SpringerLink
Log in

Probabilistic Analysis of Slope Using Bishop Method of Slices with the Help of Subset Simulation Subsequently Aided with Hybrid Machine Learning Paradigm

  • Original Paper
  • Published:
Indian Geotechnical Journal Aims and scope Submit manuscript

Abstract

The use of probabilistic analysis of slopes as a useful technique for determining the level of uncertainty in various variables has grown. In this study, a probabilistic analysis of a representative embankment with a height of 12 m under seismic conditions was carried out utilizing the UPSS ADD-INs 3.0 and Subset Simulation methodologies. The seismic coefficients kh of 0.12, 0.14, and 0.18 were all taken into consideration. In order to account for uncertainty in soil properties including cohesiveness, angle of internal friction, and unit weight of soil, the study used lognormal random fields and Cholesky matrices. The use of Subset Simulation enabled the fast calculation of the reliability index and the probability of failure, providing significant insights into the embankment's failure risk. In addition, a hybrid computational technique was used to optimize the worst-case scenario for failure probability. To address a gap in the literature, this work focused on develo** a probabilistic analysis using subset simulation and a hybrid Artificial Neural Network-Teaching Learning-Based Optimization model. The performance of this model was evaluated and compared to existing hybrid models built using seven different swarm intelligence methods. During the validation phase, it was observed that the proposed Artificial Neural Network-Teaching Learning-Based Optimization model outperformed other hybrid models, exhibiting a high determination coefficient value of 0.9974 and a low root mean square error value of 0.0226. This superiority can be attributed to the Teaching Learning-Based Optimization component, which emphasizes global search by incorporating a teaching phase to improve less optimal solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Flowchart 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

SS:

Subset simulation

Pf :

Probability of failure

ANN:

Artificial neural network

UPSS:

Uncertainty propagation using subset simulation

FS:

Factor of safety

β:

Reliability index

LEM:

Limit equilibrium method

SRM:

Strength reduction method

LAM:

Limit analysis method

FEM:

Finite element method

FORM:

First-order reliability method

FSM:

First-order second moment

MCS:

Monte Carlo simulation

RA:

Reliability analysis

NN:

Neural network

OA:

Optimization algorithm

PSO:

Particle swarm optimization

ABC:

Artificial bee colony

ACO:

Ant colony optimization

ALO:

Ant lion optimizer

ICA:

Imperialist competitive algorithm

TLBO:

Teaching–learning-based optimization

DFCC:

Dedicated freight corridor

MCMCS:

Markov chain Monte Carlo simulation

GWO:

Grey wolf optimizer

GA:

Genetic algorithm

BBO:

Biography-based optimization

ru :

Pore water pressure ratio

References

  1. Baecher GB, Christian JT (2005) Reliability and statistics in geotechnical engineering. John Wiley & Sons, Hoboken

    Google Scholar 

  2. Fenton GA, Griffiths DV (2002) others, Probabilistic foundation settlement on spatially random soil. J Geotech Geoenviron Eng 128:381–390

    Article  Google Scholar 

  3. Cheng YM, Lansivaara T, Wei WB (2007) Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34:137–150

    Article  Google Scholar 

  4. Reale C, Xue J, Pan Z, Gavin K (2015) Deterministic and probabilistic multi-modal analysis of slope stability. Comput Geotech 66:172–179. https://doi.org/10.1016/j.compgeo.2015.01.017

    Article  Google Scholar 

  5. Chowdhury RN, Xu DW (1995) Geotechnical system reliability of slopes. Reliab Eng Syst Saf 47:141–151

    Article  Google Scholar 

  6. Li D, Zhou C, Lu W, Jiang Q (2009) A system reliability approach for evaluating stability of rock wedges with correlated failure modes. Comput Geotech 36:1298–1307

    Article  Google Scholar 

  7. Li D-Q, Jiang S-H, Chen Y-F, Zhou C-B (2011) System reliability analysis of rock slope stability involving correlated failure modes. KSCE J Civ Eng 15:1349–1359

    Article  Google Scholar 

  8. Ang AH-S, Tang WH (1984) Probability concepts in engineering planning and design, vol. 2: Decision, risk, and reliability. John Wiley & Sons INC., Hoboken, pp. 1984, 608.

