A New Method of Regional Mining Subsidence Control for Sustainable Development in Coal Areas

Abstract

Coordinated and sustainable development of production-living-ecological space (PLES) is directly related to the global energy security and quality of life in coal areas. However, the current surface subsidence control methods have some problems, such as low resource recovery rate, high cost, insufficient materials, which are difficult to meet the requirements for the PLES sustainable development in coal areas. Under this background, based on characteristics of surface subsidence and deformation due to sub-critical extraction, the large protection area, and high deformation tolerance in PLES of mining areas, the new method of regional mining subsidence control was proposed, with the combination of source control and ground rehabilitation. The effectiveness of the method was verified by numerical simulation results and practical applications, and the application principles and implementation methods were proposed. The research results could provide technical support for the sustainable development of coal areas in major coal producing countries of the world.

1. Introduction

As one of the three pillars of the world’s primary energy consumption [1], coal can ensure global energy security, and has made important contributions to the development of the world economy. However, conventional coal mining will cause rock strata movement, surface subsidence, aerological risks [2], and methane explosions [3], and induce problems, such as excavation damage, occupancy, collapse, and pollution [4,5,6,7,8,9]. These issues not only pose a serious threat to ground buildings (structures), ecological environment, and human settlements, but also has caused serious conflicts among production-living-ecological space in various mining areas in the world (Figure 1).

Zonguldak, Turkey, with a population of 300,000, contains multiple coal seams in Kozlu hard coal basin. Underground coal mining has caused damage to surface buildings (structures), road cracks, etc. The buildings above the basin are mainly shanty towns, and local residents have endured damage caused by surface subsidence for many years [10,11,12]. Pennsylvania has more than 50 years of mining history, and about 600 longwall faces have been mined. The mining of 25 faces has resulted in various road damage, including compression uplift, transverse cracks, longitudinal cracks, joint faults, and lane-to-shoulder separation, etc. [13], resulting in significant economic losses. As one of the coal producers and consumers in the world, China is also facing serious conflicts of production-living-ecological space in its coal mining areas. In several large coal bases in the Yellow River Basin of China, the contradiction between the mining-induced aquifer destruction and the ecological protection is prominent in semiarid area of the upper and middle reaches of the Yellow River [14]. In addition, the conflict between mining subsidence and urban development and cultivated land protection in densely populated areas of the Huanghuai Plain is extremely severe. The conflicts between production, living, and ecological space of mining areas also exist in large coal mining countries, such as Russia and India [15,16]. The existing coal mining is simple to cause the problem of production-living-ecological space conflict in mining areas. Therefore, how to realize the coordinated development of underground coal mining in mining areas and the production-living-ecological space on the ground is a bottleneck problem in the world’s major coal countries.

In general, the movement of rock strata and surface subsidence caused by coal mining are the main causes of PLES conflicts in various mining areas around the world (Figure 2). Therefore, the fundamental way to solve the problem is to control mining subsidence from the source and change passive governance to active prevention. After long-term research and engineering practice of scholars both at home and abroad, the world’s major coal countries have formed a relatively complete mining subsidence control theory and technical system, which mainly includes coordinated extraction to control the distribution of surface deformation [17], partial extraction, such as strip or pillar mining to reduce settlement and deformation [18], backfill mining to reduce settlement and deformation [19], bed separation grouting to control settlement and deformation [20,21].

Strip mining and filling mining are the most direct and effective methods to control the surface deformation and solve the PLES conflict in mining areas. However, the high resource loss rate of strip mining, high cost, and low efficiency of filling mining cannot meet the requirements of high-quality development of the PLES in mining areas. Under this background, based on the characteristics of large PLES protection area and the large difference in deformation tolerance, this paper will propose a regional strata movement control mode for green mining to achieve the coordinated and high-quality development of PLES in coal mining areas. The effectiveness of this proposed mode will be analyzed by numerical simulation, and the application principles and implementation methods will be put forward. Finally, the technology will be used in Huayuan Coal Mine, Wugou Coal Mine, and No.12 Coal Mine of Pingmei. The research results can provide technical support for the high-quality and integrated development of underground coal mining and ground PLES in mining areas of coal countries around the world.

