# Quantitative Evaluation of Karst Developmental Differences Based on Improved Analytic Hierarchy Process and Multidimensional Extension Matter Element Model

Authors: Xinyi Wang; Yu Zou; Qi Wang; Xiaoman Liu; Pingqing Zhang; Jianlin Li; Mengjie Yao
Journal: Geofluids
 (2019)

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## Abstract

In this study, limestone solubility, rock thickness, burial depth, hydrodynamic cycle, and geological tectonic of mine No. 13 in the Pingdingshan coalfield (China) were selected to evaluate the degree of karst development. The weight of each index factor to the karst development was determined by using the improved analytic hierarchy process. The multidimensional extensional matter model was used to determine the degree of karst development of the four mining areas (named 1st to 4th) of the Pingdingshan mine No. 13. The results show that the degree of karst development differs zonally, with 1st and 2nd mining areas presenting the lowest degree of karst development (grade II-IV, for an average quantification value of 3.0) and 4th mining area having the highest degree (grade IV-V, for an average quantification value of 4.7). In the vertical direction, the development degree of the vertical layer L1-L4 karst in the Carboniferous Taiyuan Formation is grade IV-V, with an average quantitative value of 4.5, whereas the layers L5-L7 in the Taiyuan Formation had a III-V grade, with an average quantitative value of 3.75, and the Cambrian limestone grade was II-IV, for an average quantitative value of 2.75, i.e., the development degree of karst gradually decreases from shallow to deep.


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## Body

## 1. Introduction

Carbonate karst usually refers to the dissolution of carbonate rocks caused by acidic fluids, resulting in a large number of holes, caves, and fractures. Because the geological structure, lithological characteristics, hydrodynamic cycling conditions, burial depth, and various other factors all present spatial differences, the development degree of karst varies according to the burial depth or the location along the (zonal) plane.Many studies have investigated the characteristics and differences of the development of karst under water-rich and hydraulic conditions, as well as the factors responsible [1–5]. Sokolov [6] held that karst development is a geological process in which soluble rock is destroyed by dissolved water flow. It is mainly controlled by four conditions: rock solubility, rock permeability, groundwater mobility, and groundwater dissolution capacity. Legrand and Stringfield [7] studied the factors that affect the permeability of rock formations in karst areas, as well as briefly describe the developmental characteristics of karst, including the typical surface features such as sparse streams and bare rocks, as well as underground features comprising karst caves. In the 1960s and 1970s, the karst research group of the Institute of Geology of the Chinese Academy of Sciences elaborated on the lithology, dissolution mechanism, and the geological structure characteristics of the carbonate rock and the regional development characteristics of karst in China [8]. Ford and Williams and Fornós et al. [9, 10], respectively, delineated the influence of chemical characteristics, geological structure, climate, and other factors of lithologic karst water on karst development and karst development characteristics; these studies demonstrated that in addition to typical coastal karstification, meteoric water recharge and possibly deep recharge from hypogenic sources can affect the features of karst. Huang and Wang [11] investigated the recharge channel of a groundwater in a Karst mining area by using an environmental isotope method and found that the main recharge source in the north of Taihang Mountains is in a carbonate-exposed area of China. Lancia et al. [12] conducted combined experiments and a hydrogeological evaluation method to determine the water-conducting characteristics of karst-developed rock masses; the limits of continuum modeling for karst media were addressed by combining two methods. Yao et al. [13] established a fully coupled antivelocity theoretical control model based on factors such as water flow, karst fissure erosion characteristics, and permeability change and used it to predict the karst water inrush time under different geological conditions; the results showed that the inverse velocity theory is capable of predicting the occurrence of water inrush under different conditions. Sauro et al. [14] conducted detailed statistics on the distribution and direction of karst development in southern Italy and analyzed the differences in karst development under different geological structures. Finally, we conclude that the development of the cave was strictly guided by a few favorable surfaces with stratigraphic and tectonic origins. Chen et al. [15] explained the spatial variability of Cambrian limestone karst development based on the solubility of rocks, water permeability, water chemistry, and water cycle characteristics of the Pingdingshan mining area in China. Chitsazan et al. [16] compared the karst development of the Kano anticline in Iran’s Zagros Mountains with that of the Shotori Mountains in central Iran and proposed that the difference in their karst development was caused by the difference of the geological structure and rainfall. Zhou et al. [17] investigated the spatial and geographical patterns of 4960 karst caves in Guizhou of China and studied the influence and development of lithology, structure, climate, hydrology, and elevation on the distribution, quantity, and spatial pattern of the caves. Sun et al. [18] and Lipar and Webb [19] showed that the CO2 content has a great impact on the degree of karst development. The erosive capacity is stronger when the CO2 content is higher in a rock formation. The erosive capacity of CO2 is higher when it is coupled with the participation of groundwater. As the depth increases, the replenishment of CO2 in the water is insufficient, so the circulation of the groundwater is slowed down and the erosive capacity of CO2 is reduced. Thus, the development of karst in a coalfield eventually occurs via vertical zonation, where the development of the shallow karst becomes deeper and stronger. Li et al. [20, 21] studied the correlation between groundwater and the morphology of karst and established a model of the karst development degree using a hydrochemical kinetic-fractal index based on experimental corrosion data, thereby providing foundations for quantitative evaluations of the morphology and development of karst. Zhang et al. [22] selected six main factors that affect the development of karst as evaluation indexes and established an evaluation system for the underground karst development degree by combining the analytic hierarchy process with a Bayesian method. This method was then employed for the preliminary identification of the karst development status in railway tunnel engineering, thereby providing theoretical foundations to facilitate quantitative evaluations of the karst development degree.As shown above, many research results on the characteristics and differences of karst development exist, but these mostly consist in qualitative description and chart comparisons. However, few quantitative analyses exist to evaluate the degree of karst development difference from multiple factors by using modern methods [23, 24]. That is, the quantitative identification of karst developmental differences based on comprehensive index thresholds merits further study. Therefore, the Carboniferous and Cambrian limestone strata of the Ji coal seam floor formation of the Pingdingshan coalfield mine No. 13 are further studied in this paper. The five following influencing factors are selected as index factors for characterizing karst development differences: limestone lithology, limestone thickness, burial depth, hydrodynamic cycle, and geological structure. A mathematical model for calculating the comprehensive index threshold and for identifying the degree of development of limestone karst in a certain spatial range is established by coupling an improved analytic hierarchy process and the multidimensional extension matter element model. The results of this study are expected to provide strong technical support for objectively and clearly discriminating the differences in karst development characteristics.


## 2. Research Methods

### 2.1. Improved Analytic Hierarchy Process

Determining the weight value of each index factor is the key to evaluate the degree of karst development, and the selection of the most appropriate methodology is crucial for ensuring the accuracy of the identification results. At present, the methods commonly used to determine weights are the analytic hierarchy process and the entropy weight method [25–27].The analytic hierarchy process (AHP) is a practical multicriteria decision-making method. This method can express complex problems in an orderly hierarchical structure and can deal with qualitative and quantitative evaluation indicators in decision-making schemes. The improved AHP uses the three-scale method of the optimal transfer matrix to construct the judgment matrix and calculate the weight. Compared with the standard AHP, it can improve the accuracy and objectivity of the judgment results and greatly enhance the operability.The comparison of the relative importance of selected indicators is the basis for constructing the judgment matrix in the improved AHP. If the former indicator is more important than the latter one, then it is assigned the value of 1. If the former indicator is as important as the latter one, then 0 is taken, and if the latter indicator is more important than the previous one, the value -1 is assigned. The structural judgment matrix is constructed, and the weight of each evaluation index is finally determined [25].Firstly, judgment matrixA is constructed according to the importance of the influencing factors:
(1)A=a11a12⋯a1ja21a22⋯a2j⋯⋯⋯⋯ai1ai2⋯aij,where aij=1 indicates that i is more important than j, aij=0 means that i and j are equally important, and aij=‐1 means that j is more important than i.MatrixR is the optimal transfer matrix for matrix A, and the value of each element in matrix R can be calculated by equation rij=1/n∑k=1naik−ajk=1/n∑k=1naik+akj, where n is the number of evaluation indicators. So, R is
(2)R=r11r12⋯r1jr21r22⋯r2j⋯⋯⋯⋯ri1ri2⋯rij.MatrixD is the judgment matrix for matrix R, and each element value in matrix D can be calculated using equation dij=exprij. So, D is
(3)D=d11d12⋯d1jd21d22⋯d2j⋯⋯⋯⋯di1di2⋯dij.Weightωi of a single indicator factor can be calculated using Equation (4) according to each element value in matrix D:
(4)ωi=∐k=1ndikn∑k=1n∐k=1ndikn.


