# Hierarchic Analysis Method to Evaluate Rock Burst Risk

Authors: Ming Ji; Hong-jun Guo; Yi-dong Zhang; Tao Li; Lin-sheng Gao
Journal: Mathematical Problems in Engineering
 (2015)

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## Abstract

In order to reasonably evaluate the risk of rock bursts in mines, the factors impacting rock bursts and the existing grading criterion on the risk of rock bursts were studied. By building a model of hierarchic analysis method, the natural factors, technology factors, and management factors that influence rock bursts were analyzed and researched, which determined the degree of each factor’s influence (i.e., weight) and comprehensive index. Then the grade of rock burst risk was assessed. The results showed that the assessment level generated by the model accurately reflected the actual risk degree of rock bursts in mines. The model improved the maneuverability and practicability of existing evaluation criteria and also enhanced the accuracy and science of rock burst risk assessment.


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## Body

## 1. Introduction

Rock bursts are dynamic disasters in coal mines involving coal or rock. When the strength limit of the coal rock mass mechanical system is reached, the energy accumulated in the mine roadway and the coal rock around the stop is released suddenly, sharply, and violently. The power generated by these explosive accidents throws coal and rock into the roadways. Generally, the coal rock mass vibrates, and the explosion destroys the supports, facility, and roadways and can also result in human casualties. Rock bursts may also lead to other mine disasters such as gas and coal dust explosions, fires, floods, and destruction of the ventilation systems and even cause the ground above to shake and damage to buildings [1–3].Rock bursts are a typical dynamic disaster in the coal mining process and are a direct threat to coal production and the safety of persons and property. Rock bursts have become a topic of interest in rock mechanics research. They are influenced by many factors, happen suddenly, and are highly destructive. Therefore, it is essential to provide a theoretical basis for controlling rock bursts; this can be done by studying regular patterns and precursor information to evaluate the risk degree of the occurrence of rock bursts [3].Mu et al. [4, 5] studied the mechanism of roof strata impacting coal bursts by physical simulation experiments, UDEC discrete element numerical simulations, theoretical analysis, and engineering practices. Then, they proposed the principle of coal rock burst failure and roof strata inducing burst and the damage criterion for rock bursts. Their work provided guidelines for the prevention and control of rock bursts.Li et al. [6] simulated the impact of faults on mine pressure distribution in coal mining processes. They studied the change law of the peak supporting pressure in the working face under different conditions such as different fault dips, strength, fall, and main roof thickness. The results showed that peak supporting pressure decreased when the fault dip decreased as the working face advanced up the fault wall to the fault. Conversely, the peak increased rapidly first and then stayed steady when the main roof’s strength increased. The rock burst hazard is less likely in the former condition than in the latter.He et al. [7] used a microseismic monitoring system to study the temporal and spatial variations of the mining processes in the working face of the Huating coal mine, which is in an earthquake zone: synclinal axis is prone to strong mining earthquake and high impact force; the cycle of strong mining earthquake is short and of high frequency, and before strong mining earthquake occurred, the vibration energy appeared “calm” or downward trend, which along with the number rising energy shock can be used as precursory information for predicting the synclinal strong mining earthquake.Dou et al. [8, 9] studied monitoring principles and classification criteria to forecast shock hazards and formed the temporal classification prediction system for rock bursts. Practice has proved that this technology greatly improved the accuracy of the prediction of rock bursts.Ge et al. [10], Yi et al. [11], and Li et al. [12] used a fuzzy evaluation model and analytic hierarchy process to study the degree of influence of each factor in rock bursts and to determine the danger level of rock bursts in order to provide a feasible method for mine evaluation and the prediction of dynamic disasters of rock bursts.Song et al. [13] studied the relationship between entropy equation and dissipative structures and proposed a system of rock burst activity and analyzed it by its entropy. The results showed that rock bursts generally occur in dissipative structures. Then, they would form a new and ordered structure and achieved good results through practical application in Yanbei mine.Adoko et al. [14] used a fuzzy inference system, adaptive neural fuzzy inference system, and measured data to study the relationship between a rock burst and its influencing factors and to predict the intensity of rock bursts under mitigating conditions. Their method was in good agreement with actual situations, suggesting that it is effective for predicting the impact of mine dangers.Dong et al. [15, 16] used the engineering of 36 mines from home and abroad in rock burst conditions and data for training samples and established a random forest analysis model of rock burst grade determination. At the same time, they used the samples that did not participate in the training sample for model testing and evaluation, and the results highly coincided with actual records. Compared to the SVM and neural network method, the false positive rate of the random forest analysis model was reduced by 10% and 20%, respectively, and it provided an effective method to determine the grade of rock bursts.


