in Ordos coalfield were used to verify the validity of the proposed method. The tests results indicate that modified bursting energy index increases linearly with increasing uniaxial compressive strength. The parameter A, which is used to fit relation between total input and elastic strain energy density, has a significant effect on the modified bursting energy index. A large value of parameter A means more elastic strain energy before the peak strength while a small value indicates most of input energy was dissipated. Finally, the coal burst proneness of these two coal mines was evaluated with the modified index. The results of modified index are consistent with that of laboratory tests, and more reasonable than that from original bursting energy index because it removed the dissipated strain energy from the total input strain energy density.


Introduction
Coal burst, which involves the sudden and violent ejection of coal into roadways, is one of the most serious disaster encountered in coal mines. Since 1738, the first coal burst was issued in Britain; this type of geological disaster was reported in most of countries, including Canada, South Africa, USA, India, France, and so on. For example, in the United States, two coal bursts occurred at Crandall Canyon Mine in Utah in 2007 and resulted in the death of nine workers, which is one of the most severe coal burst accidents [1]. In Australia, more than 900 fatal incidents occurred in coal mines from 1957 and 2008 [2]. Especially, in China, it is one of most serious disaster in deep mining [3]. For instance, a burst disaster was reported in Longjiabao coal mine with 9 fatalities and 12 severely injured on June 6th, 2019. Several months ago, on October 20th, 2018, a coal burst occurred in Yuncheng coal mine and resulted in 21 fatalities. Therefore, the coal burst severely threatens personnel safety and may delay the project schedule in coal mine. Therefore, studies on the occurrence, predication, and control of coal burst events have great scientific and engineering significance [4,5].
A large number of researches have been conducted on the coal burst, which general can be classified into following two types: One is monitoring methods and the other is control techniques.
For the first one, the methods, such as drilling bits method, micro-seismic monitoring (including multi-index monitoring technique [6], multiplet approach method [7], frequency spectrum analysis method [8], micro-seismic activity, energy characteristics, signal characteristics, spatiotemporal distribution law, and micro-seismic precursory characteristics of rock burst hazard [9][10][11][12][13]), electromagnetic emissions (including electromagnetic emission graded warning model [14] and noncontact mine pressure comprehensive evaluation method [15][16][17]), and the integrated micro-seismic and electromagnetic radiation method [18] have been widely used. On the other hand, many control techniques, including preventative controls and mitigating controls, have been proposed for controlling coal burst during mining [19]. The preventative controls are a technique by optimizing the mine design to avoid burst event, such as pillar design (including yield-stable-yield pillar [20], yield-stable pillar [21], critical pillar [22], and abutment pillars [23]), protective coal seam [24], and the shape and direction of roadways [25]. The mitigating controls are measures to further decrease the impact of coal burst. For example, directional hydraulic fracturing [26], the constant-resistance and large-deformation bolt [27], and de-stress drilling [28].
There are two different perspectives or scales to discuss the coal burst. One is coal sample physical mechanical properties. The coal burst proneness indexes, which can be obtained by the laboratory tests conducted on coal samples, is used to judge coal burst proneness with corresponding standards. The other perspective is mining. Except the physical properties of coal sample, the coal burst is also determined by mining methods (different unloading rate, pillar design, and mining speed), geological features (such as geo-stress, joints), and even roadway direction. In this paper, the work is focused on the first perspective.
Coal burst proneness is an inherent characteristic of coal, which can be aroused by the sudden release of elastic energy under unloading conditions. Therefore, the evaluation of coal burst proneness of coal samples is the first step and essential for the predication and controlling of coal burst. At present, many discriminant indexes and criteria, based on energy, strength, or failure duration, have been proposed [6]. For instance, Dai et al. [29] studied the feasibility of evaluating the coal burst proneness by modulus index, which is defined as the ratio of softening modulus at the post-peak to the elastic modulus before the peak strength. Xu et al. [30] proposed a new energy release rate index, which was successfully verified by predicting the position of rock burst in a coal mine. Gong et al. [31] developed a peak-strength strain energy storage index and a new criterion for rock burst proneness, which was validated by estimating the rock burst proneness of nine rock materials. Besides, the elastic strain potential energy index, the decrease modulus index, and brittleness index were also proposed in the literature [32].
Among these indexes, four coal burst proneness indexes, namely uniaxial compressive strength (Rc), failure duration time (DT), elastic strain energy index (Wet), and bursting energy index (Ke), were widely used and recommended by Chinese standard (GB/T 25217. . Then, Yang et al. [33] extended these indexes into Australia coal mines. Su et al. [34] discussed the relationship between these indexes and indicated that the bursting energy index may overestimate the coal burst proneness. Generally, the design of support in burst-prone areas are totally different from that without bursting proneness. For the coal mine without bursting proneness, the control method can be confirmed by surrounding rock grade, including normal bolt, cable, shouting concrete, and steel arch. However, in burst-prone areas, the control techniques are more complex. Some pretreatment measures are de-stress drilling and directional hydraulic fracturing. Besides, the pillar design, coal seam, and bolt pattern should satisfy dynamic deformation. Therefore, overestimation of the coal burst proneness may cause the original safe coal mine to be wrongly classified as probable bursting, which will lead to designing change. Otherwise, the underestimation of coal burst proneness will threaten the productivity severely. However, the original bursting energy index (Ke) is defined as the ratio of total input energy density before the peak strength to the released strain energy density after peak strength. The total input energy density at the peak point includes elastic and dissipated strain energy density. The elastic strain energy keeps accumulating during loading process while dissipated strain energy is dissipated during the loading stage. Therefore, the original bursting energy index may overestimate the coal burst proneness.
In order to solve this problem, a modified bursting energy index, defined as the ratio of elastic strain energy at the peak strength and the released strain energy density after peak strength, was proposed to evaluate the coal burst proneness. The calculation method for this index was also introduced. The reliability of the present index is verified through tests on two typical coal mines in Ordos coalfield, China.

