System reliability analysis of soil slopes through constrained optimization

Abstract

As a slope may have numerous potential slip surfaces, its failure probability as a system is usually different from that of a single slip surface. Nevertheless, the system failure probability of a slope is often governed by several representative slip surfaces. How to identify the representative slip surfaces is important for system reliability analysis of soil slopes. Previous studies on representative slip surface identification mainly focus on circular slip surfaces within the framework of limit equilibrium methods; there are also relevant researches, albeit limited, within the framework of finite element/finite difference analyses based on the shear strength reduction method. By viewing the task of representative slip surface identification as a multidesign point identification problem, a barrier-based optimization method is suggested in this paper to identify representative slip surfaces of arbitrary shape based on the shear strength reduction method. A multiple starting point strategy is suggested to enhance its efficiency. For the three slopes examined in this paper, the method suggested is capable of identifying representative slip surfaces efficiently without prior assumption on their shapes.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

References

  1. Cheng YM, Lansivaara T, Wei WB (2007) Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34:137–150. https://doi.org/10.1016/j.compgeo.2006.10.011

    Article  Google Scholar 

  2. Ching J, Phoon KK, Hu YG (2009) Efficient evaluation of reliability for slopes with circular slip surfaces using importance sampling. J Geotech Geoenviron Eng 135:768–777. https://doi.org/10.1061/(ASCE)gt.1943-5606.0000035

  3. Ching JY, Phoon KK, Hu YG (2010) Observations on limit equilibrium-based slope reliability problems with inclined weak seams. J Eng Mech-ASCE 136:1220–1233. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000160

    Article  Google Scholar 

  4. Cho SE (2013) First-order reliability analysis of slope considering multiple failure modes. Eng Geol 154:98–105. https://doi.org/10.1016/j.enggeo.2012.12.014

    Article  Google Scholar 

  5. Chowdhury R, Xu D (1993) Rational polynomial technique in lope-reliability analysis. Geotech Eng-ASCE 119:1910–1928. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:12(1910)

    Article  Google Scholar 

  6. Chowdhury RN, Xu DW (1995) Geotechnical system reliability of slopes. Reliab Eng Syst Saf 47:141–151. https://doi.org/10.1016/0951-8320(94)00063-T

    Article  Google Scholar 

  7. Cornell CA (1972) First-order uncertainty analysis of soil deformation and stability. In: P. L (ed) proceedings of the first international conference on application of statistics and probability to soil and structural engineering, University of Hong Kong Press, University of Hong Kong, Pok Fu lam, Hong Kong, 13–16

  8. Dawson EM, Roth WH, Drescher A (1999) Slope stability analysis by strength reduction. Geotechnique 49:835–840. https://doi.org/10.1680/geot.1999.49.6.835

    Article  Google Scholar 

  9. Der Kiureghian A, Dakessian T (1998) Multiple design points in first and second-order reliability. Struct Saf 20:37–49. https://doi.org/10.1016/s0167-4730(97)00026-x

    Article  Google Scholar 

  10. Di Matteo L, Pauselli C, Valigi D, Ercoli M, Rossi M, Guerra G, Cambi C, Ricco R, Vinti G (2018) Reliability of water content estimation by profile probe and its effect on slope stability. Landslides 15:173–180. https://doi.org/10.1007/s10346-017-0895-7

    Article  Google Scholar 

  11. Ditlevsen O (1979) Narrow reliability bounds for structural systems. J Struct Mech 7:453–472. https://doi.org/10.1080/03601217908905329

    Article  Google Scholar 

  12. Duncan JM (1996) State of the art: limit equilibrium and finite-element analysis of slopes. J Geotech Eng-ASCE 122:577–596. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(577)

  13. Duncan JM (2000) Factors of safety and reliability in geotechnical engineering. J Geotech Geoenviron Eng 126:307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)

  14. Dyson AP, Tolooiyan A (2019) Probabilistic investigation of rfem topologies for slope stability analysis. Comput Geotech 114:103129. https://doi.org/10.1016/j.compgeo.2019.103129

    Article  Google Scholar 

  15. Griffiths DV, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron Eng 130:507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507)

  16. Griffiths DV, Lane PA (1999) Slope stability analysis by finite elements. Geotechnique 49:387–403. https://doi.org/10.1680/geot.1999.49.3.387

