# Research on Subsidence Prediction Method of Water-Conducting Fracture Zone of Overlying Strata in Coal Mine Based on Grey Theory Model

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## Abstract

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^{−2}coal seam, China, this study established a similar material test model of mining overburden. The deformation characteristics of overlying strata in the mining process of coal seam were studied by using distributed optical fiber sensing technology, and the development height of water flowing fractured zone was determined. According to the equidistant sampling characteristics of Brillouin optical time domain reflection technology and the principle of the grey theory model, the settlement prediction model of the water-conducting fracture zone was established. By analyzing and comparing the prediction accuracy of the GM (1, 1) model, grey progressive model, and metabolic model, the optimal method for settlement prediction of the water-conducting fracture zone was discussed. The results show that, for the metabolic model, with the increase in the number of test sets and the decrease in the number of prediction sets, the mean square error ratio c and the small error probability p of the prediction accuracy evaluation parameters display a downward trend. The accuracy is related to the sudden change in the settlement of the water-conducting fracture zone caused by the breaking of the key stratum of the overlying rock. The optimal time of test sets selected for the best settlement prediction model is 7~8, and that of prediction sets selected is 5~6. For the GM (1, 1) model and the grey progressive model, the prediction accuracy of mining overburden subsidence is grade 4, which is not suitable for settlement prediction of water-flowing fractured zones.

## 1. Introduction

## 2. Prediction Method of Mining-Induced Overburden Subsidence Based on Grey Theory

#### 2.1. Basic Principle of Grey Theory Model

^{(0)}to obtain a new sequence X

^{(1)}. The prediction formula for the GM (1, 1) model is shown as follows [19].

#### 2.2. Model Accuracy Test

- (1)
- Posteriori error test

_{1}denotes the mean square error of the original sequence ${X}^{(0)}(k)$, and S

_{2}denotes the mean square error of the residual sequence Δ(i), $\overline{\Delta}$ denotes the mean of the residual sequence Δ(i).

- (2)
- Grey correlation degree test

#### 2.3. Grey Theory Prediction Method of Overburden Subsidence Based on Distributed Strain Monitoring

_{1}and H

_{2}, namely, the sampling interval of the Brillouin optical time domain reflection technology; and $\epsilon (H)$ denotes the strain of the rock test section.

## 3. Similar Material Model Test of Mining Overburden Deformation

#### 3.1. The Scheme of Similar Material Model Test

^{−2}coal seam, the mining method is the strike longwall mining method; the working face is 180 m long in the strike direction, with an average burial depth of 135 m. The length, width, and height of the indoor similar material model test device are 3 m × 2 m × 0.3 m, respectively. According to the similarity principle, the geometric similarity ratio ${C}_{l}$ = 100 and the stress similarity ratio ${C}_{\sigma}$ = 150 in the similar material model test.

^{−2}coal seam is taken as the research object. The thickness of coal seam mining is 4.2 cm, and the mining length of the coal seam working face is 5 cm. In order to grasp the deformation characteristics of overlying strata in the process of coal seam mining, 4 sensing optical fibers, A1, A2, A3, and A4, were arranged along the vertical direction of the model, which were 50 cm, 115 cm, 190 cm, and 250 cm away from the left side of the model frame, respectively. The BOTDR instrument (AV6419) was used in the experiment. The sensing fiber layout and coal seam mining scheme in the mining overburden model test are shown in Figure 2.

#### 3.2. The Strain Distribution Characteristics of Mining Overburden Rock and the Height Determination of Water-Conducting Fractured Zone

^{−2}coal seam mining.

#### 3.3. Grey Model Prediction of Mining Overburden Deformation

## 4. Parameter Optimization Evaluation Method of Grey Theory Prediction Model

- (1)
- Precision evolution characteristics of the grey model

- (2)
- Prediction accuracy analysis and evaluation of the grey model

## 5. Conclusions

- (1)
- The subsidence prediction model of the water-conducting fracture zone is established by combining the equidistant sampling data of mining overburden strata of Brillouin optical time domain technology with the GM (1, 1) model. Six kinds of subsidence prediction schemes of mining overburden strata are designed by introducing a grey progressive model and metabolic model, and the subsidence of the water-conducting fracture zone of overburden strata in the mining process of coal seam working face is predicted.
- (2)
- For the metabolic model, the prediction model is related to the mutation of the settlement of the water-conducting fracture zone caused by the breaking of the key stratum of the overlying rock. As for predicting the settlement of the water-conducting fracture zone in the overlying strata of the Shendong Coal Mine, the optimal number of model training is 7 to 8, and the number of predictions is 5 to 6 times. In this case, the prediction accuracy can reach level 1.
- (3)
- The prediction method of overlying strata settlement based on the GM (1, 1) model and grey progressive model is not suitable for the settlement prediction of the water-conducting fracture zone because the model data sequence is too long and the prediction accuracy in the middle and late stage of coal seam mining is gradually reduced.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Accuracy Grade | Mean Square Deviation Ratio | Probability of Small Error | Correlation Degree |
---|---|---|---|

Grade 1 (good) | C ≤ 0.35 | p ≥ 0.95 | r ≥ 0.9 |

Grade 2 (qualified) | 0.35 < C ≤ 0.5 | 0.8 ≤ p < 0.95 | r ≥ 0.8 |

Grade 3 (barely) | 0.5 < C ≤ 0.65 | 0.7 ≤ p < 0.8 | r ≥ 0.7 |

Grade 4 (unqualified) | C > 0.65 | p < 0.7 | r ≥ 0.6 |

Lithology | Prototype | Model | |||||
---|---|---|---|---|---|---|---|

Thickness (m) | Volume Weight (kN/m ^{3}) | Compressive Strength (MPa) | Thickness (cm) | Volume Weight (kN/m ^{3}) | Compressive Strength (kPa) | Proportion Number | |

