A Study on the Variation Characteristics of Floor Fault Activation Induced by Mining

Abstract

Coal seam floor water inrush is one of the most significant hazards affecting the safety of coal mine operations. To prevent water inrush incidents, it is critical to investigate the evolution of fault characteristics during the mining of working faces. This study takes the 4104 working face of the Heshan mine in China as the engineering case, and a fluid–solid–damage coupling numerical model of the mining process is established. COMSOL multiphysics software is employed to analyze the evolution of fault characteristics in the coal seam floor under mining-induced disturbances. The results show that under mining disturbances, the stress on the fault plane decreases initially and then increases, with higher stress at the sides and lower stress in the center. These stress variations induce alternating states of sliding and stability on the fault plane, indicating that fault reactivation manifests as a dynamic, non-equilibrium process. As the rock mass gradually deteriorates, the stress field at the fault zone undergoes redistribution, leading to fault reactivation. This process further exacerbates damage to the rock mass, resulting in a continuous increase in the permeability coefficient within the fault zone, thereby elevating the probability of water inrush hazards. Areas with more severe damage typically exhibit higher permeability, forming high-risk zones for water inrush. This study explores the characteristics of fault reactivation and its relationship with the seepage field, providing a theoretical basis for coal mining enterprises to prevent and control fault-induced water inrush.

1. Introduction

In China, coal resources are one of the primary energy sources, used in the nation’s development. As coal mining transitions from shallow to deep mining, underground water inrush accidents have become one of the most serious hazards affecting coal mine safety [1,2,3]. Water inrush accidents triggered by fault reactivation account for approximately 80% of all water-related accidents [4]. According to calculations by the National Bureau of Statistics of China, from 2012 to 2022, a total of 118 fatal water-related accidents occurred in China, resulting in 450 deaths [5]. Once a water inrush accident occurs, it poses a significant threat to the safety of mine personnel and the normal operation of the mine. Therefore, it is crucial to conduct research on the development characteristics of fault reactivation and seepage induced by mining disturbances in the coal seam floor. Understanding these dynamics is essential for implementing effective preventive measures to mitigate water hazards in mines.

In the field of mining engineering, significant research has been conducted on the mechanisms of mine water inrush in China, including in relation to theories such as the “Three Zones Theory” [6], the In situ Tension and Zero-position Failure Theory [7], and the Key Strata Theory [8]. The central concept of these theories is that, under the combined effects of mining-induced stress and confined aquifer pressure, fractures in the mine floor continuously propagate and develop until they form water-conducting pathways, resulting in water inrush accidents. The presence of faults in the mining face complicates the situation, as mining-induced disturbances and water pressure not only influence the extension of floor fractures, but also trigger fault reactivation [9]. This reactivation increases rock fragmentation near the fault, making it more susceptible to forming water-conducting channels [10]. Scholars worldwide have conducted extensive research in this field. Some have statistically analyzed fault populations within mining areas, describing the characteristics of each fault based on its distribution, length, vertical displacement, and dip angle, and predicting fault behavior under stress conditions [11,12]. Further research has revealed that the occurrence of water inrush in fault zones is closely related to the fault’s geometry and its proximity to the working face. The closer the working face is to the fault, the more pronounced the mining-induced impact on the fault plane. Moreover, the shear stress on the hanging wall is higher than that on the footwall, leading to a greater risk of failure. Faults with smaller dip angles tend to form water-conducting channels earlier [13], and when the fault dip coincides with the maximum expansion line, significant relative displacement occurs between the hanging wall and footwall, greatly increasing the risk of water inrush [14]. In regard to further research into fluid–solid coupling theory, Terzaghi [15] was the first to apply the fluid–solid coupling mechanism to investigate the relationship between the deformation of saturated soils and pore water pressure, proposing the concepts of effective stress and one-dimensional consolidation theory. Biot [16] expanded upon this work by extending the problem from one dimension to three dimensions, thus laying the foundation for fluid–solid coupling in mining engineering. The fluid–solid coupling theory organically links fault deformation with aquifer water pressure, which has subsequently triggered a series of coal mine water inrush studies based on this theory [17,18,19,20]. This development has advanced fault-induced water inrush research to a new stage.

Regarding the study of fault water inrush mechanisms under fluid–solid coupling conditions, methods such as field experiments, similar material simulation experiments, and numerical simulations are commonly employed. Field experiments provide results that closely align with real-world engineering scenarios, but they are relatively challenging to conduct [21]. Therefore, similar material simulation experiments and numerical simulations are more widely used. Similar material simulation experiments can intuitively reflect the changes in faults during different stages of mining [22]. By arranging measurement points on the model, the depth of floor failure and the height of confined water rise can be measured. This data can then be used to analyze and summarize the relationships between fault reactivation, floor rock mass unloading, the fracture development rate, and the progressive rise of confined water [23,24]. However, this method mainly offers a macroscopic view, which makes it difficult to perform real-time quantitative calculations for parameters like rock mass seepage velocity and stress. In contrast, numerical simulations have clear advantages in this regard, providing real-time data at various points. By analyzing the graphs from the experiments, one can clearly observe the evolution and characteristics of the stress field and seepage field in the model [25,26]. For instance, Kruszewski et al. [27] collected substantial in situ stress data and developed a static 3D geomechanical model to predict the spatial distribution of the in situ stress field. This was used to assess fault reactivation risk in the Ruhr region of Germany. Liu et al. [28] combined elastoplastic thin plate theory with numerical simulation methods, specifically analyzing the influence of mining distance and pore water pressure on floor damage. Zhu et al. [29] and Levasseur et al. [30] conducted research on the Excavation Damaged Zone (EDZ) formed during underground excavation. Their work revealed that when confined water enters fractures in the rock mass surrounding the EDZ under hydraulic pressure, it exerts a dual effect: weakening the rock strength and altering the rock mass permeability. Moreover, different researchers have also obtained results through simulation experiments, revealing the deformation and stress conditions of fault zones during the advancement of the working face [31], as well as the dynamic development patterns and distribution characteristics of floor bearing pressure, seepage vectors, and seepage velocity [32]. Additionally, they have studied the entire process of fault activation, fracture development, and the formation of water-conducting pathways in the floor [33,34,35], as well as the influence of the fault dip angle on water inrush in floor rock strata [36]. Based on this, Herrera-Herbert et al. [37] employed ANFIS technology to predict the probability of fault-induced water inrushes. They selected water pressure, the distance from the working face, the fault throw, mining height, the coal seam dip angle, and the aquiclude thickness as the six influencing factors. The prediction results were a perfect match with the actual outcomes. Motyka et al. [38] adopted a hydrochemical method, detecting water hazard zones by monitoring changes in the chloride ion concentration within the pores of rock samples to prevent water hazards. This method was successfully applied at the Olkusz-Pomorzany mine. These theoretical research achievements and practical applications have significantly reduced the occurrence of coal mine water inrush accidents, guaranteeing the safe extraction of coal resources.

In summary, significant progress has been achieved through the research on fault-induced water inrush mechanisms. Nevertheless, compared to the existing research findings, this paper focuses on assessing the risks of fault reactivation and floor water inrush. It primarily investigates the characteristics of fault stress field distribution, fault reactivation, damage evolution, and permeability coefficient variation. Regarding the research methodology, on one hand, it emphasizes the influence of rock mass damage by introducing a damage variable into the fluid–solid coupling theory. Based on this and utilizing geological data from China’s Heshan mine, a fluid–solid–damage excavation model was established using the COMSOL Multiphysics 6.0 simulation software. On the other hand, by manually setting the properties of the filling materials in the goaf within the model, the effect of goaf filling in regard to the actual longwall mining method can be simulated, making the model more realistic. This study aims to further refine the theoretical foundation of floor water inrush induced by fault reactivation. Through in-depth research on the evolution of fault-related characteristics, it provides a scientific basis for coal mining enterprises in regard to preventing and controlling fault-induced water inrush disasters.

2. Materials and Methods

2.1. Materials

2.1.1. Engineering Background

Working face 4104 is situated in the initial mining zone of Coal Seam No. 4 (Mining Coal Seam Identification Number, the coal seam within the Permian Heshan Formation) in the Heshan mine, China, where coal extraction was conducted using the inclined mining method. The No.4 coal seam is classified as a relatively stable medium-thickness seam, with an average thickness of 2.16 m and an average dip angle of 7°. The working face has a strike length of 118 m and a dip length of 465 m. The surface elevation ranges from +128 to +140 m, while the working face elevation is between −334 and −260 m.

Based on the conditions exposed in regard to the 4104 rail gateway and the 4104 belt gateway, no significant faults or folding structures were observed, although minor faulting was more developed in localized areas. The first fault, F_A28° (with a fault throw of 0.26 m and a dip angle of 28°), was revealed at a distance of 150 m from the cut, and it was a normal fault. The second fault, F_B86° (with a fault throw of 0.46 m and a dip angle of 86°), was revealed to be 265 m from the cut and was also a normal fault. A schematic layout of the working face is shown in Figure 1.

