An improved model to predict the water-inrush risk under an unconsolidated confined aquifer based on analytic hierarchy process and information value method

Abstract

To prevent water inrush hazards of mining under the Quaternary unconsolidated confined aquifer in North China coalfield, it is necessary to build a water inrush prediction model to guarantee coal safety production. The current method of evaluating mining hazards under unconsolidated confined aquifers is easy to fall into the problems of simple superposition of evaluation factors, large subjectivity of the factor selection, and low accuracy of prediction results. In this paper, an analytic hierarchy process (AHP) is improved according to contribution of information value method (IVM) to analyze the impact of water inrush factors. The factor weight values are considered in calculating the total information value of IVM to build a coupled AHP-IVM model. The information value of each factor is calculated through IVM, and area under curve (AUC) value is used to rank the factors, to exclude the subjective judgment of the importance of each factor. The geological and hydrogeological data of Qinan coal mine in Huaibei coalfield are analyzed and organized. The results suggest that the coupled AHP-IVM model has an AUC value of 0.8309, indicating its great potential and practical significance for future mining operations.

Keywords:

• Word
• unconsolidated confined aquifer
• water inrush risk
• analytic hierarchy process
• information value method
• coupled AHP-IVM model

1. Introduction

A layer of unconsolidated confined aquifer composed of sandy soil and gravel as the frame exists at the bottom of the Quaternary unconsolidated soils in the concealed coalfields of North China. The anisotropic aquifer is directly covered on the top of the coal seam. The presence of such aquifers increases the risk of hydrogeological hazards (e.g. water inrush hazards) which is considered as one of the most important issues threatening the safe coal production in north China (Khan et al. 2018, 2020). It is the most important problem threatening the safety of coal mining operations (Wu Q and Zhou 2008; Wang XZ 2012; Sun WJ et al. 2016; Wu Q et al. 2017; Wang F et al. 2019; Xue et al. 2022; Xue et al. 2023). It is crucial to establish a scientific and practical model for predicting water inrush in mining under the unconsolidated confined aquifer. Reducing water inrush can effectively improve the efficiency of coal mining.

To effectively predict the water inrush hazard under unconsolidated confined aquifers, many experts have studied mining under unconsolidated confined aquifers controlled by various factors in recent years. For instance, Wu Q et al. (2016) proposed three maps-two predictions method. Xu JL et al. (2009) and Xu W et al. (2013) concluded that water inrush hazard is related to overlying strata failure and proposed a method of predicting the water inrush hazard zone. Chen LW et al. (2016) applied the multi-information superposition method to determine the water inrush areas. Lu et al. (2019) proposed multi-type-four-double (MTFD) evaluation technology to predict water inrush from the roof. Ma, Duan, Zhang (2022), Ma et al. (2022) and (Li et al. 2015) proposed a one-dimensional radial three-phase flow model to predict water–silt inrush hazard of fault rock by numerical simulation. By GIS technology and entropy weight theory, a multi-source information evaluation method for the risk of water inrush from coal floor was proposed and verified by Li, Zhang, Luo, et al. (2022) and Li, Zhang, Long, et al. (2022). Zhang and Wang proposed a novel off-the-shelf two-step assessment approach including Fisher discriminant analysis and classification algorithm on the same transformed low-dimensional data to predict the water abundance level (Zhang and Wang 2021). No single method can address all issues associated with the water inrush phenomenon. Therefore, the prediction accuracy of water inrush risk can be effectively improved by combining different methods, and it is a crucial research direction to use AHP method combined with other methods for water inrush assessment.

AHP method is an effective tool to solve complex decision-making problems for multi-objectives, which is commonly used to calculate the weight of different factors as well as to combine it with other methods to assess water inrush risk. Wang et al. and Yang et al. (2012, 2017) constructed a secondary fuzzy comprehensive evaluation system and considered the impact of various factors on the water inrush from qualitatively to quantitatively. Li LP et al. (2015) proposed an evaluation system of attribute synthetic, which comprehensively considered the weight and the membership of factors. Li B and Chen (2016) put forward a coupled model based on the grey relational analysis (GRA) method and AHP method. Ruan et al. (2019) thought the judgment matrix of AHP method determined by personal experience has great variations or even errors. Wang Q et al. (2022) evaluated the results obtained from the certainty factor (CF) and logistic regression (LR) models for estimating water-inrush risk. Li JL et al. (2021) established the fractal-AHP-VI model of floor water inrush based on the fractal theory. The combined weight (CW) method and the fuzzy matter-element analysis (FMEA) method were used to analyze and evaluate the control effect of subsiding land by Wang ZY et al. (2021).

However, there are still some limitations to these coupled models, which do not emphasize the influence of geological background on each evaluation factor. Therefore, it is necessary to put forward an objective judgment method to compare the impact of each factor under specific geological background, and then improve AHP method and reduce the error caused by individual subjective judgment. In this study, IVM is selected as the effective method to improve AHP method.

Its advantage lies in the evaluation of AHP factors through IVM to obtain the weight of each factor, so that the importance of factors is not affected by subjectivity. IVM can transform the measured factor affecting the research object into the information value and evaluate the correlation between factor and research object, which can effectively reflect the influence on water inrush risk under a specific geological background (Wu Q et al. 2011; Hu et al. 2019).

