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

  • Thanh Son Nguyen
  • Suched LikitlersuangEmail author
Original Paper


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.


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



Volumetric water content




Normal total stress


Correlation coefficient between two arbitrary points in a soil layer


Independent standard normal samples


Slope angle


Normalised correlation length


Effective friction angle


Cross-correlation coefficient between the SWCC parameters a & n


Shear strength of saturated-unsaturated soils


Average unit weight of slice ith


Angle of the base of the ith slice


Mean of a normal distribution


Standard deviation of a normal distribution


Residual volumetric water content


Saturated volumetric water content


Absolute distances between two points in the horizontal direction


Absolute distances between two points in the vertical direction


Mean of a lognormal distribution


Standard deviation of a lognormal distribution

a, n, m

SWCC parameters


Width of the ith slice

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

Correlation matrix


Total pressure head


Height of slope


Height of the ith slice


Indicator function


Hydraulic conductivity


Saturated permeability


Hydraulic conductivity in the horizontal direction


Hydraulic conductivity in the vertical direction


Width of slope

L1, L2

Lower triangular matrices


Horizontal correlation length


Vertical correlation length


random field numerical identifier


Random field elements


Number of realisations


Total number of slices


Failure probability


Applied flux boundary


Cross-correlation matrix


Pore air pressure


Pore water pressure


Weight of the ithslice


Horizontal direction

\( {X}_i^G \)

Cross-correlation standard Gaussian random field


Vertical direction

Zi(x, y)

Lognormal random field



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).


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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

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