Seismic displacement of gravity walls by a two-body model

Gravity walls retaining dry soil are modeled as a system of two bodies: (a) the gravity wall that slides along the wall-foundation soil boundary and (b) the critical soil wedge in the soil behind the wall. The strength of the system is defined by both the frictional and the cohesional components of resistance. The angle of the prism of the critical soil wedge behind the wall is obtained using the limit equilibrium method. The model accounts for changes in the geometry of the backfill soil behind the wall by considering the displacements at the end of each time step under limit equilibrium. The model shows that the standard (single) block model is over-conservative for the extreme case of critical-to-applied-seismic acceleration ratios less than about 0.30, but works well for cases where this ratio ranges between 0.5 and 0.8. The model is applied to predict the seismic displacement of gravity walls (a) tested in the shaking-table and (b) studied numerically by elaborate elasto-plastic analyses.