A New Quantitative Method for Risk Assessment of Coal Floor Water Inrush Based on PSR Theory and Extension Cloud Model

In order to scienti ﬁ cally and reasonably assess the risk of water inrush from the coal seam ﬂ oor, considering the in ﬂ uence of natural environmental factors such as hydrogeology, mining, and human intervention, the PSR model of ecosystem health evaluation was introduced, and the risk evaluation indicator system of water inrush from the coal seam ﬂ oor was established. In order to solve the randomness and fuzziness of water inrush event evaluation, the evaluation model is constructed based on extension cloud theory and is applied in the 12123 working face of Pan Er coal mine of Huainan Mining Group . The application results show that the evaluation results are basically consistent with the actual situation, which shows that the model can be used in the actual evaluation work and is scienti ﬁ c.


Introduction
China is the most important coal producer and consumer in the world, and the proportion of coal consumption will remain above 50% for a long time. With the gradual depletion of shallow coal resource reserves and the deepening of coal mining depth, the mine hydrogeological conditions are becoming increasingly complex, the influencing factors of mine water inrush are increasing, and the mechanism and types of water inrush are complex and changeable, which affect the normal production of a coal mine. Mine water inrush accidents will not only cause casualties but also cause obvious economic losses. For example, five people died in a water leakage accident at Shanmushu Coal Mine in Yibin City, Sichuan Province, on December 14, 2019. A water leakage accident occurred in Xiaoyun coal mine in Jining City, Shandong Province, on September 10, 2018. Although there were no casualties, the mine was submerged, resulting in a direct economic loss of 25.6614 million yuan in this accident. Therefore, the reasonable and accurate risk assessment of water inrush in coal mine is of great practical significance to grasp the state of water disaster prevention and control in a coal mine and ensure the safety production in a coal mine.
In the 1960s, Chinese scholars first proposed the concept of water inrush coefficient, which is defined as the value of water pressure borne by the coal seam floor unit thickness of the water-resistant layer, and continuous improvement has been widely used [1]. Wang et al. determined a comprehensive evaluation system of coal mine floor water inrush risk consisting of 4 first-level indicators and 13 second-level indicators and used the analytic hierarchy process to distribute the indicator weights [2]. Meng et al. proposed a water inrush risk assessment method based on the impermeability and resistance to water pressure of floor aquifuge. The specific method is to simultaneously consider floor lithology and structural characteristics as parameters for water inrush prediction and use the maximum principal curvature of the floor surface to characterize floor structure characteristics. Compared with the conventional water inrush coefficient method, this method takes into account the lithology and structure features of the floor and utilizes a maximum principal curvature of the floor surface to predict the floor structure features [3]. Li et al. aimed at the problem that the traditional water inrush coefficient method cannot accurately assess the water inrush risk of a floor under specific conditions, through the analysis of the distribution of water inrush points and the scale of water inrush events, combined with the three indicators of Ts, M, and q, the water inrush vulnerability is divided into four levels: safety, medium safety, potential danger, and high risk [4]. Fan et al. analyzed the mechanical mechanism of water inrush (WIFSL) from separated layers, derived theoretical discriminants of the first stage and periodic WIFSL based on this, and used the water inrush coefficient method to divide the water inrush risk [5].
With the development of modern information technology and related knowledge theories, the application of these methods for evaluation and prediction has gradually become a hot research field. Wu et al. established a floor water inrush assessment model based on an artificial neural network and geographic information system [6]. Liu et al. established a coal seam floor water inrush prediction system using the neural network and decision tree algorithm and obtained the coal seam floor water inrush law. The results show that the prediction system based on data mining classification technology is a practical and feasible system [7]. Through the statistical analysis of water inrush accident data, Shi et al. concluded that when evaluating the risk of water inrush from the coal seam floor, the water inrush coefficient of the coal seam floor and the water content of aquifer should be considered at the same time and used support vector machines to establish a mine safety evaluation grade prediction model [8].
Li et al. established a floor water inrush evaluation model based on grey relational analysis and analytic hierarchy process [9]. Wu et al. obtained 4 types and 12 scenario elements of mine water inrush evolution through case analysis of typical water inrush accidents and, combined with the Bayesian network, proposed a water inrush accident probability assessment framework [10]. Qiu et al. proposed an evaluation system combining attribute mathematics theory and analytic hierarchy process [11]. Li et al. used 8 kinds of water chemical components as indicators, combined with principal component analysis and Fisher discriminant analysis, to construct a water inrush water source identification model, and used the hydrological data of Xiandewang coal mine to verify the results. The results show that the model can improve the accuracy of mine water inrush source identification [12].
Water inrush from the floor of the coal seam is a complex geological phenomenon. The above evaluation of water inrush from the floor of the coal seam only considers natural environmental factors such as hydrogeology, while neglect-ing the influence of mining and the effect of human intervention. As a result, the assessment indicator system established may be incomplete. Based on this, this paper uses the PSR model to establish the assessment indicator system of coal floor water inrush risk. In view of the randomness and fuzziness of water inrush events, the extension cloud theory is introduced to construct the assessment model, and the actual data of the site is collected to verify the validity of the model.  [13]. The core idea of the model is that human social and economic activities will exert pressure on the natural environment and resources and pressure will cause changes in the state of the environment. In order to cope with these changes, human society takes measures to response, thereby reducing the environmental pressure caused by human activities and ensuring the sustainability of the environmental system. The PSR model reveals the internal relationship between social development, human activities, and the environment and can represent a continuous feedback mechanism between various indicators. PSR and its improved models have been applied in water resource sustainability evaluation [14], primary energy production capacity evaluation [15], food chain safety analysis [16], and environmental risk management of marine protected areas [17].

