Analytical Solution to Ultimate Lateral Pressure on a Vertical Plate in Undrained Soil

Abstract

For a vertical plate emerging on the surface of undrained cohesive soil, the adhesion between the plate and soil considerably impacts the lateral soil pressure on it. However, very few closed-form solutions have been published to address this seemingly simple problem; they either are restricted to certain conditions or overpredict the ultimate lateral pressure. This paper applies both the lower-bound and upper-bound methods of plasticity to develop a rigorous analytical solution to the ultimate lateral pressure, allowing for the undrained shear strength of soil to increase linearly with depth and a general adhesion on the interface. A method is presented to extend the static stress field throughout the soil mass to validate the lower-bound values. The developed solution is found to be an exact solution for homogeneous soil; the predicted results for nonhomogeneous soil fall within a narrow range bounded by the lower and upper limit values, with the range of errors mostly being within 1%. The solution reduces to the classic Bell’s relationship in the undrained condition if ignoring the adhesion on the interface. When the full active pressure behind the plate is mobilized, the upper-bound solution is rigorous but the lower-bound one is not unless examining a smooth surface. However, the predicted results are close enough to more rigorous ones to be used in engineering practice.