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Reliability of spatially variable soil slope based on nonlinear failure criterion

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Abstract

The reliability analysis of slope under the nonlinear failure criterion is investigated in this paper. The two-dimensional random fields are generated by using Karhunen–Loève (KL) expansion method. Based on the generated random fields, the simplified Bishop’s method with nonlinear failure criterion is used to calculate the factor of safety. Then, Monte Carlo simulation is used to estimate the reliability of slope. Example analyses are carried out to verify the presented method. The effect of the nonlinearity coefficient m on the failure probability of slope is investigated in this paper. The results show that the failure probability obtained by using the nonlinear failure criterion is higher than that calculated by using linear Mohr–Coulomb criterion.

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References

  • Bai T, Huang X, Li C (2013) Slope stability analysis considering spatial variability of soil properities. J Zhejiang Univ (eng Sci) 47:2221–2226

    Google Scholar 

  • Bishop AW (1955) The use of the slip circle in the stability analysis of earth slopes. Geotechnique 5:7–17

    Article  Google Scholar 

  • Bishop AW, Webb DL, Lewin PI (1965) Undisturbed samples of London Clay from the Ashford Common shaft: strength–effective stress relationships. Geotechnique 15:1–31

    Article  Google Scholar 

  • 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 

  • Cho SE (2007) Effects of spatial variability of soil properties on slope stability. Eng Geol 92:97–109

    Article  Google Scholar 

  • Cho SE (2010) Probabilistic assessment of slope stability that considers the spatial variability of soil properties. J Geotech Geoenviron Eng 136:975–984

    Article  Google Scholar 

  • Deng D, Zhao L, Li L (2015) Limit equilibrium slope stability analysis using the nonlinear strength failure criterion. Can Geotech J 52:563–576

    Article  Google Scholar 

  • Dyson AP, Tolooiyan A (2019) Probabilistic investigation of RFEM topologies for slope stability analysis. Comput Geotech 114:103129

    Article  Google Scholar 

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

    Article  Google Scholar 

  • El-Ramly H, Morgenstern NR, Cruden DM (2003) Probabilistic stability analysis of a tailings dyke on presheared clay-shale. Can Geotech J 40:192–208

    Article  Google Scholar 

  • Gao Y, Wu D, Zhang F (2015) Effects of nonlinear failure criterion on the three-dimensional stability analysis of uniform slopes. Eng Geol 198:87–93

    Article  Google Scholar 

  • Griffiths DV, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron 130:507–518

    Article  Google Scholar 

  • Griffiths DV, Huang J, Fenton GA (2009) Influence of spatial variability on slope reliability using 2-D random fields. J Geotech Geoenviron Eng 135:1367–1378

    Article  Google Scholar 

  • Guo X, Dias D, Pan Q (2019) Probabilistic stability analysis of an embankment dam considering soil spatial variability. Comput Geotech 113:103093

    Article  Google Scholar 

  • Jamshidi Chenari R, Zamanzadeh M (2016) Uncertainty assessment of critical excavation depth of vertical unsupported cuts in undrained clay using random eld theorem. Sci Iran 23:864–875

    Google Scholar 

  • Javankhoshdel S, Cami B, Chenari RJ, Dastpak P (2021) Probabilistic analysis of slopes with linearly increasing undrained shear strength using RLEM approach. Transp Infrastruct Geotechnol 8:114–141

    Article  Google Scholar 

  • Jiang J, Baker R, Yamagami T (2003) The effect of strength envelope nonlinearity on slope stability computations. Can Geotech J 40:308–325

    Article  Google Scholar 

  • Jiang SH, Li DQ, Zhang LM, Zhou CB (2014) Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Eng Geol 168:120–128

    Article  Google Scholar 

  • Johari A, Fooladi H (2020) Comparative study of stochastic slope stability analysis based on conditional and unconditional random field. Comput Geotech 125:103707

    Article  Google Scholar 

  • Johari A, Talebi A (2019) Stochastic analysis of rainfall-induced slope instability and steady-state seepage flow using random finite-element method. Int J Geomech 19:4019085

    Article  Google Scholar 

  • Lacasse S, Nadim F (1997) Uncertainties in characterising soil properties. Publikasjon-Norges Geotekniske Institutt 201:49–75

    Google Scholar 

  • Laloy E, Rogiers B, Vrugt JA, Mallants D, Jacques D (2013) Efficient posterior exploration of a high-dimensional groundwater model from two-stage MCMC simulation and polynomial chaos expansion. Water Resour Res 49:2664–2682

