The fuzzy comprehensive evaluation of water and sand inrush risk during underground mining

Abstract

Taking the geological conditions of a typical coal mine as an example, a fuzzy comprehensive estimation model is developed for judgment of mine water and sand inrush caused by underground mining. According to the geological prototype, three basic conditions of water and sand inrush disaster induced by mining under thin bedrock and thick loose aquifer are revealed. Using analytic hierarchy process (AHP) to determine the weights of evaluation index factors, nine evaluation factors are chosen, and then the degree of membership of evaluation factors is determined through qualitative and quantitative two ways. The dangers of water and sand inrush in the study area are quantitatively analyzed. The risks are divided into four ranks, through calculating, the hazard level of water and sand inrush disaster in study area is 3, it is high risk. The fuzzy system is efficient and easy to use, and the evaluation results are in good accordance with the reality, and provide the decision basis for the safety production of the coal mine.

Keywords

Fuzzy comprehensive evaluation mine water and sand inrush analytic hierarchy process evaluation index factor

1 Introduction

China is one of the largest coal resources and coal production country in the world, rich in coal resources, and mine disaster is also most serious. As one of the five coal mine disaster, the mine water disaster occurs frequently. To minimize the disaster, a clear understanding of the mechanism of water damage, timely and accurate safety evaluation, is a problem to be solved. It has also been concerned about by the growing number of scholars.

In the study of the formation fracture development law and water inrush from roof, the “three bands” theory, zero failure theory and critical layer theory in academia are generally recognized and widely used [1]. In order to make the results of the detection water and sand inrush more efficient, reliable, comprehensive, the concept of vulnerability assessment is introduced. The vulnerability is an important indicator as a measure of risk performance, indicates that the system to maintain itself stability against disasters, contains adaptability, risk and restoring force [2]. Vulnerability study started early in other countries, involved a wide field [3], such as disaster science, ecological environment, engineering and other [4, 5]. The groundwater vulnerability assessment which Aller put forward in 1987 was adopted by the US Environmental Protection Agency [6]. Then Europe, Canada and other countries and regions promoted and used to assess groundwater vulnerability [7], and developed several sets of mature evaluation methods [8]. There are several fuzzy system methods, including fuzzy mountain clustering [9], subtractive clustering [10], fuzzy inference techniques [11], and fuzzy set [12], that can handle the uncertainty of certain information. The fuzzy comprehensive evaluation or the fuzzy cluster analysis [13 –15] is an effective method to discriminating mine water bursting sources.

In coal mining, water and sand inrush is a complex issue, involving hydrogeology, engineering geology, mining methods, aquifer and aquifuge properties of the roof, and many other factors. With the complex and difficult mining intensified, hydrogeological conditions are more complex [16]. The one hand, some factors that cannot be described by a precise number, but only fuzzy concept; on the other hand, there is no one to one function relationship between the change and disaster of various factors, impossible to establish a precise mathematical model to solve. The fuzzy theory in dealing with these issues has a unique effect. A secondary fuzzy comprehensive evaluation system was constructed [17]. A vulnerability index was proposed that coupled the analytic hierarchy process (AHP) with the geographic information system (GIS) [18]. These methods are all genuine contributions to the study of roof or floor water inrush assessment, but are subject to limitations to water and sand inrush from roof.

In this paper, the working face of thin bedrock is the geological prototype. When mining, the working face may occur water and sand inrush and other accidents. So the weights of evaluation index factors is determined by analytic hierarchy process, a fuzzy comprehensive estimation model is developed for judgment of mine water and sand inrush caused by underground mining. It is necessary to explore the safety evaluation mechanism in this particular geological condition of coal mining, guide for the efficient, safe mining of coal resources under conditions of thin bedrock.

2 Fuzzy evaluation method

2.1 Factors domain of the evaluation object

$U = {u_{1} {, u}_{2}, \dots {, u}_{m}}$ (1)

There are m evaluation indexes, indicating that the object to be evaluated will be judged and described in what ways.

