Three-parameter Kerr soil model: finite element formulation and applications in transient dynamic analyses

Abstract

Soil-structure interaction is a topic of paramount importance in civil engineering, as the method of soil modeling directly influences the static and dynamic performance of structures supported by elastic foundations. Simplified models, such as Winkler's, while widely adopted, fail to adequately represent the effects of distributed stiffness and lateral interaction. In this context, multiparameter models, like those proposed by Pasternak and Kerr, offer a more realistic characterization of soil behavior. This work aims to develop and implement the explicit formulation of the stiffness matrix for Kerr's soil model, based on the Finite Element Method, and apply it to transient dynamic analyses of beams. The methodology employs Euler-Bernoulli beam finite elements with two nodes and four degrees of freedom, discretized mass in condensed form, and mass-proportional damping. The equation of motion is solved using the Backward Acceleration Method, an implicit, symplectic, and energy-conserving temporal integration scheme. Three dynamic problems involving beams on elastic foundations are analyzed: a free-ended beam subjected to a concentrated moment, a simply supported beam under variable dynamic loading, and a cantilever beam under a concentrated force. In all cases, the performance of Winkler, Pasternak, and Kerr soil models is compared. The principal results indicate that the Winkler model leads to larger displacements and lower frequencies due to its simplified formulation. The Pasternak model, by incorporating lateral interaction, reduces oscillation amplitudes and periods. The Kerr model, conversely, exhibits the most rigid response, with smaller displacements and higher natural frequencies. Comparison with literature results confirms the validity of the proposed model, highlighting its applicability in dynamic analyses of beams on elastic foundations.