Vulnerability Assessment of Mine Flooding Disaster Induced by Rainstorm Based on Tri-AHP

Abstract

As a disaster-bearing body, the coal mine is vulnerable to the impact threat of rainstorm disasters, which easily induce flooding accidents. In view of this, this study is designed to propose the vulnerability assessment method of rainstorm-induced coal mine flooding disasters. On account of the scientific theory of disaster risk, the evaluation model and index system of coal mine flooding disaster induced by rainstorm covering exposure, fortification level, and resilience are constructed, while the vulnerability assessment method based on Tri-AHP method is proposed. Study results demonstrate that population exerts the greatest impact on exposure, wellhead elevation matters the most for fortification level, and the emergency plan has a dominant influence on resilience. Therefore, for coal mines, it is suggested to strengthen the special rainstorm emergency plan drill, improve the fortification level, and solidify the emergency duty during the rainy season. In this study, the rainstorm disaster vulnerability assessment method of coal mine is innovatively put forward, which is conducive to sustainable energy and environmental development.

1. Introduction

The global climate change is related to the time-to-time occurrence of extreme weather, such as rainstorms. Torrential rainfall and constant rainfall are prone to inducing flood disasters characterized by heavy rain, short duration, spreading space of disaster points, and the chain and mutation of loss [1,2,3]. The sixth Intergovernmental Panel on Climate Change (IPCC) assessment report has revealed that the frequency and intensity of rainstorm and waterlogging disasters in the world’s densely populated cities will be significantly increased [4]. Under the dual influence of global climate change and urbanization, rainstorm disasters will not only cause serious economic losses and social problems, but also threaten people’s lives and property safety [5,6]. Recent years have witnessed Beijing, Guangzhou, Zhengzhou, Nanjing, and other cities suffering from rainstorm and waterlogging disasters, especially the “7.20” extraordinary rain disaster in Zhengzhou, Henan province, which caused river embankments, severe urban waterlogging, farmland flooding, traffic shutdown, heavy casualties, and property losses [7]. Figure 1 shows the flooded tunnel in Zhengzhou City, China.

Figure 1. The flooded tunnel in Zhengzhou City, China.

Coal is China’s main energy source, and according to incomplete statistics, the total energy consumption of China in 2021 was about 5.24 billion tons of standard coal, of which coal consumption accounted for about 56.0% [8,9,10]. Coal mine is a disaster-bearing body seriously affected by rainstorm disaster for rainstorm will not only induce abnormal underground water gushing, but also lead to flooded well disasters [11]. In August 2010, a rainstorm flooding well disaster caused 18 casualties in the Hongyuan Coal Mine in Tonghua, Jilin Province, China, as well as a direct economic loss of 23.638 million yuan. In June 2016, rainstorm struck Qianxinan Prefecture, Guizhou Province, China, giving rise to a soaring river level in the province, flooding into the well, and killing eight people. In October 2019, the Dipka mine, one of India’s largest coal mines, encountered a flooding disaster caused by torrential rainfall, resulting in production shutdown and fuel shortages at some power plants. In October 2021, a rainstorm hit Shanxi, China, with precipitation exceeding 200 mm in 18 counties, forcing 60 coal mines to close down. In July 2022, a coal mine in Teda, Sindh, Pakistan was occupied by rainwater, trapping ten mine workers. Figure 2 shows the mine flooding disaster induced by rainstorm.

Figure 2. Mine flooding disaster induced by rainstorm.

It can be known from the above analysis that the disaster of well flooding caused by rainstorms extensively threaten safe production in coal mines. Therefore, this study aims to conduct a quantitative assessment of the vulnerability of coal mine flooding disaster induced by rainstorm. To achieve the objective, it is necessary to complete the following tasks: (1) construct the evaluation model and index system; (2) determine the weight of each evaluation index; (3) propose the vulnerability assessment method.

2. Literature Review

The word vulnerability derives from the Latin “vulnerare”, with the meaning of “possibly damaged by”, which was mainly used in the field of natural disaster in the early stage and then extended to the domains of climate change, ecological environment, social economy, and sustainable development [12,13,14]. In recent years, scholars have conducted multi-perspective and multilayer research on it.

