Ultimate Bearing Capacity of Vertically Uniform Loaded Strip Foundations near Slopes Considering Heterogeneity, Anisotropy, and Intermediate Principal Stress Effects

Accurate prediction of the bearing capacity of foundations near slopes remains challenging when soils exhibit heterogeneity and anisotropy. Although numerical simulations can account for these effects with high precision, they are computationally demanding and provide limited physical insight. Analytical solutions that can explicitly incorporate spatial variability, directional dependence, and the influence of intermediate principal stress are still lacking. This study addresses this gap by developing an analytical solution for the ultimate bearing capacity of strip foundations near slopes based on the Unified Strength Theory (UST). The method assumes a uniformly distributed surface load and a single-sided failure mode, while introducing heterogeneity and anisotropy coefficients to represent the depth dependent and directional variation of cohesion. Validation against published theoretical, numerical, and experimental results demonstrates strong agreement, with a maximum deviation of 6.2%. Parametric sensitivity analysis indicates that increasing the heterogeneity coefficient from 0 to 1 enhances bearing capacity by 67.9–83.4%, while increasing the anisotropy coefficient from 0.6 to 1.4 reduces it by 20.8–22.3% for different base roughness. Neglecting the intermediate principal stress results in a 64.5–67.9% underestimation of the ultimate bearing capacity with different anisotropy coefficients and base roughness. The proposed analytical model based on the UST provides improved quantitative accuracy and theoretical generality, enabling safer and more economical design of foundations near slopes under heterogeneous and anisotropic soil conditions.