Numerical modelling method for inelastic and frequency-dependent behavior of shallow foundations

This paper presents a novel framework with which the inelastic behavior and the frequency-dependent dynamic characteristics of soil-foundation system can be represented with a computationally efficient numerical model. The inelastic behavior of soil in the vicinity of a shallow foundation is represented with a macro-element which is based on the classical plasticity theory. The frequency-dependent property of soil-foundation system is represented with a recursive parameter model. The framework allows integration of both models such that both the inelastic behavior and the frequency-dependent characteristics can be captured. The proposed method is verified against FE analysis of a shallow foundation in the two dimensional parametric space of frequency and inelasticity. The verification shows that the model using the proposed framework can fully represent the inelastic cyclic behavior at low frequency excitation and the dynamic response at high frequency excitation. The method provides an approximate solution for the cases in-between, e.g. a foundation subjected large amplitude high-frequency excitation. As an application example, the method is applied to an analysis of a bridge pier subjected to earthquake loading.