Study on the evolutionary characteristics of coal burst proneness under the action of multiple mining disturbances

Coal burst is a serious hazard in deep coal mining. To investigate the coal burst proneness evolution during multiple mining disturbances (MMD), this paper implemented a range of uniaxial cyclic loading–unloading tests coupled with acoustic emission (AE) measurement to simulate the loading–unloading effects of the MMD. The maximum load was used to simulate the highest load that the coal has endured in history, the loading–unloading rate was used to simulate the mining speed, and the loading–unloading cycles were used to simulate the number of mining disturbances. Finally, the burst proneness indexes of the damaged coal sample are measured and compared with the origin coal sample. Analysis on the experiment results suggest that, the burst proneness increases when the maximum load is 30% of the uniaxial compressive strength (UCS), interestingly, when the low loading–unloading rate is applied, 50% of the UCS enlarge the burst proneness as well. However, it decreases when the maximum load is 70% of the UCS. Sensitivity analysis indicates that the maximum load, loading–unloading rate, and loading–unloading cycles exhibit decreasing influence sensitivity to the elastic modulus, as well as to the UCS and duration of dynamic fracture. Similarly, the influence sensitivity of maximum load, loading–unloading cycles, and loading–unloading rate to the elastic strain energy index decreases, as well as to the bursting energy index. To ensure the safety of coal mining, it is crucial to avoid the disturbances that would put the coal under low loading and low loading rate.


| INTRODUCTION
Coal bursts are a significant hazard that endangers the safety of coal mining, occurring with high frequency and intensity in recent years because of the increased depth. 1 Multiple mining disturbances (MMD) refer to the various forms of disturbance caused by various mining activities during coal mining.MMD could bring about the loading-unloading effect, causing changes in crack propagation and stress in coal and surrounding rock.This phenomenon has been recognized as the main triggering factor of several serious bursts, include the "8.2" coal burst accident in Tangshan Coal Mine and the "4.8" coal burst accident in Menkeqing Coal Mine, wherein excavation of adjacent coal seams, working faces and roadways caused the MMD.Among them, the "8.2" accident caused seven deaths, and the "4.8" accident resulted in a partial blockage of the roadway and forced the working face to stop production for nearly 10 months.On the other hand, it is well-known that the burst proneness is a significant intrinsic factor that contributes to the occurrence of coal burst. 2 Therefore, studying the effect of MMD and burst proneness could understanding the mechanism and controlling methods of coal burst.
Burst proneness is a critical intrinsic factor that contributes to the occurrence of coal burst, and has been extensively investigated by scholars using theoretical analysis and experimental methods.These researches have focused on improving the evaluation index and investigating the changing patterns under various influencing factors.Gong et al. 3 established a criterion for burst proneness by utilizing the residual elastic energy index.Khan et al. 4 developed the elastic modulus damage index according to the energy evolution characteristics under various loading rates.Lu et al. 5 proposed the effective elastic strain energy release rate and verified the reliability of the evaluation results through physical compression experiments.In the research results concerning the changing patterns of coal burst proneness under various influencing factors, Liu et al. 6 and Ouyang et al. 7 studied the influence of gas pressure and content on the coal burst proneness, respectively.Their findings indicated that as gas pressure or gas content increase, coal burst proneness decreases.Liu et al. 8 and Guo et al. 9 demonstrated that water injection can effectively reduce burst proneness, although a noticeable time effect exists.Zhao et al. 10 carried out numerical experiments on burst proneness of "roof-coal" compound structure under different height ratios, roof strength, homogeneity and interface angle by RFPA2D.The research findings suggest that the burst proneness of compound structures is higher than determination results on pure coal seam and rock stratum, and is closer to actual condition.Liu et al. 11 explored the impact of creep predamage on coal burst proneness.With the increase of creep predamage degree, the uniaxial compressive strength (UCS), elastic strain energy index, and bursting energy index first increase and then decrease, but the variation trend of duration of dynamic fracture is opposite to the other indexes.
Simultaneously, regarding the impact of mining disturbances on the mechanical characteristics of coalrock mass, research results have primarily focused on the establishment of surrounding rock damage models and the exploration of damage evolution laws.Feng et al. 12 established a model to calculate the damage zone in the surrounding rocks of circular tunnels by took into account the unloading effect during excavation.Wang et al. 13 investigated the effect of mining unloading on the damaged zone around the roadway by using borehole photography and ultrasonic testing techniques.Wu et al. 14 investigated the evolution of the damage to the near-field rocks surrounding the drift, and established the relationship between the convergence deformation and damage zone radius of the surrounding rock.Song et al. 15 investigated the development of excavation damaged zones (EDZs) around a rectangular coal roadway under mininginduced pressure.They found the complexity of EDZ development under the proposed loading conditions involves tensile and shear failures, the development of remote cracks, and the effect of roadway geometry.Li et al. 16 and Verma et al. 17 believed that the high support pressure induced by mining is different from the disturbance caused by blasting, and it constantly moves forward as the longwall face advances.
Loading-unloading effects is the main characteristic of the MMD.However, the impact of loading-unloading effects on the coal burst proneness is still absent.Unlike previous studies that mainly investigated single mining disturbances, our research focuses on the cumulative effects of MMD on coal burst proneness.This approach allows us to capture the complex interactions and longterm impacts that are often overlooked.Understanding the evolutionary characteristics of burst proneness under MMD can help identify potential hazards and implement effective preventive measures to safeguard the lives and well-being of miners.At the same time, by studying the evolution of burst proneness, mining engineers can optimize mining practices to reduce the occurrence of coal bursts.Minimizing such incidents leads to increased mining efficiency and productivity, contributing to the sustainable development of the coal mining industry.
LIU ET AL.

