# Energy Variation Law and Rockburst Characteristics of Coal under Cyclic Loading

Authors: Hongjun Guo; Ming Ji; Dapeng Liu; Mengxi Liu; Gaofeng Li; Jingjing Chen; Hongjie Chen
Journal: Shock and Vibration
 (2021)

---

## Abstract

Coal mining involves numerous challenges and safety risks owing to the complex engineering properties of coal bodies, which include discontinuities, heterogeneity, and anisotropy. In this paper, the strain energy during the coal deformation process is redivided in combination with cyclic loading and unloading tests to determine the energy evolution law and discuss the rockburst tendency characteristics. The results show that the elastic strain energy, and particularly the base-material strain energy, consistently dominates during the energy adjustment process, which is an important indicator of rockburst tendency. The elastic energy index and rebound deformation index also show that moderate plastic deformation (e.g., crack expansion and local penetration) can reduce the rockburst tendency level and prevent rockburst accidents. On the basis of the obtained results, precracking and pressure relief measures of blasting are adopted on site in advance of the working face, and good safety and economic benefits are achieved. These findings, thus, provide an important engineering reference for mines under similar conditions.


---

## Body

## 1. Introduction

Coal bodies are a special engineering rock mass with generally higher degrees of discontinuities, heterogeneity, and anisotropy than other rock types [1]. Coal bodies typically face complex genesis and stress environment conditions, large mining disturbances, and harsh production settings. Extensive research from a variety of perspectives has, therefore, aimed to comprehensively grasp the relevant characteristics of coal and effectively guide engineering practice, including studies on coal-rock interactions [2, 3], size effects [4, 5], bedding effects [6], gas content [7, 8], temperature [5, 9], water content [5, 10], fine and microcharacteristics [11–13], and acoustic emission characteristics [14, 15].Remarkable progress has been achieved in recent years regarding the mechanical properties and energy evolution of coal under cyclic loading [16–22]. Yang et al. [2] established and discussed the energy-driving mechanism of combined coal-rock failure based on the mechanical response, energy evolution, and deformation and failure characteristics. Li et al. [23] studied the seepage and damage evolution characteristics of gas-bearing coal under three cyclic loading and unloading stress paths. Zhang et al. [15] characterized the damage evolution process of raw coal samples using acoustic emission positioning technology, proposed a time-space dimension cluster analysis method based on the k-means algorithm, and determined useful information regarding instability signs. Liu et al. [24] proposed that the elastic energy index of coal reaches a maximum at the elastic-plastic critical point when a rockburst is most likely to occur. Numerical calculation methods have also been used to study coal rockburst tendencies.However, the abovementioned studies rarely addressed the influence of cracks on the energy evolution and rockburst characteristics of coal. Therefore, in this paper, the energy composition within coal bodies during the loading and unloading process is redivided considering the fracture strain energy [25], and the rockburst tendency characteristics are discussed on the basis of evolution law of each strain energy.


## 2. Experiment Overview

The coal sample used in the experiment was collected from the #8 coal seam in the third mining area of a mine in the Xianyang mining area and processed into standard cylinder specimens of Φ50 × H100 mm in accordance with national standards, as shown in Figure1.Figure 1
Coal samples.The experimental instrument is shown in Figure2, and the specific method is as follows:(1)
Conventional uniaxial compression experiments: the average uniaxial compressive strengthσc of the coal specimens is obtained by adopting the displacement control mode with a loading rate of 0.02 mm/s.(2)
Cyclic loading and unloading experiments: the displacement control mode and a loading/unloading rate of 0.02 mm/s are adopted. The change ofσ1 follows 0 ⟶ σ0 ⟶ σu ⟶ σ0 + dσ ⟶ σu ⟶ σ0 + 2dσ ⟶ … ⟶ σu ⟶ σ0 + ndσ, where σ0 = (75%–80%)σc, σu = (1%–5%)σc, dσ = 5%σc, and n is the cycles. This procedure is repeated until the coal sample is destroyed.Figure 2
SANS testing system at the China University of Mining and Technology.