Füssel et al. presented a generally applicable conceptual framework of vulnerability that combines a nomenclature of vulnerable situations and a terminology of vulnerability concepts based on the distinction of four fundamental groups of vulnerability factors [15]. Li et al. presented a first attempt to provide a prototype framework that can assess ecological vulnerability and evaluate potential impacts of natural, social, economic, environmental pollution, and human health elements on ecological vulnerability with integrating spatial analysis of Geographic Information System (GIS) method and multi-criteria decision analysis [16]. Sarker et al. aim to assess the livelihood vulnerability of riverine communities by applying the Intergovernmental Panel on Climate Change (IPCC) vulnerability framework and the livelihood vulnerability index [17]. Zhao et al. proposed a root cause analysis method based on Fuzzy Cognitive Map (FCM) to evaluate the vulnerability of a subway system. Using text mining and expert interviews, they constructed a causal model composed of human behavior, equipment and facilities, safety management, emergency rescue, and environment, to simulate the vulnerability of subway system within the FCM framework [18,19]. By comprehensively utilizing GIS spatial analysis and risk evaluation model and selecting 6 vulnerability indicators based on social and economic data in Wuhan, Zhou established the vulnerability evaluation index system of rainstorm and flood disaster in Wuhan, and conducted the vulnerability evaluation in 13 exampled districts [20]. Huang et al. built an urban waterlogging vulnerability index system based on the disaster system theory and the “Pressure-state-response” model (PSR). They used the data in Xi’an Statistical Yearbook to extract urban waterlogging vulnerability index, adopted the AHP method to calculate the index weight, proposing urban waterlogging vulnerability index, and comprehensively analyzing and evaluating the vulnerability degree of urban waterlogging in Xi’an [21]. Mafei et. al examined the impact of rainstorms on the vulnerability of urban⁻public transport systems consisting of both ground bus and metro systems. Through the changes in the node scale, network efficiency, and passenger volume in the maximal connected component of the Bus-Metro CBN, a vulnerability operator to quantitatively calculate the vulnerability of the Bus-Metro CBN was constructed [22]. Zhu et al. selected 11 evaluation indicators from rainstorm and flood disaster factors, hazard inducing environments, and hazard bearing factors. They adopted the FAHP-CRITIC method group to obtain the weight of each evaluation index, established a rainstorm and flood disaster risk assessment model on the ArcGIS platform, and prepared the risk assessment map of rainstorm and flood disaster [23]. Sun et al. constructed a risk assessment model and index system for coal mine flood disaster, and proposed a risk assessment method based on the projection pursuit and fuzzy cluster analysis [24]. Jiang et al. established a fast and accurate landslide risk prediction model for open-pit mine dumps based on machine learning, in order to prevent landslide geological disasters in open-pit mine dumps under the effect of heavy rainfall [25].

In summary, the existing studies involve the conceptual connotation of vulnerability, evaluation framework and evaluation methods, with most of the research subjects being urban subway systems, while few studies address the vulnerability of coal mine rainstorm disasters. In view of this, this study constructs an evaluation model and index system of disaster flooding induced by rainstorm covering exposure, fortification level and resilience, and proposed a vulnerability assessment method based on Tri-AHP (Triangular Fussy Analytic Hierarchy Process) method, which was applied in coal mines in Sanmenxia, Henan Province, China. This study exploratively proposes the rainstorm disaster vulnerability assessment method in coal mine, providing a basis for rainstorm disaster prevention and is of great significance for the sustainable development of energy and environment.

3. Methods

3.1. Assessment Model

Disaster vulnerability is composed of three elements, namely exposure, sensitivity and resilience [26]. The disaster-bearing body and spatial location of the disaster carrier exposed to the disaster factors are important factors affecting the exposure. The higher the exposure of the disaster carrier, the greater the damage affected by the disaster. Sensitivity is determined by the nature of the carrier itself. Characterizing the ability of the body to resist the disaster factors, the higher the level of the body, the lower its sensitivity. Resilience focuses on managing disaster risk and responding to emergency, which is the ability to mitigate the impact of disasters and the ability to recover from disasters [27,28,29]. Based on the above theory, the vulnerability assessment of rainstorm-induced coal mine flooding disasters include three elements:, exposure, fortification, and resilience. The evaluation model is shown in Figure 3.