Existing AHP methods still need to rely on personal experience to construct the judgment matrix. If ranking is based on experience, it is easy to be preconceived or poorly considered, resulting in inaccurate prediction results. Under different geological environments, the impact of each factor is different. The importance of the factors involved in the risk assessment was ranked using the IVM method. Subjective errors of the judgment matrix can be avoided by using the IVM method. This paper proposes a coupled model to evaluate the water inrush risk by the improved AHP method, and applies it to Qinan coal mine to verify the effectiveness of this model.

2. Hydrogeological and geological setting

The Huaibei coalfield is located in the northern part of Anhui Province, China, bordering Jiangsu and Henan Provinces in the northeast and west, respectively (Figure 1a). The multi-stage tectonic movements of Indosinian, Early Yanshanian and Late Yanshanian are superimposed, resulting in a series of complex network patterns of EW, NNE and NE trending structures interwoven in the study area, such as Banqiao-Guzhen fault, Subei fault, Xiayi fault, Fengwo fault and Guzhen-Changfeng fault (Figure 1b) (Zhang et al. 2020).

Figure 1. Regional geological structure of the Qinan coal mine in the Huaibei coalfield (a) Location of the Huaibei coalfield; (b) Regional geological structure of the Huaibei coalfield; (c) Regional geological structure of the Qinan coal mine.

The Qinan coal mine is located in the southeast of Huaibei coalfield, which is a typical North China-type coal mine, and its mineable coal seams are directly covered by Cenozoic loose strata (Figure 1b). Constrained by the Sunan syncline, the Qinan coal mine is a monoclinic structure that strikes north–south and slopes eastward with a dip angle of about 15°. Furthermore, normal faults are the main structural features in the study area, accompanied by small-scale folds (Figure 1c). The coal mine covers an area of 35 km² and contains three main minable coal seams named No. 3₂, 7₂ and 10, respectively.

According to the lithology, thickness, water-bearing medium and burial conditions of the formation, the unconsolidated Cenozoic formation can be divided into three aquifuges and four aquifers from top to bottom, which are the first aquifer, the first aquifuge, the second aquifer, the second aquifuge, the third aquifer, the third aquifuge and the fourth aquifer, respectively (Figure 2). The physical parameters and hydrological parameters of the rock stratum are shown in Table 1. The parameters of these aquifers can be found in Table 2. The fourth aquifer is directly covered on the coal strata. The location and depth of water inrush points are shown in Table 3. Since the third aquiclude develops steadily and has excellent water-proof performance in the region, the fourth aquifer and the lower aquifers have no direct hydraulic connection with meteoric water and surface water under normal circumstances. The fourth aquifer usually has good water storage capacity, showing the characteristics of high pressure and strong seepage. Meanwhile, this aquifer directly overlays the Permian strata, which is the main source of water-inrush for shallow coal resources mining. As the research object of this paper, the coal seams under the unconsolidated confined aquifers in Qinan coal mine are No. 3₂, 7₂. According to the hydrogeological account of Qinan coal mine, there have been 21 water-inrush accidents during mining under the unconsolidated and confined aquifer. Therefore, a reasonable and effective water inrush risk assessment is of great significance to ensure safe mining operations.

Figure 2. Stratigraphic column and aquifer division.

Table 1. The physical parameters and hydrological parameters of the rock stratum.

Lithology	Density (g/cm^3)	Water content (%)	Water absorption (%)	Strength of compressive (MPa)	Strength of extension (MPa)	Internal friction angle (°)	Cohesion	Elasticity modulus (MPa)	Poisson ratio
Sandy mudstone	2.70	1.10	1.54	38.0	2.08	28.12	5.83	0.14	0.20
Mudstone	2.74	1.38	1.78	34.4	1.38	34.06	2.60	0.11	0.23
Siltstone	2.71	1.83	2.20	10.6	2.02	32.41	4.04	0.24	0.19
Sandstone	2.84	0.26	0.45	83.4	4.85	33.88	4.93	0.27	0.18

Table 2. The parameters of the aquifers.

Aquifers	Thickness (m)	Water inflow q (L/(s.m))	Permeability coefficient K (m/d)	Water richness
The first aquifer	15–30	0.10 ∼ 5.35	1.03 ∼ 8.67	Medium ∼ Extremely abundant
The second aquifer	10–60	0.10 ∼ 3.00	0.92 ∼ 10.95	Medium ∼ Abundant
The third aquifer	20–80	0.14 ∼ 1.21	0.513 ∼ 5.47	Medium ∼ Abundant
The fourth aquifer	0–57	0 ∼ 0.19	0 ∼ 0.638	Weak ∼ Medium

Table 3. The location and depth of water inrush points.

