# Analysis of Formation Mechanism of Slightly Inclined Bedding Mudstone Landslide in Coal Mining Subsidence Area Based on Finite–Discrete Element Method

^{1}

^{2}

^{3}

^{4}

^{*}

(This article belongs to the Section Engineering Mathematics)

## Abstract

**:**

^{3}in volume. It is composed of Jurassic mudstone and is a traction landslide caused by the coal mining subsidence area. The formation of the landslide is affected by internal factors and inducing factors. The internal factors are mainly geotechnical types and engineering geological properties, and the inducing factors are mainly coal mining activities and rainfall. By analyzing and summarizing the calculation process of the slope model prior to the landslide in 2D-Block and GeoStudio numerical simulation software, the sliding process of the slightly inclined bedding mudstone landslide in the Tanshan Coal Mine is divided into four stages: slope creep, slope deformation, landslide movement and landslide accumulation. GeoStudio software is used to calculate the stability of the Tanshan Coal Mine landslide under natural and rainfall conditions. The landslide is in a stable state under natural conditions and is basically stable under rainfall conditions. By comparing the calculation results of the limit equilibrium method and the finite element limit equilibrium method, we find that the calculated stability coefficient is more accurate when the appropriate constitutive model is selected. The research results have important reference significance for the prevention and control of the gently inclined bedding mudstone landslide of the overlying mountain in the coal mining subsidence area of the Loess Plateau.

## 1. Introduction

^{4}m

^{3}due to coal seam mining [8]. In addition, unreasonable mining also worsens environmental problems [3]. This has brought direct harm to the surrounding ecological environment and the safety of people’s lives and property, and it has seriously affected sustainable economic development and social stability in the region [9]. Therefore, the study of landslides in coal mining subsidence areas has important guiding significance for disaster prevention and reduction [10].

## 2. Regional Geological Environment Background

## 3. Materials and Methods

#### 3.1. Laboratory Geotechnical Test

^{3}), ${m}_{0}$ is the mass of the soil sample (g), and $V$ is the ring-cutter volume (cm

^{3}).

#### 3.2. Numerical Simulation

#### 3.2.1. Discrete Element Numerical Simulation Method

- (1)
- Model establishment

- (2)
- Constitutive model

- (3)
- Parameter selection

^{5}Pa. Substituting into Formulas (4)–(7), we obtain ${K}_{n}=\left(Ea\right)/\left(2b\right)=3\times {10}^{5}$ Pa, ${K}_{s}={K}_{n}/\left[2\left(1+\gamma \right)\right]\approx 1.2\times {10}^{6}$ Pa, $J{K}_{n}={K}_{n}/L=3\times {10}^{4}$ Pa, $J{K}_{s}={K}_{s}/L=1.2\times {10}^{4}$ Pa, and other soil layer parameters can be obtained in the same way. Due to the discretization of the slope, the cohesion $c$ is taken as 0 and $\phi $ is taken as the internal friction angle corresponding to the residual strength. The selection of stiffness parameters and strength indexes is shown in Table 1.

#### 3.2.2. Finite Element Numerical Simulation Method

- (1)
- Model establishment

- (2)
- Parameter selection

#### 3.3. Landslide Stability Analysis

#### 3.3.1. Overview of Landslide Stability Analysis Method

#### 3.3.2. Limit Equilibrium Method and Finite Element Limit Equilibrium Method Based on GeoStudio

- (1)
- Model establishment

- (2)
- Parameter selection

## 4. Results

#### 4.1. Landslide Type and Deformation Failure Characteristics

#### 4.1.1. Landslide Type and Morphological Characteristics

^{2}, the volume is 10,875,000 m

^{3}, and the sliding direction is 295°. From the material composition and scale of the landslide, it is a giant bedrock landslide. From analysis of the landslide deformation characteristics and motion properties, it is a traction landslide. The main body of the landslide in the Tanshan Coal Mine is composed of Jurassic mudstone. Reconstructed by history and human activities reveals that the original topography of the landslide has been destroyed and changed, but the overall shape of the landslide is still basically clear, the outline of the landslide can be identified, the shape of the back wall of the landslide is irregular, the height of the scarp is 1–5 m, and the boundary line of the side wall is obvious. There are two levels of platforms on the sliding body, which are steep up and slow down, with an overall slope of about 20°. The leading edge of the landslide was in the air and was a deep-cut valley. The original slope height was about 180 m, and the slope was about 30°.

