Non-linear coupled approach for the evaluation of seismic slope displacements

The design procedures to evaluate earthquake-induced sliding displacements typically refer to three different approaches: simplified methods; displacements methods and advanced dynamic methods. In the first class of methods, empirical relationships are used to predict the permanent slope displacement. The second class includes simplified dynamic analysis, by means of the conventional Newmark rigid block model, as well as through its improvements to account for soil deformability. The dynamic site response and the sliding block displacements are computed separately in the “decoupled” approach or simultaneously in the “coupled” analysis (stick-slip model). The advanced dynamic methods are based on finite element (FEM) or finite difference (FDM) formulations, which permit to account for topography and heterogeneity by two or three dimensional analysis. The paper describes the developments of a 1D lumped-mass stick-slip model for a layered subsoil including more generalized assumptions than a previous version (Ausilio et al., 2008). The depth of the sliding surface is considered not necessarily coincident with that of the bedrock, and located in a generic layer. This latter can be identified during the analysis. In the non-linear site response analysis, a recent soil damping formulation was used (Phillips & Hashash, 2009). In this formulation, a reduction factor modifying the extended Masing loading/unloading strain-stress relationship was introduced. The predictions of the coupled stick-slip model with non-linear soil behaviour were compared with the results of the equivalent linear approach for ideal slopes to show the effects of non linearity on seismic performance. Besides, the results show that the sliding surface depth, automatically researched, is function of main ground motion parameters.