Water inrush points	x	y	z
1	39,501,534	3,701,470	−525.6
2	39,502,274	3,700,303	−166
3	39,501,164	3,699,525	−543.6
4	39,500,989	3,699,468	−542.3
5	39,502,356	3,700,326	−166
6	39,502,093	3,700,304	−166
7	39,499,385	3,699,826	−446.6
8	39,502,356	3,700,326	−126
9	39,501,280	3,699,417	−450.3
10	39,499,876	3,698,780	−482
11	39,499,339	3,700,422	−412.4
12	39,499,275	3,697,102	−359.2
13	39,500,290	3,702,268	−370.5
14	39,500,826	3,703,420	−476.5
15	39,501,780	3,702,384	−614.7
16	39,499,321	3,699,434	−423
17	39,501,301	3,700,048	−523.6
18	39,499,167	3,701,504	−103
19	39,504,223	3,699,272	−491.9
20	39,501,338	3,704,992	−547.1
21	39,504,115	3699253	−533.7

3. AHP method and its improvement

3.1. AHP method

AHP is an analytical method that combines qualitative and quantitative analysis to conduct a risk assessment and has been widely used in the coal mine field (Ruan et al. 2019). The weight value of each factor is calculated by AHP method, and the calculation process can be divided into four steps:

1. Establishing a comprehensive evaluation system of factors.

2. Constructing the judgment matrix D using the 1–9 scales, as shown in Equation 1(1) $$D=\left(\begin{array}{cccc}{x}_{11}\hfill & x_{12}\hfill & \dots \hfill & x_{\text{1n}}\hfill \\ x_{21}\hfill & x_{22}\hfill & \dots \hfill & x_{\text{2n}}\hfill \\ ⋮\hfill & ⋮\hfill & ⋮\hfill & ⋮\hfill \\ x_{\mathrm{m}1}\hfill & x_{\mathrm{m}2}\hfill & \cdots \hfill & x_{\text{mn}}\hfill \end{array}\right)$$(1) . (1) $$D=\left(\begin{array}{cccc}{x}_{11}\hfill & x_{12}\hfill & \dots \hfill & x_{\text{1n}}\hfill \\ x_{21}\hfill & x_{22}\hfill & \dots \hfill & x_{\text{2n}}\hfill \\ ⋮\hfill & ⋮\hfill & ⋮\hfill & ⋮\hfill \\ x_{\mathrm{m}1}\hfill & x_{\mathrm{m}2}\hfill & \cdots \hfill & x_{\text{mn}}\hfill \end{array}\right)$$(1) Where x_mn is the comparing result of the importance of the m th factor and the n th factor (Saaty 1980).

3. Consistency test of the judgment matrix, as shown in Equations 2(2) $$C_{\mathrm{R}}=C_{\mathrm{I}}/R_{\mathrm{I}}$$(2) and 3(3) $$C_{\mathrm{I}}=\left({\lambda }_{\max }–n\right)/\left(n-1\right)$$(3) . (2) $$C_{\mathrm{R}}=C_{\mathrm{I}}/R_{\mathrm{I}}$$(2) (3) $$C_{\mathrm{I}}=\left({\lambda }_{\max }–n\right)/\left(n-1\right)$$(3) Where C_R is the random consistency ratio, C_I is the consistency check index, R_I is the average random consistency index (Table 4), λ_max is the largest eigenvalue of the judgment matrix, and n is the quantity of the assessment indices (Saaty 1980).

   The consistency ratio (C_R) is obtained by comparing the C_I with the appropriate one of the following set of numbers, each of which is an average random consistency index (R_I) derived from a sample randomly generated reciprocal matrix using the scale l/9, l/8, …, 1, . .8, 9 to see if it is about 0.10 or less. Saaty mentioned that the C_R of less than 0.1 will be acceptable (Saaty 1980).

   When C_R < 0.1, the judgment matrix satisfies the consistency test; otherwise, the judgment matrix needs to be adjusted.

4. Under the condition that the judgment matrix satisfies the consistency test, the weight vector of the evaluation factors can be calculated.

Table 4. Values of random consistency index.

n	1	2	3	4	5	6	7	8
RI	0	0	0.52	0.89	1.12	1.26	1.36	1.41

3.2. The shortcomings of AHP method and its improvement

AHP method quantifies the subjective judgment relationship between the indexes by means of the 1–9 scale method proposed by Saaty, constructs the quantity judgment matrix and makes consistency test (Saaty 1980). However, decision-makers assessed based on their professional knowledge, experience, and subjective judgment. Therefore, there have been many improved methods proposed to reduce the search costs caused by the original judgment matrix. Ruan et al. (2019) used Dempster-Shafer (D–S) synthetic rule to improve the 1–9 scales method, which took full advantage of each expert’s opinion and reduced the subjective error caused by an individual decision-maker. Shi et al. (2020) calculated the integrated weight by combining AHP with the entropy weight method. The reliability of the total weight is better than that calculated by the original judgment matrix. However, it is difficult to quantify the influence of geological conditions and establish risk-grade standards of water inrush. In general, the impact of each evaluation factor on water inrush is different due to the complexity of geological conditions.