## 2. Rock Burst Evaluation Basis and Risk Level of the Research Object

Existing research on the basis of magnitude strength and throw coal categorized rock bursts into four levels: micro shock (level I), weak shock (level II), medium impact (level III), and shock (level IV). The risk classification bases are shown in Table1.Table 1
Magnitude strength and throw coal method of rock burst evaluation.
Magnitude strength
Weight of thrown coal/t
Risk level
<1
5
Micro shock (level I)
<1
5–10
Weak shock (level II)
1-2
10–50
Medium impact (level III)
>2
>50
Shock (level IV)The rock burst risk rating of ten mines which followed the standard in Table1 was shown in Table 2.Table 2
Research mine rock burst risk rating.
Mine number
1
2
3
4
5
6
7
8
9
10
Risk rating
II
III
IV
IV
I
III
II
II
IV
IVThe weight of thrown coal is not easy to determine and divide and fewer influence factors were considered in the classification method above, so the operability of the method is poor, and it should not be full used in comprehensive evaluation of rock burst influence factors analysis. And the coal magnitude strength and the weight of thrown coal also have little effect in control or reduce the influence of coal rock burst.


## 3. Rock Burst Influence Factors Analysis

The reasons for the occurrence of rock bursts are complex and various and can generally be divided into three types: natural factors, technical factors, and organizational management. Natural factors include mining depth, mechanical properties of coal and rock, geological structure, coal thickness, and burst tendency of coal rock. Technical factors include roof control, degree of production concentration, pressure relief, and rings of coal burst. Organizational management factors include investments, such as improper measures taken and training, as shown in Figure1.Figure 1
Rock burst influence factors.


## 4. Establishing the Analytic Hierarchy Process (AHP) Model

In order to improve the operability and practicability of evaluations on the basis of risk grades, analytic hierarchy process (AHP) model was established to grade evaluations and provide guidance.


### 4.1. The Principle of Analytic Hierarchy Process (AHP)

Analytic hierarchy processes regard complicated multiobjective decision-making problems as a system in which the target is decomposed into multiple goals or standards and multiple indices of several levels through the qualitative index fuzzy quantification method to calculate single hierarchy sorting and total ordering.Hierarchic analysis method can be simplified into following steps.(1)
Construction of judgment matrix: the judgment matrix is used to represent the importance of every element relative to one of the upper elements, the form of which is shown in Table3. Dij is the element judgment matrixP and is given based on the 1–9 scale put forward by Saaty [17], as shown in Table 4.
(2)
The weight and maximum eigenvalueλmax of judgment matrix.
(a)
Calculation ofOi product of elements in every row of judgment matrix is as follows:(1)Oi=∏j=1ndij,i=1,2,3,…,n.
(b)
Calculation ofvth root of Oi is as follows:(2)Ei¯=Oin.
(c)
Standardization of the matrixE¯=[E¯1,E¯2,…,E¯n]T is as follows:(3)Ei=Ei¯∑i=1nEi¯.
E
=
[
E
1
,
E
2
,
…
,
E
n
]
T is the eigenvector figured out.
(d)
Calculation ofλmax maximum eigenvalue of eigenvector is as follows:(4)λmax⁡=1v∑i=1VPEiEi.
(3)
Consistency check of judgment matrix includes the following.
(a)
Calculation of consistency indexCI is as follows:(5)CI=λmax⁡-vv-1.
(b)
Verification of corresponding average random consistency indexRI is as shown in Table 5.
(c)
Calculation of consistency ratioCR is as follows:(6)CR=CIRI.
When CR < 0.10, the consistency of the judgment matrix is considered reasonable, or proper correction should be made to the judgment matrix.Table 3
Judgment matrix.
Judgment matrixP
D
1
D
2
⋯
D
n
D
1
D
11
D
12
⋯
D
1
n
D
2
D
21
D
22
⋯
D
2
n
⋮
⋮
⋮
⋮
⋮
D
n
D
n
1
D
n
2
⋯
D
n
nTable 4
The relative importance judgment of each element.
Scale
Meaning
1
The importance ofDi and Dj is equal
3
D
i and Dj are slightly important
5
D
i and Dj are obviously important
7
D
i and Dj are strongly important
9
D
i and Dj are vitally important
2, 4, 6, 8
The median of two adjacent judgments described above
Reciprocal
D
i
j
=
1
D
j
iTable 5
Average random consistency index RI.
n
1
2
3
4
5
6
7
8
9
RI
0
0
0.58
0.9
1.12
1.24
1.32
1.41
1.45


