# Surface Subsidence Prediction Method for Backfill Mining in Shallow Coal Seams with Hard Roofs for Building Protection

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Simulation Experiment

#### 2.1. Overview of Study Area

#### 2.2. Numerical Model and Simulation Scheme

_{0}is the maximum surface subsidence value; m is the mining thickness of the coal seam; and α is the dip angle of the coal seam.

#### 2.3. Physical Simulation Experiment Design

## 3. Surface Subsidence Characteristics of Fill Mining in Shallow Coal Seam with a Hard Roof

#### 3.1. Numerical Simulation Results and Analysis

- (1)
- Surface subsidence characteristics of different filling ratio schemes in backfill mining

- (2)
- Vertical stress distribution characteristics of different mining schemes along the main section

- (3)
- Surface movement and deformation law of different filling ratio schemes

#### 3.2. Physical Simulation Results and Analysis

## 4. Case Application

^{2}or less.

#### 4.1. Surface Subsidence Prediction Method

_{0}is the maximum surface subsidence value of full mining; m is the thickness of the coal seam; q is the surface subsidence coefficient; α is the dip angle of the coal seam; C(x) and C(y) are the subsidence distribution coefficients of point A (x, y) in main strike and dip sections; l and L are the calculated mining widths along the strike and dip directions after considering the inflection point offset; r is the major influence radius of the strike direction; and r

_{1}and r

_{2}are the major influence radii of the dip direction, where r

_{1}is the downhill direction and r

_{2}is the uphill direction.

_{d}is the equivalent mining height and ρ is the filling ratio of backfill mining.

#### 4.2. Selection of Expected Parameters

#### 4.3. Design of the Scheme and Analysis of the Results

## 5. Conclusions

- (1)
- A simulation was conducted to analyze the variation characteristics of maximum surface subsidence with advancing distance for both the toppling and backfill mining methods, with filling ratios of 20%, 40%, 60%, and 80%. It was observed that when the filling ratio is not less than 60%, surface movement and deformation exhibit a continuous and gradual trend, and there is no occurrence of fracture in the hard roof. Practical experience has demonstrated that backfill mining is highly effective in controlling surface movement and deformation during shallow coal seam mining with a hard roof.
- (2)
- Numerical and physical simulation methods were employed to investigate the characteristics of surface movement and deformation in toppling and backfill mining. It was demonstrated that the surface movement and deformation characteristics in the backfill mining of shallow coal seams with a high filling ratio and a hard roof generally follow the typical surface subsidence patterns observed in fully exploited horizontal coal seams. The prediction model using the probability integral method proved effective in accurately forecasting surface subsidence.
- (3)
- A prediction method for surface subsidence in backfill mining was proposed. Taking Yungang Mine as an example, five schemes with filling ratios of 65%, 70%, 75%, 80%, and 85% were designed. Finally, considering factors such as the level of damage to surface structures, filling costs, and filling technology, a filling ratio of 85% was determined as the optimal subsidence control scheme.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Relationship between maximum surface subsidence values and advancing distance of working face.

**Figure 4.**Vertical stress distribution of different mining schemes. (

**a**) Vertical stress distribution of strata in caving mining. (

**b**) Vertical stress distribution of strata in backfill mining with a 70% filling ratio. (

**c**) Vertical stress distribution of strata in backfill mining with a 90% filling ratio.

**Figure 5.**Vertical stress distribution of filling body along the strike direction in the main section.

**Figure 6.**Surface movement and deformation curves for filling ratios of 80% and 85%. (

**a**) Surface subsidence curve along the main section. (

**b**) Tilt curve along the main section. (

**c**) Horizontal movement curve along the main section. (

**d**) Horizontal deformation curve along the main section.

**Figure 7.**Schematic diagram of an overburden structure in deep coal mining. (

**a**) Caving mining; (

**b**) backfill mining.

**Figure 8.**Similar-material models of shallow coal seam mining. (

**a**) Caving mining [45]; (

**b**) backfill mining (the advancing distance of the working face is 80 m); (

**c**) backfill mining (the advancing distance of the working face is 140 m); (

**d**) backfill mining (the advancing distance of the working face is 200 m).

Rock Stratum | Thickness (m) | Bulk Modulus (GPa) | Shear Modulus (GPa) | Cohesion (MPa) | Tensile Strength (MPa) | Internal Friction Angle Φ (°) | Density (kg/m ^{3}) |
---|---|---|---|---|---|---|---|