## 3. Classification and Calculation Method of Strain Energy

The specimen is only affected by the axial load of the test machine in the uniaxial cyclic loading and unloading experiments. Figure3 shows the composition of the internal strain energy of the coal sample under one loading and unloading cycle, in which we and wp are the elastic strain energy and plastic strain energy, respectively, and σ1+ and σ1− are the loading stress and unloading stress.Figure 3
Internal strain energy of the coal sample.The strain energy can be expressed as(1)w=we+wp,w=∫εp1εe2σ1+dε1,we=∫εe1εe2σ1−dε1,where w is the total strain energy, and εp and εe satisfy(2)εp=εp2−εp1,εe=εe2−εe1,εp2=εe1.It can be seen from Figure3 that the strain recovery rate is different during unloading, which is related to the random distribution of grains and fractures in the coal body. When the stress environment changes, the grains can respond quickly, while the fracture response lags behind, which is beneficial to understand the coal’s dynamic failure [1]. Therefore, according to the composition and deformation characteristics of the coal body, the deformation can be divided into immediate recovery base-material deformation and delayed recovery fracture deformation (the internal cracks do not immediately change from compression to expansion). Figure 4 shows that the rebound deformation in the initial unloading stage is mainly base-material elastic deformation, which changes approximately linearly [25]. The section with good linear rebound is selected, and a tangent AC is drawn. The area of ABC is then the base-material strain energy wg during the load cycle, that is,(3)wg=12σ1uεg,where σ1u is the stress at an unloading point and εg is the reversible strain of the coal base-material.Figure 4
Classification and calculation of strain energy.The fracture strain energywc is then(4)wc=we−wg.The relationship between the strain energy, stability, and rockburst tendency of coal under cyclic loading and unloading can be analyzed by equations (1)–(4).


## 4. Experiment Analysis and Discussion

### 4.1. Result Analysis

The stress-strain curves of the conventional uniaxial compression experiments are shown in Figure5, yielding an average uniaxial compressive strength of 19.53 MPa.Figure 5
Stress-strain curves of the uniaxial compression experiments.According to the experimental scheme, 75%σc is selected as the initial unloading point. The stress-strain curves of each coal sample under cyclic loading and unloading are shown in Figure 6.Figure 6
Stress-strain curves from cyclic loading and unloading. (a) #1. (b) #2. (c) #3. (d) #4. (e) #5.
(a)(b)(c)(d)(e)Figure6 shows that specimens #1–#5 were destroyed after 12, 12, 4, 1, and 9 loading and unloading cycles, respectively. Specimens #1, #2, and #5 experienced more loading and unloading cycles and were, therefore, selected for further analysis to study the energy evolution in each cycle.The strain energy is calculated using equations (1)–(4) according to the abovementioned classification and calculation method of strain energy. The energy-stress level curves are shown in Figure 7. The stress level represents the ratio of the load at each unloading point to the failure strength of the respective coal sample.Figure 7
Energy-stress level curves.
(a)(b)Figure7 shows a consistent variation trend of the internal strain energy of each coal sample. The elastic strain energy increases with increasing stress level (i.e., number of cycles). Stress levels less than 90% increase approximately linearly, whereas the plastic strain energy initially decreases and then rapidly increases during the 1-2 loading and unloading cycles prior to failure. Additional changes are not substantial during the intermediate process, and base-material strain energy changes are close to those of the elastic strain energy. The change of fracture strain energy is not significant under low-stress conditions, but increases when the stress level exceeds 90%. It can, therefore, be concluded that the rapid change of each strain energy under high-stress conditions can be used as an indicator prior to coal failure.The energy-ratio-stress-level curves are shown in Figure8 to further explore the relationship between each strain energy and input energy.Figure 8
Relationship between the strain energy ratio and stress level. (a) #1. (b) #2. (c) #5.
(a)(b)(c)Figure8 shows that, in different loading and unloading cycles, approximately 80%–95% of the input energy is transformed into elastic strain energy. When the stress level exceeds 90% (i.e., 1-2 loading and unloading cycles prior to specimen failure), the elastic strain energy conversion rate significantly decreases, the plastic strain energy increases, and the coal enters the failure process, whereas within the elastic strain energy, the ratio of base-material strain energy to fracture strain energy essentially remains at 3–5:1. This indicates that the recovery of unloading deformation is mainly base-material rebound prior to failure.


