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

^{1}

^{2}

^{3}

^{4}

^{*}

## 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

- Zhou, W.; Yin, W.; Peng, X.; Liu, F.; Yang, F. Comprehensive evaluation of land reclamation and utilisation schemes based on a modified VIKOR method for surface mines. Int. J. Min. Reclam. Environ.
**2018**, 32, 93–108. [Google Scholar] [CrossRef] - Fedorova, L.; Kulyandin, G.; Savvin, D. Geocryological analysis of rocks to predict adverse freeze-and-thaw effects. J. Min. Sci.
**2019**, 55, 1023–1031. [Google Scholar] [CrossRef] - Hong, Y.; Shao, Z.; Shi, G.; Dou, Y.; Wang, W.; Zhang, W. Freeze-thaw effects on stability of open pit slope in high-altitude and cold regions. Geofluids
**2021**, 2021, 8409621. [Google Scholar] [CrossRef] - Luo, X.; Jiang, N.; Fan, X.; Mei, N.; Luo, H. Effects of freeze-thaw on the determination and application of parameters of slope rock mass in cold regions. Cold Reg. Sci. Technol.
**2015**, 110, 32–37. [Google Scholar] [CrossRef] - Groeneveld, B.; Topal, E. Flexible open-pit mine design under uncertainty. J. Min. Sci.
**2011**, 47, 212–226. [Google Scholar] [CrossRef] - Chang, Z.; Cai, Q.; Ma, L.; Han, L. Sensitivity analysis of factors affecting time-dependent slope stability under freeze-thaw cycles. Math. Probl. Eng.
**2018**, 2018, 7431465. [Google Scholar] [CrossRef] [Green Version] - Xin, L.; Huang, C.; Tao, C.; Rui, J.; Wang, S.; Wang, J.; Feng, G.; Zhang, S.; Qiu, C.; Wang, C. Development of a Chinese land data assimilation system: Its progress and prospects. Prog. Nat. Sci.
**2007**, 17, 881–892. [Google Scholar] [CrossRef] - Zhou, Y.; Zhou, W.; Lu, X.; Jiskani, I.; Li, L. Evaluation index system of green surface mining in china. Miner. Metall. Proc.
**2020**, 37, 1093–1103. [Google Scholar] [CrossRef] - Ding, Y.; Ye, B.; Liu, S.; Shen, Y.; Wang, S.; Yang, M. Monitoring of frozen soil hydrology in macro-scale in the Qinghai-Xizang Plateau. Chin. Sci. Bull.
**2000**, 45, 1143–1149. [Google Scholar] [CrossRef] - Wang, X.; Li, S.; Sun, Y.; Zhang, C.; Liu, G. Influence of freeze-thaw cycling on the soil mechanical properties of open-pit mine dump under different moisture contents. Environ. Earth Sci.
**2021**, 80, 279. [Google Scholar] [CrossRef] - Booshehrian, A.; Wan, R.; Su, G. Thermal disturbances in permafrost due to open pit mining and tailings impoundment. Minerals
**2020**, 10, 35. [Google Scholar] [CrossRef] [Green Version] - Roman, L.; Ze, Z. Effect of freezing-thawing on the physico-mechanical properties of a Morianic clayey loam. Soil Mech. Found. Eng.
**2010**, 47, 96–101. [Google Scholar] [CrossRef] - Zhang, Z.; Roman, L.; Ma, W.; Feng, W.; Zhao, S. The freeze-thaw cycles-time analogy method for forecasting long-term frozen soil strength. Measurement
**2016**, 92, 483–488. [Google Scholar] [CrossRef] - Xu, W.; Han, M.; Li, P. Influence of freeze-thaw cycles on mechanical responses of cemented paste tailings in surface storage. Int. J. Min. Reclam. Environ.
**2020**, 34, 326–342. [Google Scholar] [CrossRef] - Liu, B.; Ma, Y.; Zhang, G.; Xu, W. Acoustic emission investigation of hydraulic and mechanical characteristics of muddy sandstone experienced one freeze-thaw cycle. Cold Reg. Sci. Technol.
**2018**, 151, 335–344. [Google Scholar] [CrossRef] - Akgun, H.; Kockar, M. Design of anchorage and assessment of the stability of openings in silty, sandy limestone: A case study in Turkey. Int. J. Rock. Mech. Min.
**2004**, 41, 37–49. [Google Scholar] [CrossRef] - Ma, L.; Zhao, J.; Zhang, J.; Xiao, S. Slope stability analysis based on leader dolphins herd algorithm and simplified Bishop method. IEEE Access
**2021**, 9, 28251–28259. [Google Scholar] [CrossRef] - Meng, F.; Zhai, Y.; Li, Y.; Li, Y.; Zhang, Y. Experimental study on dynamic tensile properties and energy evolution of sandstone after freeze-thaw cycles. Chin. J. Rock Mech. Eng.
**2021**, 40, 2445–2453. [Google Scholar] - Li, J.; Zhu, L.; Cao, S. Damage characteristics of sandstone pore structure under freeze-thaw cycles. Rock Soil Mech.
**2019**, 40, 3524–3532. [Google Scholar] - Ni, X.; Shen, X.; Zhu, Z. Microscopic characteristics of fractured sandstone after cyclic freezing-thawing and triaxial unloading tests. Adv. Civ. Eng.
**2019**, 2019, 6512461. [Google Scholar] [CrossRef] [Green Version] - Mousavi, S.; Tavakoli, H.; Moarefvand, P.; Rezaei, M. Assessing the effect of freezing-thawing cycles on the results of the triaxial compressive strength test for calc-schist rock. Int. J. Rock. Mech. Min.