Top soil | 4 | 0.25 | 0.16 | 0.10 | 0.05 | 15 | 1200 |

Fine sandstone | 4 | 1.37 | 0.94 | 0.90 | 0.75 | 30 | 2400 |

Gritstone | 12 | 1.07 | 0.74 | 0.80 | 0.65 | 30 | 2300 |

Fine sandstone | 4 | 1.37 | 0.94 | 0.90 | 0.75 | 30 | 2400 |

Gritstone | 20 | 0.96 | 0.61 | 0.70 | 0.60 | 30 | 2300 |

Conglomerate | 8 | 1.15 | 0.73 | 0.80 | 0.70 | 28 | 2100 |

Gritstone | 20 | 0.96 | 0.61 | 0.70 | 0.60 | 30 | 2300 |

Conglomerate | 6 | 1.03 | 0.65 | 0.75 | 0.60 | 28 | 2100 |

Fine sandstone | 20 | 1.56 | 1.16 | 1.20 | 0.90 | 35 | 2500 |

Coal | 2 | 0.67 | 0.40 | 0.60 | 0.50 | 25 | 1800 |

Silty sandstone | 10 | 5.00 | 4.00 | 4.00 | 3.50 | 35 | 2400 |

Filling Ratio of the Backfill Body | Bulk Modulus (MPa) | Shear Modulus (MPa) | Cohesion (MPa) | Tensile Strength (MPa) | Internal Friction Angle Φ (°) | Density (kg/m ^{3}) |
---|---|---|---|---|---|---|

Filling ratio of 20% | 4 | 2 | 0.03 | 0.02 | 20 | 1000 |

Filling ratio of 40% | 6.3 | 3.1 | 0.03 | 0.02 | 20 | 1000 |

Filling ratio of 60% | 8.7 | 4.3 | 0.03 | 0.02 | 20 | 1000 |

Filling ratio of 80% | 11.1 | 5.4 | 0.03 | 0.02 | 20 | 1000 |

Rock Stratum | Actual Rock Properties | Model Rock Properties | ||||
---|---|---|---|---|---|---|

Thickness (m) | Density (kg/m ^{3}) | Single-Axis Compressive Strength (MPa) | Thickness (m) | Density (kg/m ^{3}) | Single-Axis Compressive Strength (MPa) | |

Top soil | 4 | 1200 | 5 | 4 | 1500 | 0.063 |

Fine sandstone | 4 | 2400 | 110 | 4 | 1500 | 0.688 |

Gritstone | 12 | 2300 | 70 | 12 | 1500 | 0.457 |

Fine sandstone | 4 | 2400 | 110 | 4 | 1500 | 0.688 |

Gritstone | 20 | 2200 | 70 | 20 | 1500 | 0.477 |

Conglomerate | 8 | 2250 | 85 | 8 | 1500 | 0.567 |

Gritstone | 20 | 2200 | 70 | 20 | 1500 | 0.477 |

Conglomerate | 6 | 2250 | 85 | 6 | 1500 | 0.567 |

Fine sandstone | 20 | 2400 | 130 | 20 | 1500 | 0.813 |

Coal | 2 | 1600 | 30 | 2 | 1500 | 0.281 |

Silty sandstone | 10 | 2500 | 100 | 10 | 1500 | 0.600 |

Rock Stratum | Ratio of Component/% | The Proportion of Each Component in the Cement/% | |||
---|---|---|---|---|---|