The receiver operating characteristic curve (ROC) is a graphical technique used to assess the accuracy of model. AUC is defined as the area enclosed by the coordinate axis under ROC. The closer AUC is to 1.0, the higher the authenticity of the detection method is. When it is equal to 0.5, it has the lowest authenticity and no application value. The larger AUC is, the greater contribution of this factor to water inrush is (Fan et al. 2014).The subjective judgment of AHP method mainly depend on the division of the importance of different factors. In this study, the information value of each factor is calculated through IVM, and the value of AUC is used to rank the factors, to exclude the subjective judgment of the importance of each factor. In order to determine the importance of various evaluation factors on water inrush, the success rate curve method is selected to combine with IVM (Fan et al. 2014). The horizontal axis represents the area percentage of the information value from high to low, while the vertical axis represents the proportion of the water inrush hazards occurring within the corresponding information value. The larger AUC value is, the greater the importance of the factor has on water inrush. According to AUC value, the importance of factors on water inrush can be divided into four categories, named relatively important (I), medium important (II), important (III), absolutely important (IV), respectively, as shown in Equation 3(3) $$C_{\mathrm{I}}=\left({\lambda }_{\max }–n\right)/\left(n-1\right)$$(3) as follows: (4) $$\{\begin{array}{c}{X}_{\mathrm{i}}\subset I{x}_{\mathrm{i}}<d_1\\ X_{\mathrm{i}}\subset \mathrm{II}{d}_1<x_{\mathrm{i}}<d_2\\ X_{\mathrm{i}}\subset \mathrm{III}{d}_2<x_{\mathrm{i}}<d_3\\ X_{\mathrm{i}}\subset \mathrm{IV}{x}_{\mathrm{i}}>d_3\end{array}$$(4)

Where X_i is the evaluation factor, x_i is AUC value of X_i, d₁, d₂, d₃ is the classification threshold and calculated by Equation 5(5) $$\{\begin{array}{c}{d}_{\mathrm{m}}=x_{\min }+\frac{x_{\max }-x_{\min }}{n}(m=1;n=4)\\ d_{\text{m + 1}}=d_{\mathrm{m}}+\frac{x_{\max }-x_{\min }}{n}(m=1,2;n=4)\end{array}$$(5) as follows: (5) $$\{\begin{array}{c}{d}_{\mathrm{m}}=x_{\min }+\frac{x_{\max }-x_{\min }}{n}(m=1;n=4)\\ d_{\text{m + 1}}=d_{\mathrm{m}}+\frac{x_{\max }-x_{\min }}{n}(m=1,2;n=4)\end{array}$$(5)

Where x_max and x_min are the maximum and the minimum AUC value of the evaluation factor, respectively.

Based on this classification, the importance of the evaluation factors can be compared objectively, and the degree of importance is shown in Table 5.

Table 5. Comparison Table of importance degree.

Importance degree	I	II	III	IV
I	1	1/2	1/3	1/4
II	2	1	1/2	1/3
III	3	2	1	½
IV	4	3	2	1

3.3. IVM method

IVM developed from information theory is an effective quantitative evaluation method, which can transform the measured factor value affecting research object into the information value (Ruan and Huang 2001; Wu C and Qiao 2009; Xu W et al. 2013; Peng et al. 2021). The key point of IVM is to judge the possibility of water inrush hazards by calculating the total information value of the study area. In general, the greater the information value is, the greater the possibility of water inrush hazards has. The total information value calculation is mainly divided into two steps:

1. Calculating the information value of individual evaluation factors, as in Equation 6(6) $$I_{\mathrm{i}}=\hspace{0.17em}\ln \hspace{0.17em}\frac{N_{\mathrm{i}}/N}{S_{\mathrm{i}}/S}$$(6) .

(6) $$I_{\mathrm{i}}=\hspace{0.17em}\ln \hspace{0.17em}\frac{N_{\mathrm{i}}/N}{S_{\mathrm{i}}/S}$$(6)

Where I_i is the information value of evaluation factor x_i, dimensionless; N_i is the total amount of distribution units of water inrush contain the factor x_i, dimensionless; N is the total of distribution units of water inrush in the study area, dimensionless; S_i is the total of the evaluation factors units containing the factor x_i in the study area, dimensionless; S is the total of evaluation unit of study area, dimensionless.

• 2. Calculating the total information value of evaluation factors, as in Equation 7(7) $$I=\sum _{\text{i = 1}}^{\mathrm{n}}{I}_i=\sum _{\text{i=}1}^{\mathrm{n}}\hspace{0.17em}\ln \hspace{0.17em}\frac{N_{\mathrm{i}}/N}{S_{\mathrm{i}}/S}$$(7) .

(7) $$I=\sum _{\text{i = 1}}^{\mathrm{n}}{I}_i=\sum _{\text{i=}1}^{\mathrm{n}}\hspace{0.17em}\ln \hspace{0.17em}\frac{N_{\mathrm{i}}/N}{S_{\mathrm{i}}/S}$$(7)

Where I is the total information value, dimensionless.

3.4. The shortcomings of IVM and its improvement

By calculating the total information value of evaluation factors, IVM can judge the possibility of water inrush hazards in the different parts of the study area. However, the contribution rate of each factor for the water inrush hazard is different. If the factors are simply analyzed without considering their weight, the accuracy of evaluation model would be reduced. In order to determine the weight of factors, an improved AHP is chosen to describe the importance. In this model, the importance of AHP method is introduced to describe the importance of different factors in IVM method. But its importance is evaluated by calculating AUC value, and the process of calculating AUC value is objective. Thus, IVM is improved as Equation 8(8) $$I_{\mathrm{W}}=\sum _{\text{i = 1}}^{\mathrm{n}}{w}_{\mathrm{i}}{I}_{\mathrm{i}}$$(8) . (8) $$I_{\mathrm{W}}=\sum _{\text{i = 1}}^{\mathrm{n}}{w}_{\mathrm{i}}{I}_{\mathrm{i}}$$(8)

Where I_W is the total information value considering the weight of the factor, dimensionless; w_i is the weight value of evaluation factor x_i, dimensionless; I_i is the information value of evaluation factor x_i, dimensionless.

