Vibration of Foundations on Incompressible Soils with No Elastic Region

Abstract

The dynamic response of rigid foundations supported on a homogeneously nonlinear elastoplastic half‐space is investigated in the context of nonlinear finite‐element (FE) analysis. The constitutive equation for the half‐space is described by a bounding surface plasticity model with a vanishing elastic region. This model is based on a total stress formulation in which the plastic modulus is determined from an interpolated exponential hardening rule. The incompressibility constraint is handled via the mean dilatational formulation of the B‐method. The computational problem associated with the disparity between the longitudinal and shear wave velocities is addressed in the context of radiation boundary condition. The relative significance on the foundation response of the more rapidly propagating P waves, as they reflect spuriously from the FE boundaries, is investigated. It is shown that the reflected P waves have no significant influence on the dynamic response of finite‐size foundations; nor do they have any significant effect on the response of strip foundations vibrating in the rocking mode. Furthermore, it is shown that nonlinear effects can have a significant influence on the dynamic response of vibrating foundations over a wider range of excitation frequencies than originally thought. The numerical simulations presented in this paper are performed using data on real soils determined from resonant column, cyclic triaxial, and other one‐dimensional “radial” loading tests.