  9. Phoon K-K (2008) Reliability-based design in geotechnical engineering: computations and applications. CRC Press, Florida

    Book  Google Scholar 

  10. Sivakumar Babu GL, Mukesh MD (2004) Effect of soil variability on reliability of soil slopes. Geotechnique 54:335–337

    Article  Google Scholar 

  11. Low BK, Tang WH (1997) Probabilistic slope analysis using Janbu’s generalized procedure of slices. Comput Geotech 21:121–142

    Article  Google Scholar 

  12. Tang WH, Yucemen MS, Ang A-S (1976) Probability-based short term design of soil slopes. Can Geotech J 13:201–215

    Article  Google Scholar 

  13. Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope stability analysis. J Geotech Eng 120:2180–2207

    Article  Google Scholar 

  14. Malkawi AIH, Hassan WF, Abdulla FA (2000) Uncertainty and reliability analysis applied to slope stability. Struct Saf 22:161–187

    Article  Google Scholar 

  15. Cornell CA (1972) First-order uncertainty analysis of soil deformation and stability.

  16. Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div 100:111–121

    Article  Google Scholar 

  17. Ditlevsen O (1981) Uncertainty modeling with applications to multidimensional civil engineering systems. McGraw-Hill International Book Company, New York.

  18. Hammersley JM, Handscomb DC (1964) percolation processes In: Monte Carlo methods. Springer, pp 134–141.

  19. Robert CP, Casella G, Casella G (1999) Monte Carlo statistical methods. Springer.

  20. Low BK (2003) Practical probabilistic slope stability analysis. Proc Soil Rock Am 12:22–26

    Google Scholar 

  21. El-Ramly H, Morgenstern NR, Cruden DM (2002) Probabilistic slope stability analysis for practice. Can Geotech J 39:665–683

    Article  Google Scholar 

  22. Wang Y, Cao Z, Au S-K (2011) Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Can Geotech J 48:162–172

    Article  Google Scholar 

  23. Cao Z, Wang Y, Li D (2017) Probabilistic approaches for geotechnical site characterization and slope stability analysis. Springer.

  24. Hammersley JM, Handscomb DC (1964) The general nature of Monte Carlo methods In: Monte Carlo Methods. Springer, pp 1–9

  25. Fishman GS (1996) Random tours. Monte Carlo, pp. 335–491.

  26. Engelund S, Rackwitz R (1993) A benchmark study on importance sampling techniques in structural reliability. Struct Saf 12:255–276

    Article  Google Scholar 

  27. Schuëller GI, Pradlwarter HJ (2007) Benchmark study on reliability estimation in higher dimensions of structural systems—an overview. Struct Saf 29:167–182

    Article  Google Scholar 

  28. Melchers RE, Beck AT (2018) Structural reliability analysis and prediction. John wiley & sons, Hoboken

    Google Scholar 

  29. Low BK, Tang WH (1997) Efficient reliability evaluation using spreadsheet. J Eng Mech 123:749–752

    Google Scholar 

  30. Low BK, Tang WH (2004) Reliability analysis using object-oriented constrained optimization. Struct Saf 26:69–89

    Article  Google Scholar 

  31. Low BK, Tang WH (2007) Efficient spreadsheet algorithm for first-order reliability method. J Eng Mech 133:1378–1387

    Google Scholar 

  32. Au S-K, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Prob Eng Mech 16:263–277

    Article  Google Scholar 

  33. Au SK, Ching J, Beck JL (2007) Application of subset simulation methods to reliability benchmark problems. Struct Saf 29:183–193. https://doi.org/10.1016/j.strusafe.2006.07.008