Brief Descriptions of Coal Burst Proneness Indexes
According to Chinese standard (GB/T 25217.  [35], the coal burst proneness can be classified into three different grades: none, low, and high. The specific index values for each grade are listed in Table 1. Through the uniaxial compression tests on the standard coal samples, uniaxial compressive strength (UCS) and dynamic failure duration time, which is defined as the time span from the peak stress to complete failure of coal specimen, can be easily obtained. Figure 1 shows the calculation method and definition of the index Wet. As shown in Figure 1, Wet is the ratio of elastic strain energy density to the dissipated strain energy density when the axial loading k  is equal to 75~85% of the peak strength of coal specimen. The index Wet can be calculated by a single cyclic loading-unloading uniaxial compression test. The formula for index Wet is listed as follows.
where k a u is the total input energy density during loading process. Parameters For the index Ke, which is defined as the ratio of accumulated strain energy density before the peak strength a u to the released strain energy density after peak strength r u , can be calculated with uniaxial compression test. As shown in Figure 2, the formula for index Ke is listed as follows: Similarly, the parameters a u and r u can be expressed by following equations: r a u u u  (8) where u is the total energy density during entire loading process. Parameters  As shown in Figure 3, it is known that the total input energy density at the peak point includes two parts: elastic strain energy density ae u and dissipated strain energy density ad u . The elastic strain energy keeps accumulating during loading process. For the dissipated strain energy, it will be dissipated during the loading stage because of the closure of micro-cracks, material damage, and plastic deformation. As a result, dissipated strain energy has little effect on the energy released at the post-peak stage. However, from Figure 2 and Equation Error! Reference source not found., it indicates that both elastic and dissipated strain energy are used to calculate the bursting energy index, which may overestimate the coal burst proneness, especially for that of strong plastic coal.

Definition of the Modified Index
In this section, a modified bursting energy index p e K , which is defined as the ratio of elastic strain energy at the peak strength to the released strain energy density after peak strength and can be expressed by the following equation: where the parameters ae u and ad u can be expressed as follows: where parameter 0 p  is permanent strain after unloading from the peak point.
Obviously, the key to calculate the index p e K is obtaining the elastic strain density at the peak strength point ae u accurately. Because of the dispersion and heterogeneity of the coal specimen strength [36], it is impossible to conduct the unloading test on coal specimens at the peak strength point. Gong et al. [37] proposed a new method to calculate the peak elastic strain energy storage index for different rock specimens, such as sandstone, granite, and marble. In this study, this method was introduced and validated to obtain elastic strain density at the peak point for coal specimens.
According to the results of Gong et al. [31], a series of single cyclic loading-unloading uniaxial compression under different stress level k (the ratio of unloading point stress and uniaxial compressive strength) first are carried out. For each cyclic loading-unloading test, the total input and elastic strain energy density can be calculated and the results indicated that the k ae u (elastic strain energy density when unloading at stress level k) increases lineally as the k a u (total input strain energy density when unloading at stress level k) increases, which can be expressed as follows: where the parameters A and B are fitting coefficients and they are constant for the same rock specimens. Further, the elastic strain energy ae u can be calculated by the following equation: Therefore, the modified bursting energy index can be calculated combining the Equations Error! Reference source not found. and Error! Reference source not found..
Based on the previous analysis, the following method is recommended to obtain the index Error! Reference source not found., Error! Reference source not found., and Error! Reference source not found.

