Derivation of Shukla's generalized expression of seismic passive earth pressure on retaining walls with cohesive-frictional backfill by the inclined slice element method

Shukla developed a generalized expression for the dynamic passive earth pressure from cohesive -frictional soil backfill by considering the equilibrium of a passive failure wedge (International Journal of Geotechnical Engineering 2013; 7(4): 443-446). In this paper, the inclined slice element approach is used to derive this expression under seismic loading conditions. Using this method, the nonlinear distribution of passive earth pressure and its application position are obtained with a few assumptions. By taking the failure surface as a plane, the analytical expression for the critical angle of failure surface is also derived. The generalized expressions can be applied to the calculation for cohesive or cohesionless backfill for specialized cases static and dynamic conditions. The total passive forces from the derived expressions are consistent with Rankine's expression, Coulomb's expression, and Mononobe-Okabe's expressions.