Figure 3. Theoretical model of vulnerability assessment.

By virtue of data collection, field research and expert discussion, in assessing exposure, consideration is mainly on population, asset value and productivity. While assessing fortification capability, elevation of wellhead, waterproof coal pillar, subsidence and crack area, abandoned wells, embankment project, etc., are taken into consideration mostly. In terms of resilience assessment, emergency plan, emergency material, early warning mechanism and management system are mainly taken into consideration. As a result, the evaluation index system is constructed as shown in Figure 4.

Figure 4. Evaluation index system.

3.2. Method of Tri-AHP

The triangular fuzzy number is a commonly used fuzzy number in the field of risk assessment [30], which can be expressed as $M=(l,m,\mu )(l\le m\le \mu )$, where, $l$, $m$, and $\mu$, respectively, represent the value with the least likelihood of the risk probability, the value in the middle of the likelihood, and the value with the greatest likelihood. The triangular blur number is shown in Figure 5 [31]. Then, the Tri-AHP method is adopted to evaluate the index weight as follows [32,33,34].

Figure 5. Triangular fuzzy number.

3.2.1. Construct a Triangular Fuzzy Judgment Matrix

The “1~9 scaling method” is employed to collect experts’ opinions on the significance of the evaluation index, based on which the fuzzy interval evaluation value of each evaluation index is determined, so that the ratio between the evaluation index is obtained, which can be replaced by the simplified triangular fuzzy number. The triangular fuzzy judgment matrix is shown in Equation (1):

$$F_{n\times n}=\left(\begin{array}{cccccc}1& f_{12}& \cdots & f_{1i}& \cdots & f_{1n}\\ f_{21}& 1& \cdots & f_{2i}& \cdots & f_{2n}\\ \cdots & \cdots & 1& \cdots & \cdots & \cdots \\ f_{i1}& f_{i2}& \cdots & 1& \cdots & f_{in}\\ \cdots & \cdots & \cdots & \cdots & 1& \cdots \\ f_{n1}& f_{n2}& \cdots & f_{ni}& \cdots & 1\end{array}\right)$$

(1)

In the equation, $f_{ij}$ represents the contracted triangular fuzzy number while $f_{ji}$ refers to the reciprocal of the corresponding triangular fuzzy number, as shown in Table 1.

Table 1. Quantitative scale of triangular fuzzy number.

Reduced Fuzzy Number	Triangular Fuzzy Number	Inverse
1	(1,1,1)	(1,1,1)
1′	(1,1,3)	(1/3,1,1)
2′	(1,2,4)	(1/4,1/2,1)
3′	(1,3,5)	(1/5,1/3,1)
4′	(2,4,6)	(1/6,1/4,1/2)
5′	(3,5,7)	(1/7,1/5,1/3)
6′	(4,6,8)	(1/8,1/6,1/4)
7′	(5,7,9)	(1/9,1/7,1/5)
8′	(6,8,10)	(1/10,1/8,1/6)
9′	(7,9,11)	(1/11,1/9,1/7)

The reductive triangular fuzzy matrix is tested to meet the consistency requirements, using the triangular fuzzy number instead of the corresponding simplified fuzzy number, thus obtaining the judgment matrix represented by the triangular fuzzy number, as shown in Equation (2):

$$\begin{array}{l}{F}_{n\times n}={(l_{ij},m_{ij},n_{ij})}_{n\times n}\\ =\left(\begin{array}{cccccc}\left[1,1,1\right]& \left[l_{12},m_{12},{\mu }_{12}\right]& \cdots & \left[l_{1i},m_{1i},{\mu }_{1i}\right]& \cdots & \left[l_{1n},m_{1n},{\mu }_{1n}\right]\\ \left[l_{21},m_{21},{\mu }_{21}\right]& \left[1,1,1\right]& \cdots & \left[l_{2i},m_{2i},{\mu }_{2i}\right]& \cdots & \left[l_{2n},m_{2n},{\mu }_{2n}\right]\\ \cdots & \cdots & \ddots & \cdots & \cdots & \cdots \\ \left[l_{i1},m_{i1},{\mu }_{i1}\right]& \left[l_{i2},m_{i2},{\mu }_{i2}\right]& \cdots & \left[1,1,1\right]& \cdots & \left[l_{in},m_{in},{\mu }_{in}\right]\\ \cdots & \cdots & \cdots & \cdots & \ddots & \cdots \\ \left[l_{n1},m_{n1},{\mu }_{n1}\right]& \left[l_{n2},m_{n2},{\mu }_{n2}\right]& \cdots & \left[l_{ni},m_{ni},{\mu }_{ni}\right]& \cdots & \left[1,1,1\right]\end{array}\right)\end{array}$$