Coal Burst Proneness Evaluation in Coal Mines
In this section, two typical coal mines, namely Pojianghaizi (PJ) and Tangjiahui (TJH), were used to discuss the validity of the proposed method by comparing coal burst proneness with the Chinese standard (GB/T 25217.  [35] and test results. As shown in Figure 4, PJ coal mine is located in northwest Ordos city with a distance about 40 km and TJH coal mine located in northeast Ordos city with a distance about 130 km. The PJ coal mine has a width of 4.6 km, length of 13.2 km, and 668 million ton of coal resources. The mainly mineable coal seams are coal #3, coal #4, and coal #5 with mining depths in the range of 506-640 m under the ground, approximately. The TJH coal mine has a width of 5.1 km, length of 8.5 km, and 310 million ton of coal resources, and contains three mainly mineable coal seams namely coal #4, coal #5, and coal #6 with different depths varying from 357 m to 576 m under the ground surface. To obtain the standard coal specimens, some coal blocks (Figure 5a) were collected from PJ and TJH coal mines first, and then, the collected coal blocks were cut into standard specimens of length 50 mm, width 50 mm, and height 100 mm (Figure 5b). The loading surfaces of all specimens were then polished in accordance with the standards of the International Society for Rock Mechanics [38].
The tests were conducted by the RMT-150C servo-controlling testing machine, as shown in Figure 5(c), and the maximum vertical loading capacity and confining pressure of RMT-150C are 1000 kN and 50 MPa, respectively. This system has two controlling modes during test and can record data simultaneously. According to Liang et al. [39], the uniaxial compressive strength increases as loading rate increases and the recommended loading strain rate is from 10 -5 to 10 -3 s -1 . Therefore, in this study, displacement control mode with a constant speed of 0.002 mm/s was selected.

PJ Coal Mine
The specimens were collected from 113101 work face with depth of about 522 m. As listed in Table 2, three groups of single cyclic loading-unloading uniaxial compression tests were carried out on coal specimens. For each group, there are four specimens with different unloading stress level k.  Table 2 and the representative loading-unloading stress-strain curves for each group are shown in Figure 6.  Based on Equation Error! Reference source not found., the date listed in Table 2 were used to study the relationship between elastic strain energy density and total input strain energy density. The linear fitting equations for each group of specimens are listed as follows: where the parameter R 2 is correlation coefficient. The fitting curves are shown in Figure 7 and data are listed in Table 3. From Equation Error! Reference source not found. and Figure 7, it can be found that the parameters A for the three groups are 0.7912, 0.7952, and 0.7960 respectively. The average value of parameter A is 0.7419 and the percentage errors listed in Table 3 showed that all the groups are lower than 0.5%, indicating that parameter A for the same coal type is nearly constant. On the other hand, for the parameter B, the average value is -3.43 × 10 -4 and percentage errors for the three groups are 5.539%, 4.665%, and 2.624% respectively, which is quite acceptable. Therefore, it can be concluded that the parameters A and B for a specific coal type can be considered as constant and the average values can be used for calculation in Equation Error! Reference source not found..    Figure 8 shows the stress-strain curves of four typical coal specimens under uniaxial compression condition. It can be found that the stress-strain behavior of all the coal specimens contains three different stages, i.e., fissure closure, elastic deformation, and post-peak. At the fissure closure stage, the curves show a downward concave shape because the closure of pre-existing micro fissures and pores in coal. With the increasing of axial loading, stress-strain behavior turns into elastic deformation and post-peak stages gradually. An obvious stress drop (from point B to C in Figure 8. For example, for specimen K-4, the stress decreases from 6.95 MPa to 2.31 MPa while strain increases from 0.0095 to 0.0114.) can be observed in the post-peak stage, meaning that the coal specimens have the characteristics of the brittle failure. According to the average values of A and B listed in Table 2    According to Table 1 and tests results, the four indexes recommended by Chinese standard (GB/T 25217.  [35] are obtained and the coal burst proneness grade for each index are judged respectively, as shown in Table 5. According to the above laboratory tests results [31,40], one can conclude that no injected coal fragments with almost intact sample indicates no burst proneness, a minor ejected fragment with slight ejection sound and some macroscopic cracks means low burst proneness, and a large amount of ejected fragments with loud sound and severely broken sample indicates high proneness. Figure 9 shows the ultimate failure mode of coal specimens under uniaxial compression test. From Figure 9, it is evident that the coal spalling and split cracks can be observed on the specimen surface. Further, these spalled coal fragments fell off from the specimens with slight sound and formed some voids on the surfaces, which demonstrates that the coal burst proneness is low. Therefore, the test results validated that the index

