Kelvin–Voigt and Boltzmann Viscoelastic Models for Footing’s Soil–Structure Interaction

This paper presents a practical numerical procedure for the study of structures on foundations subjected to soil consolidation settlements, using the Finite Element Method (FEM) coupled with the Boundary Element Method (BEM). A theoretical application is presented for a structure built on saturated soft soil, employing the Kelvin–Voigt and Boltzmann viscoelastic models. The Kelvin–Voigt model is suitable for situations where uniform or negligible initial settlements are assumed before the onset of soil consolidation, whereas the Boltzmann model allows for the consideration of differential movements, including both immediate and time-dependent displacements. This study shows that, although the same viscoelastic parameters are adopted for both models, the differences in internal forces and resulting displacements can be significant due to the distinct relative stiffnesses. The choice of viscoelastic model directly impacts the prediction of structural behavior. The analyses were conducted considering an iterative coupling between the FEM and BEM systems, using an MATLAB R2024a routine developed by the authors. Despite the differences between the models, the results obtained were consistent with the technical literature, reinforcing the applicability of the proposed procedure.