River sand | Mica Powder | Cement | Gypsum | Calcium Carbonate | |

Top soil | 80 | 17 | 3 | 50 | 50 |

Fine sandstone | 73 | 15 | 12 | 50 | 50 |

Gritstone | 74 | 16 | 10 | 70 | 30 |

Fine sandstone | 73 | 15 | 12 | 50 | 50 |

Gritstone | 74 | 16 | 10 | 70 | 30 |

Conglomerate | 73 | 15 | 12 | 50 | 50 |

Gritstone | 74 | 16 | 10 | 70 | 30 |

Conglomerate | 73 | 15 | 12 | 50 | 50 |

Fine sandstone | 71 | 13 | 16 | 70 | 30 |

Coal | 79 | 16 | 5 | 70 | 30 |

Silty sandstone | 71 | 13 | 16 | 70 | 30 |

Filling Ratio of the Backfill Body | Bulk Modulus (MPa) | Shear Modulus (MPa) | Cohesion (MPa) | Tensile Strength (MPa) | Internal Friction Angle Φ (°) | Density (kg/m ^{3}) |
---|---|---|---|---|---|---|

90% filling ratio | 12.7 | 6.2 | 0.03 | 0.02 | 20 | 1000 |

70% filling ratio | 9.5 | 4.7 | 0.03 | 0.02 | 20 | 1000 |

**Table 6.**Prediction parameters of the probability integral method in the mining area surrounding Yungang Mine.

Name of Coal Mine | Subsidence Coefficient (q) | Horizontal Movement Coefficient (b) | Tangent of Major Influence Angle (tan β) | Propagation Angle of Extraction (θ_{0}) | Inflection Point Offset (S_{0}) |
---|---|---|---|---|---|

Datong | 0.5 | 0.3 | 1.6 | 90° − 0.8α | 0.18 H |

Sitaigou | 0.55 | 0.25 | 1.5 | 90° − 0.8α | 0.2 H |

**Table 7.**Prediction parameters of the probability integral method for backfill mining in Yungang mine.

Subsidence Coefficient (q) | Horizontal Movement Coefficient (b) | Tangent of Major Influence Angle (tan β) | Propagation Angle of Extraction (θ_{0}) | Inflection Point Offset (S_{0}) |
---|---|---|---|---|

0.65 | 0.3 | 1.5 | 90° − 0.8α | 0.1 H |

**Table 8.**Extreme values of movement and deformation for surface buildings and structures in each scheme.

Filling Ratio (%) | Maximum Subsidence (mm) | Tilt (mm/m) | Horizontal Migration (mm) | Horizontal Deformation (mm/m) |
---|---|---|---|---|

85 | 188 | 2.9 | 48 | 1.3 |

80 | 252 | 3.9 | 72 | 1.8 |

75 | 313 | 4.8 | 95 | 1.9 |

70 | 382 | 5.9 | 115 | 2.6 |

65 | 439 | 6.7 | 138 | 3.0 |

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## Share and Cite

**MDPI and ACS Style**

Huo, W.; Li, H.; Guo, G.; Wang, Y.; Yuan, Y.
Surface Subsidence Prediction Method for Backfill Mining in Shallow Coal Seams with Hard Roofs for Building Protection. *Sustainability* **2023**, *15*, 15791.
https://doi.org/10.3390/su152215791

**AMA Style**

Huo W, Li H, Guo G, Wang Y, Yuan Y.
Surface Subsidence Prediction Method for Backfill Mining in Shallow Coal Seams with Hard Roofs for Building Protection. *Sustainability*. 2023; 15(22):15791.
https://doi.org/10.3390/su152215791

**Chicago/Turabian Style**

Huo, Wenqi, Huaizhan Li, Guangli Guo, Yuezong Wang, and Yafei Yuan.
2023. "Surface Subsidence Prediction Method for Backfill Mining in Shallow Coal Seams with Hard Roofs for Building Protection" *Sustainability* 15, no. 22: 15791.
https://doi.org/10.3390/su152215791