Modal analysis for kinematic response of flexible cantilever retaining wall

Seismic response of flexible cantilever wall retaining a semi-infinite viscoelastic soil under plane strain condition is investigated in this study. A novel modal analysis is derived based on the assumption of vanishing vertical displacements of the soil-wall system. The horizontal displacements of the soil-wall system are expressed by a series of modes in terms of the separate variable method. The boundary value problem is solved by considering the soil-wall interaction. Good agreement of the proposed solution results with those by the available methods confirms its accuracy. Closed-form solutions are derived for the following: (i) the displacement and stress field of the soil-wall system; (ii) the stiffness in the mth mode and dynamic Winkler modulus of the soil; (iii) translational and rotational response factors of the wall; (iv) the displacement amplification factor at the wall top. Kinematic response of the soil-wall system is evaluated in order to assess dynamic behavior of the wall.