# Relationship between Surface Subsidence Range and Geological Mining Conditions Using Numerical Simulation and Machine Learning

Authors: Yanjun Zhang; Fushuai He; Jiayuan Kong; Yuanhao Zhu; Lingfei Wang
Journal: Scientific Programming
 (2022)

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## Abstract

With the increase of mined-out areas and geological disasters, it is necessary to study the influence range of mining. Moreover, with the growth in the amount of data, machine learning methods are commonly used to predict the surface subsidence. The 10 mm subsidence boundary is an important indicator to determine the influence range, and FLAC3D is suitable for solving the nonlinear large deformation problems. Therefore, it can be used to explore the relationship between the influence range of the surface movement (L) and geological mining conditions. Taking working faces A and B of two mines, through the establishment of a numerical model, the relationship between L and bedrock thickness, loose layer thickness, working face mining length, and overlying rock lithology is explored by using the control variable method. Moreover, the variation law is analyzed theoretically and mechanically. The results show that L is positively correlated with the thickness, while negatively correlated with the mining length. Similarly, L shows a slight increase after the key layer becomes weak. This study provides a scientific basis for reasonable coal mining and protection of surface buildings in the mining area. Integrating machine learning into the numerical model further increases the model throughput. The findings show that machine learning models had high accuracy in predicting surface subsidence, with the random forest trees and regression models having lower time and high accuracy, respectively.


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## Body

## 1. Introduction

Coal mining has caused varying degrees of damage to the surface, seriously affecting the safety of ground buildings. FLAC3D is a finite element difference software based on the Lagrange algorithm, which has unique advantages in simulating stability, vibration, and large nonlinear deformation problems. At present, FLAC3D has been widely used in grouting reinforcement and filling mining [1, 2], slope stability [3], goaf stability analysis [4, 5], and mining subsidence [6, 7] and has become increasingly mature. In terms of mining subsidence, many scholars have explored the laws of rock, surface movement, and deformation under various geological mining conditions by means of numerical simulations. For example, Liu et al. [8] used FLAC3D to explore the subsidence law of coal mining under the condition of large mining width and obtained higher simulation accuracy compared with the measured value. Similarly, Yu et al. [9] used FLAC3D numerical simulation as a technical means to explore the law of surface movement and deformation of thick loose layers with large mining heights. The authors obtained the conclusion that the surface subsidence is proportional to the overburden lithology and the subsidence velocity is inversely proportional to the overburden lithology.Likewise, Zhang et al. [10] used FLAC3D to simulate the influence of increasing mining working face and mining depth on the substation and its surrounding areas and obtained a series of results. Taking Xieqiao Mine as the research background, Pang and Xu [11] obtained the influence range of the surface movement by constructing the FLAC3D coal seam mining model. Moreover, they summarized the migration law of overlaying rock under different advancing distances. However, these scholars have only studied the range of surface movement for a single special geological and mining factor and lack comprehensive consideration of multiple factors to study the range of surface movement. It is believed that the thickness of the loose layer and bedrock, the lithology of the overlying rock, and the mining length of the working face are some of the most important factors that can significantly affect the law of surface movement and deformation [9–12].In view of this, the establishment of the FLAC3D three-dimensional numerical model, we use the control variable method to explore and investigate different trends in the influence range of surface movement. Furthermore, we study the trends in the change of bedrock and loose layer thickness, the mining length of the working face, and the physical, as well as the mechanical properties of the overlying rock. Moreover, with the growth in the amount of data, machine learning methods are usually used to predict the surface subsidence. Through simulation study, we obtain the correlation equation between the influence range of surface movement (10 mm subsidence boundary) and the geological mining conditions. Subsequently, this provides reference for coal mining under three different conditions and for the protection of buildings in the mining area. The following are the major contributions of the research conducted in this paper:(i)
We study the influence range of mining(ii)
The variation law is analyzed theoretically and mechanically(iii)
The study provides scientific basis for reasonable coal mining and protection of surface buildings in mining area(iv)
Machine learning method is integrated into the numerical model to predict the surface subsidenceThe rest of this paper is organized as follows: In Section2, we offer an overview of the materials and methods. Section 3 offers a brief discussion over the machine learning methods. Section 4 is about the datasets and evaluation metrics. Moreover, experimental details are presented. In Section 5, results are discussed. We summarize the major findings and outcomes of this research in Section 6. Finally, Section 7 concludes this paper with directions for further research and investigation.


## 2. Materials and Methods

### 2.1. Overview of the Study Area

The mining coal seam of working face A is 4 # coal seam. The size of the working face is 1000 m × 200 m. The average inclination angle of the coal seam is 2°, belonging to near-horizontal coal seam. The average mining depth is 500 m, and the average mining thickness is 2.3 m. The thickness of loess is 20 m. The working face adopts fully mechanized top coal caving and uses a long-wall retreating mining method. The all caving method is used to manage the roof. In order to avoid accidental results, this paper also selects another working face B under different geological conditions to explore. The mining coal seam of working face B is 3 # coal seam. The size of the working face is 1000 m × 200 m. The coal seam is near-horizontal coal seam. The average mining depth is approximately 313.5 m, and the average mining thickness is 4.4 m. The thickness of loess is 15.5 m. The working face adopts fully mechanized top coal caving and uses a long-wall retreating mining method. The all caving method is used to manage the roof. The layout of the observation station is shown in Figure1.Figure 1
Layout diagram of the observation station. (a) Working face A; (b) working face B.
(a)(b)


### 2.2. The Influence Range of Surface Movement

After coal mining, the stress balance around the goaf is damaged, and the rock strata move, deform, and destroy. When the goaf area reaches a certain range, the influence of underground mining is transmitted to the surface, which can cause surface movement and deformation. Subsequently, this can form a surface movement basin larger than the goaf area [13–15]. The horizontal distance from the boundary point on the main section of the moving basin (10 mm subsidence boundary) to the boundary of the coal pillar side is called the influence range of the surface movement (denoted by L in this paper) [16, 17]. Figure 2 shows the influence range of the surface movement.Figure 2
Influence range of the surface movement.


