# A Comprehensive Numerical Modeling Study for Parameter Optimization and Slope Stability Analysis in the Baganuur Lignite Coal Mine

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Numerical Model

#### 2.1.1. Limit Equilibrium Method (LEM)

#### 2.1.2. Finite Element Method (FEM)

#### 2.2. Model Description

#### 2.3. Material Properties

_{1}, σ

_{2,}σ

_{3}are principal stress, and I:

#### 2.4. Factor of Safety (FS) and Strength Reduction Factor (SRF)

_{f}is the shear stress on the sliding surface, calculated as follows:

_{f}and Ø

_{f}are

_{f}

_{=}reduced cohesion, Ø

_{f}reduced friction angle, and τ

_{f}= shear stress.

## 3. Results and Discussion

^{®}2012 developed by Geo-Slope International Limited and the slopes’ computed factor of safety ranged from 0.8 to 1.33, suggesting critical to poor slope stability when exposed to landslide-triggering agents. Hence, slope stabilization is required on the mine tailing dumps at Enyigba to prevent major landslide occurrence, and Wang [36] explores the analytical solution of FoS to accommodate the effects of groundwater on the stability of the dump slope.

#### 3.1. Numerical Simulation of the Dump Slope Stability for Impact of Height, Dip Angle, and Safety Berm

#### 3.1.1. The Impact of Differences in Dump Height

#### 3.1.2. The Impact of Differences in the Dip Angle of the Dump

#### 3.1.3. Design of the Internal Dump

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FEM | Finite element method |