According to the geological report, the roof and floor of the coal seam are composed of dense and hard siliceous limestone or limestone, which exhibit weak water-bearing properties. However, beneath the coal seam floor, there is a strongly karstic aquifer (the lower section of the Heshan Formation aquifer), which is the primary water-conducting layer, directly beneath the floor. Additionally, the presence of faults within the working face provides natural pathways for water inrush from the floor. Therefore, it is necessary to study the characteristics of fault reactivation in the floor to better understand and mitigate the risk of water inrush.

2.1.2. Establishment of the Numerical Model

COMSOL multiphysics is a multi-physics coupling simulation software based on the finite element method, which is widely used in the modeling and analysis of complex physical processes in science and engineering fields [39,40]. Its core function is to solve the partial differential equation (PDE) of multi-physical field coupling through the use of the numerical method, which helps users predict physical phenomena in real scenes.

Based on the hydrogeological conditions of the 4104 working face, the fluid–solid–damage coupling model for the working face passing through the fault was constructed using COMSOL Multiphysics 6.0 simulation software, as shown in Figure 2.

The model is symmetrical in the x-axis direction in terms of both the physical and geometric conditions. Therefore, to reduce the computational effort, the model is symmetrically processed, and only half of the model is simulated. To eliminate the influence of boundary effects, a 65 m protective coal pillar is reserved on the right side in the advancing direction of the working face. A geometric model with a strike length (y direction) of 660 m, a dip length (x direction) of 130 m, and a height (z direction) of 120 m is established, with a coal seam thickness of 3 m. To accurately represent the heterogeneous properties of rock strata, the model employed region-specific meshing strategies, where mesh densities and element sizes were adaptively assigned according to the mechanical and hydrological characteristics of each geological unit. This approach ensured a balance was achieved between computational efficiency and numerical accuracy.

The following boundary conditions are implemented:

• Roller supports are applied to the front, rear, and right boundaries of the model, while the left boundary is set as a symmetrical boundary. The overlying strata of the model have a thickness of 345 m, and the average unit weight of the strata is 26.6 kN/m³. A vertical downward boundary load of 9.2 MPa is applied at the top of the model to simulate the self-weight stress of the overlying rock. The bottom boundary is fixed to restrict normal displacement.
• Seepage Boundary Conditions: The periphery and bottom of the model are set as no-flow boundaries. During mining, the goaf is connected to the atmosphere, and the water head pressure is set to atmospheric pressure. A linearly increasing water pressure is applied to the top of the aquifer to simulate the impact of non-uniform water pressure on the aquiclude. The initial water pressure p₀ at the top of the aquifer is set to 1.6 MPa. Based on the geological report on the 4104 longwall face in China’s Heshan coal mine, the physical and mechanical parameters of the rock strata in the model are listed in

  Table 1. The model’s physical and mechanical parameters.

  Rock Formation	Density ρ (kg∙m−3)	Elastic Modulus E (GPa)	Poisson Ratio ν	Internal Friction Angle φ (°)	Tensile Strength ft (MPa)	Compressive Strength fc (MPa)	Permeability Coefficient K (m/s)	Porosity ϕ
  Overlying strata	2400	14	0.31	25	5	40	4.6 × 10−9	0.02
  Coal seam roof	2660	23	0.32	28	3.6	31	5.7 × 10−9	0.009
  Coal seam	1580	4	0.36	36	0.3	17	1.7 × 10−8	0.024
  Coal seam floor	2600	22	0.24	40	3.2	30	8.9 × 10−9	0.008
  Water-bearing layer	2450	12	0.28	41	2.2	24	9.6 × 10−8	0.12
  Fault	1800	4	0.35	22	0.6	10	1.6 × 10−7	0.18
  Filling material	2000	1.2	0.34	32	2	19	3.2 × 10−9	0.1

  .

As illustrated in the simulated excavation diagram (Figure 3), the model simulates the following process: the working face is continuously mined from right to left, starting from the initial cut position. The first excavation step is set to 20 m, with each subsequent mining step advancing by 15 m. Faults F_A28° and F_B86° are defined at 150 m and 265 m, respectively. To represent the realistic collapsed goaf area of the roof, the material parameters in the excavated zones are manually assigned as backfill material properties in the software.

2.2. Methods

2.2.1. Coal Seam Mining Dynamics Theoretical Analysis

Before coal seam extraction, the rock mass is in an initial stress equilibrium state. After the extraction, the equilibrium of the rock mass is disrupted, and the stress within the rock mass redistributes, forming a new stress field. As shown in Figure 4, the stress field can be divided into three zones based on pressure changes: the stress reduction zone, the stress concentration zone, and the stress stable zone.

To study the stress condition at any point in the coal seam floor after mining-induced disturbances, the area in front of the coal face along the direction of mining advancement is selected for analysis. The floor of the coal seam is assumed to be an elastic body, and the bearing pressure is considered the primary distributed load acting on it. For ease of calculation without losing its essence, the stress distribution in the stress concentration zone is approximated as linear over two sections, with the respective lengths denoted as x₁ and x₂, while the stress influence range of the stress stable zone is denoted as x₃. The pore water pressure P_w in the confined aquifer beneath the floor is treated as a uniformly distributed load, which is used to establish the floor mechanical model, as shown in Figure 5. In this model, k represents the maximum concentrated stress coefficient; λ denotes the average unit weight of the overlying strata, in kN/m³; and H is the depth of the coal seam floor, in meters.

According to the theory of elasticity [41], considering a semi-infinite body subjected to a vertically distributed stress, with an intensity of q(x) along its boundary, the stress at any point within the semi-infinite body can be calculated. To achieve this, a coordinate system is established, as shown in Figure 5. First, a differential element of length dξ is selected at a distance ξ from point o along the boundary. The concentrated stress exerted by the differential element at point M (x, z) within the plane is given by dF = qdξ. The stress induced at point M by this differential element is expressed as:

$$\left\{\begin{array}{c}\begin{array}{c}d{\sigma }_z={\displaystyle \frac{2qd\xi }{\pi }}{\displaystyle \frac{z^3}{{\left[z^2+(x-\xi {)}^2\right]}^2}}\\ d{\sigma }_x={\displaystyle \frac{2qd\xi }{\pi }}{\displaystyle \frac{z(x-\xi {)}^2}{{\left[z^2+(x-\xi {)}^2\right]}^2}}\end{array}\\ d{\tau }_{\mathrm{zx}}={\displaystyle \frac{2qd\xi }{\pi }}{\displaystyle \frac{z^2(x-\xi )}{{\left[z^2+(x-\xi {)}^2\right]}^2}}\end{array}\right.$$

(1)

To determine the total effect of the distributed load on point M, the stresses induced by each differential element must be summed up. This is conducted by integrating the expression (1), which represents the stress induced by each differential element of the concentrated load. By integrating this over the length of the boundary subjected to the distributed load, the total stress at point M can be calculated as follows:

$$\left\{\begin{array}{c}\begin{array}{c}{\sigma }_z={\int }_a^b{\displaystyle \frac{2qd\xi }{\pi }}{\displaystyle \frac{z^3}{{\left[z^2+(x-\xi {)}^2\right]}^2}}\\ {\sigma }_x={\int }_a^b{\displaystyle \frac{2qd\xi }{\pi }}{\displaystyle \frac{z(x-\xi {)}^2}{{\left[z^2+(x-\xi {)}^2\right]}^2}}\end{array}\\ {\tau }_{\mathrm{zx}}={\int }_a^b{\displaystyle \frac{2qd\xi }{\pi }}{\displaystyle \frac{z^2\left(x-\xi \right)}{{\left[z^2+(x-\xi {)}^2\right]}^2}}\end{array}\right.$$

(2)

In the equation, a and b are the integration limits, which define the range of the distributed stress; ξ represents the horizontal distance from the origin of the coordinate system, measured in meters (m); x is the horizontal distance from point M to the differential element; and z is the vertical distance from point M to the differential element.

According to Figure 5, point M is primarily subjected to bearing stresses, Z₁(x), Z₂(x), the uniformly distributed load λH, and the aquifer pore water pressure P_w. The bearing stress expressions for the two segments can be derived based on a linear relationship, as follows:

$$\left\{\begin{array}{c}{Z}_1(x)={\displaystyle \frac{k\lambda H}{x_1}}x\\ Z_2\left(x\right)={\displaystyle \frac{\left(1-k\right)\lambda H}{x_2}}x+{\displaystyle \frac{\left(k-1\right)x1+k{x}_2}{x_2}}\lambda H\end{array}\right.$$

(3)

where Z₁(x) is the stress in the plastic zone of the stress concentration area (MPa), Z₂(x) is the stress in the elastic zone of the stress concentration area (MPa), k is the maximum concentrated stress coefficient, x₁ is the width of the plastic zone in the stress concentration area (m), and x₂ is the width of the elastic zone in the stress concentration area (m).

