Fuzzy comprehensive risk evaluation of roof water inrush based on catastrophe theory in the Jurassic coalfield of northwest China

Abstract

The risk assessment of roof water inrush is of great significance for sustainable development of mine and ecological environment. Taking the Jurassic coalfield in northwest China as an engineering background, we firstly selected nine indexes influencing roof water inrush based on three essential conditions with the water source, the water inrush channel and the mining space, i.e., unit water inflow, flushing fluid consumption, aquifer thickness, effective aquiclude thickness, lithological association of the effective aquiclude, inclined length of coalface, buried depth of coal seam, mining thickness and advancing speed of coal mining, and then established the hierarchy structure model for mutation evaluation of roof water inrush. Secondly, the expert scoring method and trapezoidal fuzzy distribution were chosen to construct the initial fuzzy membership function based on the characteristics with fuzziness and mutability of roof water inrush. Thirdly, based on quantized recursion operation with the normalization formula and the (non) complementarity principle, total mutation membership function value was calculated, and the water inrush risk grade was determined. Eventually, the proposed method has successfully predicted the water inrush risk in the first mining face of Jinjitan coal mine. The research achievements provide an important reference for the sustainable development of the Jurassic coalfield.

Keywords

Jurassic coalfield risk evaluation of roof water inrush the mutation theory fuzzy analysis sustainabledevelopment

1 Introduction

With the gradual depletion of coal resources in the Eastern China and the aggravating contradictions between the resources and environment in the central China, the development focus of coal resources has shifted to the fragile eco-geological environment of northwestern China [1 –3]. With the enlargement of Jurassic coal seam mining scale in northwest China, roof water inrush, bringing out secondary ecological geological disasters such as drop of phreatic water level in sand layer, shallow water resources destruction, surface drought and desertification, was occurred with shallow coal seam and large mining thickness, which is seriously affecting the sustainable development of regional economy and mine safety. For example, mine water inflow of many coalfaces in Jinjie coal mine and Yuyang coal mine of Shenmu mining area exceeded 600m³/h, leading to serious threat on the production safety. The water inrush accident with 1200m³/h mine water inflow occurred at the s1201 coalface of Ningtiaota coal mine, resulting in an economic loss of nearly 200 million yuan. Therefore, it is of great practical and theoretical significance to study the roof water inrush risk of the Jurassic Coalfield in northwest China for realizing the sustainable development of the water resources and mine safe exploitation.

At present, great progress has been made in risk assessment of roof water inrush. Wu [4 –7] proposed the concept of “three maps-two predictions”, which was successfully applied to predict the roof water inrush risk. Liu et al. [8] adopted probabilistic neural network method to forecast the water rich characteristics of coal seam roof sandstone based on analysis of the water flowing fractured zone height. Liu et al. [9] and Yang et al. [10] researched the water rich zoning of roof aquifer and the development height of water flowing fractured zone based on the analytic hierarchy process and fuzzy cluster analysis, respectively, which provided the important basis for the mine safety production. Li [11] combined with the expert knowledge database, weight database of coal mine water disaster and the spatial knowledge acquisition, excavation and analysis of GIS to comprehensively evaluate the water disaster and roof caving safety in Yaoqiao coal mine, which provided a reference in mining practice. Li et al. [12] established the comprehensive assessment on coal roof water bursting risk in karst area on the basis of systematical analyses of water abundance characteristics of aquifer in coal seam roof, structural features, water-resisting ability for aquifuge, effects of mining disturbance on coal seam roof by fuzzy comprehensive evaluation. Yang et al. [13] developed a fuzzy comprehensive estimation model for judgment of mine water and sand inrush caused by underground mining based on the geological prototype. Zhang et al. [14] established the Fuzzy Matter-Element model of mine roof water inrush by combining fuzzy theory and matter element theory in order to obtain the relationship between the mine roof water inrush grade and its influencing factors. Fan et al. [15] studied the risk evaluation methods of water and sand inrush from coal roof based on the dimensionless multi-factor information fusion technique in Yushenfu coal mine, which had certain significance for mining area planning, mining method selection and disaster prevention and control. Wu et al. [16] used the key stratum theory and the cusp catastrophe theory to analyze the occurrence mechanism of the roof water inrush in Dafoshi coal mine, and thought that sudden breaking and destabilization of key stratum in bedrock is the cause of roof water inrush. Li et al. [17] combined with field geological mapping, in situ and laboratory tests to carry out the zoning of engineering geological conditions in Yushenfu mine area based on the geological information from the coal exploration, which can provide decision– making foundation for roof water inrush risk evaluation. Ning et al. [18] established the evaluation method of water inrush risk in shallow buried coal seam, providing theoretical basis and technical support for the design of the coal mining area in the western mining area. Du [19] evaluated geological environment of mining area before mining based on the GIS spatial information quantitative management of various factors and the support vector machine theory, predicted zoning of geological environment after mining, and put forward technical measures for protecting geological environment of coal mining activities in ecologically fragile areas.