    Article  Google Scholar 

  34. Shariati M, Armaghani DJ, Khandelwal M, Zhou J, Khorami M (2021) Assessment of longstanding effects of fly ash and silica fume on the compressive strength of concrete using extreme learning machine and artificial neural network. J Adv Eng Comput 5:50–74

    Article  Google Scholar 

  35. Shariati M, Mafipour MS, Mehrabi P, Shariati A, Toghroli A, Trung NT, Salih MNA (2021) A novel approach to predict shear strength of tilted angle connectors using artificial intelligence techniques. Eng Comput 37:2089–2109

    Article  Google Scholar 

  36. Deng J, Gu D, Li X, Yue ZQ (2005) Structural reliability analysis for implicit performance functions using artificial neural network. Struct Saf 27:25–48

    Article  Google Scholar 

  37. Deng J (2006) Structural reliability analysis for implicit performance function using radial basis function network. Int J Solids Struct 43:3255–3291

    Article  Google Scholar 

  38. Cho SE (2009) Probabilistic stability analyses of slopes using the ANN-based response surface. Comput Geotech 36:787–797

    Article  Google Scholar 

  39. Erzin Y, Cetin T (2012) The use of neural networks for the prediction of the critical factor of safety of an artificial slope subjected to earthquake forces. Sci Iran 19:188–194

    Article  Google Scholar 

  40. Zhao H (2008) Slope reliability analysis using a support vector machine. Comput Geotech 35:459–467

    Article  Google Scholar 

  41. Kang F, Xu Q, Li J (2016) Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence. Appl Math Model 40:6105–6120. https://doi.org/10.1016/j.apm.2016.01.050

    Article  MathSciNet  Google Scholar 

  42. Kumar V, Samui P, Himanshu N, Burman A (2019) Reliability-based slope stability analysis of durgawati earthen dam considering steady and transient state seepage conditions using MARS and RVM. Indian Geotech J 49:650–666. https://doi.org/10.1007/s40098-019-00373-7

    Article  Google Scholar 

  43. Li S, Zhao H, Ru Z (2017) Relevance vector machine-based response surface for slope reliability analysis. Int J Numer Anal Methods Geomech 41:1332–1346

    Article  Google Scholar 

  44. Yang J, Cheng L, Ran L (2021) Research on slope reliability analysis using multi-kernel relevance vector machine and advanced first-order second-moment method. Eng Comput 23:1–12

    Google Scholar 

  45. Samui P, Lansivaara T, Bhatt MR (2013) Least square support vector machine applied to slope reliability analysis. Geotech Geol Eng 31:1329–1334

    Article  Google Scholar 

  46. He X, Xu H, Sabetamal H, Sheng D (2020) Machine learning aided stochastic reliability analysis of spatially variable slopes. Comput Geotech 126:103711

    Article  Google Scholar 

  47. Bardhan A, Samui P (2022) Probabilistic slope stability analysis of Heavy-haul freight corridor using a hybrid machine learning paradigm. Transp Geotech 37:100815. https://doi.org/10.1016/j.trgeo.2022.100815

    Article  Google Scholar 

  48. Bardhan A, Manna P, Kumar V, Burman A, Žlender B, Samui P (2021) Reliability analysis of piled raft foundation using a novel hybrid approach of ann and equilibrium optimizer. Comput Model Eng Sci 128:15885. https://doi.org/10.32604/cmes.2021.015885

    Article  Google Scholar 

  49. Liou S-W, Wang C-M, Huang Y-F (2009) Integrative discovery of multifaceted sequence patterns by frame-relayed search and hybrid PSO-ANN. J UCS 15:742–764

    Google Scholar 

  50. Koopialipoor M, Fallah A, Armaghani DJ, Azizi A, Mohamad ET (2019) Three hybrid intelligent models in estimating flyrock distance resulting from blasting. Eng Comput 35:243–256. https://doi.org/10.1007/s00366-018-0596-4