### 2.2. Extension Matter Element Model

#### 2.2.1. Basic Theory

Everything has its own unique properties, and each differs from other things. The extension matter element theory [25, 26] is a new theory that describes the internal structural relationship and attribute changes for things. If M is the thing described, then C is a feature of thing M and V is the magnitude of feature C. Thus, the matter element matrix for the thing is
(5)R=M,C,V.In general, a thing has many characteristics, and the matrix of matter elements withn features is
(6)R=M,C1,C2,⋮Cn,V1,V2,⋮Vn,=R1R2⋮Rn,where Ri=M,Ci,Vi,i=1,2,⋯,n.


#### 2.2.2. Model Establishment

Assuming thatn factors affect karst development, then the degree of karst development can be divided into H grades. The matter element matrix of grade j can be expressed as
(7)Rj=Mj,C1,C2,⋮Cn,Vj1,Vj2,⋮V,jn=MjC1C2⋮Cn<xj1,yj1><xj2,yj2>⋮<xjn,yjn>,where Rj denotes the matter element matrix when the degree of karst development is grade j, Mj is the jth grade of karst development, and Vji=<xji,yji> denotes the range of values when the first index that affects karst development is grade j, j=1,2,⋯,h, i=1,2,⋯,n.For all levels ofh, the nodal matter element matrix comprising the allowable range for each index factor is as follows:
(8)RD=D,C,VD=DC1C2⋮Cn<xD1,yD1><xD2,yD2>⋮<xDn,yDn>,where RD represents the nodal matter element matrix of the karst development degree, D is the set of karst development degree grades, and VDi=<xDi,yDi> is the allowable range of index factor Ci in D. Vji∈VDi, j=1,2,⋯,h, i=1,2,⋯,n.


#### 2.2.3. Extension Material Evaluation

2.2.3.1. Definition of Proximity. For the evaluated things expressed by Equation (6), let
(9)pVi,Vji=Vi−xji+yji2−12yji−xji,(10)pVi,VDi=Vi−xDi+yDi2−12yDi−xDi.In the formula,Vi is the measure of the evaluation index factor; pVi,Vji and pVi,VDi represent the “proximity” of Vi to intervals Vji and VDi, respectively; pVi,VDi>0 denotes that Vi is not in the interval VDi; and pVi,VDi≤0 denotes that Vi is in the interval VDi.(1) Relevance Evaluation. Then,
(11)KjVi=−pVi,Vjivi,Vi∈Vji,pVi,VjipVi,VDi−pVi,Vji,Vi∉Vji.In the formula,KjVi is the correlation between the karst development degree and defined grade.To evaluate objectM, the comprehensive correlation with grade j is as follows:
(12)KjM=∑i=1nωiKjVi,where ωi is the index factor weight calculated using the formula.The evaluation grade can be determined by selecting the maximum value of the comprehensive correlation degree:(13)KSM=maxKjM.


## 2.1. Improved Analytic Hierarchy Process

Determining the weight value of each index factor is the key to evaluate the degree of karst development, and the selection of the most appropriate methodology is crucial for ensuring the accuracy of the identification results. At present, the methods commonly used to determine weights are the analytic hierarchy process and the entropy weight method [25–27].The analytic hierarchy process (AHP) is a practical multicriteria decision-making method. This method can express complex problems in an orderly hierarchical structure and can deal with qualitative and quantitative evaluation indicators in decision-making schemes. The improved AHP uses the three-scale method of the optimal transfer matrix to construct the judgment matrix and calculate the weight. Compared with the standard AHP, it can improve the accuracy and objectivity of the judgment results and greatly enhance the operability.The comparison of the relative importance of selected indicators is the basis for constructing the judgment matrix in the improved AHP. If the former indicator is more important than the latter one, then it is assigned the value of 1. If the former indicator is as important as the latter one, then 0 is taken, and if the latter indicator is more important than the previous one, the value -1 is assigned. The structural judgment matrix is constructed, and the weight of each evaluation index is finally determined [25].Firstly, judgment matrixA is constructed according to the importance of the influencing factors:
(1)A=a11a12⋯a1ja21a22⋯a2j⋯⋯⋯⋯ai1ai2⋯aij,where aij=1 indicates that i is more important than j, aij=0 means that i and j are equally important, and aij=‐1 means that j is more important than i.MatrixR is the optimal transfer matrix for matrix A, and the value of each element in matrix R can be calculated by equation rij=1/n∑k=1naik−ajk=1/n∑k=1naik+akj, where n is the number of evaluation indicators. So, R is
(2)R=r11r12⋯r1jr21r22⋯r2j⋯⋯⋯⋯ri1ri2⋯rij.MatrixD is the judgment matrix for matrix R, and each element value in matrix D can be calculated using equation dij=exprij. So, D is
(3)D=d11d12⋯d1jd21d22⋯d2j⋯⋯⋯⋯di1di2⋯dij.Weightωi of a single indicator factor can be calculated using Equation (4) according to each element value in matrix D:
(4)ωi=∐k=1ndikn∑k=1n∐k=1ndikn.


## 2.2. Extension Matter Element Model

### 2.2.1. Basic Theory

Everything has its own unique properties, and each differs from other things. The extension matter element theory [25, 26] is a new theory that describes the internal structural relationship and attribute changes for things. If M is the thing described, then C is a feature of thing M and V is the magnitude of feature C. Thus, the matter element matrix for the thing is
(5)R=M,C,V.In general, a thing has many characteristics, and the matrix of matter elements withn features is
(6)R=M,C1,C2,⋮Cn,V1,V2,⋮Vn,=R1R2⋮Rn,where Ri=M,Ci,Vi,i=1,2,⋯,n.


### 2.2.2. Model Establishment

Assuming thatn factors affect karst development, then the degree of karst development can be divided into H grades. The matter element matrix of grade j can be expressed as
(7)Rj=Mj,C1,C2,⋮Cn,Vj1,Vj2,⋮V,jn=MjC1C2⋮Cn<xj1,yj1><xj2,yj2>⋮<xjn,yjn>,where Rj denotes the matter element matrix when the degree of karst development is grade j, Mj is the jth grade of karst development, and Vji=<xji,yji> denotes the range of values when the first index that affects karst development is grade j, j=1,2,⋯,h, i=1,2,⋯,n.For all levels ofh, the nodal matter element matrix comprising the allowable range for each index factor is as follows:
(8)RD=D,C,VD=DC1C2⋮Cn<xD1,yD1><xD2,yD2>⋮<xDn,yDn>,where RD represents the nodal matter element matrix of the karst development degree, D is the set of karst development degree grades, and VDi=<xDi,yDi> is the allowable range of index factor Ci in D. Vji∈VDi, j=1,2,⋯,h, i=1,2,⋯,n.