LEM | Limit equilibrium method |

SRF | Strength reduction factor |

FS | Factor of safety |

FDM | Finite difference method |

DSR | Double strength reduction |

SSR | Shear strength reduction |

IWD | Internal waste dump |

DH | Dump height |

DA | Dump angle |

## References

- Park, J.; Kwon, E.; Chung, E.; Kim, H.; Battogtokh, B.; Woo, N.C. Environmental Sustainability of Open-Pit Coal Mining Practices at Baganuur, Mongolia. Sustainability
**2019**, 12, 248. [Google Scholar] [CrossRef] - Rouainia, M.; Davies, O.; O’Brien, T.; Glendinning, S. Numerical Modelling of Climate Effects on Slope Stability. Proc. Inst. Civil. Eng.-Eng. Sustain.
**2009**, 162, 81–89. [Google Scholar] [CrossRef] - Kaithola, A.; Verma, D.; Gupte, S.S.; Singh, N.T. A Coal Mine Dump Stability Analysis—A Case Study. Geomaterial
**2011**, 1, 1–13. [Google Scholar] [CrossRef] - Göktepe, F.; Keskin, I. A Comparison Study between Traditional and Finite Element Methods for Slope Stability Evaluations. J. Geol. Soc. India
**2018**, 91, 373–379. [Google Scholar] [CrossRef] - Liu, S.Y.; Shao, L.T.; Li, H.J. Slope Stability Analysis Using the Limit Equilibrium Method and Two Finite Element Methods. Comput. Geotech.
**2015**, 63, 291–298. [Google Scholar] [CrossRef] - Nguyen, P.M.V.; Wrana, A.; Rajwa, S.; Różański, Z.; Frączek, R. Slope Stability Numerical Analysis and Landslide Prevention of Coal Mine Waste Dump under the Impact of Rainfall—A Case Study of Janina Mine, Poland. Energies
**2022**, 15, 8311. [Google Scholar] [CrossRef] - Onyango, J.; Zhang, C. Numerical Analysis of Slope Stability by Strength Reduction in Finite Elements Using ANSYS a Case Study of Qinglong-Xingyi Expressway Contract Section T1(K11+790~K11+875). Environ. Earth Sci. Res. J.
**2019**, 6, 89–96. [Google Scholar] [CrossRef] - Guo, T.; Zhou, W.; Li, Z.; Zhang, C.; Cai, Q.; Tian, Y.; Qin, H.; Liu, F.; Jiskani, I.M.; Zhang, D. Optimization of Land Saving and Loss Reducing and Slope Stability Variation Patterns in Open-Pit Mine. Geofluids
**2021**, 2021, 6620235. [Google Scholar] [CrossRef] - Fredlund, D. Computer Software for Slope Stability Analysis. 1976. Available online: https://www.researchgate.net/publication/347986725_Computer_software_for_slope_stability_analysis (accessed on 28 April 2023).
- Manouchehrian, A.; Gholamnejad, J.; Sharifzadeh, M. Development of a Model for Analysis of Slope Stability for Circular Mode Failure Using Genetic Algorithm. Environ. Earth Sci.
**2014**, 71, 1267–1277. [Google Scholar] [CrossRef] - Cai, F.; Ugai, K. Discussion: Slope Stability Analysis by Finite Elements. Géotechnique
**2001**, 51, 653–654. [Google Scholar] [CrossRef] - Beyabanaki, S.A.R. A Comparison between Using Finite Difference and Limit Equilibrium Methods for Landslide Analysis of Slopes Containing a Weak Layer. Am. J. Eng. Res.
**2020**, 9, 68–79. [Google Scholar] - Gupte, S. Optimisation of Internal Dump Capacity and Stability Analysis in a Coal Mine—A Case Study. In Proceedings of the First Asia Pacific Slope Stability in Mining Conference, Brisbane, Australia, 6–8 September 2016; Australian Centre for Geomechanics: Perth, Australia, 2016; pp. 557–570. [Google Scholar]
- Deng, D.; Li, L.; Zhao, L. Limit Equilibrium Method (LEM) of Slope Stability and Calculation of Comprehensive Factor of Safety with Double Strength-Reduction Technique. J. Mt. Sci.
**2017**, 14, 2311–2324. [Google Scholar] [CrossRef] - Phase2-2D Finite Element Program for Calculating Stresses and Estimating Support around Underground Excavations. 2001. Available online: https://www.rocscience.com/downloads/phase2/Phase2_ModelReference.pdf (accessed on 28 April 2023).
- Slide2-Documentation. Available online: https://www.rocscience.com/help/slide2/documentation (accessed on 28 April 2023).
- GeoStudio Reference Manuals—GeoStudio Support. Available online: https://www.geoslope.support/kb/article/10-geostudio-reference-manuals/ (accessed on 30 April 2023).
- GeoWizard—Free Programs for Geoengineers. Available online: http://www.geowizard.org/doc_hyrcan_tutorials.html (accessed on 28 April 2023).
