Lateral translation of a circular pile in cohesive soil: exact plasticity solution

A fundamental problem in theoretical soil mechanics, and one with an interesting history, involves determining the lateral force per unit length required to translate a rigid circular pile (or other cylindrical object) through a body of rigid–plastic cohesive soil. A dimensionless factor $α$ is typically used to specify the shear strength of the pile–soil interface relative to that of the soil. Previous studies using the method of characteristics, or slip-line method, have succeeded in establishing an exact solution for the special case of a fully rough pile (⁠$α=1$⁠). The slip-line solution developed in this paper is shown to be exact (i.e. to give strict lower- and upper-bound collapse loads that coincide) over the full range of $α$⁠, including the complementary special case of a perfectly smooth pile (⁠$α=0$⁠). The exact value of the lateral bearing capacity factor N varies from 9·20117 to 11·9400 as $α$ varies from 0 to 1. To verify that the incomplete slip-line stress field can be extended throughout the soil in a manner that is both statically and plastically admissible, over the full range of $α$⁠, traditional analytical extension methods employing slip lines and stress discontinuities are supplemented by a novel numerical stress field extension technique based on finite-element limit analysis.