Comprehensive Evaluation Index
System. Water inrush from coal floor is a complex system event with continuous feedback. The mining disturbance of coal can be regarded as pressure, which has an impact on the state of the hydrological environment around the coal seam, and then, the production department takes measures to respond, as shown in Figure 1. Based on this idea, combined with literature [2][3][4][5][6][7][8][9][10][11][12], the risk assessment of coal floor water inrush is established. For the pressure type indicators, it mainly refers to the mining factors. Mining is the inducing factor of water inrush, including coal seam conditions and mining methods. Coal seam conditions include mining depth, mining thickness, and inclined length of working face. For the state indicators, there are mainly geological structure, aquifer, and aquiclude indicators. The geological structure is the main factor and control factor of water inrush. The development degree of the geological structure is closely related to water inrush from the coal seam floor, which can be characterized by structural properties and the development of the geological anomaly body, which includes the karst collapse column. The existence of a confined aquifer under the coal seam floor is the prerequisite of floor water inrush. The water pressure of the aquifer is the power source of floor water inrush, and the aquifer water yield property is the material basis of water inrush, so the water pressure and aquifer water yield property can be used as indicators. Aquiclude is the condition to prevent water inrush from the floor, and its ability to prevent water inrush depends on the thickness of effective aquiclude and the integrity of aquiclude. For response indicators, it mainly refers to the subjective activities of production departments or teams, including personnel factors, equipment factors, and management factors, specifically including personnel refuge awareness, personnel safety skills, integrity of waterproof and drainage equipment, availability of waterproof and drainage equipment, perfection of water prevention and control system, and implementation of water prevention and control measures. The risk indicator system of water inrush from the coal floor is shown in Figure 2, the first-level indicator is the water inrush risk of the coal seam floor, and the second-and third-level indicators are shown in the figure.

Evaluation Model Establishment
3.1. Extension Cloud Theory. Coal floor water inrush is affected by internal and external factors, which have the characteristics of dynamic and nonlinear. The assessment of its risk also has the characteristics of uncertainty, especially randomness and fuzziness. The cloud model is proposed by Deyi et al., considering both fuzziness and randomness, which realizes the transformation of uncertainty between qualitative concept and quantitative value [18]. For the risk of water inrush, there are both positive and negative indicators. Matter-element extension analysis can transform the contradiction of indicators into compatibility, which is proposed by Chinese scholar Professor Cai [19]. Therefore, the cloud model theory and matter-element extension theory are introduced to establish the coal floor water inrush risk evaluation model based on the extension cloud theory.
In order to clearly explain the steps of applying this model to assessment, the specific principles of the extension cloud theory are explained. Suppose C is a qualitative concept in the quantitative domain V, x ∈ V represents a random realization on C, denoting the certainty of x to C as μ ðxÞ ∈ ½ 0, 1, and μ ðxÞ is a random number with a stable tendency, then the distribution of x on V forms a cloud C ðxÞ; the dots are called cloud drops. The cloud model is generally represented by three eigenvalues of expectation Ex, entropy En, and hyperentropy He. Assuming cloud CðEx, En, HeÞ, Ex is the central value after the qualitative concept C which is transformed into a numerical value, that is, the average value.
En is a measure of the uncertainty of the qualitative concept C, and the degree of ambiguity of the qualitative concept C increases as the value of En increases. He is a measure of entropy uncertainty, and the degree of dispersion of C increases with the increase of He value. Due to the universality of the normal cloud model, for the qualitative fuzzy concept C of real problems, the normal cloud model is selected for analysis [20].
In the matter-element theory, the matter-element is defined as the basic element R of things, where N represents the name of the thing, c represents the feature of the thing, and V represents the value of the feature of the thing; using the feature value ðEx, En, HeÞ in the cloud model instead of V gets the cloud matter-element model: 3.2. Weight Distribution Determination. The accuracy of the indicator weight will directly affect the accuracy of the evaluation results, mainly subjective weight method and objective weight method. By using the analytic hierarchy process, the importance of all the second-and third-level indicators is evaluated, respectively, and the fuzzy evaluation matrix A is obtained. Using formula (2), matrix A is calculated, and the corresponding weight vector W = ½W 1 , W 2 , W n T . Using formula (3), the characteristic matrix W * = ðW ij Þ n×n of fuzzy evaluation matrix A is obtained. Finally, the consistency indicators IðA, W * Þ of fuzzy judgment matrix A and characteristic matrix W * are obtained by formula (4), and the consistency test is carried out to judge whether the weight is reasonable.
Pressure mining disturbance