### 2.3. FLAC3D Numerical Simulation

#### 2.3.1. Principles of the FLAC3D

FLAC3D is a simulation calculation software developed by Itasca in the United States, which can simulate the stress characteristics of the three-dimensional structures such as soil and rocks. The software is based on the Lagrange algorithm and uses the finite difference explicit algorithm to obtain the time step solution of all the motion equations (including internal variables) of the model, which can track the progressive failure and collapse of the material. FLAC3D is suitable for simulating the mechanical behavior of rock and soil materials, especially for simulating large deformation and distortion, which can accurately analyze the movement and deformation laws of rock and surface after coal seam mining. Further details of the software can be found in [18, 19].In order to establish the calculation model, it is necessary to mesh division, select the constitutive model, and give boundary conditions to obtain the initial equilibrium state of the model. Then, the engineering simulation analysis is carried out through excavation or changing the boundary conditions [20, 21].


#### 2.3.2. Model Establishment

The three-dimensional numerical model is established based on the actual stratum structure of working face A. The model size is 3000 m × 1000 m × 515.3 m, and the excavation size is 1000 m × 200 m × 2.3 m. The model adopts the Mohr–Coulomb calculation criterion; the boundary adopts displacement constraint mode; thex-direction boundary adopts x-direction constraint; the y-direction boundary adopts y-direction constraint; the bottom constraint has three directions of displacement; the top surface is a free surface; and the initial stress field is calculated according to the gravity stress field of rock mass [22, 23]. Table 1 illustrates the physical and mechanical parameters of each layer that are used as parts of the model. The FLAC3D model is shown in Figure 3.Table 1
Physical and mechanical parameters of working face A.
LithologyThickness (m)Density (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Friction angle (°)Loess201825750.820.0217Siltstone200264025685.961130Mudstone110256622004.359.5622Medium grained sandstone170261031697.8414.426Coal2.313498760.732.3825Fine-grained sandstone13266028606.1212.721Figure 3
Numerical model of working face A.The numerical simulation model is constructed according to the geological conditions and distribution of the coal and rock strata in working face B, as shown in Figure4. The model size is 3000 m × 1000 m × 327.9 m, and the excavation size is 1000 m × 200 m × 4.4 m. The Mohr–Coulomb calculation criterion is still used in the model. The physical and mechanical parameters of each layer of the model are shown in Table 2.Figure 4
Numerical model of working face B.Table 2
Physical and mechanical parameters of working face B.
LithologyThickness (mDensity (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Friction angle (°)Loess15.51713680.810.0315Siltstone 160264025205.210.138Gritstone1214.8263330627.7211.832Medium grained sandstone13.7259828866.811.429Siltstone 24.6264025205.210.138Fine grained sandstone4.9265126505.5610.528Coal4.415798930.742.527Gritstone 210263330627.7211.832


#### 2.3.3. Simulation Accuracy Analysis

Taking working face A as an example, the subsidence value of surface movement is extracted from the FLAC3D, and the simulation accuracy of some points with a larger subsidence value is listed in Table 3. This should be noted that the surface subsidence value is the result extracted after the numerical model is balanced, so it can be equated with the subsidence value after the actual coal seam mining is stable. According to the surface movement data, compared with the measured subsidence value after stability, the maximum absolute error of the simulation is less than 50 mm, and the maximum relative error is less than 5%. The absolute error and relative error are small enough (considerably), indicating that the FLAC3D numerical simulation results are significantly accurate [24].Table 3
Comparison of simulated and measured subsidence.
NumberMeasured subsidence (mm)Simulated subsidence (mm)Absolute error (mm)Relative error (%)Z11313131630.2Z212731303302.4Z312421286433.5Z412381264262.1Z512141239252.1Z611811210282.4Z71172117640.3Z811181139211.9Z910751098232.1


## 2.1. Overview of the Study Area

The mining coal seam of working face A is 4 # coal seam. The size of the working face is 1000 m × 200 m. The average inclination angle of the coal seam is 2°, belonging to near-horizontal coal seam. The average mining depth is 500 m, and the average mining thickness is 2.3 m. The thickness of loess is 20 m. The working face adopts fully mechanized top coal caving and uses a long-wall retreating mining method. The all caving method is used to manage the roof. In order to avoid accidental results, this paper also selects another working face B under different geological conditions to explore. The mining coal seam of working face B is 3 # coal seam. The size of the working face is 1000 m × 200 m. The coal seam is near-horizontal coal seam. The average mining depth is approximately 313.5 m, and the average mining thickness is 4.4 m. The thickness of loess is 15.5 m. The working face adopts fully mechanized top coal caving and uses a long-wall retreating mining method. The all caving method is used to manage the roof. The layout of the observation station is shown in Figure1.Figure 1
Layout diagram of the observation station. (a) Working face A; (b) working face B.
(a)(b)


## 2.2. The Influence Range of Surface Movement

After coal mining, the stress balance around the goaf is damaged, and the rock strata move, deform, and destroy. When the goaf area reaches a certain range, the influence of underground mining is transmitted to the surface, which can cause surface movement and deformation. Subsequently, this can form a surface movement basin larger than the goaf area [13–15]. The horizontal distance from the boundary point on the main section of the moving basin (10 mm subsidence boundary) to the boundary of the coal pillar side is called the influence range of the surface movement (denoted by L in this paper) [16, 17]. Figure 2 shows the influence range of the surface movement.Figure 2
Influence range of the surface movement.


## 2.3. FLAC3D Numerical Simulation

### 2.3.1. Principles of the FLAC3D

FLAC3D is a simulation calculation software developed by Itasca in the United States, which can simulate the stress characteristics of the three-dimensional structures such as soil and rocks. The software is based on the Lagrange algorithm and uses the finite difference explicit algorithm to obtain the time step solution of all the motion equations (including internal variables) of the model, which can track the progressive failure and collapse of the material. FLAC3D is suitable for simulating the mechanical behavior of rock and soil materials, especially for simulating large deformation and distortion, which can accurately analyze the movement and deformation laws of rock and surface after coal seam mining. Further details of the software can be found in [18, 19].In order to establish the calculation model, it is necessary to mesh division, select the constitutive model, and give boundary conditions to obtain the initial equilibrium state of the model. Then, the engineering simulation analysis is carried out through excavation or changing the boundary conditions [20, 21].