TJH Coal Mine
The specimens of TJH coal mine were collected from 63,103 work face with depth of about 464 m. According to the results of PJ coal mine, the parameters A and B for a specific coal type can be considered as constant, therefore, only one group of single cyclic loading-unloading uniaxial compression tests were carried out on TJH coal specimens. Calculated data of k a u , k ae u , and d k a u for four specimens with different unloading rates is listed in Table 6. When unloading rate k increases from 51% to 89%, the index Wet varying from 1.44 to 1.48 with the percentage error in the range of 1.41%-10.12%. The results indicate that elastic strain energy index Wet is not a constant but has a large fluctuation even for a same type of specimen.
The fitting curve for this group of coal specimens is shown in Figure 10. From Equation Error! Reference source not found. and Figure 10, it can be found that the parameters A and B for TJH coal mine specimens are 0.5979 and -2.54 × 10 -4 , respectively.  Figure 10. Relationship between elastic strain energy density and total input strain energy density for TJH coal mine. Specimen T-1 Specimen T-2 Specimen T-3 Specimen T-4

Stress(MPa)
Strain(mm/mm) Figure 11. Stress-strain curves of four typical specimens in TJH coal mine. Figure 11 shows stress-strain curves of four typical specimens in TJH coal mine. Like PJ coal mine, the stress-strain behavior also contains fissure closure, elastic deformation, and post-peak stages. The difference is that the fissure closure stage maintains turns into elastic deformation stage until strains approximately are 0.33%, 0.42%, 0.40%, and 0.48% for specimen T-1, T-2, T-3, and T-4 respectively, indicating that a large number of micro fissures and pore exist in the coal.
According to the uniaxial compression stress-strain curves and values of parameters A and B listed in Equation (16), the energy density parameters u ,  Table 7. From Table 7, it can be found that the index  Furthermore, as shown in Table 8, the coal burst proneness grade for TJH coal mine was judged with the four indexes respectively by the Chinese standard (GB/T 25217.   Figure 12 shows the ultimate failure mode of two typical specimen in TJH coal mine. From Figure 12, only some surface cracks can be observed and there is little surface spalling after specimen failure. The specimens almost keep intact the rock status, which indicates that there is no coal burst proneness for specimens in TJH coal mine. However, the index Ke shows a low burst proneness, which is different from the test results. Therefore, the modified bursting energy index, with an average value of 1.3117, is more reasonable for separating the dissipated energy from the total input energy density.

Relationship between Different Parameters
The relationship between different parameters for coal specimens in PJ coal mine is first discussed. Figure 13 shows the relation between indexes of From Figure 14, it also can be found that the index of Furthermore, the relationships between different parameters for specimens in TJH coal mine have also been investigated and the fitting curves are shown in Figure 15. The results showed similar characteristics with PJ coal mine. As introduced by Gong et al. [31], a greater value of parameter A indicates a higher capability of elastic strain energy storage. Actually, the parameter A relates to the strength and micro-structure of specimen. The harder the coal specimen, the fewer the primary cracks and micro-defects, and greater the parameter A. Otherwise, more primary cracks and micro-defects will cause a lower value of parameter A. Li et al. [41] investigated the energy evolution characteristics under triaxial compression conditions and found that except the dissipative strain energy, the total input strain energy and elastic strain energy all increase as the confining pressure increases. Because the initial micro-defects and fissures were compressed by the confining pressure gradually, the increasing confining pressure changed the micro structure. Therefore, the energy density changes with a changing internal structure, which is consistent with the experimental results.
According to the definition of indexes u is about 41.4%, which causes the real coal burst proneness to be lower than that of the index e K . In this case, the low coal burst proneness can be given by the index e K because it is greater than 1.5 and less than 5. However, the modified bursting energy index p e K indicates that there is no coal burst proneness and agrees well with the test results (shown in Figure  12), which is more reasonable because it removed the dissipated strain energy from the total input strain energy density.

Conclusions
The original bursting energy index has not distinguished the dissipated strain energy from the total input strain energy density, which may cause an overestimation for coal burst proneness. Based on the strain energy storage index at peak strength, a modified bursting energy index was proposed, and its calculation method and effectiveness were also verified by tests on two typical coal mines. The following conclusions can be drawn: (1) Three groups of single cyclic loading-unloading uniaxial compression tests for PJ coal mine specimens showed that the relationship between k a u and k ae u is linear and parameters A and B can be considered as constant for a type of coal specimen.
(2) The experimental results revealed that both the indexes of