Introduction

Coal, accounting for 56.8% of energy, is widely used in the daily production and living (Duan and Zhao 2021). China, as one of the largest countries in coal production and consumption, plays an important role in the generation of coal energy. Nearly 60% of the coal resources are produced in the Carboniferous and Permian North China-type coal fields. Especially, these coal seams are often accompanied by the strong water yield limestone aquifers such as the Ordovician limestone aquifers. With the increase of the mining depth, disasters frequently occur under the complex geological conditions (Chen et al. 2018). Among them, the water disaster, ranked second in the coal mine disasters, has always plagued the coal mine safe production (Donnelly 2006; Mahato et al. 2018). In the past few decades, 1184 water accidents occurred in China, with 4735 deaths. These water disasters have caused a large number of casualties and property losses (Wang and Park 2003). Therefore, it is an important task to scientifically predict the coal seam floor water inrush above confined water.

Many scholars have carried out substantial research on the floor water disasters, promoting a series of theories and industry standards. The Slesarev formula, a formula of safe water pressure, regards the floor as a beam with uniform load and both ends fixed. The maximum water pressure value acting on the beam was regarded as the safe water pressure value (Liu et al. 2018a). the floor was divided into three zones in the down three zones theory, namely, the fissure zone, the intact strata zone and the confined water conductive zone. Among them, the intact strata zone has an inhibitory effect on water inrush (Hu et al. 2021). The rock strata with the strongest bearing capacity between the floor and the aquifer was served as the key strata in key strata theory. Its breaking mechanism has a certain relationship with the law of water inrush (Wang et al. 2021). The floor failure depth theory is the development depth of the floor water conducting fracture zone, deduced from the semi-infinite body theory and the slip field theory (Liu et al. 2018b). The water inrush coefficient, a ratio of the water pressure to the thickness of aquifuge, was treated as the criterion for judging whether the water inrush occurs. It is widely applied in the water inrush evaluation of coal mines (Sun et al. 2020). However, with the deepening of coal mining depth, the complex geological conditions exacerbate the occurrence of water inrush accidents. Only considering these two indicators to measure water inrush is often inconsistent with the actual situation. In addition, the floor water inrush is a geological phenomenon under the combined action of multi information (He et al. 2021). The complexity of the factors, the inconsistency of the dimensions, and the simultaneous development of both qualitative and quantitative factors pose challenges to the decision-making technology of the floor water inrush.

