Study on evaluation index system of sustainable development of mine water resources based on PSO-AHP model and fuzzy comprehensive evaluation

Abstract

Water resources is an important basic energy. The determination of weights is one of the important indexes in water resources evaluation system and reasonable allocation of weights is the key to quantitative evaluation. In order to establish a scientific evaluation index system of the influence of mining disturbance on water resources for purpose of a more reliable and effective evaluation result and realizing the protection of water resources system, a comprehensive evaluation system of water resources based on PSO-AHP model is proposed in the paper. Combined with the specific geological environment characteristics of mines, this paper establishes a four-level evaluation index system after identifying the factors affecting water resources and ecological environment. By applying the particle swarm optimization (PSO) to the analytic hierarchy process (AHP) and fuzzy comprehensive evaluation method, a PSO-AHP model and then a fitness function are constructed to solve and optimize the weight values in the evaluation index system, and the calculated weight values are checked by consistency checking method. The evaluation results suggest that the index system can accurately reflect the impact of mining on water resources and water ecological environment and etc., providing certain reference value for sewage resourcing and reducing the harmful effect on environment by sewage discharge.

Keywords

Water resources ecologically vulnerable area particle swarm optimization analytic hierarchy process fuzzy comprehensive evaluation method

1 Introduction

China is a country with serious drought and water shortage and the coal resources is rich whose output has consistently ranked first in the world for many years. Some experts believe that in the next half century, coal consumption will still account for more than half of primary energy consumption [1]. Therefore, coal resources are the energy necessary for China’s social development, and the important role of coal resources in China’s energy resources will not change [2].

With the continuous exploitation of coal resources, the overlying strata of the coal seam subsided to the coal goaf, successively forming caving zone, fractured zone and continuous deformation zone in the vertical space [3]. When the water flowing fractured zone is destroyed to the upper water-resisting layer, it will lead to the groundwater flowing into the pit through the newly-formed water-conductive fissure [4, 5]. In order to ensure normal mining conditions, measures such as mine drainage [6] and depressurization as well as drainage of mine wastewater [7] shall be taken to reduce the impact of continuous groundwater from the roadway and the mining surface on the mine production [8]. The free drainage of the coal aquifers and the loss of the quaternary aquifers caused by the artificial drainage and water flowing fracture formed by mining have severely damaged the underground and surface water resources, making shortage of water resources in Northwest China more prominent [9].

2 State of the art

The relationship between coal resources and water resources is dynamic [10]. Before the exploitation of coal resources, both are two kinds of natural resources that co-existed in a certain area and there’s no contradiction or coordination between them [11]. However, with the exploitation of coal resources, the coal mining system and the water resources ecosystem will be interrelated and affect each other [12].

2.1 Impact of coal mining on water resources system

The research on the impact and damage of coal resource mining on the ecological environment of local water resources can be divided into macro impact and micro impact. At the macro level, some scholars have considered the impact of coal resource mining on the regional water resources circulation system, while others have estimated the impact on the total amount of regional water resources or the impact of total pollution, focusing on the “quantity” estimation and research. There are few studies on this field, mainly because it’s difficult to obtain data, and the estimation accuracy is affected by the credibility and efficiency of the original data. At the micro level, the main consideration is the damage and pollution of water resources caused by coal mining. The research focuses on the pollution mechanism of water resources, that is, the “quality” impact.

The impact of coal mining on groundwater mainly includes two aspects: (1) The occurrence environment of groundwater affected by the mining process, which means the damage of overlying strata caused by mining, including deformation and fissures, further resulted in leakage and seepage of groundwater. See Fig. 1 for structural variation of natural coal-measure aquifer system driven by coal. (2) Inevitably pollution of mechanical equipment, personnel and others for underground mining to the underground ecological environment, especially to the groundwater. Of which, part of the gas and liquid enters the groundwater circulation system directly through rock cracks and gaps, and the other part enters the groundwater circulation system through the water source that supplies groundwater, including the infiltration through aeration zone, direct injection through tunnels, lateral infiltration of surface water bodies, and vertical leakage between aquifers, geological structure and so on.

Fig. 1

Structural Variation of Natural Coal-measure Aquifer System Driven by Coal.

The impact of coal mining on surface water also includes two aspects: (1) changes (deformation) of rock structure caused by large-scale coal mining will result in changes of surface water occurrence environment, which may cause loss or transfer of surface water; (2) Pollution and damage of surface water caused by surface production activities, and pollution of surface water system caused by underground discharge. The latter includes the pollutants carried by the underground drainage water entering the surface water circulation system, the pollutants discharged from the production and daily life of the ground industrial zone entering the surface water circulation system, and the harmful substances of the ground gangue dump during rainy day entering the surface water.

