Advertisement

Reliability analysis of unsaturated soil slope stability under infiltration considering hydraulic and shear strength parameters

  • Thanh Son Nguyen
  • Suched LikitlersuangEmail author
Original Paper
  • 51 Downloads

Abstract

In general, soil properties, including shear strength and hydraulic parameters, are characterised as a spatial variability. This paper aims to investigate the effect of spatial variability of the soil properties on slope stability during rainfall infiltration. The effective friction angle, saturated hydraulic conductivity, and soil water characteristic curve parameters of sand are simulated using random field theory. A seepage analysis is conducted using the random finite element method to obtain pore water pressure distribution. A stability analysis is performed to show the variation of safety factors and failure probability. The results show that the random field of the soil-water characteristic curve produces a significant variation of pore water pressure, while the random field of the effective friction angle is the most important parameter for probabilistic stability analysis.

Keywords

Random field Probabilistic analysis Permeability Soil-water characteristic curve (SWCC) Shear strength Rainfall infiltration 

Notation

θ

Volumetric water content

ψ

Suction

σ

Normal total stress

ρ(τxy)

Correlation coefficient between two arbitrary points in a soil layer

ξ

Independent standard normal samples

β

Slope angle

δ

Normalised correlation length

ϕ’

Effective friction angle

ρa,n

Cross-correlation coefficient between the SWCC parameters a & n

τf

Shear strength of saturated-unsaturated soils

γi

Average unit weight of slice ith

αi

Angle of the base of the ith slice

μlnz

Mean of a normal distribution

σlnz

Standard deviation of a normal distribution

θr

Residual volumetric water content

θs

Saturated volumetric water content

τx

Absolute distances between two points in the horizontal direction

τy

Absolute distances between two points in the vertical direction

μz

Mean of a lognormal distribution

σz

Standard deviation of a lognormal distribution

a, n, m

SWCC parameters

bi

Width of the ith slice

\( {C}_{n_e\times {n}_e} \)

Correlation matrix

h

Total pressure head

H

Height of slope

hi

Height of the ith slice

I

Indicator function

k

Hydraulic conductivity

ks

Saturated permeability

kx

Hydraulic conductivity in the horizontal direction

ky

Hydraulic conductivity in the vertical direction

L

Width of slope

L1, L2

Lower triangular matrices

lx

Horizontal correlation length

ly

Vertical correlation length

ms

random field numerical identifier

ne

Random field elements

nM

Number of realisations

ns

Total number of slices

Pf

Failure probability

q

Applied flux boundary

R

Cross-correlation matrix

ua

Pore air pressure

uw

Pore water pressure

Wi

Weight of the ithslice

x

Horizontal direction

\( {X}_i^G \)

Cross-correlation standard Gaussian random field

y

Vertical direction

Zi(x, y)

Lognormal random field

Notes

Acknowledgements

This research was supported by the Thailand Research Fund Grant No. DBG-6180004 and the Ratchadapisek Sompoch Endowment Fund (2019), Chulalongkorn University (762003-CC). The first author would like to acknowledge the Ratchadapisek Sompote Fund (2019) for Postdoctoral Fellowship, Chulalongkorn University. The second author would like to acknowledge the Royal Society-Newton Advanced Fellowship (NA170293).