(2)

3.2.2. Determine the Weight of the Evaluation Indicators

According to the constructed triangular fuzzy number judgment matrix, Equations (3)–(5) are used to calculate the fuzzy synthesis degree $P_i$:

$$P_i=S_i\otimes {\left[{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{P}_{fi}^j}}\right]}^{-1}$$

(3)

$$S_i={\displaystyle \sum _{j=1}^n{P}_{fi}^j}=\left({\displaystyle \sum _{j=1}^n{l}_j,{\displaystyle \sum _{j=1}^n{m}_j,}{\displaystyle \sum _{j=1}^n{\mu }_j}}\right)$$

(4)

$${\left[{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{P}_{fi}^j}}\right]}^{-1}=\left(\frac{1}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{\mu }_i^j}}},\frac{1}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{m}_i^j}}},\frac{1}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{l}_i^j}}}\right)$$

(5)

If the fuzzy synthesis degrees are recorded as $P_1$ and $P_2$, when $P_1>P_2$, the triangular fuzzy function relationship can be represented by Figure 6 [35]. The horizontal coordinate represents the value range of the triangular fuzzy number, and the vertical coordinate represents the membership degree of triangular fuzzy number.

Figure 6. Triangular fuzzy function relation.

In the function relationship represented in Figure 6, the intersection between the two triangular fuzzy numbers is called the confidence level of the fuzzy judgment, which is represented by $d_i$. It can be seen from the figure that the value the value of $d_i$ can be represented by a segment function, as shown in Equation (6):

$$\mu (d)=\left\{\begin{array}{cc}1& (m_1\ge m_2)\\ 0& (l_2\ge {\mu }_1)\\ \frac{l_2-u_1}{(m_1-u_1)-(m_2-l_2)}& (others)\end{array}\right.$$

(6)

Similarly, it is feasible to calculate that the $i$ triangular fuzzy number $P_i$ is greater than the value of the confidence level of $\mu (d_i)$, as expressed in Equation (7):

$$\mu (P_i\ge P_1,P_2,\cdots ,P_k)=\min \left[\mu (P_i\ge P_1),\mu (P_i\ge P_2),\cdots ,\mu (P_i\ge P_k)\right]$$

(7)

When $\mu (d_i)=\min \left[\mu (P_i\ge P_k)\right](k=1,2,\cdots ,n,k\ne i)$, the weight vectors of each evaluation index in the same standard layer are indicated by Equation (8):

$$w_0={(\mu (d_1),\mu (d_2),\cdots ,\mu (d_n))}^T$$

(8)

The normalized weight vectors are indicated by Equation (9):

$$w_0={(\mu {(d_1)}^{\prime },\mu {(d_2)}^{\prime },\cdots ,\mu {(d_n)}^{\prime })}^T$$

(9)

where $\mu {(d_i)}^{\prime }=\frac{\mu (d_i)}{{\displaystyle \sum _{i=1}^n\mu (d_i)}}$ and ${\displaystyle \sum _{i=1}^n\mu {(d_i)}^{\prime }}=1$.

3.3. Assessment of Vulnerability

According to the constructed evaluation index system, after the weight of each index is obtained with Tri-AHP, the vulnerability evaluation value can be expressed by Equation (10):

$$V=\sqrt[3]{{\displaystyle \sum E_i{w}_i}\cdot {\displaystyle \sum F_i{w}_i}\cdot {\displaystyle \sum R_i{w}_i}}$$

(10)

Here, $E_i$ represents the normalized value of each exposure index, $F_i$ represents the normalized value of each fortification index, $R_i$ represents the normalized value of each resilience index, $w_i$ represents the weight of each index.