### 2.3.2. Model Establishment

The three-dimensional numerical model is established based on the actual stratum structure of working face A. The model size is 3000 m × 1000 m × 515.3 m, and the excavation size is 1000 m × 200 m × 2.3 m. The model adopts the Mohr–Coulomb calculation criterion; the boundary adopts displacement constraint mode; thex-direction boundary adopts x-direction constraint; the y-direction boundary adopts y-direction constraint; the bottom constraint has three directions of displacement; the top surface is a free surface; and the initial stress field is calculated according to the gravity stress field of rock mass [22, 23]. Table 1 illustrates the physical and mechanical parameters of each layer that are used as parts of the model. The FLAC3D model is shown in Figure 3.Table 1
Physical and mechanical parameters of working face A.
LithologyThickness (m)Density (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Friction angle (°)Loess201825750.820.0217Siltstone200264025685.961130Mudstone110256622004.359.5622Medium grained sandstone170261031697.8414.426Coal2.313498760.732.3825Fine-grained sandstone13266028606.1212.721Figure 3
Numerical model of working face A.The numerical simulation model is constructed according to the geological conditions and distribution of the coal and rock strata in working face B, as shown in Figure4. The model size is 3000 m × 1000 m × 327.9 m, and the excavation size is 1000 m × 200 m × 4.4 m. The Mohr–Coulomb calculation criterion is still used in the model. The physical and mechanical parameters of each layer of the model are shown in Table 2.Figure 4
Numerical model of working face B.Table 2
Physical and mechanical parameters of working face B.
LithologyThickness (mDensity (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Friction angle (°)Loess15.51713680.810.0315Siltstone 160264025205.210.138Gritstone1214.8263330627.7211.832Medium grained sandstone13.7259828866.811.429Siltstone 24.6264025205.210.138Fine grained sandstone4.9265126505.5610.528Coal4.415798930.742.527Gritstone 210263330627.7211.832


### 2.3.3. Simulation Accuracy Analysis

Taking working face A as an example, the subsidence value of surface movement is extracted from the FLAC3D, and the simulation accuracy of some points with a larger subsidence value is listed in Table 3. This should be noted that the surface subsidence value is the result extracted after the numerical model is balanced, so it can be equated with the subsidence value after the actual coal seam mining is stable. According to the surface movement data, compared with the measured subsidence value after stability, the maximum absolute error of the simulation is less than 50 mm, and the maximum relative error is less than 5%. The absolute error and relative error are small enough (considerably), indicating that the FLAC3D numerical simulation results are significantly accurate [24].Table 3
Comparison of simulated and measured subsidence.
NumberMeasured subsidence (mm)Simulated subsidence (mm)Absolute error (mm)Relative error (%)Z11313131630.2Z212731303302.4Z312421286433.5Z412381264262.1Z512141239252.1Z611811210282.4Z71172117640.3Z811181139211.9Z910751098232.1


## 2.3.1. Principles of the FLAC3D

FLAC3D is a simulation calculation software developed by Itasca in the United States, which can simulate the stress characteristics of the three-dimensional structures such as soil and rocks. The software is based on the Lagrange algorithm and uses the finite difference explicit algorithm to obtain the time step solution of all the motion equations (including internal variables) of the model, which can track the progressive failure and collapse of the material. FLAC3D is suitable for simulating the mechanical behavior of rock and soil materials, especially for simulating large deformation and distortion, which can accurately analyze the movement and deformation laws of rock and surface after coal seam mining. Further details of the software can be found in [18, 19].In order to establish the calculation model, it is necessary to mesh division, select the constitutive model, and give boundary conditions to obtain the initial equilibrium state of the model. Then, the engineering simulation analysis is carried out through excavation or changing the boundary conditions [20, 21].


## 2.3.2. Model Establishment

The three-dimensional numerical model is established based on the actual stratum structure of working face A. The model size is 3000 m × 1000 m × 515.3 m, and the excavation size is 1000 m × 200 m × 2.3 m. The model adopts the Mohr–Coulomb calculation criterion; the boundary adopts displacement constraint mode; thex-direction boundary adopts x-direction constraint; the y-direction boundary adopts y-direction constraint; the bottom constraint has three directions of displacement; the top surface is a free surface; and the initial stress field is calculated according to the gravity stress field of rock mass [22, 23]. Table 1 illustrates the physical and mechanical parameters of each layer that are used as parts of the model. The FLAC3D model is shown in Figure 3.Table 1
Physical and mechanical parameters of working face A.
LithologyThickness (m)Density (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Friction angle (°)Loess201825750.820.0217Siltstone200264025685.961130Mudstone110256622004.359.5622Medium grained sandstone170261031697.8414.426Coal2.313498760.732.3825Fine-grained sandstone13266028606.1212.721Figure 3
Numerical model of working face A.The numerical simulation model is constructed according to the geological conditions and distribution of the coal and rock strata in working face B, as shown in Figure4. The model size is 3000 m × 1000 m × 327.9 m, and the excavation size is 1000 m × 200 m × 4.4 m. The Mohr–Coulomb calculation criterion is still used in the model. The physical and mechanical parameters of each layer of the model are shown in Table 2.Figure 4
Numerical model of working face B.Table 2
Physical and mechanical parameters of working face B.
LithologyThickness (mDensity (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Friction angle (°)Loess15.51713680.810.0315Siltstone 160264025205.210.138Gritstone1214.8263330627.7211.832Medium grained sandstone13.7259828866.811.429Siltstone 24.6264025205.210.138Fine grained sandstone4.9265126505.5610.528Coal4.415798930.742.527Gritstone 210263330627.7211.832