According to Equation (3), the stresses generated at point M due to the bearing stresses, Z₁(x), Z₂(x), the uniformly distributed load λH, and the aquifer pore water pressure P_w can be calculated. The vertical stresses are denoted as σ_z1, σ_z2, σ_zλ, and σ_zp for each respective component. The horizontal stresses are denoted as σ_x1, σ_x2, σ_xλ, and σ_xp. The shear stresses are denoted as τ_zx1, τ_zx2, τ_zxλ, and τ_zxp.

The stress generated at point M due to the bearing stress Z₁(x) can be expressed as follows:

To facilitate an understanding of the influence of the secondary stress field formed after excavation, as illustrated in Figure 6, within the two-dimensional plane, the resultant force σ_Z1(x) acting on point M below the coal seam floor can be broken down into two components along the horizontal and vertical directions, denoted as σ_x1 and σ_z1, respectively. However, point M is actually subjected to three-dimensional stresses and, thus, the shear stress, τ_zx1. The specific calculation formulas are presented below.

The stress effect of abutment stress Z1(x) at point M is shown in Figure 6:

Figure 6. Schematic diagram of stress Z_1(x) acting at point M.

Figure 6. Schematic diagram of stress Z_1(x) acting at point M.

$$\left\{\begin{array}{c}\begin{array}{c}{\sigma }_{z_1}={\displaystyle \frac{\gamma Hkz\left(x_1-x\right)}{\pi \left[z^2+{\left(x-x_1\right)}^2\right]}}+{\displaystyle \frac{\gamma Hkx\left[\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)+\mathit{arctan}\left(\frac{x}{z}\right)\right]}{\pi x_1}}\\ {\sigma }_{x_1}={\displaystyle \frac{\gamma Hkz\left(x-x_1\right)}{\pi \left[z^2+{\left(x-x_1\right)}^2\right]}}+{\displaystyle \frac{\gamma Hkx\left[\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)+\mathit{arctan}\left(\frac{x}{z}\right)\right]}{\pi x_1}}+{\displaystyle \frac{\gamma Hkz\mathit{ln}\frac{z^2+{\left(x_1-x\right)}^2}{z^2+x^2}}{\pi x_1}}\end{array}\\ {\tau }_{zx1=}{\displaystyle \frac{\gamma Hk{z}^2}{\pi \left[z^2+{\left(x-x_1\right)}^2\right]}}-{\displaystyle \frac{\gamma Hkz\left[\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)+\mathit{arctan}\left(\frac{x}{z}\right)\right]}{\pi x_1}}\end{array}\right.$$

(4)

Similarly, the stress effect of abutment stress Z2(x) at point M is shown in Figure 7:

Figure 7. Schematic diagram of stress Z_2(x) acting at point M.

Figure 7. Schematic diagram of stress Z_2(x) acting at point M.

$$\left\{\begin{array}{c}{\sigma }_{z2}={\displaystyle \frac{\gamma H\left(k-1\right)\left[x_1\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)-x_1\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)\right]}{\pi x_2}}\\ +{\displaystyle \frac{\gamma H\left(k-1\right)\left[x\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)-x\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)\right]}{\pi x_2}}\\ +{\displaystyle \frac{\gamma Hk\left[\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)-\mathit{arctan}\left(\frac{x_1-x}{z}\right)\right]}{\pi }}\\ +{\displaystyle \frac{z\left[\left(H-Hk\right)\lambda x{x}_1-Hk\lambda x{x}_2+\left(Hk-H\right)\lambda x^2\right]+x_{2}z\left[Hk\lambda x_2+\left(H-Hk\right)\lambda x+\left(Hk-H\right)\lambda x_1\right]}{\pi x_2\left[z^2+{\left(x_2-x\right)}^2\right]}}\\ -{\displaystyle \frac{z\left[\left(H-Hk\right)\lambda x{x}_1-Hk\lambda x{x}_2+\left(Hk-H\right)\lambda x^2\right]+x_{1}z\left[Hk\lambda x_2+\left(H-Hk\right)\lambda x+\left(Hk-H\right)\lambda x_1\right]}{\pi x_2\left[z^2+{\left(x_1-x\right)}^2\right]}}\\ \begin{array}{c}\\ {\sigma }_{x2}={\displaystyle \frac{\gamma H\left(k-1\right)\left[x_1\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)-x_1\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)\right]}{\pi x_2}}\\ +{\displaystyle \frac{\gamma H\left(k-1\right)\left[x\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)-x\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)\right]}{\pi x_2}}\\ +{\displaystyle \frac{\gamma Hk\left[\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)-\mathit{arctan}\left(\frac{x_1-x}{z}\right)\right]}{\pi }}\\ -{\displaystyle \frac{z\left[\left(H-Hk\right)\lambda x{x}_1-Hk\lambda x{x}_2+\left(Hk-H\right)\lambda x^2\right]+x_{2}z\left[Hk\lambda x_2+\left(H-Hk\right)\lambda x+\left(Hk-H\right)\lambda x_1\right]}{\pi x_2\left[z^2+{\left(x_2-x\right)}^2\right]}}\\ +{\displaystyle \frac{z\left[\left(H-Hk\right)\lambda x{x}_1-Hk\lambda x{x}_2+\left(Hk-H\right)\lambda x^2\right]+x_{1}z\left[Hk\lambda x_2+\left(H-Hk\right)\lambda x+\left(Hk-H\right)\lambda x_1\right]}{\pi x_2\left[z^2+{\left(x_1-x\right)}^2\right]}}\\ {\tau }_{zx2}={\displaystyle \frac{\gamma Hkz\left[\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)-\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)\right]}{\pi x_2}}\\ +{\displaystyle \frac{\gamma Hz\left[\mathit{arctan}\left(\frac{\left(x_1-x\right)}{z}\right)-\mathit{arctan}\left(\frac{\left(x_2-x\right)}{z}\right)\right]}{\pi x_2}}\\ +{\displaystyle \frac{z^2\left[\left(H-Hk\right)\lambda x_1-Hk\lambda x_2\right]+{\lambda x}_1{z}^{2}H\left(k-1\right)}{\pi x_2\left[z^2+{\left(x_1-x\right)}^2\right]}}\\ -{\displaystyle \frac{z^2\left[\left(H-Hk\right)\lambda x_1-Hk\lambda x_2\right]+{\lambda x}_2{z}^{2}H\left(k-1\right)}{\pi x_2\left[z^2+{\left(x_2-x\right)}^2\right]}}\\ \end{array}\end{array}\right.$$

(5)

The stress produced at point M by the uniformly distributed load λH is shown in Figure 8:

Figure 8. Schematic diagram of stress Z₃ acting at point M.

Figure 8. Schematic diagram of stress Z₃ acting at point M.

$$\left\{\begin{array}{c}{\sigma }_{z3}={\displaystyle \frac{\lambda H\left[\mathit{arctan}\left(\frac{\left({x_3+x_2+x}_1-x\right)}{z}\right)-\mathit{arctan}\left(\frac{x_2{+x}_1-x}{z}\right)\right]}{\pi }}\\ +{\displaystyle \frac{\lambda Hz\left({x_3+x_2+x}_1-x\right)}{\pi \left[z^2+{\left({x_3+x_2+x}_1-x\right)}^2\right]}}-{\displaystyle \frac{\lambda Hz\left({x_2+x}_1-x\right)}{\pi \left[z^2+{\left({x_2+x}_1-x\right)}^2\right]}}\\ \begin{array}{c}{\sigma }_{x3}={\displaystyle \frac{\lambda H\left[\mathit{arctan}\left(\frac{\left({x_3+x_2+x}_1-x\right)}{z}\right)-\mathit{arctan}\left(\frac{x_2{+x}_1-x}{z}\right)\right]}{\pi }}\\ -{\displaystyle \frac{\lambda Hz\left({x_3+x_2+x}_1-x\right)}{\pi \left[z^2+{\left({x_3+x_2+x}_1-x\right)}^2\right]}}+{\displaystyle \frac{\lambda Hz\left({x_2+x}_1-x\right)}{\pi \left[z^2+{\left({x_2+x}_1-x\right)}^2\right]}}\\ {\tau }_{zx3}={\displaystyle \frac{\lambda H{z}^2}{\pi \left[z^2+{\left({x_3+x_2+x}_1-x\right)}^2\right]}}-{\displaystyle \frac{\lambda H{z}^2}{\pi \left[z^2+{\left({x_2+x}_1-x\right)}^2\right]}}\end{array}\end{array}\right.$$

(6)

Assuming the distance between the coal seam floor and the upper surface of the aquifer is h, through coordinate transformation, the coordinates of point M under the distributed water pressure load can be expressed as M′ (x, h − z). Let z′ = (h − z). Therefore, the stress at point M induced by confined water pressure Pw is shown in Figure 9:

Figure 9. Schematic diagram of stress P acting at point M.

