# Study on Stability Discrimination Technology of Stope Arch Structure

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^{2}

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## Abstract

**:**

_{i}and unbroken rock strata arch development height H

_{ig}. The theoretical calculation shows that when the width:depth ratio of the working face is 1.60, the height of the arch structure exceeds the bedrock top, which is consistent with the numerical simulation results and verifies the correctness of the formula. By defining the instability coefficient C of rock strata arch structure, a method to judge the stability of the arch structure is provided. The theoretical calculation shows that the critical width L

_{0}of the arch structure instability is 134 m, which is not much different from the numerical simulation results of 136 m, and the correctness of the formula is proved. The research results have particular reference value for preventing ground disasters caused by underground coal mining and controlling ground subsidence and provide a reference for the application of the particle flow method in studying rock strata movement.

## 1. Introduction

## 2. Method

#### 2.1. Overview of Study Area

#### 2.2. Rock Strata Breaking Theory and Arch Structure Height Calculation Method

#### 2.2.1. Rock Strata Breaking Theory

#### 2.2.2. Calculation Method of Arch Structure Height

_{i}.

- (1)
- According to the fracture space form of the positive trapezoidal mining rock strata, the hanging length of the rock layer i is calculated:l
_{i}= L − 2H_{i}cotψ

_{iT}is the ultimate tensile strength of the rock layer i; h

_{i}is the thickness of rock layer i; q

_{i}is the uniformly distributed load on the rock layer i. (This can also be replaced by the criterion of rock strata shear strength, but generally, the ultimate span formed by bending is smaller than that formed by shear stress, so the tensile strength criterion is selected here as the criterion [10]).

_{ik}. If l

_{i}= l

_{ik}, then the fracture height of the rock strata:

_{i}= Σh

_{j}(j = 1, …, i), H

_{i}and i can be solved.

- (2)
- Calculation of development height of unbroken rock strata arch.

_{ig}of broken rock layer i:

_{0}− H

_{i}).

- (3)
- Calculation of rock strata arch development height.

#### 2.3. Numerical Simulation of Particle Flow Code

#### 2.3.1. Principle of Particle Flow Code

#### 2.3.2. Model Establishment and Parameter Calibration

- (1)
- Model establishment

^{2}, as shown in Figure 7. According to the drilling data, the model sets five representative rock strata, generating 174,366 particles, and simulates mining by deleting the particles corresponding to the coal seam.

^{2}) to simulate the natural accumulation of strata. The open-off cut is 50 m from the left boundary of the model, and 8 m is used to simulate the mining along the strike of the coal seam. After the coal seam is excavated, the force is balanced until the average ratio of the unbalanced force is less than or equal to 1 × 10

^{−5}.

- (2)
- Parameter calibration

## 3. Results

#### 3.1. Analysis of Evolution Law of Rock Arch Structure

#### 3.2. Analysis of Arch Structure Height Variation

#### 3.3. Critical Width Analysis of Arch Structure Instability

_{0}is average mining depth, h is arch height, H

_{s}is loose layer thickness. The instability coefficient is related to the stability of the rock strata arch structure, and the stability of the arch is divided into four categories according to the value range, as shown in the following Table 2.

- (1)
- Discriminant formula for breaking position of rock strata

_{(i+1)k}> l

_{i}≥ l

_{ik}, it is known that the trapezoidal breaking area of the rock strata has reached the rock layer i. Namely:

- (2)
- Calculation equation of critical width

- (3)
- Simultaneous Formulas (9) and (10) are used to inverse the critical width L
_{0}and breaking position i of the instability of the unknown rock strata arch structure.

_{0}of arch structure instability is 134 m, which is not much different from the numerical simulation results of 136 m, which proves the correctness of the formula.

