Application of Research on Risk Assessment of Roadway Roof Falls Based on Combined Weight Matter Element Extension Model

Abstract

Roof falls in coal mine roadways are the main causes of many casualties, shutdowns and production plan delays. To understand the relationship between the influencing factors of roadway roof fall accidents and the importance ranking of the accidents, we will reduce safety accidents in coal mines. To enable the timely prediction and control of roadway roof fall risks, based on the investigation of many roadway roof fall risk factors, 12 evaluation indexes such as the roadway roof rock thickness, geological conditions and roadway section shape were selected. An evaluation index system of roadway roof fall risks is constructed. A risk degree standard of roadway roof falls is proposed. The risk evaluation model of roadway roof falls was established by using the combination weight of the analytic hierarchy process (AHP), entropy weight method (EW) and matter element extension theory. According to the principle of the maximum membership degree, the risk degree of roadway roof falls is determined. Based on Java Web, a risk assessment system for roadway roof falls was developed. We name the system Multiple Weight-Material Element Web (MW-MEW). The MW-MEW system was used to evaluate the risk degree of roof falls in the C9 return airway of the Xingu Coal Mine. Compared with the evaluation results of the AHP matter element extension model, it is found that the evaluation results of the MW-MEW system are more in line with the actual engineering conditions. The successful application of the MW-MEW system will provide new avenues for the quantitative evaluation of roof fall risks in coal mine roadways.

1. Introduction

Coal is an indispensable resource for all countries in the world, and plays a role in promoting economic and social development and ensuring energy security [1,2]. Roadway roof falls are common safety accidents in coal mining. They have a high frequency of occurrence and cause great harm, causing a lot of fear for staff [3,4]. There are many factors affecting roof falls. These factors sometimes lead to accidents independently. Sometimes they combine with each other to cause accidents. Some factors may contain implicit elements that are not readily apparent and easily overlooked, yet they play a crucial role. More importantly, roof falls may be influenced by a combination of hidden factors, which in turn can be influenced by multiple factors simultaneously. There may be a complex network relationship between these factors. This has led to long-term research, but the reasons for collapses are still complex and realistic results are yet to be reported. Therefore, it is necessary to correctly evaluate the safety of roadway roof falls and the timely prevention and handling of the risk of roadway roof falls. This can reduce the occurrence of such accidents and ensure the safety of personnel and property.

In recent years, researchers at home and abroad have carried out a lot of research on the risk assessment of roadway roof collapses, and have reported a lot of important research results. Xing et al. [5] calculated the entropy weight and grey correlation degree of roof disasters in coal mine roof accidents by using the entropy weight and grey correlation analysis methods. Roof disasters during construction are divided into three levels, and countermeasures to prevent roof accidents have been put forward. Liu et al. [6] proposed an evaluation method based on expert knowledge to evaluate the safety of coal mine roofs, the risk degree of roof events and the investment benefit of roof emergency plans. This method uses the expert investigation method to analyze the main influencing factors of the occurrence of coal mine roof events, which provides a fuzzy comprehensive evaluation of the safety of roof accident events. Mahdevari et al. [7] established a neural–fuzzy hybrid model to approximate the nonlinear relationship between the maximum displacement of roadway roof subsidence and geomechanic characteristics. It is found that the threshold of roof subsidence is 66%. Maiti et al. [8] established a relative risk model for fatal roadway roof fall accidents. Potential fatalities (PFs), relative risk of fatalities (RRF) and safety measure effectiveness (SME) are key indicators of mine safety performance. They have been successfully applied in 292 underground coal mines in India. Yao [9] selected six evaluation indexes, including the thickness of the loosening ring, amount of roof separation, stress–intensity ratio, construction quality of the anchor rod (cable), water content of the roof and crack length. The entropy weight method is used to determine the weight of each index. The matter element extension theory is used to establish the risk assessment model of deep roadway roof falls. It is found that the risk level of roof falls has an obvious correlation with roof deformation. Miao et al. [10] built a mine gas safety situation prediction model using natural language processing technology. An accurate management and control information system based on data mining technology and intelligent technology was developed. The ability and efficiency of mine roadway roof safety management are improved. Brook et al. [11] applied the two methods of coal mine roadway roof rating (CMRR) and rock mass rating (RMR), respectively, to the safety evaluation of underground coal mine roadway roofs. They found that the two techniques showed consistency in roadway roof evaluation in most areas of the mine. But there are differences in the overall rating of complex geological regions. Chen et al. [12] evaluated the roof fall risk of stratified rock mass roadways. The evaluation model of tunnel roof falls based on the analytic hierarchy process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was established. A comprehensive evaluation index system for roof collapses of roadways is proposed. The weight of each index is calculated by the combination of the analytic hierarchy process (AHP) and expert validity matter elements. Therefore, the influence of human factors on the evaluation results is reduced. Young et al. [13] took two underground coal mines in the western United States as engineering cases. The main parameters affecting roof falls of roadways are analyzed. The prediction index of tunnel roof falls was put forward. Tiejun et al. [14] aimed to understand the relationship between the influencing factors of roadway roof fall accidents and the importance of accidents according to the characteristics of the expert evaluation language and the semantic network connection between the factors. It is proposed to embed the cloud model into the ANP (analytic network process) to solve the above problems. The construction process and analysis steps of the cloud ANP are given.

The underground geomechanical environment of coal mines is complex and changeable, so the risk assessment of roadway roof falls should involve many factors [15,16,17]. However, the above evaluation method is too simple to correctly judge the actual situation of roof falls in coal mine roadways. It is necessary to study it further. Through the comprehensive analysis of various factors, the risk evaluation method of roadway roof falls in line with objective reality is obtained. Therefore, in view of the evaluation of the risk of roof falls in coal mine roadways, this paper uses the combination weight of the analytic hierarchy process (AHP), entropy weight method (EW) and the matter element extension theory to establish the risk evaluation model of roadway roof falls. According to the principle of the maximum membership degree, the risk degree of roadway roof falls is determined. Based on Java Web, a roadway roof fall risk assessment system was developed. We name the system Multiple Weight-Material Element Web (MW-MEW). The system cannot only avoid the subjectivity of an individual evaluation but can also effectively solve the problem of single factors affecting the risk evaluation of roadway roof falls. It provides a new avenue for the study of the cost of risks of roof falls in coal mine roadways.

2. Establish Evaluation Index System

Roof collapses in coal mining are caused by the interaction of many factors. This paper performs an analysis of the main factors. Based on the investigation of a large number of risk factors of roadway roof falls, the relevant factors affecting the risk assessment of roadway roof falls were extracted. A risk evaluation system U of roadway roof falls is established. An analysis method is used to divide the factors of roadway caving risk assessments according to the nature of the influencing factors and the engineering characteristics. Among them, the criterion layer includes the roadway structure characteristics U₁, roadway roof characteristics U₂, and roadway engineering conditions U₃, and the indicator layer includes 12 indicators. See Figure 1 for details. The overview of the indicators is shown in

Table 1. Overview of roadway roof fall risk evaluation index.

