Dynamic Impedance Functions of a Square Foundation Estimated with an Equivalent Linear Approach

Abstract

This paper presents the role of the intensity of an earthquake on the estimation of dynamic impedance functions. For various seismic shaking we will have different nonlinear behavior of the soil, which may have significant effects on the amplitude and shape of the dynamic stiffness and damping coefficient. However, under the assumption of linear elastic behavior of the soil, loss of soil stiffness under strong shaking is not taken into account in the dynamic impedance functions. The dynamic impedance functions are estimated using an equivalent linear process and compared relative to the linear elastic case. The vibrations originate from the rigid foundation embedded in the soil layer, which are subjected to harmonic loads of translation, rocking, and torsion. The dynamic responses of the rigid surface foundation are solved from the wave equations by taking into account their interaction. The solution is formulated using the frequency domain boundary element method (BEM), in conjunction with Kausel-Peek Green’s function for a layered stratum and the thin layer method (TLM) to account for the interaction between the soil-foundation. A parametric analysis is performed for surface foundation in a semi-infinite soil limited by bedrock and subjected to three earthquake records.