In fact, roof water inrush is a very complex system, whose influencing factors are diverse and fuzzy. What’s more, the roof water resisting strata in mining disturbance under the action of bending deformation is the process of energy accumulation, when the effective aquiclude displacement increases to a critical value, the aquiclude will suddenly lose stability. That is, roof water inrush has mutability. Therefore, this paper proposed the risk assessment method of roof water inrush by fuzzy evaluation and catastrophe theory based on the analysis of the risk factors of roof water inrush, and successfully applied the method to engineering practice.

2 Study area

The Yushenfu mining area is located in the north of Yulin city, Shaanxi, which belongs to the Yuyang district of Yulin city and Shenmu county. The boundary of Yushenfu mining area is irregular polygon, whose total area is about 6334 km² with maximum length 1.6 km and width 97 km, as shown in Fig. 1. The study area is located in the border of the Maowusu Desert southeast and the northern Loess Plateau, where water resources are poor, and the geological and ecological environment is fragile. The average annual rainfall in this area is 400 mm, and the annual average evaporation is 2388.7 mm, which belongs to semi-arid climate area [20].

Fig.1

Location of study area.

The geological structure of this area is simple without faults. From top to bottom, the stratigraphic succession consists of Quaternary (Aeolian sand $Q_{4}^{col}$ , Sara Wusu aquifer Q_3s, Lishi loess Q₂₁), Neogene (Baode laterite N₂b), Jurassic (An’ding formation J_2a, Zhiluo formation J_2z, Yan’an formation J_2y). Sara Wusu formation, the most important aquifer and the target layer for water conservation and coal mining protection, are widely distributed in this area, which has water supply significance and control the ecological environment of the mining area. In addition, Lishi loess Q₂l, Baode laterite N₂b and bedrock layer are the main effective aquiclude in study area.

3 Risk factors analysis on roof water inrush

Conditions for the occurrence of coal mine roof water inrush disaster are complex, which are affected by many factors, such as the scale and property of overlying aquifers, coal seam characteristics, mining method, and thickness, strength and failure form of overburden strata [21]. Considering that that the index values should be easily accessible and most of the information about water inrush under certain geological conditions can be described with several key factors as few as possible, the risk factors selection of roof water inrush evaluation is very important for a realistic evaluation results. Water source, water inrush channel and mining space are the sufficient conditions for roof water inrush. For this reason, the risk assessment indexes of roof water inrush were selected from three aspects of water source, water inrush channel and mining space, which were analyzed as follows.

3.1 Water rich property of aquifer

The water rich property of aquifers can reflect the basic characteristics of aquifers to some extent. Therefore, unit water inflow, flushing fluid consumption and aquifer thickness were chosen as risk indexes of water rich property of aquifer.

(1) Unit water inflow

Unit water inflow, an important parameter to reflect the water enrichment of aquifer, is water inflows of water level in the holewell every drop one meter in the pumping test [22]. To determine the degree of water enrichment more accurately, the water inflow for different apertures and drawdowns are converted into the unit in flow of a drill with a 91 mm diameter and a 10 m drawdown. The greater the unit water inflow values, the better the water rich capacity of aquifers and the mutual recharge relationship between aquifers.

(2) Flushing fluid consumption

Flushing fluid consumption is a sign that reflects the permeability of rock formations. The change of water level and denseness of drilling fluid is an important index to represent the hydraulic properties of drilling strata. In other words, the greater the amount of drilling fluid used, the greater the coefficient of permeability.

(3) Aquifer thickness

Aquifer thickness is the most intuitionistic factor to characterize the water abundance of aquifers, which directly affects the water content of aquifers. In general, the greater the aquifer thickness is, the greater the water content of the aquifer in the unit thickness is, and the greater the water abundance is.

3.2 Characteristics of the effective aquiclude

The formation of the water inrush channel depends on the characteristics of the effective aquiclude. Therefore, effective aquiclude thickness and lithological association of the effective aquiclude were chosen as risk indexes of the effective aquiclude characteristics.

(1) Effective aquiclude thickness

The effective aquiclude thickness is calculated by the distance between the top of mining seam and bottom of Quaternary loose aquifer minus the height of water flowing fractured zone which is formed after mining the whole height at one time. Generally speaking, the smaller the effective aquiclude thickness is, the greater the risk of water inrush.