2. Methods

According to the characteristics of PLES in mining areas, this section will study the regional surface subsidence control method (RSSC) for the coordinated and high-quality development of the PLES, and discuss the principles and design methods of this proposed technology. Finally, numerical simulation method will be used to verify the feasibility of the application of this technology.

2.1. Technical Principle

Strip mining and filling mining are mainly used to protect the safety of important buildings and structures on the ground, such as a high-voltage tower, a section of highway, or a small village. However, the area of the mining area is generally very large. If strip mining is entirely used for underground coal mining, it will cause a great waste of coal resources. If the filling mining technology is fully adopted to ensure the coordinated development of PLES, it will affect the coal output and economic benefits, and the shortage of filling materials is also a problem. Neither of these two methods can meet the requirements of surface deformation control for the integrated development of PLES in the mining areas. Therefore, a new surface subsidence control method is urgently needed to realize the coordinated development of the underground coal mining and the production-living-ecological space on the ground.

According to the relationship between the mining degree of the working face and surface deformation [22], when the mining degree is small, the surface subsidence increases slowly with the increase in the mining area of the working face. When the mining degree exceeds a certain critical value, the surface deformation will increase sharply (Figure 1). For the purpose of reducing the surface deformation, the mining range of the working face can be controlled within the critical value of the mining degree. According to the characteristics of the surface deformation law under insufficient mining, the large protected area of PLES, and large difference in deformation tolerance, a new integrated technology for regional rock strata and surface subsidence control method was developed, with the combination of source control and ground rehabilitation (Figure 2).

The principle of the technology is to replace the strip coal pillars with the band-shaped filling body, control the mining range within the critical value of the mining degree, and fully use the control effect of the overlying strata to reduce the degree of strata and surface movement. By this technology, the damage on the ground can be easily repaired and treated to meet the needs of the environment and living space. Meanwhile, the filling cost can be reduced greatly and the resource recovery rate can be improved significantly. When using this method to control the surface subsidence, the larger the filling range, the smaller the surface movement and deformation value, the lighter the disturbance degree of PLES of mining areas, the higher the total coal mining cost, and the lower the production efficiency. On the contrary, if the filling area is small, the mining efficiency will increase. Meanwhile, the surface movement and deformation will increase, and the disturbance degree of PLES will also increase. Therefore, when using this regional subsidence control technology for coal mining design, it is necessary to achieve a balance between coal mining benefits and the protection of PLES in the mining area. This balance point depends on the deformation control requirements and remediation measures of typical targets in PLES.

2.2. Feasibility Analysis of RSSC Method

In order to verify the effectiveness of RSSC method, numerical models will be established by the numerical simulation method under the fully caving coal mining method, strip mining, backfill mining, and regional surface subsidence control method. Based on the simulation results, the surface subsidence control effect of RSSC method will be analyzed.

2.2.1. Model Establishment

With the development of modern computer technology, an increasing amount of numerical calculation methods based on finite element, finite difference, boundary element, and discrete element theory have been used to solve geotechnical, tunnel, and mining engineering problems [23,24,25,26], and a large number of numerical simulation software have been developed. At present, the more mature numerical simulation software mainly includes FLAC, ANSYS, UDE, Geostudio, Plaxis, etc. ANSYS can use the method of point-line-one-side to establish a three-dimensional geometric model, but it lacks the function of joint fracture network of rock mass. UDE can simulate various mechanical problems in geotechnical engineering, but its element body is mainly a rigid body element, which cannot fully show the elastoplasticity of rock strata. Geostudio analysis module is used more, and simple to use, but for coal excavation 3D function is relatively lacking. Plaxis has certain advantages for soil stability calculation or seepage calculation in soil. It has a strong function in the stability analysis of tunnels, but there are some shortcomings in mining. FLAC (Fast Lagrangian Analysis of Continua) is an explicit finite partition method based on Lagrangian algorithm. It was developed by Itasca Consulting Company in 1986. It can well simulate the mechanical process of failure or plastic flow when geological materials reach ultimate yield or ultimate strength. It is suitable for simulating large-scale deformation by analyzing the characteristics of progressive failure and instability in this process. Therefore, FLAC3D numerical simulation software has significant advantages over other software in the application of mining subsidence simulation, and is the most commonly used numerical simulation software for mining subsidence of coal mine.