Figure 9. Schematic diagram of stress P acting at point M.

$$\left\{\begin{array}{c}{\sigma }_{zp}={\displaystyle \frac{P_w\left[\mathit{arctan}\left(\frac{\left({x_3+x_2+x}_1-x\right)}{z^{\prime }}\right)+\mathit{arctan}\left(\frac{x}{z^{\prime }}\right)\right]}{\pi }}\\ +{\displaystyle \frac{P_w{z}^{\prime }\left({x_3+x_2+x}_1-x\right)}{\pi \left[{z^{\prime }}^2+{\left({x_3+x_2+x}_1-x\right)}^2\right]}}+{\displaystyle \frac{P_w{z}^{\prime }x}{\pi \left({z^{\prime }}^2+x^2\right)}}\\ \begin{array}{c}{\sigma }_{xp}={\displaystyle \frac{P_w\left[\mathit{arctan}\left(\frac{\left({x_3+x_2+x}_1-x\right)}{z^{\prime }}\right)+\mathit{arctan}\left(\frac{x}{z^{\prime }}\right)\right]}{\pi }}\\ -{\displaystyle \frac{P_w{z}^{\prime }\left({x_3+x_2+x}_1-x\right)}{\pi \left[{z^{\prime }}^2+{\left({x_3+x_2+x}_1-x\right)}^2\right]}}-{\displaystyle \frac{P_w{z}^{\prime }x}{\pi \left({z^{\prime }}^2+x^2\right)}}\\ {\tau }_{zxp}={\displaystyle \frac{P_w{z^{\prime }}^2}{\pi \left[{z^{\prime }}^2+{\left({x_3+x_2+x}_1-x\right)}^2\right]}}-{\displaystyle \frac{P_w{z}^{\prime }}{\pi \left({z^{\prime }}^2+x^2\right)}}\end{array}\end{array}\right.$$

(7)

By superimposing the stress components induced at point M from the various stress distributions mentioned above, we obtain the total stress distribution expression at any point along the coal seam floor in the direction of working face advancement. The total stress at an arbitrary point in the floor rock can be expressed as [42]:

$$\left\{\begin{array}{c}\begin{array}{c}{\sigma }_z={\sigma }_{z1}+{\sigma }_{z2}+{\sigma }_{z3}-{\sigma }_{zp}\\ {\sigma }_x={\sigma }_{x1}+{\sigma }_{x2}+{\sigma }_{x3}-{\sigma }_{xp}\end{array}\\ {\tau }_{zx}={\tau }_{zx1}+{\tau }_{zx2}+{\tau }_{zx3}-{\tau }_{zxp}\end{array}\right.$$

(8)

From Equation (8), the maximum principal stress, minimum principal stress, and maximum shear stress at any point beneath the coal seam floor can be calculated as follows:

$$\left\{\begin{array}{c}{\sigma }_1={\displaystyle \frac{{\sigma }_x+{\sigma }_z}{2}}+\sqrt{{\left({\displaystyle \frac{{\sigma }_x-{\sigma }_z}{2}}\right)}^2+{{\tau }_{zx}}^2}\\ {\sigma }_3={\displaystyle \frac{{\sigma }_x+{\sigma }_z}{2}}-\sqrt{{\left({\displaystyle \frac{{\sigma }_x-{\sigma }_z}{2}}\right)}^2+{{\tau }_{zx}}^2}\end{array}\right.$$

(9)

$${\tau }_{max}=\sqrt{{\left({\displaystyle \frac{{\sigma }_x-{\sigma }_z}{2}}\right)}^2+{{\tau }_{zx}}^2}$$

(10)

In the above equations, σ₁ is the maximum principal stress (MPa) and σ₃ is the minimum principal stress (MPa).

Among them, the mechanical model for coal mining under fault-developed conditions is shown in Figure 10:

2.2.2. Analysis of Fault Loading and Reactivation Conditions

The stress at any point beneath the coal seam floor after mining has been partially calculated, and the expressions for the normal stress and shear stress on the fault plane are as follows:

Based on Figure 6, Figure 7, Figure 8 and Figure 9 that illustrate the stress analysis at point M below the coal seam floor, the combined effect of the redistributed stress field in the surrounding rock mass after coal seam excavation and the water pressure on the fault under fault existence conditions can be obtained, as shown in Figure 11. Using two-dimensional plane stress analysis, the stresses acting on the fault plane can be broken down into horizontal $\left({\tau }_s\right)$ and vertical stresses ${(\sigma }_n)$ that are parallel and perpendicular to the fault plane, respectively.

$${\sigma }_n={\sigma }_z{\cos }^2\theta +{\sigma }_x{\sin }^2\theta +2{\tau }_{zx}\mathit{sin}\theta \mathit{cos}\theta$$

(11)

$${\tau }_s=\left({\sigma }_x-{\sigma }_z\right)\sin \theta \cos \theta +{\tau }_{zx}\left({\cos }^2\theta -{\sin }^2\theta \right)$$

(12)

where σ_z is the vertical (overburden) stress, σ_x is the horizontal stress, τ_zx is the shear stress between the vertical and horizontal directions, and θ is the dip angle of the fault.

When fault reactivation occurs, relative frictional sliding happens within the rock mass along the fault plane. Under the influence of normal stress, frictional resistance develops on the fault plane. Therefore, the actual shear stress acting on the fault plane is:

$${\tau }^{\prime }=\left|{\tau }_s\right|-\left|\mu {\sigma }_n\right|$$

(13)

In the equation, μ is the coefficient of friction.

The condition for fault slip and activation can be expressed as:

$${\tau }^{\prime }=\left|{\tau }_s\right|-\left|\mu {\sigma }_n\right|>0$$

(14)

2.2.3. Fluid–Solid Coupling Governing Equations

Based on elasticity theory and the theory of porous media, assuming the porous medium is an elastic body and satisfies the generalized Hooke’s law, and using Biot’s effective stress principle, the governing equations under stress–seepage coupling can be derived from the fundamental equations of solid mechanics (with tensile stress considered positive) as in [43].

In regard to elastic mechanics, the static equilibrium equation of a solid is:

$${\sigma }_{i,jj}+F_i=0$$

(15)

In the equation, σ_i,jj is the total stress tensor and F_i is the volume force.

In porous media, the total stress is decomposed into effective stress σ′_ij and pore water pressure, p (MPa).

$${\sigma }_{i,jj}={{\sigma }^{\prime }}_{i,jj}-\alpha p{\delta }_{ij}$$

(16)

In the equation, α is Biot’s coefficient (0 ≤ α ≤ 10) and δ_ij is a Kronecker symbol.

The effective stress and strain satisfy Hooke’s law:

$${\sigma }_{i,jj}=2\mathrm{G}{\epsilon }_{ij}+\lambda {\epsilon }_{kk}{\delta }_{ij}$$

(17)

In the equation, $G={\displaystyle \frac{E}{2\left(1+2\upsilon \right)}}$ is the shear modulus, $\lambda ={\displaystyle \frac{2G\upsilon }{1-2\upsilon }}$ is the Lame constant, ${\epsilon }_{ij}={\displaystyle \frac{1}{2}}\left(u_{i,j}+u_{j,i}\right)$ is the strain tensor, $u_i$ is the displacement component, and ν is Poisson’s ratio.

Substitute the constitutive relationship into the total stress equilibrium equation:

$$\left(2\mathrm{G}{\epsilon }_{ij}+\lambda {\epsilon }_{kk}{\delta }_{ij}\right)-\alpha p_i+F_i=0$$

(18)

The derivative of the strain tensor is expanded and simplified:

$$G{u}_{i,jj}+\left(\lambda +G\right)u_{j,ji}-\alpha p_i+F_i=0$$

(19)

Bring $\lambda ={\displaystyle \frac{2G\upsilon }{1-2\upsilon }}$ into the formula, and the modified equation is:

$$G{u}_{i,jj}+{\displaystyle \frac{G}{1-2\nu }}{u}_{j,ji}-\alpha p_i+F_i=0$$

(20)

In the equation, E is the elastic modulus (GPa), G is the shear modulus (GPa), ν is Poisson’s ratio, u_i,jj represents the second derivative of displacement u_i (where i = x, y, z) with respect to direction j, and F_i is the component of the body force in the i-direction (where i = x, y, z).