(2) Lithological association of the effective aquiclude

The lithological association of the effective aquiclude is also an important index to evaluate the characteristics of the effective aquiclude. Different lithology shows different mechanical characteristics, so it has different failure characteristics in engineering practice.

3.3 Mining space

Mining space is a sufficient condition for forming roof water inrush. Therefore, inclined length of coalface, buried depth of coal seam, mining thickness and advancing speed of coal mining were chosen as risk indexes of the mining space.

(1) Inclined length of coalface, buried depth of coal seam and mining thickness

Research shows that the larger the inclined length of coalface, buried depth of coal seam and mining thickness are, the greater the risk of roof water inrush [23].

(2) Advancing speed of coal mining

During the mining process, the advancing speed of the working face is accelerated, and the roof rock layer can be controlled effectively, which can reduce the height of the water flowing fractured zone and the risk of water inrush from the roof [24, 25].

4 Methodology

An effective method of roof water inrush risk assessment is of great significance to the continuous and safe production of mine. Therefore, the risk assessment method of roof water inrush was proposed by fuzzy evaluation and catastrophe theory based on the characteristics of roof water inrush, whose evaluation flow chart was shown in Fig. 2.

Fig.2

Evaluation flow chart.

4.1 Relationship between evaluation grade and total membership function values

Based on the analysis of the roof water inrush influence factors and existing mine data, the water inrush risk evaluation grade was divided into four grades: dangerous, less dangerous, safe and relatively safe, and the corresponding relationship between the evaluation grade and the total mutation membership function value was shown in Table 1.

Table 1
Relationship between evaluation grade and total membership function values

Total mutation membership function values [1.0,0.9] (0.9,0.7] (0.7,0.5] [0.5,0]

Evaluation grade Dangerous Less dangerous Safe Relatively safe

Total mutation membership function values	[1.0,0.9]	(0.9,0.7]	(0.7,0.5]	[0.5,0]
Evaluation grade	Dangerous	Less dangerous	Safe	Relatively safe

4.2 Establishment of hierarchy model for mutation evaluation

The hierarchy structure model for mutation evaluation of roof water inrush was established based on the above analysis of roof water inrush risk factors, as shown in Fig. 3.

Fig.3

Hierarchy structure model for mutation evaluation of roof water inrush.

4.3 Construction of initial membership function

Risk factors of roof water inrush can be divided the discrete index and the continuous index. In Fig. 3, the flushing fluid consumption A₂ and lithological association of the effective aquiclude B₂ belong to the discrete index, while the rest of factors belong to the continuous index. The discrete indexes can hardly be measured by classical mathematical models. For this reason, the discrete indexes were changed into fuzzy language based on the fuzzy mathematics method, and then the initial fuzzy membership function value was determined by the expert scoring method [26, 27]. For the other seven continuous indexes, the quantitative description was adopted, and the initial fuzzy membership function was determined by the trapezoid distribution in the fuzzy distribution and the mining practice data.

4.3.1 Discrete index

The expert scoring method was chosen to determine the initial membership function value of the discrete index.

(1) Expert scoring method

The j representative experts were invited to give the evaluation values ranging from 0 to 1 of each project with their own experience, and a scoring matrix was obtained, as shown in Equation (1). $\begin{matrix} p = [p_{1}, p_{2}, p_{3} \dots p_{j}] \\ and q = [p_{1} + p_{2} + p_{3} + \dots + p_{j}] / j \end{matrix}$ (1)

Where p_j is the evaluation value. Hence, the initial membership function value of the discrete index was calculated.

(2) The membership function value of the discrete index

② Flushing fluid consumption A₂

The flushing fluid consumption was divided into five grades: very high, high, moderate, low and very low. In this paper, ten experts were invited to evaluate the membership function value of “very high” grade. After calculating, it was concluded that the membership function value of “very high” grade was 0.95. Similarly, the membership function values of “high”, “moderate”, “low” and “very low” grade were 0.85, 0.60, 0.45 and 0.15, respectively.

① Lithological association of the effective aquiclude B₂

Based on the stratigraphic characteristics and mining practice in the study area, the lithological association of the effective aquiclude can be divided into three grades, namely, loess layer, combination of loess and laterite layer, combination of loess, laterite and bedrock layer, whose corresponding membership function values were 0.90, 0.75 and 0.20 by expert scoring method.

4.3.2 Continuous index

The trapezoid fuzzy distribution was chosen to determine the initial membership function value of the continuous index.

