A practical Equivalent Linear Spring–Damper model for nonlinear soil–structure interaction under seismic loading

Conventional soil–structure interaction (SSI) analyses often rely on linear soil representations, which are attractive for routine engineering applications but may provide inaccurate structural response estimates under moderate to strong seismic loading due to the neglect of nonlinear soil behaviour. Although advanced nonlinear models can capture these effects, their computational and modelling demands limit their practical use. This study proposes an Equivalent Linear Spring–Damper (ELSD) formulation that retains the simplicity of spring-dashpot SSI models while incorporating key nonlinear soil effects. The model follows a non-iterative strain-compatible equivalent linear approach, in which foundation stiffness and damping are modified through empirical relationships that estimate shear modulus reduction and damping increase from the effective peak ground acceleration (EPGA) of the applied earthquake and the site shear-wave velocity ( v s , 30 ). These relationships are derived from three-dimensional finite element simulations covering clay-type soft soil conditions and ground motions with varying intensity and frequency content, and are evaluated through SSI simulations over a broad range of seismic demands. The results show that the proposed formulation provides a closer approximation of nonlinear SSI response than the conventional linear model, particularly under stronger shaking where stiffness degradation and damping increase become more significant. The proposed framework therefore offers a computationally efficient tool for practical seismic SSI analysis within the investigated calibration range, although its applicability beyond these conditions requires further assessment.