## 2.3.3. Simulation Accuracy Analysis

Taking working face A as an example, the subsidence value of surface movement is extracted from the FLAC3D, and the simulation accuracy of some points with a larger subsidence value is listed in Table 3. This should be noted that the surface subsidence value is the result extracted after the numerical model is balanced, so it can be equated with the subsidence value after the actual coal seam mining is stable. According to the surface movement data, compared with the measured subsidence value after stability, the maximum absolute error of the simulation is less than 50 mm, and the maximum relative error is less than 5%. The absolute error and relative error are small enough (considerably), indicating that the FLAC3D numerical simulation results are significantly accurate [24].Table 3
Comparison of simulated and measured subsidence.
NumberMeasured subsidence (mm)Simulated subsidence (mm)Absolute error (mm)Relative error (%)Z11313131630.2Z212731303302.4Z312421286433.5Z412381264262.1Z512141239252.1Z611811210282.4Z71172117640.3Z811181139211.9Z910751098232.1


## 3. Machine Learning

In this paper, the localities of the surface subsidence area were first documented by means of a wide inspection. A four-dimensional distribution of subsidence was then delivered for constructing and assessing learning models. The statistics logged into the dataset were subdivided into twofold segments of training (70 percent) and testing (30 percent) datasets. The link between surface sinking sites and the effective variables was evaluated in the research region, and drawings of the features causing land subsidence were generated by means of basic information (geographical and satellite pictures) in a raster format. A land subsidence map of the vulnerability zoning was created for further study, and the findings were assessed using simple regression (SR), boosted regression tree (BT), random forest trees (RFT), and support vector machine (SVM) models [25]. The assessment findings showed that machine learning models had high accuracy in predicting surface subsidence, with the BRT and SR models having high accuracy, respectively. Therefore, machine learning algorithms may be used for land use planning and groundwater management. The model is shown in Figure 5.Figure 5
The proposed model for machine learning and model training.Regression-based machine learning models describe the link and association among various variables by drawing a trend line from to the observed data. In a linear model of regression, a straight line is employed. However in nonlinear or logistic models of regression, a bent line is drawn. In case of the variables (independent) amendment, you may use regression to anticipate how the variable (dependent) will change. Simple linear regression models are useful to assess the association and link among two or more than two variables (quantitative). Decision trees are supervised learning techniques that may be used for classification as well as regression. The basic concept behind decision trees is to find the descriptive features that hold the maximum (related) information about the features of the target and subsequently divide the dataset along their values. This division essentially leading in values of the target feature that are as uncontaminated as reasonable for the fundamental datasets. Note that SVM models conduct vigorous regression for quantitative responses through grouping predictors in the observation space and commissioning a collection of inner products to exploit the correlations between observations. A cooperative of unpruned decision trees, individually created by using a sample of the bootstrap in the dataset (training) and randomly picked subgroups of variables (predictors) as candidates for separating tree nodes are used in the random forest regression.


## 4. Results

### 4.1. Relationship between L and Bedrock Thickness

Under the conditions of good simulation results above, the control variable method was used to explore the relationship between the influence range of the surface movement and its relationship with other factors by changing the thickness of the bedrock. During experimentations, one of the premises was that the mining length was 1000 m, and the thickness of the loose layer and the lithology of overlaying rock remained unchanged. In the experiment, the thickness of mudstone in working face A and the thickness of siltstone in working face B were changed, respectively, and the thickness variation range was 0 m–120 m. The calculation results were extracted from FLAC3D, and the relationship between the variation of the influence range of surface movement ΔL and the variation of rock thickness Δm is shown in Figure 6.Figure 6
Relationship between variation of influence range of the surface movement and variation of bedrock thickness. (a) Working face A and (b) working face B.
(a)(b)From the experimental results in Figure6, it can be obtained that the linear relationship between ΔL and Δm is approximately linear, and the influence range of the surface movement increases with the increase of bedrock thickness, which is a positive correlation. After abstraction, the linear regression equation of ΔL and Δm in working face A is ΔL=0.68Δm, and the linear regression equation of ΔL and Δm in working face B is ΔL=1.23Δm.


### 4.2. Relationship between L and Thickness of Loose Layer

Under the premise that the mining length was 1000 m and the bedrock thickness and the overlaying rock lithology remained unchanged, the thickness of the loose layer was changed to explore its influence on the range of surface movement. The thickness of the loose layer in working face A increased from 0 m to 120 m, and the thickness of the loose layer in working face B increased from 0 m to 124.5 m. The relationship between the variation of the range of surface movement ΔL and the variation of the thickness of the loose layer Δh is shown in Figure7.Figure 7
Relationship between variation of influence range of surface movement and variation of loose layer thickness. (a) Working face A and (b) working face B.
(a)(b)It can be seen from Figure7 that the overall relationship between ΔL and Δh is approximately linear. The influence range of the surface movement increases with the increase of the thickness of the loose layer, which is a positive correlation. After abstraction, the linear regression equation of ΔL and Δh in working face A can be fitted as follows: ΔL=0.71Δh, but the influence range of surface movement increases abruptly when the loose layer is 120 m. The linear regression equation of ΔL and Δh in working face B is ΔL=0.42Δh.


### 4.3. Relationship between L and Mining Length

The relationship between the influence range of the surface movement and the mining length of the working face was studied by changing the excavation length of working faces A and B (according to the starting distance of 0.25–0.5 times the mining depth, the initial lengths of working faces A and B were determined to be 300 m and 200 m, respectively). The thickness of bedrock, loose layer, and lithology of the overlying rock were unchanged. The advancing distance of working face A was 100 m each time and that of working face B was 200 m each time. The excavation results were counted and the relationship between the variation of the influence range of surface movement ΔL and the variation of mining length Δs is plotted as shown in Figure8.Figure 8
Relationship between variation of influence range of the surface movement and variation of mining length. (a) Working face A and (b) working face B.
(a)(b)It can be seen from Figure8 that the two working faces show the same regularity. The influence range of the surface movement is negatively correlated with the mining length, and ΔL and Δs show a linear relationship as a whole. After abstraction, the linear regression equation of ΔL and Δs in working face A is ΔL=−0.11Δs, and the linear regression equation of ΔL and Δs in working face B is ΔL=−0.05Δs.