In recent, the multi-criteria decision-making (MCDM) was applied to the water inrush assessment. Hu et al. (2019) constructed a water inrush prediction model to evaluate the water inrush risk of Qiuji coal mine working face, combining AHP and EWM. Niu et al. (2020) adopted the linear weighting method to construct an improved water inrush coefficient model to predict the risk of coal seam floor water inrush on the limestone aquifer. The number, complexity and feature extraction of coal seam floor water inrush factors increase the difficulty of these evaluation methods in the operation process. The PCA reduces the dimensions of many factors affecting the floor water inrush to extract the principal components. It avoids the problems caused by excessive information. Shi et al. (2015) adopted the PCA and the machine learning methods to induce and extract the influencing factors of floor water inrush. Ju and Hu (2021) established a water inrush identification model to study the water inrush risk of Xieqiao coal mine on the basis of PCA method and grey situation decision method. Li et al. (2020) established an identification model of floor water inrush source, combining PCA and Fisher discriminant analysis. It eliminates the overlapping influence between indicators, resulting in an improvement of the identification accuracy of water inrush sources. Zhang et al. (2022) proposed a BP neural network prediction model of water inrush based on PCA and depth confidence network (DBN) to predict the risk of water inrush in actual working face. In addition, the PCA plays a certain role in the analysis of mine water source pollution degree and the identification of water diversion channel (Salifu et al. 2012; Liu et al. 2019). In MCDM, the method such as AHP was used to divide weights according to expert experience. The preference of experts will lead to uncertainty of weights (Zhang et al. 2021). To eliminate subjective uncertainty, the entropy weight method was applied to determine the weight of water inrush influencing factors in water inrush evaluation (Gao et al. 2022). Compared with subjective evaluation method, the entropy weight method is more accurate and objective. However, the traditional entropy weight method has limitations because of ignoring the conflict between indicators. It is characterized by instability. To eliminate the impact of this deficiency, the CRITIC, considering the conflicts between indicators, was used to determine the weight of indicators (Zhang et al. 2020). Also, this method plays an important role in the identification of water inrush sources (Casagrande et al. 2020). Meanwhile, multiple methods were utilized for constructing combined weights (Wu et al. 2021a). However, the weight coefficients of these methods are often calculated by the linear weighting and the multiplicative weighting. Because of the imbalance of preferences, it may not reflect the comprehensive weight of indicators more accurately. The KIC can constrain the difference of weights determined by various decision methods, improving the accuracy of the combination weight (Osses et al. 2013). Moreover, the comprehensive evaluation includes multiple methods, such as fuzzy comprehensive evaluation (Zhou et al. 2022), composite index method (Yu et al. 2022), attribute mathematics theory (Xu et al. 2021), TOPSIS (Shi et al. 2020), evidence theory (Li et al. 2021), set pair analysis (Li et al. 2018) and matter element analysis (Zhang et al. 2019). In terms of dealing with multiple attribute factors, the TOPSIS can better solve the problem of inconsistent factor dimensions. At the same time, the ideal solutions are delimited to rank the evaluation samples. This method was widely used in the evaluation of water abundance and water inrush (Qiu et al. 2020; Qu et al. 2021). The decision-making of coal seam floor water inrush often involves spatial information related to decision-making information. The decision problem uses multi standard decision analysis in the spatial domain to evaluate the schemes and standards (Yang et al. 2018). GIS, an information processing tool, has the ability to automate, manage and analyze various spatial data (Liu et al. 2020). The decision-making information can be obtained from the geographical data. It can better reflect the spatial information of floor water inrush after being processed by a variety of standards (Wu et al. 2017).

In consideration of the above researches, the current study aims to construct a combined weighted WIRI evaluation model based on the TOPSIS method. The employ of PCA and CRITIC ensures the objectivity of weights, avoiding the loss of indicator information and reflecting the relevance of indicators. The application of KIC improves the scientificity of the construction of combined weights. The WIRI evaluation model can reflect the water inrush risk degree of the samples. This model can provide guidance for coal mining planning and water disaster prevention.

Study area

Xinyugou coal mine is located in Jiexiu city, Shanxi province, with a mine field area of 9.56 km2. The mining elevation ranges from 1060 m asl to 200 m asl. The mine field is situated at the junction of the hilly area on the northern edge of Taiyue mountain and Jinzhong basin. The terrain is generally high in the south and low in the north (Fig. 1). The Zhangjian river runs through the mine field from south to north, with a length of 3.1 km. The highest flood level of it ranges from 1020 m asl to 910 m asl. The well-field has a semi-arid continental monsoon climate in the north warm temperate zone, with an obvious Continental climate features.

Fig. 1
figure 1

Location of study area

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Geological conditions

According to the drilling and ground geological data, the strata of the mine field from old to new are the Ordovician, the Carboniferous, the Permian and the Quaternary, respectively. An anticline is located on the east side of the mine field, with a formation dip ranging from 10° to 20°. The fault structure is developed, without the founding of collapse column and magmatic rock intrusion. The main coal-bearing strata in the mine field are the Lower Permian Shanxi formation and the Upper Carboniferous Taiyuan formation. The No. 9 coal seam, as one of main mineable coal seams, occurs in the Carboniferous Taiyuan formation, with a thickness ranging from 0.3 m to 3.25 m.