Based on the geological and mining conditions of a mine in Ordos, Inner Mongolia, a numerical calculation model was established by FLAC3D 6.0 software. The size of the numerical model is 2000 m × 2000 m × 663 m. The model is divided into 118,400 units, and each unit is 50 m in length and width. The model height varies with the rock strata. The bottom boundary of the model is fully constrained, the periphery is a horizontal displacement constrained boundary, and the roof is a free boundary. The numerical model is shown in Figure 3. The constitutive model is Mohr-Coulomb model. The distribution of each rock strata and the mechanical parameters of the numerical calculation model are shown in

Table 1. Parameters of model reference and rock strata.

Rock Name	Thickness	Density	Compressive Strength	Tensile Strength	Internal Friction Angle	Cohesive Force	Elastic Modulus
	/m	/kg/m3	/MPa	/MPa	/°	/MPa	/GPa
Topsoil	86	1984	15.7	5.55	20	7.95	3.12
Sandy mudstone 5	27	2118	27.8	8.23	23	8.89	8.19
Weak cementation sandstone 4	200	2118	27.2	2.1	27	5.58	10.80
Medium-grained sandstone 2	14	2350	24.8	3.39	28	1.58	10.69
Sandy mudstone 4	22	2467	29.4	3.35	27	4.35	9.22
Weak cementation sandstone 3	40	2274	32.3	3.03	26	6.99	10.59
Weak cementation sandstone 2	50	2376	26.1	3.39	28	7.39	7.94
Weak cementation sandstone 1	120	2418	30.8	3.26	27	5.23	9.37
Sandy mudstone 3	23	2405	33.3	3.44	31	5.78	10.85
Medium-grained sandstone 1	10	2490	49.6	3.92	23	5.68	24.01
Sandy mudstone 2	33	2453	22.4	3.76	26	2.28	7.005
Coal seam	6	1210	13.45	1.35	6	3.00	1.57
Sandy mudstone 1	32	2409	29.6	4.15	27	6.50	9.51

.

2.2.2. Simulation Scheme

In order to analyze and study the surface subsidence control effects of different mining methods, the following mining schemes were designed (

Table 2. Design scheme of conventional mining method.

Schemes	Mining Methods	Extraction Length	Work Face Length	Work Face Number	Mining Thickness
		/m	/m	/each	/m
1	Roof-caved mining	1000	200	6	6
2	Strip mining	1000	100	6	6
3	Backfill mining	1000	200	6	6

). The physical and mechanical parameters of the coal seam and filling body are shown in

Table 3. Physical and mechanical parameters of filling body.

Mechanical Parameters	Bulk Modulus	Shear Modulus	Internal Friction Angle	Cohesive Force	Density	Poisson Ratio
	/GPa	/GPa	/(°)	/MPa	/(kg/m3)
Coal seam	1.35	0.587	6	8.89	1210	0.31
backfill body	0.21	0.095	28	2	1500	0.3

. The simulated working face advanced 1000 m, and the face length was 200 m. Six working faces were simulated, with a total mining range of 1000 m × 1200 m. The designed recovery rate of strip mining was 50%. Under the entire backfill mining, the backfill rate was 85%. The mining design method of regional subsidence control was to fill the second and the fourth working faces, and leave a 100 m coal pillar between the third and the fourth working faces, with a recovery rate of 92.3%. In order to further analyze the effect of the regional control method, the following mining schemes were designed (

Table 4. Design scheme of regional control method.

Schemes	Mining Methods	Extraction Length	Backfill Face Length	Work Face Number	Mining Thickness
		/m	/m	/each	/m
4	Regional control method	1000	100	6	6
5	Regional control method	1000	150	6	6
6	Regional control method	1000	200	6	6
7	Regional control method	1000	250	6	6
8	Regional control method	1000	300	6	6

), and the sizes of the backfill faces were 100 m, 150 m, 200 m, 250 m, and 300 m, respectively.

2.2.3. Simulation Results and Analysis

According to the surface subsidence values of main sections of all models, the surface subsidence curves were drawn. In order to compare and analyze the surface subsidence under different mining methods, the surface subsidence curves were drawn, as shown in Figure 4. Compared with the fully caving mining method, the surface subsidence values are smaller by other mining methods. In order to better compare the effect of surface subsidence control, the surface subsidence curves were drawn under backfill mining, strip mining, and RSSC methods, as shown in Figure 5. In order to compare and analyze the influence of the filling face sizes on RSSC method, the surface subsidence values of different filling face sizes were plotted, as shown in Figure 6.

