General Solution for Active Earth Pressure on Rigid Walls Under Strip Surcharge on Retained Soils Using Variational Method

Abstract

Hypothesis of the slip surface shape in retained soils makes most of the existing methods for active earth pressure on rigid walls be of no logical basis. The present work aims to rigorously calculate the earth pressure under general conditions. Based on the limit equilibrium conditions of a soil mass retained by rigid walls under a distanced backfill strip surcharge, a variational calculus method was developed to compute the active earth pressure on the walls. A functional relationship between the earth thrust and critical slip surface of the retained soil, and the normal stress acting on it without considering the hypothesis of the slip surface shape, were established. A unified closed-form solution for the earth thrust was derived and could be obtained using an implicit solution technique via MATLAB. The analysis model is of high generality, and the effects of 11 basic parameters on the earth thrust and the corresponding slip surface were analyzed. Some of the considered parameters were the soil properties, soil–wall interface friction angle, wall height, strip surcharge, dip angle between the wall back and soil top surface, horizontal net distance from the wall back to the surcharge, and distribution width of the surcharge. The examples showed that the earth thrusts calculated using the proposed method were approximately 4–16% higher than Coulomb’s solutions but 3–11% lower than traditional stress distribution solutions based on the elastic theory. The proposed method in which the critical slip surface shape need not be subjectively assumed has comparatively more extensive applicability.