Calculation Method for Active Non-limit Earth Pressure of Cohesive Soil on a Rigid Wall Based on the Nonlinear Mohr–Coulomb Failure Criterion

Abstract

This work introduces a theoretical framework for determining the active non-limit earth pressure of cohesive soil on a base-rotating rigid wall. The framework incorporates the nonlinear Mohr–Coulomb failure criterion, the Duncan–Chang hyperbolic stress–strain relationship, the log-spiral potential failure surface in retained soil, and a horizontal slice method for the earth pressure evaluation. The proposed method allows quantitative determination of displacement-dependent earth pressure and its distribution along the wall back. Practical wall movement in the at-rest state is considered, and the tension crack depth near the soil surface is calculated based on the soil tensile strength cut-off. Analysis results highlight the nonlinear variation of the mobilized soil shear strength vertically, influenced by the nonlinear Mohr–Coulomb failure criterion. As the wall rotation increases, the earth pressure follows a convex parabolic distribution with a tension failure zone near the soil surface and no pressure at the wall base. The resultant of the earth pressure reduces and its application point descends while the tension crack depth expands, though always remaining less than the Rankine’s earth pressure. A practical example shows that the at-rest earth pressure can be up to 1.3 times greater than the active earth pressure, with the resultant application point approximately 5% higher. Parameter study exhibits that the active non-limit earth pressure correlates nonlinearly with the soil ultimate tensile stress and nonlinear coefficient, particularly as wall movement increases. Active non-limit earth pressures vary within 86% across different soil cohesions, and up to 50% under varying ultimate tensile stresses and nonlinear coefficients. Overturning safety factors of the wall in the active non-limit state differ significantly from those in the at-rest state, especially under varying soil cohesions.