Evaluating Indicator	Overview of Indicators	Index Property
Stable rock thickness U11/m	The roadway bolt (cable) support needs to be anchored in a stable rock stratum with a certain thickness. In order to ensure the anchoring effect, the stable rock thickness is one of the direct influencing factors.	Quantification
Geological condition U12	The geological conditions of the roadway strata include the buried depth of the roadway, the tectonic stress, the fault of the surrounding rock of the roadway and the groundwater condition. The more complex the geological conditions, the more easily the roadway is deformed.	Characterization
Cross-section shape of roadway U13	The shape of the roadway section is one of the key factors affecting the stability of the surrounding rock. The cross-section shape will affect the stress distribution of the surrounding rock of the roadway, resulting in different stress states. In general, the stability of the surrounding rock of the roadway with a circular cross-section shape is the best.	Characterization
Angle between maximum horizontal principal stress and roadway U14/°	With the increase in the angle between the maximum horizontal principal stress and the roadway, the damage degree of the roof and floor of the roadway also increases. When the angle is 90°, the damage to the surrounding rock in the roadway is the most serious.	Quantification
The amount of displacement of roof strata U21/m	The subsidence of roof strata is an observation index clearly stipulated in the “Coal Mine Safety Regulations”. After it exceeds the critical deformation value, physical phenomena such as roof falls occur in the roadway. It is obtained by field measurement.	Quantification
Visible fracture development situation U22/pcs	The development of fissures reflects the stability of the roof, which is accurately monitored by the roof peeper.	Quantification
Compressive strength of roof rock U23/MPa	The tensile strength of the roof rock characterizes the bearing capacity of the roof. Due to the action of gravity, the surrounding rock in the shallow area of the roof is subjected to tensile stress. If the tensile stress exceeds the tensile strength of the rock, a large number of cracks will appear in the roof rock.	Quantification
Water content of roof rock U24	Groundwater will weaken the mechanical properties of rock mass. This leads to physical and chemical changes in the mechanical properties of the roof, reducing the roof’s load bearing capacity.	Characterization
Roof stability U25	The stability of coal mine roadway roofs directly affects the risk of roof falls. The better the stability of the roof, the lower the risk of roof falls.	Characterization
Surrounding disturbance U31	The greater the disturbance stress around the roadway, the more easily the roof of the roadway falls.	Characterization
Maximum exposure time U32/d	The longer the roadway roof is exposed to air, the lower the strength of the exposed rock mass, and the worse the stability of the roof.	Quantification
Supporting quality U33	The quality of the support directly reflects the stability of the roadway roof. The better the support quality, the better the stability of the roof.	Characterization

.

3. Calculate Index Weights

3.1. Analytic Hierarchy Process (AHP) to Calculate the Weight

The analytic hierarchy process (AHP) [18] first divides the nature of the analysis object into related factors. Then, the related factors are classified to form a multi-level structure model. The relative importance of each factor is judged by experience or experts. According to the importance degree, the weight is obtained, and the characterization analysis is transformed into a quantitative analysis. The specific calculation steps are as follows:

(1) Construct judgment matrix:

The 1–9 scale method [19] was used to determine the importance of the evaluation index elements at each level. The judgment matrix expression (1) is established.

$$A={\left(a_{ij}\right)}_{n\times n}$$

(1)

$a_{ij}$ is the relative importance of risk factor i to risk factor j at this level.

$${\mathrm{a}}_{\mathrm{i}\mathrm{j}}=\frac{1}{{\mathrm{a}}_{\mathrm{j}\mathrm{i}}},{\mathrm{a}}_{\mathrm{i}\mathrm{i}}=1,\left(\mathrm{i}=\mathrm{1,2},\dots ,\mathrm{n}\right),\left(\mathrm{j}=\mathrm{1,2},\dots ,\mathrm{n}\right)$$

(2) Calculate weight:

After establishing the judgment matrix, the weight of each index is calculated by Expression (2). Common calculation methods include the feature method and root method. The root method is used in this paper.

$${\mathrm{G}}_{\mathrm{i}}^{\prime }=\frac{\overline{{\mathrm{G}}_{\mathrm{i}}^{\prime }}}{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\overline{{\mathrm{G}}_{\mathrm{i}}^{\prime }}}$$

(2)

${G^{\prime }}_i$ is the weight of the ith evaluation index after unitization.

$a_{ij}$ is the element in the judgment matrix A.

In Expression (2), there is Expression (3).

$$\overline{{\mathrm{G}}_{\mathrm{i}}^{\prime }}=\sqrt[\mathrm{n}]{{\prod }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{a}}_{\mathrm{ij}}}$$

(3)

(3) Calculate the maximum eigenvalue:

$${\mathsf{\lambda }\frac{1}{\mathrm{n}}{\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left[\frac{{\left(\mathrm{A}{\mathrm{G}}^{\prime }\right)}_{\mathrm{i}}}{{\mathrm{G}}_{\mathrm{i}}^{\prime }}\right]}_{max}$$

(4)

${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum eigenvalue

(4) Check consistency:

After the consistency index C_I is calculated, the random consistency index (

Table 2. Random consistency index.

Order	1	2	3	4	5	6	7	8	9
RI	0.00	0.00	0.58	0.9	1.12	1.24	1.32	1.41	1.45

) of the judgment matrix is checked. The value of consistency index R_I is obtained. Then, the test coefficient C_R of the matrix is calculated.

$${\mathrm{C}}_{\mathrm{R}}=\frac{{\mathrm{C}}_{\mathrm{I}}}{{\mathrm{R}}_{\mathrm{I}}}$$

(5)

$C_R$ is the test coefficient of the matrix.

$C_I$ is the consistency index.

$R_I$ is a random consistency index.

In Expression (5),

$${\mathrm{C}}_{\mathrm{I}}=\frac{{\mathsf{\lambda }}_{\max }}{\mathrm{n} - 1}$$

(6)

If C_R < 0.1, the constructed judgment matrix passes the consistency test. In contrast, if the consistency test is not passed, the judgment matrix needs to be reconstructed and calculated.