2.2 Comments level domain

Reviews set is a set that evaluators may make various overall results of the evaluation to being evaluation object, expressed by V. $V = {v_{1}, v_{2}, \dots, v_{n}}$ (2)

In fact, it’s a division in the change interval of the evaluated objects. Among them, V_i is the i-th evaluation results, n is the total number of the evaluation results.

2.3 Single factor evaluation, fuzzy relation matrix R

Starting from a single factor evaluation, the degree of membership of the evaluation object to the evaluation collection V is determined, which is called single factor fuzzy evaluation. After the configuration of the grade fuzzy subsets, the evaluated subjects will be quantified one by one from each factor u_i (i = 1, 2, …, m). That is, the degree of membership of the evaluated objects to each grade fuzzy subsets is determined, and then gets the fuzzy relation matrix. $R = (\begin{matrix} r_{11} & r_{12} & \dots & r_{1 n} \\ r_{21} & r_{22} & \dots & r_{2 n} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ r_{m 1} & r_{m 2} & \dots & r_{mn} \end{matrix})$ (3)

R is a fuzzy relationship between universe U of factor sets in mind and universe V evaluation sets.

When determining affiliation, based on evaluation grade, the evaluation object is usually made scores by experts or relevant professionals. After counting scoring results, r_ij is obtained based on the method of absolute value subtrahend. $r_{ij} = {\begin{matrix} 1 (i = j) \\ 1 - c \sum | x_{ki} - x_{kj} | (i \neq j) \end{matrix}$ (4)

Among the formula:

r_ij (i = 1, 2, …, m ; j = 1, 2, … , n) means the membership degree of the evaluated object from the factor u_i to the grade fuzzy subset v_i;

x_ki means the measured data of the i-th evaluation factor and the k water and sand bursting sample.

c can be appropriately selected, makes 0 ≤ r_ij ≤ 1.

2.4 Fuzzy weight vector of evaluation factors

To reflect the importance of each factor, each factor U will be assigned a corresponding weight a_i (i = 1, 2, …, m), a_i is usually required to meet a_i ≥ 0, ∑a_i = 1. a_i represents i-th factor weight, then a fuzzy set A, composed of each weight, is the weight set.

2.5 Multifactor fuzzy evaluation

Through the suitable synthetic operator A and the fuzzy relation matrix R, vector B of each evaluated fuzzy comprehensive evaluation results was synthesized.

Fuzzy comprehensive evaluation model is Equation (5).

$\begin{matrix} B & = & A \cdot R \\ = & (a_{1}, a_{2}, \dots, a_{m}) (\begin{matrix} r_{11} & r_{12} & \dots & r_{1 n} \\ r_{21} & r_{22} & \dots & r_{2 n} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ r_{m 1} & r_{m 2} & \dots & r_{mn} \end{matrix}) \\ = & (b_{1}, b_{2}, \dots, b_{n}) \end{matrix}$ (5)

Among the formula, b_j (j = 1, 2, …, n) is obtained by calculating of A and the j-th column of R, means the membership degree of the evaluated object from the whole to the grade fuzzy subset v_i.

2.6 Fuzzy comprehensive assessment analysis

The results of fuzzy comprehensive evaluation is the membership degree of the evaluated object to each grade fuzzy sets, it is generally a fuzzy vector, rather than a point value. Plural evaluation objects are compared and sorted, comprehensive scores each evaluation object are calculated, sorted by size, preferred according to order.

3 Fuzzy comprehensive evaluation models

3.1 Geological prototype

No.3 coal is the main coal seam of 8301 face in Jining mining area, Shandong province, China. The aquifer, related to the No. 3 coal seam mining, includes bedrock aquifer (including roof sandstone aquifer, red beds weathering zone and coal weathering zone), Quaternary bottom aquifer. The main characteristics of the coal face are thick coal seam, thin bedrock, rock is weak due to weathering, and overlying loose aquifer is thick. According to the results of exploration drilling and pumping tests, Quaternary bottom aquifer belongs to moderate water yield property. When mining, the working face may occur water and sand inrush and other accidents. Therefore, it is necessary to explore the safety evaluation mechanism in this particular geological condition of coal mining, guide for the efficient, safe mining of coal resources under conditions of thin bedrock.

