Skip to main content
SpringerLink
Log in

Probabilistic slope stability analysis: state-of-the-art review and future prospects

  • State-of-the-art paper
  • Published:
Innovative Infrastructure Solutions Aims and scope Submit manuscript

Abstract

Conventionally adopted deterministic slope stability analyses do not consider the influence of uncertainties related to geotechnical properties as well as failure mechanism in slope stability assessments. In this regard, probabilistic study of slope stability rationally incorporates the influence of parameter uncertainty. This paper presents a comprehensive review of the currently available probabilistic methods, their evolution and their recent advancements with respect to slope stability analyses. A description about the different approaches is provided, including the approximate approaches and Monte Carlo simulation-based approaches. The efficiencies and shortcoming of each of these methods and their evolution in dealing with probabilistic analyses of slopes are elucidated. The influence of the uncertainties related to soil heterogeneity inherent spatial variability of shear strength parameters and geological uncertainty on the probabilistic slope stability analyses are discussed. The critical review brings out that incorporation of geological uncertainty and probabilistic seismic slope stability analyses needs lot of research and development. It is also noted that probabilistic stability assessment of retained or reinforced natural slopes are yet to receive proper attention from the geotechnical engineering fraternity. This review article would aid the readers in a critical and comprehensive knowledge of the existing developments in probabilistic slope stability analyses, while highlighting the pathway for future research.

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. Tang WH, Yucemen MS, Ang AHS (1976) Probability-based short term design of soil slopes. Can Geotech J 13(3):201–215. https://doi.org/10.1139/t76-024

    Article  Google Scholar 

  2. El-Ramly H, Morgernstern NR, Cruden DM (2002) Probabilistic slope stability analysis for practice. Can Geotech J 39(3):665–683. https://doi.org/10.1139/t02-034

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Cho SE (2009) Probabilistic assessment of slope stability that considers the spatial variability of soil properties. J Geotech Geoenviron 136(7):975–984. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000309

    Article  Google Scholar 

  5. Javankhoshdel S, Bathurst RJ (2014) Simplified probabilistic slope stability design charts for cohesive and cohesive-frictional (c -ϕ) soils. Can Geotech J 51(9):1033–1045. https://doi.org/10.1139/cgj-2013-0385

    Article  Google Scholar 

  6. Chakraborty R, Dey A (2019) Effect of toe cutting on hillslope stability. In: IV A, Maji V (eds) Geotechnical applications, vol 13. Lecture notes in civil engineering, Springer, Singapore, p 191–198

  7. Griffiths D, Lane P (1999) Slope stability analysis by finite elements. Geotechnique 49(3):387–403. https://doi.org/10.1680/geot.1999.49.3.387

    Article  Google Scholar 

  8. Sjöberg J (1999) Analysis of the Aznalcollar pit slope failures—a case study. In Detournay and Hart (eds) FLAC and numerical modeling in geomechanics, p 63–70. Balkema, Rotterdam

  9. Rahman NA, Tabassum N, Islam MR (2021) Different aspects of slope failures considering large deformation: application of smoothed particle hydrodynamics (SPH). Inn Infra Sols 6(37):1–15. https://doi.org/10.1007/s41062-020-00405-9

    Article  Google Scholar 

  10. Lumb P (1966) The variability of natural soils. Can Geotech J 3(2):74–97. https://doi.org/10.1139/t66-009

    Article  Google Scholar 

  11. Lumb P (1970) Safety factors and the probability distribution of soil strength. Can Geotech J 7(3):225–242. https://doi.org/10.1139/t70-032

    Article  Google Scholar 

  12. Wu TH, Kraft LM (1970) Safety analysis of slopes. J Soil Mech Found Div ASCE 96(3):609–630

    Article  Google Scholar 

  13. Matsuo M, Kuroda K (1974) Probabilistic approach to design of embankments. Soils Found 14(2):1–17. https://doi.org/10.3208/sandf1972.14.2_1

    Article  Google Scholar 

  14. Alonso EE (1977) Risk analysis of slopes and its application to slopes in Canadian sensitive clays. Géotechnique 26(3):453–472. https://doi.org/10.1680/geot.1976.26.3.453

    Article  Google Scholar 

  15. Whitman RV (1984) Evaluating calculated risk in geotechnical engineering. J Geotech Eng ASCE 110(2):143–188. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:2(143)

    Article  Google Scholar 

  16. Mostyn GR, Soo S (1992) The effect of autocorrelation on the probability of failure of slopes. In: Proceedings of 6th Australia, New Zealand conference on geomechanics: geotechnical risk, p 542–546

  17. DeGroot DJ (1996) Analysing spatial variability of in situ soil properties. In: Shackelford CD et al (eds) GSP 58, uncertainty in the geologic environment: from theory to practice. ASCE, New York, pp 210–238

    Google Scholar 

  18. Elkateb T, Chalaturnyk R, Robertson PK (2003) An overview of soil heterogeneity: quantification and implications on geotechnical field problems. Can Geotech J 40(1):1–15. https://doi.org/10.1139/t02-090