(1) The trapezoid fuzzy distribution

The membership function of the fuzzy set on the real number set R is usually called fuzzy distribution, which contains rectangular distribution, trapezoid distribution, Gauss distribution and Cauchy distribution [28]. When the membership function of the objective fuzzy phenomenon is similar to that of a given fuzzy distribution, the fuzzy distribution is chosen as the desired membership function, and then the realistic parameters are identified by empirical knowledge or data experiments, so as to obtain the specific membership function. The partial small type and partial large type of the trapezoid fuzzy distribution were chosen to determine the membership function of the continuous indexes, whose distribution map were shown inFig. 4.

Fig.4

Distribution map of trapezoid fuzzy: (a) Partial small type,(b) Partial large type.

① Partial small type distribution

The partial small type distribution is generally applied to the inverse index, that is, the index value is opposite to the trend of the evaluation value. The membership function of the partial small type distribution was shown in Equation (2). $A (x) = {\begin{matrix} 1 & x ⩽ a \\ \frac{b - x}{b - a} & a < x < b \\ 0 & x ⩾ b \end{matrix}$ (2)

② Partial large type distribution

The partial large type distribution is generally applied to the positive index, that is, the index value is consistent with the trend of the evaluation value. The membership function of the partial large type distribution was shown in Equation (3). $A (x) = {\begin{matrix} 0 & x ⩽ a \\ \frac{x - a}{b - a} & a < x < b \\ 1 & x ⩾ b \end{matrix}$ (3)

(2) The membership function of the continuous index

① Positive index

The greater the unit water inflow A1, aquifer thickness A3, inclined length of coalface C1, buried depth of coal seam C2 and mining thickness C3, the greater the risk of water inrush, which belong to the positive index.

Based on the drilling unit water inflow, the water rich property of aquifer was divided into four levels, namely, weak water enrichment (q < 0.1 L/s•), medium water enrichment (0.1 L/s• <q≤1.0 L/s•), strong water enrichment (1.0 L/s• <q≤5.0 L/s•) and stronger water enrichment (q > 5.0 L/s•) [20]. The initial membership function of the unit water inflow was shown in Equation (4) based on the partial large type distribution map. $a_{1 μ} = {\begin{matrix} 0 & μ ⩽ 0.1 L / s • m \\ \frac{μ - 0.1}{4.9} & 0.1 L / s • m < μ < 5 L / s • m \\ 1 & μ ⩾ 5 L / s • m \end{matrix}$ (4)

Similarly, the initial membership function of the aquifer thickness A₃, inclined length of coalface C₁, buried depth of coal seam C₂ and mining thickness C₃ were shown in Equations (5∼8) based on the partial large type distribution map and drilling investigation, respectively. $a_{3 w} = {\begin{matrix} 0 & w ⩽ 20 m \\ \frac{w - 20}{40} & 20 m < w < 60 m \\ 1 & w ⩾ 60 m \end{matrix}$ (5)

$c_{1 μ} = {\begin{matrix} 0 & μ ⩽ 100 m \\ \frac{μ - 100}{200} & 100 m < μ < 300 m \\ 1 & μ ⩾ 300 m \end{matrix}$ (6)

$c_{2 v} = {\begin{matrix} 0 & v ⩽ 100 m \\ \frac{v - 100}{500} & 100 m < v < 600 m \\ 1 & v ⩾ 600 m \end{matrix}$ (7)

$c_{3 w} = {\begin{matrix} 0 & w ⩽ 2 m \\ \frac{w - 2}{10} & 2 m < w < 12 m \\ 1 & w ⩾ 10 m \end{matrix}$ (8)

② Inverse index

The greater the effective aquiclude thickness B₁ is and the faster the advancing speed of coal mining C₄ is, the greater the risk of water inrush. The initial membership function of the effective aquiclude thickness was shown in Equation (9) based on the partial small type distribution map and drilling investigation. $b_{1 μ} = {\begin{matrix} 1 & μ ⩽ 40 m \\ \frac{μ - 40}{40} & 40 m < μ < 80 m \\ 0 & μ ⩾ 80 m \end{matrix}$ (9)

The initial membership function of the advancing speed of coal mining was shown in Equation (10) based on the partial small type distribution map and mining practice. $c_{3 t} = {\begin{matrix} 1 & t ⩽ 3 m / d \\ \frac{t - 3}{12} & 3 m / d < t < 15 m / d \\ 0 & t ⩾ 15 m / d \end{matrix}$ (10)

4.4 Determination of mutation types of indicators at all levels

Catastrophe theory, put forward by the French mathematician Tom Rene on the basis of the topology and the structural stability theory, is mathematical theory on the compliance of system state variables to control variables [29]. The critical point of the catastrophe theory system was classified according to the potential function of the system, and seven kinds of elementary mutation models were summed up based on the change characteristics of the state near the critical point [30, 31]. In order to facilitate the analysis, the cusp catastrophe model, swallowtail catastrophe model and butterfly catastrophe model were introduced in this paper, whose system diagrams were shown in Fig. 5.

