Effects of Displacement Hardening on the Seismic Design of Anchored Walls

A reliable assessment of earthquake-induced permanent displacements is a fundamental step for both displacement-based and force-based methods applied to the seismic design of embedded anchored walls. Acceleration reduction factors recommended by the codes for a force-based design of these structures derive from parametric studies of the performance of gravity walls or slopes. This may lead to either conservative or unconservative results and is certainly misleading from the point of view of the physics of the problem. Based on the results of an extensive numerical study, this work clarifies the mechanisms by which anchored walls accumulate permanent displacements during earthquakes, showing that full mobilization of soil passive strength requires displacements of the order $u_{\mathrm{r}}/H\approx 1\%–2\%$, making the assumption of rigid-perfectly plastic behavior of the system unsuitable. Moreover, both the critical acceleration and the pattern of final displacements depend on the plastic mechanism effectively activated within the soil-wall-anchor system. The issue of the proper choice of performance factors to be used in a force-based design of anchored walls is also addressed, and a new method is outlined for a preliminary calculation of the permanent displacements of the wall. Finally, the paper critically reviews two methods recently proposed in the literature to compute earthquake-induced wall displacements. All three methods account for the soil-wall system nonlinearity and hardening during the earthquake. The results discussed herein, together with the complementary work presented by the same authors in a companion paper, provide a thorough conceptual framework for the performance-based seismic design of anchored walls.