A multi-level analysis method for evaluating the risk of roof caving and its application

Abstract

Roof collapse is the most frequent production accident in the mine production process, which seriously threatens the efficient and safe production of the mine. Therefore, it is urgent to carry out practical research on the roof collapse tendency of the roadway. After searching and analyzing the relevant documents, the primary influencing factors of roof collapse risk based on AHP are determined, namely engineering geology, rock mass support, construction management and natural environment. After refining the main influencing factors, the evaluation factor set is obtained, the fuzzy comprehensive evaluation relationship matrix is established, and the fuzzy comprehensive evaluation model of roof collapse risk is obtained. Finally, the quantitative evaluation of no collapse risk, weak collapse risk, medium collapse risk and high collapse risk is carried out. Taking a metal mine as an example, the risk of roof collapse of its C11 haulage roadway is selected for fuzzy evaluation. The evaluation result is high collapse risk, which is consistent with the evaluation result of the current specification, indicating that the model can be used for mine roof collapse risk evaluation. This method of estimating roof collapse has been applied on-site, which is consistent with the actual situation and has achieved good results. It has guiding significance for predicting the stability of tunnels and supporting operations.

Keywords

Analytic hierarchy process risk assessment roof collapse fuzzy theory

1 Introduction

Mining has entered the stage of kilometer deep well. The instability of roadway roof caused by high ground stress, high temperature, high karst water pressure and mining disturbance has become one of the major disasters restricting the safe mining of mines. Scholars have done a lot of research work in roadway collapse risk assessment [1].

For many years, traditional artificial intelligence methods have been applied to engineering disaster risk analysis to achieve the purpose of evaluation and control, such as support vector machine [2], neural network [3], and Gaussian process regression [4].However, only considering the single factor to analyze the risk of tunnel collapse will produce a slightly deviated result from the reality. Because the single factor can not reflect the actual construction situation, the evaluation results are not accurate and can not provide accurate suggestions for decision makers. In contrast, the multi factor evaluation model can greatly improve the accuracy of prediction results due to a better understanding of risk factors [5].For example, a multi factor fuzzy evaluation model for predicting the risk of water inrush disaster is proposed [6]. The echo of monitoring data and numerical simulation data improves the accuracy of structural safety risk assessment [5]. Apply the multi-level evaluation framework to perceive the safety risk of building damage caused by tunnel [7].

Martin et al [8] proposed an evaluation method of tunnel brittle fracture zone and unstable zone based on the relationship between soil cohesion and rock uniaxial compressive strength. This method divides the failure modes into plastic failure, block failure and brittle failure, and puts forward a method to predict the failure location [9]. Goricki et al [10] proposed a tunnel excavation and support method considering rock types and characteristics. Li et al [11] studied the cause of tunnel collapse during construction and proposed a method to quantify the weathering degree, groundwater level and joints. There are various methods that can be used to investigate potential risk factors in underground excavation projects [12], and we can conduct more in-depth research based on them [13].

In recent years, people have proposed a variety of evaluation methods to investigate the potential risk factors of tunnel excavation projects [14], including risk matrix method [15], analytic hierarchy process method [16], fault tree method [17], artificial neural network method [18], fuzzy comprehensive evaluation method [19], cloud computing model [20], Bayesian network and event expansion model Dempster-Shafer (DS) evidence theory [21]. Jang and Yang [22] proposed a risk index called W-RMR, which can evaluate the section and vault of the tunnel according to the existing rock classification index (RMR), in order to select the supporting materials for the next step. Then, Shin et al [23] identified 17 influencing factors of collapse caused by tunnel construction, mainly including tunnel geometry, geology, discontinuity, groundwater level, excavation conditions and support means, and then developed a nonlinear modular calculation method based on artificial neural network (ANN) [24].

