Dynamic Evolution of Fractures in Overlying Rocks Caused by Coal Mining Based on Discrete Element Method
Abstract
:1. Introduction
2. Geologic Background and Establishment of Numerical Model
2.1. Geologic Background
2.2. Numerical Simulation Based on the Discrete Element Method (DEM)
2.2.1. Model Construction
- (1)
- Model Size. If the constructed model is overly large, it will excessively occupy the processing space of the computer and reduce the computing rate of the model, which is not conducive to the analysis of the results. If the model is too small, it will be incapable of accurately analyzing the properties and environment of the research object, resulting in a significantly larger error in the final analysis results. For our model, the size of the two-dimensional numerical calculation model generated using the “block” command in the UDEC is X × Y = 500 m × 300 m (length × height). The numerical simulation model is illustrated in Figure 2.
- (2)
- Grid Generation. Thin elements should be avoided in important areas of the model to minimize the difference in the grid size. Similar to the design of the model size, the degree of detail in the grid generation also has an impact on the computational speed. Regarding stress and displacement, mesh refinement means using more and smaller elements to divide the research object in the model. Generally, the finer the mesh, the higher the calculation accuracy of stress and displacement. A fine mesh can more accurately capture the stress concentration and deformation gradient changes inside the medium. In terms of the characteristics of mining-induced fracture development, mesh refinement can more accurately simulate the initiation, propagation path, and process of fractures. In a coarse mesh, fractures may propagate in a rather rough manner, failing to reflect the subtle changes during the fracture propagation process. In contrast, a refined mesh can capture more micro-mechanical information, making the simulation results of the fracture propagation closer to the actual situation. However, more elements and nodes require more memory to store the model information and intermediate calculation results. The principle of grid generation should be adhered to, that is, that the grid is refined in the key areas of the study object to obtain accurate data, and coarser grids can be assigned in areas distant from the key areas to alleviate the computational burden. The grid generation command for this simulation is Zone generate. The focus area is within the Y coordinate range of (52, 182). The final model contains 157,912 elements.
2.2.2. Allocation of Parameters and Boundary Conditions
- (1)
- Mechanical Parameters. When assigning mechanical properties in the UDEC, it is divided into two components, namely, the rock mass and structural surfaces. The mechanical properties of the rock mass include the bulk modulus, density, elastic modulus, tension, cohesion, and shear strength. The mechanical properties of the structural surfaces include normal stiffness, tangential stiffness, and cohesion. The physical and mechanical parameters employed in the experiment were mainly derived from physical experiments conducted on rock samples collected from the site, and field sampling involved collecting three columnar samples each of fine sandstone, coarse sandstone, coal, carbonaceous mudstone, mudstone, medium sandstone, siltstone, and sandy mudstone for rock mechanics and physical parameter experiments (such as uniaxial compression and Brazilian splitting tests). Table 2 and Table 3 presents the average values obtained from the three sets of data for each rock type. These average values were then compared with empirical formulas and rock physico-mechanical parameters in databases to ensure their accuracy. The physical and mechanical parameters of the rock mechanics are shown in Table 2, and the parameters of the structural surfaces are presented in Table 3.
- (2)
- Boundary Conditions. The Mohr–Coulomb plasticity model was employed, with 100 m of rock retained on both sides to eliminate the boundary effect. Based on the burial depth at the top of the model, an evenly distributed load of 9 MPa was applied at the top boundary, and a stress gradient of 2.5 MPa/100 m was set. Due to coal mining, the boundary conditions of the rock layers in the unique equilibrium state were altered, and the significance and the path of the strain at each point in the stress field of the rock mass, as well as the stress ratio in the abnormal criterion, would change [36], so a new equilibrium state could be attained, within which the rock mass could be deformed, be crushed, and shift. The sideways pressure coefficient derived for the different burial depths was set as 1.0 [14] (Figure 3). The sides of the model were regarded as rolling support boundaries, and the bottom was set as a fixed boundary (Figure 4).
3. Theoretical Analysis of the Development and Morphology of the Mining Fractures
3.1. Methods for Calculating Fractal Dimension
3.2. Experienced Formula for Calculating the Development of Mining Fractures
3.3. Theoretical Calculation of Fracture Development Height During Mining
3.3.1. Determination of the Locations of the Critical Rock Layers
3.3.2. Determination of the Height of the Free Space Below the Rock Layer
3.4. The Theory of the Development of Mining-Induced Fractures
4. Results and Discussion
4.1. Development Characteristics of Mining-Induced Fractures
4.2. Fractal Evolution Law of Mining-Induced Fractures
4.3. Development Height of Mining-Induced Fractures
4.4. Development Morphology of Mining-Induced Fractures
5. Conclusions
- (1)
- The spatiotemporal dynamics characterize the evolution of the overburden failure movement. During coal mining, as the working face advances, the overburden and the immediate roof begin to collapse. After the sub-key stratum fractures, the overburden layer undergoes the first periodic failure, and the failure pattern is trapezoid shaped. As the distance between the working face and the coal face increases, the height of the step-shaped band also increases. The overburden layer gradually collapses from bottom to top, and a large number of shear fractures develop before the height of the mining-induced fractures reaches the maximum value. The shear fractures are more developed at the ends of the cut and the other end of the working face than in the middle, and the width of the shear fractures above is significantly greater than that of the fractures below. Both ends develop through-cutting inter-bedding fractures, while only a small number of non-through-cutting fractures develop in the middle. When the height of the mining-induced fractures reaches the maximum value, the shear fractures gradually close and eventually close completely. The through-cutting inter-bedding fractures at both ends are the main channels for connecting the aquifers and causing water-related hazards.
