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An analytical method for quantifying the correlation among slope failure modes in spatially variable soils

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Abstract

An efficient analytical method for quantifying the correlation between performance functions of different slope failure modes in spatially variable soils is proposed, and its performance in slope system reliability analysis is investigated. First, a new correlation coefficient (NCC) is proposed to evaluate the correlation among slope failure modes considering spatial variability. For comparison and verification, the simulation-based correlation coefficient (SCC) is also presented. Second, appying these two types of correlation coefficients, the effects of soil spatial variability on the representative slip surfaces (RSSs) and the system probability of slope failure are investigated using different system reliability methods, including a probabilistic network evaluation technique, a risk aggregation approach, and a bimodal bounds method. A single-layered cohesive slope is investigated to illustrate the validity of the proposed NCC. The results indicate that the proposed NCC can efficiently and accurately quantify the correlation among slope failure modes considering soil spatial variability. The number of RSSs indicated by the NCC is in good agreement with the number obtained using the SCC. The system failure probabilities of slope stability obtained with the SCC and the NCC using a risk aggregation approach are generally comparable. Also, the system reliability bounds of slope stability obtained using the NCC are relatively close together and comparable to those obtained using the SCC. Thus, the NCC shows good performance when evaluating the correlation among slope failure modes, and was effectively applied to analyze a single-layered cohesive slope considering soil spatial variability.

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References

  • Ang HS, Tang WH (1984) Probability concepts in engineering planning and design, vol. II, decision, risk, and reliability. Wiley, New York

    Google Scholar 

  • Cho SE (2013) First-order reliability analysis of slope considering multiple failure modes. Eng Geol 154:98–105

    Article  Google Scholar 

  • Chowdhury RN, Xu DW (1994) Slope system reliability with general slip surfaces. Soils Found 34(3):99–105

    Article  Google Scholar 

  • Chowdhury RN, Xu DW (1995) Geotechnical system reliability of slopes. Reliab Eng Syst Saf 47(3):141–151

    Article  Google Scholar 

  • Chu XS, Li L, Wang YJ (2015) Slope reliability analysis using length-based representative slip surfaces. Arab J Geosci 8(11):9065–9078

    Article  Google Scholar 

  • Ditlevsen O (1979) Narrow reliability bounds for structural systems. J Struct Mech 7(4):453–472

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Fan HJ, Huang QD, Liang R (2014) Reliability analysis of piles in spatially varying soils considering multiple failure modes. Comput Geotech 57:97–104

    Article  Google Scholar 

  • Fenton GA, Griffiths DV (2008) Risk assessment in geotechnical engineering. Wiley, New York

    Book  Google Scholar 

  • GEO-SLOPE International Ltd (2008) Stability modeling with Slope/W (2007 Version). GEO-SLOPE International Ltd., Calgary

  • Haldar S, Babu GS (2008) Effect of soil spatial variability on the response of laterally loaded pile in undrained clay. Comput Geotech 35(4):537–547

    Article  Google Scholar 

  • Hicks MA, Samy K (2002) Influence of heterogeneity on undrained clay slope stability. Q J Eng Geol Hydrogeol 35(1):41–49

    Article  Google Scholar 

  • Hong HP, Roh G (2008) Reliability evaluation of earth slopes. J Geotech Geoenviron 134(12):1700–1705

    Article  Google Scholar 

  • Huang JS, Griffiths DV, Fenton GA (2010) System reliability of slopes by RFEM. Soils Found 50(3):343–353

    Article  Google Scholar 

  • Huang JS, Lyamin AV, Griffiths DV, Krabbenhoft K, Sloan SW (2013) Quantitative risk assessment of landslide by limit analysis and random fields. Comput Geotech 53:60–67

    Article  Google Scholar 

  • Ji J, Low BK (2012) Stratified response surfaces for system probabilistic evaluation of slopes. J Geotech Geoenviron 138(11):1398–1406

    Article  Google Scholar 

  • Jiang SH, Li DQ, Cao ZJ, Zhou CB, Phoon KK (2015) Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation. J Geotech Geoenviron 141(2):04014096

    Article  Google Scholar 

  • Li L, Chu XS (2015a) Multiple response surfaces for slope reliability analysis. Int J Numer Anal Methods 39(2):175–192