| 3681
The present paper first introduced the physical meaning and acquisition methods of each burst proneness index.Subsequently, the quasi-static uniaxial cyclic loading-unloading tests were conducted to simulate the MMD experienced by coal in actual engineering, the influence of MMD on the coal burst proneness is explored.The test results were compared with the original test plan, the burst proneness and AE characteristics under various test conditions were analyzed, as well as the sensitivity of various influencing factors.Lastly, some basic data and reference opinions were provided to support the development of antiburst measures in practical mining processes.

| BURST PRONENESS INDEXES
There are various indexes to characterize the coal burst proneness.The present paper uses elastic modulus (E), UCS (R C ), elastic strain energy index (W ET ), bursting energy index (K E ), and duration of dynamic fracture (DT) to characterize this property.The stress-strain curve of coal samples contains abundant information, including burst proneness.Figure 1 illustrates the typical stress-strain curve.OA, AB, BC, and CD stages correspond to the compaction, elastic, yield, and failure stages, respectively.ε 1 , ε 2 , ε 3 , and ε 4 are the strain values corresponding to the loads in the compaction, elastic, yield, and failure stages, respectively.
The elastic modulus refers to the ratio of stress to strain of an object when it is subjected to external force within the elastic stage, and characterizes the ability of an object to resist elastic deformation. 18,19The slope of curve IAB in Figure 1 can be used to represent.The greater the elastic modulus, the greater the stiffness of the coal, the less likely it is to undergo deformation, and the stronger the burst proneness as well.
UCS reflects the ability of coal to store elastic energy when subjected to external forces, and is positively correlated with burst proneness. 20,21As indicated in Figure 1, σ 0 is the UCS of the coal sample.
3][24] The greater the index, the stronger the burst proneness of coal.According to the stress-stain curve, it can be calculated as: where W 3 is the accumulated elastic strain energy, which is the area surrounded by the curve BE and the ε axis in Figure 1, kJ/m 3 ; W 4 is the consumed plastic strain energy, which is the area surrounded by the curve OAB and the curve BE in Figure 1, kJ/m 3 ; ε 1 and ε 2 are the unloading residual strain and the unloading point strain, respectively.The bursting energy index (K E ) is defined as the ratio of the strain energy accumulated before the peak value of the stress-strain curve to the strain energy consumed after the peak value during the uniaxial compression. 25,26The greater the index, the stronger the burst proneness of coal.According to the stress-stain curve, it can be calculated as: where W 1 is the strain energy accumulated before the peak value, which is the area surrounded by the curve OABC and the ε axis in Figure 1, kJ/m 3 ; W 2 is the strain energy consumed after the peak value, which is the area surrounded by the curve CD and the ε axis in Figure 1, kJ/m 3 ; ε 3 is the corresponding strain value when the stress is loaded to the peak value; ε 4 is the corresponding strain value when the coal sample is completely damaged.The duration of dynamic fracture is defined as the time from ultimate strength to complete failure of coal samples under uniaxial compression, 27 as shown in Figure 1.The smaller the value, the stronger the burst proneness of coal.
F I G U R E 1 Typical stress-strain curve.
To investigate the impact of MMD on the coal burst proneness, the present research used the quasi-static uniaxial compression cycle loading-unloading test to simulate the loading-unloading effects generated by MMD.The coal sample characteristics, apparatus and testing plan are described as follows.