Assuming the pores are fully saturated, the fluid is incompressible, and it fills the entire pore space, the governing seepage equation can be derived from the mass conservation equation and Darcy’s law, as follows:

$$𝛻·\left[-{\displaystyle \frac{K}{{\gamma }_w}}𝛻\left(p+{\gamma }_{w}z\right)\right]=Q_s$$

(21)

In the equation, K is the permeability coefficient of the rock (m/s), γ_w is the unit weight of the fluid (N/m³), z is the vertical coordinate, and Q_s is the mass source term.

2.2.4. Influence of Damage Variables on Solid Elements

Considering that when rock mass undergoes plastic deformation it is no longer an intact body but rather a fractured and damaged material, a damage variable D is introduced to account for its effect on the mechanical parameters of the rock mass. According to elastic damage theory, when the stress or strain state of an element satisfies a given damage threshold, the element begins to experience damage. The expression for the elastic modulus of the damaged material is given by:

$$E=\left(1-D\right)E_0$$

(22)

In the equation, D is the damage variable; E is the elastic modulus of the damaged material, assumed to be a scalar; and E₀ is the elastic modulus of the undamaged material, also assumed to be a scalar.

To assess the form of rock mass damage and determine the damage factor, the maximum tensile stress criterion and the Mohr–Coulomb strength criterion are used as the failure criteria for determining tensile damage and shear damage in the rock mass. The limiting conditions for damage initiation are as follows:

$$\left\{\begin{array}{c}{F}_1={\sigma }_1-f_t=0\\ F_2=-{\sigma }_3+{\displaystyle \frac{1+\sin \phi }{1-\sin \phi }}{\sigma }_1-f_c=0\end{array}\right.$$

(23)

where f_t is the uniaxial tensile strength of the rock mass (MPa); f_c is the uniaxial compressive strength of the rock mass (MPa); φ is the internal friction angle of the rock (°); and σ₁ and σ₃ are the maximum principal stress and minimum principal stress, respectively.

Based on the type of damage occurring in the rock mass, the damage variable can be determined using the following expression [44]:

$$D=\left\{\begin{array}{c} 0 F_1<0 F_2<0\\ 1-{\left|{\displaystyle \frac{{\sigma }_t}{f_{t0}}}\right|}^2 F_1=0 {dF}_1>0\\ 1-{\left|{\displaystyle \frac{{\sigma }_c}{f_{c0}}}\right|}^2 F_2=0 {dF}_2>0\end{array}\right.$$

(24)

In the equation, σ_t is the maximum tensile stress (MPa); σ_c is the minimum compressive stress, (MPa); f_t0 is the tensile stress that the rock mass is subjected to (MPa); and f_c0 is the shear stress that the rock mass is subjected to (MPa).

2.2.5. Impact of Damage Variables on the Seepage Field

Due to the damage occurring in the rock mass, the changes in the stress field simultaneously affect the seepage field. The relationship between porosity and stress conditions is given as [43]:

$$\varphi =\left({\varphi }_0-{\varphi }_r\right)\mathit{exp}\left({\alpha }_{\varphi }{\overline{\sigma }}_v\right)+{\varphi }_r$$

(25)

In the equation, ϕ₀ is the initial porosity of the rock mass under the initial stress state; ϕ_r is the limit value of the porosity of the rock mass; α_ϕ is the stress sensitivity coefficient of the porosity, with a typical value of α_ϕ = 5.0 × 10⁻⁸ Pa⁻¹; and ${\overline{\sigma }}_v$ is the mean effective stress (where tensile stress is considered positive and compressive stress is considered negative).

The formula for calculating the mean effective stress ${\overline{\sigma }}_v$ is as follows:

$${\overline{\sigma }}_v=\left({\sigma }_1+{\sigma }_2+{\sigma }_3\right)/3+\alpha p$$

(26)

In the formula, σ₂ is the second principal stress (MPa).

Considering that the permeability coefficient is closely related to both porosity and the damage variable, and assuming a cubic relationship between permeability and porosity, while also accounting for the influence of the damage factor, the permeability coefficient of the rock mass can be expressed as [44]:

$$K=K_0{\left(\varphi /{\varphi }_0\right)}^3\mathit{exp}\left({\alpha }_{k}D\right)$$

(27)

In the equation, K₀ is the permeability coefficient under the initial stress state (m/s) and α_k is the damage influence coefficient on permeability, with α_k = 5.0 indicating the impact of damage on permeability.

3. Results

Considering the heterogeneous characteristics of the rock mass within the fault zone, the Weibull probability density function is used to represent the variability in its properties [9,45]:

$$F\left(\lambda \right)={\displaystyle \frac{m}{{\lambda }_0}}{\left({\displaystyle \frac{\lambda }{{\lambda }_0}}\right)}^{m-1}exp\left[-{\left({\displaystyle \frac{\lambda }{{\lambda }_0}}\right)}^m\right]$$

(28)

where $\lambda$ represents Young’s modulus; ${\lambda }_0$ is the shape parameter (also known as the Weibull modulus), which controls the distribution’s skewness; and m is the scale parameter, which determines the characteristic scale of the property being modeled.

The relevant theoretical formulas described in Section 2 were input into the multiphysics coupling software COMSOL 6.0 to compute the constructed numerical model, and the simulation results were obtained.

3.1. Stress Distribution Characteristics of the Floor Fault

3.1.1. Analysis of Normal Stress Variation on F_A28° Fault

Figure 12 presents the normal stress distribution contour plots of the fault plane at various mining advancement distances. From the figure, it can be observed that during the mining process, regions of reduced compressive stress appear on the fault plane. As the working face advances, these low-stress regions move closer to the boundary between the coal seam floor and the fault, with the magnitude of the stress reduction gradually increasing. There is also a trend wherein compressive stress transitions into tensile stress. When the working face has advanced 155 m (exposing the fault), the coal at the fault–coal seam interface has been extracted, forming a goaf. At this point, the stress in the surrounding rock near the interface is released, and the rock mass is subjected to tensile stress.

As illustrated in Figure 12a, the initial manifestation of significant stress redistribution occurs at the lower extremity of the floor fault, exhibiting a compressive stress reduction to approximately 5.5 MPa, substantially lower than adjacent fault segments. With progressive face advancement, this stress-relief zone migrates along the advancement direction, while the previously affected region undergoes partial stress recovery.

As shown in Figure 12b–d on the process of the working face advancing towards but not crossing the fault: As the working face advances towards the fault without crossing it, the vertical distance between the working face and the fault plane gradually decreases. The overall mining-induced effects on the fault plane intensify, with the stress state consistently manifesting as compressive stress. Furthermore, the distribution characteristics of compressive stress on the fault plane become increasingly pronounced as the distance between the fault and the working face diminishes. Specifically, the magnitude of the stress trough (minimum compressive stress) decreases significantly. The spatial position of this trough consistently aligns vertically with the working face. Conversely, the segment of the fault plane ahead of the trough position experiences a substantial increase in compressive stress, forming a stress peak.

This phenomenon occurs because the goaf provides a stress relief space for the fault rock mass. The removal of the upper coal seam, which had previously confined the fault rock mass, allowed the rock mass to deform. Consequently, the stress within the fault rock mass is released, leading to a reduction in stress and the formation of the stress trough. As the working face approaches the fault, the zone of elevated stress within the abutment pressure zone formed ahead of the working face coal wall also moves closer to the fault plane. This proximity results in a significant impact on the lower section of the fault located ahead of the coal wall, causing the compressive stress in the affected fault zone to increase, characteristic of the observed stress peak.

When the working face exposes the fault, as shown in Figure 12e, a stress reduction zone appears at the upper end of the floor fault. Furthermore, a small area of tensile stress develops in the fault zone immediately below the working face coal wall.

This occurs because the upper end of the floor fault is now exposed to the goaf. The fault rock mass at this location begins to undergo decompression, and the tensile action acting upon it intensifies. Consequently, the stress state within the rock mass transitions from compressive stress to tensile stress.

When the working face completely crosses the fault, due to the compaction of the backfill material within the goaf, the distribution characteristics of the normal stress on the F_A28° fault revert to those resembling the pre-mining undisturbed stress state.

By utilizing the monitoring line installed within the F_A28° fault, the variation law of the fault’s normal stress could be further determined, as illustrated in Figure 8.

Figure 13 presents the normal stress variation curve along the centerline of the F_A28° fault. As can be observed from the figure:

• The overall distribution of the normal stress of the fault across different mining stages exhibits a characteristic pattern of lower stress in the middle section and higher stress at both ends.
• The stress evolution demonstrates a distinct trend: initial decrease → subsequent increase → eventual stabilization.
• The closer the working face approaches the fault, the lower the magnitude of the compressive stress trough becomes. Furthermore, the amplitude of this stress reduction increases significantly with decreasing distance.