3.2 Selection of evaluation object and influential factors

According to the geological prototype, the formation of water and sand inrush disaster induced by mining under thin bedrock and thick loose aquifer requires three basic conditions: sources of water and sand C₁; hydrodynamic conditions and predisposing factors C₂; flow passage of water and sand C₃. After considering the three factors, 9 factors are selected as evaluation factors, they are the thickness of confined water-bearing sand layer C₁₁, the aquosity of overlying confined aquifer C₁₂, the liquefaction of confined water-bearing sand layer C₁₃, the water supply C₂₁, the pressure of confined aquifer C₂₂, the development degree of original fissures C₃₁, the ratio of mining depth and mining thickness C₃₂, the method of workface roof management C₃₃, the properties of Quaternary bottom aquifuge C₃₄.

3.3 Model establishment of fuzzy comprehensive evaluation

Based on choosing the evaluation object and influencing factors, the indicator framework model of different levels is established by the method of fuzzy mathematics (Fig. 1).

This indicator is divided into three levels of frames, which are the target layer, the first index layer, the second index layer. The target layer of water and sand flow disaster is represented by U, the first index layer includes 3 evaluation conditions, and the second index layer includes 9 evaluation factors.

3.4 Division of risk grades

The evaluation set is composed of collection of grades, denoted by V. The safety assessment grades of water and sand inrush disaster are divided into 4 grades; they are extremely high risk, high risk, general risk, low risk. So V = {v₁, v₂, v₃, v₄} = {lowrisk, general risk, high risk, extremely high risk}.

3.5 Weight of index factor

3.5.1 Analytic hierarchy process

(1) Judgment matrix

The evaluation factors set U and the judgments set V are set up. The relative importance values of u_i to u_j are expressed by u_ij. The judgment matrix T is established. $T = [\begin{matrix} U_{11} & U_{12} & \dots & U_{1 m} \\ U_{21} & U_{22} & \dots & U_{2 m} \\ \dots & \dots & \dots & \dots \\ U_{m 1} & U_{m 2} & \dots & U_{mm} \end{matrix}]$ (6)

(2) Order of importance

According to the judgment matrix, the eigenvectors are obtained corresponding to the maximum eigenvalues. The order of evaluation factors importance is gained according to the obtained eigenvectors, and then normalization process, weight distribution is obtained.

Each row of the judgment matrix can be normalized: $\bar{u_{ij}} = \frac{u_{ij}}{\sum_{k = 1}^{m} u_{ik}} (i, j = 1, 2, \dots, m)$ (7)

Each column of the normalized judgment matrix is added according to column: $\bar{W_{i}} = \sum_{j = 1}^{m} \bar{u_{ij}} (i, j = 1, 2, \dots, m)$ (8)

Normalization processing of vector $\bar{W} = (\bar{W_{1}}, \bar{W_{2}}, \dots, \bar{W_{m}})$ $a_{i} = \frac{\bar{W_{i}}}{\sum_{j = 1}^{m} \bar{W_{j}}} (i, j = 1, 2, \dots, m)$ (9)

The results of A = (a₁, a₂, … , a_m) are the desired eigenvectors.

Solving maximum eigenvalues of judgment matrix λ_max: $λ_{\max} = \frac{1}{m} \sum_{i = 1}^{m} \frac{{(TA)}_{i}}{a_{i}}$ (10)

Among the formula, (TA) _i represents the i-th element of the vector TA. $TA = [\begin{matrix} {(TA)}_{1} \\ {(TA)}_{2} \\ \dots \\ {(TA)}_{m} \end{matrix}] = [\begin{matrix} u_{11} & u_{12} & \dots & u_{1 m} \\ u_{21} & u_{22} & \dots & u_{2 m} \\ \dots & \dots & \dots & \dots \\ u_{m 1} & u_{m 2} & \dots & u_{mm} \end{matrix}] \cdot [\begin{matrix} a_{1} \\ a_{2} \\ \dots \\ a_{m} \end{matrix}]$ (11)

(3) Test

Testing randomness and consistency of judgment matrix, to determine whether the eigenvectors are reasonable, the empirical formula of test is: $CR = \frac{CI}{RI}$ (12)

Among the formula, CR is the random consistency ratio of the judgment matrix; CI is the consistency index of the judgment matrix: $CI = \frac{1}{M - 1} (λ_{max} - m)$ (13)

CI is the mean random consistency index.