    Article  Google Scholar 

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

    Article  Google Scholar 

  18. Hassan AM, Wolff TF (1999) Search algorithm for minimum reliability index of earth slopes. J Geotech Geoenviron Eng 125:301–308. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:4(301)

    Article  Google Scholar 

  19. Hohenbichler M, Rackwitz R (1982) First-order concepts in system reliability. Struct Saf 1:177–188. https://doi.org/10.1016/0167-4730(82)90024-8

    Article  Google Scholar 

  20. Hostettler S, Jöhr A, Montes C, D’Acunzi A (2019) Community-based landslide risk reduction: a review of a red cross soil bioengineering for resilience program in Honduras. Landslides 16:1779–1791. https://doi.org/10.1007/s10346-019-01161-3

    Article  Google Scholar 

  21. Huang HW, Wen SC, Zhang J, Chen FY, Martin JR, Wang H (2018) Reliability analysis of slope stability under seismic condition during a given exposure time. Landslides 15:2303–2313. https://doi.org/10.1007/s10346-018-1050-9

    Article  Google Scholar 

  22. Huang J, Griffiths DV, Fenton GA (2010) System reliability of slopes by rfem. Soils Found 50:343–353. https://doi.org/10.3208/sandf.50.343

    Article  Google Scholar 

  23. Itasca Consulting Group, Inc. (2019) FLAC3D —Fast Lagrangian Analysis of Continua in Three-Dimensions, ver. 7.0. Itasca, Minneapolis

  24. Ji J, Low BK (2012) Stratified response surfaces for system probabilistic evaluation of slopes. J Geotech Geoenviron Eng 138:1398–1406. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000711

    Article  Google Scholar 

  25. Kang F, Li J, Xu Q (2017) System reliability analysis of slopes using multilayer perceptron and radial basis function networks. Int J Numer Anal Methods 41:1962–1978. https://doi.org/10.1002/nag.2709

    Article  Google Scholar 

  26. Krahn J (2003) The 2001 r.M. hardy lecture: the limits of limit equilibrium analyses. Can Geotech J 40:643–660. https://doi.org/10.1139/t03-024

    Article  Google Scholar 

  27. Li DQ, Xiao 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. https://doi.org/10.1007/s10346-015-0569-2

  28. Li DQ, Wang L, Cao ZJ, Qi XH (2019) Reliability analysis of unsaturated slope stability considering swcc model selection and parameter uncertainties. Eng Geol 260:105207. https://doi.org/10.1016/j.enggeo.2019.105207

    Article  Google Scholar 

  29. Li L, Chu X (2016) Risk assessment of slope failure by representative slip surfaces and response surface function. KSCE J Civ Eng 20:1783–1792. https://doi.org/10.1007/s12205-015-2243-6

    Article  Google Scholar 

  30. Li L, Wang Y, Cao Z (2014) Probabilistic slope stability analysis by risk aggregation. Eng Geol 176:57–65. https://doi.org/10.1016/j.enggeo.2014.04.010

    Article  Google Scholar 

  31. Li L, Wang Y, Cao Z, Chu X (2013) Risk de-aggregation and system reliability analysis of slope stability using representative slip surfaces. Comput Geotech 53:95–105. https://doi.org/10.1016/j.compgeo.2013.05.004

    Article  Google Scholar 

  32. Li XY, Zhang LM, Gao L, Zhu H (2017) Simplified slope reliability analysis considering spatial soil variability. Eng Geol 216:90–97. https://doi.org/10.1016/j.enggeo.2016.11.013

    Article  Google Scholar 

  33. Liu LL, Cheng YM, Wang XM (2017) Genetic algorithm optimized Taylor kriging surrogate model for system reliability analysis of soil slopes. Landslides 14:535–546. https://doi.org/10.1007/s10346-016-0736-0

    Article  Google Scholar 

  34. Liu LL, Deng ZP, Zhang S, Cheng YM (2018) Simplified framework for system reliability analysis of slopes in spatially variable soils. Eng Geol 239:330–343. https://doi.org/10.1016/j.enggeo.2018.04.009

    Article  Google Scholar 

  35. Liu SY, Shao LT, Li HJ (2015) Slope stability analysis using the limit equilibrium method and two finite element methods. Comput Geotech 63:291–298. https://doi.org/10.1016/j.compgeo.2014.10.008

