Exact Slip-Line Solution for Seismic Passive Earth Pressure Considering Stress Singularity and Its Application

The slip-line method can accurately predict the passive earth pressure on retaining walls, but the exact slip-line solution considering stress singularity under general conditions has not been reported in the literature. Based on the limit equilibrium theory, the backfill behind the wall is assumed to be an ideal rigid-plastic material that follows the Mohr–Coulomb failure criterion. Various influence parameters are taken into account in the analysis model. The slip-line stress field in the plastic zone behind the wall under general conditions is solved by using the slip-line method, following which the exact slip-line solution to pseudostatic seismic passive earth pressure considering stress singularity is derived. Making use of the dimensionless analysis method, a new passive earth pressure equation is deduced, the geometric and mechanical similarity principle is proposed, and the effects of stress singularities including normal singularity, nonsingularity, and abnormal singularity on the slip-line solution are revealed. The results of this study show that the present slip-line solutions to seismic passive earth pressure agree well with the results available in the literature and are always less than or equal to the planar failure-surfaces based Coulomb’s solution; for the cohesionless soil satisfying the nonsingularity conditions, the slip-line solutions are completely consistent with the results by the Mononobe–Okabe method. The verification confirms that the passive earth pressure derived from the slip-line stress field with folding can be directly used for engineering design. The proposed Kp contour-map method is expected to be a practical method for accurate estimation of passive earth pressure in engineering application.