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Reliability analysis of slope with cross-correlated spatially variable soil properties using AFOSM

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Abstract

Efficient approaches for slope reliability computation with spatially variable soil properties are of great interest. In this paper, an advanced first-order second-moment method (AFOSM) combined with the limit equilibrium method (LEM) is adopted for efficient slope reliability analysis considering cross-correlated random fields of shear strength parameters. In the slope reliability analysis, random fields of the soil shear strengths are locally discretized along the slip surface. A systematic framework is presented for constructing a full correlation matrix incorporating both autocorrelation and cross correlation for the shear strength parameters in multiple soil layers, which could be useful for multi-layered slope reliability analysis involving cross-correlated spatially variable soil properties. A single-layered c–φ slope and a two-layered c–φ slope are investigated to illustrate and validate the proposed approach. As regards the examples, parametric studies show that slope reliability decreases with an increase in the autocorrelation distance and the cross-correlation coefficient between c and φ. Moreover, the effect of the vertical autocorrelation distance on the slope reliability is much more significant than that of the horizontal autocorrelation distance. The directly searched minimum reliability indices are all smaller than those computed with the deterministic critical slip surface. The slope reliability indices are affected by the number of slices, however, if a sufficient number of slices are used to represent the random field, increasing the number of slices does not significantly affect the reliability indices. The AFOSM is quite efficient for slope reliability analysis with spatially variable soil properties and its accuracy is satisfactory compared to the MCS. Although only a two-layered slope is considered in the illustrative example for convenient demonstration and easy understanding, the AFOSM is generally applicable to slopes with multiple soil layers.

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Abbreviations

A k :

Autocorrelation matrix of strength parameters for the kth soil layer

D k :

Correlation matrix of strength parameters for the kth soil layer

F :

Correlation matrix of strength parameters for a slip surface penetrating multiple soil layers

θ h :

Horizontal autocorrelation distance

θ v :

Vertical autocorrelation distance

ρ i , j :

Autocorrelation coefficients between the values of the same strength parameter at the midpoints of the ith and jth segments

c i , j :

Cross-correlation coefficients between the values of the ith and jth parameters

g(X):

Limit state function

X :

A vector of correlated random variables

β :

Reliability index

α i :

Sensitivity coefficient of random variable Xi

x * :

Maximum probabilistic point

μ Xi :

Mean value of random variable Xi

σ Xi :

Standard deviation of random variable Xi

ρ Xi , Xj :

Correlation coefficient between random variables Xi and Xj

μ N :

Mean value of the equivalent normal random variable for the non-normal random variable at x*

σ N :

Standard deviation of the equivalent normal random variable for the non-normal random variable at x*

\(\phi \left( \bullet \right)\) :

Standard normal probability density function

\(\Phi ^{{ - 1}} \left( \bullet \right)\) :

Inverse standard normal CDF

\(F_{X} \left( \bullet \right)\) :

CDF of the original random variable

\(f_{X} \left( \bullet \right)\) :

PDF of the original random variable

F s :

Safety factor

W :

Weight of the slice

V :

Vertical seismic inertia force

U :

Pore water pressure at the base of the slice

ψ :

Inclination angle of the slice base to the horizontal

b :

Width of the slice

c :

Cohesion of the soil

φ :

Friction angle of the soil

M c :

Moment about the center of the failure arc

R :

Radius of the failure arc

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Acknowledgements

Financial supports provided by the National Key R&D Program of China (No. 2018YFC0407103) and the National Natural Science Foundation of China (No. 51109151) are gratefully acknowledged. The authors also would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.

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Authors and Affiliations

  1. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, No. 24 South Section 1, Yihuan Road, Chengdu, 610065, China

    Zhenyu Wu, Junru Li, Kang Bian & Jiankang Chen

  2. College of Hydraulic and Hydroelectric Engineering, Sichuan University, No.24 South Section 1, Yihuan Road, Chengdu, 610065, China

    Zhenyu Wu, Junru Li, Kang Bian & Jiankang Chen

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  1. Zhenyu Wu
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  2. Junru Li
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  3. Kang Bian
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Correspondence to Jiankang Chen.

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Wu, Z., Li, J., Bian, K. et al. Reliability analysis of slope with cross-correlated spatially variable soil properties using AFOSM. Environ Earth Sci 80, 675 (2021). https://doi.org/10.1007/s12665-021-09963-2

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