2.2 Impact of water resources system on coal mining

Similar to most industrial production activities, the mining of coal resources requires the consumption and utilization of water resources. The consumption of water resources mainly distributes in: water sprinkling for dust prevention during underground production, water consumption in coal washing plants, and water used for ground washing. However, unlike other industrial productions, the mine water needed during the underground mining process is generally greater than the demand for water resources in coal mine production. In other words, the total water resources in the coal production process have less restriction on the coal production itself. Therefore, the restriction of water resources on the production of coal resources is mainly reflected in the restriction on industrial production activities. The extreme case is the damage to industrial production activities caused by floods, which threatens the safety of human life. At present, the flood disasters in coal mine areas mainly include: water bursting and flooding in mine, roof flooding, water accumulation in roadways and goaf. Of which, water bursting and flooding in mine is the worst. Once such accident occurs, it will result in extensive damage, even system collapse, to the coal resource production system.

3 Methodology

The determination of weight is an important part of comprehensive evaluation, and the rationality of the determination directly affects the scientificity and reliability of the comprehensive evaluation results. Reasonable allocation of weights is the key to quantitative evaluation. Common weight determination methods include analytic hierarchy process (AHP), expert consultation (Delphi), and fuzzy cluster analysis and so on. As the actual comprehensive evaluation often lacks sample data, and most of the indicators are qualitative, the commonly used weight determination method is the AHP method. The AHP method is a multi-objective or multi-scheme decision-making method that combines qualitative and quantitative methods. When determining weights, the consistency of the judgment matrix is the core element of the method. Due to inconsistencies in the level of knowledge and opinions among evaluation experts, the judgment matrix usually does not have satisfactory consistency, so the reliability of the weight values derived from the judgment matrix is difficult to be guaranteed. Therefore, many scholars have studied the consistency improvement method of judgment matrix, and most of them use mathematical transformation to convert judgment matrix to consistency matrix. However, in the process of mathematical conversion, the original judgment information of the decision maker, which is crucial for the judgment matrix to keep this in it, is not considered, and the improvement scheme may not reflect the true preference of the decision maker, resulting in the result inconsistent with the actual situation. And when the AHP method is used to determine the weight, once the judgment matrix is determined, the consistency of the judgment matrix and the weight value are also determined, neither of which can be improved. In order to maximize the original information keeping of the decision maker, and to make the judgment matrix have better consistency and improve the weight value when the judgment matrix is determined, this paper proposed to apply the particle swarm optimization (PSO) algorithm to the analytic hierarchy process (AHP) to construct PSO-AHP model, and then apply it to the calculation and optimization of weight values, so as to make the results of comprehensive evaluation more scientific and reliable.

3.1 Particle swarm optimization (PSO) algorithm

Particle swarm optimization (PSO) was proposed by Kennedy and Eberhart in 1995 [13], which was derived from the simulation of the search strategy of bird swarm hunting behavior. Imagine a group of birds searching for food in an area and there is only one piece of food in this area, the simplest and most effective search strategy is to search for the area around the bird that is currently closest to the food. Inspired by this search pattern, PSO is applied to practical optimization problems. In PSO, the solution of each optimization problem corresponds to the position of a bird in the search space, which is called particle. Each particle has its own position and velocity (deciding the direction and distance of the particle’s movement), and also a fitness value determined by an optimized function. The particle swarm follows the current optimal particle to search in the solution space.

PSO algorithm can be described as [14]: in an N-dimensional target search space, the number of particle swarms is m, and each particle i contains an n-dimensional position vector x_i = (x_i1, x_i2, ... , x_in) and velocity vector v_i = (v_i1, v_i2, ... , v_in). Remember the optimal position p_i obtained when particle i searches for n-dimensional space. In each iteration, particle i adjusts its velocity vector according to its own inertia and the optimal empirical group p_i = (p_i1, p_i2, ... , p_in₎, and then adjusts its position. The quality of the particle is measured by the fitness function f (x). $v_{in}^{k + 1} = v_{in}^{k} + c_{1} r_{1} (p_{in}^{k} - x_{in}^{k}) + c_{2} r_{2} (p_{gn}^{k} - x_{in}^{k})$ (1) $x_{in}^{k + 1} = x_{in}^{k} + v_{in}^{k + 1} (i = 1, 2, \dots, m; n = 1, 2, \dots, N)$ (2)

Where, r₁ and r₂ are random numbers with a value between (0,1); the learning factors c₁ and c₂ are non-negative constants, and appropriate c₁ and c₂ can accelerate convergence and are not limited to local optimum. v_in∈[-v_max,v_max], v_max is set according to the problem and is constant.

3.2 Analytic hierarchy process (AHP)

Analytic Hierarchy Process (AHP) in system engineering theory is a better method for determining weights. It is a multi-objective and multi-criteria decision-making method that divides various factors in complex problems into related, ordered and organized levels, and is an effective method combining quantitative analysis and qualitative analysis.

