# Aging Stability Analysis of Slope Considering Cumulative Effect of Freeze–Thaw Damage—A Case Study

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Mechanism

- ${a}_{11}^{\prime}=\frac{1}{16\pi G}\left[\left(3-4\mu -\mathrm{cos}{\theta}_{0}\right)\left(1+\mathrm{cos}{\theta}_{0}\right)\right]$,
- ${a}_{12}^{\prime}=\frac{1}{16\pi G}\left(2\mathrm{sin}{\theta}_{0}\right)\left[\mathrm{cos}{\theta}_{0}-\left(1-2\mu \right)\right]$,
- ${a}_{22}^{\prime}=\frac{1}{16\pi G}\left[4\left(1-\mu \right)\left(1-\mathrm{cos}{\theta}_{0}\right)+\left(1+\mathrm{cos}{\theta}_{0}\right)\left(3\mathrm{cos}{\theta}_{0}-1\right)\right]$,
- $A=\gamma H\left(\lambda {\mathrm{cos}}^{2}\beta +{\mathrm{sin}}^{2}\beta \right)$,
- $B=\gamma H\left(\lambda -1\right)\mathrm{sin}\beta \mathrm{cos}\beta .$

## 3. Results

## 4. Discussion

_{s}of seven slope forms can be obtained when the aging parameters of slope are deteriorated by 10%, 15%, 20%, and 0%. Considering that the damage of rock is a progressive failure process, and the degradation rate is inconsistent in different periods, the classical Freundlich model is selected to fit the heterogeneous degradation process. The fitting curves are shown in Figure 11.

^{2}, while the cross-sectional area of the recovered coal is 312.59 m

^{2}. Taking the density of coal as 1.54 t/m

^{3}, the stripping ratio of sidewall mining is only 0.69 m

^{3}/t. According to the mining speed of 200 m/a and the mining rate of 95%, 91,500 tons of coal resources can be recovered every year. It can be seen that after the secondary design of the original slope into a long-term aging slope, the resource recovery rate of the mine can be improved, and the economic benefit is very significant.

## 5. Conclusions

- (1)
- Under the combined action of repeated freeze–thaw cycles and confining pressure, the rock mass of the mine in the seasonally frozen area develops a composite compression-shear expansion at the tip of the crack. The theoretical frost-heave force increases linearly with the increase of mining depth. The rock mass with small shear modulus, small fracture toughness, and large Poisson’s ratio is more prone to frost-heave fracture failure. As the inclination angle of the fracture changes from the horizontal to the vertical direction, the theoretical frost-heave force gradually decreases until it tends to be stable, and the change rate is small in the near-horizontal and vertical directions and large in the inclined direction 20–70°.
- (2)
- Taking the BP mine as an example, 35 groups of slope models with different aging strength parameters as well as slope shapes were designed by selecting the internal friction angle, cohesion, and gravity that have a significant impact on the simulation results as attenuation factors. The aging slope angle corresponding to the given safety coefficient was determined by functional fitting of the numerical simulation results. According to the difference in service life at different positions of open-pit slope, the design concept of long-term aging slope is innovatively proposed.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Relationship between the cracking angle and the crack inclination angle corresponding to different Poisson’s ratio.

**Figure 10.**Safety factor corresponding to different slop angles when the aging parameter deteriorates by 5%. (

**a**) α = 36°; (

**b**) α = 38°; (

**c**) α = 40°; (

**d**) α = 42°; (

**e**) α = 45°; (

**f**) α = 48°; AND (

**g**) α = 51°.

**Figure 11.**Fitting curves of slope angle and safety factors when aging parameters deteriorate by 5%, 10%, 15%, 20%, and 0%.

**Figure 13.**Calculation results of long-term aging slope stability. (

**a**) Before parameter attenuation; (

**b**) after parameter attenuation.

Mining Method | Equipment Application | External Dump | Internal Dump |
---|---|---|---|

Non-continuous mining system | Single-bucket excavator + Truck + Bulldozer | The only choice in the initial stage of mining, resulting in long exposure time of slope | Short haul distance and low cost but only applicable to horizontal or near-horizontal strata |

Dragline + Bulldozer | |||

Continuous mining system | Bucket-wheel excavator + Belt conveyor + Stacker + Bulldozer | ||

Semi-continuous mining system | Single-bucket excavator + Truck + Fixed crushing station + Belt conveyor + Stacker + Bulldozer | ||

Single-bucket excavator + Mobile crusher + Belt conveyor + Stacker + Bulldozer |

Stratum | Young’s Modulus (GPa) | Poisson’s Ratio | Fracture Toughness (MPa·m ^{1/2}) | Crack Length (m) | Crack Ratio |
---|---|---|---|---|---|

Sandstone | 3.12 | 0.214 | 28.6 | 0.02–0.3 | <15 |

Coal | 0.24 | 0.36 | 13.0 | 0.02–0.3 | <15 |

Aging Parameters | Group 1 | Group 2 | Group 3 | Group 4 | Group 5 |
---|---|---|---|---|---|

Cohesion | −5% | −10% | −15% | −20% | ±0% |

Friction angle | −5% | −10% | −15% | −20% | ±0% |

Gravity | +5% | +10% | +15% | +20% | ±0% |

F_{s} | ±0% | −5% | −10% | −15% | −20% |
---|---|---|---|---|---|

1.3 | 44.5 | 41.2 | 39.8 | 38.4 | 37.2 |

1.2 | 47.5 | 43.4 | 41.9 | 40.5 | 39.3 |

1.1 | 51.0 | 45.9 | 44.3 | 42.8 | 41.6 |

1.0 | 55.1 | 48.7 | 47.1 | 45.6 | 44.4 |

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**MDPI and ACS Style**

Chang, Z.; Zhang, W.; Zhao, G.; Dong, F.; Geng, X. Aging Stability Analysis of Slope Considering Cumulative Effect of Freeze–Thaw Damage—A Case Study. *Minerals* **2022**, *12*, 598.
https://doi.org/10.3390/min12050598

**AMA Style**

Chang Z, Zhang W, Zhao G, Dong F, Geng X. Aging Stability Analysis of Slope Considering Cumulative Effect of Freeze–Thaw Damage—A Case Study. *Minerals*. 2022; 12(5):598.
https://doi.org/10.3390/min12050598

**Chicago/Turabian Style**

Chang, Zhiguo, Weiguang Zhang, Gang Zhao, Fa Dong, and Xinyu Geng. 2022. "Aging Stability Analysis of Slope Considering Cumulative Effect of Freeze–Thaw Damage—A Case Study" *Minerals* 12, no. 5: 598.
https://doi.org/10.3390/min12050598