#### 4.1.2. Deformation and Failure Characteristics of the Landslide

#### 4.2. Numerical Simulation Results

#### 4.2.1. Numerical Simulation Results of Discrete Element Method

- (1)
- Numerical simulation results only considering the coal mining subsidence area

- (2)
- Numerical simulation results of landslide process

#### 4.2.2. Finite Element Numerical Simulation Results

- (1)
- Displacement analysis

- (2)
- Stress analysis

#### 4.3. Calculation Results of Landslide Stability

## 5. Discussion

#### 5.1. Necessity of Combining Discrete Element Method with Finite Element Method to Analyze Landslide Formation Mechanism

#### 5.2. Analysis of the Influencing Factors on the Landslide in the Coal Mining Subsidence Area

#### 5.2.1. Internal Factors

#### 5.2.2. Inducing Factors

- (1)
- Coal mining activities

- (2)
- Rain

#### 5.3. Analysis of Formation Mechanism of Overlying Landslide in the Coal Mining Subsidence Area

#### 5.3.1. Slope Deformation Stage

#### 5.3.2. Slope Creep Stage

#### 5.3.3. Landslide Movement Stage

#### 5.3.4. Landslide Accumulation Stage

#### 5.4. Comparison of Calculation Methods of Landslide Stability Coefficient

## 6. Conclusions

- (1)
- The slightly inclined bedding mudstone landslide in the Tanshan Coal Mine is 850 m long from east to west, 500 m wide from north to south, 10–20 m thick, 475,000 m
^{2}in total area, 10,875,000 m^{3}in volume and has a sliding direction of 295°. The main body of the landslide is composed of Jurassic mudstone. From the material composition and scale of the landslide mass, the landslide belongs to a giant bedrock landslide. From analysis of landslide deformation characteristics and movement properties, the landslide is a traction landslide caused by a coal mining subsidence area. - (2)
- Discrete element simulation analysis considering only the coal mining subsidence area shows that when the coal mining subsidence area collapse is completed, the creep deformation of the slope is not enough to lead to the formation of a landslide, which indicates that the formation of the landslide in the Tanshan Coal Mine is closely related to rainfall and surface water infiltration. When the contact surface between strong weathering and moderate weathering is set as a weak zone in the model, the simulation results are consistent with the actual sliding situation of the landslide.
- (3)
- The formation of the slightly inclined bedding mudstone landslide in the Tanshan Coal Mine is mainly due to the joint action of internal factors and inducing factors. The internal factors are mainly controlled by geotechnical types and engineering geological properties. The inducing factors are mainly coal mining activities and rainfall.
- (4)
- The sliding process of the landslide is divided into four stages: slope creep, slope deformation, landslide movement and landslide accumulation.
- (5)
- By comparing the calculation results of the limit equilibrium method and the finite element limit equilibrium method, we found that under the rainfall condition, the stability coefficient obtained by the two methods is about 5%, which is mainly due to the fact that the normal stress at the bottom of the strip in the limit equilibrium method is caused by the gravity of the strip and cannot simulate the actual stress distribution. The finite element limit equilibrium method not only calculates the stress closer to that of the real situation, but it also provides the local safety factor of each soil strip. Therefore, selecting the appropriate constitutive model, using the finite element method to simulate the stress distribution of the slope, and then importing it into the limit equilibrium equation for calculation makes the calculation results more accurate.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Finite element calculation model of slope before landslide and after mining in the Tanshan Coal Mine.

**Table 1.**Calculation parameters of discrete element numerical simulation before landslide in the Tanshan Coal Mine.

Parameter | Bulk Density | ${\mathit{K}}_{\mathit{n}}$ | ${\mathit{K}}_{\mathit{s}}$ | $\mathit{\phi}$ | $\mathit{c}$ | $\mathit{J}{\mathit{K}}_{\mathit{n}}$ | $\mathit{J}{\mathit{K}}_{\mathit{s}}$ | $\mathit{J}\mathit{\phi}$ | $\mathit{J}\mathit{c}$ | |
---|---|---|---|---|---|---|---|---|---|---|

Name | kN/m^{3} | Pa | Pa | ° | Pa | Pa | Pa | ° | Pa | |

Loess | 18 | 3.0 × 10^{5} | 1.2 × 10^{5} | 11 | 0 | 3.0 × 10^{4} | 1.2 × 10^{4} | 11 | 0 | |