    Article  Google Scholar 

  36. Low BK, Tang WH (2007) Efficient spreadsheet algorithm for first-order reliability method. J Eng Mech-ASCE 133:1378–1387. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:12(1378)

  37. Low BK, Zhang J, Tang WH (2011) Efficient system reliability analysis illustrated for a retaining wall and a soil slope. Comput Geotech 38:196–204. https://doi.org/10.1016/j.compgeo.2010.11.005

    Article  Google Scholar 

  38. Ma J, Su A, Zhang J, Wen T, Wang Y (2019) Reliability analysis for a large and complex landslide in the three gorges reservoir area (China) based on incomplete information. Geomatics, Natural Hazards and Risk 10:181–196. https://doi.org/10.1080/19475705.2018.1518274

    Article  Google Scholar 

  39. Ma JZ, Zhang J, Huang HW, Zhang LL, Huang JS (2017) Identification of representative slip surfaces for reliability analysis of soil slopes based on shear strength reduction. Comput Geotech 85:199–206. https://doi.org/10.1016/j.compgeo.2016.12.033

    Article  Google Scholar 

  40. Metya S, Mukhopadhyay T, Adhikari S, Bhattacharya G (2017) System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines. Comput Geotech 87:212–228. https://doi.org/10.1016/j.compgeo.2017.02.017

    Article  Google Scholar 

  41. Periçaro GA, Santos SR, Ribeiro AA, Matioli LC (2015) Hlrf-bfgs optimization algorithm for structural reliability. Appl Math Model 39:2025–2035. https://doi.org/10.1016/j.apm.2014.10.024

    Article  Google Scholar 

  42. Potts DM (2003) Numerical analysis: a virtual dream or practical reality? Geotechnique 53:535–573. https://doi.org/10.1680/geot.2003.53.6.535

    Article  Google Scholar 

  43. Wu XZ (2015) Development of fragility functions for slope instability analysis. Landslides 12:165–175. https://doi.org/10.1007/s10346-014-0536-3

    Article  Google Scholar 

  44. Zeng P, Jimenez R (2014) An approximation to the reliability of series geotechnical systems using a linearization approach. Comput Geotech 62:304–309. https://doi.org/10.1016/j.compgeo.2014.08.007

    Article  Google Scholar 

  45. Zeng P, Jimenez R, Jurado-Piña R (2015) System reliability analysis of layered soil slopes using fully specified slip surfaces and genetic algorithms. Eng Geol 193:106–117. https://doi.org/10.1016/j.enggeo.2015.04.026

    Article  Google Scholar 

  46. Zhang J, Huang HW, Juang CH, Li DQ (2013) Extension of hassan and wolff method for system reliability analysis of soil slopes. Eng Geol 160:81–88. https://doi.org/10.1016/j.enggeo.2013.03.029

    Article  Google Scholar 

  47. Zhang J, Huang HW, Zhang DM (2012) Performance of subset simulation applied to a simple system reliability problem. In: Phoon KK, Beer M, Quek ST, Pang SD (eds) Proceedings of the 5th Asian-Pacific symposium on structural reliability and its applications. Research Publishing, Singapore, pp 133–138

    Google Scholar 

  48. Zhang J, Zhang LM, Tang WH (2011) New methods for system reliability analysis of soil slopes. Can Geotech J 48:1138–1148. https://doi.org/10.1139/t11-009

    Article  Google Scholar 

  49. Zhang LY, Zheng YR (2004) An extension of simplified bishop method and its application to non-circular slip surface for slope stability analysis. Rock Soil Mech 25:927–929 (in Chinese). https://doi.org/10.16285/j.rsm.2004.06.019

    Article  Google Scholar 

Download references

Funding

This work was substantially supported by Shuguang Program from Shanghai Education Development Foundation and Shanghai Municipal Education Commission (19SG19), National Key R&D Programmes of China (2018YFC0809600, 2018YFC0809601), National Natural Science Foundation of China (51538009, 41672276, 51979158), Key Innovation Team Program of MOST of China (2016RA4059), and Fundamental Research Funds for the Central Universities.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jie Zhang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Duan, X., Zhang, J., Huang, H. et al. System reliability analysis of soil slopes through constrained optimization. Landslides 18, 655–666 (2021). https://doi.org/10.1007/s10346-020-01447-x

Download citation

Keywords

  • System reliability
  • Multiple design points
  • Representative slip surfaces
  • Constrained optimization