Winkler Stiffness Intensity for Flexible Walls Retaining Inhomogeneous Soil

The Winkler method is often adopted for the evaluation of the seismic response of retaining walls, and several closed form solutions in the literature present values for Winkler stiffness intensity (i.e., stiffness per unit area of wall) for certain simplified conditions. A common assumption in these solutions is that the wall is a rigid body. This paper presents an extensive parametric analysis of Winkler stiffness intensity for flexible elastic walls retaining inhomogeneous elastic soil. The finite element software framework OpenSees is used in the DesignSafe cyberinfrastructure to perform the analyses. The wall is cantilevered from a fixed base and its flexural stiffness is varied relative to the soil stiffness to cover a reasonable range. Pseudo-static excitation is applied to soil elements using horizontal body forces, producing variable wall and soil displacements. The Winkler stiffness intensity is then computed based on (i) the horizontal stress mobilized at the soil-wall interface, and (ii) the difference in displacement between the wall and the soil in the free-field. Results show that both wall flexibility and soil inhomogeneity significantly influence the Winkler stiffness intensity. In particular, the Winkler stiffness intensity for flexible walls can be up to three times greater than the values computed for rigid walls due to shear stresses mobilized at the wall-soil interface as the wall rotates due to flexure. This result indicates that Winkler stiffness intensity is not a fundamental soil parameter, and that values must be carefully selected to account for boundary conditions.