    Article  Google Scholar 

  19. Li KS, Lumb P (1987) Probabilistic design of slopes. Can Geotech J 24(4):520–535. https://doi.org/10.1139/t87-068

    Article  Google Scholar 

  20. Chowdhury RN, Sidi I, Tang WH (1988) Discussion: reliability model on progressive slope failure. Géotechnique 38(4):641–646. https://doi.org/10.1680/geot.1988.38.4.641

    Article  Google Scholar 

  21. Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope stability analysis. J Geotech Eng ASCE 120(12):2180–2207. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2180)

    Article  Google Scholar 

  22. Lacasse S, Nadim F (1996) Uncertainties in characterizing soil properties. In: Shackelford CD et al (eds) GSP 58, uncertainty in the geologic environment: from theory to practice. New York, ASCE, pp 49–75

    Google Scholar 

  23. Paice GM (1997) Finite element analysis of stochastic soils. PhD thesis, University of Manchester

  24. Griffiths DV, Fenton GA (2000) Influence of soil strength spatial variability on the stability of an undrained clay slope by finite elements. In: Griffiths DV et al (eds) GSP 101, Proceedings of GeoDenver symposium, slope stability 2000, ASCE, p 184–193

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

    Article  Google Scholar 

  26. Whitman RV (2000) Organizing and evaluating uncertainty in geotechnical engineering. J Geotech Geoenviron ASCE 126(7):583–593. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:7(583)

    Article  Google Scholar 

  27. Huang J, Fenton G, Griffiths DV, Li D, Zhou C (2017) On the efficient estimation of small failure probability in slopes. Landslides 14(2):491–498. https://doi.org/10.1007/s10346-016-0726-2

    Article  Google Scholar 

  28. Chen F, Zhang R, Wang Y, Liu H, Böhlke T, Zhang W (2020) Probabilistic stability analyses of slope reinforced with piles in spatially variable soils. Int J Approx Reason 122:66–79

    Article  Google Scholar 

  29. Lee SW, Ching J (2020) Simplified risk assessment for a spatially variable undrained long slope. Comput Geotech 117:103228. https://doi.org/10.1016/j.compgeo.2019.103228

    Article  Google Scholar 

  30. Hassan AM, Wolff TF (1999) Search algorithm for minimum reliability index of earth slopes. J Geotech Geoenviron ASCE 125(04):301–308. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:2(194.2)

    Article  Google Scholar 

  31. Mbarka S, Baroth J, Ltifi M, Hassis H, Darve F (2010) Reliability analyses of slope stability. Eur J Environ Civ Eng 14(10):1227–1257. https://doi.org/10.1080/19648189.2010.9693293

    Article  Google Scholar 

  32. Griffiths DV, Fenton GA, Denavit MD (2007) Traditional and advanced probabilistic slope stability analysis. In: Phoon KK et al (eds) Proceedings of GeoDenver 2007 symposium, ASCE, Virginia, p 1–10. https://doi.org/10.1061/40914(233)19

  33. Hicks MA, Nuttall JD, Chen J (2014) Influence of heterogeneity on 3D slope reliability and failure consequence. Comput Geotech 61:198–208. https://doi.org/10.1016/j.compgeo.2014.05.004

    Article  Google Scholar 

  34. Kitch WA (1994) Deterministic and probabilistic based analyses of reinforced soil slopes. PhD thesis, University of Texas at Austin.

  35. Tun YW, Pedroso DM, Scheuermann A, Williams DJ (2016) Probabilistic reliability analysis of multiple slopes with genetic algorithms. Comput Geotech 77:68–76. https://doi.org/10.1016/j.compgeo.2016.04.006

    Article  Google Scholar 

  36. Bhattacharya G, Jana D, Ojha S, Chakraborty S (2003) Direct search for minimum reliability index of earth slopes. Comput Geotech 30(6):455–462. https://doi.org/10.1016/S0266-352X(03)00059-4

    Article  Google Scholar 

  37. Baecher GB, Christian JT (2003) Reliability and statistics in geotechnical engineering. Wiley, Hoboken

    Google Scholar 

  38. Cui L, Sheng D (2005) Genetic algorithms in probabilistic finite element analysis of geotechnical problems. Comput Geotech 32(8):555–563. https://doi.org/10.1016/j.compgeo.2005.11.005

    Article  Google Scholar 

  39. 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 

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

    Article  Google Scholar 

  41. Yang X (2014) Nature-inspired optimization algorithms. Elsevier, Amsterdam

    Google Scholar 

  42. Phoon KK (2008) Reliability-based design in geotechnical engineering. Computations and applications. CRC Press, London. https://doi.org/10.1201/9781482265811

    Book  Google Scholar 

  43. https://www.bentley.com/en/products/brands/plaxis

  44. Sarma CP, Murali Krishna A, Dey A (2014) Probabilistic slope stability analysis considering spatial variability of soil properties: influence of correlation length. In: Oka F, Murakami A, Uzuoka R, Kimoto S (eds) Proceedings 14th IACMAG Kyoto, Japan, p 1125–1130

  45. DeWolfe GF, Griffiths DV, Huang J (2010) Probabilistic and deterministic slope stability analysis by random finite elements GeoTrends: the progress of geological and geotechnical engineering in Colorado at the Cusp of a New Decade. GPP 6. https://doi.org/10.1061/41144(391)9

  46. https://www.finesoftware.eu/geotechnical-software/

  47. U.S. Army Corps of Engineers (1997) Engineering and design: introduction to probability and reliability methods for use in geotechnical engineering. Department of the Army, Washington, D.C. Engineer Technical Letter 1110-2-547.

