A simple model for inelastic footing response to transient loading

This paper presents a mechanical analogue which models the response of a rigid circular footing on an ideal elastoplastic half‐space to transient loads. In the rational analysis of pile‐driving dynamics, the response of soil at the base of a pile is often approximated by a footing on a semi‐infinite half‐space. Most existing base models employ the well‐known Lysmer analogue to model the elastic response of the soil at the pile base, and account for the inelastic soil behaviour through the inclusion of a plastic slider with a slip load equal to the ultimate failure load of the footing. The improved model provides a force response which is significantly closer to the ideal response than existing models. The paper commences with a review of analytical solutions for the dynamic response of a rigid circular footing on an elastic half‐space. Existing mechanical analogs for the system are reviewed, and an automatic matching process proposed which improves the accuracy of the analogs under transient loading. The inelastic response is then studied using the finite element method, and the mechanical analogs are modified to allow representation of the observed inelastic behaviour. Examples are presented illustrating close agreement between the proposed models and finite element analyses for a range of Poisson's ratio. The improved models have direct application for one‐dimensional models of pile driving, particularly in the back‐analysis of data from dynamic testing of piles. They are also applicable to studies of dynamic compaction.