| Coal sample characteristics
The coal samples utilized in the test were obtained from Manlailiang Coal Mine of Inner Mongolia, China.The coal cores were taken out by dense drilling of coal samples, then processed into cylindrical standard coal samples with height of 100 mm and diameter of 50 mm, as per ASTM standard.The parallelism of the end face is less than 0.05 mm, and the deviation of the verticality is not more than 0.25°.To minimize the discreteness of the test results as much as possible, coal samples with relatively complete appearance, without obvious defects, and roughly equal natural density were selected for the comparative tests.The natural density of the coal samples are between 1237.59 and 1324.17kg/m 3 , and the average density is 1285.34kg/m 3 .

| Apparatus
The apparatus comprises a loading system and an acoustic emission (AE) system.The principle of the test system is shown in Figure 2. RMT-301 electro-hydraulic servo rock and concrete mechanics testing system was adopted as a loading system.During the test, the system automatically collects and dynamically displays the load and deformation information in real time.And the DS5-32B AE monitoring system was adopted in the test.The AE system has a sampling frequency of 3 MHz, the threshold value is 50, and the magnification is 40 dB.RS-2A wide-band sensor was adopted, and the main frequency band is 60-400 kHz.Four AE sensors were arranged on the sample.The arrangement scheme of AE sensors is shown in Figure 2.During the test, the AE system dynamically monitors and records the AE information such as amplitude, ringing count, energy and impact number in real time.

| Testing plan
In the present study, burst proneness indexes of some standard coal samples were initially measured as the original test plan.Subsequently, uniaxial compression cycle loading-unloading tests were conducted, and the burst proneness indexes of damaged coal samples were measured and compared with those of the original test plan.The test procedure is depicted in Figure 3.
First, eight standard coal samples were selected for the uniaxial compression test.The test indicated that when the load reaches approximately 30% of the UCS, the coal sample transitions from the compaction stage to the elastic stage, and the stress-strain curve undergoes a significant change, as shown in Figure 1.As the load reaches about 70% of the UCS, the coal sample enters the yield stage from the elastic stage.The burst proneness indexes of eight original standard coal samples were measured, and their average values were taken as the burst proneness indexes of the original test plan.Table 1 illustrates the test results.According to the classification criteria of burst proneness in China (i.e., R C ≥ 14, W ET ≥ 5, K E ≥ 5, and 50 < DT ≤ 500), it is determined that the original coal samples have strong burst proneness.
Second, the quasi-static uniaxial cyclic loadingunloading tests were conducted to simulate the loadingunloading effects generated by MMD.The maximum load was used to simulate the highest load that coal has endured in history.Corresponding to the critical stress values of each stage demonstrated in Figure 1, the proposed maximum loads are 0.3σ 0 , 0.5σ 0 , and 0.7σ 0 , respectively.In the test, they are 9.6, 16, and 22.4 kN, respectively.Considering the influence of the advancing rate of excavation to the burst proneness of coal, the loading-unloading rate was used to simulate the mining speed.Referring to previous researches on the impact of loading-unloading rates on the mechanical characteristics of coal, [28][29][30][31][32] while taking into account the capabilities of the testing equipment.The rates are set 0.001, 0.002, and 0.005 mm/s, respectively.Corresponding to the coal response at slower mining speed, moderate mining speed and faster mining speed, respectively.The loading-unloading cycles are repeated to simulate the number of disturbances.Considering the different excavation layouts and the number of mining disturbances experienced by coal during actual mining T A B L E 1 Burst proneness indexes of original test plan.processes, the cycles are set 3, 5 and 7, respectively.The orthogonal test plan is shown in Table 2.
Finally, the burst proneness indexes of the damaged coal samples that underwent uniaxial cyclic loading-unloading tests were measured, and compared with the original test plan.The variation characteristics of coal burst proneness were investigated and sensitivity analysis of influencing factors were implemented.

