Winkler Solution for Seismic Earth Pressures Exerted on Flexible Walls by Vertically Inhomogeneous Soil

A solution for the response of flexible retaining walls excited by vertically propagating shear waves in inhomogeneous elastic or viscoelastic soil is obtained using the weak form of the governing differential equation of motion associated with the Winkler representation of earth pressures, as a function of relative displacement between the wall and free-field soil. Inputs to the model include the soil shear wave velocity profile, flexural stiffness of the wall, elastic boundary conditions at the top and bottom of the wall, motion at the surface of the retained soil, and mass distribution along the wall. The proposed solution was first verified against an available closed-form Winkler solution for uniform soil and then with elastodynamic solutions for a wall supporting an infinite uniform elastic soil. A validation exercise was then performed using centrifuge data from flexible underground structures embedded in sand, shaken by suites of ground motions. Seismic earth pressures and bending moments were also computed using limit-equilibrium procedures based on horizontal inertial forces acting within an active wedge. The proposed solution compares favorably with the experimental data, whereas limit equilibrium procedures produce biased predictions.