Theoretical and numerical modeling of a shallow foundation stiffness based on the theory of elastic half-space

The paper presents the derivation of equations for the calculation of the spring constants k_y, k_z, and k_ϕ and the spring coefficients β_y, β_z, and β_ϕ used in the modeling of a foundation with a rectangular base on elastic soil. All the equations were derived based on information provided in literature, for example, Barkan, Gorbunov-Possadov, and Whitman et al. To demonstrate the application of these equations in practice, two numerical models of a reinforced concrete frame structure that was built on soil were created using Abaqus FEA software. Model A represents a complex three-dimensional numerical model that consists of a reinforced concrete frame structure, which has a soil layer beneath it. Model B represents a simple three-dimensional numerical model consisting of a reinforced concrete frame structure, where the stiffness of the soil layer beneath the structure was modeled with vertical, horizontal, and rocking spring constants applied to the bottom of each foundation. Due to the nonlinear boundary condition used in the supports of the concrete frame model, such as contact and friction, all the involved loads were incorporated into a single load case, and a large displacement formulation was used in the analysis. The authors focused on the method of a simplified modeling of frame structures founded on soil. To conduct comparative analyses, two columns and two beams from each model were selected, from which the internal forces and displacements were compared. The findings of the comparative analysis are presented in tables and then discussed.