Hydrogeological conditions

The main aquifers in the study area are the Ordovician carbonate karst fissure aquifer, the Carboniferous clastic rock, carbonate karst fissure aquifer, the Permian clastic rock fissure aquifer and the Quaternary loose rock pore aquifer (Fig. 2). Among them, the water level buried depth of the Ordovician karst aquifer is 59.50 m. The water level elevation is 911.22 m asl. The Ordovician karst aquifer is characterized by poor-medium water abundance, with a unit inflow ranging from 0.0772 L/s·m to 0.1431L/s·m. The main aquifuge in the study area is the Benxi Formation of the Middle Carboniferous. Its lithology is aluminous mudstone, with a general thickness of 15 m. The Upper Carboniferous and the Lower Permian are mainly composed of plastic mudstone and sandy mudstone, with a thickness generally ranging from 2.00 to several meters. The No. 9 coal seam, located above the Ordovician aquifer, was threatened by confined water. Therefore, the risk of floor water inrush was taken as the research object of this paper.

Fig. 2
figure 2

Hydrogeological distribution of the study area

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Methods

A WIRI evaluation model was constructed based on TOPSIS to evaluate the risk of water inrush on the karst aquifers. It mainly includes the following steps (Fig. 3): (1) Selection of the water inrush evaluation indicators (2) Determination of the weight of the evaluation index (3) Building of the WIRI evaluation model (4) Evaluation and verification of model results.

Fig. 3
figure 3

Flowchart of the research method

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Selection of water inrush evaluation indicators

The construction of the evaluation index system plays a crucial role in the water inrush evaluation. The evaluation results are affected by the selection of the evaluation index. Thus, we selected 7 factors as the evaluation indicators, considering the geological conditions, the hydrogeological conditions and the mining activities, i.e., the fault fractal dimension, the coal seam dip angle, the mining depth, the slope length of panel, the aquifuge thickness, the water pressure and the water abundance. Also, the single factor thematic maps (Fig. 4) were drawn combined with the geospatial information of each sample data. The effect of evaluation indicators on water inrush was divided into two types: the positive correlation and the negative correlation. Among them, the factors positively related to the risk of water inrush are the fault fractal dimension, the coal seam dip angle, the mining depth, the slope length of panel, the water pressure and the water abundance. While, the factor negatively related to the risk of water inrush is only the aquifuge thickness.

Fig. 4
figure 4

Thematic map of evaluation indicators

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PCA

The PCA, proposed by Pearson (1901), carries out the dimension reduction to transform linearly dependent original variables into independent new variables. The weight determination specific steps of PCA are as follows:

  • Data standardization. The original data matrix E = (eij) m × n is constituted by m samples and n evaluation indicators. The standard data matrix F = (fij) m×n is constructed as follows:

$${f}_{ij}=\frac{{e}_{ij}-\overline{{e }_{j}}}{{\sigma }_{j}}$$
(1)

where eij is the standard value of i samples on j evaluation indicators; \(\overline{{e }_{j}}\) is the mean value of jth evaluation indicators, \(\overline{{e }_{j}}=\sum\limits_{i=1}^{m}{e}_{ij}/m\), i = 1, 2, …, m, j = 1, 2, …, n; sj is the standard deviation of jth evaluation indicators, \({\sigma }_{j}=\sqrt{\sum\limits_{i=1}^{m}{({e}_{ij}-\overline{{e }_{j}})}^{2}}/m-1\), i = 1, 2, …, m, j = 1, 2, …, n.

  • Construction of correlation matrix. The correlation matrix G is calculated as follows:

$$G={(g_{ij})}_{n\times n}=\begin{pmatrix}g_{11}&g_{12}&\cdots&{\text{ g}}_{1n}\\g_{21}&g_{22}&\cdots&{\text{ g}}_{2n}\\\vdots&\vdots&\ddots&\vdots\\g_{n1}&g_{n2}&\cdots&{\text{ g}}_{nn}\end{pmatrix}$$
(2)

where \({g}_{ij}=\sum\limits_{k=1}^{n}({f}_{ki}-\overline{{f }_{i}})({f}_{ki}-\overline{{f }_{j}})/\sqrt{\sum\limits_{k=1}^{n}{({f}_{ki}-\overline{{f }_{i}})}^{2}}\sqrt{\sum\limits_{k=1}^{n}{({f}_{kj}-\overline{{f }_{j}})}^{2}}\).

