# Time Series Effect on Surface Deformation above Goaf Area with Multiple-Seam Mining

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## Abstract

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## 1. Introduction

## 2. Engineering Background and Numerical Model Construction

#### 2.1. Engineering Background

#### 2.2. Numerical Model Building

^{2}. For thin and fine coal seams, the size of the numerical model must be much larger than the influence range of the coal seam excavation considering the actual stratum occurrence status and characteristics of the goaf distribution. Therefore, the six boundary dimensions of the model are determined as follows: the upper boundary is bounded by a +200 m overburden (i.e., the surface, assuming the surface terrain is flat), the lower boundary is bounded by a −400 m rock layer, the distances of the left and right boundaries are 2.7 km each, and the distances of the front and rear boundaries are 3.6 km each. The goaf is evenly distributed in the middle area, and the cumulative area of the model is 9.72 km

^{2}; this ensures that the boundary of the study area is not affected when it is loaded, and ensures the accuracy of the numerical analysis.

^{2}. The loading method only considers the self-weight of each layer, and the effect of force is not considered in other directions. As the numerical model has a large buried depth, the ground load can be ignored, i.e., the upper surface of the model is a free surface, and is not subjected to loading effects and constraints [35,36,37].

## 3. Analysis of Mining Time Series Effect on Ground Deformation Law in Goaf Collapse Area of Multiple Coal Seams

#### 3.1. Determination of Different Mining Sequence Models

#### 3.2. Analysis of the Results of Mining Timing Effects on the Law of Ground Deformation

#### 3.2.1. Deformation Contour Map Description

- (1)
- Analysis of monitoring results of vertical ground settlement

- (2)
- Analysis of monitoring results of horizontal surface deformation

#### 3.2.2. Analysis of Deformation Law of Near-Surface Deep Cover Rock in Goaf

#### 3.2.3. Analysis of “S” Curve of Surface Subsidence Deformation Index of Typical Section

^{−4}cm; in contrast, the surface subsidence curve at the section Y = 1600 is in the form of a conventional “single valley,” with the ground depression as the main part, and the maximum surface uplift is only 5.4 × 10

^{−4}cm.

#### 3.2.4. Analysis of “S” Curve of Horizontal Deformation Index of Typical Section

#### 3.2.5. D Effect Reduction and Optimization of Mining Order in Goaf Surface Subsidence Area

- (1)
- As the depth of the first coal seam increases, the surface collapse gradually slows down. If the first coal seam is deep enough or overlies a hard rock layer, the surface collapse deformation may not extend to the surface, and the surface may be less (or not) affected by the goaf. However, if the first coal seam is shallow and the mechanical properties of the overlying rock layer are poor, it may cause significant deformation of the surface, such that the degree of cell grid distortion is greater, and the peak of the surface collapse is higher.
- (2)
- When the first coal seam is the same, the degree of ground subsidence is determined using the secondary coal seam. After the first coal seam is mined, the overburden moves, and the mechanical properties are reduced. The secondary coal seam mining is disturbed again, and the deformation of the overburden is intensified. Therefore, if the secondary coal seam is closer to the surface, the degree of surface collapse is more evident.
- (3)
- The four types of mining sequences cause large differences in the surface subsidence deformation. Nevertheless, comprehensively considering the indicators that characterize the stability and suitability of the surface (horizontal deformation indicators (displacement and slope) and vertical deformation indicators (settlement, slope, and curvature)), order IV is determined to be the best order. Simultaneously, it is considered that the mining sequence IV takes “7 coal” as the first coal seam. This can avoid the long construction period for the roadway, lack of output, and low mechanical operation efficiency, and can ensure a high utilization rate of the coal seam in the mining area. However, actual coal mines often adopt mining sequence I, which is considered to be the most unfavorable for the control of surface stability. Therefore, it is recommended that mine engineers comprehensively consider the actual stratum and mining factors and formulate and compare a variety of mining schemes, so as to obtain the optimal mining order.

## 4. Conclusions

- (1)
- The center position of the surface deformation (vertical settlement and horizontal deformation) of the four groups of mining sequences is stable, but the deformation ranges and amounts are quite different; however, the settlement deformation is the main difference. Among them, the deformation of mining sequence I is the largest at 62.7 cm. Mining sequences 2 and 4 are basically the same, at only 22% of the value of mining sequence I.
- (2)
- An analysis of multiple indicators (inflection point, stagnation point, and slope) of the surface deformation curve shows that the greater the surface deformation, the more evident the curve unevenness and slope change; the greater the unevenness of the foundation stress, the more severe the damage to the surface structure, and the worse suitability for surface construction.
- (3)
- As the depth of the first coal seam increases, the surface settlement gradually slows down. If the first coal seam is deep enough or overlies a hard rock layer, the mined-out area will have little or no impact on the surface settlement and deformation. However, if the first coal seam is shallow and/or the mechanical properties of the overlying rock layer are poor, it may result in significant surface deformation.
- (4)
- When the first coal seam is the same, the ground subsidence is determined by the secondary coal seam. After the first coal seam is mined, the overburden moves, and the mechanical properties are reduced. The secondary coal seam mining disturbs the overburden again, which intensifies the deformation of the overburden, causing the degree of the ground subsidence to be more evident.
- (5)
- Based on comprehensively considering the indicators that characterize the stability and suitability of the ground, mining sequence IV is considered as the optimal solution. It is recommended to make a rational choice of sequence before multi-seam mining, or to replace a less-effective sequence with the optimal mining sequence in time. This can not only avoid or overcome the long construction period for the roadway, lack of output, and low mechanical operation efficiency, but can also ensure a high utilization rate of the coal seam in the mining area.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Surface walls and foundation damage above the mining area. (

