Skip to main content
SpringerLink
Log in

Effect of 2-D Random Field Discretization on Failure Probability and Failure Mechanism in Probabilistic Slope Stability

  • Original paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

This paper investigates, using the random field theory and Monte Carlo simulation, the effects of random field discretization on failure probability, p f, and failure mechanism of cohesive soil slope stability. The spatial sizes of the discretized elements in random field Δx, Δy in horizontal and vertical directions, respectively, are assigned a series of combinational values in order to model the discretization accuracy. The p f of deterministic critical slip surface (DCSS) and that of the slope system both are analyzed. The numerical simulation results have demonstrated that both the ratios of Δy/λ y (λ y  = scale of fluctuation in vertical direction) and Δx/λ x (λ x  = scale of fluctuation in horizontal direction) contribute in a similar manner to the accuracy of p f of DCSS. The effect of random field discretization on the p f can be negligible if both the ratios of Δx/λ x and Δy/λ y are no greater than 0.1. The normalized discrepancy tends to increase at a linear rate with Δy/λ y when Δx/λ x is larger than 0.1, and vice versa for p f of DCSS. The random field discretization tends to have more considerable influence on the p f of DCSS than on that of the slope system. The variation of p f versus λ x and λ y may exhibit opposite trends for the cases where the limit state functions of slope failure are defined on DCSS and on the slope system as well. Finally, the p f of slope system converges in a more rapid manner to that of DCSS than the failure mechanism does to DCSS as the spatial variability of soil property grows from significant to negligible.

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
Fig. 8

Similar content being viewed by others

References

  • Ang AH-S, Tang WH (2007) Probability concepts in engineering: emphasis on applications to civil and environmental engineering, 2nd edn. John Wiley and Sons, Inc., Hoboken

    Google Scholar 

  • Ching J, Phoon KK (2013) Effect of element sizes in random field finite element simulations of soil shear strength. Comput Struct 126:120–134

    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 ASCE 136(7):975–984

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Duncan JM, Wright SG (2005) Soil strength and slope stability. John Wiley & Sons. Inc., Upper Saddle River

    Google Scholar 

  • El-Ramly H, Morgenstern NR, Cruden DM (2002) Probabilistic slope stability analysis for practice. Can Geotech J 39(3):665–683

    Article  Google Scholar 

  • Fenton GA, Vanmarcke EH (1990) Simulation of random fields via local average subdivision. J Eng Mech ASCE 116(8):1733–1749

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Jha SK, Ching J (2013) Simulating spatial averages of stationary random field using the Fourier series method. J Eng Mechanics 139(5):594–605

    Article  Google Scholar 

  • Ji J (2014) A simplified approach for modeling spatial variability of undrained shear strength in out-plane failure mode of earth embankment. Eng Geol 183:315–323

    Article  Google Scholar 

  • Ji J, Chan CL (2014) Long embankment failure accounting for longitudinal spatial variation: a probabilistic study. Comput Geotech 61:50–56

    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 

  • 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 Eng ASCE 141(2):04014096(13)

    Article  Google Scholar 

  • Jimenez R, Sitar N (2009) The importance of distribution types on finite element analyses of foundation settlement. Comput Geotech 36(3):474–483

    Article  Google Scholar 

  • Jurado-Piña R, Jimenez R (2015) A genetic algorithm for slope stability analyses with concave slip surfaces using custom operators. Eng Optim 47(4):453–472

    Article  Google Scholar 

  • Li L, Chu XS (2011) An improved particle swarm optimization algorithm with harmony strategy for the location of critical slip surface of slopes. China Ocean Eng 25(2):357–364

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Li L, Chu XS (2015b) Comparative study on response surfaces for reliability analysis of spatially variable soil slope. China Ocean Eng 29(1):81–90

    Article  Google Scholar 

  • Li L, Chu XS (2015c) Risk assessment of slope failure by representative slip surfaces and response surface function. KSCE J Civ Eng. doi:10.1007/s12205-015-2243-6

    Google Scholar 

  • Li L, Yu GM, Chen Z, Chu XS (2010) Discontinuous flying particle swarm optimization algorithm and its application to slope stability analysis. J Cent South Univ Technol 17(4):852–856

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Li L, Cheng YM, Chu XS (2013b) A new approach to the determination of the critical slip surfaces of slopes. China Ocean Eng 27(1):51–64

    Article  Google Scholar 

  • Li DQ, Qi XH, Zhou CB, Phoon KK (2014a) Effect of spatial variability of shear strength parameters that increase linearly with depth on reliability of infinite slopes. Struct Saf 49:45–55

    Article  Google Scholar 

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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Low BK, Lacasse S, Nadim F (2007) Slope reliability analysis accounting for spatial variation. Georisk 1(4):177–189

    Google Scholar 

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

    Google Scholar 

  • Vanmarcke E, Shinozuka M, Nakagiri S, Schuëller G, Grigoriu M (1986) Random fields and stochastic finite elements. Struct Saf 3(3–4):143–166

    Article  Google Scholar 

  • Wang Y, Cao Z, Au S-K (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, 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 

Download references

Acknowledgments

The present work was supported by National Natural Science Foundation of China (Grant Nos. 51274126, 51008167, and 51179080), China Scholarship Council (CSC), and National Program on Key Basic Research Project (973 Program, Grant No. 2013CB036403). The financial supports are gratefully acknowledged.

Author information

Authors and Affiliations

  1. School of Civil Engineering, Qingdao University of Technology, Qingdao, China

    Liang Li & Xuesong Chu

Authors
  1. Liang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xuesong Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liang Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, L., Chu, X. Effect of 2-D Random Field Discretization on Failure Probability and Failure Mechanism in Probabilistic Slope Stability. Geotech Geol Eng 34, 437–447 (2016). https://doi.org/10.1007/s10706-015-9955-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-015-9955-8

Keywords

Search

Navigation