| TEST RESULTS
Each test scheme in Table 2 was conducted seven times.To enhance the accuracy and reliability of the research, we selected five sets of data with higher similarity for comprehensive analysis.This approach aimed to mitigate the influence of coal sample heterogeneity and eliminate the impact of extreme test data.Considering that the maximum load of each test plan corresponds to the critical values of different stages at the stress-strain curve.And based on the preliminary analysis of the results, it is inferred that the maximum load has the greatest influence on burst proneness of the damaged coal samples.The test results will be grouped based on the maximum load, and the variation laws of burst proneness indexes will be further analyzed in the following sections.

| Elastic modulus and UCS
The elastic modulus and UCS showed the same variation laws, as shown in Figure 4A.Table 3 presents the range of values obtained from the test results.And the changes compared with the original test plan are shown in Figure 4B.When the maximum load is 9.6 kN, the relative increases of elastic modulus and UCS compared to the original test plan were 3.69%-8.16%and 5.22%-16.16%,respectively.As the loading-unloading rate decreases, the corresponding increase becomes greater.Uniaxial compressive load will compact the initial cracks inside the coal.Therefore, under the same uniaxial compression load, a smaller loading-unloading rate can result in a better compaction effect.The elastic modulus and UCS increase with increasing density of the coal sample.
When the maximum load reached 16 kN, the relative decreases of elastic modulus and UCS in test 6 compared to the original test plan were 2.49% and 0.54%, respectively.Meanwhile, in test 4, the relative increases of elastic modulus and UCS were 4.16% and 11.02%, respectively.In comparison, they were 2.60% and 3.39% in test 5, respectively.The reason is that the loading-unloading rate in test 6 is larger than that of tests 4 and 5, which caused a decrease in the compaction effect of uniaxial compression load on the compaction stage of coal samples in test 6.When the maximum load increases to 16 kN, the coal samples in the elastic stage will continue to be damaged due to cyclic loading-unloading.Due to the poor compaction effect in the previous stage, the damaged coal samples in test 6 will suffer more damage compared with tests 4 and 5, and the degree of damage is greater than that in the original state, resulting in a certain degree of decrease in both indexes.Comparing test 4 and test 5, the elastic modulus and UCS of test 4 are greater than those of test 5.The reason is that the damaged coal samples in test 4 have a better compaction effect on the compaction stage due to the smaller loading-unloading rate.After entering the elastic stage, the degree of damage is less than test 5.
When the maximum load reached 22.4 kN, the relative decreases of elastic modulus and UCS compared to the original test plan were 11.28%-12.47%and 18.94%-23.29%,respectively.The coal samples that get into the yield stage will continue to be damaged due to cyclic loading-unloading progress.Decreasing the loading-unloading rate improves the effectiveness of damage, while also leading to a greater reduction in the elastic modulus and UCS.
To summarize the variations of elastic modulus and UCS described above, both indexes increase when the maximum load is 30% of the UCS, when the low loading-unloading rate is applied, 50% of the UCS enlarge the indexes as well, the burst proneness of coal is enhanced under these conditions.However, both indexes decrease when the maximum load is 70% of the UCS.Under these conditions, the burst proneness of coal is decreased.The smaller the loading-unloading rate, the better the compaction effect in the compaction stage and the damage effect in the yield stage of the coal sample under cyclic loading-unloading progress.