References

  1. Baecher GB, Christian JT (2003) Reliability and statistics in geotechnical engineering. Wiley, New YorkGoogle Scholar
  2. Cho SE (2007) Effects of spatial variability of soil properties on slope stability. Eng Geol 92(3):97–109.  https://doi.org/10.1016/j.enggeo.2007.03.006 CrossRefGoogle Scholar
  3. 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 CrossRefGoogle Scholar
  4. Cho SE (2012) Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation. Eng Geol 133:30–39.  https://doi.org/10.1016/j.enggeo.2012.02.013 CrossRefGoogle Scholar
  5. Cho SE (2014) Probabilistic stability analysis of rainfall-induced landslides considering spatial variability of permeability. Eng Geol 171:11–20.  https://doi.org/10.1016/j.enggeo.2013.12.015 CrossRefGoogle Scholar
  6. Deng ZP, Li DQ, Qi XH, Cao ZJ, Phoon KK (2017) Reliability evaluation of slope considering geological uncertainty and inherent variability of soil parameters. Comput Geotech 92:121–131.  https://doi.org/10.1016/j.compgeo.2017.07.020
  7. Dou HQ, Han TC, Gong XN, Qiu ZY, Li ZN (2015) Effects of the spatial variability of permeability on rainfall-induced landslides. Eng Geol 192:92–100.  https://doi.org/10.1016/j.enggeo.2015.03.014 CrossRefGoogle Scholar
  8. Duncan JM (2000) Factors of safety and reliability in geotechnical engineering. J Geotech Geoenviron 126(4):307–316.  https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307) CrossRefGoogle Scholar
  9. Fenton GA, Griffiths DV (2008) Risk assessment in geotechnical engineering. Wiley, New YorkCrossRefGoogle Scholar
  10. Fredlund DG, Xing A (1994) Equations for the soil-water characteristic curve. Can Geotech J 31(4):521–532.  https://doi.org/10.1139/t94-061 CrossRefGoogle Scholar
  11. Fredlund D, Morgenstern NR, Widger R (1978) The shear strength of unsaturated soils. Can Geotech J 15(3):313–321.  https://doi.org/10.1139/t78-029 CrossRefGoogle Scholar
  12. Fredlund DG, Rahardjo H, Fredlund MD (2012) Unsaturated soil mechanics in engineering practice. John Wiley & Sons, New YorkGoogle Scholar
  13. Geo-Studio (2012) Seepage modeling with SEEP/W and slope stability analysis with SLOPE/W. Geo-Slope International Ltd, CanadaGoogle Scholar
  14. Griffiths D, Fenton GA (2004) Probabilistic slope stability analysis by finite elements. J Geotech Geoenviron 130(5):507–518.  https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507) CrossRefGoogle Scholar
  15. 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 CrossRefGoogle Scholar
  16. 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 CrossRefGoogle Scholar
  17. Jiang S-H, Li D-Q, Zhang L-M, Zhou C-B (2014) Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method. Eng Geol 168:120–128.  https://doi.org/10.1016/j.enggeo.2013.11.006 CrossRefGoogle Scholar
  18. Jiang SH, Huang JS (2016) Efficient slope reliability analysis at low-probability levels in spatially variable soils. Comput Geotech 75:18–27.  https://doi.org/10.1016/j.compgeo.2016.01.016
  19. Leong EC, Rahardjo H (1997) Permeability functions for unsaturated soils. J Geotech Geoenviron 123(12):1118–1126.  https://doi.org/10.1061/(ASCE)1090-0241(1997)123:12(1118) CrossRefGoogle Scholar
  20. 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
  21. Liu K, Vardon P, Hicks M, Arnold P (2017) Combined effect of hysteresis and heterogeneity on the stability of an embankment under transient seepage. Eng Geol 219:140–150.  https://doi.org/10.1016/j.enggeo.2016.11.011 CrossRefGoogle Scholar
  22. Lu N, Likos WJ (2006) Suction stress characteristic curve for unsaturated soil. J Geotech Geoenviron 132(2):131–142.  https://doi.org/10.1061/(ASCE)1090-0241(2006)132:2(131
  23. Lu N, Godt JW, Wu DT (2010) A closed-form equation for effective stress in unsaturated soil. Water Resour Res 46(5):W05515.  https://doi.org/10.1029/2009WR008646
  24. Nguyen TS, Likitlersuang S, Ohtsu H, Kitaoka T (2017) Influence of the spatial variability of shear strength parameters on rainfall induced landslides: a case study of sandstone slope in Japan. Arab J Geosci 10(16):369.  https://doi.org/10.1007/s12517-017-3158-y CrossRefGoogle Scholar
  25. Nguyen TS, Likitlersuang S, Jotisankasa A (2018) Influence of the spatial variability of the root cohesion on a slope-scale stability model: a case study of residual soil slope in Thailand. Bull Eng Geol Environ 1–15.  https://doi.org/10.1007/s10064-018-1380-9
  26. Oh S, Lu N (2015) Slope stability analysis under unsaturated conditions: case studies of rainfall-induced failure of cut slopes. Eng Geol 184:96–103.  https://doi.org/10.1016/j.enggeo.2014.11.007 CrossRefGoogle Scholar
  27. Papagianakis A, Fredlund D (1984) A steady state model for flow in saturated–unsaturated soils. Can Geotech J 21(3):419–430.  https://doi.org/10.1139/t84-046 CrossRefGoogle Scholar
  28. Phoon KK, Kulhawy FH (1999a) Evaluation of geotechnical property variability. Can Geotech J 36(4):625–639.  https://doi.org/10.1139/t99-039
  29. Phoon KK, Kulhawy FH (1999b) Characterization of geotechnical variability. Can Geotech J 36(4):612–624.  https://doi.org/10.1139/t99-038
  30. Phoon KK (2008) Reliability-based design in geotechnical engineering: Computations and Applications. Taylor & Francis, London & New YorkGoogle Scholar
  31. Phoon K-K, Santoso A, Quek S-T (2010) Probabilistic analysis of soil-water characteristic curves. J Geotech Geoenviron 136(3):445–455.  https://doi.org/10.1061/(ASCE)GT.1943-5606.0000222 CrossRefGoogle Scholar
  32. Richards LA (1931) Capillary conduction of liquids through porous mediums. J Appl Phys 1(5):318–333.  https://doi.org/10.1063/1.1745010 Google Scholar
  33. Sainak AN (2004) Application of three-dimensional finite-element method in parametric and geometric studies of slope stability. In: Advances in Geotechnical Engineering (Skempton Conference), vol 2. Thomas Telford, London, pp 933–942Google Scholar
  34. Santoso AM, Phoon K-K, Quek S-T (2011) Effects of soil spatial variability on rainfall-induced landslides. Comput Struct 89(11):893–900.  https://doi.org/10.1016/j.compstruc.2011.02.016 CrossRefGoogle Scholar
  35. 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.  https://doi.org/10.1016/j.enggeo.2009.11.006 CrossRefGoogle Scholar
  36. Yang C, Sheng D, Carter JP, Huang J (2012) Stochastic evaluation of hydraulic hysteresis in unsaturated soils. J Geotech Geoenviron 139(7):1211–1214.  https://doi.org/10.1061/(ASCE)GT.1943-5606.0000833 CrossRefGoogle Scholar
  37. Yeh HF, Lee CC, Lee CH (2008) A rainfall-infiltration model for unsaturated soil slope stability. J Environ Eng Manag 18(4):261–268Google Scholar
  38. Zhang L, Fredlund D, Zhang L, Tang W (2004) Numerical study of soil conditions under which matric suction can be maintained. Can Geotech J 41(4):569–582.  https://doi.org/10.1139/t04-006 CrossRefGoogle Scholar
  39. Zhu H, Zhang LM, Zhang L, Zhou C (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 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Centre of Excellence in Geotechnical and Geoenvironmental Engineering, Department of Civil Engineering, Faculty of EngineeringChulalongkorn UniversityBangkokThailand

Personalised recommendations