The basic idea of AHP is roughly the same as the process of thinking and judgment on complex decision-making problems. When analyzing a problem, the decision maker shall firstly have a clear understanding of the nature of the problem, clarify the scope of the problem, the factors involved, the interrelationships and affiliation of the factors, and final problem to be solved. According to the qualitative analysis of the schemes, list the various sides that reflect the effects of the schemes, gather them into groups according to certain common characteristics of the schemes, and consider the common characteristics between them as some of the new levels in the scheme comparison factors, these factors themselves are combined according to another set of characteristics, forming another higher level of factors, until a single highest factor is formed, which is the ultimate goal of comprehensive comparison of schemes.

3.3 Construction of PSO-AHP model

(1) Establish hierarchical structure model of the comprehensive evaluation system [15].

Assume that there are four levels of indicators in the comprehensive evaluation system from top to bottom, which are layer A, B, C, and D. Layer A is the overall objective of the system evaluation with only one element; layer B, C, and D are the criterion layer, the sub-criteria layer, and the target layer respectively, which are recorded as n_b, n_c and n_d_.

(2) Construction of judgment matrix

For the elements of layer B, C, and D, pairwise comparison is conducted with the elements of the above layer respectively as the criterion. Usually, the 1–9 scale method is used to describe the relative importance of each element. And the judgment matrix of layer B is obtained as: A_K = (a_ij) _{n_b×n_b}, where the element a_ij represents the relative importance of the element B_i to the element B_j from the perspective of layer A. The judgment matrix of layer C is: $B_{K} = {b_{ij}^{k} | i, j = 1 \sim n_{c}; k = 1 \sim n_{b}}_{n_{c} \times n_{c}}$ , and the judgment matrix of layer D is: $C_{K} = {c_{ij}^{k} | i, j = 1 \sim n_{d}; k = 1 \sim n_{c}}_{n_{d} \times n_{d}}$ .

(3) Establish the weight optimization model

1) Determination of the objective function

The optimization of the weight value corresponding to the judgment matrix A_K = (a_ij) _{n_b×n_b} is taken as an example. The single-ranking weight of each element in layer B is set as ω _K , k = 1∼n_b. If the judgment matrix A_k satisfies a_ij = ω_i/ω_j (i, j = 1 ∼ n_b), then A_k has complete consistency and below formula is obtained: $\sum_{i = 1}^{n_{b}} | \sum_{k = 1}^{n_{b}} (a_{ik} ω_{k}) - n_{b} ω_{i} | = 0$ (3)

The smaller the value at the left end of formula (3), the higher the consistency of A_k When formula (3) is true, A_k has complete consistency. Therefore, the calculation and optimization of the weight value of each element in layer B can be summarized as the following optimization problem, that is, the objective function is shown as: $MinCIF (n_{b}) = \sum_{i = 1}^{n_{b}} - \sum_{k = 1}^{n_{b}} (a_{ik} ω_{k}) - n_{b} ω_{i} - / n_{b}$ (4)

2) Constitution of constraint conditions ${\begin{matrix} \sum_{k = 1}^{n_{b}} ω_{k} = 1 \\ ω_{k} > 0 (k = 1 \sim n_{b}) \end{matrix}$ (5)

CIF (n_b) in formula (4) is a consistency index function, which is a nonlinear optimization problem that is difficult to be handled with conventional methods. Therefore, the optimal weight corresponding to the matrix A_k is the weight value corresponding to the minimum value obtained by CIF (n_b). Although A_k has been determined, its corresponding weight value can be optimized through the solution of above optimization problem.

(4) PSO solves weight optimization model and performs consistency test

PSO is used to solve the weight optimization model. The specific solution process is detailed in the model solution section. PSO can solve total hierarchical ranking and check its consistency, that is, to determine the ranking weight of the same level of elements to the highest level and to test the consistency of each judgment matrix. This process is performed layer by layer from the highest level to the lowest level. The total ranking weight of each element in layer B is ω_k (k = 1 ∼ n) and the consistency index function is CIF (n_b). The ranking weight of each element in layer C is $ω c_{i}^{A} = \sum_{k = 1}^{n_{b}} ω_{k} ω c_{i}^{k} (i = 1 \sim n_{c})$ and the consistency index function is ${CIF}^{A} (n_{c}) = \sum_{k = 1}^{n_{b}} ω_{k} {CIF}^{k} (n_{c})$ the total ranking weight of each element in layer D is $ω d_{i}^{A} = \sum_{k = 1}^{n_{c}} ω c_{k}^{A} ω d_{i}^{k} (i = 1 \sim n_{d})$ , and the consistency index function is ${CIF}^{A} (n_{d}) = \sum_{k = 1}^{n_{c}} ω c_{k}^{A} {CIF}^{k} (n_{d})$ .

