Passive Earth Pressure and Soil Arch Shape: A Two-Dimensional Analysis

This paper introduces an analytical method for passive earth pressure calculation based on a rigorous stress field analysis within the sliding wedge. Unlike traditional horizontal layer methods, this approach directly solves for the stress state at any point within the wedge by analyzing the equilibrium of 2D differential soil elements under appropriate boundary conditions, eliminating the need for a priori assumptions about the soil arch shape. The method yields the passive earth pressure distribution on the retaining structure and derives the soil arch shape analytically from major principal stress trajectories. This derived arch shape differs notably from conventional circular or parabolic assumptions, especially at higher soil–wall friction angles. Parametric studies show that the passive earth pressure coefficient increases with internal friction angle and surcharge. However, a key finding is the non-monotonic dependence of the passive earth pressure coefficient on the soil–wall friction angle, contrasting with many existing theories. Comparisons show predictions by the proposed method align well with experimental data, particularly offering a better representation of pressure distributions in the lower regions of retaining walls compared to Coulomb theory and other existing methods.