- (2)
- Initially, during the advance of the working face from 0 to 70 m, mining disturbances cause rapid fracture development, resulting in an increase in the fractal dimension to 1.116. Subsequently, as the working face advances from 70 to 160 m, both the sub-key stratum and the primary key stratum are damaged, leading to a decrease in the fractal dimension to 1.284. Finally, when the working face advances from 160 to 300 m, the overburden layer reaches a fully mined-out state, and the generation and compression of new and old fractures stabilize, resulting in a stable fluctuation in the fractal dimension. Combining fractal theory, a fractal permeability model of the overburden affected by mining was established based on the K-C equation, and it was found that the permeability of the mining-induced fractures is positively correlated with their fractal dimension. Specifically, as the fractal dimension increases, the complexity of the fracturing network increases, thereby enhancing permeability. This relationship can be attributed to the fact that the more complex fracture network provides more fluid channels, thereby facilitating easier fluid transport. The fractal dimension of the overburden fractures in different regions shows different trends as mining proceeds.
- (3)
- According to the numerical simulation results, the correlation between the WFZH and the excavation steps of the working face is an S-shaped curve. The WFZH exhibits a stepwise increase, with a sudden increase at each stage. This is because the rock layer overlying the basic roof breaks periodically after the basic roof is fractured, making the entire rock mass more prone to fracture and subsidence, and ultimately, leads to a stepwise increase phenomenon. The numerical simulation results indicate that the WFZH is approximately 112 m, and the fracture–mining ratio is 14.93. The WFZH, calculated using its formula, ranges from 85.43 to 106.3 m, and the fracture–mining ratio ranges from 11.39 to 14.17. The WFZH, calculated based on the key stratum theory, extends to the 16th layer of the coarse sandstone in the roof. The calculated WFZH ranges from 97 to 113 m, and the fracture–mining ratio ranges from 12.93 to 15.07. The three calculation results are similar.
- (4)
- The numerical simulation results reveal that the development shape of the mining fractures is a trapezoid, with a lower-left angle of approximately 48° and a lower-right bottom angle of about 50°. This is similar to the theoretical calculation result of 48°, verifying the accuracy and reliability of the theoretical calculations and numerical simulation results.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Author | Research Results | Date |
---|---|---|
Xiao et al. [20] | Three stages of “slow growth-accelerated growth-periodic increase” | 2025 |
Zheng et al. [21] | The shape of the plastic failure zone was a typical trapezoid | 2025 |
Li et al. [22] | The overburden rock’s displacement zone forms an “arch-beam” structure, starting from 160 m | 2024 |
Song et al. [23] | Overburden structure on the development WFZH is studied and revealed | 2024 |
Zhang et al. [24] | The fracture development process can be divided into three stages: extensive development of new fractures, partial compaction of fractures, and closure of numerous fractures | 2024 |
Xu et al. [25] | The fractal dimension can be divided into four stages in time and two stages in space | 2024 |
Zhang et al. [26] | The evolution process and development characteristics of inter-layered rock fractures have been revealed | 2024 |
Lithology | Density (kN·m–3) | Tension (MPa) | Bulk (GPa) | Shear (GPa) | Cohesion (MPa) | Friction (°) |