Fig.5

System diagram of catastrophic model: (a) Cusp catastrophe model (b) Swallowtail catastrophe model (c) Butterfly catastrophe model.

4.5 Deduction of normalization formula

All critical points set of the potential function f (x) of the catastrophe model structure the equilibrium surface. When f′ (x) =0 and f′ (x) =0, the equilibrium surface equation and the singular point set of the equilibrium surface can be obtained, respectively. The bifurcation equations, expressed in terms of state variables, which reflect the relation between state variables and control variables, can be obtained by f′ (x) =0 and f′ (x) =0. And then the normalized formulas, derived by the bifurcation equations, which can translate the different qualitative states of each control variable into the comparable qualitative states in the system, is the basic operational formula for comprehensive analysis and judgment using catastrophe theory. The normalized formulas of three mutation models were shown in Table 2.

Table 2
The normalized formulas of three mutation models

Type Number of state variables Number of control variables Potential function form Equilibrium surface form Bifurcation equations Normalized formulas

Cusp catastrophe model 1(x) 2(μ, ν) V (x) = x⁴ + μx² + νx 4x³ + 2μx + ν = 0 μ = -6x², v = 8x³ x_μ = μ^1/2, x_v = v^1/3

Swallowtail catastrophe model 1(x) 3(μ, ν, ω) V (x) = x⁵ + μx³ + νx² + ωx 5x⁴ + 3μx² + 2νx + ω = 0 μ = -10x² v = 20x³, ω = -15x⁴ x_μ = μ^1/2, x_v = v^1/3, x_ω = ω^1/4

Butterfly catastrophe model 1(x) 4(μ, ν, ω, t) V (x) = x⁶ + tx⁴ + μx³ + νx² + ωx 6x⁵ + 4tx³ + 3μx² + 2νx + ω = 0 μ = -15x², v = 40x³, ω = -45x⁴, t = 24x⁵ x_v = μ^1/2, x_v = v^1/3, x_ω = ω^1/4, x_t = t^1/5

Type	Number of state variables	Number of control variables	Potential function form	Equilibrium surface form	Bifurcation equations	Normalized formulas
Cusp catastrophe model	1(x)	2(μ, ν)	V (x) = x⁴ + μx² + νx	4x³ + 2μx + ν = 0	μ = -6x², v = 8x³	x_μ = μ^1/2, x_v = v^1/3
Swallowtail catastrophe model	1(x)	3(μ, ν, ω)	V (x) = x⁵ + μx³ + νx² + ωx	5x⁴ + 3μx² + 2νx + ω = 0	μ = -10x² v = 20x³, ω = -15x⁴	x_μ = μ^1/2, x_v = v^1/3, x_ω = ω^1/4
Butterfly catastrophe model	1(x)	4(μ, ν, ω, t)	V (x) = x⁶ + tx⁴ + μx³ + νx² + ωx	6x⁵ + 4tx³ + 3μx² + 2νx + ω = 0	μ = -15x², v = 40x³, ω = -45x⁴, t = 24x⁵	x_v = μ^1/2, x_v = v^1/3, x_ω = ω^1/4, x_t = t^1/5

4.6 Determination of total mutation membership function value

The total mutation membership function value was calculated based on the normalized formula of each mutation model and (non) complementarity principle. When there exists the obvious correlation action between the control variables, the principle of complementarity was chosen, and then the mean value of the corresponding mutation level should be taken as the membership function value of the system. On the contrary, the minimum value of the corresponding mutation level should be taken as the membership function value of the system, that is, the principle of non complementarity [32 –34].

5 Engineering application

5.2 Engineering background

The 101 coalface is the first mining face of Jinji coal mine which belongs to Shaanxi future energy limited company. The JT6 borehole is located at the intersection between the center of coalface inclined direction and 310 m distance from the open-off cut in the first mining face, whose drill hole columnar section was shown in Fig. 6. In Fig. 6, the thickness of aquifer is 32 m. In the 101 coalface, mining thickness, buried depth of coal seam, inclined length of coalface and advancing speed of coal mining are 5 m, 265.7 m, 280 m and 12 m/d, respectively. In the JT6 borehole, the unit water inflow is 3.0 L/s• and the flushing fluid consumption belongs to the “medium” grade in field measurement.

Fig.6

JT6 drill hole columnar section.

