Skip to main content
SpringerLink
Log in

Grey wolf optimization approach for searching critical failure surface in soil slopes

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Detection of critical failure surface and associated minimum factor of safety (F) constitutes a constrained global optimization problem during the task of slope analysis. Morgenstern–Price method is an established limit equilibrium-based technique satisfying both moment and force equilibrium of all slices in the failure mass has been used to evaluate F against slope failure. The main objective of current study is to investigate the applicability and efficiency of grey wolf optimization (GWO) in solving slope stability problem. GWO is a nature inspired metaheuristic optimization method which mimics the social interaction between a pack of grey wolves in their endeavour to search, hunt and prey. The effectiveness of the recently developed GWO is examined by analyzing four different slope problems. Each soil slope model has been analysed for wolf pack size (NP) range 10–50 and maximum iteration count \( (k_{\hbox{max} } ) \) range 50–250. In effect, the number of evaluated functions (NFE) is found to lie in the range of 500–12,500. The results demonstrate that the GWO technique can detect the critical failure surface with very good accuracy. Furthermore, the statistical analysis is presented in terms of best \( F_{\text{b}} \), worst \( F_{\text{w}} \), mean \( \overline{F} \), standard deviation (SD) and % error (%E) of the optimum solutions i.e. factor of safety (F) from 10 independent runs. The effect of GWO parameters such as NP and \( k_{\hbox{max} } \) to obtain optimum solution are also presented. The \( F_{\text{b}} , \, F_{\text{w}} , \, \overline{F} \;{\text{and}}\;{\text{SD}} \) for 1st slope model are (1.7295, 1.7296, 1.7295, 0.000038) and they have been obtained for maximum NFE equal to 12,500. Similarly, for 2nd and 3rd slope model, the respective values are (1.4032, 1.4038, 1.4034, 0.000209) and (1.2530, 1.2546, 1.2537, 0.000741). The discrepancy or percentage error (%E) in best \( F_{\text{b}} \) from optimum (F) for NFE up to 500 are found to be equal to (0.0615, 0.2531, 0.8419) for studied slope models respectively. The evaluation of safety factor F for the fourth slope model has been studied for four different combinations of earthquake loadings and pore water pressures. The values of SD for all four cases are reported for maximum NFE equal to 12,500. It is found that uncertainty in reported F reduces if higher numbers of objective function evaluations are performed. This proves the excellent performance of GWO in evaluating minimum F of the slope.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Fellenius W (1936) Calculation of stability of earth dams. In: Transactions second congress on large dams, pp 445–465

  2. 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 

  3. Lowe J, Karafaith L (1960) Stability of earth dams upon draw down. In: Proceedings 1st Pan-Am conference soil mechanics and foundation engineering, Mexico City, pp 537–552

  4. Morgenstern NR, Price VE (1965) The analysis of the stability of general slip surfaces. Géotechnique 15:79–93. https://doi.org/10.1680/geot.1965.15.1.79

    Article  Google Scholar 

  5. Spencer E (1967) A method of analysis of the stability of embankments assuming parallel inter-slice forces. Géotechnique 17:11–26. https://doi.org/10.1680/geot.1967.17.1.11

    Article  Google Scholar 

  6. Spencer E (1973) Thrust line criterion in embankment stability analysis. Géotechnique 23:85–100. https://doi.org/10.1680/geot.1973.23.1.85

    Article  Google Scholar 

  7. Janbu N (1973) Slope stability computations. Dam Engineering Casagrande. Wiley, London, pp 47–86

    Google Scholar 

  8. Janbu N (1975) Slope stability computations. Int J Rock Mech Min Sci Geomech Abstr 12:67. https://doi.org/10.1016/0148-9062(75)90139-4

    Article  Google Scholar 

  9. Greco VR (1996) Efficient Monte Carlo technique for locating critical slip surface. J Geotech Eng 122:517–525. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(517)

    Article  Google Scholar 

  10. Malkawi AIH, Hassan WF, Sarma SK (2001) Global search method for locating general slip surface using Monte Carlo techniques. J Geotech Geoenviron Eng 127:688–698. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:8(688)