When the CIF^A (n_d) value is less than a certain criteria, it can be considered that the total ranking results of the elements in layer D have satisfactory consistency, and the total ranking weights of the elements calculated based on this are acceptable; otherwise, the maximum direction improvement method and interval number improvement method will be used to adjust the judgment matrix [16] until the appropriate criteria are met.

3.4 Solution of PSO-AHP model

For PSO-AHP model proposed in this paper, the PSO algorithm is used to encode the particles, construct the fitness function, solve the weights and carry out optimization.

The initial stage of model solution. ➀ Use AHP to establish a hierarchical structure model for the comprehensive evaluation system; ➁ Construct a hierarchy judgment matrix according to the relative importance of the factors; ➂ Determine the parameters of the PSO algorithm: the number of particle swarms n, the maximum number of iterations N, two learning factors c₁ and c₂, the variation range [-v_max,v_max] of the inertia coefficient vin and so on.

Use PSO to solve weight optimization model. 1) Generate initial solution of the particle: Generate random numbers in (0,1) and normalize it to make it a feasible solution. 2) Calculate the fitness of the initial particle: take the feasible solution into the objective function to calculate the fitness of the initial particle, and select the global optimal particle. 3) Update particle iteration: the individual optimal value is the particle in the first iteration of the initial particle; in the subsequent iteration, the individual optimal value is the optimal point determined when the solution space moves.4)Determine whether the updated particles meet the constraint conditions: If not, normalize the particles.5)Calculate the fitness level of the updated particles: Compare and select the best particle position and the best global position. 6) Determine whether the optimal solution meets the iteration termination condition: if yes, iteration stops, then output the optimal solution obtained from the model and move to step 7);if not, return to step 3) and repeat the process.7) Calculate the consistency ratio value corresponding to the judgment matrix. If the consistency requirements are not met, use the maximum direction improvement method and interval number Improvement method to adjust the judgment matrix, then returns to step 1) and restart the whole step.

Output the global optimal position, corresponding weight value and consistency index function value Min CIF.

4 Result analysis and discussion

This paper takes the Nalinhe No. 2 mine as the research object and conducts research on the “comprehensive evaluation index system of coal-water coordinated development “ in order to achieve the protection of the water resources system in the mining area, which is in line with the requirements of sustainable development and fundamental interests of the people in the arid and semi-arid regions of northwestern China. It has great theoretical significance and practical value.

4.1 Overview of the study area

Located in the eastern part of the Mu Us Desert, Nalinhe No. 2 well field has the characteristics of plateau desert landforms, and the surface is covered by Quaternary sand. Most of them are crescent or wave-shaped dunes, and there’s no bedrock exposed. The vegetation in the area is sparse and it is a semi-desert area.

The well field is generally a westward inclined monoclinic structure, with a tendency of 260 ° to 280 ° and a stratum inclination of 1 to 3 °. The attitude of stratum varies but not much along the direction and inclination. There are wide wave-like undulations along the direction, but large faults and fold structures as well as the intrusion of magmatic rocks are not found in the area. It’s a simple coal field with a simple structure.

The direct water-filling aquifers in the well field are mainly fissure aquifers, followed by pore aquifers. The water abundance of direct water-filling aquifers is weak, and the recharge and runoff conditions are poor. The weak lateral runoff of confined groundwater outside the area is taken as main water source, and atmospheric precipitation as the secondary water source. The hydrogeological boundary is simple.

The coal-bearing stratum of the well field is Mid-Jurassic Yan’an formation (J2y), which belongs to coal-bearing construction of giant inland basin. It is a set of terrigenous clastic deposits consisting of gray and dark gray sandstone, siltstone, sandy mudstone, mudstone and coal seam. It’s parallel above the extension formation of the underlying Triassic. The top boundary is covered by the parallel unconformity of the Zhuluo formation. The total thickness of exposed coal-bearing strata in the well field is 349.81 m on average, and there are 26 coal-bearing strata, with an average thickness of 12.16 m. It contains 5 layers of mineable coal seams, and the total thickness of minable coal seam is 5.71∼11.50 m, with an average of 8.00 m. According to the reserves, thickness, and interval of each coal seam, the descending mining sequence is adopted in principle, and upper 3-1 and 3-1 coal seams are mined firstly. Therefore, the upper 3-1 and 3-1 coal seams are taken as the object of this study.

4.2 Construction of index system

By analyzing and summarizing the research results of existing scholars on the coordinated development of coal-water and consultation of relevant experts in related fields, the specific geological environment characteristics and mining methods of Nalinhe No. 2 well field, the comprehensive effect evaluation index system of coordinated development of coal and water in the mining area was established. The results are shown in Table 1.