$H_{li} = 26 h_{m}$ (11)

Where H_li is the development height of water flowing fractured zone, m; h_m is mining thickness, m. After calculating, H_li= 130 m. Therefore, the effective aquiclude thickness is 94.5 m. In Fig. 6, the lithological association of the effective aquiclude is a combination of loess, laterite and bedrock layer.

5.2 Water inrush risk evaluation

The risk assessment of roof water inrush in the 101 coalface was as follows based on the analysis of the above steps.

(1) Relationship between evaluation grade and total membership function values, and hierarchy structure model for mutation evaluation of roof water inrush were established, which were shown in Table 1 and Fig. 2.

(2) The initial membership function values were determined based on the proposed method and mining conditions in the 101 coalface, as shown in Table 3.

Table 3
The roof water inrush risk evaluation index and calculation results

Indexes A B C

A₁ A₂ A₃ B₁ B₂ C₁ C₂ C₃ C₄

Initial membeship function value 0.59 0.60 0.30 0 0.20 0.90 0.33 0.30 0.75

Initial index normalization value 0.77 0.84 0.74 0 0.58 0.95 0.69 0.74 0.94

Intermediate indexes value 0.74 0.29 0.69

Normalization values of intermediate index 0.86 0.66 0.91

Total mutation membership function value 0.66

Indexes	A	B	C
Initial membeship function value	0.59	0.60	0.30	0	0.20	0.90	0.33	0.30	0.75
Initial index normalization value	0.77	0.84	0.74	0	0.58	0.95	0.69	0.74	0.94
Intermediate indexes value	0.74	0.29	0.69
Normalization values of intermediate index	0.86	0.66	0.91
Total mutation membership function value	0.66

(3) The mutation types were determined.

For instance, the water rich property of aquifer A contains three indexes, which belongs to the swallowtail catastrophe model based on the system diagram of catastrophic model. Similarly, the characteristics of the effective aquiclude B, mining space C and risk evaluation of roof water inrush U belong to cusp catastrophe model, butterfly catastrophe model and swallowtail catastrophe model, respectively.

(4) The normalization calculation was carried out based on different mutation types.

For example, initial index normalization value x_A1= $A_{1}^{1 / 2}$ =0 . 59^1/2= 0.77, x_A2= $A_{2}^{1} / 3$ =0 . 60^1/3 = 0.84, x_A3= $A_{3}^{1 / 4}$ =0 . 30^1/4= 0.74. The three initial indexes of water rich property of aquifer A have no obvious correlation action, so x_A= min(x_A1, x_A2, x_A3) = 0.74. Similarly, x_B= 0.29 and x_C= 0.69, as shown in Table 3. The normalization values of intermediate index A,B and C were further calculated as follows, U_A= $x_{A}^{1 / 2}$ =0.74¹/2= 0.86, U_B= $x_{B}^{1 / 3}$ =0 . 29¹/3= 0.66, U_C= $x_{C}^{1 / 4}$ =0 . 69^1/4= 0.91, which were shown in Table 3.

(5) Total mutation membership function value and evaluation grade of roof water inrush were determined.

Total mutation membership function value U = min (U_A, U_B, U_C) = 0.66 based on the principle of non complementarity. Therefore, the roof water inrush risk evaluation grade in the 101 coalface was indentified as “safe” grade. There was no roof water inrush hazard in the actual mining process of the 101 working face, which verified the feasibility of the proposed method.

6 Conclusions

Based on the fuzziness and mutation characteristics of roof water inrush and mining geological condition, the fuzzy analysis and catastrophe theory were adopted to evaluate the risk of roof water inrush in the Jurassic Coalfield of northwest China. The results are as follows.

(1) Nine indexes influencing roof water inrush were selected based on three essential conditions with the water source, the water inrush channel and the mining space, i.e., unit water inflow, flushing fluid consumption, aquifer thickness, effective aquiclude thickness, lithological association of the effective aquiclude, inclined length of coalface, buried depth of coal seam, mining thickness and advancing speed of coal mining, and then the hierarchy structure model for mutation evaluation of roof water inrush were established.

(2) The initial fuzzy membership function was structured based on the expert scoring method and trapezoidal fuzzy distribution.

(3) Based on quantized recursion operation with the normalization formula and the (non)-complementarity principle, total mutation membership function value was calculated, and the water inrush risk grade was determined. Eventually, the proposed method has successfully predicted the water inrush risk in the first mining face of Jinjitan coal mine.

This research provides a reference for predicting roof water inrush risk under large-scale mining conditions in Western China in order to realize the sustainable development of the water resources and mine safe exploitation.

Footnotes

Acknowledgments

This work was supported by the State Key Program of the National Natural Science Foundation of China [grant number 41430643], and the National Basic Research Program of China (973 Program) [grant number 2015CB251601].