Generally, the direct cause of roadway roof fall or even collapse is closely related to the stability of the tunnel face [25], which is affected by objective and complex geological conditions and subjective manual work. In history, collapse accidents occurred in the process of mining and construction. It is often caused by inadequate understanding of geological conditions and improper construction operations, which has brought huge economic losses. The occurrence mechanism of deep rock mass disaster is complex[26], and the requirements for deformation and stability of roadway are higher and higher. Although bolting and shotcreting support has been widely used to prevent roadway roof fall and collapse, it is a technical challenge to evaluate the risk of roof collapse during continuous roadway use, which will ultimately affect the safety and normal operation of the tunnel. Therefore, it is urgent to quantify and evaluate the risks in the process of roadway construction and use.

The difference of the existing research on the risk evaluation of mine roadway roof collapse lies in the different selection of influencing factors and the different degree of influence of each factor on the evaluation results [27], so the final evaluation results are different. Especially when determining the weight of influencing factors, different methods have a great impact on the accuracy of the results. The research on the prediction of roadway roof collapse has made some achievements, but it still needs to be deeply studied in the fine evaluation of roof collapse risk. Using the fuzzy comprehensive evaluation method based on analytic hierarchy process, this paper puts forward four influencing factors: engineering geology, rock mass support, construction and management and natural disasters, and then regards these four factors affecting the risk of roadway roof collapse as a multi-level fuzzy set, establishes the risk grade evaluation index, and then quantitatively evaluates the risk grade of roof collapse by determining the membership degree.

2 Multilevel analysis model

2.1 Materials and methods

Establishment of fuzzy comprehensive evaluation model. When constructing the fuzzy comprehensive evaluation model, in order to coincide with the actual situation, analytic hierarchy process is mostly used. In fact, it is to comprehensively evaluate the existing evaluation standards and real measured values through fuzzy comprehensive calculation. When carrying out fuzzy comprehensive evaluation, the following three conditions should be met at the same time [28]: (1) evaluation factor set U ={ U₁U₂U₃ . . . U_n }, (2) evaluation set V ={ V₁V₂V₃ . . . V_n }, (3) A fuzzy mapping f of each evaluation factor set U to V, fU → V. That is, if any single factor u ∈ U is selected, there is a fuzzy comprehensive evaluation set B (u) ∈ f (V), and the fuzzy comprehensive matrix R, R = (r_ij) _nm, i = 12 . . . , n ; j = 12 . . . , m. which is called (U, V, R) as the mathematical model of comprehensive evaluation.

Because different evaluation factors have different effects on the evaluation results, in order to accurately represent the degree of influence, an influencing factor weight set a is defined, which is called the fuzzy subset of influencing factors of U, and its expression is: A = (A₁, A₂, . . . , A_n), where: A_i (0 ⩽ A_i ⩽ 1) Is the membership of U_i to A. When the fuzzy comprehensive matrix R and the influencing factor subset A are determined, the fuzzy comprehensive evaluation result of the event is: $\begin{matrix} B = A \times R = (A_{1}, A_{2}, \dots, A_{n}) \\ \times [\begin{matrix} r_{11} & \dots & r_{1 m} \\ ⋮ & ⋱ & ⋮ \\ r_{n 1} & \dots & r_{nm} \end{matrix}] = (b_{1}, b_{2}, \dots, b_{m}) \end{matrix}$

Among them, b_j is the subordinate degree of grade j of fuzzy comprehensive evaluation of coal seam impact risk. According to the maximum subordinate principle, b_k is defined as the maximum subordinate degree index x. b_k = max {b₁, b₂, . . . , b_m}, then the fuzzy comprehensive evaluation of coal seam impact risk is grade k.

2.2 Fuzzy comprehensive evaluation of roof collapse risk

According to the evaluation model, the fuzzy comprehensive evaluation of roof collapse risk should determine the evaluation factor set, evaluation set and fuzzy comprehensive relationship matrix. The evaluation factors of roof collapse risk are diverse. The accuracy, pertinence and effectiveness of factor indicators should be fully considered, and the key influencing factors can be indicated. Appropriate parameters should be selected based on the above conditions.