    Article  Google Scholar 

  • Li D, Xiao T, Cao Z, Zhou C, Zhang L (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 

  • Li KS, Lumb P (1987) Probabilistic design of slopes. Can Geotech J 24:520–535

    Article  Google Scholar 

  • Li X, Zhang L, Gao L, Zhu H (2017) Simplified slope reliability analysis considering spatial soil variability. Eng Geol 216:90–97

    Article  Google Scholar 

  • Li Y, Yang X (2019) Seismic displacement of 3D slope reinforced by piles with nonlinear failure criterion. Int J Geomech 19:4019042

    Article  Google Scholar 

  • Liu LL, Deng ZP, Zhang SH, Cheng YM (2018) Simplified framework for system reliability analysis of slopes in spatially variable soils. Eng Geol 239:330–348

    Article  Google Scholar 

  • Liu X, Wang Y, Li DQ (2019) Investigation of slope failure mode evolution during large deformation in spatially variable soils by random limit equilibrium and material point methods. Comput Geotech 111:301–312

    Article  Google Scholar 

  • Low BK, Lacasse S, Nadim F (2007) Slope reliability analysis accounting for spatial variation. Georisk 1:177–189

    Google Scholar 

  • Luo N, Bathurst RJ, Javankhoshdel S (2016) Probabilistic stability analysis of simple reinforced slopes by finite element method. Comput Geotech 77:45–55

    Article  Google Scholar 

  • Maksimovic M (1989) Nonlinear failure envelope for soils. J Geotech Eng 115:581–586

    Article  Google Scholar 

  • Penman A (1953) Shear characteristics of a saturated silt, measured in triaxial compression. Geotechnique 3:312–328

    Article  Google Scholar 

  • Skempton AW (1985) Residual strength of clays in landslides, folded strata and the laboratory. Geotechnique 35:3–18

    Article  Google Scholar 

  • Tan XT, Dong X, Fei S, Gong W, Xiu L, Hou X, Ma H (2020) Reliability analysis method based on KL expansion and its application. Chin J Geotech Eng 42:808–816

    Google Scholar 

  • Tang GP, Li L, Zhao LH, Chen JY (2015) Inclined slices method for limit analysis of slope stability with nonlinear failure criterion. Yantu Lixue/rock Soil Mech 36:2063–2072

    Google Scholar 

  • Xu J, Yang X (2019) Seismic stability of 3D soil slope reinforced by geosynthetic with nonlinear failure criterion. Soil Dyn Earthq Eng 118:86–97

    Article  Google Scholar 

  • Zhang XJ, Chen WF (1987) Stability analysis of slopes with general nonlinear failure criterion. Int J Numer Anal Met 11:33–50

    Article  Google Scholar 

  • Zhu B, Pei H, Yang Q (2019a) Reliability analysis of submarine slope considering the spatial variability of the sediment strength using random fields. Appl Ocean Res 86:340–350

    Article  Google Scholar 

  • Zhu D, Griffiths DV, Fenton GA (2019b) Worst-case spatial correlation length in probabilistic slope stability analysis. Geotechnique 69:85–88

    Article  Google Scholar 

  • Zhu D, Griffiths DV, Huang J, Fenton GA (2017) Probabilistic stability analyses of undrained slopes with linearly increasing mean strength. Géotechnique 67:1–14

    Article  Google Scholar 

Download references

Acknowledgements

This research was financially supported by grants of the Natural Science Foundation of Ningxia (Nos. 2020BEB04004 and 2021AAC03074) and the First Class Discipline Construction in Ningxia (No. NXYLXK2021A03).

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Authors and Affiliations

  1. School of Civil and Hydraulic Engineering, Ningxia University, Yinchuan, 750021, Ningxia, China

    Yukuai Wan, Xinyue Gao & Lei Zhu

  2. Engineering Research Center for Efficient Utilization of Modern Agricultural Water Resources in Arid Regions, Ministry of Education, Yinchuan, 750021, Ningxia, China

    Yukuai Wan, Xinyue Gao & Lei Zhu

  3. School of Civil Engineering, Suzhou University of Science and Technology, Suzhou, 215129, China

    Di Wu

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  1. Yukuai Wan
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  2. Xinyue Gao
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  3. Di Wu
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  4. Lei Zhu
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Correspondence to Lei Zhu.

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Wan, Y., Gao, X., Wu, D. et al. Reliability of spatially variable soil slope based on nonlinear failure criterion. Nat Hazards 117, 1179–1189 (2023). https://doi.org/10.1007/s11069-023-05868-4

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