When CR < 0.1, the weight distribution is reasonable, otherwise, the judgment matrix needs to be re-adjusted.

3.5.2 Weight calculation

The scores of the second level factors are calculated (Table 1).

To establish the judgment matrix: $T = [\begin{matrix} 1 & 2 & \frac{1}{5} & \frac{1}{3} & \frac{1}{9} & \frac{1}{6} & \frac{1}{7} & \frac{1}{8} & \frac{1}{8} \\ 2 & 1 & \frac{1}{3} & \frac{1}{3} & \frac{1}{8} & \frac{1}{3} & \frac{1}{5} & \frac{1}{6} & \frac{1}{6} \\ 5 & 3 & 1 & 4 & \frac{1}{5} & 2 & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\ 3 & 3 & \frac{1}{4} & 1 & \frac{1}{5} & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{3} \\ 9 & 8 & 5 & 5 & 1 & 7 & 5 & 3 & 4 \\ 6 & 3 & \frac{1}{2} & 2 & \frac{1}{7} & 1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{3} \\ 7 & 5 & 3 & 3 & \frac{1}{5} & 2 & 1 & \frac{1}{2} & \frac{1}{2} \\ 8 & 6 & 4 & 4 & \frac{1}{3} & 3 & 2 & 1 & 2 \\ 8 & 6 & 5 & 3 & \frac{1}{4} & 3 & 2 & \frac{1}{2} & 1 \end{matrix}]$

$\bar{W}$ is obtained according to the Equations (7) and (8), then through the normalization process, according to the Equation (9) A can be calculated: $\begin{matrix} A & = & (0 . 018, 0 . 026, 0 . 077, 0 . 046, 0 . 337, 0 . 063, \\ 0.109, 0.175, 0 . 150) \end{matrix}$

CR = 0.0604 <0.1 is calculated by the Equations (11–13). This shows that the weight distribution of the judgment matrix is reasonable, and also shows that the judgment matrix has a satisfactory consistency.

4 Result analysis of fuzzy comprehensive assessment

4.1 Membership function

Some indicators of causing water and sand inrush disaster are difficult to quantify, belong to fuzzy state. When evaluation standards are not unified, the evaluation could easily lead to inaccurate; the fuzzy theory will solve this problem by “membership”.

In this paper, the membership means the “contribution degree” of each indicator to the water and sand inrush disaster. The second-level indicators are divided into six qualitative indicators and three quantitative indicators. The each index membership will be calculated by using different methods. The qualitative indicators include C₁₂, C₁₃, C₁₄, C₃₂, C₃₃, and C₃₄. The membership of each index is divided into four levels: (small, medium, large, huge) = (0, 0.4, 0.7, 1.0). The smaller membership is, the lower contribution of the indicator is. The quantitative indicators include C₁₁, C₂₂, and C₃₂. The membership function is calculated by the Equations (14–16): $C_{11} = {\begin{matrix} 0 & (h \leq 0 m) \\ \frac{h}{100} & (0 < h < 100 m) \\ 1 & (h \geq 100 m) \end{matrix}$ (14) $C_{22} = {\begin{matrix} 0 & (p \leq 0.3 MPa) \\ \frac{p - 0.3}{0.7} & (0.3 < p \leq 1 MPa) \\ 1 & (p > 1 MPa) \end{matrix}$ (15) $C_{32} = {\begin{matrix} 0 & (x > 100) \\ \frac{x - 30}{70} & (30 < x \leq 100) \\ 1 & (x \leq 30) \end{matrix}$ (16)