Based on the vulnerability assessment value V, the vulnerability level of rainstorm induced coal mine flooding disaster is determined, as shown in Table 2.

Table 2. Vulnerability level of mine flooding disaster induced by rainstorm.

Vulnerability Level	V
High	0.8 ≤ V ≤ 1
Medium-High	0.6 ≤ V < 0.8
Medium	0.4 ≤ V < 0.6
Medium-Low	0.2 ≤ V < 0.4
Low	0 ≤ V < 0.2

4. Case Study

4.1. Background

Henan Province is located in the central region of China with high land in the west and low in the east. It is an area with more serious rainstorm disasters in China, characterized by high intensity, long duration and significant sudden occurrence [36]. In July 2007, Sanmenxia City, Henan Province, a city located in the western part of Henan Province between east longitude 110.21′42″~112.01′24″ and north latitude 33.31′24″~35.05′48″ (Figure 7), having 8 production mines with a production capacity of about 10.05 million tons at present, was hit by a torrential rainfall reaching 115.2 mm. The Dongfeng well of Zhijian Coal Mine in the city was flooded with a riverbed of water, swallowing two horizontal tunnels, leaving 69 people trapped in the well [37].

Figure 7. Location of the study site.

4.2. Survey of Disaster-Bearing Bodies

In order to assess the vulnerability of the coal mine flooding disaster caused by the rainstorm, it is of necessity to investigate the disaster-bearing body of coal mines, and obtain the basic information, fortification level, and resilience of the coal mines. According to the evaluation index system constructed in Figure 3, the key influencing factors involving flood fortification in relevant standards and regulations and laws are selected, and the coal mine vulnerability questionnaire is established, as shown in Table 3.

Table 3. Coal mine vulnerability questionnaire.

Index Layer	Sub-Index Layer	Investigation Content
Exposure	Population E1	Number of employees E11
	Asset value E2	Net value of fixed assets (million yuan) E21
	Productivity E3	Approved capacity (million tons) E31
Fortification	Elevation of well F1	Whether the elevation of well is higher than the local highest flood level over the years F11
	Waterproof coal pillar F2	Whether the waterproof coal pillar is reserved as required and not damaged F21
		Whether the width of waterproof coal pillar is determined according to the width of water conducting fracture zone F22
	Subsidence and Crack F3	Whether the subsidence and crack area are backfilled and compacted in time F31
		Whether the water accumulation in subsidence and crack area is monitored F32
	Abandoned wells F4	Whether the abandoned wells is blocked in time F41
		Whether the abandoned wells is provided with drainage ditch at the wellhead F42
	Embankment project F5	Whether flood control measures such as embankment construction and ditch excavation are taken F51
Resilience	Emergency plan R1	Whether the emergency plan for rainstorm disaster has been prepared and regularly practiced R11
	Emergency material R2	Whether emergency water pumps, pipelines, and other flood control and disaster relief equipment and materials are stored R21
	Early warning mechanism R3	Whether to actively coordinate with local meteorological, water conservancy, and other relevant departments to establish a flood disaster early warning mechanism R31
	Management system R4	Whether flood disaster prevention is included in the safety management system R41
		Whether the inspection system for key parts and key links in rainy season has been established R42
		Whether emergency evacuation system is established when rainstorm may cause major danger R43

The vulnerability of 8 coal mines in Sanmenxia is investigated, with the survey results of exposure, fortification level, and resilience shown in Table 4, Table 5 and Table 6.

Table 4. Survey results of exposure.

Number	Coal Mine	E11	E21	E31
1	Gengcun	3924	52,369	360
2	Guanyintang	1160	16,387	45
3	Shihao	2301	30,441	120
4	Liangjiawa	400	4741	35
5	Longwangzhuang	947	47,551	70
6	Jiuliuba	343	13,044	45
7	Changcun	2999	29,830	180
8	Qianqiu	3121	20,746	150

Table 5. Survey results of fortification.