**2019**, 123, 104090. [Google Scholar] [CrossRef] - Park, J.; Hyun, C.; Park, H. Changes in microstructure and physical properties of rocks caused by artificial freeze-thaw action. B. Eng. Geol. Environ.
**2015**, 74, 555–565. [Google Scholar] [CrossRef] - Yavuz, H.; Altindag, R.; Sarac, S.; Ugur, I.; Sengun, N. Estimating the index properties of deteriorated carbonate rocks due to freeze–thaw and thermal shock weathering. Int. J. Rock Mech. Min.
**2006**, 43, 767–775. [Google Scholar] [CrossRef] - Wang, J.; Xuan, Z.; Jin, Q.; Sun, W.; Liang, B.; Yu, Q. Mesoscopic structural damage and permeability evolution of Shale subjected to freeze–thaw treatment. Sci. Rep.
**2022**, 12, 2202. [Google Scholar] [CrossRef] - Takarli, M.; Prince, W. Damage in granite under temperature variations. In Encyclopedia of Thermal Stresses; Hetnarski, R.B., Ed.; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Ju, M.; Li, X.; Li, X.; Zhang, G. A review of the effects of weak interfaces on crack propagation in rock: From phenomenon to mechanism. Eng. Fract. Mech.
**2022**, 263, 108297. [Google Scholar] [CrossRef] - Wang, Y.; Yi, X.; Gao, S.; Liu, H. Laboratory Investigation on the effects of natural fracture on fracture evolution of granite exposed to freeze-thaw-cyclic (FTC) loads. Geofluids
**2021**, 2021, 6650616. [Google Scholar] [CrossRef] - Jiang, R.; Dai, F.; Liu, Y.; Li, A.; Feng, P. Frequency characteristics of acoustic emissions induced by crack propagation in rock tensile fracture. Rock Mech. Rock Eng.
**2021**, 54, 2053–2065. [Google Scholar] [CrossRef] - Azarafza, M.; Feizi-Derakhshi, M.; Azarafza, M. Computer modeling of crack propagation in concrete retaining walls: A case study. Comput. Concrete
**2017**, 19, 509–514. [Google Scholar] [CrossRef] - Saadat, M.; Taheri, A. A numerical approach to investigate the effects of rock texture on the damage and crack propagation of a pre-cracked granite. Comput. Geotech.
**2019**, 111, 89–111. [Google Scholar] [CrossRef] - Song, Z.; Wang, Y.; Konietzky, H.; Cai, X. Mechanical behavior of marble exposed to freeze-thaw-fatigue loading. Int. J. Rock Mech. Min.
**2021**, 138, 104648. [Google Scholar] [CrossRef] - Li, J.; Zhou, K.; Liu, W.; Deng, H. NMR research on deterioration characteristics of microscopic structure of sandstones in freeze-thaw cycles. T. Nonferr. Metal. Soc.
**2016**, 26, 2997–3003. [Google Scholar] [CrossRef] - Gambino, G.; Harrison, J. Rock engineering design in frozen and thawing rock: Current approaches and future directions. ISRM Eur. Rock Mech. Symp. EUROCK
**2017**, 191, 656–665. [Google Scholar] [CrossRef] - Avcı, K.; Akgun, H.; Doyuran, V. Assessment of rock slope stability along the proposed Ankara-Pozantı Autoroad in Turkey. Environ. Geol.
**1999**, 37, 137–144. [Google Scholar] [CrossRef] - Akgun, H. Remediation of the geotechnical problems of the Hasankeyf Historical Area, Southeastern Turkey. Environ. Geol.
**2003**, 44, 522–529. [Google Scholar] [CrossRef] - Azarafza, M.; Akgun, H.; Ghazifard, A.; Asghari-Kaljahi, E.; Rahnamarad, J.; Derakhshani, R. Discontinuous rock slope stability analysis by limit equilibrium approaches–A review. Int. J. Digit. Earth
**2021**, 14, 1918–1941. [Google Scholar] [CrossRef] - Mirsayar, M.; Razmi, A.; Aliha, M.; Berto, F. EMTSN criterion for evaluating mixed mode I/II crack propagation in rock materials. Eng. Fract. Mech.
**2018**, 190, 186–197. [Google Scholar] [CrossRef] - Wang, Q.; Yang, J.; Zhang, C.; Zhou, Y.; Li, L.; Wu, L.; Huang, R. Determination of dynamic crack initiation and propagation toughness of a rock using a hybrid experimental-numerical approach. J. Eng. Mech.
**2016**, 142, 04016097. [Google Scholar] [CrossRef] - Sih, G.; Tang, X. Simultaneous occurrence of double micro/macro stress singularities for multiscale crack model. Theor. Appl. Fract. Mec.
**2006**, 46, 87–104. [Google Scholar] [CrossRef] - Parra, A.; Morales, N.; Vallejos, J.; Nguyen, P. Open pit mine planning considering geomechanical fundamentals. Int. J. Min. Reclam. Environ.
**2018**, 32, 221–238. [Google Scholar] [CrossRef] - Li, J.; Zhou, K.; Liu, W.; Zhang, Y. Analysis of the effect of freeze-thaw cycles on the degradation of mechanical parameters and slope stability. B. Eng. Geol. Environ.
**2018**, 77, 573–580. [Google Scholar] [CrossRef]

**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 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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