A Comprehensive Formulation for Soil-Foundation Stiffness Considering Multi-Story Structures: Extension of Winkler’s Model for Strip Footings

Soil-Structure Interaction (SSI) is a critical factor in seismic design, particularly for structures located on soft soils, where the dynamic interplay between the foundation and the surrounding soil significantly influences structural behavior during seismic events. This interaction affects not only the seismic response of the structure but also the transfer and distribution of forces between the foundation and the soil medium. As such, accurately accounting for SSI in seismic analyses is essential to ensure both safety and performance. Traditional approaches to modeling SSI often employ springs with specified stiffness values, which act as simplified representations of the more complex soil-structure system. These springs are designed to replace full-scale, computationally intensive soil-structure models. The stiffness of these springs depends on various parameters, including soil properties and the characteristics of both the substructure and superstructure. However, despite their wide application, many existing methods are limited in scope.
Previous research has primarily focused on calculating soil stiffness beneath basic foundation shapes, such as circular or rectangular foundations, while neglecting more complex scenarios, such as the presence of middle and edge strips in strip foundations. Additionally, most computational relationships available in the literature rely solely on geometric properties of the foundation. These approaches fail to account for the superstructure’s influence, including its height, weight and natural period, which restricts their applicability in real-world engineering design scenarios. This gap in the understanding of SSI for strip foundations necessitates the development of more comprehensive and practical models.
This study addressed these limitations by proposing new relationships to calculate the stiffness of soil beneath strip foundations, explicitly considering the presence of superstructures with heights ranging from 1 to 15 stories. The analysis was based on extensive three-dimensional numerical simulations conducted using the Finite Element Method (FEM) in OpenSees platform. The models employed soft soils especially from groups D and E, as classified by seismic design codes, to ensure the results were applicable to a broad range of soil conditions. The study investigated the combined effects of foundation dimensions, soil properties, and the number of stories of the structure on the resulting soil stiffness.
The findings revealed that soil stiffness was influenced not only by the physical dimensions of the foundation but also by the dynamic properties of the overlying structure. A comparison between the proposed model and experimental data demonstrated excellent agreement, underscoring the model’s reliability. For example, the average inter-story lateral displacement in both the proposed and experimental models was calculated as 0.02 meters. Moreover, the maximum lateral displacement at the roof level was 24 mm in the experimental model and 23.4 mm in the proposed model. These results confirm the high accuracy and robustness of the proposed relationships.
The newly developed relationships offer a practical, efficient, and precise alternative to more complex numerical simulations, making them highly valuable for engineering design applications. By incorporating both soil and superstructure characteristics, the proposed model bridges the gap in existing research and provides a reliable framework for analyzing and designing structures that account for soil-structure interaction in seismic conditions