### 4.4. Relationship between L and Overlaying Rock Lithology

On the basis of the mining length of 1000 m, the thickness of the rock layer and the thickness of the loose layer were kept unchanged, and the physical and mechanical parameters of the rock layer were changed to explore the relationship between the influence range of the surface movement and the lithology of the overlaying rock. In order to have a representative choice to change the key layer parameters, the original hard key layer was replaced by sandy mudstone and mudstone. In the experiment, the medium grained sandstone layer of working face A and the gritstone 1 layer of working face B were changed, respectively. The physical parameters of the changed and replaced rock are shown in Table4.Table 4
Changing physical and mechanical properties of rock.
<!—Col Count:6-->LithologyThickness (m)Density (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Medium grained sandstone261031697.8414.426Gritstone1263330627.7211.832Sandy mudstone257024004.89.8623Mudstone256622004.359.5622The influence range of the surface movement under the corresponding strata of working face A and B is shown in Table5, respectively. Through Table 5, it is known that the influence range of the surface movement increases by 4% and 6.6%, respectively. Furthermore, after replacing medium grained sandstone in working face A with sandy mudstone and mudstone, while the influence range of the surface movement increases by 2.5% and 3.4%, respectively, after replacing strata in working face B. The influence range of the surface movement is slightly affected by the rock mechanical properties as well.Table 5
Changes of influence range of surface movement.
Working faceLithologyThe influence range of surface movementWorking faceLithologyThe influence range of surface movementAMedium grained sandstone470BGritstone1354ASandy mudstone489BSandy mudstone363AMudstone501BMudstone366


### 4.5. Relationship between L, Geological Conditions, and Mining Conditions

From the above experiments, it can be seen that the influence range of the surface movement L is linear with the thickness of bedrock, the thickness of loose layer, and the mining length. At the same time, it will be affected by the mechanical properties of the rock. The relationship between L and geological mining conditions is as follows:(1)L=am+bh+cs+d,where a, b, and c represent the overlaying rock thickness, loose layer thickness, and mining length slope parameters, respectively. They are related to geological and mining conditions; d is the correction number related to the mechanical properties of the rock strata.Thea, b, and c coefficients have been obtained by using the control variable method in Sections 4.1–4.3, and the simulation results in Section 4.4 can be substituted into the relational expression. The relational expression of working face A between L and geological mining conditions is as follows: L=0.68m+0.71h−0.11s+d, combined with geological mining parameters, when the key layer is medium grained sandstone, d = 239.4 m; when replaced by sandy mudstone, d = 258.4 m; when replaced by mudstone, d = 270.4 m. The relationship of working face B between L and geological mining conditions is L=1.23m+0.42h−0.05s+d, when the key layer is gritstone, d = 31 m; when replaced by sandy mudstone, d = 40 m; when replaced by mudstone, d = 43 m, it can be seen that d increases gradually as the rock becomes weak.


### 4.6. Machine Learning to Predict Surface Subsidence

We used four machine learning approaches to predict the surface subsidence, i.e., simple regression, support vector machines, boosted trees, and random forest trees. Figure9 shows the time needed for training the model and prediction durations. The random forest tree was almost comparable to the SVM in terms of training time, but we observed lower prediction durations than the SVM, regression, and boosted trees (i.e., 3.56% to 7.33%). The durations are shown in seconds. Figure 10 shows the accuracy of various methods in RMSE and MAPE. The accuracy of the prediction approach is measured using the well-known parameters, i.e., root mean square error (RMSE) and MAPE. The MAPE values are shown in percentages where the lower ones are better than the higher values. Again, the RMSE and MAPE values confirm the efficiency of the random forest trees than the regression and SVM. As mentioned in Section 3, the entire dataset was divided into training (70 percent) and testing (30 percent) and the accuracy is computed with respect to the latter one.Figure 9
The training and prediction times of various techniques (seconds) (lower values denote more efficient schemes than the higher values and vice versa).Figure 10
Accuracy of various techniques in terms of RMSE and MAPE.


## 4.1. Relationship between L and Bedrock Thickness

Under the conditions of good simulation results above, the control variable method was used to explore the relationship between the influence range of the surface movement and its relationship with other factors by changing the thickness of the bedrock. During experimentations, one of the premises was that the mining length was 1000 m, and the thickness of the loose layer and the lithology of overlaying rock remained unchanged. In the experiment, the thickness of mudstone in working face A and the thickness of siltstone in working face B were changed, respectively, and the thickness variation range was 0 m–120 m. The calculation results were extracted from FLAC3D, and the relationship between the variation of the influence range of surface movement ΔL and the variation of rock thickness Δm is shown in Figure 6.Figure 6
Relationship between variation of influence range of the surface movement and variation of bedrock thickness. (a) Working face A and (b) working face B.
(a)(b)From the experimental results in Figure6, it can be obtained that the linear relationship between ΔL and Δm is approximately linear, and the influence range of the surface movement increases with the increase of bedrock thickness, which is a positive correlation. After abstraction, the linear regression equation of ΔL and Δm in working face A is ΔL=0.68Δm, and the linear regression equation of ΔL and Δm in working face B is ΔL=1.23Δm.


## 4.2. Relationship between L and Thickness of Loose Layer

Under the premise that the mining length was 1000 m and the bedrock thickness and the overlaying rock lithology remained unchanged, the thickness of the loose layer was changed to explore its influence on the range of surface movement. The thickness of the loose layer in working face A increased from 0 m to 120 m, and the thickness of the loose layer in working face B increased from 0 m to 124.5 m. The relationship between the variation of the range of surface movement ΔL and the variation of the thickness of the loose layer Δh is shown in Figure7.Figure 7
Relationship between variation of influence range of surface movement and variation of loose layer thickness. (a) Working face A and (b) working face B.
(a)(b)It can be seen from Figure7 that the overall relationship between ΔL and Δh is approximately linear. The influence range of the surface movement increases with the increase of the thickness of the loose layer, which is a positive correlation. After abstraction, the linear regression equation of ΔL and Δh in working face A can be fitted as follows: ΔL=0.71Δh, but the influence range of surface movement increases abruptly when the loose layer is 120 m. The linear regression equation of ΔL and Δh in working face B is ΔL=0.42Δh.


