Evaluation of the Active and Passive Pseudo-dynamic Earth Pressures using Finite Element Limit Analysis and Second-order Cone Programming

This paper presents a numerical model for the evaluation of the active and passive seismic earth pressure coefficients against the retaining structures subjected to pseudo-dynamic loading using the lower bound limit analysis coupled with finite element discretization and second-order cone programming. The active and passive pseudo-dynamic earth pressures are formulated as functions of the earthquake non-dimensional wavelength as well as the local site effects originated from the backfill damping characteristics and the elastic properties of the underlying foundation. Results generally show that the retaining wall tends to instability by increasing the seismic intensity. In particular, it is shown that when the input acceleration at the base of the wall increases, the active and passive lateral earth pressure coefficients undergo increment and decrement, respectively. Moreover, the pseudo-dynamic active and passive earth pressures are bounded between their static and pseudo-static equivalents. Indeed, it is revealed that when trivial wavelengths are encountered, the influence of seismic loading vanishes due to the counteracted inertia force increments and the static solution is reached. On the contrary, when very high wavelengths are assumed, especially for shorter walls, the acceleration fields become homogeneous lending support to the contention that the pseudo-dynamic earth pressure starts from the pseudo-static asymptote values. The soil-wall interface friction angle is also observed to considerably affect the limit earth pressure coefficients due to the augmented shear resistance provision. Furthermore, foundation elasticity is shown to be as important as the backfill damping characteristics in the pseudo-dynamic site response analysis.