New Method for Computing Slip-Line Fields and Earth-Pressure Coefficients in Cohesionless Backfills

Abstract

A simplified numerical method was proposed for computing the slip-line field, as well as the associated earth-pressure coefficient, in a cohesionless backfill with an inclined surface lying behind an inclined rough wall. The potential failure zone, in either active or passive cases, was divided into the Rankine zone, which was rigorously obtained by the theory of plasticity, and the transition zone being further divided into a series of triangular slices. Within the transition zone, the theoretical relationship between the inclination of the interslice force and that of the slip surface was established by satisfying the Mohr–Coulomb failure criterion, and equations involving the forces on a typical slice were formulated in accordance with the force and moment equilibrium conditions. An iterative procedure was presented for computing the lateral forces on the wall by adjusting the inclination of the slip surface until the stress condition on the upper boundary of the transition zone was satisfied, resulting in the two families of slip lines. Several examples demonstrate the slip-line field configurations, and the computed earth-pressure coefficients were found to agree fairly well with those of other numerical methods. The determination of earth pressures and the associated critical failure surface play an important role in the design of retaining walls and other problems of geotechnical engineering. Conventional methods are frequently used for this purpose, but the errors involved are sometimes unacceptably large in cases of inclined rough walls. Hence, certain numerical methods have been employed, which, despite their sophistication, have not yet approached exact solutions. This paper presents a simplified numerical procedure for approaching theoretical slip-line fields and earth-pressure coefficients for the most frequently encountered cases of inclined rough walls with inclined cohesionless backfills. With this method, no assumptions need to be made about the shape of the slip surface or the inclinations of the forces acting on the boundaries of the triangular slices, into which the potential slip zone is divided. Furthermore, both the stress equilibrium condition and the Mohr–Coulomb criterion were completely satisfied within the failure zone and on its boundaries. An effective iterative procedure was provided for determining the slip surface location, which converged rapidly, resulting in an approximately theoretical configuration of slip-line field and associated earth-pressure coefficient values if a sufficiently large number of triangular slices were employed.