(5) Obtain index weight:

The weight of the index layer to the criterion layer is multiplied by the weight of the criterion layer to the target layer. The weight of each index factor to the total target is obtained. If O indices of the target layer U are U₁, U₂ …, U_O, these weights on P are ${\mathrm{G}}_{{\mathrm{W}}_{\mathrm{i}}}=({\mathrm{G}}_1^{\prime },{\mathrm{G}}_2^{\prime },\dots ,{\mathrm{G}}_{\mathrm{O}}^{\prime })$. The weight vector of ${\mathrm{U}}_{\mathrm{i}}(\mathrm{i}=1,2,\dots ,\mathrm{O})$ to its index U_i1, U_i2, …, U_if is ${\mathrm{G}}_{{\mathrm{P}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{ij}}}=({\mathrm{G}}_{\mathrm{i}1}^{\prime },{\mathrm{G}}_{\mathrm{i}2}^{\prime },\dots ,{\mathrm{G}}_{\mathrm{if}}^{\prime })$. The following is the weight of ${\mathrm{U}}_{\mathrm{ij}}(\mathrm{j}=1,2,\dots ,\mathrm{f})$ to the target layer U:

$${\mathrm{G}}_{\mathrm{P}{\mathrm{P}}_{\mathrm{ij}}}={\mathrm{G}}_{\mathrm{P}{\mathrm{P}}_{\mathrm{i}}}\times {\mathrm{G}}_{{\mathrm{P}}_{\mathrm{i}}{\mathrm{P}}_{\mathrm{ij}}}$$

(7)

$G_{P{P}_i}$ is the weight of the criterion layer ${ U}_{xy}(x=\mathrm{1,2},\dots ,o)$ to the target layer U.

$G_{P_i{P}_{\mathit{ij}}}$ is the weight of the index layer $U_{xy}(x=\mathrm{1,2},\dots ,o;y=\mathrm{1,2},\dots ,l)$ to the criterion layer $U_x$.

The weight vector of each indicator is put into Expression (7). The weight of each indicator can be calculated.

3.2. Entropy Weight (EW) Method to Calculate the Weight

The entropy weight method [20] is a method of customer weighting. According to the variation degree of each evaluation index, the entropy value is determined. The entropy value is used to determine the weight of each index. If the index variation degree is smaller, the index weight value is smaller. On the contrary, the greater the index weight. The entropy weight calculation steps of m evaluations and n evaluation indexes are as follows:

(1) Standardized treatment:

Based on the risk evaluation index system of roadway roof falls, the matrix B = (b_ij)_m×n is obtained by standardizing the original matrix R = (r_ij)_m×n according to Expression (8).

$${\mathrm{b}}_{\mathrm{ij}}=\frac{{\mathrm{r}}_{\mathrm{ij}}-{\mathrm{r}}_{\min }}{{\mathrm{r}-{\mathrm{r}}_{\min }}_{\max }}$$

(8)

$b_{ij}$ is the data after the standardization of the original data.

$r_{ij}$ is the ith initial value of the jth index.

$r_{jmax}$ is the maximum initial value of the jth index.

$r_{jmin}$ is the minimum initial value of the jth index.

In the formula, _i = (1, 2, …, m); _j = (1, 2, …, n).

(2) Calculated entropy:

$${\mathrm{H}}_{\mathrm{j}}=-\frac{1}{\ln \mathrm{m}}\left[{\sum }_{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{e}}_{\mathrm{ij}}\times \ln {\mathrm{e}}_{\mathrm{ij}}\right]$$

(9)

$H_j$ is the entropy value of the jth index.

In Expression (9),

$${\mathrm{e}}_{\mathrm{ij}}=\frac{1+{\mathrm{b}}_{\mathrm{ij}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{m}}\left(1+{\mathrm{b}}_{\mathrm{ij}}\right)}$$

(10)

$b_{ij}$ is the index data after the standardization of the jth index of the ith thing.

b_ij is the index data after the standardization of the j index of the i thing.

(3) Computated entropy weight:

$${\mathrm{Q}}_{\mathrm{j}}=\frac{1-{\mathrm{H}}_{\mathrm{j}}}{\mathrm{n}-{\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{H}}_{\mathrm{j}}}$$

(11)

$Q_j$ is the entropy weight of the jth index $Q_j\in \left[\mathrm{0,1}\right]$.

Expression (11) satisfies the following conditions:

$${\sum }_{\mathrm{j}=1}^{\mathrm{n}}{\mathrm{Q}}_{\mathrm{j}}=1$$

(12)

3.3. Calculate Combination Weights

The analytic hierarchy process uses expert experience to calculate the weight of each index with certain subjectivity. The entropy weight law can obtain a completely objective index weight based on the difference in the index data. The two methods of calculating weights have their own limitations. The Lagrange multiplier method [21] is used for weight combination weighting. The weights obtained by the analytic hierarchy process and the weights obtained by the entropy weight method are combined and weighted. This can reflect the importance of each index. To ensure that the weights of each indicator are more objective and reasonable, it can more accurately reflect the weight coefficient W_j of each index in the surrounding rock of the roadway roof.

$${\mathrm{W}}_{\mathrm{j}}=\frac{\sqrt{{\mathrm{G}}_{\mathrm{j}}\times {\mathrm{Q}}_{\mathrm{j}}}}{{\sum }_{\mathrm{j}=1}^{\mathrm{n}}\sqrt{{\mathrm{G}}_{\mathrm{j}}\times {\mathrm{Q}}_{\mathrm{j}}}}$$

(13)

$W_j$ is the combined weight of the jth evaluation index $W_j\in \left[\mathrm{0,1}\right]$ ${\sum }_{j=1}^n{W}_j=1$.

$G_j$ is the jth evaluation index weight obtained by the analytic hierarchy process.

$Q_j$ is the jth evaluation index weight obtained by the entropy weight method.

In Expression (13), G_j is the weight of each index obtained by the analytic hierarchy process, and Q_j is the weight of each index obtained by the entropy weight method.

4. Construct AHP-EW Combined Weight Matter Element Extension Model

4.1. Determine the Risk Evaluation Set of Roadway Roof Falls

The three-level fuzzy comprehensive evaluation method is used to quantitatively evaluate the risk degree of roadway roof falls from the indicator layer, the criterion layer and the goal layer. Based on the investigation of a large number of roadway roof fall risk factors, the evaluation set of the roadway roof fall risk evaluation grade is divided into five grades from low to high: very low risk (I), low risk (II), medium risk (III), high risk (IV) and very high risk (V). The corresponding meaning of each grade is shown in

Table 3. Risk evaluation index level of roadway roof falls.