## 4.3. Relationship between L and Mining Length

The relationship between the influence range of the surface movement and the mining length of the working face was studied by changing the excavation length of working faces A and B (according to the starting distance of 0.25–0.5 times the mining depth, the initial lengths of working faces A and B were determined to be 300 m and 200 m, respectively). The thickness of bedrock, loose layer, and lithology of the overlying rock were unchanged. The advancing distance of working face A was 100 m each time and that of working face B was 200 m each time. The excavation results were counted and the relationship between the variation of the influence range of surface movement ΔL and the variation of mining length Δs is plotted as shown in Figure8.Figure 8
Relationship between variation of influence range of the surface movement and variation of mining length. (a) Working face A and (b) working face B.
(a)(b)It can be seen from Figure8 that the two working faces show the same regularity. The influence range of the surface movement is negatively correlated with the mining length, and ΔL and Δs show a linear relationship as a whole. After abstraction, the linear regression equation of ΔL and Δs in working face A is ΔL=−0.11Δs, and the linear regression equation of ΔL and Δs in working face B is ΔL=−0.05Δs.


## 4.4. Relationship between L and Overlaying Rock Lithology

On the basis of the mining length of 1000 m, the thickness of the rock layer and the thickness of the loose layer were kept unchanged, and the physical and mechanical parameters of the rock layer were changed to explore the relationship between the influence range of the surface movement and the lithology of the overlaying rock. In order to have a representative choice to change the key layer parameters, the original hard key layer was replaced by sandy mudstone and mudstone. In the experiment, the medium grained sandstone layer of working face A and the gritstone 1 layer of working face B were changed, respectively. The physical parameters of the changed and replaced rock are shown in Table4.Table 4
Changing physical and mechanical properties of rock.
<!—Col Count:6-->LithologyThickness (m)Density (kg·m−3)Bulk modulus (MPa)Tension (MPa)Cohesion (MPa)Medium grained sandstone261031697.8414.426Gritstone1263330627.7211.832Sandy mudstone257024004.89.8623Mudstone256622004.359.5622The influence range of the surface movement under the corresponding strata of working face A and B is shown in Table5, respectively. Through Table 5, it is known that the influence range of the surface movement increases by 4% and 6.6%, respectively. Furthermore, after replacing medium grained sandstone in working face A with sandy mudstone and mudstone, while the influence range of the surface movement increases by 2.5% and 3.4%, respectively, after replacing strata in working face B. The influence range of the surface movement is slightly affected by the rock mechanical properties as well.Table 5
Changes of influence range of surface movement.
Working faceLithologyThe influence range of surface movementWorking faceLithologyThe influence range of surface movementAMedium grained sandstone470BGritstone1354ASandy mudstone489BSandy mudstone363AMudstone501BMudstone366


## 4.5. Relationship between L, Geological Conditions, and Mining Conditions

From the above experiments, it can be seen that the influence range of the surface movement L is linear with the thickness of bedrock, the thickness of loose layer, and the mining length. At the same time, it will be affected by the mechanical properties of the rock. The relationship between L and geological mining conditions is as follows:(1)L=am+bh+cs+d,where a, b, and c represent the overlaying rock thickness, loose layer thickness, and mining length slope parameters, respectively. They are related to geological and mining conditions; d is the correction number related to the mechanical properties of the rock strata.Thea, b, and c coefficients have been obtained by using the control variable method in Sections 4.1–4.3, and the simulation results in Section 4.4 can be substituted into the relational expression. The relational expression of working face A between L and geological mining conditions is as follows: L=0.68m+0.71h−0.11s+d, combined with geological mining parameters, when the key layer is medium grained sandstone, d = 239.4 m; when replaced by sandy mudstone, d = 258.4 m; when replaced by mudstone, d = 270.4 m. The relationship of working face B between L and geological mining conditions is L=1.23m+0.42h−0.05s+d, when the key layer is gritstone, d = 31 m; when replaced by sandy mudstone, d = 40 m; when replaced by mudstone, d = 43 m, it can be seen that d increases gradually as the rock becomes weak.


## 4.6. Machine Learning to Predict Surface Subsidence

We used four machine learning approaches to predict the surface subsidence, i.e., simple regression, support vector machines, boosted trees, and random forest trees. Figure9 shows the time needed for training the model and prediction durations. The random forest tree was almost comparable to the SVM in terms of training time, but we observed lower prediction durations than the SVM, regression, and boosted trees (i.e., 3.56% to 7.33%). The durations are shown in seconds. Figure 10 shows the accuracy of various methods in RMSE and MAPE. The accuracy of the prediction approach is measured using the well-known parameters, i.e., root mean square error (RMSE) and MAPE. The MAPE values are shown in percentages where the lower ones are better than the higher values. Again, the RMSE and MAPE values confirm the efficiency of the random forest trees than the regression and SVM. As mentioned in Section 3, the entire dataset was divided into training (70 percent) and testing (30 percent) and the accuracy is computed with respect to the latter one.Figure 9
The training and prediction times of various techniques (seconds) (lower values denote more efficient schemes than the higher values and vice versa).Figure 10
Accuracy of various techniques in terms of RMSE and MAPE.