Table 1
“Coal-Water” Coordinated Evaluation Index System

Target level Criterion level Sub-criterion level Index level

Comprehensive effect evaluation index system A for coordinated development of coal-water Geological System B₁ Coal water occurrence relationship C₁ Covering lithology and composite structure C₁X₁

Lithology between coal and waterC₁X₂

Aquifer thickness C₁X₃

Water barrier capacity C₂ Water barrier thickness and permeability coefficient C₂X₁

Water barrier lithology C₂X₂

Water barrier position C₂X₃

Coal seam parameter C₃ Coal seam depth C₃X₁

Coal seam inclination C₃X₂

Natural System B₂ Physical geography C₄ Vegetation coverage C₄X₁

Land type C₄X₂

Hydrometeorology C₅ Annual precipitation C₅X₁

Water system distribution C₅X₂

Mining system B₃ Mining parameter C₆ Coal mining method and mining technology C₆X₁

Working surface width C₆X₂

Working face advancement length C₆X₃

Working face advancement degree C₆X₄

Coal seam mining thickness C₆X₅

Mining speed C₆X₆

Goaf parameter C₇ Goaf area C₇X₁

Time parameter C₈ Duration of overburden failure C₈X₁

Roof parameterC₉ Roof management mode C₉X₁

Fissure parameter C₁₀ Fissure development degree C₁₀X₁

Resource utilization C₁₁ Water consumption per ton of coal C₁₁X₁

Ecological environment system B₄ Environmental damage and treatment C₁₂ Discharge of production wastewater C₁₂X₁

Mine drainage rate and destination C₁₂X₂

Key population change rate C₁₂X₃

Reclamation rate of subsided land C₁₂X₄

Groundwater level C₁₃ Drop range of regional groundwater level C₁₃X₁

Impact of water flowing fractured zone on overlying aquifer C₁₃X₂

Geological hazard system B₅ Sudden water bursting accident C₁₄ Max. water bursting amount C₁₄X₁

Number of deaths C₁₄X₃

Number of people under coercion C₁₄X₄

Land subsidence and cracks C₁₅ Destroyed land type C₁₅X₁

Destroyed land area C₁₅X₂

Ground fissure development degree C₁₅X₃

Socioeconomic system B₆ Economic impact on the region C₁₆ GDP change rate of the mining area C₁₆X₁

Proportion of coal output value in regional GDP C₁₆X₂

Social adaptation C₁₇ Public support of the project C₁₇X₁

Relocation and resettlement rate C₁₇X₂

4.3 Apply PSO-AHP model to solve the weight value of the evaluation factors

By distributing questionnaires to more than 40 experts and scholars in related fields, mine management and staff, the importance between two indicators at the same level compared in the index system was obtained, and the importance of each influencing factor was initially determined and the initial values was assigned and the judgment matrix was constructed. For some of the main influencing factors, the rationality of the judgment matrix assignment can be analyzed and verified through the method given above, and if necessary, the assignment can be further modified, and finally the judgment matrix of the adjacent two layers are A-B, B-C and C- CX respectively. The matrix was calculated to obtain the weight value of each influencing factor. The weight calculation results of the group decision criterion level and sub-criterion level are shown in Table 2.

Table 2
Weighting for Group Decision Criterion Level and Sub-criterion Level

$A - B = | \begin{matrix} 1 . 0000 & 2 . 9078 & 2 . 7906 & 1 . 9604 & 2 . 7314 & 3 . 2499 \\ 0 . 3439 & 1 . 0000 & 1 . 2715 & 0 . 9379 & 1 . 5709 & 3 . 4730 \\ 0 . 3583 & 0 . 7865 & 1 . 0000 & 0 . 8204 & 1 . 0302 & 1 . 8024 \\ 0 . 5101 & 1 . 0662 & 1 . 2189 & 1 . 0000 & 1 . 6521 & 3 . 4457 \\ 0 . 3661 & 0 . 6366 & 0 . 9707 & 0 . 6053 & 1 . 0000 & 2 . 8480 \\ 0 . 3077 & 0 . 2879 & 0 . 5548 & 0 . 2902 & 0 . 3511 & 1 . 0000 \end{matrix} |$ $B_{1} - C_{1 - 3} = | \begin{matrix} 1.0000 & 1.6457 & 3.2985 \\ 0.6076 & 1.0000 & 2.2753 \\ 0.3032 & 0.4395 & 1.0000 \end{matrix} |$