### 4.2. Construction of Risk Evaluation Indices of Impulsion Pressure

#### 4.2.1. Construction of Index Judgment Matrix

According to the hierarchical structure diagrams of factors affecting impulsion pressure (shown in Figure1), a preferential judgment matrix can be established as follows:(1)
Judgment matrixA-B is shown in Table 6.(2)
Judgment matrixB1-C is shown in Table 7.(3)
Judgment matrixB2-C is shown in Table 8.(4)
Judgment matrixB3-C is shown in Table 9.Table 6
Judgment matrixA-B and parameters.
Natural factors
Geological factors
Organization management factors
Weight
Maximum eigenvalue
Consistency ratio
Natural factors
1
3
4
0.6337
3.0092
0.0089 < 0.10
Geological factors
1/3
1
1
0.1919
Organization management factors
1/4
1
1
0.1744Table 7
Judgment matrixB1-C and parameters.
Judgment matrix
Mining depth
Mechanical properties of coal and rock
Geological structure
Coal thickness
Burst tendency of coal rock
Weight
Maximum eigenvalue
Consistency ratio
Mining depth
1
1/2
4
3
3
0.2636
5.0721
0.0161 < 0.1
Mechanical properties of coal and rock
2
1
7
5
5
0.4758
Geological structure
1/4
1/7
1
1/2
1/3
0.0538
Coal thickness
1/3
1/5
2
1
1
0.0981
Burst tendency of coal rock
1/3
1/5
3
1
1
0.1087Table 8
Judgment matrixB2-C and parameters.
Judgment matrix
Roof control
Degree of production concentration
Pressure relief
Rings of coal burst
Weight
Maximum eigenvalue
Consistency ratio
Roof control
1
1/3
1/5
2
0.1098
4.0201
0.0075 < 0.10
Degree of production concentration
3
1
1/2
5
0.3005
Pressure relief
5
2
1
7
0.5267
Rings of coal burst
1/2
1/5
1/7
1
0.0630Table 9
Judgment matrixB3-C and parameters.
Judgment matrix
Investment
Prevention measures
Training
Weight
Maximum eigenvalue
Consistency ratio
Investment
1
1/3
2
0.2493
3.0536
0.0515 < 0.10
Prevention measures
3
1
3
0.5936
Training
1/2
1/3
1
0.1571Based on judgment matrix constructed, the weight of every factor can be figured out by using Matlab [18]. The results are shown in Table 10.Table 10
Every factor weight summary table.
First grade index
Weight
Second index
Weight
Analysis on factors affecting impulsion pressure
Natural factors
0.10473
Mining depth
0.16705
Mechanical properties of coal and rock
0.30154
Geological structure
0.034103
Coal thickness
0.062147
Technical factors
0.63699
Burst tendency of coal rock
0.06887
Roof control
0.021066
Degree of production concentration
0.057676
Pressure relief
0.10109
Organization management factors
0.25828
Rings of coal burst
0.012089
Investment
0.043473
Prevention measures
0.10351
Training
0.027386


#### 4.2.2. Quantization and Standardization of the Risk Index of Rock Bursts

According to information on rock bursts in mines in China, the mining depth, gas content, and coal seam thickness, and so forth can be found. However, in order to meet the requirements of the model, it is necessary to quantify the qualitative description in the sample. The quantitative methods are as follows.(1)
Mining depth: Statistical analysis shows that the deeper the mining depth, the higher the possibility of a rock burst occurring. The quantitative values are shown in Table11.(2)
Mechanical characteristics of coal and rock: Generally, for coal and rock, the more the energy retention is internally and the less the energy is released, the more the possibility of rock bursts occurs. The impact energy index and elastic energy index to characterize the mechanical properties of coal and rock are shown in Table12.(3)
Geological structure: The power in the movement of strata generates a variety of geological structures, such as folds and faults, which have a greater effect on rock bursts.According to the relationship between the number of rock bursts and geological structures in coal mines, conclusions were drawn as detailed in Table13.(4)
Coal seam thickness: According to statistics, coal seam thickness relates to the occurrence of rock bursts, corresponding to results in Table14.(5)
Burst tendency of coal rock: Rock bursts can occur in any coal seam. The more brittle and hard the coal is, the less the impact energy is needed and the more it is likely to burst. So, impact energy index, elastic energy index, and dynamic destruction time are generally used to measure the possibility. The quantitative results are given in Table15.(6)
Roof control: The occurrence of a rock burst is influenced by the strata mainly above the coal seam, which has great intensity and thickness, and the method of processing the roof such as packing and caving. The quantitative values are given in Table16.(7)
Pressure relief circumstances: According to the actual effects of taking preventative measures, such as pressure relief blasting, drill hole pressure relief, and mining liberated seams, the likelihood of rock bursts occurring changes. The scores are given in Table17.(8)
The other factors and quantitative scores are shown in Table18.Table 11
Mining depth and quantitative scores.
Mining depth/m
<350
350–500
500–800
800–1000
>1000
Scores
2
4
6
8
10Table 12
Physical and mechanical characteristics of coal and surrounding rock and quantitative scores.
Impact energy index
<1
1–1.5
1.5–3
3–5
>5
Elastic energy index
<1
1-2
2–3.5
3.5–5
>5
Scores
2
4
6
8
10Table 13
Geological structure and quantitative scores.
Geological structure types
Local anomaly
Local structure anomaly
Coal seam thickness variation, thinning and thinning out, and cavity
Roof and floor fold
Downfold, upfold, and fault
Scores
2
4
6
8
10Table 14
Coal seam thickness and quantitative scores.
Coal seam thickness/m
<2.0
2.0–4.0
4.0–6.0
6.0–8.0
>8.0
Scores
2
4
6
8
10Table 15
Coal rock burst tendency and quantitative scores.
Elastic energy index
<1.5
1.5–3.0
3.0–5.0
5.0–7.0
>7.0
Dynamic failuretime/ms
<2.0
2.0–3.0
3.0–4.0
4.0–5.0
>5.0
Scores
2
4
6
8
10Table 16
Roof control and quantitative scores.
Distance from hard and thick roof  to coal seam/m
<100
100–80
80–60
60–40
<40
Scores
2
4
6
8
10Table 17
Pressure relief circumstances and quantitative scores.
Probability of stress reduction/%
<25
25–40
40–55
55–80
>80
Scores
2
4
6
8
10Table 18
The other factors and quantitative scores.
Degree of production centralization
None
Low
Medium
Relatively high
High
Rings of coal burst
None
Few
Several times
Frequently
Uninterrupted
Investment
High
Relatively high
In general
Less
None
Prevention measures
Good effect
Fully
In general
Less
None
Training
More
Relatively more
In general
Less
None
Scores
2
4
6
8
10