Evaluating Indicator	Order of Evaluation
	I	II	III	IV	V
	Very Low Risk	Low Risk	Intermediate Risk	High Risk	Very High Risk
Stable rock thickness U11/m	6.0~7.5	4.5~6.0	3.0~4.5	1.5~3.0	0~1.5
Geological condition U12	Simple 0~2	Relatively Simple 2~4	Relatively Complicated 4~6	Complicated 6~8	Extremely Complicated 8~10
Cross-section shape of roadway U13	Roundness 8~10	Arch 6~8	Rectangle 4~6	Trapezium 2~4	Miscellaneous 0~2
Angle between maximum horizontal principal stress and roadway U14/°	0~18	18~36	36~54	54~72	72~90
The amount of displacement of roof strata U21/m	0~0.07	0.07~0.14	0.14~0.21	0.21~0.28	0.28~0.5
Visible fracture development situation U22/pcs	0~2	2~4	4~6	6~8	8~10
Compressive strength of roof rock U23/MPa	200~250	150~200	100~150	100~50	0~50
Water content of roof rock U24	No Seepage 0~2	Micro-seepage Water 2~4	Micro-water Exit 4~6	A Little Water Flow 6~8	Heavy Water Flow 8~10
Roof stability U25	Stabilization 8~10	Relatively Stable 6~8	Relative Destabilization 4~6	Destabilization 2~4	Extreme Destabilization 0~2
Surrounding disturbance U31	No Impact 0~2	Minimal Impact 2~4	Small Impact 4~6	Great Impact 6~8	Profound Impact 8~10
Maximum exposure time U32/d	0~5	5~15	10~30	30~60	50~100
Supporting quality U33	Goodliness 8~10	Good 6~8	General 4~6	Poor 2~4	Very Poor 0~2

.

In order to facilitate the calculation of the correlation degree and comprehensive evaluation grade of each evaluation index, and to ensure that the calculation results are more scientific, the evaluation indexes in Table 3 are dimensionless according to Formula (14). The processing results are shown in

Table 4. Evaluation index level of roadway roof fall risks without dimensional treatment.

Evaluating Indicator	Order of Evaluation
	I	II	III	IV	V
	Very Low Risk	Low Risk	Intermediate Risk	High Risk	Very High Risk
Stable rock thickness U11/m	0.8~1.0	0.6~0.8	0.4~0.6	0.2~0.4	0.0~0.2
Geological condition U12	0.0~0.2	0.2~0.4	0.4~0.6	0.6~0.8	0.8~1.0
Cross-section shape of roadway U13	0.8~1.0	0.6~0.8	0.4~0.6	0.2~0.4	0.0~0.2
Angle between maximum horizontal principal stress and roadway U14/°	0.0~0.2	0.2~0.4	0.4~0.6	0.6~0.8	0.8~1.0
The amount of displacement of roof strata U21/m	0.0~0.14	0.14~0.28	0.28~0.42	0.42~0.56	0.56~1.00
Visible fracture development situation U222/pcs	0.0~0.2	0.2~0.4	0.4~0.6	0.6~0.8	0.8~1.0
Compressive strength of roof rock U23/MPa	0.8~1.0	0.6~0.8	0.4~0.6	0.2~0.4	0.0~0.2
Water content of roof rock U24	0.0~0.2	0.2~0.4	0.4~0.6	0.6~0.8	0.8~1.0
Roof stability U25	0.8~1.0	0.6~0.8	0.4~0.6	0.2~0.4	0.0~0.2
Surrounding disturbance U31	0.0~0.2	0.2~0.4	0.4~0.6	0.6~0.8	0.8~1.0
Maximum exposure time U32/d	0.0~0.05	0.05~0.15	0.15~0.30	0.30~0.60	0.60~1.00
Supporting quality U33	0.8~1.0	0.6~0.8	0.4~0.6	0.2~0.4	0.0~0.2

.

$$q_j^{,}=\left\{\begin{array}{c}\frac{{\mathrm{q}}_{\mathrm{j}}-{\mathrm{q}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{q}}_{\mathrm{m}\mathrm{i}\mathrm{n}}} \to \mathrm{The} \mathrm{bigger} \mathrm{the} \mathrm{better} \mathrm{the} \mathrm{factor}\\ \frac{{\mathrm{q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{q}}_{\mathrm{j}}}{{\mathrm{q}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{q}}_{\mathrm{m}\mathrm{i}\mathrm{n}}} \to \mathrm{The} \mathrm{smaller} \mathrm{the} \mathrm{better} \mathrm{the} \mathrm{factor}\end{array}\right.$$

(14)

In Expression (14), ${\mathrm{q}}_{\mathrm{j}}^{\prime }=(1,2,\dots ,\mathrm{n})$ is the actual value of the evaluation of an evaluation index; ${\mathrm{q}}_{\mathrm{j}}^{\prime }$ is the evaluation standard value of an evaluation index after standardization; ${\mathrm{q}}_{\max }$ is the upper limit of the evaluation value of an evaluation index; ${\mathrm{q}}_{\min }$ is the lower limit of the evaluation standard value of an evaluation index.

4.2. AHP-EW Combined Weight Element Extension Model

According to the matter element extension theory [22], the establishment steps of the matter element extension model are as follows:

(1) Determine the classical domain:

The classical domain matrix of the evaluation index can be expressed as a formula.

$${\mathrm{R}}_{0\mathrm{t}}=\left[\mathrm{N},{\mathrm{C}}_{\mathrm{j}},{\mathrm{V}}_{0\mathrm{tj}}\right]=\left[\begin{array}{ccc}\mathrm{N}& {\mathrm{C}}_1& ⟨{\mathrm{a}}_{0\mathrm{t}1},{\mathrm{b}}_{0\mathrm{t}1}⟩\\ & {\mathrm{C}}_2& ⟨{\mathrm{a}}_{0\mathrm{t}2},{\mathrm{b}}_{0\mathrm{t}2}⟩\\ & ⋮& ⋮\\ & {\mathrm{C}}_{\mathrm{n}}& ⟨{\mathrm{a}}_{0\mathrm{tn}},{\mathrm{b}}_{0\mathrm{tn}}⟩\end{array}\right]$$

(15)

In the formula, R_0t is the classical domain matter element; N is the whole matter element to be evaluated; C_j (j = 1, 2, …, n) is the evaluation index of the thing N; V_0tj = <a_0tj, b_0tj> is the evaluation index C_j of the classical domain matter element in t (t = 1, 2, …, g); the value range of the evaluation grade is the classical domain; a_0tj is the lower limit of the classical domain; b_0tj is the upper limit of the classical domain.

(2) Determine the section domain:

The section domain matrix of the evaluation index is expressed as the following formula:

$${\mathrm{R}}_{\mathrm{q}}=\left[\mathrm{N},{\mathrm{C}}_{\mathrm{j}},{\mathrm{V}}_{\mathrm{qj}}\right]=\left[\begin{array}{ccc}\mathrm{N}& {\mathrm{C}}_1& ⟨{\mathrm{a}}_{\mathrm{q}1},{\mathrm{b}}_{\mathrm{q}1}⟩\\ & {\mathrm{C}}_2& ⟨{\mathrm{a}}_{\mathrm{q}2},{\mathrm{b}}_{\mathrm{q}2}⟩\\ & ⋮& ⋮\\ & {\mathrm{C}}_{\mathrm{n}}& ⟨{\mathrm{a}}_{\mathrm{qn}},{\mathrm{b}}_{\mathrm{qn}}⟩\end{array}\right]$$

(16)

In the formula, R_q is a nodal matter element; V_qj = <a_qj, b_qj> is the value range of N for evaluation indicators C_j (j = 1, 2, …, n), which is the section field.