| Elastic strain energy index and bursting energy index
The elastic strain energy index and the bursting energy index showed different variation laws from elastic modulus and UCS. Figure 5A illustrates the variation trend of both indexes.Table 4 presents the range of values obtained from the test results.And the changes compared with the original test plan are shown in Figure 5B.
When the maximum load is 9.6 kN, the relative increases of elastic strain energy index and bursting energy index compared to the original test plan were 20.20%-39.32% and 23.63%-32.83%,respectively.A higher number of loading-unloading cycles corresponds to a great increase.The compactness of damaged coal samples is improved in tests 1-3, due to the compaction effect of the uniaxial compression load.So the plastic deformation and the consumed energy decrease during the loading process, which leads to an increase in the elastic strain energy index.As stated in Section 4.1, the compaction effect leads to an increase in the UCS.So, there is an increase in the amount of strain energy that is accumulated before the stress-strain curve reaches its peak.Meanwhile, the compaction effect also leads to an increase in the elastic modulus.A higher elastic modulus is indicative of more brittle failure characteristics in coal samples, resulting in a shorter duration for the stress-strain curve to drop from peak to complete failure.So, there is a reduction in the amount of strain energy that is consumed after the peak.Eventually, resulting in a certain degree of increase in the bursting energy index.
When the maximum load reached 16 kN, the relative decreases of elastic strain energy index and bursting energy index in test 6 compared to the original test plan were 3.88% and 0.17%, respectively.Meanwhile, in test 4, the relative increases of both indexes were 12.92% and 11.54%, respectively, while in test 5, they were 6.76% and 0.86%, respectively.After entering the elastic stage, the degree of damage in test 6 increases under cyclic loading-unloading, more energy is consumed by the plastic deformation, resulting in a decrease in the elastic strain energy index.Meanwhile, there is a decrease in the accumulated strain energy before reaching the peak stress on the stress-strain curve, while the consumed strain energy after the peak increased, resulting in a decrease in the bursting energy index.Comparing test 4 and test 5, both indexes of test 4 are greater than those of test 5.The damaged coal samples in test 4 have a better compaction effect on the compaction stage due to the smaller loading-unloading rate, and the degree of damage is less than test 5.The coal samples in test 4 exhibit superior strength, which enables them to better withstand the plastic deformation.Meanwhile, the coal samples in test 4 exhibit less internal damage, such as cracks, in areas where stress concentration is more likely to induce plastic deformation.During the loading process, there is less plastic deformation generated, resulting in lower energy dissipation and a relatively larger elastic strain energy index.Simultaneously, there is more strain energy accumulated before the stress-strain curve reaches its peak in test 4, resulting in a higher bursting energy index.
When the maximum load reached 22.4 kN, the relative decreases of elastic strain energy index and bursting energy index compared to the original test plan were 11.44%-24.22%and 19.71%-26.03%,respectively.As the number of cycles increases, the amount of decrease in both indexes also increases.The damaged coal samples in the yield stage undergo increasing damage under cyclic loading-unloading.With the increase of cycles, the degree of damage also increases.During the loading process, more energy is dissipated due to plastic deformation, resulting in a greater reduction in the elastic strain energy index.Meanwhile, the stress-strain curve presents a certain degree of discontinuity due to the internal damage of the coal sample.The curve before the peak becomes no longer smooth and presents a serrated shape.The area surrounded by the curve and ε axis also relatively decreases in this stage, leading to a certain degree of reduction in the accumulated deformation energy before the peak stress, resulting in a decrease in the bursting energy index.
In summary, both indexes increase when the maximum load is 30% of the UCS, when the low loading-unloading rate is applied, 50% of the UCS enlarge the indexes as well.Under this condition, the coal burst proneness increases.The more the loading-unloading cycles, the greater the amount of increase.However, both indexes decrease when the  maximum load is 70% of the UCS.Under this condition, the coal burst proneness decreases.The more the loading-unloading cycles, the greater the amount of decrease.

| Duration of dynamic fracture
Figure 6A illustrates the variation of duration of dynamic fracture.Table 5 presents the range of values obtained from the test results.And the changes compared with the original test plan are shown in Figure 6B.When the maximum load is 9.6 kN, the damaged coal samples in tests 1-3 have a shorter duration of dynamic fracture compared to the original test plan after undergoing the compaction stage during uniaxial compression.The relative decrease was 6.75%-50.92%.As stated in Section 4.1, the smaller the loading-unloading rate, the larger the elastic modulus and UCS.The increase in stiffness and brittleness of coal samples results in a shorter duration of dynamic fracture.
When the maximum load reached 16 kN, the relative increase of duration of dynamic fracture in test 6 compared to the original test plan was 6.36%.Meanwhile, the relative decreases in tests 4 and 5 were 29.24% and 4.43%, respectively.The reasons for this phenomenon are consistent with the variation of elastic modulus and UCS under the same test conditions.The stiffness of coal increases with a larger elastic modulus, resulting in a shorter duration of dynamic fracture.
When the maximum load reached 22.4 kN, the relative increase in duration of dynamic fracture compared to the original test plan was 14.82%-42.54%.A decrease in the loading-unloading rate results in a more favorable damage effect on the coal samples, which leads to an increase in the duration of dynamic fracture.
The variation of duration of dynamic fractures under the test conditions follows the same pattern as the variations of the elastic modulus and UCS.As the elastic modulus and UCS increase, the duration of dynamic fracture decreases, and the coal burst proneness becomes stronger.
It should be noted that although the average values of duration of dynamic fracture for each test show a certain pattern of variation.But the individual data of duration of dynamic fractures for each coal sample sometimes exhibit significant dispersion.Even for coal samples under the same test, their results may differ by several times.Therefore, it is necessary to be cautious when only choosing the duration of dynamic fracture as the index parameter to evaluate the impact of MMD on the coal burst proneness.

