Dynamic analysis of flexible cantilever wall retaining elastic soil by a modified Vlasov–Leontiev model

•Seismic response of flexible cantilever wall is obtained analytically.•A new soil–wall displacement model for the transverse kinematics is proposed.•The unknown functions in the model are determined in terms of Hamilton׳s principle.•A mechanical model is improved to evaluate the proposed method physically.•Parametric study is adopted to investigate dynamic response of the soil–wall system.

Dynamic response of a flexible cantilever wall retaining elastic soil to harmonic transverse seismic excitations is determined with the aid of a modified Vlasov–Leontiev foundation model and on the assumption of vanishing vertical displacement of the soil medium. The soil–wall interaction is taken into consideration in the presented model. The governing equations and boundary conditions of the two unknown coupled functions in the model are derived in terms of Hamilton׳s principle. Solutions of the two unknown functions are obtained on the basis of an iterative algorithm. The present method is verified by comparing its results with those of the existing analytical solution. Moreover, a mechanical model is proposed to evaluate the presented method physically. A parametric study is performed to investigate the effects of the soil–wall system properties and the excitations on the dynamic response of the wall.