  48. Wang Y, Cao ZJ, Au SK (2011) Practical reliability analysis of slope stability by advanced Monte Carlo Simulations in spreadsheet. Can Geotech J 48(1):162–172. https://doi.org/10.1139/T10-044

    Article  Google Scholar 

  49. Roberts C, Casella G (1999) Monte Carlo statistical methods. Springer, Berlin

    Book  Google Scholar 

  50. Wang Y, Cao ZJ, Au SK (2010) Efficient Monte Carlo Simulation of parameter sensitivity in probabilistic slope stability analysis. Comput Geotech 37(7–8):1015–1022. https://doi.org/10.1016/j.compgeo.2010.08.010

    Article  Google Scholar 

  51. Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Eng Mech 16(4):263–277. https://doi.org/10.1016/S0266-8920(01)00019-4

    Article  Google Scholar 

  52. Au SK, Beck JL (2003) Subset Simulation and its application to probabilistic seismic performance assessment. J Eng Mech 129(8):1–17. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(901)

    Article  Google Scholar 

  53. Wang Y (2012) Uncertain parameter sensitivity in Monte Carlo simulation by sample reassembling. Comput Geotech 46:39–47. https://doi.org/10.1016/j.compgeo.2012.05.014

    Article  Google Scholar 

  54. Li L, Wang Y, Cao ZJ, 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 

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

    Article  Google Scholar 

  56. Dyson AP, Tolooiyan A (2019) Prediction and classification for finite element slope stability analysis by random field comparison. Comput Geotech 109:117–129. https://doi.org/10.1016/j.compgeo.2019.01.026

    Article  Google Scholar 

  57. Fang HW, Chen YF, Hou ZK, Xu GW, Wu JX (2020) Probabilistic analysis of a cohesion-frictional slope using the slip-line field theory in a Monte-Carlo framework. Comput Geotech 120:103398. https://doi.org/10.1016/j.compgeo.2019.103398

    Article  Google Scholar 

  58. Morgenstern NR (2000) Performance in geotechnical practice. HKIE Trans 7(2):2–15. https://doi.org/10.1080/1023697X.2000.10667819

    Article  Google Scholar 

  59. Ji J, Liao HJ, Low BK (2012) Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations. Comput Geotech 40:135–146. https://doi.org/10.1016/j.compgeo.2011.11.002

    Article  Google Scholar 

  60. Tabarroki M, Ahmad F, Banaki R, Jha SK, Ching J (2013) Determining the factors of safety of spatially variable slopes modeled by random fields. J Geotech Geoenviron 139(12):2082–2095. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000955

    Article  Google Scholar 

  61. Javankhoshdel S, Luo N, Bathurst RJ (2017) Probabilistic analysis of simple slopes with cohesive soil strength using RLEM and RFEM. Georisk Assess Manag Risk Eng Syst Geohazards 11(3):231–246. https://doi.org/10.1080/17499518.2016.1235712

    Article  Google Scholar 

  62. Jiang SH, Li DQ, Cao ZJ, Zhou CB, Phoon KK (2014) Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo Simulation. J Geotech Geoenviron ASCE 141(2):1–13. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001227

    Article  Google Scholar 

  63. Le TMH (2014) Reliability of heterogeneous slopes with cross-correlated shear strength parameters. Georisk Assess Manag Risk Eng Syst Geohazards 8(4):250–257. https://doi.org/10.1080/17499518.2014.966117

    Article  Google Scholar 

  64. Li DQ, Jiang SH, Cao ZJ, Zhou W, Zhou CB, Zhang LM (2015) A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties. Eng Geol 187:60–72. https://doi.org/10.1016/j.enggeo.2014.12.003

    Article  Google Scholar 

  65. Jamshidi CR, Alaie R (2015) Effects of anisotropy in correlation structure on the stability of an undrained clay slope. Georisk Assessment Manag Risk Eng Syst Geohazards 9(2):109–123. https://doi.org/10.1080/17499518.2015.1037844

    Article  Google Scholar 

  66. Allahverdizadeh P, Griffiths DV, Fenton GA (2015) The Random Finite Element Method (RFEM) in probabilistic slope stability analysis with consideration of spatial variability of soil properties. In: Proceedings of International foundation congress and equipment expo. p1946–1955. https://doi.org/10.1061/9780784479087.178

  67. Hicks M, Samy K (2002) Reliability-based characteristic values: a stochastic approach To Eurocode 7. Ground Eng 35(12):30–34

    Google Scholar 

  68. Hicks MA, Chen J, Spencer WA (2008) Influence of spatial variability on 3D slope failures. In: Proceedings 6th international conference on computer simulation in risk analysis and hazard mitigation, Cephalonia, Greece, p 335–342

  69. Hicks MA, Spencer WA (2008) 3D finite element modelling of slope reliability. In: 8th WCCM and 5th ECCOMAS, Venice, Italy