2.2.1 Determination of influencing factors

(1) Engineering geology (B₁)

In situ stress (C₁), in-situ stress mainly includes self weight stress of rock mass and stress generated or residual by tectonic movement. It is generally believed that the greater the in-situ stress, the worse the stability of the roadway. The specific influence of in-situ stress on the stability of roadway roof mainly depends on the size and direction of principal stress and the parameters such as roadway layout orientation. Rock integrity (C₂), rock integrity, refers to the integrity of rock mass after being transformed by tectonic movement. The characterization indexes include crack spacing, rock mass volume, joint number Jv and rock quality index RQD. Fault development (C₃): the fault is a structure in which the crust is broken under stress and the rock blocks on both sides of the fault surface are significantly displaced. The fault with large scale can extend hundreds of meters along the strike, and the fault with small scale is only tens of centimeters. Groundwater (C₄),groundwater macroscopically affects the humidity of the environment where the roadway is located, and poses a potential threat to the stability of the roadway roof.

(2) Rock mass support (B₂)

Rock mass support can significantly improve the stability of deep roadway roof. Reasonable and economic rock mass support can effectively maintain the stability of roadway roof and reduce the risk of collapse. At present, there are many rock mass support methods, and reasonable support methods need to consider safety and reasonable time.

Advance support (C₅). Advance support refers to the auxiliary measures taken to maintain the stability of the roadway before the excavation of the roadway face. The main methods are pipe shed and advance small conduit grouting. Permanent support (C₆). Permanent support, also known as secondary support. The roadway roof with long design life and poor geological conditions must be permanently supported. The means adopted mainly include bolt shotcrete support, steel arch frame, anchor mesh cable support, etc. Grouting reinforcement (C₇). Firstly, grouting holes are arranged for grouting reinforcement, and the slurry is injected into the surrounding rock through pressure. The grouting pressure makes the slurry diffuse to the cracks of the surrounding rock to form a reinforcement zone, so as to improve the strength and integrity of the rock mass and reduce the risk of roof collapse.

(3) Construction management (B₃)

Construction method (C₈). The construction method mainly refers to the sequence and technology of roadway roof excavation and support. Different construction methods have different degrees of damage to surrounding rock. For example, the damage degree of surrounding rock caused by mining machine excavation is much lower than that caused by vibration crack caused by drilling and blasting method.Field monitoring (C₉). The means and frequency of on-site monitoring can effectively predict and avoid roof instability and collapse. Roof collapse is sudden, but there will be obvious signs before large-scale collapse, such as sudden increase of surrounding rock stress, increase of crack width and so on. The accuracy and reliability of instruments used in field monitoring also affect the risk of roof collapse. Quality management (C₁₀). Fine management is very important for safe production. If the stability of roof and surrounding rock can be managed according to standardization and refinement, the risk of roof collapse and collapse will be reduced. Complete construction management not only affects the construction progress, but also affects the final construction quality and safety. The quality and safety of construction are affected by the allocation of manpower and equipment, production control, interface between processes, implementation of operating procedures, implementation of design progress, etc. Therefore, poor site organization and management will affect the construction quality. This paper takes the construction quality compliance as the scoring standard of on-site management index. Construction quality compliance refers to whether the construction conforms to the drawings and the degree of completion.

(4) Natural environment (B₄)

Precipitation (C₁₁), which changes the groundwater level, changes the migration law of seepage field in rock mass, and affects the stability of roof. Natural disasters (C₁₂), micro-seismic events and earthquake disasters impact the roadway roof. The impact energy makes the cracks in the rock mass expand, the aquifer seepage channel opens, and the roof is more prone to instability and collapse.

Natural environment mainly refers to climate conditions, geographical location, land and sea changes, natural disasters and so on. Among them, the impact on the stability of underground roadway is mainly reflected in extreme bad weather, such as precipitation, which will lead to the change of groundwater level. In addition, the activity of geological plate will also induce the instability of roadway roof. For example, frequent microseisms and seismicity will not only cause impact energy to the roof, but also aggravate the seepage of water bearing rock overlying the roof, which will cause irreversible damage to the roof.

