Comparison of analytical and numerical approaches for stress analysis beneath a slab foundation

The design of slab foundations relies on the accurate assessment of the interaction between the structure and the soil base, particularly on the reliable determination of contact stresses. The choice of calculation method directly affects the results of bearing capacity evaluation and the prediction of soil deformations. Analytical approaches, such as the corner points method, are traditionally widely used in engineering practice due to their simplicity and relatively low labor intensity. However, these methods are based on simplified assumptions regarding the stress–strain state of the soil, which can lead to errors under specific conditions, such as non-uniform loading, complex geometry, or heterogeneous soil composition. Modern numerical methods, particularly finite element modeling, allow for a more detailed consideration of soil behavior, including elastic–plastic properties and realistic boundary conditions. Nevertheless, they require significant computational resources, expertise in specialized software, and comprehensive input data on soil properties. Therefore, a comparative study of the results obtained using the analytical corner points method and numerical modeling is relevant both for verifying the accuracy and applicability limits of traditional approaches and for refining influence coefficients to adapt calculation methods to current engineering requirements. Understanding the quantitative and qualitative differences between these methods will enable engineers to make informed decisions when selecting a calculation approach depending on the design conditions, while also optimizing the balance between accuracy, available resources, and calculation time. The article presents a comparison of contact stresses in a soil base under a rectangular slab foundation obtained by the analytical corner points method and finite element numerical modeling for elastic–linear and elastic–plastic soil models (with the Mohr–Coulomb strength criterion). The aim of the study is to refine the influence coefficients used in the corner points method, to identify quantitative and qualitative differences between the approaches, and to outline the boundaries of their correct application. The comparison revealed significant discrepancies not only in the values of contact stresses but also in the shape of their distribution surface. Preliminary discrepancy coefficients for the studied case have been determined.