### 2.2.3. Extension Material Evaluation

2.2.3.1. Definition of Proximity. For the evaluated things expressed by Equation (6), let
(9)pVi,Vji=Vi−xji+yji2−12yji−xji,(10)pVi,VDi=Vi−xDi+yDi2−12yDi−xDi.In the formula,Vi is the measure of the evaluation index factor; pVi,Vji and pVi,VDi represent the “proximity” of Vi to intervals Vji and VDi, respectively; pVi,VDi>0 denotes that Vi is not in the interval VDi; and pVi,VDi≤0 denotes that Vi is in the interval VDi.(1) Relevance Evaluation. Then,
(11)KjVi=−pVi,Vjivi,Vi∈Vji,pVi,VjipVi,VDi−pVi,Vji,Vi∉Vji.In the formula,KjVi is the correlation between the karst development degree and defined grade.To evaluate objectM, the comprehensive correlation with grade j is as follows:
(12)KjM=∑i=1nωiKjVi,where ωi is the index factor weight calculated using the formula.The evaluation grade can be determined by selecting the maximum value of the comprehensive correlation degree:(13)KSM=maxKjM.


## 2.2.1. Basic Theory

Everything has its own unique properties, and each differs from other things. The extension matter element theory [25, 26] is a new theory that describes the internal structural relationship and attribute changes for things. If M is the thing described, then C is a feature of thing M and V is the magnitude of feature C. Thus, the matter element matrix for the thing is
(5)R=M,C,V.In general, a thing has many characteristics, and the matrix of matter elements withn features is
(6)R=M,C1,C2,⋮Cn,V1,V2,⋮Vn,=R1R2⋮Rn,where Ri=M,Ci,Vi,i=1,2,⋯,n.


## 2.2.2. Model Establishment

Assuming thatn factors affect karst development, then the degree of karst development can be divided into H grades. The matter element matrix of grade j can be expressed as
(7)Rj=Mj,C1,C2,⋮Cn,Vj1,Vj2,⋮V,jn=MjC1C2⋮Cn<xj1,yj1><xj2,yj2>⋮<xjn,yjn>,where Rj denotes the matter element matrix when the degree of karst development is grade j, Mj is the jth grade of karst development, and Vji=<xji,yji> denotes the range of values when the first index that affects karst development is grade j, j=1,2,⋯,h, i=1,2,⋯,n.For all levels ofh, the nodal matter element matrix comprising the allowable range for each index factor is as follows:
(8)RD=D,C,VD=DC1C2⋮Cn<xD1,yD1><xD2,yD2>⋮<xDn,yDn>,where RD represents the nodal matter element matrix of the karst development degree, D is the set of karst development degree grades, and VDi=<xDi,yDi> is the allowable range of index factor Ci in D. Vji∈VDi, j=1,2,⋯,h, i=1,2,⋯,n.


## 2.2.3. Extension Material Evaluation

2.2.3.1. Definition of Proximity. For the evaluated things expressed by Equation (6), let
(9)pVi,Vji=Vi−xji+yji2−12yji−xji,(10)pVi,VDi=Vi−xDi+yDi2−12yDi−xDi.In the formula,Vi is the measure of the evaluation index factor; pVi,Vji and pVi,VDi represent the “proximity” of Vi to intervals Vji and VDi, respectively; pVi,VDi>0 denotes that Vi is not in the interval VDi; and pVi,VDi≤0 denotes that Vi is in the interval VDi.(1) Relevance Evaluation. Then,
(11)KjVi=−pVi,Vjivi,Vi∈Vji,pVi,VjipVi,VDi−pVi,Vji,Vi∉Vji.In the formula,KjVi is the correlation between the karst development degree and defined grade.To evaluate objectM, the comprehensive correlation with grade j is as follows:
(12)KjM=∑i=1nωiKjVi,where ωi is the index factor weight calculated using the formula.The evaluation grade can be determined by selecting the maximum value of the comprehensive correlation degree:(13)KSM=maxKjM.


## 3. Hydrogeological Characteristics of the Study Domain

### 3.1. Geological Characteristics

The mine No. 13 of the Pingdingshan coalfield (abbreviated as mine No. 13) is located 17 km northeast of Pingdingshan City, in Henan Province, China. At present, Ji15,17 coal seam of Shanxi Formation of Permian is mainly mined (Ji coal for short). The mine is bounded by the normal faults of Xingguosi and Goulifeng on its northwestern and southeastern sides, respectively. Its northeastern side is bounded by the outcrop of the coal seam of the Ji group, and the southwestern side by the contour line of the 800 m floor. The dimensions of the mine are approximately 15 km long and 2.3-5 km wide; the area of the minefield is about 53.6 km2. Currently, the main coal mining is the Shanxi group of the Permian era, which has been divided into the 1st, 2nd, 3rd, and 4th mining area in the plane (as shown in Figure 1). The 1st and 2nd mining areas have both been excavated. The analysis of the actual monitoring data since June 2006 showed that the total mine water inflow in mine No. 13 ranged from 180 to 550 m3/h, with an average of 353.57 m3/h. The underground water inflow values and the mean values in the four mining areas are shown in Table 1.Figure 1
Distribution map of the mining area and geological structure of mine No. 13.Table 1
Undermine water inflow of mine No. 13 (m3/h).
Position
Minimum value
Maximum value
Average value
1st mining area
15
170
43.13
2nd mining area
15
390
168.61
3rd mining area
20
220
114.87
4th mining area
145
190
162.18
The whole mine
180
550
353.57The main structure of mine No. 13 is the southwestern wing of the Xiangjia anticline, while the northwestern part is a monoclinic structure. The southeastern part is affected by the wedging of the Lingwushan syncline and the Baishishan anticline, both of which are accompanied by faults. During the exploration of the minefield, 26 faults were found, which can be divided into five groups according to their direction: A (355°), B (70°), C (45°), D (300°), and E (315°). Among them, the Xiangjia No. 1 normal fault distributes throughout the whole mining area of the mine and blocks the hydraulic connection between the mine and the outside. The Goulifeng normal fault in the 3rd mining area and the Xingguosi, Xiangjia No. 2, and Zhangzhuang normal faults in the 4th mining area also block the hydraulic connection between the mine and the outside. The Xiaxie, Ziyunsi, and Jianggou faults in the 1st and 2nd mining areas and the Rengou, Zhaizhuang, Chendong, Longwangmiao, Shiliuyuan, and Yanzhang normal faults in the 3rd mining area have destroyed the integrity of the limestone aquifer to varying degrees and should have an impact on future mining operations. The geological structure distribution of the mine is shown in Figure1.