2.2.2 Determination of evaluation factor set

According to the determined influencing factors, four influencing factors are selected as the first-class index of fuzzy comprehensive evaluation of coal seam impact risk, namely: engineering geology, rock mass support, construction management and natural environment. These four factors are defined as primary evaluation indicators.

2.2.3 Determination of evaluation set

Combined with the current national standards and actual needs on roadway collapse risk [29], the fuzzy comprehensive evaluation set V.

Where V = {V₁, V₂, V₃, V₄}, V₁ has no collapse risk, V₂ is weak collapse risk, V₃ is medium collapse risk and V₄ is high collapse risk.

2.2.4 Multi level analysis in fuzzy evaluation

When there are many factors affecting the risk of roadway collapse, the proportion of roof collapse can not be determined accurately. At this time, simple comprehensive evaluation can not meet the actual needs. The fuzzy comprehensive evaluation based on analytic hierarchy process can solve the problem well. This paper first searched the papers on roof stability analysis of tunnel engineering in the wos and cnki databases in the last ten years, and conducted a literature survey on roof stability of 70 mining tunnels and 30 urban tunnels, which cover typical metal mining tunnels, coal mining tunnels, urban subway tunnels, underground water conveyance tunnels, etc. These tunnels include not only permanently used refuge tunnels, power supply and distribution caverns and underground parking lots, but also temporary tunnels for short-term transportation. Through the investigation of the theme and key words of the paper, the factors affecting the stability of the roof are determined. The key words of these studies focus on four aspects: engineering geology, rock mass support, construction management and natural environment impact. The four factors are further divided, covering all secondary influencing factors included in the literature research, and the evaluation system as shown in Fig. 1 is constructed.

Fig. 1

Comprehensive evaluation index system for risk evaluation of roadway roof fall.

2.2.5 Determine the weight of evaluation factors at all levels

The comprehensive evaluation of roof collapse risk is a complex system engineering, and the four factors affecting roof stability must be systematically analyzed. A reasonable evaluation index system is the prerequisite for scientific and effective evaluation. Analytic Hierarchy Process (AHP) first establishes a progressive hierarchical structure of the analysis object, clearly reflects the relationship between various relevant factors, and can use less qualitative and quantitative information to quantify the decision-making process, thus simplifying the comprehensive evaluation problem. Figure 1 lists a total of 12 evaluation indicators affecting roof stability, and these 12 evaluation indicators have both quantitative and stereotyped factors. After the comprehensive evaluation index system is established by the analytic hierarchy process, each factor needs to be quantified. The limit value of the quantitative evaluation factor is divided according to the national norms and standards. For the standardized evaluation indicators, a total of 15 experts were formed to conduct qualitative evaluation. The 15 experts were from senior researchers of scientific research institutes, experienced field engineers and senior managers of enterprises.

The important link of fuzzy comprehensive evaluation to realize the transition from qualitative evaluation to quantitative evaluation is to calculate the weight of evaluation influencing factors. Whether the weight calculation is accurate or not affects the results of fuzzy comprehensive evaluation. The existing methods to determine the weight include efficacy coefficient method, index weighting method, neural network analysis method, analytic hierarchy process, grey analysis method and so on. Because there are many evaluation factors of roadway roof collapse risk and different evaluation factors are closely related, the weight of each factor is calculated based on analytic hierarchy process (AHP) [30], and then some experienced scholars in relevant fields are consulted to obtain the relevant evaluation matrix through consistency test calculation. Using analytic hierarchy process to determine the weight is to first build a judgment matrix, and then use the judgment matrix to determine the weight value of evaluation factors and establish a judgment matrix. $A = [\begin{matrix} \begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix} & \begin{matrix} \dots & a_{1 m} \\ \dots & a_{2 m} \end{matrix} \\ \begin{matrix} ⋮ & ⋮ \\ a_{n 1} & a_{n 2} \end{matrix} & \begin{matrix} ⋮ \\ \dots & a_{nm} \end{matrix} \end{matrix}]$

Where: Aij = 1/Aji. The element Aij in the judgment matrix A represents the relative importance of the element Ai to Aj, i.e $a_{ij} = w_{i} / w_{j}$ (1)

Where: Wi and Wj are the scale values of the importance of elements Ai and Aj respectively. The judgment matrix mainly quantifies the importance of elements through the 1 9 scale method, as shown in Table 1.