References

W.P.

, Duan

Z.H.

, Hua

J.M.

, Ye

G.J.

, Zhao

X.J.

, Yang

H.K.

and Fu

L.Q.

, Evaluation of present geological environment and prediction of its variation caused by mining in yushenfu mine area of north shanxi, Journal of Engineering Geology 8(3) (2000), 324–333.

Wang

S.M.

, Huang

Q.X.

, Fan

L.M.

, Yang

Z.Y.

and Shen

, Study on overburden aquclude and water protection mining regionazation in the ecological fragile mining area, Journal of China Coal Society 35(1) (2010), 7–13.

Zhang

J.C

, and Peng

S.P.

, Water inrush and environmental impact of shallow seam mining, Environmental Geology 48(8) (2005), 1068–1076.

, Xu

, and Zhang

, Further research on “three maps-two predictions”method for prediction on coal seam roof water bursting risk, Journal of China Coal Society 41(6) (2016), 1341–1347.

, Huang

X.L.

, Dong

D.L.

, Yin

Z.R.

and Li

J.M.

, Three maps-two prediction’s method to evaluate water bursting condition on roof coal, Journal of China Coal Society 25(1) (2000), 60–65.

, Liu

Y.Z.

, Zhou

W.F.

, Li

B.Y.

and Zhao

, Evaluation of water inrush vulnerability from aquifers overlying coal seams in the menkeqing coal mine, China. Mine Water & the Environment 34(3) (2015), 258–269.

, Liu

S.Q.

, Zhai

Y.L.

, Lian

H.Q.

and Zhang

, Evaluation of a coal seam roof water inrush: Case study in the Wangjialing coal mine, China, Mine Water & the Environment (2017), 1–11. doi:10.1007/s10230-017-0459-z .

Liu

D.M.

, Lian

H.Q.

, Han

and Li

, Study on water enrichment prediction of coal roof sandstone aquifer based on PNN, Coal Science 33(9) (2014), 336–338.

Liu

S.W.

, Li

W.P.

and Liu

Q.Q.

, Application of analytic hierarchy process fuzzy clustering analysis method for mine water disaster, Coal Science 2 (2017), 208–210.

10.

Yang

G.Y.

, Chen

, Gao

S.L.

and Ma

, The development height of water flowing fractured zone based on analytic hierarchy process and fuzzy clustering analysis, Journal of Mining & Safety Engineering 32(2) (2015), 206–212.

11.

Y.L.

, Method and application of the prevention and control of water disasters in Yaoqiao Coal Mine based on multi-source information fusion, Ph.D. Dissertation, China University of Mining and Technology, 2010.

12.

, Guo

, Li

H.K.

, Ding

J.P.

, Qiu

H.T.

and Wang

X.Q.

, General evaluation of water inrush risk of coal seam roof in karst Area based on fuzzy comprehensive evaluation, China Coal 38(8) (2012), 51–54.

13.

Yang

W.F.

, Xia

X.H.

, Pan

B.L.

, Gu

C.S.

and Yue

J.G.

, The fuzzy comprehensive evaluation of water and sand inrush risk during underground mining, Journal of Intelligent & Fuzzy Systems 30 (2016), 2289–2295.

14.

Zhang

W.Q.

, Li

and Yu

H.L.

, The correlation analysis of mine roof water inrush grade and influence factors based on Fuzzy Matter-Element, Journal of Intelligent & Fuzzy Systems 31 (2016), 3163–3170.

15.

Fan

L.M.

, Ma

X.D.

, Jiang

and Cheng

, Risk evaluation on water and sand inrush in ecologically fragile coal mine, Journal of China Coal Society 41(3) (2016), 531–536.

16.

Y.P.

, Yang

Y.G.

and Xie

P.S.

, Application of cusp catastrophe theory in the study of roof water inrush, Coal Science and Technology 35(3) (2007), 41–44.

17.

W.P.

, Ye

G.J.

and Zhang

, Study on the engineering geological conditions of protected water resources during coal mining action in Yushenfu mine area in the north Shaanxi Province, Journal of China Coal Society 25(5) (2000), 449–454.

18.

Ning

J.G.

, Liu

X.S.

, Tan

Y.L.

, Wang

and Zhang

, Water-preserved mining evaluation in shallow seam with sandy mudstone roof, Journal of Mining & Safety Engineering 32(5) (2015), 814–820.

19.

P.P.

, Research on geologic environment effects induced by coal mining in ecological weakness area and assessment techniques–A case study taking Yushenfu Mining District in Northern Shanxi Province, Ph.D. Dissertation, China University of Mining and Technology, 2011.

