Dynamic Slope Stability Analysis by a Reliability-Based Approach

The analysis of earth slopes situated in seismic areas has been extensively investigated in literature using deterministic approaches where average values of the input parameters are used and a global safety factor or a permanent displacement at the toe of the slope is calculated. In these approaches, a decoupled analysis is usually performed in which a constant critical seismic acceleration is first calculated based on a pseudo-static representation of earthquake effects. Then, the permanent soil displacement is computed by integration of the real acceleration record above the critical acceleration. A reliability-based approach for the seismic slope analysis is introduced in this paper. This approach is more rational than the traditional deterministic methods since it enables to take into account the inherent uncertainty of the input variables. Furthermore, the deterministic model used in the reliability analysis is based on a rigorous coupled analysis that simultaneously captures the fully non linear response of the soil and history of the real acceleration record. This model is based on numerical simulations using the dynamic option of the finite difference FLAC3D software. The acceleration time history records used in this analysis is the one registered at the Lebanese Geophysical Center of the National Council for Scientific Research. The performance function used in the reliability analysis is defined with respect to the horizontal permanent displacement at the toe of the slope. The random variables considered in the analysis are the cohesion c and the shear modulus G of the soil since it was shown that these parameters have the most influence on slope displacements. The Stochastic Response Surface Methodology (SRSM) is utilized for the assessment of the probability distribution of the horizontal permanent displacement at the toe of the slope. The results have shown that the mean value of the permanent displacement is highly influenced by the coefficient of variation of the cohesion, the greater the scatter in c the higher the horizontal permanent displacement. Based on the probability distribution of the permanent displacement, the failure probability with respect to the exceedance of an allowable maximal permanent displacement was evaluated and discussed. At the end of the paper, a case study of a typical Lebanese slope is presented and analyzed to illustrate this approach