## 5. Discussion

### 5.1. Analysis of Relationship between L and Bedrock Thickness

From the above, it can be seen that the simulation results of two working faces in different regions are similar, which confirms that the study of surface movement and deformation by FLAC is credible and correct. Therefore, only one of the working faces is selected to discuss in the following sections. Under the condition that the mining length is 1000 m and the lithology of the overlaying rock and the thickness of the loose layer are unchanged. Furthermore, taking working face B as an example, the subsidence value obtained by changing the thickness of siltstone is plotted as the subsidence curve, as shown in Figure11.Figure 11
Subsidence curve of siltstone thickness variation.It can be seen from Figure11 that with the increase of siltstone thickness, the maximum surface subsidence value gradually decreases. However, the surface influence range slightly increases, and the basic shape of the curve is similar and gradually becomes flat. The increase of bedrock thickness improves the stability of rock strata and makes the surface subsidence value smaller. At the same time, the thickness of the bedrock makes the mining depth larger. According to the positive correlation between the surface influence range and the mining depth, the larger the mining depth is, the larger the surface influence range is, which is consistent with the experimental results of the larger influence range of the surface movement with the increase of bedrock thickness.


### 5.2. Analysis of Relationship between L and Loose Layer Thickness

Under the premise of mining length 1000 m, rock thickness, and rock lithology unchanged, taking A working face as an example, changing the thickness of the loose layer, the curve diagram of each subsidence result is drawn as Figure12.Figure 12
Subsidence curve of loose layer thickness variation.It can be seen from Figure12 that the shape change of the subsidence curve of 0–100 m in the loose layer is small, and the subsidence curve changes significantly at 120 m, which is manifested as the increase of subsidence value and the increase of surface influence range. This may be due to the excessive load caused by the thick loose layer that destroys the stability of the bedrock and makes surface subsidence occur again. The influence range of the surface movement increases with the increase of the thickness of the loose layer, which is consistent with the characteristics of wide influence range under the geological conditions of a thick loose layer. The experiment further confirms the known law of surface movement and deformation.


### 5.3. Analysis of Relationship between L and Mining Length

Taking working face B as an example, the subsidence curve is drawn as shown in Figure13 after extracting and counting the obtained surface movement deformation values. As can be seen from Figure 13, the maximum subsidence point is moving forward as the working face advances, and the subsidence value is increasing, eventually forming a bowl basin on the surface. When the excavation is 200 m, 400 m, and 600 m, respectively, the angle between the tangent and the horizontal line near the inflection point of the subsidence curve is 31°, 47°, and 50°, respectively. During the propulsion process, the angle between the tangent and the horizontal line near the inflection point increases continuously, the angle growth decreases gradually, and the subsidence curve becomes steeper and steeper, which is consistent with the decreasing and gradually stable influence range of the surface movement.Figure 13
Subsidence curves under different mining lengths.The stress nephogram of 200 m, 400 m, and 600 m excavation are shown in Figures14(a)–14(c). Through the stress nephogram, it can be found that the rock mass forms a pressure arch after the mining is completed. With the increase of the excavation length, the vault part continues to extend, and the reasonable axis of the arch under the vertical uniform load is a quadratic parabola. Therefore, the stability of the actual pressure arch is reduced, which leads to a greater mining length. Moreover, the more intense the surface movement basin activity is, the steeper the subsidence curve is. Similarly, the steeper the subsidence curve is, then smaller the influence range of the surface movement is. This reasonably explains the principle that the influence range of the surface movement changes with the mining length.Figure 14
Stress nephogram under different excavation lengths: (a) advanced to 200 m, (b) advanced to 400 m, and (c) advanced to 600 m.
(a)(b)(c)


### 5.4. Analysis of the Relationship between L and Overlaying Lithology

Under the condition of controlling the mining length of 1000 m and the thickness of rock and loose layer unchanged, the subsidence curves of each experimental results of working face A and B are shown in Figure15. It can be observed from Figure 15(a) that the subsidence value essentially increases obviously after replacing the hard core layer of medium grained sandstone in working face A with soft sandy mudstone and mudstone, respectively. Moreover, the maximum subsidence value is close to the thickness of coal seam excavation (2300 mm), which indicates that without the support of the key layer, the rock strata will be completely collapsed and compacted. This means that it will have a great impact on the ground, and the corresponding parameter d is also large (about 250 m). It can be seen from the subsidence curve, as shown in Figure 15(b), that after replacing the hard key layer of working face B with sandy mudstone and mudstone, the subsidence value increases significantly but the maximum subsidence does not reach the mining thickness (4400 mm). The reason is that there are also siltstone key layers in addition to gritstone. The support effect of this nonsingle key layer has a good protective effect on surface movement and failure, and the parameter d is small (about 40 m).Figure 15
Comparison of subsidence curves of changing rock mechanical parameters. (a) Working face A; (b) working face B.
(a)(b)


## 5.1. Analysis of Relationship between L and Bedrock Thickness

From the above, it can be seen that the simulation results of two working faces in different regions are similar, which confirms that the study of surface movement and deformation by FLAC is credible and correct. Therefore, only one of the working faces is selected to discuss in the following sections. Under the condition that the mining length is 1000 m and the lithology of the overlaying rock and the thickness of the loose layer are unchanged. Furthermore, taking working face B as an example, the subsidence value obtained by changing the thickness of siltstone is plotted as the subsidence curve, as shown in Figure11.Figure 11
Subsidence curve of siltstone thickness variation.It can be seen from Figure11 that with the increase of siltstone thickness, the maximum surface subsidence value gradually decreases. However, the surface influence range slightly increases, and the basic shape of the curve is similar and gradually becomes flat. The increase of bedrock thickness improves the stability of rock strata and makes the surface subsidence value smaller. At the same time, the thickness of the bedrock makes the mining depth larger. According to the positive correlation between the surface influence range and the mining depth, the larger the mining depth is, the larger the surface influence range is, which is consistent with the experimental results of the larger influence range of the surface movement with the increase of bedrock thickness.


## 5.2. Analysis of Relationship between L and Loose Layer Thickness

Under the premise of mining length 1000 m, rock thickness, and rock lithology unchanged, taking A working face as an example, changing the thickness of the loose layer, the curve diagram of each subsidence result is drawn as Figure12.Figure 12
Subsidence curve of loose layer thickness variation.It can be seen from Figure12 that the shape change of the subsidence curve of 0–100 m in the loose layer is small, and the subsidence curve changes significantly at 120 m, which is manifested as the increase of subsidence value and the increase of surface influence range. This may be due to the excessive load caused by the thick loose layer that destroys the stability of the bedrock and makes surface subsidence occur again. The influence range of the surface movement increases with the increase of the thickness of the loose layer, which is consistent with the characteristics of wide influence range under the geological conditions of a thick loose layer. The experiment further confirms the known law of surface movement and deformation.