### 4.3. Establishing the Comprehensive Index and Grade Features

Taking the first seven mines as the training samples of the hierarchic analysis method model, the quantitative values of the factors are shown in Table19.Table 19
The quantitative values of the factors impacting rock bursts.
Mine ID
Mining depth
Mechanical characteristics of coal and rock
Geological structure
Coal thickness
Burst tendency of coal rock
Roof control
Pressure relief
Degree of production concentration
Rings of coal burst
Investment
Prevention measures
Training
1
6
2
4
2
4
10
4
6
6
4
8
4
2
6
6
8
4
4
8
6
2
6
6
2
8
3
8
6
10
4
10
6
4
10
8
4
8
8
4
6
8
10
6
10
10
4
6
8
6
8
10
5
6
2
2
2
4
2
10
6
2
4
2
4
6
4
6
6
8
6
6
10
6
8
8
8
10
7
4
4
2
2
8
4
8
4
4
4
6
4The comprehensive evaluation index of rock bursts can be obtained by multiplying the standardized data in Table19 by the corresponding weights in Table 10. The specifics are shown in Table 20.Table 20
Correlation table of risk rating of rock bursts.
Mine ID
1
2
3
4
5
6
7
Comprehensive index
5.0038
6.0494
8.004
8.1954
3.6114
6.4552
4.2156
Actual grade
Low impact
Medium impact
Strong impact
Strong impact
Micro-impact Medium
Medium impact
Low impactAccording to Table20, by comparing the quantitative value of the comprehensive evaluation index of the risk of rock bursts and the actual rock burst strength, the risk of rock bursts can be divided into four grades. The quantitative value of the influencing factors of rock bursts in the range of 2.0 to 4.0 is representative of micro-impact (level I); the range of 4.0 to 6.0 is representative of low impact (level II); the range of 6.0 to 8.0 is representative of medium impact (level III); and the range of 8.0 to 10.0 is representative of strong impact (level IV), as shown in Table 21.Table 21
Evaluation of the risk of rock burst grade features by hierarchic analysis method.
The quantitative value of risk rating
Risk rating
2.0–4.0
Micro-impact (level I)
4.0–6.0
Low impact (level II)
6.0–8.0
Medium impact (level III)
8.0–10.0
Strong impact (level IV)


### 4.4. Verifying the Model Evaluation

To verify the model’s applicability, the risks of rock bursts were verified in the last 3 mines that did not participate in the training. Table22 presents the specific information of the model evaluation.Table 22
Verification of the model evaluation.
Mine ID
Mining depth
Mechanical characteristics of coal and rock
Geological structure
Coal thickness
Burst tendency of coal rock
Roof Control
Pressure release
Degree of production concentration
Rings of coal burst
Investment
Prevention measures
Training
Comprehensive index
Model results
Actual grade
Contrast result
1
6
4
2
2
4
2
2
6
2
2
4
2
3.2411
Level I
Micro-impact
Coincidence
2
6
6
6
4
4
8
8
6
8
8
8
10
6.4373
Level III
Medium impact
Coincidence
3
2
2
10
2
8
10
10
10
8
10
6
8
7.2163
Level III
Medium impact
CoincidenceAccording to Table22, the results of the model evaluation were in agreement with the actual situations of rock bursts, which meant the hierarchic analysis method model was effective and reasonable in evaluating the risk of rock bursts in mines, and the results have guiding significance in practice.