  • Extraction of principal components. The principal component coefficient matrix H = (hij)m×n is defined through the outcome of the eigenvalues and eigenvectors of the correlation matrix. Further, the corresponding principal component expression is established as follows:

$$\left\{\begin{array}{l}Y_1=h_{11}X_1+h_{12}X_2+...+h_{1n}X_n\\Y_2=h_{21}X_1+h_{22}X_2+...+h_{2n}X_n\\...\\Y_m=h_{m1}X_1+h_{p2}X_2+...+h_{mn}X_n\end{array}\right.$$
(3)

where Y1, Y2, …, Ym are principal components; hmn is the principal component score coefficient; and X1, X2, …, Xn are standard values.

  • Weight determination. The calculation of weight mainly includes the following steps: the calculation of each index scores in the principal components are carried on, combined the extracted characteristic values of the principal components with the coefficients in the linear relationship of the principal components; the score coefficients of the principal component in the model are defined (Eq. (4)), combined the each index score in the principal component with the corresponding variance contribution rate of the principal component; the score coefficient is normalized to obtain the weight value of each index (Eq. (5)).

$$\chi_i=\left|\frac{\sum\limits_{i=1}^m\gamma_i\delta_i}{\sum\limits_{i=1}^m\delta_i}\right|$$
(4)
$$\alpha_i=\frac{\chi_i}{\sum\limits_{i=1}^m\chi_i}$$
(5)

where χi is the score coefficient of the principal component. δi is the corresponding variance contribution rate of the principal component, \({\delta }_{i}={\lambda }_{i}/\sum\limits_{i=1}^{m}{\lambda }_{i}\); γi is the score of each index in the principal component, \({\gamma }_{ij}\text{=}{h}_{ij}/\sqrt{{\lambda }_{i}}\), λi is the eigenvalue of the correlation matrix, i = 1 ~ m, j = 1 ~ n. αi is the weight of the water inrush evaluation index.

CRITIC

The CRITIC is a more scientific objective weighting method (Diakoulaki et al. 1995). It determines the index weight according to the contrast intensity and conflict between the evaluation indicators. Also, the difference and correlation between the indicators is considered. The calculation steps are as follows.

  • Standardization of evaluation indicators. According to the effect of evaluation index on water inrush, the standardized equations are classified into the positive correlation and the negative correlation.

$${e}_{ij}^{*}=\frac{{e}_{ij}-\mathrm{min}({e}_{ij})}{\mathrm{max}({e}_{ij})-\mathrm{min}({e}_{ij})}$$
(6)
$${e}_{ij}^{*}=\frac{\mathrm{max}({e}_{ij})-{e}_{ij}}{\mathrm{max}({e}_{ij})-\mathrm{min}({e}_{ij})}$$
(7)

where e*ij is the standardized data; eij is the original data; min(eij) and max(eij) are the minimum and maximum values of each evaluation index, respectively.

  • Calculation of standard deviation and correlation coefficient. In CRITIC, the standard deviation and correlation coefficient are applied to represent the difference and conflict between indicators, respectively. The larger the standard deviation, the greater the difference between the indicators. A positive correlation coefficient indicates that the conflict between the indicators is smaller. The standard and correlation coefficients between indicators are calculated as follows:

$${S}_{j}=\sqrt{\frac{\sum\limits_{i=1}^{m}{({e}^{*}{}_{ij}-\overline{{e }^{*}{}_{j}})}^{2}}{m-1}}$$
(8)
$${r}_{kl}=\frac{\sum\limits_{i=1}^{m}({e}^{*}{}_{ik}-\overline{{e }^{*}{}_{k}})({e}^{*}{}_{il}-\overline{{e }^{*}{}_{l}})}{\sqrt{\sum\limits_{i=1}^{m}{({e}^{*}{}_{ik}-\overline{{e }^{*}{}_{k}})}^{2}\sum\limits_{i=1}^{m}{({e}^{*}{}_{il}-\overline{{e }^{*}{}_{l}})}^{2}}}$$
(9)

where \(\overline{{e }^{*}{}_{j}}\) is the mean value of the jth evaluation indicators; rkl is the correlation coefficient between evaluation indicators, k = 1, 2, …, n; l = 1, 2, …, k.