  70. Hicks MA, Spencer WA (2010) Influence of heterogeneity on the reliability and failure of a long 3D slope. Comput Geotech 37(7–8):948–955. https://doi.org/10.1016/j.compgeo.2010.08.001

    Article  Google Scholar 

  71. Low BK, Lacasse S, Nadim F (2007) Slope reliability analysis accounting for spatial variation. Georisk Assessment Manag Risk Eng Syst Geohazards 1(4):177–189. https://doi.org/10.1080/17499510701772089

    Article  Google Scholar 

  72. Srivastava A, Babu GLS (2009) Effect of soil variability on the bearing capacity of clay and in slope stability problems. Eng Geol 108(1–2):142–152. https://doi.org/10.1016/j.enggeo.2009.06.023

    Article  Google Scholar 

  73. Griffiths DV, Huang J, Fenton GA (2011) Probabilistic infinite slope analysis. Comput Geotech 38(4):577–584. https://doi.org/10.1016/j.compgeo.2011.03.006

    Article  Google Scholar 

  74. Low BK, Tang WH (1997) Reliability analysis of reinforced embankments on soft ground. Can Geotech J 34(5):672–685. https://doi.org/10.1139/t97-032

    Article  Google Scholar 

  75. Zhu H, Zhang LM, Zhang LL, Zhou CB (2013) Two-dimensional probabilistic infiltration analysis with a spatially varying permeability function. Comput Geotech 48:249–259. https://doi.org/10.1016/j.compgeo.2012.07.010

    Article  Google Scholar 

  76. Fenton GA, Griffiths DV (2008) Risk assessment in geotechnical engineering. Wiley, Hoboken

    Book  Google Scholar 

  77. Papoulis A (1991) Probability, random variables, and stochastic processes, 3rd edn. McGraw-Hill, New York

    Google Scholar 

  78. Cao Z, Wang Y (2014) Bayesian model comparison and selection of spatial correlation functions for soil parameters. Struct Saf 49:10–17. https://doi.org/10.1016/j.strusafe.2013.06.003

    Article  Google Scholar 

  79. Burgess J, Fenton GA, Griffiths DV (2019) Probabilistic seismic slope stability analysis and design. Can Geotech J. https://doi.org/10.1139/cgj-2017-0544

    Article  Google Scholar 

  80. Griffiths DV, Fenton GA (2007) Probabilistic methods in geotechnical engineering, vol 491. Springer, Berlin

    Book  Google Scholar 

  81. Phoon KK, Kulhawy FH, Grigoriu MD (1995) Reliability-based design of foundations for transmission line structures. Report TR-105000, Electric Power Research Institute, Palo Alto.

  82. Wang Y, Zhao T, Cao Z (2015) Site-specific probability distribution of geotechnical properties. Comput Geotech 70:159–168. https://doi.org/10.1016/j.compgeo.2015.08.002

    Article  Google Scholar 

  83. Wang Y, Cao Z, Li D (2016) Bayesian perspective on geotechnical variability and site characterization. Engg Geol 203:117–125. https://doi.org/10.1016/j.enggeo.2015.08.017

    Article  Google Scholar 

  84. Vanmarcke E (1977) Probabilistic modeling of soil profiles. J Geotech Eng Div 103(11):1227–1246

    Article  Google Scholar 

  85. Christakos G (1992) Random field models in earth sciences. Elsevier, Amsterdam. https://doi.org/10.1016/C2009-0-22238-0

    Book  Google Scholar 

  86. Chakraborty R, Dey A (2019) Stochastic modeling of the spatial variability of soil. In: Advances in numerical methods in geotechnical engineering, Chapter 11, Springer, Cham, p 144–155. https://doi.org/10.1007/978-3-030-01926-6_11

  87. Babu GD, Mukesh M (2004) Effect of soil variability on reliability of soil slopes. Geotechnique 54(5):335–337. https://doi.org/10.1680/geot.2004.54.5.335

    Article  Google Scholar 

  88. Schultze E (1975) Some aspects concerning the application of statistics and probability to foundation structures. In: Proceedings of 2nd international conference on the application of statistics and probability in soil and structural engineering, Aachen, 4. p 457–494

  89. Tobutt DC (1982) Monte Carlo simulation methods for slope stability. Comput Geosci 8:199–208. https://doi.org/10.1016/0098-3004(82)90021-8

    Article  Google Scholar 

  90. Nguyen VU, Chowdhury RN (1984) Probabilistic study of spoil pile stability in strip coal mines-two techniques compared. Int J Rock Mech Min Sci Geomech Abst 21:303–312. https://doi.org/10.1016/0148-9062(84)90363-2

    Article  Google Scholar 

  91. Ji H, Griffiths DV, Fenton GA (2010) System reliability of slopes by RFEM. Soils Found 50(3):343–353. https://doi.org/10.3208/sandf.50.343

    Article  Google Scholar 

  92. Nguyen VU, Chowdhury RN (1985) Simulation for risk analysis with correlated variables. Géotechnique 35:47–58. https://doi.org/10.1680/geot.1985.35.1.47