State hydrogeological conditions
Response manual intervention and measures Figure 1: PSR framework to assess coal floor water inrush.

Geofluids
where α ij is the element of row i and column j in fuzzy judgment matrix A ði, j = 1, 2, 3, ⋯, nÞ and W i,j is the element of row i and column j in the characteristic matrix W * ði, j = 1 , 2, 3, ⋯, nÞ, n is the number of indicators.
Compare the value of IðA, W * Þwith the value of t, and adjust the fuzzy judgment matrix until IðA, W * Þ ≤ t, where t represents the attitude of the decision-maker, and t = 0:1.

Cloud Generation and Computing.
When using an extension cloud model to evaluate, one of the core tasks is to transform the evaluation information into the form of a cloud. This paper introduces the grade range of the evaluation comment, the evaluation value of the index, and the cloud transformation of the evaluation result value.

Evaluation Grade and Standard
Cloud. According to the actual implementation of coal mine floor water inrush evaluation and Reference [2], the floor water inrush risk is divided into extremely high (I), high (II), general (III), low (IV), and extremely low (V). Suppose that the upper and lower limits of the evaluation index grade are T max and T min , respectively. Each grade of the evaluation index cannot be strictly distinguished and has fuzziness. The formula (5)~(7) is used for transformation. When there is only a single boundary limit in the grade interval, the default boundary parameters or expected values are determined according to the maximum upper or lower limit of the data, and then, the numerical characteristics are calculated by reference, where f is a constant, which needs to be adjusted according to the uncertainty of the index and the actual situation [21]:

Evaluation Cloud of Indicators.
The qualitative indicators are scored and assigned by experts, the quantitative indicators are collected, and the evaluation values are transformed into cloud eigenvalues to eliminate the fuzziness of subjective scoring. The approximate method is used for calculation [22]: where x i is the scoring value or data value of an indicator given by the i expert and n is the number of data values of an indicator; then, ðEx, En, HeÞ is the cloud eigenvalue of the evaluation result of the indicator.

Comprehensive Cloud of Evaluation Results.
According to the data value of each index, the assessment cloud of each indicator can be obtained through the transformation of eigenvalues. The similarity between each index and the standard cloud of each level can be calculated by using formula (12) [23]. The normalized similarity is used as the membership value to judge the evaluation level: For the three-level indicators of the same measurement, formula (12) can be used to fit, and the evaluation cloud corresponding to the two-level indicators can be obtained.

Engineering Applications
In order to verify and explain the index system and algorithm, 12123 working face of Pan Er coal mine of Huainan Mining Group is selected as the engineering background.

Geofluids
The working face has been formed and has not been mined yet. It is threatened by Ordovician limestone water, so it is necessary to evaluate the risk of floor water inrush. ith an average of 10°. The thickness of the underlying coal seam 1 is 0-3.9 m, with an average thickness of 3.0 m, and the distance between coal seam 3 and coal seam 1 is about 1.5 m, as shown in Figure 3.
According to the comprehensive analysis of the actual data of the overlying 14124, 12224, and 12124 working faces, the adjacent 12223 working face, and the upper and lower bottom drainage roadway of 12123, it is estimated that the geological structure of the 12123 working face is complex, and 27 faults will be exposed during the excavation, including the normal faults f12223-10, f12224-10, F203, f12223-x4, and f12224-6 which have great influence on the normal driving of the working face; the fall of faults f12223-10, f12224-10, and F203 is large, and coal 3 will be exposed again during driving through the fault. The pseudoroof of coal 3 is carbonaceous mudstone~mudstone; the direct roof is silty fine~medium fine sandstone, with an average thickness of about 20 m; the main roof is dark grey mudstone, with a thickness of about 4.0 m; and the floor of coal 3 is 1.2~1.0 m thick 8 m, with an average of 1.5 m. According to the surface drilling and 3D seismic data, there is no geological abnormal body such as magmatic rock intrusion into the coal seam and collapse column in the 12123 working face, as shown in Figure 4, which is the 3D seismic map of the working face.