  • Determination of indicators conflict. The conflict between evaluation indicators is calculated as follows:

$${R}_{j}=\sum_{k=1}^{n}(1-{r}_{kl})$$
(10)

where Rj is the conflict of the jth evaluation index.

  • Calculation of evaluation index information amount and weight. The information amount and weight of the evaluation index are determined by Eqs. (11) and (12), respectively.

$${t}_{j}={S}_{j}{R}_{j}$$
(11)
$${\beta }_{j}=\frac{{t}_{j}}{\sum\limits_{j=1}^{n}{t}_{j}}$$
(12)

where tj is the information amount of jth evaluation index; \({\beta }_{j}\) is the weight of jth evaluation index.

KIC

To make the combination weight as close as possible to the weights of two methods, the objective function of the combination weight is constructed by the KIC (Thiesen et al. 2019). Also, the combination weight of the evaluation index can be obtained by the Lagrange multiplier method.

$$\begin{Bmatrix}\min J(w)=\sum\limits_{j=1}^n\left(w_j\ln\frac{w_j}{\alpha_j}+w_i\ln\frac{w_j}{\beta_j}\right)\\\text{s.t.}\sum\limits_{j=1}^nw_j=1,w_j\geq0,i=1,2,\cdots,n\end{Bmatrix}$$
(13)
$${w}_{j}=\frac{\sqrt{{\alpha }_{j}{\beta }_{j}}}{\sum\limits_{j=1}^{n}\sqrt{{\alpha }_{j}{\beta }_{j}}}$$
(14)

where wj is the combination weight of the jth evaluation index.

TOPSIS

The TOPSIS, also known as the distance method of superiority and inferiority, commonly used in the multi-objective decision analysis (Baykasoğlu and Gölcük 2017; Norouzi and Namin 2019). Its basic principle is to sort by detecting the distance between the evaluation object and the optimal solution and the worst solution. If the evaluation object is closest to the optimal solution and furthest away from the worst solution, it is the best; Otherwise, it is not optimal. The specific steps are as follows:

  • Construction of weighted standardization matrix. The weighted standardization matrix \({R}^{*}={({r}_{ij}^{*})}_{m\times n}={({w}_{j}{e}_{ij}^{*})}_{m\times n}\) is constructed on the basis of the combined weight and standardized values of evaluation index.

  • Definition of positive and negative ideal solutions of water inrush. There is a certain relationship between the evaluation index and water inrush. A larger negative correlation index value implies a lower probability of water inrush; a larger the positive correlation index value indicates a higher probability of water inrush. Thus, the negative ideal solution of water inrush is the minimum value of positive correlation index or the maximum value of negative correlation index. However, the positive ideal solution of water inrush is opposite. The determination equations are as follows:

$$C^-=\left\{\left(\max\;r_{ij}^\ast\vert j\in\gamma_1\right),\left(\min\;r_{ij}^\ast\vert j\in\gamma_2\right)\right\}$$
(15)
$$C^+=\left\{\left(\min\;r_{ij}^\ast\vert j\in\gamma_1\right),\left(\max\;r_{ij}^\ast\vert j\in\gamma_2\right)\right\}$$
(16)

where C− is the negative ideal solution; C+ is the positive ideal solution; γ1 is the negative correlation index collection; γ2 is the positive correlation index collection.