    Article  Google Scholar 

  93. Tamimi S, Amadei B, Frangopol DM (1989) Monte Carlo simulation of rock slope reliability. Comput Struct 33(6):1495–1505. https://doi.org/10.1016/0045-7949(89)90489-6

    Article  Google Scholar 

  94. Fenton GA, Griffiths DV (2003) Bearing-capacity prediction of spatially random c-φ soils. Can Geotech J 40(1):54–65. https://doi.org/10.1139/t02-086

    Article  Google Scholar 

  95. Ferson S, Hajagos JG (2006) Varying correlation coefficients can underestimate uncertainty in probabilistic models. Reliab Eng Syst Saf 91:1461–1467. https://doi.org/10.1016/j.ress.2005.11.043

    Article  Google Scholar 

  96. Youssef AM, Soubra AH, Low BK (2008) Reliability-based analysis and design of strip footings against bearing capacity failure. J Geotech Geoenviron 134(7):917–928. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:7(917)

    Article  Google Scholar 

  97. Griffiths DV, Huang J, Fenton GA (2009) Influence of spatial variability on slope reliability using 2-D random fields. J Geotech Geoenviron ASCE 135(10):1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099

    Article  Google Scholar 

  98. Cho SE, Park HC (2009) Effect of spatial variability of cross-correlated soil properties on bearing capacity of strip footing. Int J Numer Anal Methods Geomech 34:1–26. https://doi.org/10.1002/nag.791

    Article  Google Scholar 

  99. Lü Q, Low BK (2011) Probabilistic analysis of underground rock excavations using response surface method and SORM. Comput Geotech 38:1008–1021. https://doi.org/10.1016/j.compgeo.2011.07.003

    Article  Google Scholar 

  100. Yucemen MS, Tang WH, Ang AHS (1973) A probabilistic study of safety and design of earth slopes. Civil Engineering Studies, Structural Research Series, 402, University of Illinois, Urbana, IL.

  101. Wolff TF (1985) Analysis and design of embankment dam slopes: a probabilistic approach. PhD. Thesis, Purdue University, Lafayette, IN.

  102. Cherubini C (1997) Data and considerations on the variability of geotechnical properties of soils. In: Proceedings of the international conference on safety and reliability (ESREL97), vol 2. Lisbon, p 1583–1591

  103. Forrest WS, Orr TL (2010) Reliability of shallow foundations designed to Eurocode 7. Georisk Assessment Manag Risk Eng Syst Geohazards 4(4):186–207. https://doi.org/10.1080/17499511003646484

    Article  Google Scholar 

  104. Hata Y, Ichii K, Tokida K (2012) A probabilistic evaluation of the size of earthquake induced slope failure for an embankment. Georisk Assessment Manag Risk Eng Syst Geohazards 6(2):73–88. https://doi.org/10.1080/17499518.2011.604583

    Article  Google Scholar 

  105. Javankhoshdel S, Bathurst RJ (2015) Influence of cross correlation between soil parameters on probability of failure of simple cohesive and c–ϕ slopes. Can Geotech J 53(5):839–853. https://doi.org/10.1139/cgj-2015-0109

    Article  Google Scholar 

  106. Fenton GA, Vanmarcke EH (1990) Simulation of random fields via local average subdivision. J Eng Mech ASCE 116(8):1733–1749. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1733)

    Article  Google Scholar 

  107. Chok YH (2009) Modelling the effects of soil variability and vegetation on the stability of natural slopes. PhD thesis, University of Adelaide, Adelaide, Australia

  108. Fenton GA, Griffiths DV (2007) Random field generation and the local average subdivision method. In: Probabilistic methods in geotechnical engineering, vol 491. p 201–223. Springer, Vienna. https://doi.org/10.1007/978-3-211-73366-0_9

  109. Vanmarcke E (1983) Random fields, analysis and synthesis. MIT Press, Cambridge

    Google Scholar 

  110. Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36(4):612–624. https://doi.org/10.1139/t99-038

    Article  Google Scholar 

  111. Kulatilake PHSW, Um JG (2003) Spatial variation of cone tip resistance for the clay site at Texas A and M University. Geotech Geolog Eng 21(2):149–165. https://doi.org/10.1023/A:1023526614301

    Article  Google Scholar 

  112. Li DQ, Qi XH, Phoon KK, Zhang LM, Zhou CB (2014) Effect of spatially variable shear strength parameters with linearly increasing mean trend on reliability of infinite slopes. Struct Saf 49:45–55. https://doi.org/10.1016/j.strusafe.2013.08.005

    Article  Google Scholar 

  113. Griffiths DV, Huang J, Fenton GA (2015) Probabilistic slope stability analysis using non-stationary random fields. In: 5th International symposium on geotechnical safety and risk, Rotterdam, p 690–695

  114. Huang L, Cheng YM, Li L, Yu S (2021) Reliability and failure mechanism of a slope with non-stationarity and rotated transverse anisotropy in undrained soil strength. Comput Geotech 132:103970. https://doi.org/10.1016/j.compgeo.2020.103970

    Article  Google Scholar 

  115. Wang Y, Zhao T, Phoon KK (2018) Direct simulation of random field samples from sparsely measured geotechnical data with consideration of uncertainty in interpretation. Can Geotech J 55(6):862–880. https://doi.org/10.1139/cgj-2017-0254

