Calculation and analysis of passive earth pressure under ultimate stress conditions

This paper develops a new method for calculating the passive earth pressure (PEP) on retaining walls under ultimate stress conditions. First, it is assumed that when the sliding wedge is in the limit equilibrium state, the soil elements on the slip surface, at the wall-soil interface, and within the wedge all reach the ultimate stress state obeying the Mohr-Coulomb criterion. The trajectory of principal stresses within the wedge takes the form of a circular arc. Subsequently, the PEP calculation equation for the retaining wall under ultimate stress conditions is derived based on the circular arc thin-layer unit method, with the unit obtained by layering along the principal stress trajectory. Furthermore, a formula for calculating the maximum friction angle (δ_max) at the wall-soil interface is proposed under passive conditions. The influence of the wall-soil interface friction angle on the distribution form, magnitude, resultant force action point of PEP, and overturning moment at the base of the retaining wall is then analyzed. Additionally, the stress state of soil elements within the sliding wedge is determined according to the Mohr-Coulomb failure criterion. Finally, the proposed method was validated against numerical simulations and model test data. The PEP under ultimate stress conditions represents the plastic upper-bound solution, while Coulomb's earth pressure serves as the plastic lower-bound solution, providing new insights for accurate assessment of PEP. The maximum wall-soil interface friction angle formulation established in this study offers a theoretical basis for determining the interface friction angle under passive conditions, particularly resolving the selection of interface friction angle when the backfill has a large internal friction angle (φ > 30°).