Table 1

Judgement matrix scale and its meaning

Scale	Meaning
1	A and B are equally important
3	A is slightly more important than B
5	A is obviously more important than B
7	A is more important than B
9	A is extremely important than B
2, 4, 6, 8	The median value of the above
	two adjacent judgments

The three steps of determining the weight by analytic hierarchy process are as follow:

Construct judgment matrix A.

Weight and maximum eigenvalue of judgment matrix

calculate the product Mi of each row element of the judgment matrix

M_{i} = \prod_{j = 1}^{n} a_{ij}

(2)

Calculate the n-th root of Mi $\bar{w_{i}} = \sqrt[n]{M_{i}}$ (3)

Normalize the vector $\bar{w} = {[\bar{w_{1}}, \bar{w_{2}} \dots \bar{w_{n}}]}^{T}$ , that is, the desired eigenvector $w_{i} = \bar{w_{i}} / \sum_{j = 1}^{n} \bar{w_{i}}$ (4)

Then W = [w₁w₂ ⋯ w_n] ^T is the eigenvector

Calculate the maximum eigenvalue of the eigenvector. $λ_{\max} = \sum_{j = 1}^{n} \frac{{(AW)}_{i}}{{nW}_{i}}$ (5)

Where (AW) _i is the ith element of vector AW. $AW = [\begin{matrix} \begin{matrix} {(AW)}_{1} \\ {(AW)}_{2} \end{matrix} \\ ⋮ \\ {(AW)}_{n} \end{matrix}] = [\begin{matrix} \begin{matrix} \begin{matrix} A_{11} \\ A_{21} \end{matrix} \\ ⋮ \\ A_{n 1} \end{matrix} & \begin{matrix} \begin{matrix} A_{12} \\ A_{22} \end{matrix} \\ ⋮ \\ A_{n 2} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} \dots \\ \dots \end{matrix} \\ \dots \end{matrix} & \begin{matrix} \begin{matrix} A_{1 n} \\ A_{2 n} \end{matrix} \\ ⋮ \\ A_{nn} \end{matrix} \end{matrix} \end{matrix}] [\begin{matrix} \begin{matrix} W_{1} \\ W_{2} \end{matrix} \\ ⋮ \\ W_{n} \end{matrix}]$

2.3 Consistency test of judgment matrix

Calculate consistency index CI $CI = (λ_{\max} - n) / (n - 1)$ (6)

Calculate the average random consistency index CR. $CR = CI / RI$ (7)

Among them, RI is the average random consistency index of the same order, and its value is shown in Table 2.

Table 2

Mean random consistency index of same order

n	1	2	3	4	5	6	7	8	9	10	11
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.49	1.51

When CR≤0.1, it indicates that the established judgment matrix has satisfactory consistency, indicating that the selection of weight meets the requirements. On the contrary, it is necessary to re determine the judgment matrix until the constructed judgment matrix meets the requirements.

2.4 Establishing fuzzy relation matrix

Using the construction process of single factor evaluation matrix for reference, a multi-level membership matrix is obtained. The single factor evaluation set can be obtained by summarizing the influence of each factor on the evaluation results. The membership function needs to be accurately determined by special methods to reduce the error. The calculation methods of membership function include binary comparison ranking method, expert scoring method, reasoning method, trisection method, fuzzy statistics method and so on. The geological conditions of coal seams in different coal mines are different, so we can’t find a membership function suitable for all factors. Combined with the actual situation, the expert scoring method is used to determine the membership function, that is, when determining the fuzzy relationship, ask a certain number of scholars and experts in relevant fields and senior engineers and technicians with rich experience to score according to the evaluation grade V. Through the processing of scoring data, the proportion of evaluation grade corresponding to different factors can be obtained. The fuzzy relationship matrix R is determined by summarizing the level proportion of different evaluation factors.