3.5. Establishment of the coupled AHP-IVM model

Risk assessment methods for water inrush consist of three parts: selecting the main evaluation factors, calculating the weight of evaluation factor, constructing the assessment model (Wu Q et al. 2017; Peng et al. 2021). Based on this framework, the establishment of the coupled AHP-IVM model can be divided into three steps (Figure 3):

Figure 3. The flowchart of the coupled AHP-IVM model.

1. Construct the comprehensive evaluation factor system and calculate the information value of factors. Thematic maps of factors are generated based on the geographic information system (GIS). Then, the information value can be calculated by Equation 6(6) $$I_{\mathrm{i}}=\hspace{0.17em}\ln \hspace{0.17em}\frac{N_{\mathrm{i}}/N}{S_{\mathrm{i}}/S}$$(6) (Yang et al. 2018).

2. Calculate the weight of each factor by the improved AHP. According to AUC value of each factors, the importance of different factor to water inrush can be analyzed, and then the improved judgment matrix was established according to Table 5. Based on the improved AHP, the factor weight is determined.

3. Construct the coupled AHP-IVM model. Based on these weight values calculated in Step 2 and the information value of factors calculated in Step 1, the coupled AHP-IVM model is established by Equation 8(8) $$I_{\mathrm{W}}=\sum _{\text{i = 1}}^{\mathrm{n}}{w}_{\mathrm{i}}{I}_{\mathrm{i}}$$(8) .

4. Application and results

4.1. The information value of controlling factors

Water inrush hazards in China are influenced by various factors (Wu Q and Zhou 2008; Chen PP and Liu 2010; Huang et al. 2012; Pang et al. 2021; Peng et al. 2021). The controlling factors can be divided into four aspects based on related studies of water inrush and the special geological and hydrogeological conditions in the Qinan coal mine:

1. Characteristics of the unconsolidated and confined aquifer. The characteristics of the aquifer are closely related to water inrush, which include the fully saturated of aquifer and coal mine pressure. The specific yield and the aquifer thickness are significant for judging the water abundance (Chen LW et al. 2018). In addition, coal mine pressure can be determined by the thickness of unconsolidated layer and the load transfer coefficient of the aquifer (Wang XZ 2012).

2. Bedrock lithology and its association. The bedrock lithology and its association are the key factors to determine the generation of water diversion channels (Palchik 2003; He et al. 2020). Four factors including the bedrock thickness, the thickest sandstone ratio in bedrock, the friable-plastic rocks ratio and the weathered bedrock thickness are selected to describe the bedrock lithology and its association.

3. Geological structure effects. Geological structures such as faults significantly contribute to the safety of coal mine production (Sun WB et al. 2019; Chen B et al. 2020). The development degree of the rock fracture shows a certain distance effect with the fault, and the closer the fault, the stronger the rock failure is, which provides conditions for water inrush. Thus, the distance from faults has an important influence on water inrush.

4. Mining activities. Under the influence of mining, the water flowing fracture zone is fully developed, which is the channel for groundwater to enter the working face, and its development height is the key to the occurrence of water inrush (Xu JL et al. 2009; He et al. 2020).

Based on the geological borehole and geological map information of the Qinan coal mine, the grading map of evaluation factors are generated by ArcGIS, as shown in Figure 4.

Figure 4. Evaluation factor grading maps in the study area (a) the thickness of the unconsolidated soils; (b) the unconsolidated confined aquifer thickness; (c) the specific yield of the unconsolidated and confined aquifer; (d) the load transfer coefficient of the unconsolidated and confined aquifer; (e) the water pressure of the unconsolidated confined aquifer; (f) the thickness of the bottom clay layer; (g) the thickness of the bedrock; (h) the thickness ratio of friable rocks to plastic rocks; (i) the proportion of the thickest sandstone in the bedrock; (j) the depth of the weathered bedrock; (k) the distance from the faults; (l) the density of the faults; (m) the height of the water flowing fracture zone; (n) the thickness of coal seam; (o) the depth of the coal roof.

According to the grading maps, the information value of controlling factors are calculated by Equation 6(6) $$I_{\mathrm{i}}=\hspace{0.17em}\ln \hspace{0.17em}\frac{N_{\mathrm{i}}/N}{S_{\mathrm{i}}/S}$$(6) , and the results are shown in Table 6.

Table 6. Information value of evaluation factors.