Table 5. The maximum subsidence values of main sections under different schemes.

Scheme	Mining Methods	Maximum Surface Subsidence Value/mm
1	Roof-caved mining	4883
2	Strip mining	587
3	Backfill mining	642
5	Regional control Method (backfill working surface: 100 m)	776
6	Regional control Method (backfill working surface: 150 m)	679
7	Regional control Method (backfill working surface: 200 m)	632
8	Regional control Method (backfill working surface: 250 m)	561
9	Regional control method (backfill working surface: 300 m)	538

shows the maximum surface subsidence values.

According to the analysis results in Figure 4, Figure 5 and Figure 6 and Table 5, the maximum surface subsidence values are 4883 mm, 587 mm, 642 mm, and 632 mm, respectively, under fully caving mining, strip mining, filling mining, and RSSC methods. Strip mining, backfill mining, and RSSC methods have good effects in controlling surface subsidence, with relatively small deformation values, and low level of disturbance to the PLES of the mining areas.

With the increase in the filling face size from 100 m to 150 m, 150 m to 200 mm, 200 mm to 250 mm, 250 mm to 300 mm under RSSC method, the maximum surface subsidence values decreased from 776 mm to 679 mm, 679 mm to 632 mm, 632 mm to 561 mm, 561 mm to 538 mm, respectively. Among them, when the size of the filling face is from 100 m to 150 m and 200 m to 250 m, the control effect is significantly improved. Moreover, the larger the size of the filling face, the smaller the surface subsidence and the better the control effect.

The strip mining method can achieve the best surface subsidence control effect, but in order to support the overlying strata, a wide coal pillar is often left, and the resource recovery rate is generally 30–40%, which will cause a large amount of resource waste. Although backfill mining has a good control effect on surface subsidence, the cost per ton of coal will increase by CNY 100–150. By analyzing the experimental results, it is shown that the RSSC method can not only reduce filling costs and improve resource recovery rates, but also effectively control surface subsidence, leading to optimization of economic, ecological, and social benefits.

3. Results

3.1. Process Design

According to the principle of regional surface deformation control technology through the combination of source control and ground rehabilitation, this technology aims to minimize the disturbance of coal mining to PLES of the mining area, control surface deformation, improve the resource recovery rate, and rehabilitate the ground, thus achieving the effect of economic, social, and environmental sustainability. The specific process is as follows (Figure 7):

• Combined with the types of typical protection targets and ecological environment protection requirements in PLES of the mining area, the technology and costs of ground restoration and treatment were fully considered under different mining impacts. The requirements for the surface deformation control were clarified for the integrated development of PLES. The indexes of typical targets were determined in the PLES space, such as surface subsidence W_g, horizontal deformation E_g, horizontal movement U_g, inclined deformation I_g, and curvature deformation K_g.
• Regional surface deformation prediction was carried out, satisfying the coordination of source reduction and damage control and ground rehabilitation. The corresponding subsidence W_p, horizontal deformation E_p, horizontal movement U_p, inclined deformation I_p, and curvature deformation K_p were calculated.
• Considering the indexes as the constraints and the economic benefit of coal mining as the optimization goal, the intelligent algorithm was used to search for the optimal design parameters of coal mining, in order that the coal mining benefits can be guaranteed to the greatest extent under the coordinated development of PLES, thereby realizing the coordinated development of the coal mining economic benefits and the environmental protection of the mining areas.

3.2. Regional Surface Deformation Prediction Method

According to the above analysis, RSSC method through the combination of source control and ground rehabilitation mainly ensures that the values of surface movement and deformation are less than the indexes of the PLES integration development in the mining area. At present, scholars have conducted a large amount of research on the deformation resistance of typical targets in the PLES, and basically clarified the indexes of different types of protection targets on the ground. At the same time, many scholars have conducted in-depth research on the ground rehabilitation techniques and costs of mining areas, which provides a basis for the determination of the indicators for the integration of PLES in mining areas [27,28,29]. Therefore, the key problem is how to predict the surface movement and deformation values with the combination of source deformation control and ground rehabilitation, and then complete the optimization of coal mining design.

