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 the free-field soil. Inputs to the model include the soil shear wave velocity profile, the flexural stiffness of the wall, the elastic boundary conditions at the top and bottom of the wall, the motion at the surface of the retained soil, and the mass distribution along the wall. The proposed solution is 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 is then performed using centrifuge data from flexible underground structures embedded in sand, shaken by suites of ground motions. Seismic earth pressures and bending moments are 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