Evaluation factor	Classification	Area ratio	Water inrush point ratio	Information value
The thickness of the unconsolidated soils	<250	0.045455	0.023691	0.651609
	250–290	0.090909	0.150884	−0.50665
	290–330	0.409091	0.271687	0.409285
	330–370	0.409091	0.328883	0.218236
	>370	0.045455	0.224855	−1.59874
The unconsolidated confined aquifer thickness	<5	0.434783	0.3291	0.278483
	5–10	0.391304	0.351807	0.106403
	10–15	0.086957	0.201885	−0.84229
	15–20	0.043478	0.079387	−0.60207
	>20	0.043478	0.037821	0.139392
The specific yield of the unconsolidated and confined aquifer	<0.15	0.739130	0.778420	−0.05179
	0.15–0.3	0.086957	0.084414	0.029681
	0.3–0.6	0.086957	0.111769	−0.25102
	0.6–1.2	0.043478	0.023199	0.628159
	>1.2	0.043478	0.002199	2.984483
The load transfer coefficient of the unconsolidated and confined aquifer	<0.84	0.043478	0.16048	−1.30591
	0.84–0.85	0.347826	0.288989	0.185313
	085–0.86	0.391304	0.254294	0.430995
	0.86–0.87	0.173913	0.195106	−0.11499
	>0.87	0.043478	0.101131	−0.84416
The water pressure of the unconsolidated confined aquifer	<2	0.045455	0.038714	0.160503
	2–2.3	0.136364	0.203007	−0.39791
	2.3–2.6	0.363636	0.245878	0.39132
	2.6–2.9	0.363636	0.207427	0.561376
	>2.9	0.090909	0.304974	−1.21037
The thickness of bottom clay layer	<15	0.347826	0.530184	−0.42152
	15–30	0.478261	0.354234	0.300197
	30–45	0.086957	0.109009	−0.22602
	45–60	0.043478	0.005336	2.097792
	>60	0.043478	0.001237	3.559847
The thickness of the bedrock	<144	0.181818	0.578688	−1.15776
	144–288	0.590909	0.226103	0.960673
	288–432	0.090909	0.120128	−0.2787
	432–576	0.090909	0.065509	0.327678
	>576	0.045455	0.009573	1.557801
The thickness ratio of friable rocks to plastic rocks	<0.1	0.608696	0.649281	−0.06455
	0.1–0.2	0.217391	0.206912	0.049408
	0.2–0.3	0.086957	0.120987	−0.33027
	0.3–0.4	0.043478	0.022420	0.662299
	>0.4	0.043478	0.000401	4.68663
The proportion of the thickest sandstone in the bedrock	<0.5	0.791667	0.629277	0.229569
	0.5–1	0.083333	0.266145	−1.16119
	1–1.5	0.041667	0.062085	−0.3988
	1.5–2	0.041667	0.036939	0.12042
	>2	0.041667	0.005554	2.01527
The depth of the weathered bedrock	<230	0.045455	0.011874	1.342343
	230–280	0.045455	0.047428	−0.0425
	280–330	0.181818	0.302008	−0.50745
	330–380	0.590909	0.332593	0.574743
	>380	0.136364	0.306096	−0.80857
The distance from the faults	<100	0.5	0.332913	0.406725
	100–200	0.045455	0.163285	−1.27878
	200–300	0.045455	0.113544	−0.91548
	300–400	0.045455	0.090036	−0.68349
	>400	0.363636	0.300222	0.191632
The density of the faults	0	0.454545	0.569196	−0.22493
	1–2	0.090909	0.146029	−0.47394
	2–3	0.045455	0.079433	−0.55819
	3–4	0.045455	0.074978	−0.50049
	>4	0.363636	0.130365	1.025819
The height of the water flowing fracture zone	<30	0.045455	0.16135	−1.26686
	30–35	0.318182	0.164934	0.657079
	35–40	0.090909	0.221064	−0.88859
	40–45	0.045455	0.216931	−1.56287
	>45	0.5	0.235721	0.751959
The thickness of coal seam	<1.5	0.136364	0.231599	−0.52968
	1.5–3	0.272727	0.317261	−0.15125
	3–4.5	0.318182	0.312428	0.018248
	4.5–6	0.227273	0.138197	0.497472
	>6	0.045455	0.000515	4.479767
The depth of the coal roof	<310	0.043478	0.046329	−0.06351
	310–460	0.086957	0.440285	−1.62201
	460–610	0.695652	0.329055	0.748626
	610–760	0.130435	0.152441	−0.15591
	>760	0.043478	0.03189	0.309975

4.2. Weight calculation by the improved AHP method

Based on the improved AHP, the weight of each factor can be calculated. The importance of each factor to water inrush hazard is obtained by the success rate curve method. From the results presented in Figure 5, AUC value of the thickness of the bedrock is 0.7409, meaning that the evaluation accuracy of the evaluation factor is 74.09%. AUC value of different evaluation factors according to the order from high to low is the height of the thickness of the bedrock (C₁), the depth of the coal roof (C₂), the height of the water flowing fracture zone (C₃), the depth of the weathered bedrock (C₄), the water pressure of the unconsolidated confined aquifer (C₅), the thickness of the loose soils (C₆), the density of the faults (C₇), the distance from the faults (C₈), the load transfer coefficient of the unconsolidated and confined aquifer (C₉), the thickness of bottom clay layer (C₁₀), the proportion of the thickest sandstone in the bedrock (C₁₁), the thickness of coal seam (C₁₂), the unconsolidated confined aquifer thickness (C₁₃), the thickness ratio of friable rocks to plastic rocks (C₁₄), the specific yield of the unconsolidated and confined aquifer (C₁₅). According to AUC value of factors, a three-level hierarchical structure for water inrush (Figure 6) is established.

Figure 5. Success rate curve of the evaluation factor.

Figure 6. Hierarchical structure for water inrush under the unconsolidated and confined aquifer.