As shown in Figure 8, the black area is the coal mine to be mined, the white area is the goaf, and the gray area is the filling compaction area after coal mining. The actual average mining thickness of the coal seam is m. Assume that the height of the filled body is m₂ after compaction, the equivalent mining height is m₁, the equivalent mining width is b, and the equivalent retention width is a, then the surface subsidence can be regarded as the joint influence of fully caving mining in the thin coal seam (m₁) and the equivalent strip mining in the thick coal mine (m₂). The regional surface subsidence values could be calculated by overlaying the pairs.

After determining the filling rate, m₁, m₂, and m satisfied the relationship in Equation (1).

$$\left\{\begin{array}{l}{m}_1=(1-\rho )m\\ m_2=\rho m\end{array}\right.$$

(1)

where ρ is the design filling rate of the working face, and the units of m, m₁, and m₂ are millimeters.

The relationship between the coal seam mining depth H and the equivalent strip mining depth H₁ satisfied the following Equation (2).

$$H_1=H+m_1$$

(2)

The original mechanical equilibrium of the overlying strata was broken after coal mining, and surface subsidence, movement, and deformation followed. The strata and surface movement was regarded as a random process, and the process could be described and modeled by the movement of particles in random media, specifical0ly, random medium theory, is usually called the probabilit integral method [30,31,32]. After nearly 50 years of research by mining subsidence workers in China, the probability integral method is listed in Guide to Roadway Coal Pillar Setting and Coal Mining in Buildings, Water Bodies, Railroads and Main Wells, and has been widely used to predict mining subsidence in China. According to the calculation formulas of probability integral of arbitrary face in horizontal or gently inclined coal seam in the Guide, the surface movement and deformation of goaf in the working face mining area could be predicted, as shown in Formulas (3)–(11).

• The value of surface subsidence at any point (x, y)

$$W(x,y)=W_{cm}{\displaystyle \underset{D}{\iint }\frac{1}{r^2}}{e}^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi$$

(3)

2.

The value of surface inclination at any point (x, y)

$$i_x(x,y)=W_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi \left(\eta -x\right)}{r^4}}\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi$$

(4)

$$i_y(x,y)=W_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi \left(\xi -y\right)}{r^4}}\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi$$

(5)

3.

The value of surface curvature at any point (x, y)

$$K_x(x,y)=W_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi }{r^4}}\left[\frac{2\pi {\left(\eta -x\right)}^2}{r^2}-1\right]\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi$$

(6)

$$K_y(x,y)=W_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi }{r^4}}\left[\frac{2\pi {\left(\xi -y\right)}^2}{r^2}-1\right]\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi$$

(7)

4.

Horizontal deformation value of the surface at any point (x, y)

$${\epsilon }_x(x,y)=U_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi }{r^3}}\left[\frac{2\pi {\left(\eta -x\right)}^2}{r^2}-1\right]\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi$$

(8)

$${\epsilon }_y(x,y)=U_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi }{r^3}}\left[\frac{2\pi {\left(\xi -y\right)}^2}{r^2}-1\right]\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi +i_y\left(x,y\right)\cdot \cot {\theta }_0$$

(9)

5.

The value of surface horizontal movement at any point (x, y)

$$U_x(x,y)=U_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi \left(\eta -x\right)}{r^3}}\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi$$

(10)

$$U_y(x,y)=U_{cm}{\displaystyle \underset{D}{\iint }\frac{2\pi \left(\xi -y\right)}{r^3}}\cdot e^{-\pi \frac{{\left(\eta -x\right)}^2+{\left(\xi -y\right)}^2}{r^2}}d\eta d\xi +W\left(x,y\right)\cdot \cot {\theta }_0$$

(11)

where η and ξ are integral variables; D is the coal seam mining area; θ₀ is the propagation angle of extraction; r is the main influence radius (m), and $r=\frac{H}{tan\beta }$; H is the mining depth, m; tanβ is the tangent of main influence angle; W_cm is the maximum surface subsidence value under full mining, mm, and $W_{cm}=mq·cos\alpha$; q is the subsidence coefficient; m is the thickness of the coal seam, m; α is the dip angle of the coal seam, (°); Ucm is the maximum horizontal movement value under full mining conditions, mm, and $U_{cm}=b{W}_{cm}$; b is the horizontal displacement coefficient.

