General limit equilibrium method for lateral earth force

Abstract

The calculation of the lateral earth force using the limit equilibrium method of slices is an indeterminate problem. An assumption regarding the direction or the magnitude of certain forces, or the position of the line of thrust can be used to render the problem determinate.A general formulation for the lateral earth force is derived in accordance with the assumptions involved in the general limit equilibrium (GLE) method. An assumption concerning a direction of the interslice forces is utilized to solve the problem of indeterminancy. Horizontal force equilibrium conditions within a sliding mass are used to compute the magnitude of the active and passive forces. The point of application of the lateral earth force is obtained by considering moment equilibrium for each slice.The coefficient of lateral earth force obtained from the GLE method agrees closely with the results obtained from most other theories. Comparisons are made to the Coulomb theory (i.e., using a planar slip surface) and other theories using a curved or a composite slip surface.Data are presented for the case of a horizontal cohesionless backfill against a vertical wall. The lateral earth force can be contoured on the grid of centers of rotation. These contours have a bell-shaped characteristic and can be used to locate the critical center of rotation.The main advantage of this method lies in its capability to analyze arbitrarily stratified soil deposits with complex geometries. Different conditions of pore-water pressure, shear strength, and external loading can be accommodated in the analysis. Factors of safety greater than 1.0 can be applied to the shear strength of the soil for design purposes. Keywords: lateral earth force, active force, passive force, general limit equilibrium, interslice forces, and coefficient of lateral earth force.