| AE MONITORING RESULTS
To monitor the damage state of coal samples, AE was utilized.The present research utilized AE ringing counts, accumulated ringing counts, energy, and accumulated energy to represent the AE characteristics of coal samples throughout the testing process.The ringing counts can reflect the frequency of AE, and also reflect the amplitude of AE signal to a certain extent.The AE energy reflects the strength of AE. ringing counts and energy in the coal samples, which were high in magnitude and densely distributed.4][35] As the load increases, there is a gradual rise in both the ringing counts and energy, with the peak value reached when the load reaches its maximum.Subsequently, with the decrease of load, the ringing counts and energy continuously decrease, and eventually entered a "quiet period."As shown in Figure 7, it is also evident that with the increase of cycles, the maximum ringing counts and energy values gradually decrease.Indicates a gradual reduction in the degree of damage of the coal samples.When the load reached its maximum, the accumulated ringing counts and accumulated energy curves exhibit a section of obvious vertical rise, showing a "ladder" rising trend.However, as the cycles increase, its increment gradually decreases.Figure 8 shows the AE characteristics in tests 4-6 when the maximum load is 50% of the UCS.The coal samples undergo the compaction and elastic stage during the test process.In the initial stage of the first cyclic, the coal samples in tests 4-6 exhibited the same AE characteristics as tests 1-3.In comparison to the coal samples in tests 1-3, the maximum ringing counts and energy values in tests 4-6 significantly increased during each cycle.This phenomenon indicates that the degree of damage to the coal samples in the elastic stage increases when subjected to loading. Figure 8 demonstrates that the AE characteristics during each cycle did not show significant laws of variation with the increase of cycles.This indicates that the coal samples in the elastic stage do not suffer severe damage during the test process, and the degree of damage does not change significantly.Alternatively, coal samples at this stage may have a certain resistance to cyclic damage, and further research is needed to determine the specific reasons and significance of this phenomenon.The accumulated ringing counts and accumulated energy curves still show a "ladder" rising trend with the increase of cycles.
Figure 9 shows the AE characteristics in tests 7-9 when the maximum load is 70% of the UCS.During this process, the coal samples enter the yield stage under the load.In the initial loading stage of the first cyclic, it showed the same AE characteristics as described before.As the load continues to increase, the ringing counts and energy increase continuously.When the load reaches its maximum, the damaged coal samples in tests 7-9 exhibit higher maximum values of ringing counts and energy than tests 1-6.This phenomenon indicates a significant increase in the degree of damage to coal samples when subjected to loading after entering the yield stage.At the same time, the results indicate that the degree of damage increases with the increase of cycles, as evidenced by the continuous increase in the maximum ringing counts and energy values shown in the Figure 9.The accumulated ringing counts and accumulated energy curves still show a "ladder" rising trend.Meanwhile, with the increase of cycles, the increment also gradually increases.

| AE characteristics during the burst proneness indexes measuring process
To measure the burst proneness indexes of damaged coal samples, uniaxial compression was applied to the samples until failure, and the AE signals were monitored in real time during the process.Figure 10 illustrates the relationship between the elastic modulus of damaged coal samples with the AE ringing counts and energy.
As shown in Figure 10, the maximum ringing counts, accumulated ringing counts, maximum AE energy, and accumulated energy all exhibit consistent patterns with the variations of the elastic modulus.The elastic modulus increases with the variations in test conditions, the corresponding AE ringing counts and energy also increase.This is due to the fact that the damaged coal samples with higher elastic modulus possess greater resistance to deformation, and the more energy absorbed by the coal body before failure.Consequently, stronger AE signals are generated during the process of failure.