### 4.2. Discussion and Application

#### 4.2.1. Elastic Energy Index

Equation (5) is defined as the elastic energy index, which characterizes the rockburst tendency of coal and rock. Larger values are associated with higher rockburst tendencies. The values under different stress levels are shown in Figure 9.(5)WET=wewp.Figure 9
Relationship between the elastic energy index and stress level.Figure9 shows that the elastic energy index roughly undergoes three processes with increasing stress level including a rapid increase and fluctuating increases and decreases. This implies that the coal body has the highest rockburst tendency when it changes from the elastic to plastic state. Under continued loading and unloading, the energy consumption of the plastic deformation strongly increases, which reduces the brittleness and elastic energy index of the coal body, namely, the rockburst tendency decreases.


#### 4.2.2. Rebound Deformation Index

Equation (6) is defined as rebound deformation index, which reflects the development degree of recoverable fractures in coal and rock and deformation recovery speed during the unloading process. Larger index values are associated with a lower degree of fracture development, faster rebound deformation, and higher rockburst tendency. The relationship with stress level is shown in Figure 10.(6)KRD=wgwc.Figure 10
Relationship between the rebound deformation index and stress level.Figure10 shows that the rebound deformation index remains essentially constant at 3–5 and that the unloading rebound is rapid. When the stress level exceeds 90%, the rebound deformation index value continuously decreases, which indicates that internal fractures have developed and expanded in the coal body, accompanied by partial crack coalescence and other irreversible deformation until the main crack forms. Before the coal body is destroyed, the low rebound deformation index state is beneficial for preventing and controlling rockburst accidents.Table1 lists the rockburst tendency indicators of the #8 coal seam.Table 1
Measurement results of the coal seam rockburst tendency.
DT (ms)WETKEσc (MPa)Measured results1166.43.212.919.5Evaluation interval>5002–5>5>14Index rockburst categoryIIIIIIIIIEvaluation rankIII, strong rockburst tendencyI- nonrockburst tendency; II- weak rockburst tendency; III- strong rockburst tendency.The values in Table1 indicate that the #8 coal seam has a high rockburst tendency and the elastic energy index is also notably lower than the value of each loading and unloading process in Figure 9. To some extent, this indicates that the coal seam has a high rockburst risk during mining and excavation disturbances in the production process, which is also confirmed by the statistics presented in Table 2. The rockburst location is shown in Figure 11.Table 2
Statistics of roadway rockburst in the third mining area.
FrequencyLocation of occurrenceSite description1Transportation roadway head-on 50 m backwardThe floor heave is about 1 m, accompanied by dense and loud coal guns2Ventilation roadway corresponding to transportation roadway head-on 50 m forwardThe floor heave is about 1.2 m, the roof is a seriously sinking or hanging bag, and many bolts (cables) in the roof and sides are broken, accompanied by dense and loud coal guns3Track roadway corresponding to transportation roadway head-on 50 m backwardThe floor heave is about 0.5 m, one roof falls, and the bolts (cables) in the roof and sides are broken individuallyThe statistics covered a period of 22 days.Figure 11
Diagram of the mining and excavation of the third mining area.The results indicate that, to reduce the influence of mining and excavation disturbances on the roadway and reduce or avoid rockburst accidents, part of the base-material strain energy that can be instantly released in the coal body is converted into fracture strain energy with a delayed release. This reduces the instantaneous release strength of the rockburst coal body and relieves the immediate danger. The blasting precracking and pressure relief measures in the advanced working face were measured at the study site, and the blasting layout of the coal body in the roadway mining side is shown in Figure12. The roof blasting hole and charge design are shown in Figure 13 according to the structural characteristics of the roadway roof. The implementation effect is good, and safer mining and higher social and economic benefits are achieved.Figure 12
Blasting layout of the roadway side.Figure 13
Blasting layout of the roadway roof. (a) Blasting layout of the roadway roof. (b) Charge design.
(a)(b)