- PLAXIS 2D—Reference Manual. Available online: https://communities.bentley.com/cfs-file/__key/communityserver-wikis-components-files/00-00-00-05-58/3113.PLAXIS2DCE_2D00_V20.02_2D00_2_2D00_Reference.pdf (accessed on 5 May 2020).
- Geoslope—Slope Stability Verification Manual. Available online: https://downloads.geoslope.com/geostudioresources/books/11/4/Slope%20Stability%20Verification%20Manual.pdf (accessed on 28 April 2023).
- Verma, D.; Kainthola, A.; Gupte, S.S.; Singh, T.N. A Finite Element Approach of Stability Analysis of Internal Dump Slope in Wardha Valley Coal Field, India, Maharashtra. Am. J. Min. Metall.
**2013**, 1, 1–6. [Google Scholar] - Pan, W.; Pan, W.; Luo, J.; Fan, L.; Li, S.; Erdenebileg, U. Slope Stability of Increasing Height and Expanding Capacity of South Dumping Site of Hesgoula Coal Mine: A Case Study. Int. J. Coal Sci. Technol.
**2021**, 8, 427–440. [Google Scholar] [CrossRef] - Behera, P.K.; Sarkar, K.; Singh, A.K.; Verma, A.K.; Singh, T.N. Dump Slope Stability Analysis—A Case Study. J. Geol. Soc. India
**2016**, 88, 725–735. [Google Scholar] [CrossRef] - Jana, A.; Dey, A. Stability Analysis of Rock Slope Using Combined Continuum Interface Element Method. In Proceedings of the Indian Geotechnical Conference, Guwahati, India, 14–16 December 2017. [Google Scholar]
- Carranza-Torres, C.; Zhao, J. Analytical and Numerical Study of the Effect of Water Pressure on the Mechanical Response of Cylindrical Lined Tunnels in Elastic and Elasto-Plastic Porous Media. Int. J. Rock. Mech. Min. Sci.
**2009**, 46, 531–547. [Google Scholar] [CrossRef] - Pal, S.; Kaynia, A.; Bhasin, R.; Paul, D. Earthquake Stability Analysis of Rock Slopes: A Case Study. Rock. Mech. Rock. Eng.
**2012**, 45, 205–215. [Google Scholar] [CrossRef] - Ulusay, R.; Aksoy, H. Assessment of the Failure Mechanism of a Highwall Slope under Spoil Pile Loadings at a Coal Mine. Eng. Geol.
**1994**, 38, 117–134. [Google Scholar] [CrossRef] - Richards, P.G.; Torr, D.G.; Torr, M.R. Photodissociation of N 2: A Significant Source of Thermospheric Atomic Nitrogen. J. Geophys. Res.
**1981**, 86, 1495. [Google Scholar] [CrossRef] - Singh, R.P.; Dubey, C.S.; Singh, S.K.; Shukla, D.P.; Mishra, B.K.; Tajbakhsh, M.; Ningthoujam, P.S.; Sharma, M.; Singh, N. A New Slope Mass Rating in Mountainous Terrain, Jammu and Kashmir Himalayas: Application of Geophysical Technique in Slope Stability Studies. Landslides
**2013**, 10, 255–265. [Google Scholar] [CrossRef] - Bishop 1955 Method of Slices|PDF. Available online: https://www.scribd.com/doc/88203869/Bishop-1955-Method-of-Slices (accessed on 29 April 2023).
- Slope Stability Computations (Janbu, 1973)|PDF. Available online: https://www.scribd.com/doc/311344815/Slope-Stability-Computations-Janbu-1973 (accessed on 29 April 2023).
- Jing, L. A Review of Techniques, Advances and Outstanding Issues in Numerical Modelling for Rock Mechanics and Rock Engineering. Int. J. Rock. Mech. Min. Sci.
**2003**, 40, 283–353. [Google Scholar] [CrossRef] - Zienkiewicz, O.C.; Cheung, Y.K. The Finite Element Method in Structural and Continuum Mechanics: Numerical Solution of Problems in Structural and Continuum Mechanics; McGraw-Hill: New York, NY, USA, 1970. [Google Scholar]
- Duncan, J.M. State of the Art: Limit Equilibrium and Finite-Element Analysis of Slopes. J. Geotech. Eng.
**1996**, 122, 577–596. [Google Scholar] [CrossRef] - Igwe, O.; Chukwu, C. Slope Stability Analysis of Mine Waste Dumps at a Mine Site in Southeastern Nigeria. Bull. Eng. Geol. Environ.
**2019**, 78, 2503–2517. [Google Scholar] [CrossRef] - Wang, Z.; Liu, B.; Han, Y.; Wang, J.; Yao, B.; Zhang, P. Stability of Inner Dump Slope and Analytical Solution Based on Circular Failure: Illustrated with a Case Study. Comput. Geotech.
**2020**, 117, 103241. [Google Scholar] [CrossRef] - Wahyudi, S.; Shimada, H.; Sasaoka, T.; Hamanaka, A.; Amarsaikhan, T.; Mao, P.; Dintwe, T.K.M.; Moses, D. Study of Internal Waste Dump-Induced Shear Stress Behavior on Pit-Slope. J. Geosci. Environ. Prot.
**2020**, 8, 71–86. [Google Scholar] [CrossRef]