Loose layer | 40 | 17 | 0.7 | 40 | 11.3 | 4.67 | 11:1:0 |

Sandy mudstone | 6 | 24.1 | 17.2 | 6 | 16.1 | 114.7 | 8:6:4 |

Fine sandstone | 5 | 28 | 36.5 | 5 | 18.7 | 243.3 | 3:5:5 |

Sandy mudstone | 7 | 24.1 | 17.2 | 7 | 16.1 | 114.7 | 8:6:4 |

Mudstone | 9 | 24.3 | 15.3 | 9 | 16.2 | 102 | 10:5:5 |

Fine sandstone | 13.5 | 28 | 36.5 | 13.5 | 18.7 | 243.3 | 3:5:5 |

Sandy mudstone | 6 | 24.1 | 17.2 | 6 | 16.1 | 114.7 | 8:6:4 |

2^{−2} coal | 4.2 | 13 | 15 | 4.2 | 8.7 | 100 | 6:5:5 |

Sandy mudstone | 6 | 24.1 | 17.2 | 6 | 16.1 | 114.7 | 8:6:4 |

2^{−3} coal | 4.2 | 13 | 15 | 4.2 | 8.7 | 100 | 6:5:5 |

Sandy mudstone | 5 | 24.1 | 17.2 | 5 | 16.1 | 114.7 | 8:6:4 |

Advancing Distance | Measured Displacement Values Based on Photogrammetry (mm) | GM(1,1) Model | Grey Progressive Model | Metabolic Model | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Predicted Value (mm) | Residual Error (mm) | Relative Residual (%) | Predicted Value (mm) | Residual Error (mm) | Relative Residual (%) | Predicted Value (mm) | Residual Error (mm) | Relative Residual (%) | ||

80 | 20.88 | 18.37 | −2.50 | 11.99 | 18.37 | −2.50 | 11.99 | 18.37 | −2.5 | 11.99 |

85 | 26.94 | 20.16 | −6.77 | 25.15 | 21.18 | −5.76 | 21.38 | 23.22 | −3.71 | 13.78 |

90 | 41.89 | 22.12 | −19.76 | 47.18 | 23.85 | −18.04 | 43.06 | 30.04 | −11.85 | 28.29 |

95 | 69.47 | 24.28 | −45.19 | 65.04 | 26.50 | −42.97 | 61.85 | 45.91 | −23.56 | 33.91 |

100 | 102.31 | 26.65 | −75.66 | 73.95 | 29.35 | −72.96 | 71.31 | 72 | −30.3 | 29.62 |

Quantity of Training Sets (Number) | Working Face Advancing Range (cm) | Quantity of Prediction Sets (Number) | Representation Methods |
---|---|---|---|

5 | 40~60 | 8 | (5, 8) |

6 | 40~65 | 7 | (6, 7) |

7 | 40~70 | 6 | (7, 6) |

8 | 40~75 | 5 | (8, 5) |

9 | 40~80 | 4 | (9, 4) |

10 | 40~85 | 3 | (10, 3) |

Number of Training Sets | Number of Predictions | Mean Square Deviation Ratio | Probability of Small Error | Grey Correlation Degree | Accuracy Grade |
---|---|---|---|---|---|

5 | 8 | 0.99 | 0.46 | 0.68 | Level 4 (unqualified) |

6 | 7 | 0.9 | 0.62 | 0.74 | Level 4 (unqualified) |

7 | 6 | 0.85 | 0.77 | 0.78 | Level 4 (unqualified) |

8 | 5 | 0.81 | 0.85 | 0.80 | Level 4 (unqualified) |

9 | 4 | 0.77 | 0.85 | 0.82 | Level 4 (unqualified) |

Number of Training Sets | Number of Predictions | Mean Square Deviation Ratio | Probability of Small Error | Grey Correlation Degree | Accuracy Grade |
---|---|---|---|---|---|

5 | 8 | 0.17 | 1.00 | 0.94 | Level 1 (excellent) |

6 | 7 | 0.22 | 1.00 | 0.92 | Level 1 (excellent) |

7 | 6 | 0.28 | 1.00 | 0.91 | Level 1 (excellent) |

8 | 5 | 0.36 | 0.92 | 0.90 | Level 2 (good) |

9 | 4 | 0.43 | 0.92 | 0.89 | Level 2 (good) |

10 | 3 | 0.52 | 0.92 | 0.88 | Level 3 (qualified) |

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## Share and Cite

**MDPI and ACS Style**

Li, J.; He, Z.; Piao, C.; Chi, W.; Lu, Y.
Research on Subsidence Prediction Method of Water-Conducting Fracture Zone of Overlying Strata in Coal Mine Based on Grey Theory Model. *Water* **2023**, *15*, 4177.
https://doi.org/10.3390/w15234177

**AMA Style**

Li J, He Z, Piao C, Chi W, Lu Y.
Research on Subsidence Prediction Method of Water-Conducting Fracture Zone of Overlying Strata in Coal Mine Based on Grey Theory Model. *Water*. 2023; 15(23):4177.
https://doi.org/10.3390/w15234177

**Chicago/Turabian Style**

Li, Jinjun, Zhihao He, Chunde Piao, Weiqi Chi, and Yi Lu.
2023. "Research on Subsidence Prediction Method of Water-Conducting Fracture Zone of Overlying Strata in Coal Mine Based on Grey Theory Model" *Water* 15, no. 23: 4177.
https://doi.org/10.3390/w15234177