### 3.2. Main Aquifer Characteristics

Two main soluble aquifer groups exist in the Ji coal seam floor in the minefield. From bottom to top, the Cambrian limestone (CL for short) karst fissure aquifer group and the Carboniferous Taiyuan group, which is a thin limestone karst fissure aquifer group, are found (Figure2). In general, the soluble aquifer group located on the northwest side of the fourth mining area was shallowly buried, and it was the recharge zone for the karst groundwater. The natural groundwater level was high in the northwest and low in the southeast.Figure 2
Column diagram of the Ji coal floor in mine No. 13.The oolitic limestone of the Cambrian Zhangxia Group and the dolomitic limestone of the Gushan group are 200 m thick and constitute the most developed karst strata in the coalfield. CL was determined in 112 boreholes (including underground exploration and drainage holes; see Table2) in mine No. 13. The thickness of the exposed limestone was 0.55–155 m, and the maximum height of the karst cave was 1.37 m. The unit water inflow of the aquifer is from an indirect water-filling aquifer of the Ji coal floor, and its value is 0.0226 L/(s·m). The water level in the Cambrian aquifer was between −493 m and −650 m, and the water level in the fourth mining area was higher than that in the third mining area.Table 2
The number and depth of hydrogeological boreholes in mining areas.
Mining area
Carboniferous Taiyuan limestone
Cambrian limestone
Quantity (number)
Hole depth (min–max, m)
Quantity (number)
Hole depth (min–max, m)
First
5
79-110
5
151-237
Second
4
95-110
3
145-226
Third
5
75-97.5
35
81-253.5
Fourth
11
48-155
69
80-272.0
Total
25
112There were 25 boreholes (including underground exploration holes and drainage holes; see Table2) in the Carboniferous Taiyuan group limestone and 112 CL boreholes in all of the strata in the Taiyuan group. Exploration data show that the Carboniferous Taiyuan group has a total thickness of about 50-75 m and is composed of limestone, sandstone, mudstone, and coal alternately deposited by sea and land. A total of seven thin layers of limestone, named L1-L7 from top to bottom (Figure 2), are sandwiched within the group, for a total thickness of about 20 m. In order to distinguish the effects of the L1–L7 thin layer of limestone on the Ji coal mine, the L1–L7 limestone was divided into L1–L4 and L5–L7 aquifer groups with a boundary at the Geng20 coal seam. In particular, L1–L4 was the direct water-filled aquifer group in the coal bottom plate, where the water level was between –352 m and –600 m. L5–L7 was the indirect water-filled aquifer in the coal floor, where the water level was between –420 m and –660 m.


### 3.3. Hydrochemical Characteristics

According to the water quality test results for eight L1–L7 limestone water samples and 12 CL groundwater samples, Table 3 shows the main ionic components in the groundwater from different aquifers in mine No. 13. The cations were mainly Na+ and Ca2+, the anions were mainly HCO3– and SO42–, and the water chemical types were all the HCO3·SO4-Na·Ca type. The total dissolved solids did not exceed 1 g/L. The overall trend indicated that the total dissolved solid contents increased as the depth of the aquifer group increased.Table 3
Contents of main ionic components in groundwater in different aquifers of mine No. 13 (mg/L).
Aquifer groups
Main ion content
Total hardness (calculated as CaCO3)
TDS
pH
Na++K+
Ca2+
Mg2+
Cl-
SO42-
HCO3-
L1-L4
90.28
67.90
36.09
46.16
128.29
365.75
318.05
551.60
7.2
L5-L7
103.38
69.38
35.18
55.94
140.15
365.75
318.00
586.91
7.1
CL
169.03
77.82
38.49
88.77
277.95
336.71
352.68
820.42
7.3


## 3.1. Geological Characteristics

The mine No. 13 of the Pingdingshan coalfield (abbreviated as mine No. 13) is located 17 km northeast of Pingdingshan City, in Henan Province, China. At present, Ji15,17 coal seam of Shanxi Formation of Permian is mainly mined (Ji coal for short). The mine is bounded by the normal faults of Xingguosi and Goulifeng on its northwestern and southeastern sides, respectively. Its northeastern side is bounded by the outcrop of the coal seam of the Ji group, and the southwestern side by the contour line of the 800 m floor. The dimensions of the mine are approximately 15 km long and 2.3-5 km wide; the area of the minefield is about 53.6 km2. Currently, the main coal mining is the Shanxi group of the Permian era, which has been divided into the 1st, 2nd, 3rd, and 4th mining area in the plane (as shown in Figure 1). The 1st and 2nd mining areas have both been excavated. The analysis of the actual monitoring data since June 2006 showed that the total mine water inflow in mine No. 13 ranged from 180 to 550 m3/h, with an average of 353.57 m3/h. The underground water inflow values and the mean values in the four mining areas are shown in Table 1.Figure 1
Distribution map of the mining area and geological structure of mine No. 13.Table 1
Undermine water inflow of mine No. 13 (m3/h).
Position
Minimum value
Maximum value
Average value
1st mining area
15
170
43.13
2nd mining area
15
390
168.61
3rd mining area
20
220
114.87
4th mining area
145
190
162.18
The whole mine
180
550
353.57The main structure of mine No. 13 is the southwestern wing of the Xiangjia anticline, while the northwestern part is a monoclinic structure. The southeastern part is affected by the wedging of the Lingwushan syncline and the Baishishan anticline, both of which are accompanied by faults. During the exploration of the minefield, 26 faults were found, which can be divided into five groups according to their direction: A (355°), B (70°), C (45°), D (300°), and E (315°). Among them, the Xiangjia No. 1 normal fault distributes throughout the whole mining area of the mine and blocks the hydraulic connection between the mine and the outside. The Goulifeng normal fault in the 3rd mining area and the Xingguosi, Xiangjia No. 2, and Zhangzhuang normal faults in the 4th mining area also block the hydraulic connection between the mine and the outside. The Xiaxie, Ziyunsi, and Jianggou faults in the 1st and 2nd mining areas and the Rengou, Zhaizhuang, Chendong, Longwangmiao, Shiliuyuan, and Yanzhang normal faults in the 3rd mining area have destroyed the integrity of the limestone aquifer to varying degrees and should have an impact on future mining operations. The geological structure distribution of the mine is shown in Figure1.


## 3.2. Main Aquifer Characteristics

Two main soluble aquifer groups exist in the Ji coal seam floor in the minefield. From bottom to top, the Cambrian limestone (CL for short) karst fissure aquifer group and the Carboniferous Taiyuan group, which is a thin limestone karst fissure aquifer group, are found (Figure2). In general, the soluble aquifer group located on the northwest side of the fourth mining area was shallowly buried, and it was the recharge zone for the karst groundwater. The natural groundwater level was high in the northwest and low in the southeast.Figure 2
Column diagram of the Ji coal floor in mine No. 13.The oolitic limestone of the Cambrian Zhangxia Group and the dolomitic limestone of the Gushan group are 200 m thick and constitute the most developed karst strata in the coalfield. CL was determined in 112 boreholes (including underground exploration and drainage holes; see Table2) in mine No. 13. The thickness of the exposed limestone was 0.55–155 m, and the maximum height of the karst cave was 1.37 m. The unit water inflow of the aquifer is from an indirect water-filling aquifer of the Ji coal floor, and its value is 0.0226 L/(s·m). The water level in the Cambrian aquifer was between −493 m and −650 m, and the water level in the fourth mining area was higher than that in the third mining area.Table 2
The number and depth of hydrogeological boreholes in mining areas.
Mining area
Carboniferous Taiyuan limestone
Cambrian limestone
Quantity (number)
Hole depth (min–max, m)
Quantity (number)
Hole depth (min–max, m)
First
5
79-110
5
151-237
Second
4
95-110
3
145-226
Third
5
75-97.5
35
81-253.5
Fourth
11
48-155
69
80-272.0
Total
25
112There were 25 boreholes (including underground exploration holes and drainage holes; see Table2) in the Carboniferous Taiyuan group limestone and 112 CL boreholes in all of the strata in the Taiyuan group. Exploration data show that the Carboniferous Taiyuan group has a total thickness of about 50-75 m and is composed of limestone, sandstone, mudstone, and coal alternately deposited by sea and land. A total of seven thin layers of limestone, named L1-L7 from top to bottom (Figure 2), are sandwiched within the group, for a total thickness of about 20 m. In order to distinguish the effects of the L1–L7 thin layer of limestone on the Ji coal mine, the L1–L7 limestone was divided into L1–L4 and L5–L7 aquifer groups with a boundary at the Geng20 coal seam. In particular, L1–L4 was the direct water-filled aquifer group in the coal bottom plate, where the water level was between –352 m and –600 m. L5–L7 was the indirect water-filled aquifer in the coal floor, where the water level was between –420 m and –660 m.