20.

Zhang

M.S.

, Dang

X.Y.

, Water resources and its environmental problems in arid and semi-arid regions– an analysis of the energy and chemical base in Northern Shaanxi Province, Yulin, Science Press, Beijing, China, 2014, pp. 35–39.

21.

Zhang

, Tang

S.J.

, Zhang

D.S.

, Fan

G.W.

and Wang

, Determination of the height of the water- conducting fractured zone in difficult geological structures: A case study in zhao gu No. 1 coal seam, Sustainability 9 (2017), 1077. http://dx.doi.org/10.3390/su9071077.

22.

State. Administration of work Safety and State Administration of Coal Mine Safety. Regulations for coal mine water prevention and control, China Coal Industry Publishing House, Beijing, pp, (2009), 65–68.

23.

Meng

Z.P.

, Shi

X.C.

and Li

G.Q.

, Deformation, failure and permeability of coal-bearing strata during longwall mining, Engineering Geology 208 (2016), 69–80.

24.

Xue

B.Y.

, Fu

Y.P.

and Guo

Y.Y.

, Study on fully mechanized coal face by Flac3D simulation of mining velocity influence on the roof strata, Journal of Taiyuan University of Technology 5 (2015), 611–615.

25.

M.S.

, The study of stress pressure and mining of the shallow coal seam in Shendong district, Master Thesis, Liaoning Technical University, Fuxin, 2002.

26.

Gai

F.L.

, Quantitative analysis method for some issues in mine geological environment impact analysis, Coal Geology of China 25(3) (2013), 47–51.

27.

Sun

X.F.

, Shao

H.Y.

, Xiao

L.X.

, Chen

G.M.

and Yang

X.H.

, Geological environment evaluation for Hongge Vanadium Titanomagnetite Mining Area based on catastrophe theory, Nonferrous Metals (Min. Section) 69 (2017), 40–43.

28.

Xie

J.J.

, Fuzzy mathematics method and its application, Huazhong University of Science and Technology Press, Wuhan, 2013, pp. 18–25.

29.

Poston

, Stewart

and Plaut

R.H.

, Catastrophe Theory and Its Applications, Pitman, 1978, pp. 25–36.

30.

Ling

F.H.

, Catastrophe Theory and Its Applications, Shanghai Jiao Tong University Press, Shanghai, 1987, pp. 65–92.

31.

Pan

, Wang

Z.Q.

and Zhang

, Application of catastrophe theory to dynamic instability of rock mass system, Science Press, Beijing, 2008, pp. 89–101.

32.

Y.H.

, He

M.C.

and Sun

X.M.

, Equivalent characteristics of membership function type in rock mass fuzzy classification, Journal of Beijing University of Science and Technology 29(7) (2007), 670–675.

33.

Liu

S.L.

, Li

W.P.

and Wang

Q.Q.

, Height of the water-flowing fractured zone of the jurassic coal seam in northwestern China, Mine Water and the Environment 37 (2018), 312–321.

34.

Liu

S.L.

, Li

W.P.

, Wang

Q.Q.

and Pei

Y.B.

, Investigation on mining-induced fractured zone height developed in different layers above Jurassic coal seam in western China, Arabian Journal of Geosciences 11 (2018), 30.

Indexes	A			B		C
	A₁	A₂	A₃	B₁	B₂	C₁	C₂	C₃	C₄
Initial membeship function value	0.59	0.60	0.30	0	0.20	0.90	0.33	0.30	0.75
Initial index normalization value	0.77	0.84	0.74	0	0.58	0.95	0.69	0.74	0.94
Intermediate indexes value	0.74			0.29		0.69
Normalization values of intermediate index	0.86			0.66		0.91
Total mutation membership function value	0.66

Fuzzy comprehensive risk evaluation of roof water inrush based on catastrophe theory in the Jurassic coalfield of northwest China

Abstract

Keywords

1 Introduction

2 Study area

3.1 Water rich property of aquifer

3.2 Characteristics of the effective aquiclude

3.3 Mining space

4 Methodology

Table 1 Relationship between evaluation grade and total membership function values Total mutation membership function values [1.0,0.9] (0.9,0.7] (0.7,0.5] [0.5,0] Evaluation grade Dangerous Less dangerous Safe Relatively safe

4.3.1 Discrete index

5 Engineering application

5.2 Engineering background

Footnotes

Acknowledgments

References

Table 1
Relationship between evaluation grade and total membership function values

Total mutation membership function values [1.0,0.9] (0.9,0.7] (0.7,0.5] [0.5,0]

Evaluation grade Dangerous Less dangerous Safe Relatively safe