Exact equivalent model for a laterally-loaded linear pile-soil system

When using the substructure method for a pile-supported structure, it is common to adopt a simple element (equivalent model) to simulate the load-deflection behavior of a laterally loaded pile. Conventionally, two kinds of equivalent models, the uncoupled spring model and the equivalent cantilever model, are used to approximate the lateral pile-head response of a laterally loaded pile. These equivalent models can not work equally-well for different pile arrangements and loading conditions because the stiffness matrix (or flexibility matrix) of these equivalent models do not entirely match that of the original pile-soil model. The response obtained will never give correct displacements and forces simultaneously. To solve this problem, this study develops an exact equivalent model, in which an artificial lateral spring is added at the base of the cantilever to modify the fixed-base cantilever model so that it can completely represent the pile-head behavior of a laterally loaded pile-soil system. For verification, comparison studies between the proposed model and conventional equivalent models are conducted to show the effectiveness of the proposed model.