Strongly weathered mudstone | 25 | 5.0 × 10^{6} | 2.1 × 10^{6} | 21 | 0 | 5.0 × 10^{5} | 2.1 × 10^{5} | 21 | 0 | |

Moderately weathered mudstone | 26 | 6.0 × 10^{6} | 2.3 × 10^{6} | 25 | 0 | 3.0 × 10^{5} | 1.2 × 10^{5} | 25 | 0 | |

Weak zone | 27 | 3.0 × 10^{5} | 1.2 × 10^{5} | 7.6 | 0 | 3.0 × 10^{4} | 1.2 × 10^{4} | 7.6 | 0 |

**Table 2.**Calculation parameters of finite element numerical simulation before landslide in the Tanshan Coal Mine.

Rock and Soil Type | Bulk Density (kN/m^{3}) | $\mathit{c}$ (kPa) | $\mathit{\phi}$ (°) |
---|---|---|---|

Loess | 18 | 35 | 20 |

Strongly weathered mudstone | 25 | 41 | 27 |

Moderately weathered mudstone | 26 | 58 | 40 |

Weak zone | 27 | 22 | 8 |

Method | Moment Equilibrium | Force Balance | Normal Force between Bars/E | Force between Tangential Bars/X | Inclination and Relationship of X/E |
---|---|---|---|---|---|

Ordinary or Fellenius | Satisfied | Unsatisfied | Unsatisfied | Unsatisfied | There is no inter-strip force |

simplified Bishop | Satisfied | Unsatisfied | Satisfied | Unsatisfied | Horizontal direction |

simplified Janbu | Unsatisfied | Satisfied | Satisfied | Unsatisfied | Horizontal direction |

Mongenstern and Price | Satisfied | Satisfied | Satisfied | Satisfied | Variables, Defining functions |

Condition | Rock and Soil Type | Bulk Density (kN/m^{2}) | $\mathit{c}$ (kPa) | $\mathit{\phi}$ (°) | Poisson’s Ratio |
---|---|---|---|---|---|

Natural | Loess | 18 | 35 | 20 | 0.35 |

Loess soil | 16 | 32 | 18 | 0.35 | |

Strongly weathered mudstone | 25 | 41 | 27 | 0.3 | |

Slip zone | 27 | 28 | 13 | 0.4 | |

Rainfall | Loess | 18 | 35 | 20 | 0.35 |

Saturated loess soil | 22 | 25 | 16 | 0.35 | |

Loess soil | 19 | 32 | 18 | 0.35 | |

Strongly weathered mudstone | 25 | 41 | 27 | 0.3 | |

Slip zone | 29 | 22 | 8 | 0.4 |

**Table 5.**Calculation results of landslide stability coefficient after sliding in the Tanshan Coal Mine.

Method | Ordinary | Bishop | Janbu | M–P | Finite Element | |
---|---|---|---|---|---|---|

Condition | ||||||

Natural | 1.905 | 2.095 | 1.936 | 1.948 | 1.802 | |

Rainfall | 1.093 | 1.150 | 1.088 | 1.094 | 1.059 |

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## Share and Cite

**MDPI and ACS Style**

Zhong, J.; Mao, Z.; Ni, W.; Zhang, J.; Liu, G.; Zhang, J.; Geng, M.
Analysis of Formation Mechanism of Slightly Inclined Bedding Mudstone Landslide in Coal Mining Subsidence Area Based on Finite–Discrete Element Method. *Mathematics* **2022**, *10*, 3995.
https://doi.org/10.3390/math10213995

**AMA Style**

Zhong J, Mao Z, Ni W, Zhang J, Liu G, Zhang J, Geng M.
Analysis of Formation Mechanism of Slightly Inclined Bedding Mudstone Landslide in Coal Mining Subsidence Area Based on Finite–Discrete Element Method. *Mathematics*. 2022; 10(21):3995.
https://doi.org/10.3390/math10213995

**Chicago/Turabian Style**

Zhong, Jiaxin, Zhengjun Mao, Wankui Ni, Jia Zhang, Gaoyang Liu, Jinge Zhang, and Mimi Geng.
2022. "Analysis of Formation Mechanism of Slightly Inclined Bedding Mudstone Landslide in Coal Mining Subsidence Area Based on Finite–Discrete Element Method" *Mathematics* 10, no. 21: 3995.
https://doi.org/10.3390/math10213995