  • Determination of water inrush index. The distance from the ith sample to the negative ideal solution and the positive ideal solution are calculated as follows:

$${D}_{i}^{-}=\sqrt{\sum_{j=1}^{n}{({r}_{ij}^{*}-{c}_{ij}^{-})}^{2}}$$
(17)
$${D}_{i}^{+}=\sqrt{\sum_{j=1}^{n}{({r}_{ij}^{*}-{c}_{ij}^{+})}^{2}}$$
(18)

where \(D_i^-\) is the distance of the ith sample to the negative ideal solution; \(D_i^+\) is the distance of the ith sample to the positive ideal solution; \(r_{ij}^\ast\) is the weighted standardized value of the jth index in the ith sample; \(c_{ij}^-\) is the value of the jth index in the set of negative ideal solutions; \(c_{ij}^+\) is the value of the jth index in the set of positive ideal solutions.

The water inrush index combined with Eqs. (17) and (18) is calculated:

$${\text{WIRI}}_{i}={D}_{i}^{-}/({D}_{i}^{-}+{D}_{i}^{+})$$
(19)

where WIRIi is the water inrush index of ith sample, the larger the value, the higher the probability of water inrush.

Results and analysis

Weight calculation of PCA

The correlation coefficients of the evaluation index were calculated by Eq. (2) to construct the correlation coefficient matrix.

$$G=\begin{pmatrix}1&\text{0.03}&-\text{0.24}&\text{0.36}&-\text{0.26}&-\text{0.19}&\,\text{0.17}\\\text{0.03}&1&\text{0.77}&\,\text{0.70}&-\text{0.26}&\text{0.78}&\text{0.83}\\-\text{0.24}&\,\text{0.77}&1&\text{0.49}&-\text{0.26}&\text{0.82}&\text{0.77}\\\text{0.36}&\text{0.70}&\text{0.49}&1&0&\text{0.54}&\text{0.84}\\-\text{0.26}&-\text{0.26}&-\text{0.26}&0\,&1&\,\,\text{0.19}&-\text{0.22}\\-\text{0.19}&\,\text{0.78}&\text{0.82}&\text{0.54}&-\text{0.19}&1&\text{0.81}\\\text{0.17}&\text{0.83}&\text{0.77}&\text{0.84}&-\text{0.22}&\text{0.81}&1\end{pmatrix}$$
(20)

Combined with the correlation coefficient matrix, the corresponding eigenvalues were calculated. Moreover, the corresponding contribution rates of each component were obtained (Table 1).

Table 1 Corresponding contribution rates of each component
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Table 1 shows that 7 components were extracted. The corresponding eigenvalues are 4.01, 1.38, 1.02, 0.21, 0.18, 0.16 and 0.05, respectively. Taking the feature greater than 1 as the criterion for extracting the principal components, the first three components were regarded as the principal components. Combined with the eigenvalues of the principal components, the relationship between the evaluation index and the principal components was constructed.

$$\left\{\begin{array}{c}Y_1=0.06X_1+0.92X_2+0.87X_3-0.79X_4-0.29X_5+0.89X_6+0.96X_7\\Y_2=0.97X_1-0.01X_2-0.32X_3+0.34X_4-0.36X_5-0.29X_6+0.12X_7\\Y_3=0.09X_1-0.02X_2-0.17X_3+0.44X_4+0.88X_5-0.05X_6+0.12X_7\end{array}\right.$$
(21)

The weight of each evaluation index was determined by Eq. (4) as 0.13, 0.17, 0.11, 0.23, 0.01, 0.13 and 0.21.

Weight calculation of CRITIC

Combined with the correlation between the evaluation index and water inrush, the standardized value of each evaluation index was calculated by Eqs. (6) and (7) (Table 2).

Table 2 Standardized value of each evaluation index
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The information amounts and weights were determined by Eqs. (9) and (10), respectively, i.e., R = (5.60, 2.63, 3.13, 3.07, 4.81, 3.06, 2.36)T, t = (1.43, 0.78, 1.03, 1.19, 1.23, 0.84, 0.71)T and \(\beta\) = (0.20, 0.11, 0.14, 0.16, 0.17, 0.12, 0.10)T. The combined weights of the water inrush indicators wj = (0.17, 0.15, 0.14, 0.21, 0.05, 0.14, 0.15) were defined by Eq. (14).

