Slip-line solution to passive earth pressure on retaining walls

Based on the limit equilibrium theory, the backfill is treated as a perfectly elastic-plastic material which follows the Mohr-Coulomb yield criterion, and is assumed to be an isotropic, homogeneous and incompressible (or non-expansive) perfectly continuous medium. The stress singularity and its stress boundary condition are introduced, and a statically determinate and solvable mathematical model for the limit equilibrium boundary value problem is established without considering the stress-strain relationship. Then the slip-line field and stress field in plastic zone of the backfill are solved by use of the slip-line method, furthermore, the passive earth pressure on retaining walls and the reaction on slip surfaces are derived. Geometric and mechanical similarity principle is presented by means of dimensionless analysis. The results show that the slip-line solution to the passive earth pressure is generally less than or equal to the Coulomb's solution, and the classical Rankine's earth pressure or the classical Coulomb's earth pressure satisfying non-singularity condition is in accordance with the slip-line solution, and the Hencky's first theorem and second theorem are not generally applicable.