## 4.1. The Principle of Analytic Hierarchy Process (AHP)

Analytic hierarchy processes regard complicated multiobjective decision-making problems as a system in which the target is decomposed into multiple goals or standards and multiple indices of several levels through the qualitative index fuzzy quantification method to calculate single hierarchy sorting and total ordering.Hierarchic analysis method can be simplified into following steps.(1)
Construction of judgment matrix: the judgment matrix is used to represent the importance of every element relative to one of the upper elements, the form of which is shown in Table3. Dij is the element judgment matrixP and is given based on the 1–9 scale put forward by Saaty [17], as shown in Table 4.
(2)
The weight and maximum eigenvalueλmax of judgment matrix.
(a)
Calculation ofOi product of elements in every row of judgment matrix is as follows:(1)Oi=∏j=1ndij,i=1,2,3,…,n.
(b)
Calculation ofvth root of Oi is as follows:(2)Ei¯=Oin.
(c)
Standardization of the matrixE¯=[E¯1,E¯2,…,E¯n]T is as follows:(3)Ei=Ei¯∑i=1nEi¯.
E
=
[
E
1
,
E
2
,
…
,
E
n
]
T is the eigenvector figured out.
(d)
Calculation ofλmax maximum eigenvalue of eigenvector is as follows:(4)λmax⁡=1v∑i=1VPEiEi.
(3)
Consistency check of judgment matrix includes the following.
(a)
Calculation of consistency indexCI is as follows:(5)CI=λmax⁡-vv-1.
(b)
Verification of corresponding average random consistency indexRI is as shown in Table 5.
(c)
Calculation of consistency ratioCR is as follows:(6)CR=CIRI.
When CR < 0.10, the consistency of the judgment matrix is considered reasonable, or proper correction should be made to the judgment matrix.Table 3
Judgment matrix.
Judgment matrixP
D
1
D
2
⋯
D
n
D
1
D
11
D
12
⋯
D
1
n
D
2
D
21
D
22
⋯
D
2
n
⋮
⋮
⋮
⋮
⋮
D
n
D
n
1
D
n
2
⋯
D
n
nTable 4
The relative importance judgment of each element.
Scale
Meaning
1
The importance ofDi and Dj is equal
3
D
i and Dj are slightly important
5
D
i and Dj are obviously important
7
D
i and Dj are strongly important
9
D
i and Dj are vitally important
2, 4, 6, 8
The median of two adjacent judgments described above
Reciprocal
D
i
j
=
1
D
j
iTable 5
Average random consistency index RI.
n
1
2
3
4
5
6
7
8
9
RI
0
0
0.58
0.9
1.12
1.24
1.32
1.41
1.45


## 4.2. Construction of Risk Evaluation Indices of Impulsion Pressure

### 4.2.1. Construction of Index Judgment Matrix

According to the hierarchical structure diagrams of factors affecting impulsion pressure (shown in Figure1), a preferential judgment matrix can be established as follows:(1)
Judgment matrixA-B is shown in Table 6.(2)
Judgment matrixB1-C is shown in Table 7.(3)
Judgment matrixB2-C is shown in Table 8.(4)
Judgment matrixB3-C is shown in Table 9.Table 6
Judgment matrixA-B and parameters.
Natural factors
Geological factors
Organization management factors
Weight
Maximum eigenvalue
Consistency ratio
Natural factors
1
3
4
0.6337
3.0092
0.0089 < 0.10
Geological factors
1/3
1
1
0.1919
Organization management factors
1/4
1
1
0.1744Table 7
Judgment matrixB1-C and parameters.
Judgment matrix
Mining depth
Mechanical properties of coal and rock
Geological structure
Coal thickness
Burst tendency of coal rock
Weight
Maximum eigenvalue
Consistency ratio
Mining depth
1
1/2
4
3
3
0.2636
5.0721
0.0161 < 0.1
Mechanical properties of coal and rock
2
1
7
5
5
0.4758
Geological structure
1/4
1/7
1
1/2
1/3
0.0538
Coal thickness
1/3
1/5
2
1
1
0.0981
Burst tendency of coal rock
1/3
1/5
3
1
1
0.1087Table 8
Judgment matrixB2-C and parameters.
Judgment matrix
Roof control
Degree of production concentration
Pressure relief
Rings of coal burst
Weight
Maximum eigenvalue
Consistency ratio
Roof control
1
1/3
1/5
2
0.1098
4.0201
0.0075 < 0.10
Degree of production concentration
3
1
1/2
5
0.3005
Pressure relief
5
2
1
7
0.5267
Rings of coal burst
1/2
1/5
1/7
1
0.0630Table 9
Judgment matrixB3-C and parameters.
Judgment matrix
Investment
Prevention measures
Training
Weight
Maximum eigenvalue
Consistency ratio
Investment
1
1/3
2
0.2493
3.0536
0.0515 < 0.10
Prevention measures
3
1
3
0.5936
Training
1/2
1/3
1
0.1571Based on judgment matrix constructed, the weight of every factor can be figured out by using Matlab [18]. The results are shown in Table 10.Table 10
Every factor weight summary table.
First grade index
Weight
Second index
Weight
Analysis on factors affecting impulsion pressure
Natural factors
0.10473
Mining depth
0.16705
Mechanical properties of coal and rock
0.30154
Geological structure
0.034103
Coal thickness
0.062147
Technical factors
0.63699
Burst tendency of coal rock
0.06887
Roof control
0.021066
Degree of production concentration
0.057676
Pressure relief
0.10109
Organization management factors
0.25828
Rings of coal burst
0.012089
Investment
0.043473
Prevention measures
0.10351
Training
0.027386


