Horizontal Soil Reaction of a Pile Segment in Cohesive Soil with Interface Slip

Under lateral loading, relative slip between a pile and the surrounding soil can occur at displacements as small as 10 − 4 pile diameters. Conventional p – y formulations, widely used in the analysis of slender laterally loaded piles, assume perfect bonding between pile and soil and do not explicitly account for the progressive interface slip, which can yield unconservative overpredictions of the overall pile stiffness. This note presents a novel semianalytical theoretical solution to predict the degradation of the elastic p – y stiffness due to the progressive slip at a cohesive pile-soil interface. The solution is developed in two dimensions by expanding the stress and displacement fields around the pile in Fourier series in the angular direction, and employing discretization at the pile-soil interface and outer boundary to satisfy boundary conditions. The formulation provides a computationally efficient alternative to finite-element and finite-difference analyses, against which it is validated, while preserving physical transparency and simple calibration. The resultant solution allows progressive interface behavior to be incorporated in a p – y analysis, providing a more realistic representation of lateral pile response under serviceability limit states.