    Article  Google Scholar 

  116. Fenton GA, Griffiths DV (2004) Reply to discussion by R. Popescu on, Bearing capacity prediction of spatially random c-φ soils. Can Geotech J 41:368–369. https://doi.org/10.1139/t03-080

    Article  Google Scholar 

  117. Pieczyńska-Kozłowska J, Puła W, Griffiths DV, Fenton GA (2015) Influence of embedment, self-weight and anisotropy on bearing capacity reliability using the random finite element method. Comput Geotech 67:229–238. https://doi.org/10.1016/j.compgeo.2015.02.013

    Article  Google Scholar 

  118. Puła W, Griffiths DV (2021) Transformations of spatial correlation lengths in random fields. Comput Geotech. https://doi.org/10.1016/j.compgeo.2021.104151

    Article  Google Scholar 

  119. Chakraborty R, Dey A (2018) A comparison of 1D and 2D spatial variability in probabilistic slope stability analysis. In: International symposium of geotechnics for transportation infrastructure, Delhi, India

  120. Li DQ, Xiao T, Cao ZJ, Zhou CB (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

    Article  Google Scholar 

  121. Chwała M (2021) Upper-bound approach based on failure mechanisms in slope stability analysis of spatially variable c-φ soils. Comput Geotech 135:104170. https://doi.org/10.1016/j.compgeo.2021.104170

    Article  Google Scholar 

  122. Evans SG (1982) Landslides and surficial deposits in urban areas of British Columbia: a review. Can Geotech J 19(3):269–288. https://doi.org/10.1139/t82-034

    Article  Google Scholar 

  123. Tang WH, Gilbert RB (1989) Average property in random two-state medium. J Eng Mech 115(1):131–144. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:1(131)

    Article  Google Scholar 

  124. Halim IS (1991) Reliability of geotechnical systems considering geological anomaly. University of Illinois, Urbana-Champaign

    Google Scholar 

  125. Hansen L, Eilertsen R, Solberg IL, Rokoengen K (2007) Stratigraphic evaluation of a Holocene clay-slide in Northern Norway. Landslides 4(3):233–244. https://doi.org/10.1007/s10346-006-0078-4

    Article  Google Scholar 

  126. De Marsily G, Delay F, Gonçalvès J, Renard P, Teles V, Violette S (2005) Dealing with spatial heterogeneity. Hydrogeol J 13(1):161–183

    Article  Google Scholar 

  127. Liao T, Mayne PW (2007) Stratigraphic delineation by three-dimensional clustering of piezocone data. Georisk Assessment Manag Risk Eng Syst Geohazards 1(2):102–119. https://doi.org/10.1080/17499510701345175

    Article  Google Scholar 

  128. Cao Z, Wang Y (2013) Bayesian approach for probabilistic site characterization using cone penetration tests. J Geotech Geoenviron 139(2):267–276

    Article  Google Scholar 

  129. Ching J, Wang JS, Juang CH, Ku CS (2015) Cone penetration test (CPT)-based stratigraphic profiling using the wavelet transform modulus maxima method. Can Geotech J 52(12):1993–2007

    Article  Google Scholar 

  130. Wang X, Wang H, Liang RY, Zhu H, Di H (2018) A hidden Markov random field model based approach for probabilistic site characterization using multiple cone penetration test data. Struct Saf 70:128–138. https://doi.org/10.1016/j.strusafe.2017.10.011

    Article  Google Scholar 

  131. Patel MD, McMechan GA (2003) Building 2-D stratigraphic and structure models from well log data and control horizons. Comput Geosci 29(5):557–567. https://doi.org/10.1016/S0098-3004(03)00039-6

    Article  Google Scholar 

  132. Li XY, Zhang LM, Li JH (2015) Using conditioned random field to characterize the variability of geologic profiles. J Geotech Geoenviron 142(4):04015096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001428

    Article  Google Scholar 

  133. Chen G, Zhu J, Qiang M, Gong W (2018) Three-dimensional site characterization with borehole data—a case study of Suzhou area. Eng Geol 234(21):65–82

    Article  Google Scholar 

  134. Schloeder CA, Zimmerman NE, Jacobs MJ (2001) Comparison of methods for interpolating soil properties using limited data. Soil Sci Soc Am J 65(2):470–479. https://doi.org/10.2136/sssaj2001.652470x

    Article  Google Scholar 

  135. Li JH, Cassidy MJ, Huang JS, Zhang LM, Kelly R (2016) Probabilistic identification of soil stratification. Géotechnique 66(1):16–26. https://doi.org/10.1680/jgeot.14.P.242

    Article  Google Scholar 

  136. Bartier PM, Keller CP (1996) Multivariate interpolation to incorporate thematic surface data using inverse distance weighting (IDW). Comput Geosci 22(7):795–799

    Article  Google Scholar 

  137. Wang Y, Zhao T (2016) Interpretation of soil property profile from limited measurement data: a compressive sampling perspective. Can Geotech J 53(9):1547–1559. https://doi.org/10.1139/cgj-2015-0545