## 5.3. Analysis of Relationship between L and Mining Length

Taking working face B as an example, the subsidence curve is drawn as shown in Figure13 after extracting and counting the obtained surface movement deformation values. As can be seen from Figure 13, the maximum subsidence point is moving forward as the working face advances, and the subsidence value is increasing, eventually forming a bowl basin on the surface. When the excavation is 200 m, 400 m, and 600 m, respectively, the angle between the tangent and the horizontal line near the inflection point of the subsidence curve is 31°, 47°, and 50°, respectively. During the propulsion process, the angle between the tangent and the horizontal line near the inflection point increases continuously, the angle growth decreases gradually, and the subsidence curve becomes steeper and steeper, which is consistent with the decreasing and gradually stable influence range of the surface movement.Figure 13
Subsidence curves under different mining lengths.The stress nephogram of 200 m, 400 m, and 600 m excavation are shown in Figures14(a)–14(c). Through the stress nephogram, it can be found that the rock mass forms a pressure arch after the mining is completed. With the increase of the excavation length, the vault part continues to extend, and the reasonable axis of the arch under the vertical uniform load is a quadratic parabola. Therefore, the stability of the actual pressure arch is reduced, which leads to a greater mining length. Moreover, the more intense the surface movement basin activity is, the steeper the subsidence curve is. Similarly, the steeper the subsidence curve is, then smaller the influence range of the surface movement is. This reasonably explains the principle that the influence range of the surface movement changes with the mining length.Figure 14
Stress nephogram under different excavation lengths: (a) advanced to 200 m, (b) advanced to 400 m, and (c) advanced to 600 m.
(a)(b)(c)


## 5.4. Analysis of the Relationship between L and Overlaying Lithology

Under the condition of controlling the mining length of 1000 m and the thickness of rock and loose layer unchanged, the subsidence curves of each experimental results of working face A and B are shown in Figure15. It can be observed from Figure 15(a) that the subsidence value essentially increases obviously after replacing the hard core layer of medium grained sandstone in working face A with soft sandy mudstone and mudstone, respectively. Moreover, the maximum subsidence value is close to the thickness of coal seam excavation (2300 mm), which indicates that without the support of the key layer, the rock strata will be completely collapsed and compacted. This means that it will have a great impact on the ground, and the corresponding parameter d is also large (about 250 m). It can be seen from the subsidence curve, as shown in Figure 15(b), that after replacing the hard key layer of working face B with sandy mudstone and mudstone, the subsidence value increases significantly but the maximum subsidence does not reach the mining thickness (4400 mm). The reason is that there are also siltstone key layers in addition to gritstone. The support effect of this nonsingle key layer has a good protective effect on surface movement and failure, and the parameter d is small (about 40 m).Figure 15
Comparison of subsidence curves of changing rock mechanical parameters. (a) Working face A; (b) working face B.
(a)(b)


## 6. Major Findings and Outcomes

The major findings of this study can be summarized as follows:(1)
Under the condition of constant mining length, overlaying rock lithology and loose layer thickness, we observed that the influence range of the surface movement is also regularly increased with the increase of bedrock thickness. The positive correlation curve shape of the two is in line with the linear function, and the slope is related to the geological and mining conditions.(2)
Under the condition that the mining length, bedrock thickness, and overlaying rock lithology remain unchanged, the influence range of the surface movement increases with the increase of the thickness of the loose layer. This shows a positive correlation and a linear relationship. However, when the loose layer reaches a certain thickness, it will lead to too much load to destroy the stability of the bedrock, therefore, essentially causing the secondary subsidence of the surface, and resulting in a sudden increase in the influence range of the surface movement.(3)
On the premise of certain geological and mining conditions, the influence range of the surface movement is negatively correlated with the mining length, and the slope is related to geological and mining conditions. The stress nephogram shows that the pressure arch is formed after the mining. The stability of the pressure arch decreases with the increase of the excavation length, and the subsidence curve becomes steeper, resulting in a smaller influence range of the surface movement.(4)
On the basis of a certain mining length and a constant thickness of the bedrock and loose layer, after replacing the key layer with a relatively weak rock, the influence range of the surface movement shows a slight increase. Based on the four factors, the relationship between the influence range of the surface movement and the geological and mining conditions is given, and the value of parameterd is obtained by substituting it into the formula, and d increases gradually with the weakening of the rock strata.(5)
Integrating machine learning in the numerical model further increases the model throughput. The findings show that machine learning models had high accuracy in predicting surface subsidence, with the random forest trees and regression models having lower time and high accuracy, respectively.


## 7. Conclusions and Future Work

In this paper, we studied the influence range of mining and analyzed the variations law theoretically and mechanically. The study provided a scientific basis for reasonable coal mining and protection of the surface buildings in the mining area. We also used machine learning methods which were integrated into the numerical model to predict the surface subsidence. On the basis of a certain mining length and a constant thickness of the bedrock and loose layer, after replacing the key layer with a relatively weak rock, the influence range of the surface movement shows a slight increase. We explored the relationship between the influence range of surface movement (L) and geological mining conditions. Through the establishment of a numerical model, the relationship between L and the bedrock and loose layer thickness, working face mining length, and overlying rock lithology is explored by using the control variable method. The results show that L is positively correlated with the thickness and negatively correlated with the mining length.In the future, we will further investigate the relationship between the influence range of surface movement (L) and geological mining conditions while taking additional parameters into account. The study is based on small amount of dataset, and further data collection approaches should be used to use vast amount of datasets. On the other hand, we will develop machine learning and Internet of Things (IoT) based algorithms to increase the prediction capability of surface subsidence.



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*Source: 8720831-2022-03-20.xml*