## 4.1. Result Analysis

The stress-strain curves of the conventional uniaxial compression experiments are shown in Figure5, yielding an average uniaxial compressive strength of 19.53 MPa.Figure 5
Stress-strain curves of the uniaxial compression experiments.According to the experimental scheme, 75%σc is selected as the initial unloading point. The stress-strain curves of each coal sample under cyclic loading and unloading are shown in Figure 6.Figure 6
Stress-strain curves from cyclic loading and unloading. (a) #1. (b) #2. (c) #3. (d) #4. (e) #5.
(a)(b)(c)(d)(e)Figure6 shows that specimens #1–#5 were destroyed after 12, 12, 4, 1, and 9 loading and unloading cycles, respectively. Specimens #1, #2, and #5 experienced more loading and unloading cycles and were, therefore, selected for further analysis to study the energy evolution in each cycle.The strain energy is calculated using equations (1)–(4) according to the abovementioned classification and calculation method of strain energy. The energy-stress level curves are shown in Figure 7. The stress level represents the ratio of the load at each unloading point to the failure strength of the respective coal sample.Figure 7
Energy-stress level curves.
(a)(b)Figure7 shows a consistent variation trend of the internal strain energy of each coal sample. The elastic strain energy increases with increasing stress level (i.e., number of cycles). Stress levels less than 90% increase approximately linearly, whereas the plastic strain energy initially decreases and then rapidly increases during the 1-2 loading and unloading cycles prior to failure. Additional changes are not substantial during the intermediate process, and base-material strain energy changes are close to those of the elastic strain energy. The change of fracture strain energy is not significant under low-stress conditions, but increases when the stress level exceeds 90%. It can, therefore, be concluded that the rapid change of each strain energy under high-stress conditions can be used as an indicator prior to coal failure.The energy-ratio-stress-level curves are shown in Figure8 to further explore the relationship between each strain energy and input energy.Figure 8
Relationship between the strain energy ratio and stress level. (a) #1. (b) #2. (c) #5.
(a)(b)(c)Figure8 shows that, in different loading and unloading cycles, approximately 80%–95% of the input energy is transformed into elastic strain energy. When the stress level exceeds 90% (i.e., 1-2 loading and unloading cycles prior to specimen failure), the elastic strain energy conversion rate significantly decreases, the plastic strain energy increases, and the coal enters the failure process, whereas within the elastic strain energy, the ratio of base-material strain energy to fracture strain energy essentially remains at 3–5:1. This indicates that the recovery of unloading deformation is mainly base-material rebound prior to failure.


## 4.2. Discussion and Application

### 4.2.1. Elastic Energy Index

Equation (5) is defined as the elastic energy index, which characterizes the rockburst tendency of coal and rock. Larger values are associated with higher rockburst tendencies. The values under different stress levels are shown in Figure 9.(5)WET=wewp.Figure 9
Relationship between the elastic energy index and stress level.Figure9 shows that the elastic energy index roughly undergoes three processes with increasing stress level including a rapid increase and fluctuating increases and decreases. This implies that the coal body has the highest rockburst tendency when it changes from the elastic to plastic state. Under continued loading and unloading, the energy consumption of the plastic deformation strongly increases, which reduces the brittleness and elastic energy index of the coal body, namely, the rockburst tendency decreases.


