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Reliability Analysis of Earth Slopes Considering Spatial Variability

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Abstract

The paper presents a computational procedure for reliability analysis of earth slopes considering spatial variability of soils under the framework of the Limit Equilibrium Method. In the reliability analysis of earth slopes, the effect of spatial variability of soil properties is generally included indirectly by assuming that the probabilistic critical slip surface is the same as that determined without considering spatial variability. In contrast to this indirect approach, in the direct approach, the effect of spatial variability is included in the process of determination of the probabilistic critical surface itself. While the indirect approach requires much less computational effort, the direct approach is definitely more rigorous. In this context this paper attempts to investigate, with the help of numerical examples, how far away are the results obtained from the indirect approach from that obtained from the direct approach. In both the approaches, it is required to use a model of discretization of random fields into finite random variables. A few such models are available in the literature for one-dimensional (1D) as well as two-dimensional (2D) spatial variability. The developed computational scheme is based on the First Order Reliability Method (FORM) coupled with the Spencer Method of Slices valid for limit equilibrium analysis of general slip surfaces. The study includes bringing out the computational advantages and disadvantages of the three commonly used discretization models. The sensitivity of the reliability index to the magnitudes of the scales of fluctuation has also been studied.

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References

  • Ang AHS, Tang WH (2007) Probability concepts in engineering: emphasis on applications to civil and environmental, 2nd edn. Wiley, New York

    Google Scholar 

  • Babu GLS, Mukesh MD (2004) Effect of soil variability on reliability of soil slopes. Geotechnique 54(5):335–337

    Article  Google Scholar 

  • Bhattacharya G, Jana D, Ojha S, Chakraborty S (2003) Direct search for minimum reliability index of earth slopes. Comput Geotech 30(6):455–462

    Article  Google Scholar 

  • Bourdeau PL, Amundaray JI (2005) Non-parametric simulation of geotechnical variability. Géotechnique 55(2):95–108

    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(7):975–984

    Article  Google Scholar 

  • Chowdhury RN, Xu D (1992) Reliability index for slope stability assessment-two methods compared. Reliab Eng Syst Saf 37(2):99–108

    Article  Google Scholar 

  • Chowdhury R, Tang WH, Sidi I (1987) Reliability model of progressive slope failure. Geotechnique 37:467–481

    Article  Google Scholar 

  • Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope analysis. J Geotech Eng Div ASCE 119(12):1910–1927

    Google Scholar 

  • Crum DA (2001) Discussion search algorithm for minimum reliability index of earth slopes by Hassan AH and Wolff TF. J Geotech Geoenviron Eng ASCE 127(02):197–198

    Article  Google Scholar 

  • DeGroot DJ (1996), Analyzing spatial variability of in situ soil properties, In Proceedings of Uncertainty’96, vol 1. Geotechnical Special Publication, 58, pp 210–238

  • Duncan JM, Wright SG (1980) The accuracy of equilibrium methods of slope stability analysis. Eng Geol 16(1–2):5–17

    Article  Google Scholar 

  • Elkateb T, Chalaturnyk R, Robertson PK (2003) An overview of soil heterogeneity: qualification and implications on geotechnical field problems. Can Geotech J 40:1–15

    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 (2003a) Probabilistic stability analysis of a tailings dyke on presheared clay-shale. Can Geotech J 40(1):192–208

    Article  Google Scholar 

  • El-Ramly H, Morgenstern NR, Cruden DM (2003b) Reply to the discussion by J. M. Duncan, M. Navin, and T. F. Wolff on “Probabilistic slope stability analysis for practice”. Can Geotech J 40(4):851–855

    Article  Google Scholar 

  • Faraha K, Ltifi M, Hassis H (2011) Reliability analysis of slope stability using stochastic finite element method. Procedia Eng 10:1402–1407

    Article  Google Scholar 

  • Greco VR (1996) Efficient monte carlo technique for locating critical slip surface. J Geotech Eng Div ASCE 117(10):517–525

    Article  Google Scholar 

  • Griffiths DV, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron Eng 130(5):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(10):1367–1378

    Article  Google Scholar 

  • Haldar A, Mahadevan S (2000) Probability reliability and statistical methods in engineering design. Wiley, New York

    Google Scholar 

  • Hasofer AM, Lind NC (1974) A extract and Invariant First Order Reliability Format. J Eng Mech ASCE 100(EM-1):111–121