| SENSITIVITY ANALYSIS OF INFLUENCING FACTORS
Sensitivity analysis of influencing factors usually refers to the analysis of the sensitivity of independent variables to dependent variables.By studying the degree of influence  of different independent variables on a certain dependent variable, the independent variables that have the most significant impact can be identified.A common approach to sensitivity analysis is to use range values to assess the sensitivity of influencing factors.The larger the range value, the greater the influence of the independent variable to the dependent variable, indicating that the independent variable is more sensitive.Figure 11 illustrates the range values of each influencing factor to various burst proneness indexes.
The range values of elastic modulus, UCS, and duration of dynamic fracture exhibit similar variation laws under various influencing factors, as depicted in Figure 11A,B,E.A larger range value indicates a stronger influence of the influencing factor to the burst proneness index.The range values under the influence of maximum load are significantly larger than those under the influence of loading-unloading rate and loading-unloading cycles.For elastic modulus, they are 5.41 and 7.06 times larger, respectively; for UCS, they are 5.27 and 7.51 times larger, respectively; for duration of dynamic fracture, they are 3.38 and 3.83 times larger, respectively.On the other hand, the range values show little difference under the influence of loading-unloading rate and loading-unloading cycles.When compared to the range values under the influence of loading-unloading rate, the range values of elastic modulus, UCS, and duration of dynamic fracture under the influence of loading-unloading cycles decreased by 23.44%, 29.81%, and 11.66%, respectively.From the above analysis, it can be concluded that the sensitivity of maximum load, loading-unloading rate and loading-unloading cycles to the elastic modulus decreases under the test conditions, as well as to the UCS and duration of dynamic fracture.
The range values of elastic strain energy index and bursting energy index exhibit similar variation laws under various influencing factors, as depicted in Figure 11C,D.The range values under the influence of maximum load are also significantly larger than those under the influence of loading-unloading cycles and loading-unloading rate.For elastic strain energy index, they are 9.64 and 7.00 times larger, respectively; for bursting energy index, they are 14.39 and 10.37 times larger, respectively.Similarly, the range values also show little difference under the influence of loading-unloading rate and loading-unloading cycles.Compared with the range value under the influence of loading-unloading cycles, the range values of elastic strain energy index and bursting energy index under the influence of loading-unloading rate decreased by 27.37% and 27.94%, respectively.The sensitivity of maximum load, loading-unloading cycles, and loading-unloading rate to the elastic strain energy index decreases under the test conditions, as well as to the bursting energy index.

| DISCUSSION
Based on the sensitivity analysis described above, the most effective and the least favorable combination plans for reducing the burst proneness indexes under test conditions can be determined.The implementation of this process can provide basic data and reference opinions for the formulation of mining plans and safety measures in practical mining, which has practical significance.Figure 12 illustrates the horizontal variation trends of burst proneness indexes under the influence of various factors.
The elastic modulus can characterize the ability of coal to resist elastic deformation.The greater the elastic modulus, the greater the stiffness of the coal, the less likely it is to undergo deformation, and the stronger the burst proneness as well.The greater the UCS, elastic strain energy index, bursting energy index, and the shorter the duration of dynamic fracture, the stronger the burst proneness of coal.Based on Figure 12, the most effective combination plan and the least favorable combination plan under each burst proneness index are presented in Tables 6 and 7, respectively.
There is an equal and greatest sensitivity of maximum load to the five indexes.Therefore, the maximum load corresponding to any of the burst proneness indexes can be selected.Combining the results from Tables 6 and 7, it can be concluded that reducing the burst proneness indexes is most effective when the maximum load is 22.4 kN, but least favorable when it is 9.6 kN.
The influence sensitivity of loading-unloading rate to the elastic modulus, UCS, and duration of dynamic fracture is greater than that to the elastic strain energy index and bursting energy index.Therefore, the loading-unloading rate corresponding to the elastic modulus, UCS, or duration of dynamic fracture can be selected.Combining the results from Tables 6 and 7, it can be concluded that reducing the burst proneness indexes is most effective when the loading-unloading rate is 0.005 mm/s, but least favorable when it is 0.001 mm/s.
The influence sensitivity of loading-unloading cycles to the elastic strain energy index and bursting energy index is greater than that to the elastic modulus, UCS, and duration of dynamic fracture.Therefore, the loading-unloading cycles corresponding to the elastic strain energy index or bursting energy index can be selected.Combining the results from Tables 6 and 7, it can be concluded that reducing the burst proneness indexes is most effective when the loading-unloading cycles is 5, but least favorable when it is 7.
Under the test conditions, it is most effective to reduce the burst proneness when the maximum load is 22.4 kN, the loading-unloading rate is 0.005 mm/s, and the loading-unloading cycles is 5. Conversely, it is least favorable to reduce the burst proneness when the maximum load is 9.6 kN, the loading-unloading rate is 0.001 mm/s, and the loading-unloading cycles is 7.
For the most effective combination plan, the elastic modulus is 1.810 GPa, the UCS is 15.094 MPa, the elastic strain energy index is 7.114, the bursting energy index is 6.485, and the duration of dynamic fracture is 409.867ms.We compared the burst proneness indexes in the most effective combination plan with the original test plan, as shown in Figure 13.
From Figure 13, it can be seen that the burst proneness of the most effective combination plan has decreased to some extent compared with the original test plan.The elastic modulus, UCS, elastic strain energy index, and bursting energy index decreased by 5.93%, 9.89%, 2.02%, and 5.89%, respectively.The duration of dynamic fracture increased by 10.53%.Although the burst proneness of the most effective combination plan has declined, but according to the classification criteria of burst proneness in China (i.e., R C ≥ 14, W ET ≥ 5, K E ≥ 5, and 50 < DT ≤ 500), the most effective combination plan still exhibits a strong burst proneness similar to the original test plan.
It can be concluded that although some combinations of influencing factors can to some extent reduce the burst proneness of coal, the effect is very limited.In the actual mining process, under the influence of this combination of factors, the coal and rock masses surrounding the roadway will become loose, which is unfavorable for preventing coal burst accidents.Meanwhile, cyclic loading-unloading can enhance the burst proneness of coal under certain conditions.Therefore, to ensure the safety of coal mining, it is crucial to avoid the influence of MMD, especially to avoid the disturbances that would put the coal under low loading and low loading rate.