## 3.3. Hydrochemical Characteristics

According to the water quality test results for eight L1–L7 limestone water samples and 12 CL groundwater samples, Table 3 shows the main ionic components in the groundwater from different aquifers in mine No. 13. The cations were mainly Na+ and Ca2+, the anions were mainly HCO3– and SO42–, and the water chemical types were all the HCO3·SO4-Na·Ca type. The total dissolved solids did not exceed 1 g/L. The overall trend indicated that the total dissolved solid contents increased as the depth of the aquifer group increased.Table 3
Contents of main ionic components in groundwater in different aquifers of mine No. 13 (mg/L).
Aquifer groups
Main ion content
Total hardness (calculated as CaCO3)
TDS
pH
Na++K+
Ca2+
Mg2+
Cl-
SO42-
HCO3-
L1-L4
90.28
67.90
36.09
46.16
128.29
365.75
318.05
551.60
7.2
L5-L7
103.38
69.38
35.18
55.94
140.15
365.75
318.00
586.91
7.1
CL
169.03
77.82
38.49
88.77
277.95
336.71
352.68
820.42
7.3


## 4. Evaluation of the Degree of Karst Development

### 4.1. Evaluation Index

The occurrence and development of karst are controlled mainly by the geological conditions, hydrogeological conditions, and water chemistry conditions. The geological conditions mainly include the formation lithology, rock thickness, burial depth, and geological structure; the hydrogeological conditions mainly comprise the hydrodynamic cycle characteristics; and the main water chemistry component is the free CO2 content of the groundwater.Based on previous results and the information for mine No. 13, we selected five indicators comprising the limestone lithology, limestone thickness, burial depth, geological structure, and water circulation capacity in order to evaluate the degree of karst development.The analysis of the 25 Carboniferous Taiyuan group boreholes and the 112 CL boreholes in mine No. 13 (Table2) showed that the mineral composition of the L1–L4 limestone was mainly limestone, whereas that of the L5–L7 limestone was mainly dolomitic limestone, and that of the CL was mainly dolomitic and oolitic limestone. Under the same conditions, homogeneous limestone is more prone to dissolution, so the L1–L4 thin limestone was vulnerable to dissolution. The dissolution rate under the action of a water flow will be faster when the limestone is thicker, and thus, the dissolution rate was faster in the CL. The overlying rock and the density of limestone are lower when the burial depth is shallower. Thus, the shallow L1–L7 limestone at the same location was more conducive to the occurrence of dissolution than the CL.The geological tectonic properties and developmental degree have important effects on the flow of groundwater and the storage of CO2 in limestone, thereby controlling the rate of dissolution.Limestone is dissolved more readily when the groundwater circulation capacity is stronger. Therefore, the fourth mining area located in the recharge zone of the soluble aquifer group was more vulnerable to the occurrence and development of dissolution than the other mining areas.The dissolution of limestone is stronger when the free CO2 content of groundwater is higher. The current L1–L7 limestone borehole collapsed due to mining, so it was not possible to extract a water sample to test the free CO2 content. Therefore, the free CO2 content was not employed as an index factor for evaluating the karst development degree in this study.In addition, a previous study [22] evaluated the degree of karst development by using the limestone water-richness as one of the indicators. The main factors that affect water-rich limestone are considered to be the limestone lithology, geological structure, and water cycle capacity, and thus, these factors were used as evaluation factors. Therefore, the water from the water-rich limestone was not used as an evaluation index factor.


### 4.2. Index Grading and Quantification

According to a previous study [15] and the actual situation in mine No. 13, the karst development degree was divided into five grades: no development = I, weak development = II, moderate development = III, high development = IV, and very high development = V. The characteristics of the evaluation index factors corresponding to the five grades were determined via the hydrogeological boreholes, and the results are shown in Table 4.Table 4
Classification of evaluation indexes for the karst development degree.
Index factor
Characteristic and assignment
Index level
A (I)
B (II)
C (III)
D (IV)
E (V)
Limestone lithology
Feature
①
②
③
④
⑤
Definition
Insoluble
Microsoluble
Relatively soluble
Soluble
Highly soluble
Assignment
1
2
3
4
5
Limestone thickness (m)
Feature
0-5
5-10
10-30
30-100
>100
Definition
Thin
Slightly thick
Medium thick
Thick
Extremely thick
Buried depth (m)
Feature
>1200
900-1200
600-900
300-600
<300
Definition
Extremely deep
Deep
Medium depth
Shallow
Very shallow
Hydrodynamic cycle
Feature
Confined water zone with slightly varying water level
Confined water zone with seasonal variation of water level
Confined water zone with annual water level change
Diving belt
Water-air mixing zone
Definition
Disadvantageous
Slightly advantageous
Relatively advantageous
Advantageous
Extremely advantageous
Assignment
1
2
3
4
5
Geological structure
Feature
Small faults or folds
Compressive faults or small folds
Compression-torsion fault or fold wing
Tensile faults or anticlinal axes or fold turning points
Tension-torsion fault or syncline axis
Definition
No development
Weak development
Relative development
Development
Extreme development
Assignment
1
2
3
4
5
Remarks: (1) A: not conducive to karst development; B: slightly favorable to karst development; C: relatively favorable for karst development; D: conducive to karst development; E: highly conducive to karst development. (2) ①: nonuniform marl, metamorphic carbonate rock; ②: uniform marl, nonuniform oolitic limestone; ③: uniform oolitic limestone, nonuniform dolomitic limestone; ④: uniform dolomitic limestone, nonuniform limestone, ⑤: uniform limestone.In order to facilitate quantitative analyses, five evaluation index factors were quantitatively assigned. The assignment method involved allocating three qualitative index factors (limestone lithology, geological structure, and water cycle conditions) with values from 1 to 5 according to the matching level (I–V). The rock thickness and burial depth were the actual measurements obtained from the boreholes, as shown in Table4.Based on the differences in karst development in the planar and vertical directions, mine No. 13 was divided into four mining areas in the planar direction, i.e., first, second, third, and fourth mining areas, and three aquifer groups in the vertical direction, i.e., L1–L4, L5–L7, and CL. The characteristics and values quantified for the evaluation index factors in each aquifer group in the different mining areas are shown in Table 5.Table 5
Quantitative evaluation index values for the degree of karst development.
Aquifer groups
Mining areas
Evaluation index
Limestone lithology
Limestone thickness
Buried depth
Hydrodynamic cycle
Geological structure
Nature
Quantitative value
Assignment
Assignment
Nature
Assignment
Nature
Assignment
L1-L4
First
Inhomogeneous limestone
4
15.8
425.8
Confined water zone with annual water level change
3
Fold wing
3
Second
Inhomogeneous limestone
4
21.2
501.2
Confined water zone with annual water level change
3
Tensile fault
4
Third
Uniform limestone
5
15.8
780.0
Water-air mixing zone
5
Superposition of anticline axis and fault
5
Fourth
Uniform limestone
5
22.2
371.3
Water-air mixing zone
5
Superposition of anticline axis and fault
5
L5-L7
First
Inhomogeneous dolomitic limestone
3
23.5
472.5
Confined water zone with seasonal variation of water level
2
Extension of folded wing
2
Second
Inhomogeneous dolomitic limestone
3
30.1
650.5
Confined water zone with slightly varying water level
1
Minor fault
2
Third
Uniform dolomitic limestone
4
19.8
812.3
Confined water zone with annual water level change
3
Axis extension of folds
2
Fourth
Uniform dolomitic limestone
4
27.7
428.3
Water-air mixing zone
5
Superposition of anticline axis and fault
4
CL
First
Inhomogeneous dolomitic limestone
3
120.0
636.0
Confined water zone with slightly varying water level
1
Extension of folded wing
2
Second
Inhomogeneous dolomitic limestone
3
155.0
840.0
Confined water zone with slightly varying water level
1
Microfault
1
Third
Uniform oolitic limestone
3
138.0
961.0
Confined water zone with seasonal variation of water level
2
Compressive fault
2
Fourth
Uniform dolomitic limestone
4
139.0
594.2
Confined water zone with annual water level change
3
Small fold belt
2The evaluation grade can be defined by choosing the maximum level of the comprehensive correlation degree calculated following equation (12) of the improved AHP multidimensional extension matter element model.


