Underestimation of Vertical Stresses in Soil Foundations Using Analytical Methods: Numerical Substantiation Considering Nonlinear Base Behavior

Abstract

raditional methods for foundation subgrade analysis are frequently based on linear-elastic models, which may lead to inaccurate estimations of the compressible thickness, particularly under high load intensities. This study aims to quantify the error of the analytical corner point method in comparison with advanced nonlinear constitutive soil models across diverse geotechnical conditions. To achieve this, a series of numerical experiments using the finite element method (FEM) was conducted for a reinforced concrete raft foundation with dimensions of 1.8×2.6 m. Two types of subgrades were analyzed: sandy soil (E=30 MPa) and clayey soil (E=15 MPa). Calculations were performed using various constitutive models, with a primary focus on the Hardening Soil Small Strain (HSsmall) model, which accounts for strain-dependent stiffness degradation.

The research results verify the hypothesis of "vertical stress concentration" within nonlinear models. It was established that the geometry of the "stress bulb" undergoes significant transformation depending on the soil type: in clayey subgrades, a more intensive stress penetration depth is observed compared to the predictions of the elastic solution. Furthermore, a redistribution of contact pressures in the central and corner zones of the raft was recorded. It is proven that the error of the analytical method increases proportionally to the load magnitude and the decrease in the soil's deformation modulus. The simulation results demonstrate the necessity of implementing correction factors for the standard tabular stress distribution coefficients α. The application of the HSsmall model provides the most reliable representation of the stress-strain state (SSS), which is critical for avoiding the underestimation of stresses in the deeper layers of the foundation base.