ABSTRACT
Studies have reported that the magnitude of seismic acceleration is significantly altered when the heterogeneity in wave velocities is considered. The stability of retaining walls is of paramount importance in geotechnical engineering. While studies are available to understand the influence of inhomogeneous wave velocities on the active thrust of granular soils, there is no research on passive stability under such conditions. The present study computes the passive resistance of dry granular soil retained by a vertical, smooth, and rigid retaining wall under harmonic base excitation. The harmonic base shaking in horizontal and vertical directions gives rise to shear and primary waves in the medium. The inhomogeneity in wave velocities has been modeled using a continuous parabolic function. The space-time-dependent horizontal and vertical seismic acceleration profiles used in the present study satisfy the stress-free boundary condition at the ground surface and displacement compatibility at the base. These complete seismic acceleration profiles have been used in the finite element lower bound limit analysis approach to estimate the seismic passive resistance. The infimum to statically admissible passive thrust conforming to the conditions by the lower bound collapse theorem is found using the second-order cone programming (SOCP) method. The passive earth pressure coefficient’s variation with the dimensionless frequency has been studied in a spectral sense for different levels of inhomogeneity. The duality of collapse theorems and the robust primal-dual interior point algorithm of the SOCP solver have been utilized to numerically estimate the nodal coordinates lying on the boundary of significant nodal velocity’s length. A three-parameter power law function is fitted to these numerical points to analytically characterize the failure surface for dry granular earth under passive conditions. These failure surfaces have been rigorously validated using the results of different numerical and analytical studies. The physical significance of these collapse patterns has been ascertained using shear strain rate and Mohr stress circles.
