A Generalized Newmark Method for the assessment of permanent displacements of flexible retaining structures under seismic loading conditions

In recent years, much attention has been paid to performance-based design of flexible retaining structures, focusing on the evaluation of the permanent deformations of the soil-structure system caused by given seismic loads, rather than on the assessment of conventional safety factors determined by comparing seismic actions and system resistance (typically based on limit equilibrium methods). While only a few examples of fully coupled, dynamic numerical simulations of flexible retaining structures adopting advanced cyclic/dynamic models for soils can be found in literature, a number of recent works have proposed simple modifications of the classical Newmark method to assess the permanent displacements of the structure at the end of the seismic excitation. Most of the aforementioned works refer to cantilevered diaphragm walls, for which the failure mechanisms at limit equilibrium are relatively simple to describe. However, this is not the case for anchored or propped flexible structures, where the velocity field at failure under a pseudo-static seismic load is quite complex and can be affected by the plastic yielding of the wall upon bending. In this work, upper- and lower-bound limit analysis FE solutions are used as a basis for the development of a Generalized Newmark Method, based on the accurate evaluation of the critical accelerations for the retaining structure and the corresponding failure mechanisms. It can be shown that, under two reasonable simplifying assumptions, a Newmark-like scalar dynamic equation of motion can be derived which, upon double integration in time, provides the magnitude of the permanent displacements associated to each failure mechanism, as provided by limit analysis. This procedure allows the reconstruction of the full permanent displacement field around the excavation, not just the evaluation of horizontal soil movements at selected points. The application of the method to a number of selected prototype excavations demonstrates the potentiality of the proposed approach, which can be extended easily to other complex geotechnical structures.