Number	Coal Mine	F11	F21	F22	F31	F32	F41	F42	F51
1	Gengcun	Yes	Yes	No	Yes	Yes	Yes	Yes	Yes
2	Guanyintang	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No
3	Shihao	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes
4	Liangjiawa	Yes	Yes	No	Yes	Yes	Yes	No	Yes
5	Longwangzhuang	Yes	Yes	No	Yes	No	Yes	Yes	Yes
6	Jiuliuba	Yes	Yes	No	Yes	Yes	Yes	Yes	No
7	Changcun	Yes	Yes	No	Yes	Yes	Yes	No	Yes
8	Qianqiu	Yes	Yes	No	Yes	No	Yes	Yes	Yes

Table 6. Survey results of resilience.

Number	Coal Mine	R11	R21	R31	R41	R42	R43
1	Gengcun	Yes	Yes	No	No	Yes	Yes
2	Guanyintang	Yes	Yes	Yes	Yes	Yes	No
3	Shihao	Yes	Yes	No	No	Yes	Yes
4	Liangjiawa	Yes	No	No	Yes	Yes	Yes
5	Longwangzhuang	Yes	Yes	Yes	Yes	Yes	No
6	Jiuliuba	Yes	Yes	Yes	Yes	Yes	No
7	Changcun	No	Yes	No	Yes	Yes	No
8	Qianqiu	Yes	Yes	No	Yes	Yes	Yes

4.3. Weight Calculation

(1)

For this study, 7 experts in the coal industry from universities, scientific research institutes and enterprises are invited to discuss the importance of each influencing factor of vulnerability, with results shown in Table 7, where the Roman numerals indicate the number of times where the level of influence is selected.

Table 7. Scoring results of vulnerability indicators importance.

Indicators	Impact on Vulnerability
	1	2	3	4	5	6	7	8	9
Exposure
Population E1							I	II	IV
Asset value E2				II	II	II	I
Productivity E3		II	III	II
Fortification
Elevation of well F1							II	I	IV
Waterproof coal pillar F2	I	II	III	I
Subsidence and Crack F3			I	II	II	II
Abandoned wells F4					I	II	IV
Embankment project F5		II	III	II
Resilience
Emergency plan R1							III	II	II
Emergency material R2				II	III	I	I
Early warning mechanism R3	I	III	II	I
Management system R4		II	II	II	I

(2)

On the grounds of the scoring table made by expert in evaluating the importance of the vulnerability influencing factors, the simple judgment matrix, E, F, and R (exposure, fortification level, and resilience), is constructed, respectively, as shown in Equations (11)–(13):

$$E=\left(\begin{array}{ccc}1& \frac{7-9}{4-7}& \frac{7-9}{2-4}\\ \frac{4-7}{7-9}& 1& \frac{4-7}{2-4}\\ \frac{2-4}{7-9}& \frac{2-4}{4-7}& 1\end{array}\right)\Rightarrow \left(\begin{array}{ccc}1& 2^{\prime }& 4^{\prime }\\ {0.5}^{\prime }& 1& 3^{\prime }\\ {0.25}^{\prime }& {0.33}^{\prime }& 1\end{array}\right)$$

(11)

$$F=\left(\begin{array}{ccccc}1& \frac{7-9}{1-4}& \frac{7-9}{3-6}& \frac{7-9}{5-7}& \frac{7-9}{2-4}\\ \frac{1-4}{7-9}& 1& \frac{1-4}{3-6}& \frac{1-4}{5-7}& \frac{1-4}{2-4}\\ \frac{3-6}{7-9}& \frac{3-6}{1-4}& 1& \frac{3-6}{5-7}& \frac{3-6}{2-4}\\ \frac{5-7}{7-9}& \frac{5-7}{1-4}& \frac{5-7}{3-6}& 1& \frac{5-7}{2-4}\\ \frac{2-4}{7-9}& \frac{2-4}{1-4}& \frac{2-4}{3-6}& \frac{2-4}{5-7}& 1\end{array}\right)\Rightarrow \left(\begin{array}{ccccc}1& 6^{\prime }& 3\prime & 1^{\prime }& 4^{\prime }\\ {0.17}^{\prime }& 1& {0.5}^{\prime }& {0.33}^{\prime }& 1^{\prime }\\ {0.33}^{\prime }& 2^{\prime }& 1& {0.5}^{\prime }& 2^{\prime }\\ 1^{\prime }& 3^{\prime }& 2^{\prime }& 1& 3^{\prime }\\ {0.25}^{\prime }& 1^{\prime }& {0.5}^{\prime }& {0.33}^{\prime }& 1\end{array}\right)$$