### 4.3. Index Weight

According to the complexity and particularity of geological structure in mine No. 13, and referring to expert opinions [28], the indexes for evaluating the degree of karst development are sorted by order of importance: limestone lithology (C1), limestone thickness (C2), burial depth (C3), water circulation capacity (C4), and geological structure (C5).Substituting the matrix elements by valueC1 to C5, judgment matrix A is constructed as follows:
(14)A=01101−101−11−1−10−1−10−11−1110−110.Using the improved AHP formula (4), the weight values of each index can be obtained:
(15)ω=C1C2C3C4C5=0.31610.07800.17350.31610.1163.


### 4.4. Evaluation of Karst Development

The karst development degree was evaluated by considering the first mining area and the L1–L4 aquifer group as an example.


#### 4.4.1. Matter Element Matrix and Nodal Domain Matrix

The degree of karst development can be divided into five grades, and the matter element matrix of each grade is as follows:(16)R1=M1C1C2C3C4C5<0,1><0,5><1200,1500><0,1><0,1>,R2=M2C1C2C3C4C5<1,2><5,10><900,1200><1,2><1,2>,R3=M3C1C2C3C4C5<2,3><10,30><600,900><2,3><2,3>,R4=M4C1C2C3C4C5<3,4><30,100><300,600><3,4><3,4>,R5=M5C1C2C3C4C5<4,5><100,200><0,300><4,5><4,5>.Following formula (8) and using the 5 Ri matrices as input, the nodal matter element matrix is
(17)RD=DC1C2C3C4C5<0,5><0,200><0,1500><0,5><0,5>.Based on formula (6), the matrix of matter elements to be evaluated is constructed as follows:
(18)R=MC1C2C3C4C5415.18425.833.


#### 4.4.2. Evaluation of Results

According to formulas (9), (10), and (11), the correlation between the karst development and definition grade (I-V) can be evaluated as follows:
(19)K=KjVi=−0.7500−0.6667−0.50000.00000.0000−0.4060−0.26850.3671−0.4733−0.8480−0.7161−0.6452−0.5269−0.2903−0.5000−0.5000−0.5000−0.3333−0.33330.00000.00000.00000.0000−0.3333−0.3333.The comprehensive correlation degree is(20)KjM=∑i=15ωiKjVi=−0.6092−0.4877−0.2208−0.0873−0.2966,which is K1=−0.6092, K2M=−0.4877, K3M=−0.2208, K4M=−0.0873, and K5M=−0.2966; then,
(21)KsM=maxKjM=K4M=−0.0873.The maximum value of the comprehensive correlation degree is selected to define the evaluation grade, yielding a karst development level IV for the L1-L4 aquifer group in the 1st mining area of mine No. 13.Similarly, the degree of karst development of other mining areas in L1-L4 limestone aquifer group can be defined, as shown in Table 6. The karst development evaluation results for the L5–L7 and CL aquifer groups in different mining areas are shown in Table 6.Table 6
Degree of karst development of different aquifer groups in mine No. 13.
Aquifer groups
Mining areas
Evaluation grade
Definition
Quantization value
Assignment
Average
L1-L4
First
IV
Development
4
4.5
Second
IV
Development
4
Third
V
Extreme development
5
Fourth
V
Extreme development
5
L5-L7
First
III
Relative development
3
3.75
Second
III
Relative development
3
Third
IV
Development
4
Fourth
V
Extreme development
5
CL
First
II
Weak development
2
2.75
Second
II
Weak development
2
Third
III
Relative development
3
Fourth
IV
Development
4


## 4.1. Evaluation Index

The occurrence and development of karst are controlled mainly by the geological conditions, hydrogeological conditions, and water chemistry conditions. The geological conditions mainly include the formation lithology, rock thickness, burial depth, and geological structure; the hydrogeological conditions mainly comprise the hydrodynamic cycle characteristics; and the main water chemistry component is the free CO2 content of the groundwater.Based on previous results and the information for mine No. 13, we selected five indicators comprising the limestone lithology, limestone thickness, burial depth, geological structure, and water circulation capacity in order to evaluate the degree of karst development.The analysis of the 25 Carboniferous Taiyuan group boreholes and the 112 CL boreholes in mine No. 13 (Table2) showed that the mineral composition of the L1–L4 limestone was mainly limestone, whereas that of the L5–L7 limestone was mainly dolomitic limestone, and that of the CL was mainly dolomitic and oolitic limestone. Under the same conditions, homogeneous limestone is more prone to dissolution, so the L1–L4 thin limestone was vulnerable to dissolution. The dissolution rate under the action of a water flow will be faster when the limestone is thicker, and thus, the dissolution rate was faster in the CL. The overlying rock and the density of limestone are lower when the burial depth is shallower. Thus, the shallow L1–L7 limestone at the same location was more conducive to the occurrence of dissolution than the CL.The geological tectonic properties and developmental degree have important effects on the flow of groundwater and the storage of CO2 in limestone, thereby controlling the rate of dissolution.Limestone is dissolved more readily when the groundwater circulation capacity is stronger. Therefore, the fourth mining area located in the recharge zone of the soluble aquifer group was more vulnerable to the occurrence and development of dissolution than the other mining areas.The dissolution of limestone is stronger when the free CO2 content of groundwater is higher. The current L1–L7 limestone borehole collapsed due to mining, so it was not possible to extract a water sample to test the free CO2 content. Therefore, the free CO2 content was not employed as an index factor for evaluating the karst development degree in this study.In addition, a previous study [22] evaluated the degree of karst development by using the limestone water-richness as one of the indicators. The main factors that affect water-rich limestone are considered to be the limestone lithology, geological structure, and water cycle capacity, and thus, these factors were used as evaluation factors. Therefore, the water from the water-rich limestone was not used as an evaluation index factor.