**Figure 2.**Numerical simulation of internal dump ((

**a**). current situation of area under study, (

**b**). main numerical simulation, (

**c**). main model parameters on AutoCAD design). Here, θ = deposit angle, α = internal dump dip angle, H = bench height, d = berm width, β = floor angle, H2 = overall bench height.

**Figure 4.**Slope design with a height of 45 m at 38° and safety berm width of 5 m (

**a**). FEM method = 0.53, (

**b**). Bishop method=0.512, (

**c**). Janbu simplified method = 0.498, (

**d**). Spencer simplified method = 0.506).

**Figure 5.**Slope design with a height of 35 m, dip angle of 28°, and safety berm width 5 m (

**a**). FEM method = 1.18, (

**b**). Bishop method = 1.066, (

**c**). Janbu simplified method = 1.057, (

**d**). Spencer simplified method = 1.063).

**Figure 6.**Slope design with a height of 30 m, a dip angle of 28°, and a safety berm width of 5 m (

**a**). FEM method = 1.21, (

**b**). Bishop method = 1.118, (

**c**). Janbu simplified method = 1.092, (

**d**). Spencer simplified method = 1.113).

**Figure 7.**Slope design with height of 50 m, dip angle of 28°, and safety berm width of 5 m (

**a**). FEM method = 1.065, (

**b**). Bishop method = 0.926, (

**c**). Janbu simplified method = 0.915, (

**d**). Spencer simplified method = 0.920).

**Figure 8.**Slope design with a height of 45 m, dip angle of 28°, and safety berm width of 5 m (

**a**). FEM method = 1.15, (

**b**). Bishop method = 1.068, (

**c**). Janbu simplified method = 1.054, (

**d**). Spencer simplified method = 1.061).

**Figure 9.**Slope design with height of 50 m, dip angle of 28°, and safety berm width of 5 m (

**a**). FEM method = 1.13, (

**b**). Bishop method = 1.056, (

**c**). Janbu simplified method = 1.042, (

**d**). Spencer simplified method = 1.051).

Dip of internal waste dump ($\alpha $) | between 25$\xb0$ and 50$\xb0$ |

Height of internal waste dump (H) | between 30 m and 50 m |

Safety berm of internal waste dump (d) | between 0 m and 15 m |

Floor rock ($\beta $) | 12$\xb0$ |

Dip of coal seam ($\theta $) | 65$\xb0$ |

Thickness of coal seam | 20 m |

Material | Unit Weight (MN/m^{3}) | Friction Angle (Degree) | Tensile Strength (MPa) | Cohesion (MPa) | Young’s Module (MPa) | Poisson’s Ratio |
---|---|---|---|---|---|---|

Internal Waste Dump | 0.02 | 28 | 0 | 0 | 24.75 | 0.35 |

Coal | 0.01 | 31.8 | 3.94 | 0.2 | 2550 | 0.42 |

Floor Rock | 0.02 | 28.3 | 4.5 | 0.4 | 3130 | 0.41 |

Dump Height with 5 m Differences | FS | |||
---|---|---|---|---|

FEM | Simplified Bishop Method | Janbu Simplified Method | Spencer Simplified Method | |

DA38° DH30 m | 0.86 | 0.749 | 0.737 | 0.745 |

DA38° DH35 m | 0.77 | 0.653 | 0.640 | 0.648 |

DA38° DH40 m | 0.65 | 0.587 | 0.576 | 0.581 |

DA38° DH45 m | 0.53 | 0.512 | 0.498 | 0.506 |

Dump Dip Angle 5° Differences | FS | |||
---|---|---|---|---|

FEM | Simplified Bishop Method | Janbu Simplified Method | Spencer Simplified Method | |

DA28° DH35 m | 1.18 | 1.066 | 1.057 | 1.063 |

DA33° DH35 m | 0.96 | 0.880 | 0.871 | 0.877 |

DA43° DH35 m | 0.62 | 0.549 | 0.538 | 0.543 |

DA48° DH35 m | 0.50 | 0.438 | 0.427 | 0.434 |

Dump Height 5 m Differences | FS | |||
---|---|---|---|---|

FEM | Simplified Bishop Method | Janbu Simplified Method | Spencer Simplified Method | |

DA28° DH30 m | 1.21 | 1.118 | 1.092 | 1.113 |

DA28° DH40 m | 1.13 | 1.062 | 1.052 | 1.059 |

DA28° DH45 m | 1.09 | 0.975 | 0.963 | 0.969 |

DA28° DH50 m | 1.065 | 0.926 | 0.915 | 0.920 |

DA28° DH45 m | FS | |||
---|---|---|---|---|

FEM | Simplified Bishop Method | Janbu Simplified Method | Spencer Simplified Method | |

Safety berm 0 m | 1.05 | 0.941 | 0.927 | 0.935 |

Safety berm 10 m | 1.12 | 1.038 | 1.025 | 1.031 |

Safety berm 15 m | 1.15 | 1.068 | 1.056 | 1.061 |

DA28° DH50 m | FS | |||
---|---|---|---|---|

FEM | Simplified Bishop Method | Janbu Simplified Method | Spencer Simplified Method | |

Safety berm 0 m | 1.03 | 0.958 | 0.945 | 0.952 |

Safety berm 10 m | 1.09 | 0.984 | 0.973 | 0.980 |

Safety berm 15 m | 1.13 | 1.056 | 1.042 | 1.051 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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**

Enkhbold, B.; Ikeda, H.; Toriya, H.; Adachi, T.
A Comprehensive Numerical Modeling Study for Parameter Optimization and Slope Stability Analysis in the Baganuur Lignite Coal Mine. *Mining* **2023**, *3*, 755-772.
https://doi.org/10.3390/mining3040041

**AMA Style**

Enkhbold B, Ikeda H, Toriya H, Adachi T.
A Comprehensive Numerical Modeling Study for Parameter Optimization and Slope Stability Analysis in the Baganuur Lignite Coal Mine. *Mining*. 2023; 3(4):755-772.
https://doi.org/10.3390/mining3040041

**Chicago/Turabian Style**

Enkhbold, Bilguun, Hajime Ikeda, Hisatoshi Toriya, and Tsuyoshi Adachi.
2023. "A Comprehensive Numerical Modeling Study for Parameter Optimization and Slope Stability Analysis in the Baganuur Lignite Coal Mine" *Mining* 3, no. 4: 755-772.
https://doi.org/10.3390/mining3040041