    Article  Google Scholar 

  • Li L, Chu XS (2016) Risk assessment of slope failure by representative slip surfaces and response surface function. KSCE J Civ Eng 20(5):1783–1792

  • Li DQ, Chen YF, Lu WB, Zhou CB (2011) Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables. Comput Geotech 38(1):58–68

    Article  Google Scholar 

  • Li L, Wang Y, Cao ZJ, Chu XS (2013) Risk de-aggregation and system reliability analysis of slope stability using representative slip surfaces. Comput Geotech 53:95–105

    Article  Google Scholar 

  • Li L, Wang Y, Cao ZJ (2014) Probabilistic slope stability analysis by risk aggregation. Eng Geol 176:57–65

    Article  Google Scholar 

  • Li DQ, Zhang L, Tang XS, Zhou W, Li JH, Zhou CB, Phoon KK (2015a) Bivariate distribution of shear strength parameters using copulas and its impact on geotechnical system reliability. Comput Geotech 68:184–195

    Article  Google Scholar 

  • Li JH, Tian YH, Mark JC (2015b) Failure mechanism and bearing capacity of footings buried at various depths in spatially random soil. J Geotech Geoenviron 141(2):04014099

    Article  Google Scholar 

  • Li DQ, Zheng D, Cao ZJ, Tang XS, Phoon KK (2016a) Response surface methods for slope reliability analysis: a review and comparison. Eng Geol 203:3–14

    Article  Google Scholar 

  • Li DQ, Qi XH, Cao ZJ, Tang XS, Phoon KK, Zhou CB (2016b) Evaluating slope stability uncertainty using coupled Markov chain. Comput Geotech 73:72–82

    Article  Google Scholar 

  • Li DQ, Xiao T, Cao ZJ, Zhou CB, Zhang LM (2016c) Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using subset simulation. Landslides 13(2):293–303

  • Li Z, Wang XR, Wang H, Liang RY (2016d) Quantifying stratigraphic uncertainties by stochastic simulation techniques based on Markov random field. Eng Geol 201:106–122

    Article  Google Scholar 

  • Low BK, Zhang J, Tang WH (2011) Efficient system reliability analysis illustrated for a retaining wall and a soil slope. Comput Geotech 38(2):196–204

    Article  Google Scholar 

  • Srivastava A, Babu GS, Haldar S (2010) Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis. Eng Geol 110(3):93–101

    Article  Google Scholar 

  • Tang XS, Li DQ, Zhou CB, Phoon KK (2015) Copula-based approaches for evaluating slope reliability under incomplete probability information. Struct Saf 52:90–99

    Article  Google Scholar 

  • Wang Y, Cao ZJ, Au SK (2011) Practical reliability analysis of slope stability by advanced Monte Carlo simulations in a spreadsheet. Can Geotech J 48(1):162–172

    Article  Google Scholar 

  • Zeng P, Jimenez R (2014) An approximation to the reliability of series geotechnical systems using a linearization approach. Comput Geotech 62:304–309

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Zhang J, Zhang LM, Tang WH (2011) New methods for system reliability analysis of soil slopes. Can Geotech J 48(7):1138–1148

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

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Acknowledgments

This work was supported by the National Science Fund for Distinguished Young Scholars (project no. 51225903), the National Natural Science Foundation of China (project nos. 51329901, 51579190, 51528901), and the Natural Science Foundation of Hubei Province of China (project no. 2014CFA001).

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Authors and Affiliations

  1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 8 Donghu South Road, Wuhan, 430072, China

    Dong Zheng, Dian-Qing Li, Zi-Jun Cao & Xiao-Song Tang

  2. Department of Civil and Environmental Engineering, National University of Singapore, Blk E1A, #07-03, 1 Engineering Drive 2, Singapore, 117576, Singapore

    Kok-Kwang Phoon

Authors
  1. Dong Zheng
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  2. Dian-Qing Li
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  3. Zi-Jun Cao
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  4. Xiao-Song Tang
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  5. Kok-Kwang Phoon
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Correspondence to Dian-Qing Li.

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Zheng, D., Li, DQ., Cao, ZJ. et al. An analytical method for quantifying the correlation among slope failure modes in spatially variable soils. Bull Eng Geol Environ 76, 1343–1352 (2017). https://doi.org/10.1007/s10064-016-0923-1

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  • DOI: https://doi.org/10.1007/s10064-016-0923-1

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