    Article  Google Scholar 

  11. Greco VR (2003) Discussion of “An efficient search method for finding the critical circular slip surface using the Monte Carlo technique”. Can Geotech J 40:221–222. https://doi.org/10.1139/t02-082

    Article  Google Scholar 

  12. Goh ATC (1999) Genetic algorithm search for critical slip surface in multiple-wedge stability analysis. Can Geotech J 36:382–391. https://doi.org/10.1139/t98-110

    Article  Google Scholar 

  13. Goh ATC (2000) Search for critical slip circle using genetic algorithms. Civ Eng Environ Syst 17:181–211. https://doi.org/10.1080/02630250008970282

    Article  Google Scholar 

  14. Zolfaghari AR, Heath AC, McCombie PF (2005) Simple genetic algorithm search for critical non-circular failure surface in slope stability analysis. Comput Geotech 32:139–152. https://doi.org/10.1016/j.compgeo.2005.02.001

    Article  Google Scholar 

  15. McCombie PF, Zolfaghari AR, Heath AC (2005) The use of the simple genetic algorithm in the non-circular analysis of slope stability. In: Civil-comp proceedings

  16. McCombie P, Wilkinson P (2002) The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis. Comput Geotech 29:699–714. https://doi.org/10.1016/S0266-352X(02)00027-7

    Article  Google Scholar 

  17. Cheng YM, Li L, Chi S, Wei WB (2007) Particle swarm optimization algorithm for the location of the critical non-circular failure surface in two-dimensional slope stability analysis. Comput Geotech 34:92–103. https://doi.org/10.1016/j.compgeo.2006.10.012

    Article  Google Scholar 

  18. Cheng Y, Li L, Chi S (2007) Performance studies on six heuristic global optimization methods in the location of critical slip surface. Comput Geotech 34:462–484. https://doi.org/10.1016/j.compgeo.2007.01.004

    Article  Google Scholar 

  19. Himanshu N, Burman A (2019) Determination of critical failure surface of slopes using particle swarm optimization technique considering seepage and seismic loading. Geotech Geol Eng 37:1261–1281. https://doi.org/10.1007/s10706-018-0683-8

    Article  Google Scholar 

  20. Kalatehjari R, Ali N, Hajihassani M, Kholghi Fard M (2012) The application of particle swarm optimization in slope stability analysis of homogeneous soil slopes. Int Rev Model Simul 5:458–465

    Google Scholar 

  21. Kalatehjari R, Ali N, Kholghifard M, Hajihassani M (2014) The effects of method of generating circular slip surfaces on determining the critical slip surface by particle swarm optimization. Arab J Geosci 7:1529–1539. https://doi.org/10.1007/s12517-013-0922-5

    Article  Google Scholar 

  22. Hajihassani M, Jahed Armaghani D, Kalatehjari R (2018) Applications of particle swarm optimization in geotechnical engineering: a comprehensive review. Geotech Geol Eng 36:705–722. https://doi.org/10.1007/s10706-017-0356-z

    Article  Google Scholar 

  23. Gordan B, Jahed Armaghani D, Hajihassani M, Monjezi M (2016) Prediction of seismic slope stability through combination of particle swarm optimization and neural network. Eng Comput 32:85–97. https://doi.org/10.1007/s00366-015-0400-7

    Article  Google Scholar 

  24. Mahdiyar A, Hasanipanah M, Armaghani DJ et al (2017) A Monte Carlo technique in safety assessment of slope under seismic condition. Eng Comput 33:807–817. https://doi.org/10.1007/s00366-016-0499-1

    Article  Google Scholar 

  25. Koopialipoor M, Jahed Armaghani D, Hedayat A et al (2018) Applying various hybrid intelligent systems to evaluate and predict slope stability under static and dynamic conditions. Soft Comput. https://doi.org/10.1007/s00500-018-3253-3

    Article  Google Scholar 

  26. Gao W, Raftari M, Rashid ASA et al (2019) A predictive model based on an optimized ANN combined with ICA for predicting the stability of slopes. Eng Comput. https://doi.org/10.1007/s00366-019-00702-7

