Slip-line solution to active earth pressure on retaining walls

Abstract

The slip-line method is commonly used to solve the limit earth pressure on retaining walls, but to date there are still a number of problems that have not yet been solved. Based on limit equilibrium theory, the backfill is considered to be an ideal elastic-plastic material, which obeys the Mohr–Coulomb yield criterion, and is assumed to be an ideal continuous medium that is isotropic, homogeneous and incompressible (or non-expansive). Various factors of influence are considered in the calculation model. An elastic overburden is proposed as a replacement for traditional tension cracks. A new concept – stress singularity – and its stress boundary conditions are introduced, and a statically determinate and solvable mathematical model for the limit equilibrium problem is established without considering the stress–strain relationship of the soil. The slip-line stress field in the plastic zone of the backfill is solved by using the slip-line method, following which the active earth pressure on retaining walls and the soil reaction on the slip surface are derived. The geometric and mechanical similarity principle is first proposed by dimensionless analysis. The results show that the slip-line solution to active earth pressure is generally always greater than or equal to Coulomb's solution, and coincides with Rankine's solution or the classical Coulomb solution that satisfies the non-singularity conditions. Hencky's first and second theorems are not generally applicable.