Calculation method of passive earth pressure for translating retaining walls

The magnitude of earth pressure is closely related to the deformation state of retaining walls. To describe the progressive shear failure characteristics of soil behind the wall under passive conditions, a novel analytical method for calculating passive earth pressure considering wall deformation is proposed. Based on Coulomb earth pressure theory and the hyperbolic mechanical model, the concepts of point deformation failure rate and area (length) deformation failure rate are introduced to quantify the stress states along the rupture surface. A static equilibrium model of a wedge body is established, and an analytical solution for passive earth pressure under non-limit conditions is derived. The results show that passive earth pressure increases nonlinearly with wall deformation, with the most significant pressure increments occurring in the upper one-third and middle regions of the wall height. An increase in the wall-soil friction angle δ leads to a decrease in the rupture angle and a more nonlinear distribution of earth pressure. The proposed method shows good agreement with Coulomb theory and experimental results, verifying its accuracy and engineering applicability. This method provides a new theoretical framework for evaluating passive earth pressure in deformable retaining structures.