3 Analysis of engineering examples

Taking a lead zinc mine in Yunnan Province as an example, the risk of mine roof collapse in C11 coal measure stratum is evaluated. The thickness of roof sandstone is 0 5.3 m, with an average of 2.8 m. The sandstone stratum generally presents large-scale wide and gentle undulation, which is an anticline structure. The anticline trend is from north to west. The spacing between 1-1 sandstone layer and 1-2 mudstone layer is 0.87 43.84 m, with an average of 20.13 m. See Table 3 for the characteristics of roof rock mass.

Table 3
Roof and floor characteristics of C11 coal seam

Roof Lithology Thickness/m Lithologic characteristics

Basic top Fine sandstone,1-2medium sandstone 3.8 13.3 Light grayish white, mainly quartz, with a small amount of mica

Direct top 1-1Sandy mudstone 2.5 6.4 Grayish black, horizontal bedding

Pseudo top Sandy mudstone,siltstone 0.1 0.4 Light gray, dense, mainly quartz

Roof	Lithology	Thickness/m	Lithologic characteristics
Basic top	Fine sandstone,1-2medium sandstone	3.8 13.3	Light grayish white, mainly quartz, with a small amount of mica
Direct top	1-1Sandy mudstone	2.5 6.4	Grayish black, horizontal bedding
Pseudo top	Sandy mudstone,siltstone	0.1 0.4	Light gray, dense, mainly quartz

The fuzzy comprehensive evaluation model of roof collapse risk of C11 coal measure strata in a mine based on analytic hierarchy process focuses on determining the weight of each influencing factor. The process of calculating the weight of mine roof collapse risk assessment factors is as follows:

Construct judgment matrix A as $A = [\begin{matrix} 3.00 & 5.00 & 1.00 & 7.00 \\ 1.00 & 3.00 & 0.33 & 6.00 \\ 0.33 & 1.00 & 0.2 & 4.00 \\ 0.17 & 0.25 & 0.14 & 1.00 \end{matrix}]$

According to formula (2) ∼ formula (5), the maximum eigenvalue of the judgment matrix is lambdamax = 0.2. The weight of evaluation factors is A = [B₁, B₂, B₃, B₄] = [0.55, 0.27, 0.13, 0.05]. From formula (6) and formula (7), CR = 0.05 < 0.1. According to the consistency test of judgment matrix, a has satisfactory consistency.

The weight calculation method of secondary evaluation factors is the same as above. Firstly, determine the judgment matrix $B_{1} = [\begin{matrix} 1.00 & 0.22 & 0.15 & 0.33 \\ 4.50 & 1.00 & 0.29 & 3.00 \\ 6.50 & 3.50 & 1.00 & 4.00 \\ 3.00 & 0.33 & 0.25 & 1.00 \end{matrix}]$ , Calculated by formula (2) -formula (5), λ_max = 4.24. The weight of evaluation factors is V_{B
₁} = [C₁, C₂, C₃, C₄] = [0.06, 0.25, 0.56, 0.13]. From formula (6) and formula (7), CR = 0.09 < 0.1. According to the consistency test of judgment matrix, B₁ has satisfactory consistency.