## 4. Discussion

## 5. Conclusions

- (1)
- The arch structure will be formed in the rock strata after underground coal seam mining, and the calculation formula of arch structure development height h is obtained by theoretical analysis, which is the sum of rock strata breaking height H
_{i}and unbroken rock strata arch development height H_{ig}. According to the numerical simulation parameters, the curve of arch height changing with a width:depth ratio of the working face is obtained. The theoretical calculation shows that when the width:depth ratio of the working face is 1.60, the height of the arch structure exceeds the top of the bedrock, and the surface begins to appear large subsidence damage, which is consistent with the numerical simulation results and verifies the correctness of the formula. The research results are more suitable for mining under a thin loose layer, that is, the ratio of loose layer thickness to mining depth is less than 20%. - (2)
- In this paper, the ratio of arch height to bedrock thickness is used to define the instability coefficient C of rock strata arch structure, which provides a method to judge the stability of the arch structure. The formula for calculating the critical width of arch structure instability is obtained by theoretical analysis. It is shown that the critical width L
_{0}of the arch structure instability is 134 m, which is not much different from the 136 m obtained by numerical simulation. The correctness of the formula is demonstrated. The results show that the instability of the arch structure is the fundamental reason for increasing the damage degree of surface subsidence. - (3)
- The biggest advantage of the particle flow method is that it can intuitively see the dynamic evolution process of rock strata movement. The results show that the particle flow method is more suitable for studying the movement and deformation of rock strata, which provides a new idea for related research.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Geographical location of mine field [27].

**Figure 3.**Rock strata movement process. (

**a**) The cantilever beam structure, (

**b**) The masonry beam structure, (

**c**) The transfer rock beam structure.

Symbol | Description | Loess Layer (S5) | Siltstone (S4) | Mudstone (S3) | Coal (S2) | Gritstone (S1) |
---|---|---|---|---|---|---|

γ (KN/m^{3}) | Volume-weight | 17 | 24 | 24 | 14.2 | 25.1 |

R (cm) | Minimum radius of particles | 20 | 20 | 20 | 20 | 20 |

R_{max}/R_{min} | Particle Radius Ratio | 1.6 | 1.6 | 1.6 | 1.6 | 1.6 |

E * (GPa) | Effective modulus of flat joint | 0.42 | 31.24 | 13.62 | 4.24 | 19.72 |

K * | Rigidity ratio of flat joint | 2 | 2 | 2 | 2 | 2 |

σ_{c} (MPa) | Average tensile strength and standard deviation of flat joints | 0.1/0.025 | 1.8/0.5 | 0.8/0.2 | 0.25/0.0625 | 1.1/0.275 |

c (MPa) | Average cohesion and standard deviation of flat joints | 4/1 | 20/5 | 20/5 | 10/2.5 | 20/5 |

Category | Instability Coefficient | Arch Structure (Yes or No) | Stability of Arch Structure |
---|---|---|---|

I | C = 0 | No (original rock strata state) | -- |

II | 0 < C < 1 | Yes | Stability |

III | C = 1 | Yes | Critical instability |

IV | C > 1 | No | Instability |

Width:Depth Ratio | Instability Coefficient | Stability of Arch Structure |
---|---|---|

0.38 | 0.40 | Stability |

0.47 | 0.43 | Stability |

0.56 | 0.46 | Stability |

0.66 | 0.49 | Stability |

0.75 | 0.52 | Stability |

0.85 | 0.56 | Stability |

0.94 | 0.73 | Stability |

1.04 | 0.76 | Stability |

1.13 | 0.80 | Stability |

1.22 | 0.83 | Stability |

1.32 | 0.86 | Stability |

1.41 | 0.89 | Stability |

1.51 | 0.92 | Stability |

1.58 | 1.00 | Critical instability |

1.60 | 1.09 | Instability |

1.69 | 1.09 | Instability |

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**MDPI and ACS Style**

Li, Q.; Zhang, Y.; Zhao, Y.; Zhu, Y.; Yan, Y.
Study on Stability Discrimination Technology of Stope Arch Structure. *Sustainability* **2022**, *14*, 11082.
https://doi.org/10.3390/su141711082

**AMA Style**

Li Q, Zhang Y, Zhao Y, Zhu Y, Yan Y.
Study on Stability Discrimination Technology of Stope Arch Structure. *Sustainability*. 2022; 14(17):11082.
https://doi.org/10.3390/su141711082

**Chicago/Turabian Style**

Li, Quansheng, Yanjun Zhang, Yongqiang Zhao, Yuanhao Zhu, and Yueguan Yan.
2022. "Study on Stability Discrimination Technology of Stope Arch Structure" *Sustainability* 14, no. 17: 11082.
https://doi.org/10.3390/su141711082