From Equations (3)–(11), it is shown that the formula for calculating the surface movement and deformation used the surface integral of the double integral over the working surface area D. When solving double integrals, the integral value can be obtained by determining the upper and lower limits of the integration interval and finding the original function of the integrand. In general, the rectangle in the vertical or horizontal direction can quickly obtain the upper and lower limits of the integrand. The upper and lower limits of the function’s forms will bring complexity and inconvenience to the integral calculation. The area of the working face is usually hundreds of square meters. If the integral calculation is performed directly on the whole working face, it will be difficult to determine the integral area and the accuracy of the integral value will be affected; therefore, it is necessary to divide the whole working face area in a certain form [33]. Working faces in conventional mining areas are mostly irregular rectangular. For the mining subsidence prediction of arbitrarily working surfaces, the current treatment is to divide the non-rectangular working area into several rectangular working faces at certain intervals, in approximately vertical or horizontal directions, and then predict the subsidence formula for each regularly divided rectangular unit, and finally record the subsidence prediction results of the entire irregular working surface according to the superposition principle [34].

The rectangular subdivision method of irregular rectangular work face is convenient for integral calculation and has high program operation efficiency. However, it has many jagged shapes in the edge region of the working face, specifically, the subdivision of the working surface is incomplete, and the prediction accuracy of the working face is missing. By studying the principle and method of triangular subdivision and combining it with the Delaunay triangulation principle, the irregular shape is divided into triangular units by interpolating points at fixed intervals in the working face area, which is a good solution to the problem of jaggedness and accuracy deficiencies in rectangular subdivision. The main triangulation algorithms based on Delaunay principle are segmented merge algorithm, incremental inserting algorithm, and the triangular net growth algorithm. The incremental inserting algorithm is widely used due to its strict theory, uniqueness, and simple implementation. In this paper, the incremental inserting algorithm was used and optimized to triangulate irregular shapes.

Based on the calculation formula of surface movement and deformation, after selecting the triangular area of the unit, the predicted value of the area could be obtained after double integral operation, and the final prediction result of the working surface could be obtained by superposition. The double integral operation is a continuous process, and the programmed computational process is not continuous; therefore, it can only be run discretely, specifically, in the numerical integration form. For the calculation of the double integral in probability integral method, numerous researchers have developed different algorithms for mining subsidence prediction systems [6,35]. Many programs can be used to calculate the double integrals, such as the Integral2 in MATLAB, line integral, variable step size composite Simpson formula, and the Monte Carlo method. The Integral2 method in MATLAB is mature and accurate, but it is seldom used for the development of mining area subsidence prediction program due to the compatibility of MATLAB. Teng et al. used the line integral method to convert the surface fraction of the working surface into a line integral of the boundary linear segment, and the accuracy of the results was improved [36]. However, the simple boundary treatment ignores the influence of mining process on arbitrary point, and the inapplicability of the boundary division of the concave and convex working faces. The Monte Carlo method is simple to calculate the double integral program. With the higher requirement for integration accuracy, the number of random samples will be larger, and the complexity of program running time will subsequently increase [37].

In this paper, variable step-size composite Simpson formula was used to realize the discrete numerical operation of the continuous double integral formula, as shown in Equations (12)–(14), thus improving the prediction efficiency and accuracy.

$$I(f)\approx \frac{hk}{9}{\displaystyle \sum _{i=0}^n{A}_i{\displaystyle \sum _{j=0}^m{B}_{j}f(x_i,y_j)}}$$

(12)

$$h=\frac{\left(b-a\right)}{2n}$$

(13)

$$k=\frac{\left(d-c\right)}{2m}$$

(14)

where n and k are equal fractions in x and y directions; [a, b] is the interval in x direction; [c, d] is the interval in y direction; A = {1, 4, 2, 4, 2, …, 4, 2, 1} n, B = {1, 4, 2, 4, 2, …, 4, 2, 1} m.

In contrast to rectangles, for each fixed x_i, the domain of integration of the triangle in the y-direction was related to x_i. When integration was performed along the x-direction, the vertical integration function was different at the inflection point; therefore, the integration calculation needed to be handled separately. In the programming design process, as in Figure 9, ΔABC was divided into ΔABD and ΔDBC to integrate separately. In the special case of a right triangle, the integral value of one of the smaller triangle was zero, and the integral value of the other triangle could be calculated directly. This design method makes the integration result conform to the actual value. At the same time, the whole working face subdivision becomes more refined and the movement and deformation prediction values are closer to the real values.