**a**) Wall cracking. (

**b**) Cracks in the wall. (

**c**) Basic cracking.

**Figure 2.**Surface fragmentation and vegetation destruction above the mining area [4]. (

**a**) Vegetation destruction. (

**b**) Groundwater depletion. (

**c**) Road collapse.

**Figure 3.**Stress-strain curve of the chosen model [34].

**Figure 5.**Contour map of surface settlement in different mining sequences. (

**a**) Mining sequence I. (

**b**) Mining sequence II. (

**c**) Mining sequence III. (

**d**) Mining sequence IV.

**Figure 7.**Subsidence display of mining sequence I. (

**a**) X = 1200 Contour map of overburden settlement. (

**b**) Y = 1600 Contour map of overburden settlement.

**Figure 8.**Subsidence display of mining sequence II. (

**a**) X = 1200 Contour map of overburden settlement. (

**b**) Y = 1600 Contour map of overburden settlement.

**Figure 9.**Subsidence display of mining sequence III. (

**a**) X = 1200 Contour map of overburden settlement. (

**b**) Y = 1600 Contour map of overburden settlement.

**Figure 10.**Subsidence display of mining sequence IV. (

**b**) X = 1200 Contour map of overburden settlement. (

**b**) Y = 1600 Contour map of overburden settlement.

**Figure 11.**Deformation law of settlement on the ground surface under different mining order conditions. (

**a**) Profile X = 1200 vertical surface deformation “S” curve. (

**b**) Profile Y = 1600 vertical surface deformation “S” curve.

**Figure 13.**3D rendering of surface collapse. (

**a**) 3D rendering of ground collapse in goaf I. (

**b**) 3D rendering of ground collapse in goaf II. (

**c**) 3D rendering of ground collapse in goaf III. (

**d**) 3D rendering of ground collapse in goaf IV.

Dot | X Coordinate Corresponding Value | Y Coordinate Corresponding Value | ||
---|---|---|---|---|

Real Mine | Model Mine | Real Mine | Model Mine | |

A1 | 4,009,900 | 1700 | 20,559,700 | 1000 |

A2 | 4,010,500 | 1900 | 20,559,900 | 1600 |

A3 | 4,011,900 | 1900 | 20,559,900 | 3000 |

A4 | 4,011,500 | 1100 | 20,559,100 | 2600 |

A5 | 4,010,300 | 900 | 20,558,900 | 1400 |

A6 | 4,009,900 | 900 | 20,558,900 | 1000 |

Mining depth: +137–350 m |

**Table 2.**Physical and mechanical parameters of each layer [4].

Lithology | Natural Density/kg·m^{−3} | Elastic Modulus E/×10 GPa | Poisson’s Ratio μ | Internal Friction Angle φ/° | Cohesion C/MPa | Tensile Strength/MPa |
---|---|---|---|---|---|---|

Quaternary | 1850 | 1.85 × 10^{−3} | 0.327 | 15.1 | 12 × 10^{−3} | 0 |

Changlu Group | 2380 | 2.75 | 0.227 | 35.4 | 1.15 | 0.77 |

Fangzi Group | 2360 | 2.87 | 0.234 | 36.1 | 1.11 | 0.65 |

Stone Box Group | 2320 | 3.28 | 0.303 | 33.2 | 1.14 | 0.74 |

Shanxi Group 1 | 2370 | 3.89 | 0.313 | 38.7 | 1.03 | 1.12 |

Coal seam 2# | 1460 | 0.35 | 0.412 | 23.9 | 1.18 | 0.27 |

Shanxi Group 2 | 2371 | 4.01 | 0.314 | 38.7 | 1.04 | 1.12 |

Coal layer 4# | 1460 | 0.37 | 0.411 | 23.9 | 1.18 | 0.27 |

Coal Seam | Mining Sequence | |||
---|---|---|---|---|

Sequence I | Sequence II | Sequence III | Sequence IV | |

2# | ① | ⑤ | ② | ③ |

4# | ② | ④ | ④ | ⑤ |

7# | ③ | ③ | ① | ① |

15# | ④ | ② | ⑤ | ④ |

19# | ⑤ | ① | ③ | ② |

Mining Sequence | Horizontal Deformation in X Direction | Horizontal Deformation in Y Direction | ||||
---|---|---|---|---|---|---|

Maximum/cm | Occurrence Coordinates | Maximum/cm | Occurrence Coordinates | |||

X/401- | Y/2055- | X/401- | Y/2055- | |||

I | 31.6 | 0500 | 9400 | 17.7 | 0200 | 9200 |

II | 6.5 | 0500 | 9400 | 4.4 | 0200 | 9200 |

III | 12.8 | 0500 | 9400 | 7.6 | 0200 | 9200 |

IV | 6.9 | 0500 | 9400 | 4.6 | 0200 | 9200 |

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**MDPI and ACS Style**

Shi, Z.; Wang, Q.; Wang, P.; He, D.; Bai, Y.; You, H.
Time Series Effect on Surface Deformation above Goaf Area with Multiple-Seam Mining. *Symmetry* **2020**, *12*, 1428.
https://doi.org/10.3390/sym12091428

**AMA Style**

Shi Z, Wang Q, Wang P, He D, Bai Y, You H.
Time Series Effect on Surface Deformation above Goaf Area with Multiple-Seam Mining. *Symmetry*. 2020; 12(9):1428.
https://doi.org/10.3390/sym12091428

**Chicago/Turabian Style**

Shi, Zhenyue, Qingbiao Wang, Pu Wang, Donglin He, Yun Bai, and Hongyue You.
2020. "Time Series Effect on Surface Deformation above Goaf Area with Multiple-Seam Mining" *Symmetry* 12, no. 9: 1428.
https://doi.org/10.3390/sym12091428