Construction of water inrush risk assessment model

The negative ideal solution and positive ideal solution of each evaluation index were determined as C− = (0, 0, 0, 0, 0.05, 0, 0) and C+  = (0.17, 0.15, 0.14, 0.21, 0, 0.14, 0.15), combined with the standardized value of the evaluation index and its weights. In addition, the ideal solution distance and WIRI corresponding to the sample data (Fig. 5) were obtained by Eq. (19).

Fig. 5
figure 5

Sample parameters of TOPSIS water inrush evaluation model

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Figure 5a shows that the negative ideal solution distances of 22 samples rangeed from 0.07 to 0.37. Among them, the negative ideal solution distances of J1, J2 and 301 were higher, i.e., 0.37, 0.34 and 0.32, reflecting a farther distance from low risk; however, the negative ideal solution distances of J9, J10 and 401 were lower, i.e., 0.07, 0.06 and 0.12, respectively, indicating a closer distance from less risk. Figure 5b shows that the positive ideal solution distances of samples ranged from 0.08 to 0.36. Moreover, the positive ideal solution distances of J9 and J10 were higher, with the values being both 0.36. It reveals a lower water inrush probability. However, the positive ideal solution distances of J1, J2 and 301 were smaller. their values were 0.08, 0.10, and 0.11, respectively, suggesting that a higher risk of water inrush. Figure 5c shows that the WIRI of the samples ranged from 0.15 to 0.82. Further, the WIRI values of J9 and J10 were lower i.e., 0.17 and 0.15, indicating a lower risk of water inrush. The WIRI of J1, J2 and 301 were higher, with the values being 0.82, 0.77 and 0.76 respectively, demonstrating a higher risk of water inrush.

Division of water inrush risk areas

Combined with the WIRI of the samples, the water inrush risk zoning in the study area were determined with GIS (Fig. 6). Moreover, the thresholds of WIRI were treated with the jenks natural breaks classification method built-in GIS (Amirruddin et al. 2020). According to the difference of the intra-class and the inter-class, the interruption value of the data was determined, namely, 0.26, 0.38, 0.52 and 0.66. Therefore, the study area was classified to five areas, i.e., the safe areas, the relatively safe areas, the transitional areas, the relatively dangerous areas and the dangerous areas.

Fig. 6
figure 6

Risk zoning map of floor water inrush in study area

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Figure 6 shows that the risk of water inrush in the study area was classified into 5 areas, namely, the safe areas (0.15 ≤ WIRI < 0.26), the relatively safe areas (0.26 ≤ WIRI < 0.38), the transitional areas (0.38 ≤ WIRI < 0.52), the relatively dangerous areas (0.52 ≤ WIRI < 0.66) and the dangerous areas (0.66 ≤ WIRI < 0.82). The risk of water inrush gradually decreased from northwest to southeast of the study area. Combined with the single-factor thematic map and the corresponding index weight, it can be found that the dip length of panel, water abundance, and mining depth play a greater role in the classification of water inrush risk. This leads to a high probability of water inrush in the northwest of the study area with a high risk of water inrush. In addition, there were 5 water inrush points in the study area, i.e., TS01, TS02, TS03, TS04 and TS05. These water inrush points were distributed in the dangerous areas and the relatively dangerous areas. Judging by the principle of maximum probability, the accuracy of the WIRI evaluation model is over 90%, indicating a good fitting effect of the actual water inrush situation.