### 4.2.2. Quantization and Standardization of the Risk Index of Rock Bursts

According to information on rock bursts in mines in China, the mining depth, gas content, and coal seam thickness, and so forth can be found. However, in order to meet the requirements of the model, it is necessary to quantify the qualitative description in the sample. The quantitative methods are as follows.(1)
Mining depth: Statistical analysis shows that the deeper the mining depth, the higher the possibility of a rock burst occurring. The quantitative values are shown in Table11.(2)
Mechanical characteristics of coal and rock: Generally, for coal and rock, the more the energy retention is internally and the less the energy is released, the more the possibility of rock bursts occurs. The impact energy index and elastic energy index to characterize the mechanical properties of coal and rock are shown in Table12.(3)
Geological structure: The power in the movement of strata generates a variety of geological structures, such as folds and faults, which have a greater effect on rock bursts.According to the relationship between the number of rock bursts and geological structures in coal mines, conclusions were drawn as detailed in Table13.(4)
Coal seam thickness: According to statistics, coal seam thickness relates to the occurrence of rock bursts, corresponding to results in Table14.(5)
Burst tendency of coal rock: Rock bursts can occur in any coal seam. The more brittle and hard the coal is, the less the impact energy is needed and the more it is likely to burst. So, impact energy index, elastic energy index, and dynamic destruction time are generally used to measure the possibility. The quantitative results are given in Table15.(6)
Roof control: The occurrence of a rock burst is influenced by the strata mainly above the coal seam, which has great intensity and thickness, and the method of processing the roof such as packing and caving. The quantitative values are given in Table16.(7)
Pressure relief circumstances: According to the actual effects of taking preventative measures, such as pressure relief blasting, drill hole pressure relief, and mining liberated seams, the likelihood of rock bursts occurring changes. The scores are given in Table17.(8)
The other factors and quantitative scores are shown in Table18.Table 11
Mining depth and quantitative scores.
Mining depth/m
<350
350–500
500–800
800–1000
>1000
Scores
2
4
6
8
10Table 12
Physical and mechanical characteristics of coal and surrounding rock and quantitative scores.
Impact energy index
<1
1–1.5
1.5–3
3–5
>5
Elastic energy index
<1
1-2
2–3.5
3.5–5
>5
Scores
2
4
6
8
10Table 13
Geological structure and quantitative scores.
Geological structure types
Local anomaly
Local structure anomaly
Coal seam thickness variation, thinning and thinning out, and cavity
Roof and floor fold
Downfold, upfold, and fault
Scores
2
4
6
8
10Table 14
Coal seam thickness and quantitative scores.
Coal seam thickness/m
<2.0
2.0–4.0
4.0–6.0
6.0–8.0
>8.0
Scores
2
4
6
8
10Table 15
Coal rock burst tendency and quantitative scores.
Elastic energy index
<1.5
1.5–3.0
3.0–5.0
5.0–7.0
>7.0
Dynamic failuretime/ms
<2.0
2.0–3.0
3.0–4.0
4.0–5.0
>5.0
Scores
2
4
6
8
10Table 16
Roof control and quantitative scores.
Distance from hard and thick roof  to coal seam/m
<100
100–80
80–60
60–40
<40
Scores
2
4
6
8
10Table 17
Pressure relief circumstances and quantitative scores.
Probability of stress reduction/%
<25
25–40
40–55
55–80
>80
Scores
2
4
6
8
10Table 18
The other factors and quantitative scores.
Degree of production centralization
None
Low
Medium
Relatively high
High
Rings of coal burst
None
Few
Several times
Frequently
Uninterrupted
Investment
High
Relatively high
In general
Less
None
Prevention measures
Good effect
Fully
In general
Less
None
Training
More
Relatively more
In general
Less
None
Scores
2
4
6
8
10


