Reliability analysis of earth slopes accounting for spatial variation

Abstract

The stability of earth slopes is an important issue in geotechnical engineering. In the routine stability analysis, soil properties are given deterministic values, based on which a lumped factor of safety is derived as the deterministic solution. One limitation of the deterministic analysis is that the parametric uncertainty which is inherent in geotechnical engineering cannot be taken into account explicitly. In contrast, the uncertainty can be accounted for by adopting probabilistic methods. However, extending deterministic slope stability analysis to probabilistic analysis is often a complicated and challenging task. The objective of this study is to develop some practical approaches of reliability assessment of earth slopes and to investigate the effect of spatial variation on slope reliability. An efficient approach of first-order reliability method (FORM) is proposed based on a recursive algorithm searching for the design point in the equivalent standard normal variable space (n-space). Based on the recursive algorithm, reliability analysis involving implicit limit state surface can be carried out via finite-difference sensitivity analysis in the n-space (probabilistic sensitivity-based FORM). The probabilistic sensitivity-based FORM is shown to be as efficient as the commonly-used response surface method for FORM (RSM-based FORM), but it needs less evaluation of the limit state surface and hence is more efficient. Application of the probabilistic sensitivity-based FORM to strength-reduction finite element slope reliability analysis is presented via two case studies. The importance of spatial variation of geotechnical properties is highlighted in this study. Based on the limit equilibrium method (LEM) of slices, two methods, namely, method of autocorrelated slices and method of interpolated autocorrelations are proposed to model the two-dimensional (2-D) spatial variability of soil properties. The iii Acknowledgement This author would like to express his deepest appreciation to his supervisor, Associate Professor Bak Kong Low, for his guidance and encouragement, and for the many invaluable discussions with him. It has been a very memorable and inspiring four-year learning experience. The author would also like to thank the Nanyang Technological University (NTU) of Singapore for granting him the scholarship (2008-2012) for this research program.

Efficient reliability method for implicit limit state surface with correlated non‐Gaussian variables

“…Multiplying L to both sides of Eqn , and using Eqn , the HL–RF recursive algorithm is reformulated to be : where n k is the k th iteration point in n‐space, g ( n k ) and ∇ g ( n k ) are the performance function and gradient vector of the performance function evaluated at n k , respectively, and R is the correlation matrix.…”

Probabilistic Strength-Reduction Stability Analysis of Slopes Accounting for 2-D Spatial Variation

“…This value is slightly higher than the F s of 1.462 as computed by Spencer's method with circular slip surface by 3.6 %. The deterministic strength-reduction stability analysis is extended into probabilistic study based on the probabilistic sensitivity-based FORM proposed by Ji [11]. In particular, spatial variation of the undrained shear strength c u of the soft foundation is modelled using the method of interpolated autocorrelations.…”