The estimated parameters of surface subsidence could be selected approximately according to the estimated parameters of strip mining, as shown in the following equations.

$$q_s=\frac{(H-30)\cdot q_c}{5000\cdot a/b-2000}$$

(15)

$$\tan {\beta }_{\mathrm{s}}=(1.076-0.0014H)\tan {\beta }_c$$

(16)

$$b_{\mathrm{s}}=\frac{10,000b_c}{10,750+7.6H}$$

(17)

where q_s and q_c are the subsidence coefficients under strip and caving mining, respectively; tanβ_s and tanβ_c are the main influence tangents under strip and caving mining, respectively; b_s and b_c are the horizontal movement coefficients under strip and caving mining, respectively.

According to the mining thickness m₁, the buried depth H, and the parameters predicted by the probability integral method, the movement and deformation of the upper thin coal seam could be obtained by Equations (3)–(11) under the fully caving mining. For the lower thick coal seam under strip mining, the working face was first divided according to the equivalent mining width and retaining width, and then the movement and deformation could be obtained by Equations (3)–(11) according to the coal mining thickness m₂, coal seam buried depth H₁, and the predicted parameters of probability integral method. Finally, the predicted values of each divided part were superimposed to obtain the predicted values of the lower part under the strip mining. The influence value of the coal seam mining on the movement and deformation at any point was obtained by superimposing the predicted values of the upper and lower coal seams under different mining methods.

According to the design principle, the extreme value of surface movement and deformation after mining shall be less than the safety indexes. In this paper, the indexes are W_g, E_g, U_g, and I_g, as shown in Section 3.1. When Equation (18) was satisfied at the same time, the mining width of the caving face could be calculated under a certain width of the filling face, and then the mining design of the working face was completed.

$$\left\{\begin{array}{l}{W}_{\mathrm{p}}\le W_{\mathrm{g}}\\ E_p\le E_g\\ U_P\le U_g\\ I_p\le I_g\end{array}\right.$$

(18)

4. Discussion

In order to verify the practical application effect of the RSSC method through the combination of source control and ground rehabilitation, three typical application cases will be selected for analysis in this section. Finally, the application prospects of the new method will be analyzed.

4.1. Application Effects in Huayuan Coal Mine of China

Huayuan Coal Mine belongs to Jining Mining Group, with a length of 6.7 km from east to west, a width of 4.5 km from north to south, and an area of 28.06 km². The designed production capacity is 450,000 t/a, and the recoverable coal resource reserves are 33.69 million tons, under dense buildings (residential buildings, cold storage, brick-concrete structures).

In the early stages of mining, strip mining was used, and the recovery rate was only about 32%, resulting in a great waste of resources. In 2009, the mine applied the RSSC method with the combination of source control and ground rehabilitation for the mining of coal under dense village clusters. The resource recovery rate increased from less than 32% to more than 85%, and the mine service life was extended from the designed 40 years to more than 100 years.

According to the observation results of surface subsidence, the maximum subsidence value is 236 mm, and the mining of the working face basically does not affect the surface buildings and facilities. While ensuring the coordinated development of PLES, 780,000 tons of coal resources were extracted efficiently, with an additional profit of CNY 490 million.

4.2. Application Effects in Pingmei No.12 Coal Mine of China

Pingmei No.12 Coal Mine belongs to Pingdingshan Tianan Coal Mining Co., Ltd. The mine has a designed production capacity of 1.2 million t/a. At present, all major mining areas have entered the residual mining stage, and the amount of coal resources under buildings, water bodies, and railways is as high as 12.343 million tons, accounting for 44.7% of the total remaining recoverable reserves.

After adopting the RSSC method, the recovery rate of coal resources is increased by more than 85% and the service life of the mine is prolonged by about 10 years. According to the observation results of surface subsidence, the maximum subsidence value is 173 mm, and mining operations in the working face do not significantly impact surface buildings and facilities. While ensuring the coordinated development of PLES, 630,000 tons of coal resources were extracted efficiently, with an additional profit of RMB 280 million.