And then, based on AUC value of the evaluation factor, the second-grade factors (C_i) and the first-grade factor (B_i) can be divided into four categories: I (C₁₃, C₁₄, C₁₅), II (C₆, C₇, C₈, C₉, C₁₀, C₁₁, C₁₂), III (C₄, C₅, B₁, B₂, B₃), IV (C₁, C₂, C₃)), respectively. Thus, an improved judgment matrix of B_i (i = 1, 2, 3, 4) under A condition, C_i (i = 5, 6, 9, 10, 13, 15) under B₁ condition, C_i (i = 1, 4, 11, 14) under B₂ condition, C_i (i = 7, 8) under B₃ condition, C_i (i = 2, 3, 12) under B₄ condition are established by comparing the corresponding factors at the same level. In addition, the quantified relationships for the factor comparison at the same level can be found in Table 5.

The greatest characteristic root and corresponding eigenvectors of each judgment matrix are calculated algorithms in Matlab environment as shown in Table 7. The weight of each second-grade factor to the first-grade and the weight of each first-grade factor to the target layer are obtained. The C_R value of each group of matrices can be calculated by Equations 2(2) $$C_{\mathrm{R}}=C_{\mathrm{I}}/R_{\mathrm{I}}$$(2) and 3(3) $$C_{\mathrm{I}}=\left({\lambda }_{\max }–n\right)/\left(n-1\right)$$(3) , and the calculation results are all less than 0.1, which means the improving judgment matrix has satisfactory consistency and can pass the consistency test.

Table 7. Judgment matrix parameters of each grade factors.

Judgment matrix	ABi	B1Ci	B2Ci	B3Ci	B4Ci
λmax	4	6.0138	4.0310	2	3
CI	0	0.0028	0.0103	0	0
CR	0	0.0022	0.0115	non-existent	0

Based on these local weight values, the weight of each second-grade factor to the target layer can be calculated. The calculation results are shown in Table 8.

Table 8. Results of the weight of the factors.

Target layer	First-grade layer	Weights	Second-grade layer	Weights
Water inrush risk assessment	The characteristics of the unconsolidated and confined aquifer	0.1429	The water pressure of the unconsolidated confined aquifer	0.04438
			The thickness of the unconsolidated soils	0.02432
			The load transfer coefficient of the unconsolidated and confined aquifer	0.02432
			The thickness of the bottom clay layer	0.02432
			The unconsolidated confined aquifer thickness	0.01278
			The specific yield of the unconsolidated and confined aquifer	0.01278
	The bedrock lithology and its association	0.1429	The thickness of the bedrock	0.06678
			The depth of the weathered bedrock	0.03961
			The proportion of the thickest sandstone in the bedrock	0.02288
			The thickness ratio of friable rocks to plastic rocks	0.01363
	The geological structure	0.1429	The density of the faults	0.07145
			The distance from the faults	0.07145
	Mining activities	0.5713	The depth of the coal roof	0.24486
			The height of the water flowing fracture zone	0.24486
			The thickness of coal seam	0.08158

4.3. Risk assessment of mine water inrush using the coupled AHP-IVM model

Due to the information value and weight values of the evaluation factors (Table 8), the coupled AHP-IVM model is established as follows: (9) $$\begin{array}{c}{I}_{\mathrm{W}}=0.04438I_1+0.02432I_2+0.02432I_3+0.02432I_4+0.01278I_5+\\ 0.01278I_6+0.06678I_7+0.03961I_8+0.02288I_9+0.01363I_{10}+\\ 0.07145I_{11}+0.07145I_{12}+0.24486I_{13}+0.24486I_{14}+0.08158I_{15}\end{array}$$(9)

By calculating the information value of each unit in the grid and dividing all the results on average, the range of different water inrush areas can be obtained. The results are shown in Table 9.

Table 9. Information value of predicted water inrush areas.

Predicted water inrush areas	Information value
Safety area	−1.1636 ∼ −0.7124
Relative safety area	−0.7124 ∼ −0.2612
Relative risk area	−0.2612 ∼ 0.1899
Risk area	0.1899 ∼ 0.6411

Based on the model and GIS, the water inrush risk zoning map of the Qinan coal mine is presented in Figure 6. Total information value (I_W) in all units of the integrated map is classified as four levels by the Jenks natural breaks classification method, named risk area, relative risk area, relative safety area, and safety area, respectively (Jenks 1967).

As shown in Figure 7, the overall risk of water inrush in the Qinan coal mine is relatively high, and the risk and relative risk areas are mainly concentrated in the central and northern parts of the study area. The west of the coal mine is the safe area. This trend is caused by the depth of the coal roof in the central and northern mining areas of the Qinan coal mine. In this model, the two most important water inrush factors are the depth of the coal roof and the height of the water flowing fracture zone. They had a weight of 0.24486. AUC value of the depth of the coal roof is 0.7230 and the height of the water flowing fracture zone is 0.7209. In this area, the average depth of the coal roof is more than 45 m, and the average development height of the water conducting fracture zone is found to 460 m–760 m. If the height of the water flowing fracture zone is greater than the distance between coal seam roof and aquifer, water inrush will occur. Therefore, this factor is very important for predicting water inrush (Xu et al. 2009) . It can be analyzed by comparing Figures 4m and 7 that the height of the water flowing fracture zone provides the risk and relative risk areas. Therefore, it is more likely that the water flowing fracture zone will continue to develop and reaches the aquifer when mining under the unconsolidated and confined aquifer with complex geological conditions.

Figure 7. Water inrush risk zonation map in the Qinan coal mine.