## 4.2.1. Construction of Index Judgment Matrix

According to the hierarchical structure diagrams of factors affecting impulsion pressure (shown in Figure1), a preferential judgment matrix can be established as follows:(1)
Judgment matrixA-B is shown in Table 6.(2)
Judgment matrixB1-C is shown in Table 7.(3)
Judgment matrixB2-C is shown in Table 8.(4)
Judgment matrixB3-C is shown in Table 9.Table 6
Judgment matrixA-B and parameters.
Natural factors
Geological factors
Organization management factors
Weight
Maximum eigenvalue
Consistency ratio
Natural factors
1
3
4
0.6337
3.0092
0.0089 < 0.10
Geological factors
1/3
1
1
0.1919
Organization management factors
1/4
1
1
0.1744Table 7
Judgment matrixB1-C and parameters.
Judgment matrix
Mining depth
Mechanical properties of coal and rock
Geological structure
Coal thickness
Burst tendency of coal rock
Weight
Maximum eigenvalue
Consistency ratio
Mining depth
1
1/2
4
3
3
0.2636
5.0721
0.0161 < 0.1
Mechanical properties of coal and rock
2
1
7
5
5
0.4758
Geological structure
1/4
1/7
1
1/2
1/3
0.0538
Coal thickness
1/3
1/5
2
1
1
0.0981
Burst tendency of coal rock
1/3
1/5
3
1
1
0.1087Table 8
Judgment matrixB2-C and parameters.
Judgment matrix
Roof control
Degree of production concentration
Pressure relief
Rings of coal burst
Weight
Maximum eigenvalue
Consistency ratio
Roof control
1
1/3
1/5
2
0.1098
4.0201
0.0075 < 0.10
Degree of production concentration
3
1
1/2
5
0.3005
Pressure relief
5
2
1
7
0.5267
Rings of coal burst
1/2
1/5
1/7
1
0.0630Table 9
Judgment matrixB3-C and parameters.
Judgment matrix
Investment
Prevention measures
Training
Weight
Maximum eigenvalue
Consistency ratio
Investment
1
1/3
2
0.2493
3.0536
0.0515 < 0.10
Prevention measures
3
1
3
0.5936
Training
1/2
1/3
1
0.1571Based on judgment matrix constructed, the weight of every factor can be figured out by using Matlab [18]. The results are shown in Table 10.Table 10
Every factor weight summary table.
First grade index
Weight
Second index
Weight
Analysis on factors affecting impulsion pressure
Natural factors
0.10473
Mining depth
0.16705
Mechanical properties of coal and rock
0.30154
Geological structure
0.034103
Coal thickness
0.062147
Technical factors
0.63699
Burst tendency of coal rock
0.06887
Roof control
0.021066
Degree of production concentration
0.057676
Pressure relief
0.10109
Organization management factors
0.25828
Rings of coal burst
0.012089
Investment
0.043473
Prevention measures
0.10351
Training
0.027386


## 4.2.2. Quantization and Standardization of the Risk Index of Rock Bursts

According to information on rock bursts in mines in China, the mining depth, gas content, and coal seam thickness, and so forth can be found. However, in order to meet the requirements of the model, it is necessary to quantify the qualitative description in the sample. The quantitative methods are as follows.(1)
Mining depth: Statistical analysis shows that the deeper the mining depth, the higher the possibility of a rock burst occurring. The quantitative values are shown in Table11.(2)
Mechanical characteristics of coal and rock: Generally, for coal and rock, the more the energy retention is internally and the less the energy is released, the more the possibility of rock bursts occurs. The impact energy index and elastic energy index to characterize the mechanical properties of coal and rock are shown in Table12.(3)
Geological structure: The power in the movement of strata generates a variety of geological structures, such as folds and faults, which have a greater effect on rock bursts.According to the relationship between the number of rock bursts and geological structures in coal mines, conclusions were drawn as detailed in Table13.(4)
Coal seam thickness: According to statistics, coal seam thickness relates to the occurrence of rock bursts, corresponding to results in Table14.(5)
Burst tendency of coal rock: Rock bursts can occur in any coal seam. The more brittle and hard the coal is, the less the impact energy is needed and the more it is likely to burst. So, impact energy index, elastic energy index, and dynamic destruction time are generally used to measure the possibility. The quantitative results are given in Table15.(6)
Roof control: The occurrence of a rock burst is influenced by the strata mainly above the coal seam, which has great intensity and thickness, and the method of processing the roof such as packing and caving. The quantitative values are given in Table16.(7)
Pressure relief circumstances: According to the actual effects of taking preventative measures, such as pressure relief blasting, drill hole pressure relief, and mining liberated seams, the likelihood of rock bursts occurring changes. The scores are given in Table17.(8)
The other factors and quantitative scores are shown in Table18.Table 11
Mining depth and quantitative scores.
Mining depth/m
<350
350–500
500–800
800–1000
>1000
Scores
2
4
6
8
10Table 12
Physical and mechanical characteristics of coal and surrounding rock and quantitative scores.
Impact energy index
<1
1–1.5
1.5–3
3–5
>5
Elastic energy index
<1
1-2
2–3.5
3.5–5
>5
Scores
2
4
6
8
10Table 13
Geological structure and quantitative scores.
Geological structure types
Local anomaly
Local structure anomaly
Coal seam thickness variation, thinning and thinning out, and cavity
Roof and floor fold
Downfold, upfold, and fault
Scores
2
4
6
8
10Table 14
Coal seam thickness and quantitative scores.
Coal seam thickness/m
<2.0
2.0–4.0
4.0–6.0
6.0–8.0
>8.0
Scores
2
4
6
8
10Table 15
Coal rock burst tendency and quantitative scores.
Elastic energy index
<1.5
1.5–3.0
3.0–5.0
5.0–7.0
>7.0
Dynamic failuretime/ms
<2.0
2.0–3.0
3.0–4.0
4.0–5.0
>5.0
Scores
2
4
6
8
10Table 16
Roof control and quantitative scores.
Distance from hard and thick roof  to coal seam/m
<100
100–80
80–60
60–40
<40
Scores
2
4
6
8
10Table 17
Pressure relief circumstances and quantitative scores.
Probability of stress reduction/%
<25
25–40
40–55
55–80
>80
Scores
2
4
6
8
10Table 18
The other factors and quantitative scores.
Degree of production centralization
None
Low
Medium
Relatively high
High
Rings of coal burst
None
Few
Several times
Frequently
Uninterrupted
Investment
High
Relatively high
In general
Less
None
Prevention measures
Good effect
Fully
In general
Less
None
Training
More
Relatively more
In general
Less
None
Scores
2
4
6
8
10