4.3. Application Effects in Wugou Coal Mine of China

The main mining seam of Wugou Coal Mine of Wanbei Coal-Electricity Group Co., Ltd. is No.10 coal seam, with high-quality coking coal. Thick unconsolidated aquifer of about 272.9 m is covered above the No.10 coal seam, especially the fourth aquifer at its bottom with an average thickness of 20.7 m, which directly covers the outcrop of mining coal and poses a serious threat to the safe mining of the shallow coal seam. In order to ensure the safe mining of the mine, a waterproof coal pillar of 60–91 m was retained, with about 12,112,600 tons of coal resources, accounting for more than 47% of the recoverable reserves of No.10 coal seam, causing serious resource loss.

After adopting the RSSC method, the development height of the water-conducting fracture zone is significantly reduced, and the original waterproof coal pillar of 60–91 m is reduced to 20 m, which greatly improves the upper limit of the mining of coal seam under the nearly loose aquifer. Moreover, 187,900 tons of coal resources were extracted, realizing economic benefits of about CNY 61 million.

In the process of the working face mining, the development height of water-conducting fracture zone in overlying strata was observed by using the borehole resistivity method. During the advancement of the filling working face, there was no clear change in the resistivity within the rock body of the overlying strata, and the resistivity value was basically within 100 Ωm, indicating that there was no clear fissure development in the overlying strata, thus effectively guaranteeing the safety of coal mining under water bodies, and protecting about 50,000 m² arable land on the ground.

4.4. Application Prospects of RSSC Method

According to BP Statistical Review of World Energy 2022 [1], the global coal production in 1981 was 3916.5142 million tons, and by 2021, the global coal production has reached 8172.6177 million tons, which has increased more than two times (Figure 10). The global coal production shows a trend of growth and stability. In general, the global coal production is maintained above 7400 million tons in order to meet the global coal consumption demand. However, the conventional coal mining will inevitably cause surface subsidence and ecological degradation, resulting in prominent conflict among the production-living-ecological space in mining areas. Although conventional coal mining can guarantee the global coal supply, it brings serious impacts on the residents and ecological environment of mining areas.

According to Section 3 and Section 4, the RSSC method can not only effectively control surface subsidence, but also increase the resource recovery rate to 100%. It is effective and can achieve the coordinated development of the production-living-ecological space in the mining area while ensuring coal supply. Therefore, the RSSC method in this paper has a potential application prospect.

5. Conclusions

Conventional coal mining will cause conflicts of production-living-ecological space in the mining area. In order to solve the problem, this paper developed a new model of regional surface subsidence control with the combination of source control and surface rehabilitation. The effectiveness and practical applications of the new method were analyzed and verified. The research results can provide technical support for high-quality development of underground coal mining and the integration of PLES in the major coal mining countries of the world.

(1)

A new method of regional surface subsidence control was proposed with the combination of source control and ground rehabilitation, considering the large-area PLES protection and large difference of deformation tolerance in the mining area, and the law of surface movement and deformation under insufficient mining. Through the numerical simulation method, the maximum surface subsidence values were 4883 mm, 587 mm, 642 mm, and 632 mm, respectively, under fully caving mining, strip mining, backfilling mining, and RSSC method. When the backfilling face size of the new method is from 100 m to 150 m and 200 m to 250 m, the control effect is significantly improved. Moreover, the larger the backfilling size, the smaller the surface subsidence and the better the control effect. The RSSC method can effectively control surface subsidence and increase the resource recovery rate to 100%.

(2)

The design and application process of the RSSC method through the combination of source control and ground rehabilitation was proposed. The prediction model of regional surface movement and deformation was constructed by using the variable step-size composite Simpson formula, which solves the problem of regional surface deformation control design and provides technical support for the coordinated development of coal mining and production-living-ecological space in the mining area.

(3)

The effectiveness of RSSC method was demonstrated through the applications in the Huayuan Mine, Pingmei No.12 Coal Mine, and the Wugou Coal Mine. It has been proven that the RSSC method can realize high-quality development of underground coal mining and the integration of PLES in the mining areas. The global coal production is maintained above 7400 million tons in order to meet the global coal consumption demand. However, conventional coal mining will inevitably cause surface subsidence and ecological degradation, resulting in the contradiction between coal mining and the sustainable development of the “production-living-ecological” space, which is very prominent in the world’s major mines. With the increase in coal production, the new method proposed will have a wider application prospect.