(12)

$$R=\left(\begin{array}{cccc}1& \frac{7-9}{4-7}& \frac{7-9}{1-4}& \frac{7-9}{2-5}\\ \frac{4-7}{7-9}& 1& \frac{4-7}{1-4}& \frac{4-7}{2-5}\\ \frac{1-4}{7-9}& \frac{1-4}{4-7}& 1& \frac{1-4}{2-5}\\ \frac{2-5}{7-9}& \frac{2-5}{4-7}& \frac{2-5}{1-4}& 1\end{array}\right)\Rightarrow \left(\begin{array}{cccc}1& 3^{\prime }& 5\prime & 4^{\prime }\\ {0.33}^{\prime }& 1& 4^{\prime }& 3\prime \\ {0.2}^{\prime }& {0.25}^{\prime }& 1& {0.5}^{\prime }\\ {0.25}^{\prime }& {0.33}^{\prime }& 2^{\prime }& 1\end{array}\right)$$

(13)

(3)

Based on the brief judgment matrices and Equations (3)–(5), the calculation results of the triangular judgment matrix of exposure, fortification level, resilience, and Pi are shown in Table 8, Table 9 and Table 10.

Table 8. Triangular fuzzy number judgment matrix of exposure.

	E1	E2	E3	Si	Pi
E1	(1,1,1)	(1,2,4)	(2,4,6)	(4,7,11)	(0.195, 0.535, 1.444)
E2	(0.25,0.5,1)	(1,1,1)	(1,3,5)	(2.25,4.5,7)	(0.11, 0.344, 0.919)
E3	(0.17,0.25,0.5)	(0.2,0.33,1)	(1,1,1)	(1.37,1.58,2.5)	(0.067, 0.121, 0.328)

Table 9. Triangular fuzzy number judgment matrix of fortification.

	F1	F2	F3	F4	F5	Si	Pi
F1	(1,1,1)	(4,6,8)	(1,3,5)	(1,1,3)	(2,4,6)	(9,15,23)	(0.139, 0.406, 1.016)
F2	(0.125,0.17,0.25)	(1,1,1)	(0.25,0.5,1)	(0.2,0.33,1)	(1,1,3)	(2.575,3,6.25)	(0.04, 0.081, 0.276)
F3	(0.2,0.33,1)	(1,2,4)	(1,1,1)	(0.25,0.5,1)	(1,2,4)	(3.45,5.83,11)	(0.053, 0.158, 0.486)
F4	(1,1,3)	(1,3,5)	(1,2,4)	(1,1,1)	(1,3,5)	(5,10,18)	(0.077, 0.271, 0.795)
F5	(0.17,0.25,0.5)	(1,1,3)	(0.25,0.5,1)	(0.2,0.33,1)	(1,1,1)	(2.62,3.08,6.5)	(0.04, 0.083, 0.287)

Table 10. Triangular fuzzy number judgment matrix of resilience.

	R1	R2	R3	R4	Si	Pi
R1	(1,1,1)	(1,3,5)	(3,5,7)	(2,4,6)	(7,13,19)	(0.168, 0.481, 1.254)
R2	(0.2,0.33,1)	(1,1,1)	(2,4,6)	(1,3,5)	(4.2,8.33,13)	(0.101, 0.308, 0.858)
R3	(0.14,0.2,0.33)	(0.17,0.25,0.5)	(1,1,1)	(0.25,0.5,1)	(1.56,1.95,2.83)	(0.037, 0.072, 0.187)
R4	(0.17,0.25,0.5)	(0.2,0.33,1)	(1,2,4)	(1,1,1)	(2.37,3.58,6.5)	(0.057, 0.132, 0.429)

(4)

Then, according to Equation (6), after obtaining all the confidence levels, the weights of exposure, fortification level, and resilience are worked out within Equations (7)–(9), as shown in Equations (14)–(16):

$$w_E=\left(0.492,0.389,0.119\right)$$

(14)

$$w_F=\left(0.331,0.098,0.193,0.274,0.104\right)$$

(15)

$$w_R=\left(0.401,0.321,0.107,0.171\right)$$

(16)

4.4. Vulnerability of Coal Min

After normalizing the survey results of the vulnerability index of 8 coal mines in Sanmenxia, Equation (10) is applied to obtain the vulnerability grade value of each coal mine, as shown in Table 11.