---|---|---|---|---|---|---|
coarse sandstone | 2580 | 3.2 | 2.3 | 1.6 | 2.0 | 38 |
mudstone | 2483 | 1.2 | 2.2 | 1.3 | 1.2 | 29 |
sand mudstone | 2680 | 1.4 | 2.3 | 1.7 | 1.6 | 29 |
siltstone | 2460 | 2.4 | 2.2 | 2.0 | 2.3 | 35 |
carbonaceous mudstone | 2245 | 1.6 | 2.1 | 1.4 | 1.7 | 28 |
coal | 1350 | 0.6 | 1.8 | 0.4 | 0.9 | 24 |
medium sandstone | 2690 | 3.3 | 2.8 | 2.1 | 2.2 | 38 |
fine sandstone | 2760 | 2.9 | 3.0 | 2.4 | 2.2 | 39 |
Lithology | Normal Stiffness (GPa) | Tangential Stiffness (GPa) | Cohesion (MPa) | Tension (MPa) |
---|---|---|---|---|
coarse sandstone | 5.1 | 3.1 | 0.25 | 0.32 |
mudstone | 3.1 | 2.1 | 0.14 | 0.25 |
sand mudstone | 5.0 | 2.8 | 0.08 | 0.15 |
siltstone | 4.1 | 2.6 | 0.11 | 0.16 |
carbonaceous mudstone | 3.6 | 2.2 | 0.07 | 0.13 |
coal | 2.3 | 1.4 | 0.04 | 0.09 |
medium sandstone | 5.4 | 3.5 | 0.20 | 0.25 |
fine sandstone | 5.6 | 3.7 | 0.23 | 0.28 |
ID | Lithology | Thickness (m) | Density (kN·m–3) | Tension (GPa) | Elasticity (GPa) |
---|---|---|---|---|---|
25 | siltstone | 19.0 | 24.60 | 2.5 | 6.3 |
24 | mudstone | 3.0 | 24.83 | 1.2 | 4.6 |
23 | siltstone | 7.0 | 24.60 | 2.5 | 6.3 |
22 | mudstone | 15.0 | 24.83 | 1.2 | 4.6 |
21 | fine sandstone | 2.0 | 27.60 | 3.4 | 33.2 |
20 | sand mudstone | 22.0 | 26.80 | 0.8 | 5.2 |
19 | mudstone | 30.0 | 24.83 | 1.2 | 4.6 |
18 | sand mudstone | 20.0 | 26.80 | 0.8 | 5.2 |
17 | fine sandstone | 17.0 | 27.60 | 3.4 | 33.2 |
16 | coarse sandstone | 16.0 | 25.80 | 2.6 | 24.6 |
15 | siltstone | 18.0 | 24.60 | 2.5 | 6.3 |
14 | coarse sandstone | 8.0 | 25.80 | 2.6 | 24.6 |
13 | mudstone | 11.0 | 24.83 | 1.2 | 8.6 |
12 | siltstone | 3.5 | 24.60 | 2.5 | 6.3 |
11 | medium sandstone | 5.0 | 26.90 | 3.3 | 28.1 |
10 | fine sandstone | 9.0 | 27.60 | 3.4 | 33.2 |
9 | siltstone | 4.0 | 24.60 | 2.5 | 6.3 |
8 | fine sandstone | 6.5 | 27.60 | 3.4 | 33.2 |
7 | medium sandstone | 6.0 | 26.90 | 3.3 | 28.1 |
6 | carbonaceous mudstone | 3.0 | 22.45 | 1.6 | 4.3 |
5 | fine sandstone | 7.0 | 27.60 | 3.4 | 33.2 |
4 | siltstone | 6.5 | 24.60 | 2.5 | 6.3 |
3 | medium sandstone | 6.0 | 26.90 | 3.3 | 28.1 |
2 | carbonaceous mudstone | 1.5 | 22.45 | 1.6 | 4.3 |
1 | sand mudstone | 2.0 | 26.80 | 0.8 | 5.2 |
Excavation Steps | Fractal Dimension | Correlation Coefficient | Breaking Characteristics |
---|---|---|---|
70 m | 1.168 | 0.9806 | sub-key stratum break |
90 m | 1.180 | 0.9957 | primary key stratum break |
120 m | 1.286 | 0.9941 | upward extension |
160 m | 1.284 | 0.9973 | reach WFFZmax |
200 m | 1.277 | 0.9846 | fracture compaction |
240 m | 1.276 | 0.9854 | tend to stabilize |
280 m | 1.278 | 0.9785 | tend to stabilize |
300 m | 1.295 | 0.9863 | tend to stabilize |
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Xu, J.; Pan, J.; Li, M.; Wang, H.; Chen, J. Dynamic Evolution of Fractures in Overlying Rocks Caused by Coal Mining Based on Discrete Element Method. Processes 2025, 13, 806. https://doi.org/10.3390/pr13030806
Xu J, Pan J, Li M, Wang H, Chen J. Dynamic Evolution of Fractures in Overlying Rocks Caused by Coal Mining Based on Discrete Element Method. Processes. 2025; 13(3):806. https://doi.org/10.3390/pr13030806
Chicago/Turabian StyleXu, Junyu, Jienan Pan, Meng Li, Haoran Wang, and Jiangfeng Chen. 2025. "Dynamic Evolution of Fractures in Overlying Rocks Caused by Coal Mining Based on Discrete Element Method" Processes 13, no. 3: 806. https://doi.org/10.3390/pr13030806
APA StyleXu, J., Pan, J., Li, M., Wang, H., & Chen, J. (2025). Dynamic Evolution of Fractures in Overlying Rocks Caused by Coal Mining Based on Discrete Element Method. Processes, 13(3), 806. https://doi.org/10.3390/pr13030806