    Article  Google Scholar 

  27. Bui XN, Muazu MA, Nguyen H (2019) Optimizing Levenberg–Marquardt backpropagation technique in predicting factor of safety of slopes after two-dimensional OptumG2 analysis. Eng Comput. https://doi.org/10.1007/s00366-019-00741-0

    Article  Google Scholar 

  28. Sari PA, Suhatril M, Osman N et al (2019) Developing a hybrid adoptive neuro-fuzzy inference system in predicting safety of factors of slopes subjected to surface eco-protection techniques. Eng Comput. https://doi.org/10.1007/s00366-019-00768-3

    Article  Google Scholar 

  29. Mohan SC, Maiti DK, Maity D (2013) Structural damage assessment using FRF employing particle swarm optimization. Appl Math Comput 219:10387–10400. https://doi.org/10.1016/j.amc.2013.04.016

    Article  MathSciNet  MATH  Google Scholar 

  30. Kahatadeniya KS, Nanakorn P, Neaupane KM (2009) Determination of the critical failure surface for slope stability analysis using ant colony optimization. Eng Geol 108:133–141. https://doi.org/10.1016/j.enggeo.2009.06.010

    Article  Google Scholar 

  31. Majumdar A, Nanda B, Maiti DK, Maity D (2014) Structural damage detection based on modal parameters using continuous ant colony optimization. Adv Civ Eng 2014:1–14. https://doi.org/10.1155/2014/174185

    Article  Google Scholar 

  32. Gao W, Karbasi M, Hasanipanah M et al (2018) Developing GPR model for forecasting the rock fragmentation in surface mines. Eng Comput 34:339–345. https://doi.org/10.1007/s00366-017-0544-8

    Article  Google Scholar 

  33. Gao W, Karbasi M, Derakhsh AM, Jalili A (2019) Development of a novel soft-computing framework for the simulation aims: a case study. Eng Comput 35:315–322. https://doi.org/10.1007/s00366-018-0601-y

    Article  Google Scholar 

  34. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf Optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  35. Muro C, Escobedo R, Spector L, Coppinger RP (2011) Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations. Behav Process 88:192–197. https://doi.org/10.1016/j.beproc.2011.09.006

    Article  Google Scholar 

  36. Kumar V, Himanshu N, Burman A (2019) Rock slope analysis with nonlinear Hoek–Brown criterion incorporating equivalent Mohr–Coulomb parameters. Geotech Geol Eng. https://doi.org/10.1007/s10706-019-00935-9

    Article  Google Scholar 

  37. Himanshu N, Burman A, Kumar V (2019) Assessment of optimum location of non-circular failure surface in soil slope using unified particle swarm optimization. Geotech Geol Eng. https://doi.org/10.1007/s10706-019-01148-w

    Article  Google Scholar 

  38. Zhu DY, Lee CF, Qian QH, Chen GR (2005) A concise algorithm for computing the factor of safety using the Morgenstern Price method. Can Geotech J 42:272–278. https://doi.org/10.1139/t04-072

    Article  Google Scholar 

  39. Yamagami T, Ueta Y (1988) Search for noncircular slip surfaces by the Morgenstern–Price method. In: Proceedings of 6th international conference on numerical methods in geomechanics, pp 1335–1340

  40. Bolton H, Heymann G, Groenwold A (2003) Global search for critical failure surface in slope stability analysis. Eng Optim 35:51–65. https://doi.org/10.1080/0305215031000064749

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    N. Himanshu, V. Kumar & A. Burman

  2. Department of Civil Engineering, Indian Institute of Technology, Kharagpur, Kharagpur, West Bengal, India

    D. Maity

  3. Faculty of Civil Engineering, Universiti Teknologi Malaysia (UTM), Skudai, Malaysia

    B. Gordan

Authors
  1. N. Himanshu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Burman
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Maity
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. Gordan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Himanshu.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Himanshu, N., Kumar, V., Burman, A. et al. Grey wolf optimization approach for searching critical failure surface in soil slopes. Engineering with Computers 37, 2059–2072 (2021). https://doi.org/10.1007/s00366-019-00927-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-019-00927-6

Keywords

Search

Navigation