Table 11. Vulnerability level of coal mines in Sanmenxia City.

Number	Coal Mine	V	Vulnerability Level
1	Gengcun	0.200067227	Medium-Low
2	Guanyintang	0.107329074	Low
3	Shihao	0.225151686	Medium-Low
4	Liangjiawa	0.085427451	Low
5	Longwangzhuang	0.154034211	Low
6	Jiuliuba	0.08499586	Low
7	Changcun	0.402844514	Medium
8	Qianqiu	0.205216119	Medium-Low

Visualizing the vulnerability level value of each coal mine in Sanmenxia by GIS tool, the spatial distribution map of the vulnerability level of the coal mine flooding disaster induced by the rainstorm in Sanmenxia is obtained, as shown in Figure 8.

Figure 8. Distribution map of coal mine vulnerability levels in Sanmenxia City.

5. Discussion

• In the exposure index, personnel have the highest weight, followed by assets, and then production capacity, with the lowest weight. The greater the personnel, assets and production exposed to the disaster factors, the higher the vulnerability of the disaster-bearing body. Among the 8 coal mines in Sanmenxia, Gengcun Coal Mine is exposed to the largest extent, and Liangjiawa Coal Mine is exposed to the lowest.
• The key elements of the fortification for rainstorm flooded well disaster mainly include elevation of wellhead, waterproof coal pillar, subsidence and crack area, abandoned wells, embankment project and others, whereinto, $w_{F_1}>w_{F_4}>w_{F_3}>w_{F_5}>w_{F_2}$, and the weight of wellhead elevation occupies the highest weight. Among the 8 coal mines in Sanmenxia, the Gengcun Coal Mine enjoys the highest fortification level, while the Liangjiawa Coal Mine and Changcun Coal Mine share the lowest fortification level. Therefore, the elevation of the coal mine wellhead shall be higher than the highest flood level in the local years, the collapsed cracked area shall be backfilled and compacted in time, and the scrapped rockshaft shall be blocked timely.
• The impact factors of emergency capacity include emergency plan, emergency materials, early warning mechanism and management system, whereinto, $w_{R_1}>w_{R_2}>w_{R_4}>w_{R_3}$, and the emergency plan enjoys the highest weight. Among the 8 coal mines in Sanmenxia, Changcun Coal Mine has the strongest emergency response capacity, while Guanyintang, Longwangzhuang and Jiuliuba coal mines behave the weakest in responding emergencies. Therefore, coal mines shall implement a special rainstorm emergency plan, regular rainstorm drills, update the emergency plan, and strengthen the emergency duty in the rainy season.
• Among the eight coal mines in Sanmenxia, Changcun Coal Mine is in a medium level of vulnerability. The other three mines, including the Gengcun Coal Mine, are in medium-low, while four others, including Guanyintang Coal Mine, are in low. Through field investigation, the assessment results are basically consistent with the actual situation of the coal mine. Therefore, coal mines shall strengthen the prevention of rainstorm disasters in accordance with relevant standards, norms, laws and regulations, reduce the vulnerability of rainstorm flooding disasters in coal mines, and ensure energy sustainability.

6. Conclusions

In allusion to the impacts of the rainstorm disaster on coal mines and the prominent vulnerability, the evaluation model and index system of rainstorm-induced coal mine flooding disasters covering exposure, fortification level and resilience are constructed in this study on the basis of disaster risk scientific theory. Meanwhile, the vulnerability assessment method based on Tri-AHP is proposed, which provides a basis for determining the scale of the coal mine rainstorm disaster vulnerability. This is conducive to the sustainable energy and environmental development, but only suits underground coal mines, as there still room for improvement in the evaluation index system and investigation content. In addition, a fuzzy evaluation method is offered in the study for other industries to conduct risk assessment.