    Article  Google Scholar 

  51. Golafshani EM, Behnood A, Arashpour M (2020) Predicting the compressive strength of normal and high-performance concretes using ANN and ANFIS hybridized with grey wolf optimizer. Constr Build Mater 232:117266. https://doi.org/10.1016/j.conbuildmat.2019.117266

    Article  Google Scholar 

  52. Le LT, Nguyen H, Dou J, Zhou J (2019) A comparative study of PSO-ANN, GA-ANN, ICA-ANN, and ABC-ANN in estimating the heating load of buildings’ energy efficiency for smart city planning. Appl Sci 9:2630

    Article  Google Scholar 

  53. Armaghani DJ, Mirzaei F, Shariati M, Trung NT, Shariati M, Trnavac D (2020) Hybrid ANN-based techniques in predicting cohesion of sandy-soil combined with fiber. Geomech Eng 20:191–205

    Google Scholar 

  54. Shariati M, Mafipour MS, Mehrabi P, Ahmadi M, Wakil K, Trung NT, Toghroli A (2020) Prediction of concrete strength in presence of furnace slag and fly ash using Hybrid ANN-GA (Artificial neural network-genetic algorithm). Smart Struct Syst Int J 25:183–195

    Google Scholar 

  55. Shariati M, Mafipour MS, Mehrabi P, Bahadori A, Zandi Y, Salih MNA, Nguyen H, Dou J, Song X, Poi-Ngian S (2019) Application of a hybrid artificial neural network-particle swarm optimization (ANN-PSO) model in behavior prediction of channel shear connectors embedded in normal and high-strength concrete. Appl Sci 9:5534

    Article  Google Scholar 

  56. Bishop AW (1955) The use of the slip circle in the stability analysis of slopes. Géotechnique 5:7–17. https://doi.org/10.1680/geot.1955.5.1.7

    Article  Google Scholar 

  57. RDSO/2007/GE:0014 (2009) Guidelines and specifications for design of formation for heavy axle load. Research Designs and Standards Organisation, Lucknow.

  58. RDSO/GE:IRS-0004 (2020) Comprehensive guidelines and specifications for railway formation. Research Designs and Standards Organisation, Lucknow.

  59. RDSO/2003/GE:G-1 (2003) Guidelines for earthwork in railway projects. Research Designs and Standards Organisation.

  60. IRC (2015) 75–2015, Guidelines for the design of high embankments, Indian Road Congress.

  61. Sabri MS, Ahmad F, Samui P (2023) Slope stability analysis of heavy-haul freight corridor using novel machine learning approach. Model Earth Syst Environ 23:1–19

    Google Scholar 

  62. Vanmarcke EH (1977) Probabilistic modeling of soil profiles. J Geotech Eng Div 103:1227–1246

    Article  Google Scholar 

  63. Fenton GA, Griffiths DV (2008) Risk assessment in geotechnical engineering. John Wiley & Sons, New York

    Book  Google Scholar 

  64. Li D-Q, **ao T, Cao Z-J, Zhou C-B, Zhang L-M (2016) Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using subset simulation. Landslides 13:293–303

    Article  Google Scholar 

  65. Zhu B, Hiraishi T, Pei H, Yang Q (2021) Efficient reliability analysis of slopes integrating the random field method and a Gaussian process regression-based surrogate model. Int J Numer Anal Methods Geomech 45:478–501

    Article  Google Scholar 

  66. Au S-K, Wang Y (2014) Engineering risk assessment with subset simulation. John Wiley & Sons, Hoboken

    Book  Google Scholar 

  67. Wang Y, Cao Z (2013) Expanded reliability-based design of piles in spatially variable soil using efficient Monte Carlo simulations. Soils Found 53:820–834

    Article  Google Scholar 

  68. Kadam AK, Wagh VM, Muley AA, Umrikar BN, Sankhua RN (2019) Prediction of water quality index using artificial neural network and multiple linear regression modelling approach in Shivganga River basin, India. Model Earth Syst Environ 5:951–962