The same as the above solution process, the remaining three judgment matrices B₁, B₂, B₃ and the corresponding weights are calculated, and the consistency coefficient is tested. The results are as follows:

$B_{2} = [\begin{matrix} 1.00 & 4.00 & 3.00 \\ 0.25 & 1.00 & 0.50 \\ 0.33 & 2.00 & 1.00 \end{matrix}]$ , λ_max = 4.20, V_{B
₂} = [C₅, C₆, C₇] = [0.63, 0.13, 0.24], CR = 0.0511 < 0.1,

$B_{3} = [\begin{matrix} 1.00 & 0.25 & 0.33 \\ 4.00 & 1.00 & 0.50 \\ 3.00 & 2.00 & 1.00 \end{matrix}]$ , λ_max = 5.19, V_{B
₃} = [C₈, C₉, C₁₀] = [0.12, 0.36, 0.52], CR = 0.0472 < 0.1,

$B_{4} = [\begin{matrix} 1.00 & 4.00 \\ 0.25 & 1.00 \end{matrix}]$ , λ_max = 4.01, V_{B
₄} = [C₁₁, C₁₂] = [0.80, 0.20], CR = 0.0039 < 0.1, $Σ V_{B_{1}} = V_{b} • (V_{B_{1}}, V_{B_{2}}, V_{B_{3}}, V_{B_{4}}) .$ $\begin{matrix} V = (0.0330, 0.1375, 0.3080, 0.0715, \\ 0.1701, 0.0351, 0.0648, 0.0156, 0.0468, \\ 0.0676, 0.0400, 0.0100) \end{matrix}$

The single factor evaluation matrices determined by the expert scoring method are: $R_{1} = [\begin{matrix} 0.17 & 0.21 & 0.58 & 0.04 \\ 0.29 & 0.14 & 0.44 & 0.13 \\ 0.11 & 0.24 & 0.53 & 0.12 \\ 0.16 & 0.21 & 0.55 & 0.08 \end{matrix}]$ $R_{2} = [\begin{matrix} 0.17 & 0.22 & 0.36 & 0.25 \\ 0.32 & 0.19 & 0.17 & 0.32 \\ 0.12 & 0.34 & 0.28 & 0.26 \end{matrix}]$ $R_{3} = [\begin{matrix} 0.27 & 0.08 & 0.31 & 0.34 \\ 0.15 & 0.22 & 0.19 & 0.44 \\ 0.09 & 0.16 & 0.30 & 0.45 \end{matrix}]$ $R_{4} = [\begin{matrix} 0.18 & 0.41 & 0.07 & 0.34 \\ 0.50 & 0.23 & 0.14 & 0.13 \end{matrix}]$

The single factor evaluation matrices determined by the expert scoring method are:

First level fuzzy comprehensive evaluation. $A_{1} = V_{B_{1}} \times R_{1} = [0.17, 0.21, 0.51, 0.11]$ $A_{2} = V_{B_{2}} \times R_{2} = [0.18, 0.24, 0.32, 0.26]$ $A_{3} = V_{B_{3}} \times R_{3} = [0.13, 0.17, 0.26, 0.44]$ $A_{4} = V_{B_{4}} \times R_{4} = [0.24, 0.37, 0.08, 0.31]$

Take the obtained B₁, B₂, B₃, B₄ as the upper evaluation matrix R, and make fuzzy transformation. Two level fuzzy comprehensive evaluation, known A = [0.55, 0.27, 0.13, 0.05], R = [A₁, A₂, A₃, A₄] ^T, B = A × R = [0.22, 0.21, 0.17, 0.40].

4 Results and discussion

Table 4 shows the comprehensive evaluation results of shield tunnel collapse risk in the construction stage.