According to the geology prototype of the engineering geology and hydrogeology conditions in the study area, and the membership function given, the fuzzy vectors of each factor are calculated. The evaluation values of single factor membership are shown in Table 2. $\begin{matrix} r_{11} & = & (0 . 5, 0 . 5, 0, 0) \\ r_{12} & = & (0 . 3, 0 . 5, 0 . 2, 0) \\ r_{13} & = & (0, 0 . 2, 0 . 8, 0) \\ r_{21} & = & (0, 0, 0 . 3, 0 . 7) \\ r_{22} & = & (0, 0 . 3, 0 . 7, 0) \\ r_{31} & = & (0 . 8, 0 . 2, 0, 0) \\ r_{32} & = & (0, 0, 0 . 3, 0 . 7) \\ r_{33} & = & (0 . 3, 0 . 5, 0 . 2, 0) \\ r_{34} & = & (0 . 8, 0 . 2, 0, 0) \end{matrix}$

4.2 Establishment of fuzzy evaluation matrix and comprehensive operation

According to the fuzzy vectors of various factors, the fuzzy transformation matrix R is established. $R = {\begin{matrix} r_{11} \\ r_{12} \\ r_{13} \\ r_{21} \\ r_{22} \\ r_{31} \\ r_{32} \\ r_{33} \\ r_{34} \end{matrix}} = [\begin{matrix} 0.6 & 0.4 & 0 & 0 \\ 0.3 & 0.5 & 0.2 & 0 \\ 0 & 0.2 & 0.8 & 0 \\ 0 & 0 & 0.3 & 0.7 \\ 0 & 0.3 & 0.7 & 0 \\ 0.8 & 0.2 & 0 & 0 \\ 0 & 0 & 0.3 & 0.7 \\ 0.3 & 0.5 & 0.2 & 0 \\ 0.8 & 0.2 & 0 & 0 \end{matrix}]$

The comprehensive evaluation calculation is carried out. $B = A \cdot R = \begin{matrix} (0.242 & 0.267 & 0.361 & 0.130) \end{matrix}$ (17)

4.3 Result analysis

Based on the weighted average principle and the maximum membership degree principle, the rank of each grade is weighted sum with the corresponding component in B. $A = \frac{\sum_{j = 1}^{n} b_{j}^{k} \cdot j}{\sum_{j = 1}^{n} b_{j}^{k}}$ (18)

Among the formula, k is the Undetermined coefficients (k = 1 or 2). When k tends to infinity, the weighted average principle is the principle of maximum membership. The use of “1, 2, 3, and 4” indicates four grades of the lower risk, general risk, high risk and extremely high risk. The data of A = 2.376 will be obtained according to the Equation (18). Therefore, the hazard level of water and sand inrush disaster in study area is 3, it is high risk.

5 Conclusions

Prediction of the water and sand inrush during mining is a complicated problem that involves many fields such as hydrogeology, engineering geology, and rock mechanics. Establishing assessment models among these fields is of the greatest significance. According to the geological prototype, three basic conditions of water and sand inrush disaster induced by mining under thin bedrock and thick loose aquifer are revealed. Using analytic hierarchy process to determine the weights of evaluation index factors, nine evaluation factors are chosen, and then the degree of membership of evaluation factors is determined through qualitative and quantitative two ways.

The risk of the water and sand inrush is assessed by calculating their weight using AHP based on the analyzed factors. The risks are divided into four ranks, through calculating, the hazard level of water and sand inrush disaster in study area is 3, it is high risk. There exists the possibility of water and sand inflow when mining under thin bedrock, some measures for mine water prevention and control should be used, such as using small mining face or slice mining. The fuzzy comprehensive evaluation system could provide the decision basis for the safety production of the coal mine.

In future research, collecting enough reliable numerical data from various physical conditions of similar mines should be used to train and validate the potential Neural Network, the prediction model by using Neural Networks would be more efficient model to predict the level of risks or vulnerability considering nine involved criteria.

Footnotes

Acknowledgments

Financial support for this work, is provided by National Natural Science Foundation of China (40802076), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and the Doctoral Science Foundation of ECUT (No. DHBK2015101), all of which are gratefully acknowledged. We also would like to express our acknowledgments to editors and the anonymous reviewers who provided useful comments that improved an earlier version of the manuscript.

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