The value range of (n) is the nodal domain; a_qj is the lower limit value of the nodal domain; b_qj is the upper limit of the node domain.

(3) Determine the matter element to be evaluated:

The matter element to be evaluated R_ij (i = 1,2, …, m; j = 1, 2, …, m) is determined by Equation (17). The evaluation index C_j of the thing N_i to be evaluated is scored. The actual value is recorded as V_ij.

$${\mathrm{R}}_{\mathrm{ij}}=\left[{\mathrm{N}}_{\mathrm{i}},{\mathrm{C}}_{\mathrm{j}},{\mathrm{V}}_{\mathrm{ij}}\right]=\left[\begin{array}{ccc}{\mathrm{N}}_{\mathrm{i}}& {\mathrm{C}}_1& {\mathrm{V}}_{\mathrm{i}1}\\ & {\mathrm{C}}_2& {\mathrm{V}}_{\mathrm{i}2}\\ & ⋮& ⋮\\ & {\mathrm{C}}_{\mathrm{n}}& {\mathrm{V}}_{\mathrm{in}}\end{array}\right]$$

(17)

$N_i$ is something to be evaluated.

$C_j$ is the evaluation index.

$V_{ij}$ is the actual value of the thing to be evaluated $N_i$ in the evaluation index $C_j$.

(4) Calculate correlation degree:

The correlation function expression of the jth index C_j (j = 1, 2, …, n) of the thing to be evaluated N_i (i = 1, 2, …, m) about the evaluation grade t(t = 1, 2, …, g) is as follows:

$${\mathrm{k}}_{\mathrm{t}}({\mathrm{V}}_{\mathrm{ij}})=\left\{\begin{array}{c}\frac{\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{0\mathrm{tj}}\right]}{\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{\mathrm{qj}}\right]-\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{0\mathrm{tj}}\right]},\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{\mathrm{qj}}\right]\ne \mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{0\mathrm{tj}}\right]\\ -\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{0\mathrm{tj}}\right]-1,\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{\mathrm{qj}}\right]=\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{ij}}\left(\mathrm{t}\right),{\mathrm{V}}_{0\mathrm{tj}}\right]\end{array}\right.$$

(18)

In Expression (18),

$$\left\{\begin{array}{c}\mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right),{\mathrm{V}}_{0\mathrm{t}\mathrm{j}}\right]=\left|{\mathrm{V}}_{\mathrm{i}\mathrm{j}}-\frac{1}{2}\left({\mathrm{b}}_{0\mathrm{t}\mathrm{j}}+{\mathrm{a}}_{0\mathrm{t}\mathrm{j}}\right)\right|-\frac{1}{2}\left({\mathrm{b}}_{0\mathrm{t}\mathrm{j}}-{\mathrm{a}}_{0\mathrm{t}\mathrm{j}}\right)\\ \mathsf{\rho }\left[{\mathrm{V}}_{\mathrm{i}\mathrm{j}}\left(\mathrm{t}\right),{\mathrm{V}}_{\mathrm{q}\mathrm{j}}\right]=\left|{\mathrm{V}}_{\mathrm{i}\mathrm{j}}-\frac{1}{2}\left({\mathrm{b}}_{\mathrm{q}\mathrm{j}}+{\mathrm{a}}_{\mathrm{q}\mathrm{j}}\right)\right|-\frac{1}{2}\left({\mathrm{b}}_{\mathrm{q}\mathrm{j}}-{\mathrm{a}}_{\mathrm{q}\mathrm{j}}\right)\end{array}\right.$$

$\rho \left[V_{ij}\left(t\right),V_{0tj}\right]$ is the distance between the index $V_{ij}\left(t\right)$ and the classical domain $V_{0tj}$.

$a_{0tj}$ is the lower limit of the classical domain.

$b_{0tj}$ is the upper limit of the classical domain.

$\rho \left[V_{ij}\left(t\right),V_{qj}\right]$ is the distance between the index $V_{ij}\left(t\right)$ and the segment domain $V_{qj}$.

$a_{qj}$ is the lower limit of the section domain.

$b_{qj}$ is the upper limit value of the nodal domain.

All the calculated correlation degrees are recorded in the form of a matrix, so the correlation matrix K is the following formula:

$$\mathrm{K}=\left[\begin{array}{cccc}{\mathrm{k}}_1\left({\mathrm{V}}_{\mathrm{i}1}\right)& {\mathrm{k}}_2\left({\mathrm{V}}_{\mathrm{i}1}\right)& \cdots & {\mathrm{k}}_{\mathrm{z}}\left({\mathrm{V}}_{\mathrm{i}1}\right)\\ {\mathrm{k}}_1\left({\mathrm{V}}_{\mathrm{i}2}\right)& {\mathrm{k}}_2\left({\mathrm{V}}_{\mathrm{i}2}\right)& \cdots & {\mathrm{k}}_{\mathrm{z}}\left({\mathrm{V}}_{\mathrm{i}2}\right)\\ ⋮& ⋮& \cdots & ⋮\\ {\mathrm{k}}_1\left({\mathrm{V}}_{\mathrm{in}}\right)& {\mathrm{k}}_2\left({\mathrm{V}}_{\mathrm{in}}\right)& \cdots & {\mathrm{k}}_{\mathrm{z}}\left({\mathrm{V}}_{\mathrm{in}}\right)\end{array}\right]$$

(19)

$k_t\left(V_{ij}\right)$ is the correlation degree of the j th index $C_j$ of the thing $N_i$ to be evaluated about the evaluation grade t.

(5) Determine the evaluation level:

$$\mathrm{S}\left({\mathrm{N}}_{\mathrm{i}}\right)=\mathrm{WK}=\left({\mathrm{W}}_1,{\mathrm{W}}_2,\dots ,{\mathrm{W}}_{\mathrm{n}}\right)\left[\begin{array}{cccc}{\mathrm{k}}_1\left({\mathrm{V}}_{\mathrm{i}1}\right)& {\mathrm{k}}_2\left({\mathrm{V}}_{\mathrm{i}1}\right)& \cdots & {\mathrm{k}}_{\mathrm{z}}\left({\mathrm{V}}_{\mathrm{i}1}\right)\\ {\mathrm{k}}_1\left({\mathrm{V}}_{\mathrm{i}2}\right)& {\mathrm{k}}_2\left({\mathrm{V}}_{\mathrm{i}2}\right)& \cdots & {\mathrm{k}}_{\mathrm{z}}\left({\mathrm{V}}_{\mathrm{i}2}\right)\\ ⋮& ⋮& \cdots & ⋮\\ {\mathrm{k}}_1\left({\mathrm{V}}_{\mathrm{in}}\right)& {\mathrm{k}}_2\left({\mathrm{V}}_{\mathrm{in}}\right)& \cdots & {\mathrm{k}}_{\mathrm{z}}\left({\mathrm{V}}_{\mathrm{in}}\right)\end{array}\right]=\left({\mathrm{S}}_1,{\mathrm{S}}_2,\dots ,{\mathrm{S}}_{\mathrm{g}}\right)$$

(20)

$K$ is the correlation degree matrix.