### 4.2.2. Rebound Deformation Index

Equation (6) is defined as rebound deformation index, which reflects the development degree of recoverable fractures in coal and rock and deformation recovery speed during the unloading process. Larger index values are associated with a lower degree of fracture development, faster rebound deformation, and higher rockburst tendency. The relationship with stress level is shown in Figure 10.(6)KRD=wgwc.Figure 10
Relationship between the rebound deformation index and stress level.Figure10 shows that the rebound deformation index remains essentially constant at 3–5 and that the unloading rebound is rapid. When the stress level exceeds 90%, the rebound deformation index value continuously decreases, which indicates that internal fractures have developed and expanded in the coal body, accompanied by partial crack coalescence and other irreversible deformation until the main crack forms. Before the coal body is destroyed, the low rebound deformation index state is beneficial for preventing and controlling rockburst accidents.Table1 lists the rockburst tendency indicators of the #8 coal seam.Table 1
Measurement results of the coal seam rockburst tendency.
DT (ms)WETKEσc (MPa)Measured results1166.43.212.919.5Evaluation interval>5002–5>5>14Index rockburst categoryIIIIIIIIIEvaluation rankIII, strong rockburst tendencyI- nonrockburst tendency; II- weak rockburst tendency; III- strong rockburst tendency.The values in Table1 indicate that the #8 coal seam has a high rockburst tendency and the elastic energy index is also notably lower than the value of each loading and unloading process in Figure 9. To some extent, this indicates that the coal seam has a high rockburst risk during mining and excavation disturbances in the production process, which is also confirmed by the statistics presented in Table 2. The rockburst location is shown in Figure 11.Table 2
Statistics of roadway rockburst in the third mining area.
FrequencyLocation of occurrenceSite description1Transportation roadway head-on 50 m backwardThe floor heave is about 1 m, accompanied by dense and loud coal guns2Ventilation roadway corresponding to transportation roadway head-on 50 m forwardThe floor heave is about 1.2 m, the roof is a seriously sinking or hanging bag, and many bolts (cables) in the roof and sides are broken, accompanied by dense and loud coal guns3Track roadway corresponding to transportation roadway head-on 50 m backwardThe floor heave is about 0.5 m, one roof falls, and the bolts (cables) in the roof and sides are broken individuallyThe statistics covered a period of 22 days.Figure 11
Diagram of the mining and excavation of the third mining area.The results indicate that, to reduce the influence of mining and excavation disturbances on the roadway and reduce or avoid rockburst accidents, part of the base-material strain energy that can be instantly released in the coal body is converted into fracture strain energy with a delayed release. This reduces the instantaneous release strength of the rockburst coal body and relieves the immediate danger. The blasting precracking and pressure relief measures in the advanced working face were measured at the study site, and the blasting layout of the coal body in the roadway mining side is shown in Figure12. The roof blasting hole and charge design are shown in Figure 13 according to the structural characteristics of the roadway roof. The implementation effect is good, and safer mining and higher social and economic benefits are achieved.Figure 12
Blasting layout of the roadway side.Figure 13
Blasting layout of the roadway roof. (a) Blasting layout of the roadway roof. (b) Charge design.
(a)(b)


## 4.2.1. Elastic Energy Index

Equation (5) is defined as the elastic energy index, which characterizes the rockburst tendency of coal and rock. Larger values are associated with higher rockburst tendencies. The values under different stress levels are shown in Figure 9.(5)WET=wewp.Figure 9
Relationship between the elastic energy index and stress level.Figure9 shows that the elastic energy index roughly undergoes three processes with increasing stress level including a rapid increase and fluctuating increases and decreases. This implies that the coal body has the highest rockburst tendency when it changes from the elastic to plastic state. Under continued loading and unloading, the energy consumption of the plastic deformation strongly increases, which reduces the brittleness and elastic energy index of the coal body, namely, the rockburst tendency decreases.