Table 4
Final value of comprehensive weight of indicators

Primary index & weight Evaluation factors Weight Final Weight

Engineering geology (B₁), Ground stress C₁ 0.06 0.0330

W = 0.55 Rock integrity C₂ 0.25 0.1375

Fault development C₃ 0.56 0.3080

Groundwater C₄ 0.13 0.0715

Rock mass support (B₂), Advance support C₅ 0.63 0.1701

W = 0.27 Permanent support C₆ 0.13 0.0351

Grouting reinforcement C₇ 0.24 0.0648

Construction management (B₃), Construction method C₈ 0.12 0.0156

W = 0.13 Field monitoring C₉ 0.36 0.0468

Quality management C₁₀ 0.52 0.0676

Natural environment (B₄), Precipitation C₁₁ 0.80 0.0400

W = 0.05 Natural disasters C₁₂ 0.20 0.0100

Primary index & weight	Evaluation factors	Weight	Final Weight
Engineering geology (B₁),	Ground stress C₁	0.06	0.0330
W = 0.55	Rock integrity C₂	0.25	0.1375
	Fault development C₃	0.56	0.3080
	Groundwater C₄	0.13	0.0715
Rock mass support (B₂),	Advance support C₅	0.63	0.1701
W = 0.27	Permanent support C₆	0.13	0.0351
	Grouting reinforcement C₇	0.24	0.0648
Construction management (B₃),	Construction method C₈	0.12	0.0156
W = 0.13	Field monitoring C₉	0.36	0.0468
	Quality management C₁₀	0.52	0.0676
Natural environment (B₄),	Precipitation C₁₁	0.80	0.0400
W = 0.05	Natural disasters C₁₂	0.20	0.0100

In the analytic hierarchy process, the setting of evaluation index and its weight is very important. These two aspects directly determine the objectivity and accuracy of the evaluation results. In the risk assessment system of tunnel roof caving and even collapse, the selection of assessment indicators must be consistent with the impact of geology, rock mass support, natural environmental conditions and man-made construction operations. In the evaluation system established in this study, the order of index weight values of layer A-B is engineering geology > rock mass support > construction management > external environment, of which engineering geology is the most important. In the case analysis, the engineering geological analysis shows that the southwest region is located at the boundary of the fault zone, with frequent geological activities and large formation water content. Therefore, under this special geological condition, the ground support becomes an important index. According to the index weight values of B-C layers in the research results, the indexes with higher weight values are C₃(0.3080) >C₅(0.1701) >C₂(0.1375) >C₄(0.0715) >C₁₀ (0.0676) >C₇ (0.0648). It can be seen that, compared with shallow shield tunnel and mountain tunnel, it is very important to master the fault in the evaluation of roof stability of deep mine roadway, and pay attention to advance support, which can improve the integrity of rock mass through grouting reinforcement. In the images of external natural factors, the possibility of rainfall induced disasters is greater than that of earthquakes and other disasters. It is necessary to strengthen the construction management level, especially the establishment of on-site management system and the completion inspection.

Taking a mine in Yunnan Province as an example, according to the principle of maximum membership relationship, the maximum membership index of C11 roadway roof collapse risk X = 0.40, and its membership index evaluation is shown in Fig. 2. The fuzzy comprehensive evaluation result of collapse risk is high risk, and the comprehensive evaluation result is in good agreement with the actual situation. The risk assessment results of mine roof collapse based on analytic hierarchy process and the actual situation on site show that the risk level of C11 roadway roof collapse is high.

Fig. 2

Membership index evaluation of C11 roadway roof collapse risk.

5 Conclusions

The risk assessment of roof collapse is of great significance to the analysis of roadway stability. There are many factors influencing the risk of roof collapse, so the fuzzy evaluation method combining quantitative and qualitative evaluation must be adopted. On the basis of fully investigating the existing literature, this paper proposes a finely divided hierarchical analysis model to evaluate the risk of roof collapse, and gives an application example, and obtains the following conclusions:

It is determined that the influencing factors of mine roadway roof collapse risk are engineering geology, rock mass support, construction and management and natural environment. The conclusion shows that engineering geology accounts for a large proportion of the factors affecting mine roof collapse risk.

A multi-level fuzzy comprehensive evaluation model of mine roadway roof collapse risk is proposed. The evaluation results obtained by applying the example of mine roadway roof surrounding rock are consistent with the field results, which proves that this method can be applied to mine roadway roof collapse risk evaluation, and puts forward a new evaluation angle for the study of mine roadway roof collapse risk fuzzy comprehensive evaluation.

It is found that the fuzzy comprehensive evaluation of mine roadway roof collapse risk based on analytic hierarchy process pays more attention to the importance and correlation between different influencing factors, and the evaluation result is more accurate.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 52074298).

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