$B_{2} - C_{4 - 5} = | \begin{matrix} 1.0000 & 0.8602 \\ 1.1625 & 1.0000 \end{matrix} |$ $B_{3} - C_{6 - 11} = | \begin{matrix} 1.0000 & 2.0713 & 1.7441 & \begin{matrix} 1.7427 \end{matrix} & 1.9984 & 1.6454 \\ 0.4828 & 1.0000 & 1.5251 & 1.1134 & 1.8427 & 1.5864 \\ 0.5734 & 0.6557 & 1.0000 & 1.3330 & 0.9928 & 1.3238 \\ 0.5738 & 0.8982 & 0.7502 & 1.0000 & 1.3029 & 2.0864 \\ 0.5004 & 0.5427 & 1.0073 & 0.7675 & 1.0000 & 1.7219 \\ 0.6078 & \begin{matrix} 0.6304 \end{matrix} & 0.7554 & 0.4793 & 0.5808 & 1.0000 \end{matrix} |$ $B_{4} - C_{12 - 13} = | \begin{matrix} 1.0000 & 1.7792 \\ 0.5620 & 1.0000 \end{matrix} |$ $B_{5} - C_{14 - 15} = | \begin{matrix} 1.0000 & \begin{matrix} 2.7751 \end{matrix} \\ 0.3603 & 1.0000 \end{matrix} |$ $B_{6} - C_{16 - 17} = | \begin{matrix} 1.0000 & \begin{matrix} 1.9015 \end{matrix} \\ 0.5259 & 1.0000 \end{matrix} |$ $C_{1} - C_{1} X_{1 - 3} = | \begin{matrix} 1.0000 & 1.3311 & 0.7920 \\ 0.7513 & 1.0000 & 0.7736 \\ 1.2626 & 1.2927 & 1.0000 \end{matrix} |$ $C_{2} - C_{2} X_{1 - 3} = | \begin{matrix} 1.0000 & 3.1517 & 2.7436 \\ 0.3173 & 1.0000 & \begin{matrix} 1.2002 \end{matrix} \\ 0.3645 & 0.8332 & 1.0000 \end{matrix} |$ $C_{3} - C_{3} X_{1 - 2} = | \begin{matrix} 1.0000 & 2.2870 \\ 0.4373 & 1.0000 \end{matrix} |$ $C_{3} - C_{3} X_{1 - 2} = | \begin{matrix} 1.0000 & 2.2870 \\ 0.4373 & 1.0000 \end{matrix} |$ $C_{4} - C_{4} X_{1 - 2} = | \begin{matrix} 1.0000 & 1.2108 \\ 0.8259 & 1.0000 \end{matrix} |$ $C_{5} - C_{5} X_{1 - 2} = | \begin{matrix} 1.0000 & 0.9749 \\ 1.0257 & 1.0000 \end{matrix} |$ $C_{6} - C_{6} X_{1 - 6} = | \begin{matrix} 1.0000 & \begin{matrix} 2.1088 \end{matrix} & 1.9039 & \begin{matrix} 1.7076 \end{matrix} & 1.3026 & 2.9164 \\ 0.4742 & 1.0000 & \begin{matrix} 1.0611 \end{matrix} & 0.9397 & 0.8483 & 1.4911 \\ 0.5252 & 0.9425 & 1.0000 & \begin{matrix} 1.1941 \end{matrix} & 1.0461 & \begin{matrix} 1.6234 \end{matrix} \\ 0.5856 & 1.0641 & 0.8375 & 1.0000 & 1.1066 & 1.6314 \\ 0.7677 & 1.1788 & \begin{matrix} 0.9559 \end{matrix} & 0.9037 & 1.0000 & 3.0297 \\ \begin{matrix} 0.3429 \end{matrix} & \begin{matrix} 0.6706 \end{matrix} & 0.6160 & 0.6130 & 0.3301 & 1.0000 \end{matrix} |$ $\begin{matrix} C_{12} - C_{12} X_{1 - 4} \\ = | \begin{matrix} 1.0000 & \begin{matrix} 1.2977 \end{matrix} & 1.4002 & \begin{matrix} 1.5925 \end{matrix} \\ 0.7706 & 1.0000 & 0.9580 & 1.2388 \\ 0.7142 & 1.0438 & 1.0000 & \begin{matrix} 0.9521 \end{matrix} \\ 0.6280 & 0.8073 & 1.0503 & 1.0000 \end{matrix} | \end{matrix}$ $C_{13} - C_{13} X_{1 - 2} = | \begin{matrix} 1.0000 & \begin{matrix} 1.2294 \end{matrix} \\ 0.8134 & 1.0000 \end{matrix} |$ $C_{14} - C_{14} X_{1 - 3} = | \begin{matrix} 1.0000 & 0.4559 & 0.9474 \\ 2.1937 & 1.0000 & 2.6068 \\ 1.0555 & 0.3836 & 1.0000 \end{matrix} |$ $C_{15} - C_{15} X_{1 - 3} = | \begin{matrix} 1.0000 & 0.7085 & 0.8156 \\ 1.4113 & 1.0000 & 0.9407 \\ 1.2261 & 1.0631 & 1.0000 \end{matrix} |$ $C_{16} - C_{16} X_{1 - 2} = | \begin{matrix} 1.0000 & \begin{matrix} 1.2304 \end{matrix} \\ 0.8127 & 1.0000 \end{matrix} |$ $C_{17} - C_{17} X_{1 - 2} = | \begin{matrix} 1.0000 & \begin{matrix} 1.1375 \end{matrix} \\ 0.8791 & 1.0000 \end{matrix} |$

The Table 2. shows that the first four factors that affect the coordinated development of coal-water are the geological system (B₁), the ecological environment system (B₄), the natural system (B₂), and the mining system (B₃), with a total weight value of 0.8129.