Stress evolution in the F_A28° fault during working face advancement:

At 95 m face advancement (55 m from F_A28° fault): The floor fault began to experience significant mining-induced disturbance. The normal stress at the lower end of the fault changed first, exhibiting a relatively small zone of influence. A compressive stress trough formed, with a magnitude of approximately 5.5 MPa. The compressive stress distribution across the remainder of the fault remained relatively stable.

At 110 m face advancement (40 m from fault): The magnitude of the compressive stress trough is similar to that at the 95 m face advancement. However, the affected zone expanded considerably. A compressive stress peak emerged at y = 220 m on the fault plane, reaching a magnitude of approximately 9.1 MPa.

At 125 m face advancement (25 m from fault): Significant changes occurred in both the trough and peak magnitudes. A compressive stress trough developed at y = 218 m, with a magnitude of ~4.7 MPa. Concurrently, the compressive stress peak at y = 230 m exceeded 10 MPa. This indicated that the pressure acting on the fault rock mass at this location exceeded its compressive strength, leading to failure and instability.

At 140 m face advancement (10 m from fault): Failure was initiated in the rock mass near y = 238 m to y = 240 m on the fault plane.

At 155 m face advancement (crossed fault by 5 m): The working face had now exposed the fault. The goaf provided stress relief and deformation space for the rock mass. Consequently, the stress state at the exposed fault location (y = 240 m) transitioned from compressive stress to tensile stress. Tensile failure occurred in the fault rock mass at y = 241 m.

At 170 m face advancement (crossed fault by 20 m): The normal stress on the fault recovered due to the compaction of the goaf backfill material.

Based on the 3D distribution diagram and the normal stress variation curve of the F_A28° fault, the following conclusions can be drawn: (1) The stress reduction zones represented by the troughs in the figures were consistently located directly beneath the goaf for each mining step. This demonstrates that mining activity induces decompression in the rock strata below the goaf. Conversely, the compressive stress in the fault zone ahead of and below the coal wall increased substantially. This indicates the presence of a zone of high stress concentration within the coal wall, which increases the load on the rock mass. Ultimately, this resulted in the characteristic stress evolution on the fault plane: an initial decrease, followed by an increase. (2) The transition of the fault plane from being entirely subject to compressive stress to experiencing localized compression and tension reflected the progressive intensification of tensile forces acting on the fault rock mass. Consequently, the failure mode transitioned from predominantly compression–shear failure to a mixed tensile–compression–shear failure.

3.1.2. Analysis of Shear Stress Variation on F_A28° Fault

Figure 14 shows the shear stress distribution (nephograms) on the plane of the F_A28° floor fault for various working face advancement distances.

The distribution of fault shear stress during the working face advancement process exhibited a trend of an initial decrease, followed by an increase, along the y-axis direction. The characteristic shear stress variation showed that the closer the working face got to the fault, the more pronounced the amplitude of change in the shear stress peak on the fault plane became. Concurrently, the concentration zone of shear stress migrated towards the coal seam–fault interface, indicating the intensifying effects of mining-induced disturbance on fault activation.

Overall, the distribution characteristics of shear stress on the F_A28° fault were relatively similar to those of normal stress. Specifically, the initial changes in shear stress distribution, as shown in Figure 14a, were quite prominent, where both a shear stress trough and a shear stress peak can be clearly observed. During the evolution from Figure 14b–d, the positions of both the shear stress trough and peak on the fault plane migrated upward along the fault elevation as the working face advances, with the magnitude of the trough progressively decreasing, while the peak magnitude increased. As the shear stress trough diminished, at the mining step corresponding to the working face passing 5 m beyond the fault, the exposed section of the F_A28° fault experienced positive shear stress. At this stage, the fault plane was subjected to the combined action of both positive and negative shear stresses simultaneously. In Figure 14f, after the working face has completely crossed the F_A28° fault and the goaf has been backfilled, the shear stress distribution on the floor fault became relatively stable, exhibiting no further significant differential stresses.

The variation law of shear stress within the F_A28° fault could be further determined through the monitoring line installed across it, as illustrated in Figure 15.

The F_A28° fault shear stress change curve, displayed in Figure 15, presents the shear stress variation curve along the centerline of the F_A28° fault. To determine whether fault reactivation and slip have occurred, a criterion diagram based on Equation (14) is provided alongside Figure 10 for each mining step.

Figure 15 presents the shear stress variation curve along the monitoring line within the F_A28° fault. As observed in the figure, the distribution profile of shear stress on the fault plane resembles a wavy line along the direction of the working face advancement, exhibiting a sequential evolution in magnitude, characterized by a decrease → increase → decrease → increase. Starting from when the working face was 55 m from the fault, the shear stress distribution across the fault plane formed distinct shear stress troughs and shear stress peaks progressively from the base upward along the fault elevation. For the specific trough and peak magnitudes corresponding to each mining step, the trough magnitude progressively decreased, while the peak magnitude progressively increased, as the working face continuously advances closer to the fault. Furthermore, according to the results displayed in Figure 10 for the F_A28° fault monitoring line, the spatial positions where these troughs and peaks occur migrated along the fault elevation in response to the advancing working face.

At the 155 m working face advancement, the F_A28° fault was exposed. Near the exposure point (y = 242 m), the direction of the shear stress on the fault changed, subjecting it to positive shear stress.

To assess whether fault slip activation occurs, a schematic diagram of the fault slip criterion for each mining step is presented based on Equations (2)–(8) and the data are shown in Figure 15.

Figure 16 displays the discrimination diagram for fault slip activation. As defined by Equations (2)–(8), the portion of the fault slip criterion curve greater than 0 indicates that slip has occurred on the fault plane, while the portion less than 0 signifies that the fault is in a stable state at that time. It can be observed from the figure that partial slip had already been initiated on the fault plane when the working face advancement reached approximately 95 m (55 m from the fault). As the working face advanced further, specifically during the period when the face was between 40 m and 10 m from the fault, certain points on the fault plane exhibited a slip–stable alternation state. However, the overall range of slip occurring on the fault plane gradually expanded. Notably, after the working face was within 10 m of the fault (immediately prior to fault exposure), the area experiencing fault slip increased significantly.

This indicates that the relationship between fault activation and the mining distance is not monotonically positive, but is closely linked to the working face advancement distance, the magnitude of the shear stress, and the redistributed stress field. Analyzing the results prior to the working face reaching within 10 m of the fault: After working face excavation, a zone of elevated stress (abutment pressure) formed ahead of the coal wall, and this abutment pressure was transmitted into the floor strata. Consequently, when this pressure reached the fault plane, the affected section of the fault experienced a substantial increase in compressive stress. The increased compressive stress acting on the fault plane enhanced the frictional resistance between the rock masses within the fault, which tends to impede slip occurrence. However, concurrently, the shear stress acting along the potential slip direction of the fault also increased during this process. This resulted in the fault exhibiting alternating slip–stable behavior.

3.1.3. Analysis of Normal Stress Variation on the F_B86° Fault

Figure 17 illustrates the distribution of normal stress on the F_B86° floor fault plane at various distances relative to the working face. The simulation results spanning from when the working face was 35 m from the F_B86° fault to when it had crossed the fault by 40 m were analyzed, revealing significant changes to the normal stress on the F_B86° fault plane during this simulated advancement sequence.

From the figure, it can be roughly observed that for the F_B86° fault, significant stress fluctuations on the fault plane only occur when the working face advanced to 260 m, exposing the fault. Near y = 363 m, the stress state on the fault plane transitioned from compressive stress to tensile stress. Prior to the working face exposing the fault, the F_B86° fault plane was entirely subject to relatively uniform compressive stress.

Specifically, when the working face was 5 m from the F_B86° fault (immediately prior to fault exposure), pronounced changes occurred in the normal stress distribution on the fault plane. A small segment of the fault near the coal wall ahead of the working face experienced tensile stress, while the remainder of the fault plane remained subject to compressive stress. When the working face advanced 10 m beyond the F_B86° fault, compaction due to goaf backfilling reconsolidated the floor strata. Consequently, under the influence of this compaction effect, the entire lower section of the F_B86° fault exhibited uniformly compressive stress.

Throughout the process from when the working face was 35 m from the F_B86° fault until immediately before fault exposure, and then advancing 25 m and beyond the fault, it is clearly observed that the normal stress acting on the F_B86° fault plane remained entirely compressive. Despite changes in the distance between the working face and the fault, the variations in compressive stress on the F_B86° fault plane were negligible. This behavior was attributed to the steep dip angle of the F_B86° fault, resulting in a relatively small projected area on the horizontal plane. Furthermore, the spatial extent of influence from the redistributed stress field (secondary stresses) induced by mining is limited. Consequently, the normal stress on the F_B86° fault plane exhibited an “insensitive” response to changes in the working face advancement distance, yet undergoes drastic changes in magnitude when stress alterations do occur.