## 4.2. Index Grading and Quantification

According to a previous study [15] and the actual situation in mine No. 13, the karst development degree was divided into five grades: no development = I, weak development = II, moderate development = III, high development = IV, and very high development = V. The characteristics of the evaluation index factors corresponding to the five grades were determined via the hydrogeological boreholes, and the results are shown in Table 4.Table 4
Classification of evaluation indexes for the karst development degree.
Index factor
Characteristic and assignment
Index level
A (I)
B (II)
C (III)
D (IV)
E (V)
Limestone lithology
Feature
①
②
③
④
⑤
Definition
Insoluble
Microsoluble
Relatively soluble
Soluble
Highly soluble
Assignment
1
2
3
4
5
Limestone thickness (m)
Feature
0-5
5-10
10-30
30-100
>100
Definition
Thin
Slightly thick
Medium thick
Thick
Extremely thick
Buried depth (m)
Feature
>1200
900-1200
600-900
300-600
<300
Definition
Extremely deep
Deep
Medium depth
Shallow
Very shallow
Hydrodynamic cycle
Feature
Confined water zone with slightly varying water level
Confined water zone with seasonal variation of water level
Confined water zone with annual water level change
Diving belt
Water-air mixing zone
Definition
Disadvantageous
Slightly advantageous
Relatively advantageous
Advantageous
Extremely advantageous
Assignment
1
2
3
4
5
Geological structure
Feature
Small faults or folds
Compressive faults or small folds
Compression-torsion fault or fold wing
Tensile faults or anticlinal axes or fold turning points
Tension-torsion fault or syncline axis
Definition
No development
Weak development
Relative development
Development
Extreme development
Assignment
1
2
3
4
5
Remarks: (1) A: not conducive to karst development; B: slightly favorable to karst development; C: relatively favorable for karst development; D: conducive to karst development; E: highly conducive to karst development. (2) ①: nonuniform marl, metamorphic carbonate rock; ②: uniform marl, nonuniform oolitic limestone; ③: uniform oolitic limestone, nonuniform dolomitic limestone; ④: uniform dolomitic limestone, nonuniform limestone, ⑤: uniform limestone.In order to facilitate quantitative analyses, five evaluation index factors were quantitatively assigned. The assignment method involved allocating three qualitative index factors (limestone lithology, geological structure, and water cycle conditions) with values from 1 to 5 according to the matching level (I–V). The rock thickness and burial depth were the actual measurements obtained from the boreholes, as shown in Table4.Based on the differences in karst development in the planar and vertical directions, mine No. 13 was divided into four mining areas in the planar direction, i.e., first, second, third, and fourth mining areas, and three aquifer groups in the vertical direction, i.e., L1–L4, L5–L7, and CL. The characteristics and values quantified for the evaluation index factors in each aquifer group in the different mining areas are shown in Table 5.Table 5
Quantitative evaluation index values for the degree of karst development.
Aquifer groups
Mining areas
Evaluation index
Limestone lithology
Limestone thickness
Buried depth
Hydrodynamic cycle
Geological structure
Nature
Quantitative value
Assignment
Assignment
Nature
Assignment
Nature
Assignment
L1-L4
First
Inhomogeneous limestone
4
15.8
425.8
Confined water zone with annual water level change
3
Fold wing
3
Second
Inhomogeneous limestone
4
21.2
501.2
Confined water zone with annual water level change
3
Tensile fault
4
Third
Uniform limestone
5
15.8
780.0
Water-air mixing zone
5
Superposition of anticline axis and fault
5
Fourth
Uniform limestone
5
22.2
371.3
Water-air mixing zone
5
Superposition of anticline axis and fault
5
L5-L7
First
Inhomogeneous dolomitic limestone
3
23.5
472.5
Confined water zone with seasonal variation of water level
2
Extension of folded wing
2
Second
Inhomogeneous dolomitic limestone
3
30.1
650.5
Confined water zone with slightly varying water level
1
Minor fault
2
Third
Uniform dolomitic limestone
4
19.8
812.3
Confined water zone with annual water level change
3
Axis extension of folds
2
Fourth
Uniform dolomitic limestone
4
27.7
428.3
Water-air mixing zone
5
Superposition of anticline axis and fault
4
CL
First
Inhomogeneous dolomitic limestone
3
120.0
636.0
Confined water zone with slightly varying water level
1
Extension of folded wing
2
Second
Inhomogeneous dolomitic limestone
3
155.0
840.0
Confined water zone with slightly varying water level
1
Microfault
1
Third
Uniform oolitic limestone
3
138.0
961.0
Confined water zone with seasonal variation of water level
2
Compressive fault
2
Fourth
Uniform dolomitic limestone
4
139.0
594.2
Confined water zone with annual water level change
3
Small fold belt
2The evaluation grade can be defined by choosing the maximum level of the comprehensive correlation degree calculated following equation (12) of the improved AHP multidimensional extension matter element model.


## 4.3. Index Weight

According to the complexity and particularity of geological structure in mine No. 13, and referring to expert opinions [28], the indexes for evaluating the degree of karst development are sorted by order of importance: limestone lithology (C1), limestone thickness (C2), burial depth (C3), water circulation capacity (C4), and geological structure (C5).Substituting the matrix elements by valueC1 to C5, judgment matrix A is constructed as follows:
(14)A=01101−101−11−1−10−1−10−11−1110−110.Using the improved AHP formula (4), the weight values of each index can be obtained:
(15)ω=C1C2C3C4C5=0.31610.07800.17350.31610.1163.


## 4.4. Evaluation of Karst Development

The karst development degree was evaluated by considering the first mining area and the L1–L4 aquifer group as an example.


### 4.4.1. Matter Element Matrix and Nodal Domain Matrix

The degree of karst development can be divided into five grades, and the matter element matrix of each grade is as follows:(16)R1=M1C1C2C3C4C5<0,1><0,5><1200,1500><0,1><0,1>,R2=M2C1C2C3C4C5<1,2><5,10><900,1200><1,2><1,2>,R3=M3C1C2C3C4C5<2,3><10,30><600,900><2,3><2,3>,R4=M4C1C2C3C4C5<3,4><30,100><300,600><3,4><3,4>,R5=M5C1C2C3C4C5<4,5><100,200><0,300><4,5><4,5>.Following formula (8) and using the 5 Ri matrices as input, the nodal matter element matrix is
(17)RD=DC1C2C3C4C5<0,5><0,200><0,1500><0,5><0,5>.Based on formula (6), the matrix of matter elements to be evaluated is constructed as follows:
(18)R=MC1C2C3C4C5415.18425.833.


### 4.4.2. Evaluation of Results

According to formulas (9), (10), and (11), the correlation between the karst development and definition grade (I-V) can be evaluated as follows:
(19)K=KjVi=−0.7500−0.6667−0.50000.00000.0000−0.4060−0.26850.3671−0.4733−0.8480−0.7161−0.6452−0.5269−0.2903−0.5000−0.5000−0.5000−0.3333−0.33330.00000.00000.00000.0000−0.3333−0.3333.The comprehensive correlation degree is(20)KjM=∑i=15ωiKjVi=−0.6092−0.4877−0.2208−0.0873−0.2966,which is K1=−0.6092, K2M=−0.4877, K3M=−0.2208, K4M=−0.0873, and K5M=−0.2966; then,
(21)KsM=maxKjM=K4M=−0.0873.The maximum value of the comprehensive correlation degree is selected to define the evaluation grade, yielding a karst development level IV for the L1-L4 aquifer group in the 1st mining area of mine No. 13.Similarly, the degree of karst development of other mining areas in L1-L4 limestone aquifer group can be defined, as shown in Table 6. The karst development evaluation results for the L5–L7 and CL aquifer groups in different mining areas are shown in Table 6.Table 6
Degree of karst development of different aquifer groups in mine No. 13.
Aquifer groups
Mining areas
Evaluation grade
Definition
Quantization value
Assignment
Average
L1-L4
First
IV
Development
4
4.5
Second
IV
Development
4
Third
V
Extreme development
5
Fourth
V
Extreme development
5
L5-L7
First
III
Relative development
3
3.75
Second
III
Relative development
3
Third
IV
Development
4
Fourth
V
Extreme development
5
CL
First
II
Weak development
2
2.75
Second
II
Weak development
2
Third
III
Relative development
3
Fourth
IV
Development
4


## 4.4.1. Matter Element Matrix and Nodal Domain Matrix

The degree of karst development can be divided into five grades, and the matter element matrix of each grade is as follows:(16)R1=M1C1C2C3C4C5<0,1><0,5><1200,1500><0,1><0,1>,R2=M2C1C2C3C4C5<1,2><5,10><900,1200><1,2><1,2>,R3=M3C1C2C3C4C5<2,3><10,30><600,900><2,3><2,3>,R4=M4C1C2C3C4C5<3,4><30,100><300,600><3,4><3,4>,R5=M5C1C2C3C4C5<4,5><100,200><0,300><4,5><4,5>.Following formula (8) and using the 5 Ri matrices as input, the nodal matter element matrix is
(17)RD=DC1C2C3C4C5<0,5><0,200><0,1500><0,5><0,5>.Based on formula (6), the matrix of matter elements to be evaluated is constructed as follows:
(18)R=MC1C2C3C4C5415.18425.833.


