Simplified models for axial static and dynamic analysis of pile foundations

Abstract

Simplified methods for static and dynamic analysis of pile foundations under lateral loading are presented. Firstly, the classical model of a Beam on an elastic Winkler Foundation (BWF) and a number of formulas for the moduli of the associated springs and dashpots are briefly reviewed. This model (1) leads to a characteristic (“mechanical”) pile length, encompassing both pile stiffness and slenderness, which has no counterpart in continuum formulations of the problem; (2) reduces the number of dimensionless groups governing the response, by one. Secondly, solutions for stiffness of single piles are derived for both homogeneous and inhomogeneous soil conditions. These solutions are based on energy principles obtained using complex-valued shape functions analogous to those used in spectral finite-element methods, which account for phase differences in the response at different elevations down the pile. Use of these functions over existing formulations based on real-valued (static) shape functions, greatly improves the accuracy of the solution in the dynamic regime. It is also shown that the exponents in monomial expressions for the static stiffness of long piles, are constrained by a condition associated with the static condensation of the stiffness matrix, and that this condition is not satisfied in a number of formulae in literature. Thirdly, solutions for grouped piles are derived using the superposition approach of Poulos. To this end, a family of interaction factors accounting for pile-soil-pile interaction is reviewed. Results are presented in the form of dimensionless graphs and charts that elucidate critical aspects of the problem. Detailed comparisons with more rigorous numerical continuum solutions are provided.