## 4.3. Establishing the Comprehensive Index and Grade Features

Taking the first seven mines as the training samples of the hierarchic analysis method model, the quantitative values of the factors are shown in Table19.Table 19
The quantitative values of the factors impacting rock bursts.
Mine ID
Mining depth
Mechanical characteristics of coal and rock
Geological structure
Coal thickness
Burst tendency of coal rock
Roof control
Pressure relief
Degree of production concentration
Rings of coal burst
Investment
Prevention measures
Training
1
6
2
4
2
4
10
4
6
6
4
8
4
2
6
6
8
4
4
8
6
2
6
6
2
8
3
8
6
10
4
10
6
4
10
8
4
8
8
4
6
8
10
6
10
10
4
6
8
6
8
10
5
6
2
2
2
4
2
10
6
2
4
2
4
6
4
6
6
8
6
6
10
6
8
8
8
10
7
4
4
2
2
8
4
8
4
4
4
6
4The comprehensive evaluation index of rock bursts can be obtained by multiplying the standardized data in Table19 by the corresponding weights in Table 10. The specifics are shown in Table 20.Table 20
Correlation table of risk rating of rock bursts.
Mine ID
1
2
3
4
5
6
7
Comprehensive index
5.0038
6.0494
8.004
8.1954
3.6114
6.4552
4.2156
Actual grade
Low impact
Medium impact
Strong impact
Strong impact
Micro-impact Medium
Medium impact
Low impactAccording to Table20, by comparing the quantitative value of the comprehensive evaluation index of the risk of rock bursts and the actual rock burst strength, the risk of rock bursts can be divided into four grades. The quantitative value of the influencing factors of rock bursts in the range of 2.0 to 4.0 is representative of micro-impact (level I); the range of 4.0 to 6.0 is representative of low impact (level II); the range of 6.0 to 8.0 is representative of medium impact (level III); and the range of 8.0 to 10.0 is representative of strong impact (level IV), as shown in Table 21.Table 21
Evaluation of the risk of rock burst grade features by hierarchic analysis method.
The quantitative value of risk rating
Risk rating
2.0–4.0
Micro-impact (level I)
4.0–6.0
Low impact (level II)
6.0–8.0
Medium impact (level III)
8.0–10.0
Strong impact (level IV)


## 4.4. Verifying the Model Evaluation

To verify the model’s applicability, the risks of rock bursts were verified in the last 3 mines that did not participate in the training. Table22 presents the specific information of the model evaluation.Table 22
Verification of the model evaluation.
Mine ID
Mining depth
Mechanical characteristics of coal and rock
Geological structure
Coal thickness
Burst tendency of coal rock
Roof Control
Pressure release
Degree of production concentration
Rings of coal burst
Investment
Prevention measures
Training
Comprehensive index
Model results
Actual grade
Contrast result
1
6
4
2
2
4
2
2
6
2
2
4
2
3.2411
Level I
Micro-impact
Coincidence
2
6
6
6
4
4
8
8
6
8
8
8
10
6.4373
Level III
Medium impact
Coincidence
3
2
2
10
2
8
10
10
10
8
10
6
8
7.2163
Level III
Medium impact
CoincidenceAccording to Table22, the results of the model evaluation were in agreement with the actual situations of rock bursts, which meant the hierarchic analysis method model was effective and reasonable in evaluating the risk of rock bursts in mines, and the results have guiding significance in practice.


## 5. Conclusions

(
1
) The probability of rock bursts is random to a certain extent. By building a model of hierarchic analysis method, the reasons for rock bursts in mines were made quantitative, and the influence was considered by various factors and the relationship between them. The model was simple, flexible, and easy to operate.(
2
) The risk degree of rock bursts evaluated through the hierarchic analysis method was in accordance with the actual degrees of risk. This indicated the assessment results of the model have some significance for mine production safety.(
3
) The model of hierarchic analysis method obtained the influence degree and comprehensive evaluation indices of the factors that affect rock bursts. It can provide a theoretical basis for the prevention and control of rock bursts and can make the prevention and control more targeted and practical.



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*Source: 184398-2015-07-28.xml*