Division of Grade Interval.
A total of 8 industry experts and coal mine personnel were invited to form an evaluation expert group. The importance evaluation matrix is obtained by using the analytic hierarchy process (AHP), and the weight value of each index is obtained according to formula (2)~(4), as shown in Table 1.
For qualitative indicators, according to the classification of water inrush risk grade, the indicator score is divided into five grades I~V. The lower the score, the greater the risk of water inrush. Qualitative indicators include coal seam conditions (C11), mining methods (C12), structural properties (C21), geological anomaly body (C22), personnel refuge awareness (C51), personnel safety skills (C52), integrity of waterproof and drainage equipment (C61), availability of waterproof and drainage equipment (C62), perfection of water prevention and control system (C71), and implementation of water prevention and control measures (C72).
For quantitative indicators, the corresponding indicator value is obtained by conversion of borehole measurement  6 Geofluids data. Among them, aquifer water yield property (C31) is characterized by unit water inflow; effective aquifuge thickness (C41) can be converted according to the empirical formula, combined with drilling geological data, coal seam dip angle, mining depth, working face length, and other data, and aquifuge integrity is represented by the permeability coefficient [24]. Combined with the actual situation and common practice of the coal mine, the grade of each indicator is divided.

Result and Discussion
Taking the indicator of coal seam conditions (C11) as an example, the expert scoring is shown in Table 2.
According to equations (8)~ (11), calculate the cloud eigenvalue of the index evaluation result, and use the cloud forward generator to get the cloud image of the index evaluation result, as shown in Figure 5. It can be seen from the figure that the evaluation of coal seam conditions (C11) by the expert group is between III and IV and is more inclined to IV, so the evaluation of this index is more concentrated.
By analogy, the cloud eigenvalues of all three-level indicator evaluation results can be obtained. According to equation (12), the similarity between all three-level index evaluation results and evaluation grades can be obtained. After normalization, the membership degree can be obtained. According to the principle of the maximum membership degree, the grade can be judged. The principle of the maximum membership degree means that if the membership degree of a comprehensive indicator is higher than that of an evaluation grade, then we will set the evaluation target as the evaluation grade. The results are shown in Table 3. The indicator of  grade II is thickness of effective aquiclude (41). The indicators of grade III are personnel refuge awareness (C51) and personnel safety skills (C52). The indicators of grade IV are coal seam conditions (C11), mining methods (C12), structural properties (C21), geological anomaly body (C22), aquifer water pressure (C32), aquiclude average tensile strength (C42), integrity of waterproof and drainage equipment (C61), availability of waterproof and drainage equipment (C62), perfection of water prevention and control system (C71), and implementation of water prevention and control measures (C72). The indicators of grade V are aquifer water yield property (C31) and integrity of aquiclude (C43).
The correlation matrix I 15×5 of all three-level indicators can be obtained from Table 3, and the weight matrix W 1×15 of all three-level indicators can be obtained from Table 1. Then, the evaluation result matrix of floor water inrush risk is G = W 1×15 ⋅ I 15×5 = ð0:03990:06120:19500:53870:1652Þ.
According to the weight value of each three-level indicator relative to each secondary indicator, combined with the evaluation value of the corresponding three-level indicator, the evaluation results of each secondary indicator are obtained, as shown in Table 4. According to the principle of maximum membership, the evaluation level of each secondary indicator is judged.

Conclusion
(1) Based on the PSR model, the assessment indicator system of coal seam floor water inrush risk is established, which is composed of 7 secondary indicators and 15 three-level indicators, including mining factors, geological structure factors, aquifer factors, aquifuge factors, personnel factors, equipment factors, and management factors, making the assessment indicator system more theoretical and complete (2) Based on the extension cloud theory and the assessment indicator system, the risk assessment model of water inrush from coal floor is constructed, which solves the fuzziness and randomness in the evaluation process and improves the accuracy of the evaluation

Data Availability
Data will be provided upon request to the corresponding author.

Conflicts of Interest
The authors declare no conflicts of interest.