Analytical solution of plastic critical depth for active earth pressure on retaining wall

The problem of critical depth for plastic zone behind the retaining wall has not yet been solved well. The conventional calculation formula is only applicable for some special cases. This paper is based on the limit equilibrium theory, in which the backfill is treated as a perfectly elastoplastic material following the Mohr-Coulomb yield criterion; and it is assumed that a family of slip lines in the plastic zone are straight lines, i.e. the plane slip surfaces. The elastic overburden is put forward to replace the conventional tension crack; and a more reasonable slip wedge analysis model is established. The analytical solutions of the plastic critical pressure and critical depth and the possible maximum depth in plastic zone for active earth pressure on retaining wall in general case are deduced using limit equilibrium method. The calculation results show that the analytical solution of the plastic critical depth is identical with the result by iterative calculation in existing literatures and the conventional calculation formula is a special case of this analytical solution.