As observed in Figure 18, excluding the scenario when the coal wall ahead of the working face was 5 m from the fault, the normal stress variation trend along the F_B86° fault monitoring line was consistent across all of the other mining stages. The stress magnitude gradually increased from approximately 4.5 MPa to around 7.0 MPa along the positive y-axis direction, with both the range of variation and the rate of increase being fundamentally similar. Comparing this simulated result with the findings presented in Figure 13 reveals that due to the exceptionally steep dip angle of the F_B86° fault, the fault plane is horizontally distant from the abutment pressure zone generated by the advancing working face. Consequently, during the working face advancement from 30 m to 5 m from the F_B86° fault, the normal stress on the fault plane exhibited low sensitivity to mining influence. This explains why its stress evolution characteristics closely aligned with the phase occurring after the working face had crossed the fault by 10 m to 40 m, during which the goaf had been backfilled and consolidated.

Analysis of the unique stress changes occurring immediately prior to F_B86° fault exposure (coal wall 5 m from fault) revealed that at the lowermost point of the F_B86° fault monitoring line, the compressive stress magnitude was 3.4 MPa, representing an approximately 24% reduction compared to the 4.5 MPa observed at other operational points. Progressing along the positive y-axis direction, the compressive stress progressively decreased, dropping to zero at y = 363.2 m, wherein it transitioned to tensile stress. Beyond y = 363.6 m, the stress state reverted to compressive stress and increased rapidly and substantially. Consequently, the F_B86° fault experienced a mixed tensile–compressive normal stress mode. This characteristic behavior was attributed to the fault segment between y = 362 m and y = 363.3 m being positioned directly beneath the working face. Following coal extraction in this zone, the floor fault rock mass deformed due to stress redistribution, intensifying the tensile effects. Stress relief was initiated, reducing the compressive stress magnitude. Conversely, the fault plane beyond y = 363.3 m exhibited a sharp compressive stress increase due to the influence of stress concentration ahead of the working face coal wall.

3.1.4. Analysis of Shear Stress Variation on the F_B86° Fault

Figure 19 presents the shear stress distribution contour plots of the F_B86° fault plane at various distances between the working face and the fault. From the figure, it can be observed that when the working face is 35 m and 20 m away from the fault, there is no significant change in shear stress on the fault plane. However, when the working face is 10 m away from the fault, the shear stress on the fault plane increases sharply, with stress levels rising dramatically, reaching a maximum value that is twice as high as the peak stress under other conditions. After the working face advances past the fault, the shear stress distribution on the fault plane stabilizes, due to the backfilling of the goaf.

This analysis shows how the proximity to the fault significantly influences shear stress behavior, particularly as the working face approaches 10 m of the fault, leading to a substantial increase in shear stress, which could heighten the risk of fault slip. After mining passes through the fault, the shear stress stabilizes due to backfilling, reducing the potential for further fault reactivation.

Figure 20 presents the shear stress variation curve along the monitoring line of the F_B86° fault. It can be deduced from the figure that for the four mining scenarios, when the working face was 35 m and 20 m from the fault and when it had passed the fault by 25 m and 40 m, the shear stress variations were similar in terms of both amplitude and trend. The shear stress magnitude was distributed within the range of 0.5 to 1.5 MPa, distributed around an average of approximately 1 MPa, and exhibited an evolution pattern of an initial decrease → subsequent increase → further decrease, with the stress direction consistently aligned with the positive y-axis.

For the mining scenario immediately prior to F_B86° fault exposure (coal wall 5 m from fault), the fault shear stress began to increase substantially near y = 362.2 m, reached a maximum magnitude of approximately 3.8 MPa at y = 362.7 m, before decreasing to 3 MPa. This behavior is attributed to the entire lower section of the F_B86° fault being situated within the influence zone of the stress concentration area ahead of the coal wall during Step 17 of the mining sequence, as evidenced in Figure 3. Consequently, shear stress acting along the positive y-axis direction exhibited continuous intensification across this fault segment.

For the mining scenario wherein the working face had advanced 10 m beyond the F_B86° fault, the fault shear stress began decreasing from 0.8 MPa along the y-axis direction, and reached zero for the first time near y = 363.5 m. A short segment of the fault beyond y = 363.5 m then exhibited negative shear stress (opposite to the y-axis direction). This behavior is attributed to the lower end of the F_B86° fault being positioned directly beneath the goaf during Step 18 of the mining sequence. While the fault segment between y = 362 m and y = 363.3 m still experienced positive shear stress due to the compaction effect from the weak backfill material in the previous goaf, floor heave occurred in the goaf. Consequently, decompression in the fault rock mass caused the acting positive shear stress to continuously diminish, eventually transitioning to negative shear stress, which then progressively increased.

Similar to Section 3.1.2, a criterion diagram based on Equation (14) is provided in Figure 20 for the F_B86° fault at different mining steps. This diagram helps to determine the conditions under which fault slip may occur.

The criterion curve indicates that when the value exceeds 0, fault slip occurs, while values below 0 suggest that the fault remains stable. By comparing the shear stress changes at each mining step, the diagram highlights the areas and stages of the fault plane that are likely to experience reactivation or slip, providing insights into the fault’s response to mining-induced stresses at various stages of mining progression.

From Figure 21, it can be observed that when the working face is 10 m away from the F_B86° fault and about to expose it, slip occurs in the upper-middle section of the fault plane. Apart from the scenario wherein the fault is fully exposed Figure 21c, no slip is observed on the fault plane at the other mining distances. This is because the F_B86° fault has a steep dip angle and a relatively narrow distribution along the strike, meaning that the fault is only significantly impacted when the working face is in very close proximity. Combined with the shear stress distribution characteristics shown in Figure 14 and Figure 15, it is evident that once the F_B86° fault is disturbed, the stress on the fault plane undergoes dramatic changes. This suggests that, at the same mining distance, faults with steeper dip angles are less sensitive to mining-induced stress disturbances compared to shallower faults, but once impacted, the degree of stress change is significantly greater. This indicates a higher risk of fault reactivation and slip for steeply dipping faults when subjected to mining activities.

3.2. Damage Evolution Pattern of the Floor Fault

3.2.1. Damage Evolution Process as the Working Face Advances Toward the F_A28° Fault from the Cut

As shown in Figure 22, the floor strata underwent failure due to mining-induced disturbances. The failure zone progressively developed with the working face advancement, wherein the regions depicted in red indicate higher degrees of damage. The damage distribution surrounding the goaf exhibited a gradual attenuation from the interior outward, with the peak damage intensity concentrated in the immediate vicinity of the excavation boundary. For a single goaf, the damage pattern manifested a distinct saddle-shaped configuration. The implementation of low-strength backfill materials effectively inhibited damage evolution within the rock mass. Consequently, after multiple mining stages, the resultant damage distribution developed a characteristic wavy pattern. When the working face is 50 m from the fault (Figure 22c), the F_A28° fault shows signs of damage for the first time. Based on stress analysis, this is caused by excessive compressive stress on the fault. As mining progresses, the damage zone on the F_A28° fault continues to develop along the fault dip direction, extending into the floor of the working face, with the extent of the damage zone growing continuously. This results in a ring-like pattern, where the central portion is severely damaged, surrounded by a less damaged area. When the working face is 25 m from the fault (Figure 22d), the shear failure zone in front of the working face connects with the fault fractures. As the working face continues to advance, the connection between the floor failure zone and the F_A28° fault expands further, increasing the extent of the damaged and connected areas.

3.2.2. Damage Evolution Process as the Working Face Advances Through the F_A28° Fault Toward the F_B86° Fault

From Figure 23, it can be observed that after the working face passes through the F_A28° fault, the F_A28° fault stabilizes due to the compaction effect of the backfilling material, and as it moves further away from the advancing working face, the stress state becomes relatively stable, with no significant development of further damage. When the working face is 5 m from the F_B86° fault (Figure 23c), just before the fault is exposed, the F_B86° fault begins to experience damage, with localized failure occurring. Compared to the initial damage onset in terms of the F_A28° fault, the F_B86° fault exhibits a wider damage zone.

This indicates that although the F_A28° fault remains stable after the working face advances past it, the F_B86° fault is subjected to more significant mining-induced stress concentrations, resulting in a larger damage zone as the working face approaches, particularly due to the fault’s steep dip angle and greater stress accumulation.

3.2.3. Damage Evolution Process as the Working Face Advances from the F_B86° Fault Toward the Stope Boundary

As the working face continues to advance after passing through the F_B86° fault and proceeds toward the end of the mining process (late-stage advancement), the influence of mining-induced disturbances on the activation of both faults is illustrated in Figure 24.