4.4. Comparison of the coupled AHP-IVM model and site situations

For comparison, the AHP and IVM models are also used for the risk assessment respectively. In this study, the AHP and IVM models are constructed using the same training data. Then, the corresponding water inrush risk zoning maps are produced, as shown in Figure 8.

Figure 8. Water inrush risk zonation map produced using (a) AHP model and (b) IVM model.

As shown in Figure 8, the distribution trend of risk and relative risk areas predicted by the IVM model is similar to that of the coupled AHP-IVM model, and the AHP model is different from that of the coupled AHP-IVM model. However, the risk areas of the IVM model is larger than the coupled AHP-IVM model. It includes large areas without actual water inrush points, which indicates a poor discriminant ability of the two independent models.

In order to verify the prediction accuracy of the model, the prediction results are compared with the actual observation in the field. The distribution of the water inrush points under unconsolidated confined aquifers in the study area are divided into three levels: small water inrush points 0 < Q ≤ 60m³/h; medium water inrush points 60 m³/h < Q ≤ 600 m³/h; large water inrush points Q > 600m³/h, the result shown in Table 10.

Table 10. Summary of water inrush points distribution.

Model	Predicted water inrush areas	Area ratio (%)	Total number of water inrush points	Water inrush points level
				Small	Medium	Large
AHP-IVM	Safety area	12.1	0	0	0	0
	Relative safety area	25.8	0	0	0	0
	Relative risk area	43.0	5	4	1	0
	Risk area	19.1	16	13	3	0
AHP	Safety area	12.1	3	3	0	0
	Relative safety area	21.9	3	3	0	0
	Relative risk area	35.7	12	9	3	0
	Risk area	30.3	3	2	1	0
IVM	Safety area	11.5	1	1	0	0
	Relative safety area	26.5	1	1	0	0
	Relative risk area	35.0	4	3	1	0
	Risk area	27.0	15	12	3	0

Table 11. Pearson’s chi squared test of predicted water inrush areas.

Predicted water inrush areas	Water inrush points of model (%)			Total	χ^2	p
	AHP-IVM	AHP	IVM
Safety area	0 (0.00)	3 (14.29)	1 (4.76)	4 (6.35)	21.664	0.001
Relative safety area	0 (0.00)	3 (14.29)	1 (4.76)	4 (6.35)
Relative risk area	5 (23.81)	12 (57.14)	4 (19.05)	21 (33.33)
Risk area	16 (76.19)	3 (14.29)	15 (71.43)	34 (53.97)
Total	21	21	21	63

Table 10 shows the advantages of the AHP-IVM method for the AHP method and the IVM method. The prediction accuracy of the coupled AHP-IVM model for all types of water inrush points is 100%. All the water inrush points are distributed in the risk area and relative risk area. The prediction accuracy of the AHP model for medium water inrush points is 100%, and for small water inrush points is 64.7%. The prediction accuracy of the IVM model for large and medium water inrush points is 100%, and for small water inrush points is 88.2%. The AHP-IVM model accuracy is higher than other models, which indicates the rationality of the model used in this study. In general, a risk zonation map included a large number of water inrush points in a small area of water inrush risk and relative risk area, indicating the model has a good discriminant ability and high prediction accuracy. The water inrush points of three models in different predicted water inrush areas were counted and analyzed Pearson’s chi-square test. The result is p < 0.01, indicating a statistically significant difference between the different models (Table 11).

Figure 9 shows that AUC value of the coupled AHP-IVM model is 0.83089, which is higher than that of the other two models. Thus, the coupling model for risk assessment of water inrush has a higher prediction accuracy and can effectively guide the safe and efficient production of coal mines under the unconsolidated and confined aquifer.

Figure 9. Success rate curve of the coupled AHP-IVM model, IVM model and AHP model.

This study is aimed at the risk of mining under unconsolidated confined aquifers and is instructive for the production activities in Qinan coal mine. Water inrush can be prevented by advanced drainage, grouting reconstruction technology, curtain grouting, partial-filling technology and retaining safety coal pillar. If more detailed geological data is available, the accuracy of this method could be improved. This research is also valuable for coal mines with similar geological conditions.

5. Conclusions

1. Based on 15 factors, a risk assessment system of water inrush is established, and the weight of each factor is calculated by the coupled AHP-IVM method, which the judgment matrix establishment is improved by the information value method.

2. The information value of the evaluation factors and the total information value in the study area is calculated. The coupled AHP-IVM model is applied to evaluate the risk of water inrush when mining under the unconsolidated and confined aquifer in the Qinan coal mine. The evaluation result indicates that the overall risk of water inrush in the coal mine is relatively high, and the risk and relative risk areas are mainly concentrated in the southern, eastern and northern parts.

3. The evaluation results of the coupled AHP-IVM model are compared with the actual water inrush points in coal mining, and the actual water inrush points are all located in the risk area and relatively risk area. The success rate curve method is applied to evaluate the coupled AHP-IVM model, and AUC value is 0.83089. The prediction results of the coupled AHP-IVM model are consistent with the actual results, and the combination of the two different methods can improve the prediction accuracy of the model and effectively serve as general guidelines for mine operations.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement

The data used to support the findings of this study are available from the corresponding author upon request.

Additional information

Funding

This work is financially supported by the National Natural Science Foundation of China under Grant [No. 41972256]. The authors sincerely thank the reviewers for their careful reading and useful comments.