A Differential Equation and the Lipschitz Condition for Pile Ultimate Bearing Capacity Based on Static Load Test

Abstract

This paper provides an alternative method for determining the ultimate bearing capacity of pile foundations based on Static Load Test (SLT) results. A differential equation modelling the relation between loads and settlements of SLT is presented as well as its solution in a form of continuous function. The notion of Lipschitz continuity in mathematical analysis is adopted and is applied to the function for finding the most critical load, which is defined as the ultimate bearing capacity. For a validation, interpretations of an SLT data using Davisson’s method and the method proposed in this paper are compared. The result shows that the interpretation using the proposed method is slightly greater than that of Davisson’s and gives a valid result.