Discussions

Weight calculation comparison

The reason for the higher evaluation accuracy of the WIRI evaluation model is that it uses a variety of more scientific decision-making methods to divide the weight of evaluation indicators. Moreover, the CRITIC was used to define weights according to the conflicts and differences of sample data. Compared with the traditional entropy weight method, its weight mainly was determined by the entropy (Eq. (22)). By comparing two different weight calculation methods (Eqs. (9) and (10)), the CRITIC can combine more information of sample data to calculate weight. It improves the calculation accuracy of weight.

$$s_j=-\frac1{\ln\;m}\sum\limits_{i=1}^mP_{ij}\;\ln\;P_{ij}$$
(22)

where sj is the entropy; m is the number of evaluation object; Pij is the standard value of each evaluation factors. At the same time, the KIC was used to superimpose the weights, ensuring the balance of comprehensive weights in various decision-making methods (Fig. 7). It improves the scientificity of weight division.

Fig. 7
figure 7

Weight distribution of evaluation indicators

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Figure 7 shows that the comprehensive weight of each evaluation index was between the weights determined by the two methods. In the PCA and the CRITIC, the weight values corresponding to the seven evaluation indicators were the same. The maximum and minimum weight values of the PCA were 0.23 and 0.01 respectively, corresponding to evaluation indicators 4 and 5; the maximum and minimum weight values of the CRITIC were 0.20 and 0.10 respectively, corresponding to evaluation indicators 1 and 7; the maximum and minimum comprehensive weights were 0.21 and 0.05 respectively, corresponding to evaluation indicators 4 and 5. It can be seen that the comprehensive weight retains the distribution characteristics of the maximum and minimum values of the evaluation indicators of the PCA weight, as well as the weight ranking characteristics of CRITIC. It can better reflect the weight of the two evaluation methods. At the same time, in the process of building the evaluation model, the multiple factors were selected as evaluation indicators to establish the evaluation index system. Compared with the traditional water inrush coefficient method, more factors were considered, which can better reflect the actual water inrush situation.

Comparative verification

To verify the accuracy of the WIRI evaluation model, the comparison with the water inrush coefficient method was carried out. Combined with the principle of the water inrush coefficient method (Wu et al. 2021b), the water inrush coefficient of the structural area is 0.06 Mpa/m; the water inrush coefficient of the complete block area is 0.10 Mpa/m. Due to the relatively developed structure in the study area, the 0.06 Mpa/m was selected as the threshold for the division of water inrush risk areas (Fig. 8).

Fig. 8
figure 8

Risk zoning map of water inrush coefficient method

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Figure 8 shows that the study area was divided into two areas, namely, the safe areas and the dangerous areas, according to the water inrush threshold of 0.06 Mpa/m. It can be seen that the dangerous areas occupied most of the study area, while the safe areas occupied a smaller part of the study area. In addition, only one water inrush point was located in the safe area, i.e., 103, implying a phenomenon inconsistent with the actual water inrush situation. If the water inrush risk of study area is distinguished by the water inrush coefficient method, there will be a large error in the actual situation of water inrush. In comparison, the prediction accuracy of the WIRI evaluation model is higher. it fits the actual water inrush situation better, with a higher accuracy. This model can provide a better guarantee for safe coal mining on confined water.

Conclusions

The WIRI evaluation model based on PCA and CRITIC was proposed. The main findings are as follows:

  • The geological and hydrogeological conditions of the study area were analyzed. 7 factors were selected as water inrush evaluation indicators to construct a water inrush evaluation system i.e., the fault fractal dimension, the coal seam dip angle, the mining depth, the dip length of panel, the aquifuge thickness, the water pressure and the water abundance.

  • The PCA extracted three principal components with a contribution of 91.46% to determine the weight of the water inrush evaluation index. The information contained in the evaluation index was relatively high. The CRITIC calculated the conflict, information and other parameters of the water inrush evaluation index to determine its weight. It makes the weight determination more objective. The combined weight was constructed by the KIC, resulting in a more scientific weight determination.

  • By constructing a WIRI evaluation model, the study area was classified into the safe areas, the relatively safe areas, the transitional areas, the relatively dangerous areas and the dangerous areas. The fitting effect is good with the actual water inrush, with a prediction accuracy being over 90%. Compared with the water inrush coefficient method, its prediction accuracy is higher. The model provides guidance for the prevention of the floor water hazards and theoretical support for the safe coal mining above confined water.