| CONCLUSIONS
To investigate the influence of MMD on the coal burst proneness, the present research conducted quasi-static uniaxial cyclic loading-unloading tests in the laboratory.The variation patterns of burst proneness indexes and the sensitivity of influencing factors were analyzed.The study has led to the following conclusions: (1) At a maximum load of 30% of the UCS, the compaction effect of the applied load leads to increased burst proneness.Smaller loading-unloading rates enhance this effect, resulting in a reduction of coal damage degree, manifested by a gradual reduction in the maximum AE ringing counts and energy.(2) When the maximum load is 50% of the UCS, burst proneness increases at lower loading-unloading rates but decreases after a threshold.The degree of damage shows no significant change with increasing loading-unloading cycles, while the AE ringing counts and energy show no obvious pattern of variation.
(3) At a maximum load of 70% of the UCS, burst proneness decreases due to entering the yield stage, while the degree of damage continues to increase with more loading-unloading cycles, which is evidenced by a gradual increase in the maximum AE ringing counts and energy.(4) Larger maximum loads in cyclic tests result in greater damage to coal samples, with corresponding increases in the maximum values of AE ringing counts and energy.(5) Through the sensitivity analysis of influencing factors, it can be concluded that the sensitivity of maximum load, loading-unloading rate and loading-unloading cycles to the elastic modulus decreases, as well as to the UCS and duration of dynamic fracture; and the sensitivity of maximum load, loading-unloading cycles and loading-unloading rate to the elastic strain energy index decreases, as well as to the bursting energy index.(6) Some influencing factors can marginally reduce coal burst proneness, but to ensure mining safety, it is crucial to avoid MMD that subjects the coal to low loading and loading rates.

F I G U R E 5
The test results (W ET and K E ). (A) Variation trend and (B) changes compared with original test plan.

F I G U R E 6 1 |
Figure7shows the AE characteristics in tests 1-3 when the maximum load is 30% of the UCS.Under this loading

F I G U R E 8
Acoustic emission characteristics of tests 4-6.(A) Ringing counts of test 4, (B) energy of test 4, (C) ringing counts of test 5, (D) energy of test 5, (E) ringing counts of test 6, and (F) energy of test 6.
Acoustic emission characteristics of tests 7-9.(A) Ringing counts of test 7, (B) energy of test 7, (C) ringing counts of test 8, (D) energy of test 8, (E) ringing counts of test 9, and (F) energy of test 9.

F
I G U R E 10 The relationship between elastic modulus and acoustic emission signals.(A) Ringing counts and (B) energy.F I G U R E 11 The range values.(A) E, (B) R C , (C) W ET , (D) K E , and (E) DT.

LIU ET AL. | 3693 F
I G U R E 12 The horizontal variation trends of burst proneness indexes.(A)E, (B) R C , (C)W ET , (D) K E , and (E) DT.

T A B L E 7 F
The least favorable combination plan.I G U R E 13 Comparison results of the indexes.
The orthogonal test plan.
T A B L E 2 F I G U R E 4 The test results (E and R C ). (A) Variation trend and (B) changes compared with original test plan.
T A B L E 3 Range of test results (E and R C ).
Range of test results (W ET and K E ).