On limiting force profile, slip depth and response of lateral piles

A wealth of numerical analyses have been performed for lateral piles using finite difference, boundary element, and finite element methods, etc. Their essence, especially for a free-head pile, is to simulate the mobilisation of the maximum (limiting) force along the pile. This paper presents new closed-form solutions for a free-head pile embedded in an elastic–plastic, non-homogeneous soil by simulating pile–soil interaction using a series of springs distributed along the pile shaft. The stiffness of each spring is theoretically related to soil modulus, pile–soil relative stiffness, and loading properties; and the limiting force is catered for by a new generic expression. The solutions permit non-linear response of the pile to be readily estimated right up to failure. They compare well with continuum-based 3D finite element analysis of a pile embedded in stratified soils, irrespective of whether the limiting force (or pile–soil relative slip) is progressively mobilised downwards as the solutions assume or not. Presented in explicit forms, the solutions allow the dominant limiting force profile (LFP) to be back-estimated against measured data, and may be used as a boundary element for simulating beam–soil interaction under lateral resistance. Ranges of input parameters are provided, in light of predictions carried out to date against 62 tested piles in clay and sand. Finally, study on three typical piles is presented to elaborate the calculation procedure.