    Article  Google Scholar 

  138. Elfeki A, Dekking M (2001) A Markov chain model for subsurface characterization: theory and applications. Math Geol 33(5):569–589. https://doi.org/10.1023/A:1011044812133

    Article  Google Scholar 

  139. Hu QF, Huang HW (2007) Risk analysis of soil transition in tunnel works. In: Proceedings of the 33rd ITA-AITES world tunnel congress—underground space the 4th dimension of metropolises, p 209–215

  140. Qi XH, Li DQ, Phoon KK, Cao ZJ, Tang XS (2016) Simulation of geologic uncertainty using coupled Markov chain. Eng Geol 207:129–140. https://doi.org/10.1016/j.enggeo.2016.04.017

    Article  Google Scholar 

  141. Norberg T, Rosén L, Baran A, Baran S (2002) On modelling discrete geological structures as Markov random fields. Math Geol 34:63–77. https://doi.org/10.1023/A:1014079411253

    Article  Google Scholar 

  142. Li Z, Wang X, Wang H, Liang RY (2016) Quantifying stratigraphic uncertainties by stochastic simulation techniques based on Markov random field. Eng Geol 201:106–122. https://doi.org/10.1016/j.enggeo.2015.12.017

    Article  Google Scholar 

  143. Wang X, Li Z, Wang H, Rong Q, Liang RY (2016) Probabilistic analysis of shield-driven tunnel in multiple strata considering stratigraphic uncertainty. Struct Saf 62:88–100. https://doi.org/10.1016/j.strusafe.2016.06.007

    Article  Google Scholar 

  144. Wang H, Wellmann JF, Li Z, Wang X, Liang RY (2017) A segmentation approach for stochastic geological modeling using hidden Markov random fields. Math Geosci 49(2):145–177. https://doi.org/10.1007/s11004-016-9663-9

    Article  Google Scholar 

  145. Ching J, Phoon KK, Wu SH (2016) Impact of statistical uncertainty on geotechnical reliability estimation. J Eng Mech 142(6):04016027

    Article  Google Scholar 

  146. Papaioannou I, Straub D (2017) Learning soil parameters and updating geotechnical reliability estimates under spatial variability—theory and application to shallow foundations. Georisk Assessment Manag Risk Eng Syst Geohazards 11(1):116–128. https://doi.org/10.1080/17499518.2016.1250280

    Article  Google Scholar 

  147. Feng X, Jimenez R (2014) Bayesian prediction of elastic modulus of intact rocks using their uniaxial compressive strength. Eng Geol 173:32–40. https://doi.org/10.1016/j.enggeo.2014.02.005

    Article  Google Scholar 

  148. Tian M, Li DQ, Cao ZJ, Phoon KK, Wang Y (2016) Bayesian identification of random field model using indirect test data. Eng Geol 210:197–211. https://doi.org/10.1016/j.enggeo.2016.05.013

    Article  Google Scholar 

  149. Xiao T, Li DQ, Cao ZJ, Tang XS (2017) Full probabilistic design of slopes in spatially variable soils using simplified reliability analysis method. Georisk Assessment Manag Risk Eng Syst Geohazards 11(1):146–159. https://doi.org/10.1080/17499518.2016.1250279

    Article  Google Scholar 

  150. Gong W, Luo Z, Juang CH, Huang H, Zhang J, Wang L (2014) Optimization of site exploration program for improved prediction of tunneling-induced ground settlement in clays. Comput Geotech 56:69–79. https://doi.org/10.1016/j.compgeo.2013.10.008

    Article  Google Scholar 

  151. Gong W, Juang CH, Martin JR II, Tang H, Wang Q, Huang H (2018) Probabilistic analysis of tunnel longitudinal performance based upon conditional random field simulation of soil properties. Tunn Undergr Space Technol 73:1–14. https://doi.org/10.1016/j.tust.2017.11.026

    Article  Google Scholar 

  152. Wang H, Wang X, Wellmann JF, Liang RY (2018) Bayesian stochastic soil modelling framework using Gaussian Markov random fields. ASCE-ASME J Risk Uncert Eng Syst Part A 4(2):04018014. https://doi.org/10.1061/AJRUA6.0000965

    Article  Google Scholar 

  153. Li DQ, Qi XH, Cao ZJ, Tang XS, Phoon KK, Zhou CB (2016) Evaluating slope stability uncertainty using coupled Markov chain. Comput Geotech 73:72–82. https://doi.org/10.1016/j.compgeo.2015.11.021

    Article  Google Scholar 

  154. Crisp MP, Jaksa M, Kuo YL, Fenton GA, Griffiths DV (2019) A method for generating virtual soil profiles with complex, multi-layer stratigraphy. Georisk Assessment Manag Risk Eng Syst Geohazards 13(2):154–163

    Article  Google Scholar 

  155. Crisp MP, Jaksa M, Kuo YL, Fenton GA, Griffiths DV (2020) Characterising site investigation performance in a two layer soil profile. Can J Civ Eng 48(2):115–123

    Article  Google Scholar 

  156. Gong W, Zhao C, Juang CH, Tang H, Wang H, Hu X (2020) Stratigraphic uncertainty modelling with random field approach. Comput Geotech 125:103681. https://doi.org/10.1016/j.compgeo.2020.103681