    Article  Google Scholar 

  69. Sarigöl M, Yesilyurt SN (2022) Flood routing calculation with ANN, SVM, GPR, and RTE methods. Pol J Env Stud 31:1–8

    Article  Google Scholar 

  70. Dalkiliç HY, Hashimi SA (2020) Prediction of daily streamflow using artificial neural networks (ANNs), wavelet neural networks (WNNs), and adaptive neuro-fuzzy inference system (ANFIS) models. Water Supply 20:1396–1408

    Article  Google Scholar 

  71. Ojha VK, Abraham A, Snášel V (2017) Metaheuristic design of feedforward neural networks: a review of two decades of research. Eng Appl Artif Intell 60:97–116

    Article  Google Scholar 

  72. Lumb P (1974) Application of statistics in soil mechanics. Soil Mech New Horiz 56:44–111

    Google Scholar 

  73. Singh A (1972) How reliable is the factor of safety in foundation engineering?. A conference paper

  74. Harr ME (1984) Reliability-based design in civil engineering. Department of Civil Engineering School of Engineering, North Carolina State

    Google Scholar 

  75. Kulhawy FH (1992) On the evaluation of soil properties. In: Kulhawy FH (ed) ASCE geotechnology. Special Publication, London, pp 95–1153

    Google Scholar 

  76. Kar SS, Roy LB (2021) Reliability analysis of a finite slope considering the effects of soil uncertainty. Int J Perform Eng 17:473–483. https://doi.org/10.23940/ijpe.21.05.p7.473483

    Article  Google Scholar 

  77. Au SK, Cao ZJ, Wang Y (2010) Implementing advanced Monte Carlo simulation under spreadsheet environment. Struct Saf 32:281–292

    Article  Google Scholar 

  78. Behar O, Khellaf A, Mohammedi K (2015) Comparison of solar radiation models and their validation under Algerian climate—The case of direct irradiance. Energy Convers Manag 98:236–251

    Article  Google Scholar 

  79. Legates DR, McCabe GJ (2013) A refined index of model performance: a rejoinder. Int J Climatol 33:1053–1056

    Article  Google Scholar 

  80. Willmott CJ (1984) On the evaluation of model performance in physical geography In: Spatial and statistic model. Springer, pp 443–460.

  81. Wong FS (1985) Slope reliability and response surface method. J Geotech Eng 111:32–53

    Article  Google Scholar 

  82. Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)?–Arguments against avoiding RMSE in the literature. Geosci Model Dev 7:1247–1250

    Article  Google Scholar 

  83. Stone RJ (1993) Improved statistical procedure for the evaluation of solar radiation estimation models. Sol Energy 51:289–291

    Article  Google Scholar 

  84. Kardani N, Aminpour M, Raja MNA, Kumar G, Bardhan A, Nazem M (2022) Prediction of the resilient modulus of compacted subgrade soils using ensemble machine learning methods. Transp Geotech 36:100827

    Article  Google Scholar 

Download references

Acknowledgements

Profs. Siu-Kui Au (University of Liverpool, UK), Yu Wang (City University of Hong Kong, China), and Zijun Cao (Wuhan University, China) are thanked for making available the MS-Excel Add-In UPSS module used in this study.

Funding

There has been no external funding.

Author information

Authors and Affiliations

  1. Civil Engineering Department, National Institute of Technology, Patna, India

    Furquan Ahmad, Pijush Samui & S. S. Mishra

Authors
  1. Furquan Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pijush Samui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. S. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

F.A. contributed to methodology, materials, programs, validation, graphics, first draft, review & editing writing; P.S. contributed to guidance. S.S.M. contributed to guidance.

Corresponding author

Correspondence to Furquan Ahmad.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmad, F., Samui, P. & Mishra, S.S. Probabilistic Analysis of Slope Using Bishop Method of Slices with the Help of Subset Simulation Subsequently Aided with Hybrid Machine Learning Paradigm. Indian Geotech J 54, 577–597 (2024). https://doi.org/10.1007/s40098-023-00796-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40098-023-00796-3

Keywords

Search

Navigation