During the development of coal resources, the geological system (B₁) and natural system (B₂) are subject to certain changes due to human activities, which are mainly passive changes, and most of the driving force for their changes is derived from the mining system (B₃). At the same time, the degree of change is mainly reflected in the ecological environment system (B₄). Therefore, this paper calculated the weight distribution of index level of the mining system (B₃) and ecological environment system (B₄) to obtain the main index of concern. See Table 3 for the calculation results of the global weights of the main index level of group decision making.

Table 3

Weights for the Main Index Level of Group Decision Making

Table 3 shows that the mining parameter (C₆) in the sub-criterion level of the mining system (B₃) is the main influencing factor, accounting for 26.5% of the weight of the mining system (B₃); the first four factors of the index level are the goaf area (C₇X₁), roof management mode (C₉X₁), duration of overburden failure (C₈X₁) and fissure development degree (C₁₀X₁), and the total weight value is 0.0788. The environmental damage and treatment (C₁₂) is the main influencing factor in the sub-criterion level of the ecological environment system, accounting for 63.0% of the weight of the ecological environment system (B₄); the first four factors of the index level are the discharge of production wastewater (C₁₂X1), drop range of regional groundwater level (C₁₃X₁), impact of water flowing fractured zone on overlying aquifer (C₁₃X₂) and mine drainage rate and destination (C₁₂X₂), and the total weight value reaches 0.1302.

4.4 Consistency test

In order to test whether the feature vector obtained by the constructed judgment matrix is reasonable, the consistency test method given above is used to solve the random consistency ratio of the judgment matrix. Only when the consistency ratio is less than 0.10, the judgment matrix has satisfactory consistency, and the feature vector after normalization is the weight vector. If the tests are not consistent, the judgment matrix needs to be readjusted until satisfactory consistency is obtained. See Table 4 for the calculation results of the consistency ratio of the single-ranking and total-ranking of the group decision matrix.

Table 4
Consistency of Single Ranking and Total Ranking of Group Decision Matrix

Ranking mode Judgment matrix Consistency ratio

Single ranking Geological system B₁ of criterion level – Sub-criterion level C_1–3 0.0088

Natural system B₂ of criterion level – Sub-criterion level C_4 - 5 0.0000

Mining system B₃ of criterion level – Sub-criterion level C_6–11 0.0099

Ecological environment system B₄ of criterion level – Sub-criterion level C_12 - 13 0.0033

Geological hazard system B₅ of criterion level – Sub-criterion level C_14 - 15 0.0052

Socioeconomic system B₆ of criterion level – Sub-criterion level C_16 - 17 0.0000

Total ranking Target level A-Criterion level matrix B 0.0111

Ranking mode	Judgment matrix	Consistency ratio
Single ranking	Geological system B₁ of criterion level – Sub-criterion level C_1–3	0.0088
	Natural system B₂ of criterion level – Sub-criterion level C_4 - 5	0.0000
	Mining system B₃ of criterion level – Sub-criterion level C_6–11	0.0099
	Ecological environment system B₄ of criterion level – Sub-criterion level C_12 - 13	0.0033
	Geological hazard system B₅ of criterion level – Sub-criterion level C_14 - 15	0.0052
	Socioeconomic system B₆ of criterion level – Sub-criterion level C_16 - 17	0.0000
Total ranking	Target level A-Criterion level matrix B	0.0111

The maximum single ranking consistency ratio is 0.0099 while the total ranking consistency ratio is 0.0111, and both are less than 0.10. It can be considered that the single ranking and the total ranking have satisfactory consistency, and the obtained weight vector is the desired result.

5 Conclusion

This paper studied the comprehensive effect evaluation of the coordinated development of coal and water resources in ecologically vulnerable areas, and successfully applied the research results to Nalinhe No. 2 mine field in Inner Mongolia. The main conclusions are as follows:

Based on previous research results of the impact assessment of coal development on water resources, water ecology and water environment, and field investigation and analysis of Nalinhe River and surrounding mining areas, the impact of coal mining on groundwater system and ecological environment system has been analyzed and summarized systematically and a total of 39 indicators of four levels of coal-water coordinated development evaluation index system was constructed.