    Article  Google Scholar 

  157. Chakraborty R, Dey A (2016) Numerical investigation of slope instability induced by hydraulic and seismic actions. In: North-east students geo-congress: NESGC 2016, Agartala, India, p 237–244

  158. Newmark NM (1965) Effects of earthquakes on dams and embankments. Géotechnique 15(2):139–160. https://doi.org/10.1680/geot.1965.15.2.139

    Article  Google Scholar 

  159. Chakraborty R, Dey A (2021) Influence of toe cutting on seismic response of a typical hill slope in north east India. In: Sitharam TG, Jakka R, Govindaraju L (eds) Local site effects and ground failures. Lecture notes in civil engineering. https://doi.org/10.1007/978-981-15-9984-2_15

  160. Yamsani SK, Dey A, Sreedeep S, Rakesh RR (2019) Vulnerability interface diagram for translational stability analysis of multilayered cover system. Int J Geomech ASCE. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001536

    Article  Google Scholar 

  161. Tsompanakis Y, Lagaros ND, Psarropoulos PN, Georgopoulos EC (2010) Probabilistic seismic slope stability assessment of geostructures. Struct Infrastruct Eng 6(1–2):179–191. https://doi.org/10.1080/15732470802664001

    Article  Google Scholar 

  162. Xiao J, Gong W, Martin JR, Shen M, Luo Z (2016) Probabilistic seismic stability analysis of slope at a given site in a specified exposure time. Eng Geol 212:53–62. https://doi.org/10.1016/j.enggeo.2016.08.001

    Article  Google Scholar 

  163. Malekpoor PS, Chenari RJ, Javankhoshdel S (2020) Discussion of “Probabilistic seismic slope stability analysis and design.” Can Geotech J 57(7):1103–1108. https://doi.org/10.1139/cgj-2019-0386

    Article  Google Scholar 

  164. Johari A, Mousavi S, Nejad AH (2015) A seismic slope stability probabilistic model based on Bishop’s method using analytical approach. Sci Iran Transac Civ Eng 22(3):728

    Google Scholar 

  165. Schneider HR, Holtz RD (1986) Design of slopes reinforced with geotextiles and geogrids. Geotext Geomembr 3(1):29–51. https://doi.org/10.1016/0266-1144(86)90013-0

    Article  Google Scholar 

  166. Leshchinsky D, Boedeker RH (1989) Geosynthetic reinforced soil structures. J Geotech Eng ASCE 115(10):1459–1478. https://doi.org/10.1061/(ASCE)0733-9410(1989)115:10(1459)

    Article  Google Scholar 

  167. Kitch WA, Gilbert RB, Wright SG (2012) Probabilistic Assessment of commercial design guides for steep reinforced slopes: implications for design. In: GeoRisk 2011: geotechnical risk assessment and management, ASCE, Atlanta, 103, 1–22. https://doi.org/10.1061/41183(418)115

  168. Cherubini C (2000) Probabilistic approach to the design of anchored sheet pile walls. Comput Geotech 26(3–4):309–330. https://doi.org/10.1016/S0266-352X(99)00044-0

    Article  Google Scholar 

  169. Li L, Liang RY (2014) Reliability-based design for slopes reinforced with a row of drilled shafts. Int J Numer Anal Methods Geomech 38(2):202–220. https://doi.org/10.1002/nag.2220

    Article  Google Scholar 

  170. Zhang J, Wang H, Huang HW, Chen LH (2017) System reliability analysis of soil slopes stabilized with piles. Eng Geol 229:45–52. https://doi.org/10.1016/j.enggeo.2017.09.009

    Article  Google Scholar 

  171. Luo N, Bathurst RJ, Javankhoshdel S (2016) Probabilistic stability analysis of simple reinforced slopes by finite element method. Comput Geotech 77:45–55. https://doi.org/10.1016/j.compgeo.2016.04.001

    Article  Google Scholar 

  172. Luo N, Bathurst RJ (2018) Probabilistic analysis of reinforced slopes using RFEM and considering spatial variability of frictional soil properties due to compaction. Georisk Assessment Manag Risk Eng Syst Geohazards 12(2):87–108. https://doi.org/10.1080/17499518.2017.1362443

    Article  Google Scholar 

  173. Luo N, Bathurst RJ (2018) Deterministic and random FEM analysis of full-scale unreinforced and reinforced embankments. Geosynth Int 25(2):164–179. https://doi.org/10.1680/jgein.17.00040

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers whose critical comment and suggestions have led to betterment of the article in terms of quality and clarity.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Meghalaya, Shillong, India

    Rubi Chakraborty

  2. Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, India

    Arindam Dey

Authors
  1. Rubi Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arindam Dey
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arindam Dey.

Ethics declarations

Conflict of interest

No potential conflict of interest was reported by the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chakraborty, R., Dey, A. Probabilistic slope stability analysis: state-of-the-art review and future prospects. Innov. Infrastruct. Solut. 7, 177 (2022). https://doi.org/10.1007/s41062-022-00784-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41062-022-00784-1

Keywords

Search

Navigation