Reliability analysis of earth slopes accounting for spatial variation
Date of Issue2013
School of Civil and Environmental Engineering
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 reliability index β is evaluated using a constrained optimization algorithm for FORM in a spreadsheet, where the conventional LEM of slices can be easily integrated with reliability analysis. Based on the two methods, the influence of 2-D spatial variability of soil strength parameters on slope reliability is investigated in detail. Results obtained by the two methods are compared. 2-D spatial variability characterization and a case study involving 2-D spatial variation are presented. A further study of probabilistic finite difference strength-reduction stability analysis involving 2-D spatial variation is also presented, based on the method of interpolated autocorrelations. Three-dimensional (3-D) slope failure is investigated in this study by probabilistic analysis which accounts for the longitudinal (out-of-plane) spatial variability of shear strength parameters. The 3-D stability model is first analyzed by LEM due to its ease of obtaining an explicit performance function and of transition to probabilistic analysis. Both spatial-averaging approach and spatial-autocorrelation approach are used for the random field analysis. Comparisons between the two methods are made. For a long earth slope, the local 3-D failure with a probabilistic critical width is emphasized. Complementary to the LEM analysis, a probabilistic 3-D strength-reduction finite difference stability analysis is also presented. Finally, an efficient approach for slope system reliability analysis using stand-alone software for deterministic stability analysis is presented. A useful procedure of identifying the local minimum-β slip surfaces is introduced, and a stratified response surface method is proposed to represent the system performance functions (in multiple failure modes). The Kounias-Ditlevsen’s bimodal bounds obtained based on multi-mode FORM analyses are compared with system Monte Carlo simulations. The bimodal bounds can be improved using SORM analysis if nonlinearity underlies any of the stratified response surfaces so obtained.