    Google Scholar 

  • Hassan AH, Wolff TF (1999) Search algorithm for minimum reliability index of earth slopes. J Geotech Geoenviron Eng ASCE 125(4):301–308

    Article  Google Scholar 

  • Hicks MA, Spencer WA (2010) Influence of heterogeneity on the reliability and failure of a long 3D slope. Comput Geotech 37:948–955

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ji J, Liao HJ, Low BK (2012) Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations. Comput Geotech 40:135–146

    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 

  • Khajehzadeh M, El-Shafie A, Taha MR (2010) Modified particle swarm optimization for probabilistic slope stability analysis. Int J Phys Sci 5(15):2248–2258

    Google Scholar 

  • Lacasse S, Nadim F (1996), Uncertainties in characterizing soil properties, In: Proceedings of Uncertainty ‘96, vol 1. Geotechnical Special Publication, 58, pp 49–75

  • Li KS, Cheung RWM (2001) Discussion search algorithm for minimum reliability index of earth slopes by Hassan Am. Wolff TF. J Geotech Geoenviron Eng 127(02):197–198

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Liang L, Xue-song C (2012) The location of critical reliability slip surface in soil slope stability analysis. Procedia Earth Planet Sci 5:146–149

    Article  Google Scholar 

  • Low BK (2003). Practical probabilistic slope stability analysis. In: Proceedings of the soil and rock America, 12th Panamerican conf. on soil mechanics and geotechnical engineering and 39th US rock mechanics symp. MIT, Cambridge, Massachusetts

  • Metya S, Bhattacharya G (2014) Probabilistic critical slip surface for earth slopes based on the first order reliability method. Indian Geotech J 44(3):329–340

    Article  Google Scholar 

  • Mostyn GR, Li KS (1993) Probabilistic slope stability analysis—state-of-play. In: Li KS, Lo S-CR (eds) Probabilistic methods in geotechnical engineering. A.A. Balkema, Rotterdam, pp 89–109

    Google Scholar 

  • Rao SS (2009) Engineering optimization: theory and practice, 4th edn. Wiley, New York

    Book  Google Scholar 

  • Salgado R, Kim D (2014) Reliability analysis of load and resistance factor design of slopes. J Geotech Geoenviron Eng ASCE 140(1):57–73

    Article  Google Scholar 

  • Schittkowski K (1980) Nonlinear programming codes: information, tests, performance. Lecture notes in economics and mathematical systems, vol 183. Springer, New York

    Google Scholar 

  • Spencer E (1967) A method of analysis of the stability of the embankments assuming parallel inter-slice forces. Geotechnique 17(1):11–26

    Article  Google Scholar 

  • Spencer E (1973) The thrust line criterion in embankment stability analysis. Geotechnique 23(1):85–100

    Article  Google Scholar 

  • Tobutt DC, Richards EA (1979) The reliability of earth slopes. Int J Numer Anal Meth Geomech 3:323–354

    Article  Google Scholar 

  • Vanmarcke EH (1977a) Probabilistic modeling of soil profiles. J Geotech Eng Div ASCE 103(11):1227–1246

    Google Scholar 

  • Vanmarcke EH (1977b) Reliability of earth slopes. J Geotech Geoenviron Eng ASCE 103(11):1247–1265

    Google Scholar 

  • Vanmarcke EH (1983) Random fields: analysis and synthesis. MIT Press, Cambridge

    Google Scholar 

  • Wang Y, Cao Z, 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 

  • 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 

Download references

Acknowledgments

This research has been supported by the AORC Scheme of the INSPIRE Program of the Department of Science & Technology (DST), Government of India and the first author is employed as a INSPIRE Fellow with DST support. This support is gratefully acknowledged. The writers also thank two anonymous reviewers for their constructive comments and suggestions.

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Engineering Science and Technology (IIEST), Shibpur, Botanic Garden, Shibpur, Howrah, 711103, West Bengal, India

    Subhadeep Metya & Gautam Bhattacharya

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  1. Subhadeep Metya
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  2. Gautam Bhattacharya
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Correspondence to Gautam Bhattacharya.

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Metya, S., Bhattacharya, G. Reliability Analysis of Earth Slopes Considering Spatial Variability. Geotech Geol Eng 34, 103–123 (2016). https://doi.org/10.1007/s10706-015-9932-2

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  • DOI: https://doi.org/10.1007/s10706-015-9932-2

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