$W$ is the combination weight.

In the formula, W is the combination weight. If max{S(N_i)} = S_t, the evaluation grade of N_i is t.

5. Develop Roadway Roof Fall Risk Assessment System

To quickly evaluate the risk of roadway roof falls, the developed roadway roof fall risk assessment system (MW-MEM) is based on a B/S architecture [23], which uses the J2EE technique [24]. We name the system Multiple Weight-Material Element Web (MW-MEW). The system development model is created using the MVC design pattern [25].

5.1. System Development Environment

IntelliJ IDEA 2022.3.2 is the system development platform, using the Java18 version of the programming language development background. The server uses Tomcat8.5. The database is MySQL57.

5.2. System Framework

The system uses the SSM framework for research and development. Spring is an open-source lightweight Java framework, which aims to provide developers with simple development methods. Spring MVC is a role that separates model objects, controllers, dispatchers, and handler objects. This ensures convenience for developers.

5.3. Implementation System

The process of the risk assessment of roadway roof falls developed by the system is shown in Figure 2. After inputting the corresponding values according to the system prompt, the weight of the risk factors of roadway roof falls and the risk assessment of roadway roof falls can be output in the form of a report. This is convenient for relevant personnel to adopt targeted safety support methods. This could reduce the risk of roadway roof caving, ensuring the security of the roadway.

6. Engineering Application

6.1. Project Overview

The Yunnan Wantian Group Xingu Coal Mine is 33.6 km away from Fuyuan County; it is located in the direction of 187°. The production capacity of the Xingu Coal Mine is 450,000 t/a. It is developed by an inclined shaft. The coal mining method used is the longwall mining method, and the whole height is mined at one time. All caving methods are used to manage the roof. The coal mining technology used is comprehensive mechanized mining, and mainly, six coal seams are mined. In this paper, the risk of roof falls in the original C9 return air contact roadway of the coal mine is evaluated and predicted.

6.2. Source of Data

Based on the risk evaluation system of coal mine roadway roof falls established in Figure 1, the expert scoring table of risk factors of roadway roof falls is compiled. Fifteen senior roadway roof fall research experts were invited to score the qualitative indicators of roadway roof fall risks. The qualitative scoring range is [0, 10]. The score results were averaged. In order to obtain the entropy weight corresponding to each evaluation index of C9 return air connection roadway, the data of eight places in this roadway are obtained according to the geological exploration data. Each place was numbered 1 to 8. The quantitative evaluation index values and the qualitative evaluation index values scored by experts are detailed in

Table 5. Roof fall index of roadway.

Lane Number	Evaluating Indicator
	U11	U12	U13	U14	U21	U22	U23	U24	U25	U31	U32	U33
1	5.12	3.66	8.82	19.50	0.08	3.00	210.00	3.56	9.45	2.56	3.00	8.65
2	4.82	4.56	7.89	22.15	0.06	1.00	220.00	4.45	8.92	2.78	6.00	7.43
3	5.86	3.29	7.88	18.92	0.07	2.00	215.00	3.41	7.82	3.15	4.00	6.84
4	6.78	4.89	8.45	20.50	0.08	2.00	202.00	4.26	8.67	3.48	7.00	8.12
5	5.72	3.19	7.09	23.32	0.07	3.00	198.00	4.56	8.09	3.07	6.00	7.68
6	5.85	3.89	8.38	19.85	0.07	1.00	214.00	5.56	9.75	3.56	3.00	7.56
7	4.79	4.57	7.65	24.15	0.08	2.00	222.00	4.85	7.93	4.87	5.00	8.23
8	6.00	5.19	8.58	17.98	0.06	2.00	218.00	3.44	7.05	2.95	6.00	7.88

. The roadway number 1 is the 10 m straight line distance between the C9 return air contact lane and the 11,901 central contact lane. The distance between the numbers from north to south is 5 m. According to Formula (8), the index standardization of Table 5 is carried out. The processing results are shown in

Table 6. Roadway roof fall index standardization.

Lane Number	Evaluating Indicator
	U11	U12	U13	U14	U21	U22	U23	U24	U25	U31	U32	U33
1	0.51	0.37	0.88	0.22	0.16	0.30	0.84	0.36	0.95	0.26	0.03	0.87
2	0.48	0.46	0.79	0.25	0.13	0.10	0.88	0.45	0.89	0.28	0.06	0.74
3	0.59	0.33	0.79	0.21	0.13	0.20	0.86	0.34	0.78	0.32	0.04	0.68
4	0.68	0.49	0.85	0.23	0.15	0.20	0.81	0.43	0.87	0.35	0.07	0.81
5	0.57	0.32	0.71	0.26	0.14	0.30	0.79	0.46	0.81	0.31	0.06	0.77
6	0.59	0.39	0.84	0.22	0.14	0.10	0.86	0.56	0.98	0.36	0.03	0.76
7	0.48	0.46	0.77	0.27	0.16	0.20	0.89	0.49	0.79	0.49	0.05	0.82
8	0.60	0.52	0.86	0.20	0.12	0.20	0.87	0.34	0.71	0.30	0.06	0.79

.

6.3. Calculate Index Weight

(1) Use the AHP method to calculate the weight of the indicators:

Based on the investigation of many risk factors of roadway roof falls, expert opinions and the actual situation in coal mine roadways, the target layer U of the analysis and evaluation system of coal mine roadway roof falls is constructed. The judgment matrices of criterion layers U1, U2 and U3 are as follows:

$${\mathrm{A}}_{\mathrm{U}}=\left[\begin{array}{ccc}1& \frac{1}{2}& 1\\ 2& 1& 1\\ 1& 1& 1\end{array}\right]$$

(21)

$${\mathrm{A}}_{{\mathrm{U}}_1}=\left[\begin{array}{cccc}1& 2& 4& 3\\ \frac{1}{2}& 1& 3& 2\\ \frac{1}{4}& \frac{1}{3}& 1& \frac{1}{3}\\ \frac{1}{3}& \frac{1}{2}& 3& 1\end{array}\right]$$

(22)

$${\mathrm{A}}_{{\mathrm{U}}_2}=\left[\begin{array}{ccccc}1& 1& 2& 1& 1\\ 1& 1& 2& 1& \frac{1}{2}\\ \frac{1}{2}& \frac{1}{2}& 1& 2& 1\\ 1& 1& \frac{1}{2}& 1& \frac{1}{3}\\ 1& 2& 1& 3& 1\end{array}\right]$$

(23)

$${\mathrm{A}}_{{\mathrm{U}}_3}=\left[\begin{array}{ccc}1& 2& \frac{1}{2}\\ \frac{1}{2}& 1& \frac{1}{3}\\ 2& 3& 1\end{array}\right]$$

(24)

According to Expressions (2)~(7) and with the help of the developed MW-MEM system, the weight value G of each evaluation index of the roadway roof fall risk is calculated as shown in

Table 7. Index weight.