In order to overcome the problem that the judgment matrix in the analytic hierarchy process (AHP) usually does not have satisfactory consistency, this paper applied the particle swarm optimization algorithm (PSO) to the analytic hierarchy process (AHP) to construct a PSO-AHP model, which guarantees the objectivity and accuracy of the weight coefficient.

Taking Nalinhe No. 2 mine as the research object, the relative importance of each influencing factor was ranked by solving the PSO-AHP model. The results show that the first four factors are geological system, ecological environment system, natural system and mining system. As the first three systems are all passive changes, most of the driving force for their change comes from the mining system. By analyzing the distribution of the weight values of each index of the mining system, the selection of mining parameters is particularly important. The selection of different mining parameters will have different impacts on the stratum structure, groundwater level, and surface ecology. Therefore, the mining parameters shall be selected reasonably in the early stages of mine development while the impact on the aquifer and ecological environment system shall be observed in the later stage. The mining parameters shall be adjusted in time to minimize the impact, which is the key to high-quality development of coal resources and has certain reference value for practical work.

The important prerequisite for the evaluation of the “coal-water” coordinated development is to determine scientific and reasonable evaluation index system. The physical geography, coal seam and geological conditions in different mining areas are different, when selecting the evaluation index, necessary adjustment shall be conducted based on actual conditions and experience. The research in this field shall be strengthened and the construction model shall be optimized gradually.

Footnotes

Acknowledgments

This research work was supported by National Key R&D Program of China (No. 2018YFC0406400), the National Natural Science Foundation of China (No. 51969021) and R&D Program of Beijing Municipal Education Commission (No. KM201810857001).

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Target level	Criterion level	Sub-criterion level	Index level
Comprehensive effect evaluation index system A for coordinated development of coal-water	Geological System B₁	Coal water occurrence relationship C₁	Covering lithology and composite structure C₁X₁
			Lithology between coal and waterC₁X₂
			Aquifer thickness C₁X₃
		Water barrier capacity C₂	Water barrier thickness and permeability coefficient C₂X₁
			Water barrier lithology C₂X₂
			Water barrier position C₂X₃
		Coal seam parameter C₃	Coal seam depth C₃X₁
			Coal seam inclination C₃X₂
	Natural System B₂	Physical geography C₄	Vegetation coverage C₄X₁
			Land type C₄X₂
		Hydrometeorology C₅	Annual precipitation C₅X₁
			Water system distribution C₅X₂
	Mining system B₃	Mining parameter C₆	Coal mining method and mining technology C₆X₁
			Working surface width C₆X₂
			Working face advancement length C₆X₃
			Working face advancement degree C₆X₄
			Coal seam mining thickness C₆X₅
			Mining speed C₆X₆
		Goaf parameter C₇	Goaf area C₇X₁
		Time parameter C₈	Duration of overburden failure C₈X₁
		Roof parameterC₉	Roof management mode C₉X₁
		Fissure parameter C₁₀	Fissure development degree C₁₀X₁
		Resource utilization C₁₁	Water consumption per ton of coal C₁₁X₁
	Ecological environment system B₄	Environmental damage and treatment C₁₂	Discharge of production wastewater C₁₂X₁
			Mine drainage rate and destination C₁₂X₂
			Key population change rate C₁₂X₃
			Reclamation rate of subsided land C₁₂X₄
		Groundwater level C₁₃	Drop range of regional groundwater level C₁₃X₁
			Impact of water flowing fractured zone on overlying aquifer C₁₃X₂
	Geological hazard system B₅	Sudden water bursting accident C₁₄	Max. water bursting amount C₁₄X₁
			Number of deaths C₁₄X₃
			Number of people under coercion C₁₄X₄
		Land subsidence and cracks C₁₅	Destroyed land type C₁₅X₁
			Destroyed land area C₁₅X₂
			Ground fissure development degree C₁₅X₃
	Socioeconomic system B₆	Economic impact on the region C₁₆	GDP change rate of the mining area C₁₆X₁
			Proportion of coal output value in regional GDP C₁₆X₂
		Social adaptation C₁₇	Public support of the project C₁₇X₁
			Relocation and resettlement rate C₁₇X₂

Study on evaluation index system of sustainable development of mine water resources based on PSO-AHP model and fuzzy comprehensive evaluation

Abstract

Keywords

1 Introduction

2 State of the art

2.1 Impact of coal mining on water resources system

3 Methodology

3.1 Particle swarm optimization (PSO) algorithm

3.3 Construction of PSO-AHP model

4 Result analysis and discussion

4.1 Overview of the study area

4.2 Construction of index system

Table 2 Weighting for Group Decision Criterion Level and Sub-criterion Level

Footnotes

Acknowledgments

References

Table 2
Weighting for Group Decision Criterion Level and Sub-criterion Level