## 4.2.2. Rebound Deformation Index

Equation (6) is defined as rebound deformation index, which reflects the development degree of recoverable fractures in coal and rock and deformation recovery speed during the unloading process. Larger index values are associated with a lower degree of fracture development, faster rebound deformation, and higher rockburst tendency. The relationship with stress level is shown in Figure 10.(6)KRD=wgwc.Figure 10
Relationship between the rebound deformation index and stress level.Figure10 shows that the rebound deformation index remains essentially constant at 3–5 and that the unloading rebound is rapid. When the stress level exceeds 90%, the rebound deformation index value continuously decreases, which indicates that internal fractures have developed and expanded in the coal body, accompanied by partial crack coalescence and other irreversible deformation until the main crack forms. Before the coal body is destroyed, the low rebound deformation index state is beneficial for preventing and controlling rockburst accidents.Table1 lists the rockburst tendency indicators of the #8 coal seam.Table 1
Measurement results of the coal seam rockburst tendency.
DT (ms)WETKEσc (MPa)Measured results1166.43.212.919.5Evaluation interval>5002–5>5>14Index rockburst categoryIIIIIIIIIEvaluation rankIII, strong rockburst tendencyI- nonrockburst tendency; II- weak rockburst tendency; III- strong rockburst tendency.The values in Table1 indicate that the #8 coal seam has a high rockburst tendency and the elastic energy index is also notably lower than the value of each loading and unloading process in Figure 9. To some extent, this indicates that the coal seam has a high rockburst risk during mining and excavation disturbances in the production process, which is also confirmed by the statistics presented in Table 2. The rockburst location is shown in Figure 11.Table 2
Statistics of roadway rockburst in the third mining area.
FrequencyLocation of occurrenceSite description1Transportation roadway head-on 50 m backwardThe floor heave is about 1 m, accompanied by dense and loud coal guns2Ventilation roadway corresponding to transportation roadway head-on 50 m forwardThe floor heave is about 1.2 m, the roof is a seriously sinking or hanging bag, and many bolts (cables) in the roof and sides are broken, accompanied by dense and loud coal guns3Track roadway corresponding to transportation roadway head-on 50 m backwardThe floor heave is about 0.5 m, one roof falls, and the bolts (cables) in the roof and sides are broken individuallyThe statistics covered a period of 22 days.Figure 11
Diagram of the mining and excavation of the third mining area.The results indicate that, to reduce the influence of mining and excavation disturbances on the roadway and reduce or avoid rockburst accidents, part of the base-material strain energy that can be instantly released in the coal body is converted into fracture strain energy with a delayed release. This reduces the instantaneous release strength of the rockburst coal body and relieves the immediate danger. The blasting precracking and pressure relief measures in the advanced working face were measured at the study site, and the blasting layout of the coal body in the roadway mining side is shown in Figure12. The roof blasting hole and charge design are shown in Figure 13 according to the structural characteristics of the roadway roof. The implementation effect is good, and safer mining and higher social and economic benefits are achieved.Figure 12
Blasting layout of the roadway side.Figure 13
Blasting layout of the roadway roof. (a) Blasting layout of the roadway roof. (b) Charge design.
(a)(b)


## 5. Conclusions

Uniaxial cyclic loading and unloading experiments and a field study were performed to address the strain energy evolution of coal. The conclusions are summarized as follows:(1)
The composition of strain energy in a coal body during loading and unloading is redivided and calculated at different stress levels.(2)
The internal strain energy of each coal sample shows a consistent trend with increasing stress level (i.e., loading and unloading cycle). The elastic strain energy accounts for 80%–95% of the input energy, in which the base-material strain energy has a dominant advantage and both increase continuously. The plastic strain energy initially decreases, then fluctuates, and rises rapidly with increasing stress level. The fracture strain energy increases when the stress level exceeds 90%. The rapid change of each strain energy under high stress can be used as an indicator of coal failure.(3)
The elastic energy index and rebound deformation index reflect the rockburst tendency characteristics of coal to a certain extent, and moderate plastic deformation (e.g., crack expansion and local coalescence) is beneficial to prevent rockbursts.(4)
The safety and economic benefits of the field practice are good, which verifies the promising nature of the results obtained here and provides engineering guidance with substantial application value.



---

*Source: 5528555-2021-05-25.xml*