Goal Layer	Criterion Layer	Criterion Layer Weight	Indicator Layer	Index Layer Weight	AHP-Calculated Weights G	EW-Calculated Weight Q	Combination Weight W
Roadway roof fall risk evaluation system U	Roadway structure characteristics U1	0.26	Stable rock thickness U11/m	0.46	0.12	0.09	0.11
			Geological condition U12	0.28	0.07	0.10	0.09
			Cross-section shape of roadway U13	0.09	0.02	0.07	0.04
			Angle between maximum horizontal principal stress and roadway U14/°	0.18	0.05	0.09	0.07
	Roadway roof characteristics U2	0.41	The amount of displacement of roof strata U21/m	0.22	0.10	0.08	0.09
			Visible fracture development situation U22/pcs	0.19	0.08	0.10	0.09
			Compressive strength of roof rock U23/MPa	0.19	0.08	0.08	0.08
			Water content of roof rock U24	0.12	0.05	0.10	0.07
			Roof stability U25	0.28	0.11	0.07	0.10
	Roadway engineering situation U3	0.33	Surrounding disturbance U31	0.30	0.10	0.08	0.09
			Maximum exposure time U32/d	0.16	0.05	0.10	0.08
			Supporting quality U33	0.54	0.18	0.06	0.11

. And the above judgment matrices all passed the consistency tests. For all the judgment matrices, GR < 0.1. Therefore, the weight distribution is reasonable, and it is not necessary to reconstruct the judgment matrix.

(2) Use the EW method to calculate the weight of each evaluation index:

According to the evaluation index data in Table 6, the matrix B = (b_ij)_8×12 is constructed. This is Expression (25).

$$\mathrm{B}=\left[\begin{array}{ccccc}0.51& 0.37& \cdots & 0.03& 0.87\\ 0.48& 0.46& \cdots & 0.06& 0.74\\ ⋮& ⋮& ⋮& ⋮& ⋮\\ 0.48& 0.46& \cdots & 0.05& 0.82\\ 0.60& 0.52& \cdots & 0.06& 0.79\end{array}\right]$$

(25)

According to Expressions (9)–(11), the data in Table 6 are input into the MW-MEM system. The weight value Q of each evaluation index of the roadway roof fall risk is calculated as shown in Table 7.

(3) Calculate the combination weights:

With the help of the MW-MEM system, according to Expression (13), the combined weight W of each evaluation index is calculated, as shown in Table 7.

6.4. Identify the Classical Domain, Section Domain, and Matter Element to Be Evaluated

This is determined according to the data from Expressions (15)–(17), Table 4 and the actual situation of the Xingu Coal Mine.

(1) Classical matter element R_0t for risk assessment of roadway roof falls:

The roof fall risk evaluation matter element R of the C9 return air contact roadway in the Xingu coal mine is composed of the risk level N of roadway roof fall, the evaluation index C and the characteristic value V.

$${\mathrm{R}}_{0\mathrm{t}}=\left[\begin{array}{cccccc}\mathrm{N}& {\mathrm{N}}_1& {\mathrm{N}}_2& {\mathrm{N}}_3& {\mathrm{N}}_4& {\mathrm{N}}_5\\ {\mathrm{C}}_1& (0.8,1.0)& (0.6,0.8)& (0.4,0.6)& (0.2,0.4)& (0.0,0.2)\\ {\mathrm{C}}_2& (0.0,0.2)& (0.2,0.4)& (0.4,0.6)& (0.6,0.8)& (0.8,1.0)\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ {\mathrm{C}}_{12}& (0.8,1.0)& (0.6,0.8)& (0.4,0.6)& (0.2,0.4)& (0.0,0.2)\end{array}\right]$$

(26)

(2) The nodal domain matrix R_q is

$${\mathrm{R}}_{\mathrm{q}}=\left[\begin{array}{ccc}\mathrm{N}& \mathrm{C}& \mathrm{V}\\ & {\mathrm{C}}_1& (0.0,1.0)\\ & {\mathrm{C}}_2& (0.0,1.0)\\ & ⋮& ⋮\\ & {\mathrm{C}}_{12}& (0.8,1.0)\end{array}\right]$$

(27)

(3) The matter element volume matrix R_ij corresponding to the roadway to be evaluated is

$${\mathrm{R}}_{ij}=\left[\begin{array}{cccc}\mathrm{lane} \mathrm{number}& {\mathrm{C}}_1& L& {\mathrm{C}}_{12}\\ 1& 0.51& \mathrm{L}& 0.87\\ \mathrm{M}& M& \mathrm{L}& \mathrm{M}\\ 8& 0.6& \mathrm{L}& 0.79\\ & & \end{array}\right]$$

(28)

6.5. Determine the Correlation Degree of Roadway Roof Collapse Risk Evaluation

According to the data in Expressions (18)–(20), Table 4 and Table 7, and with the help of the roadway roof fall risk evaluation system, MW-MEW, based on the AHP-EW combined weight matter element extension model, the comprehensive correlation degree of each evaluation index of the roadway roof fall risk is obtained. Take roadway No. 8 as an example, as shown in

Table 8. Roadway No. 8 roof fall index correlation degree.

Roadway Roof Fall Risk Level	U11	U12	U13	U14	U21	U22	U23	U24	U25	U31	U32	U33
I (Very Low Risk)	−0.33	−0.40	0.07	0.00	0.23	0.00	0.08	−0.30	−0.24	−0.24	−0.17	−0.05
II (Low Risk)	0.00	−0.20	−0.07	0.00	−0.16	0.00	−0.36	0.19	0.48	0.32	0.17	0.02
III (Intermediate Risk)	0.00	0.16	−0.65	−0.50	−0.58	−0.50	−0.68	−0.14	−0.26	−0.26	−0.60	−0.47
IV (High Risk)	−0.33	−0.14	−0.76	−0.67	−0.72	−0.67	−0.79	−0.43	−0.51	−0.51	−0.80	−0.65
V (Very High risk)	−0.50	−0.37	−0.82	−0.75	−0.79	−0.75	−0.84	−0.57	−0.63	−0.63	−0.90	−0.74

. The results of the roof fall risk grade of the C9 return air contact roadway in the Xingu Coal Mine are obtained, as shown in

Table 9. Evaluation of roadway roof fall risk comprehensive correlation degree calculation and evaluation results.

