Square block foundation resting on an unbounded soil layer: Long-term prediction of vertical displacement using a time homogenization technique for dynamic loading

In this contribution, the structural long-term response of a square block foundation resting on a soil layer over rigid bedrock is investigated in the time domain. To efficiently predict the vertical displacement of the square block foundation at periodic loading, a time homogenization technique is employed to deal with different time scales in the response of the soil-foundation system and its long-term evolution due to the foundation's inelastic and nonlinear material behavior (continuous damage, discontinuous damage, viscoelastic, elastoplastic). To correctly represent the laterally unbounded soil layer over rigid bedrock, the stiffness of the linear elastic soil is first computed in the frequency domain via the modified scaled boundary finite element method. The soil stiffness in the frequency domain is then transferred to the time domain via a lumped-parameter model representation. Subsequently, the time homogenization technique including dynamic effects is developed and applied to obtain the response of the foundation-soil system in the time domain. Consolidation of the soil layer (linear elastic) is not addressed in this contribution.