## 4.4.2. Evaluation of Results

According to formulas (9), (10), and (11), the correlation between the karst development and definition grade (I-V) can be evaluated as follows:
(19)K=KjVi=−0.7500−0.6667−0.50000.00000.0000−0.4060−0.26850.3671−0.4733−0.8480−0.7161−0.6452−0.5269−0.2903−0.5000−0.5000−0.5000−0.3333−0.33330.00000.00000.00000.0000−0.3333−0.3333.The comprehensive correlation degree is(20)KjM=∑i=15ωiKjVi=−0.6092−0.4877−0.2208−0.0873−0.2966,which is K1=−0.6092, K2M=−0.4877, K3M=−0.2208, K4M=−0.0873, and K5M=−0.2966; then,
(21)KsM=maxKjM=K4M=−0.0873.The maximum value of the comprehensive correlation degree is selected to define the evaluation grade, yielding a karst development level IV for the L1-L4 aquifer group in the 1st mining area of mine No. 13.Similarly, the degree of karst development of other mining areas in L1-L4 limestone aquifer group can be defined, as shown in Table 6. The karst development evaluation results for the L5–L7 and CL aquifer groups in different mining areas are shown in Table 6.Table 6
Degree of karst development of different aquifer groups in mine No. 13.
Aquifer groups
Mining areas
Evaluation grade
Definition
Quantization value
Assignment
Average
L1-L4
First
IV
Development
4
4.5
Second
IV
Development
4
Third
V
Extreme development
5
Fourth
V
Extreme development
5
L5-L7
First
III
Relative development
3
3.75
Second
III
Relative development
3
Third
IV
Development
4
Fourth
V
Extreme development
5
CL
First
II
Weak development
2
2.75
Second
II
Weak development
2
Third
III
Relative development
3
Fourth
IV
Development
4


## 5. Discussion

The defined karst development levels were quantitatively evaluated to facilitate their description, where the value of level I was assigned as 1, the value of level II as 2, the value of level III as 3, the value of level IV as 4, and the value of level V as 5. Quantitative evaluation of karst development in different mining areas of the same aquifer group is shown in Table6 and Figure 3. Obviously, the degree of development of L1-L4 karst in the Carboniferous Taiyuan group belongs to grade IV-V with an average quantitative value of 4.5, and that of L5-L7 in the Taiyuan group belongs to grade III-V with an average quantitative value of 3.75, while the CL belongs to grade II-IV and has an average quantitative value of 2.75. This means that the degree of karst development decreases from the shallow L1-L4 to L5-L7 and then to the deep CL. This decrease of the degree of development with increased depth can be explained by the typical attributes of a shallow layer because the burial depth of the rock layer is shallow, atmospheric rainfall is more easily assimilated, Quaternary groundwater recharge occurs, and the speed of the groundwater circulation is fast, leading the degree of karst development to be relatively high. In addition, for a shallow stratum burial depth, the load of the upper strata is smaller, and the lithology loose, which also leads to the smooth movement of groundwater.Figure 3
Diagrammatic drawing for quantitative evaluation of karst development.The quantitative assignment of the karst development degree in different aquifer groups in the same mining area is shown in Table7. Obviously, the degree of karst development of the 1st and 2nd mining areas belongs to grade II-IV and has an average quantitative value of 3.0, whereas the development degree of the 3rd mining area is grade III-V, with an average quantitative value of 4.0. Lastly, the 4th mining area has a grade IV-V development degree, with an average quantitative value of 4.7, i.e., the level of karst development in the mining area of mine No. 13 is the highest in 4th, followed by 3rd, and then 1st and 2nd. This is mainly caused by the geological structure of the 1st and 2nd mining areas being weaker than that of the 3rd and 4th mining areas (as shown in Figure 1). The degree of karst development in the 4th mining area is the highest because the limestone aquifer is relatively shallow. The degree of karst development of the 1st and 2nd mining areas is similar as this mining area was artificially divided for the sake of mining management, although their geological and hydrogeological conditions are similar.Table 7
Degree of karst development in different mining areas of mine No. 13.
Mining areas
Aquifer groups
Evaluation grade
Definition
Quantization value
Assignment
Average
First
L1-L4
IV
Development
4
3
L5-L7
III
Relative development
3
CL
II
Weak development
2
Second
L1-L4
IV
Development
4
3
L5-L7
III
Relative development
3
CL
II
Weak development
2
Third
L1-L4
V
Extreme development
5
4
L5-L7
IV
Development
4
CL
III
Relative development
3
Fourth
L1-L4
V
Extreme development
5
4.7
L5-L7
V
Extreme development
5
CL
IV
Development
4Due to the lack of detection data, the free CO2 content in the groundwater was not utilized in the evaluations of karst development in this study. However, the water quality analysis results for mine No.8 located adjacent to mine No. 13 (July 14, 2016) showed that the free CO2 content in the CL groundwater was 17.95 mg/L, where this was the water obtained from the mixing of the water from the CL and the L1–L7 limestone. The free CO2 content in the water from the L1–L7 limestone was 15.96 mg/L, and the difference was only 1.99 mg/L. These results indicate that the difference in the free CO2 content between the CL and the L1–L7 limestone groundwater was very small. Therefore, the free CO2 content may have only slightly affected the karst development evaluation results.In contrast to the linear analysis of karst development in a previous study of railway tunnel engineering, we quantitatively evaluated the differences in the karst development degree in the planar and vertical directions. Our results provide a useful reference method for similar research, and they have important practical significance for guiding the prevention and control of floor water hazards similar to that found in mine No. 13 in Ji coal.


## 6. Conclusion

(1)
Based on the improved analytic hierarchy process (AHP) and the use of the multidimensional extension matter element model, five factors, including limestone lithology, limestone thickness, burial depth, hydrodynamic cycle, and geological structure, were selected to quantitatively evaluate the karst development degree of the Pingdingshan coalfield mine No. 13. This provided a reference method for objectively and clearly evaluating the degree of development of limestone karst
(2)
The karst development of mine No. 13 shows large horizontal differences. The 1st and 2nd mining areas have a grade II-IV karst development with an average quantification value of 3.0. The grade of the 3rd mining area is III-V, with an average quantization value of 4.0, and the 4th mining area belongs to grade IV-V, for an average quantization value of 4.7. That is, the degree of karst development of the 4th mining area is the highest overall, followed by the 3rd mining area, whereas the 1st and 2nd mining areas are the least developed
(3)
The karst development of mine No. 13 is stratified in the vertical direction, reaching grades IV-V (average quantitative value of 4.5), III-V (average quantitative value of 3.75), and II-IV (average quantitative value of 2.75) for the L1-L4 in the Taiyuan Carboniferous group, the L5-L7, and the CL, respectively. That is, the degree of karst development gradually decreases from shallow to deep levels



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*Source: 5093237-2019-12-06.xml*