Lane Number	C 9 Return Air Contact Roadway Roof Fall Risk Evaluation Grade Correlation Degree
	I (Very Low Risk)	II (Low Risk)	III (Intermediate Risk)	IV (High Risk)	V (Very High Risk)	Evaluation Level
1	−0.07	−0.06	−0.41	−0.61	−0.71	II
2	−3.29 × 1014	−0.11	−0.36	−0.57	−0.68	II
3	−0.12	0.04	−0.36	−0.58	−0.68	II
4	−0.14	0.01	−0.35	−0.57	−0.69	II
5	−0.18	0.11	−0.31	−0.54	−0.66	II
6	−3.29 × 1014	−0.18	−0.41	−0.60	−0.70	II
7	−0.15	−0.06	−0.28	−0.51	−0.64	II
8	−0.12	0.04	−0.35	−0.57	−0.68	II
Mean Value	−8.21 × 1013	−0.03	−0.36	−0.57	−0.68	II

.

6.6. Roadway Evaluation Result

The evaluation grades of eight roadways are shown in Table 9, and the evaluation results are shown in Figure 3.

It can be found from Figure 3 that there is a deviation between roadway number 3 and roadway number 5 in the evaluation of the roadway number. The remaining lane numbers are basically consistent with the actual results. This shows that the established AHP-EW combined weight matter element extension model can be used to evaluate the risk of roadway roof falls. The developed MW-MEW system facilitates the calculation of the risk of roadway roof falls.

In order to verify the generalization of the model, eight C9 return air contact lanes were evaluated and compared with the results of the AHP extension model evaluation. The results are shown in

Table 10. Comparison of the evaluation results of AHP extension model and combined weight extension model.

Number	Realistic Grade	AHP Extension Model	Combination Weight Extension Model
		Evaluation Level	Evaluation Level
1	II	I	II
2	III	II	II
3	II	II	II
4	III	II	II
5	II	II	II
6	II	II	II
7	II	II	II
8	II	II	II

. According to the analysis of Table 10, the evaluation results of the combined weight extension model are basically close to the actual evaluation results. The correct rate was 75%. The accuracy of the evaluation results of the roadway according to the combined weight extension model is higher than that of the AHP extension model by 62.5%. This shows that the AHP-EW combined weight matter element extension model can accurately evaluate the risk degree of roadway roof falls.

6.7. Inspection of the Program

To improve the rigor of the results, we use another example to test the AHP-EV model. In order to avoid redundancy, the intermediate calculation process is omitted, and only the intermediate data table is displayed.

Table 11. Test roadway roof fall index.

Lane Number	Evaluating Indicator
	U11	U12	U13	U14	U21	U22	U23	U24	U25	U31	U32	U33
1	5.32	3.46	8.42	19.50	0.08	4.00	210.00	3.56	9.45	2.56	3.00	9.65

is the roadway data collection.

Table 12. R Test roadway roof fall index standardization.

Lane Number	Evaluating Indicator
	U11	U12	U13	U14	U21	U22	U23	U24	U25	U31	U32	U33
1	0.53	0.35	0.84	0.20	0.16	0.40	0.84	0.36	0.95	0.03	0.03	0.97

is the index standardization of the data.

With the help of MW-MEM system, the combined weight W of each evaluation index is calculated, as shown in

Table 13. Test index weight.

Goal Layer	Criterion Layer	Criterion Layer Weight	Indicator Layer	Index Layer Weight	Combination Weight W
Roadway roof fall risk evaluation system U	Roadway structure characteristics U1	0.26	Stable rock thickness U11/m	0.46	0.12
			Geological condition U12	0.28	0.07
			Cross-section shape of roadway U13	0.09	0.02
			Angle between maximum horizontal principal stress and roadway U14/°	0.18	0.05
	Roadway roof characteristicsU2	0.41	The amount of displacement of roof strata U21/m	0.22	0.09
			Visible fracture development situation U22/pcs	0.19	0.08
			Compressive strength of roof rock U23/MPa	0.19	0.08
			Water content of roof rock U24	0.12	0.05
			Roof stability U25	0.28	0.11
	Roadway engineering situation U3	0.33	Surrounding disturbance U31	0.30	0.09
			Maximum exposure time U32/d	0.16	0.05
			Supporting quality U33	0.54	0.18

.

According to the data, and with the help of the roadway roof fall risk assessment system MW-MEW, The comprehensive correlation degree of each evaluation index of the roof fall risk of the roadway is obtained, as shown in

Table 14. No. 1 roadway roof fall index correlation degree.

Roadway Roof Fall Risk Level	U11	U12	U13	U14	U21	U22	U23	U24	U25	U31	U32	U33
I (Very Low Risk)	−0.37	−0.31	0.09	−0.07	−0.13	−0.25	0.05	−0.30	0.06	−0.18	0.67	0.08
II (Low Risk)	−0.15	−0.10	−0.09	0.08	−0.15	0.03	−0.20	0.14	−0.73	0.22	−0.40	−0.08
III (Intermediate Risk)	0.17	−0.09	−0.71	−0.46	−0.41	−0.25	−0.60	−0.11	−0.86	−0.36	−0.80	−0.66
IV (High Risk)	−0.19	−0.39	−0.80	−0.64	−0.61	−0.50	−0.73	−0.41	−0.91	−0.57	−0.90	−0.78
V (Very High Risk)	−0.39	−0.54	−0.85	−0.73	−0.71	−0.63	−0.80	−0.56	−0.93	−0.68	−0.95	−0.83

.

The results of the risk level of roadway roof fall are obtained, as shown in

Table 15. Comprehensive correlation degree calculation and evaluation results of roof fall risk evaluation of test roadway.

Lane Number	C 9 Return Air Contact Roadway Roof Fall Risk Evaluation Grade Correlation Degree
	I (Very Low Risk)	II (Low Risk)	III (Intermediate Risk)	IV (High Risk)	V (Very High Risk)	Evaluation Level
1	−0.19	0.04	−0.22	−0.48	−0.61	II

.

7. Conclusions

(1)

Based on the investigation of many risk factors of roadway roof falls, a risk evaluation index system of roadway roof falls is constructed. The risk degree standard of roadway roof falls is proposed.

(2)

The risk evaluation model of roadway roof falls is established by using the analytic hierarchy process (AHP) method, entropy weight method (EW) combined weight and matter element extension theory. According to the principle of the maximum membership degree, the risk degree of roadway roof falls is determined. The basic characteristics of roadway roof falls are obtained.

(3)

The risk assessment system of roadway roof falls was developed using the Java programming language. The system can quickly calculate the risk of roof falls in coal mine roadways. The function of the dynamic evaluation of the roadway roof fall risk is realized.

(4)

The roof fall risk evaluation system was used to evaluate the risk degree of roof falls in the C9 return air connecting roadway of the Xingu Coal Mine. By comparing with the actual survey results, it is shown that the evaluation results using this evaluation method are consistent with the actual engineering situation onsite. In the future, it is planned to further improve the roadway roof fall risk assessment system (MW-MEW) and compare the collected data, considering more geological factors.