From Figure 24, it can be seen that, at this stage, as the working face continues to advance and moves further away from the faults, the backfilling effect in regard to the goaf becomes more pronounced. This reduces the influence of mining-induced stress and confined water pressure on the faults. Consequently, the impact on the damage evolution of both the F_A28° and F_B86° faults is minimal, and the damage zones of the two faults remain largely unchanged.

This observation indicates that the combined effect of stress relief and backfilling significantly mitigates further fault activation as mining progresses further away from the faults, stabilizing the faults’ stress states.

To highlight the damage evolution characteristics of the F_A28° fault plane during mining operations, the damage evolution behavior of the F_A28° fault plane at the longwall face advancing at a distance of 80–125 m was selected as the research subject for the analysis. A zoomed-in view of the damaged section on the fault plane is provided for detailed observations, as illustrated in Figure 25.

When the working face advanced to 80 m, damage distribution was initiated in the lower segment of the F_A28° fault plane, forming an annular damage contour. The contour exhibited intensifying red gradients from the periphery to the core until it vanished, indicating progressively increasing damage coefficients in the surrounding rock mass toward the center, wherein the core rock mass reached a complete failure state.

As the mining progressed (95–125 m advancement), distinct expansion of the fault plane damage contour was observed, with an aggravated damage intensity. Ultimately, the fault damage zone became interconnected with the floor strata failure domain.

Regarding the damage evolution characteristics of the F_B86° fault plane during mining operations, the damage evolution behavior of the F _B86° fault plane within the working face advancement section of 245 m to 290 m was selected as the research subject for the analysis, as depicted in Figure 26:

During the longwall face advancement from 245 m to 290 m, it was observed that when the working face cut through the F_B86° fault, extensive rock mass damage occurred directly across both the upper and lower sections of the F_B86° fault plane. Compared with the F_A28° fault, the F_B86° fault plane exhibited more extensive damage zones, and its damage evolution process manifested significantly more violent characteristics.

3.3. Characteristics of Fault Permeability Coefficient Variation

3.3.1. Variation Pattern of Permeability Coefficient in the F_A28° Fault

The diagram in Figure 27 presents the penetration coefficients of the F_A28° fault during mining, in the form of permeability coefficient variation curves (in units of m/s), along the monitoring line, during the advancement of the working face towards the F_A28° fault.

As shown in Figure 27, after the mining of the working face began, the permeability coefficients at different locations along the fault exhibited a trend of a rapid increase → gradual increase → sharp decrease, with an increasing elevation. Under mining-induced disturbances, a pressurized zone forms ahead of the coal wall, with its movement direction aligned with the advancing working face. As the working face gets closer to the fault, the stress on the fault increases, especially at locations closer to the coal seam floor. Consequently, the peak position of the permeability coefficient moves upward along the fault elevation as the damage spreads.

In the original rock stress state, the fault’s permeability coefficient remains stable at around 7 × 10⁻⁸ m/s. When the working face is 70 m away from the fault, the permeability coefficient of the F_A28° fault suddenly increases to approximately 1.2 × 10⁻⁵ m/s, corresponding to compressive–shear failure occurring at elevations between −340 m and −332 m. The overall peak value of the permeability coefficient increases as the working face advances, reaching its maximum value of 2.7 × 10⁻⁵ m/s at an elevation of −308.78 m when the working face is 5 m past the F_A28° fault. This represents a significant increase compared to the initial permeability coefficient, indicating that fault reactivation is one of the major factors influencing permeability.

The location of the permeability coefficient peak corresponds to areas where significant stress changes occur along the fault. The reason for this is that mining-induced stress causes notable disturbances to the fault zone, leading to plastic deformation and damage in the fractured rock mass within the fault zone. This results in rock mass instability, fracture expansion, and an increase in permeability.

3.3.2. Variation Pattern of Permeability Coefficient in the F_b86° Fault

From Figure 28, it can be seen that when the working face is 35 m and 20 m away from the F_B86° fault, the permeability coefficient of the fault remains relatively unchanged. However, when the working face is within 5 m of the fault, the permeability coefficient begins to sharply increase. After the F_B86° fault is exposed, the permeability coefficient increases further. This phenomenon is due to two primary factors: (1) the significant stress changes in the F_B86° fault zone during the retreat mining of the coal seam, which result in fault activation; and (2) the accumulation and development of damage within the F_B86° fault, leading to increased fracture apertures and a greater number of fractures within the fault’s fractured zone. Consequently, the permeability coefficient continues to rise.

This indicates a direct relationship between the mining-induced stress, fault damage evolution, and the continuous increase in permeability, highlighting the critical need to monitor permeability changes in fault zones to manage risks, such as water inrush and fault reactivation, during mining operations.

4. Discussion

4.1. Fault Water Inrush Mechanism Study

The mechanism of fault-induced water inrush primarily involves stress changes and fault reactivation caused by mining activities. As the working face advances, the stress field near the fault is redistributed, potentially leading to fault instability or slippage, which in turn activates the fracture network within the fault zone. This reactivation typically increases the permeability of the fault zone, allowing groundwater to rapidly migrate along the fracture network, forming water flow channels [46]. Simultaneously, the increase in fault permeability, coupled with hydraulic pressure, further intensifies the risk of water inrush [47]. In areas of concentrated stress and at fault intersections, the increased groundwater pressure makes water inrush highly likely. Fault-induced water inrush is typically the result of the combined effects of stress concentration, fault reactivation, and seepage [48]. Understanding the interplay between these factors is crucial for predicting and preventing water inrush events.

This study comprehensively considers the impact of damage variables on the stress field and seepage field. Through the use of theoretical analysis and numerical simulations, it systematically explains the characteristics of fault reactivation and seepage field variations under mining-induced disturbances, and explores the relationship between fault reactivation characteristics and permeability coefficients. This provides a theoretical basis for preventing fault-induced water inrush during mining operations. However, a limitation of this study is that it does not account for the effects of the temperature field. In reality, heat generated by fault slippage can accelerate fault instability and sliding [49]. Therefore, to make the theoretical results more consistent with actual conditions, further research on numerical models of water inrush under the coupling of complex physical fields is necessary.

4.2. Comparison of Characteristics of the F_A28° and F_B86° Faults

This study, using numerical simulation methods, calculated the results in terms of the characteristics of the F_A28° fault and F_B86° fault. According to the simulation results, the findings are as follows: (1) The commonality between the two faults is that the stress change trend on the fault plane first decreases and then increases, and the stress mode on the vertical plane transitions from initial pure compression to a mixed tension–compression state. (2) The differences are as follows: based on Figure 12 for a comparison, the normal stress distribution on the F_A28° fault starts to change at about 50 m from the working face, while significant stress changes on the F_B86° fault only occur upon its exposure. Despite the F_B86° fault being slower to respond to disturbances, its reaction is much more intense, with a substantial change in the normal stress state. This indicates that small-angle faults are more sensitive to mining disturbances [50], while large-angle faults react more violently to such disturbances. It is important to note that the fault dip angles used in this study (28° and 86°) differ significantly, and the characteristics of faults with dip angles between 28° and 86° in practice may not follow a simple linear relationship, which requires further research to supplement this understanding.

5. Conclusions

This study combines theoretical analysis and numerical simulations to investigate the stress variation, damage evolution, permeability coefficient changes, and damage development characteristics of the coal seam floor under the influence of fault activation. The experimental results indicate the following:

(1)

The closer the working face advances toward the fault, the more intense the stress variations on the fault plane. After stress redistribution around the goaf, the compressive and shear stresses on the fault plane beneath the goaf decrease as stress is released in the direction of the goaf. At this stage, the normal stress on the fault plane transitions from purely compressive to a mixed state involving tension and compression. In contrast, the fault plane near the coal wall, particularly at the base, experiences a significant increase in stress due to concentrated stress ahead of the working face, resulting in more severe compression. The stress distribution along the fault plane elevation eventually shows a pattern of lower stress in the center and higher stress on both sides.

(2)

Fault reactivation is a discontinuous dynamic instability process; there is a cyclical relationship between fault slip and rock mass failure. Each slip event further damages the fault zone, which in turn reduces the frictional resistance, enabling more fault slip in the future. Over time, continued fault slip can lead to the complete failure of rock bridges or unfractured parts of the fault, further reducing the resistance to slip and potentially leading to more significant fault movements.

(3)

The increase in the permeability coefficient is positively correlated with the degree of fault activation. Fault activation accelerates the damage evolution of the rock mass. Once the working face exposes the fault, the fault plane at the exposed location suffers severe damage due to accumulated fractures, resulting in the permeability coefficient reaching its maximum value. As the confined water from the aquifer seeps upward along the fault from its base, the risk of water inrush increases significantly. This indicates that fault activation during mining operations alters the permeability of the fault, and areas with greater fault damage are more likely to become inrush points.