Slip Surface and Active Earth Pressure of Cohesionless Narrow Backfill behind Rigid Retaining Walls under Translation Movement Mode

Abstract

A slip-failure surface forms in the backfill soil upon sufficient yielding or movement of the wall that retains the backfill soil. The shape of the slip-failure surface plays an important role in estimating the lateral earth pressure, including its magnitude and location of its resultant force. As retaining walls at times must be built with narrow and constrained backfill space, this study presents an analytic derivation of the slip-surface shape in narrow cohesionless soil behind a rigid retaining wall under translation movement mode of the wall. Results of a series of experimental tests were presented to demonstrate the effects of narrow backfill spaces on forming the slip surface and that the slip surfaces are curvilinear planes developed from the heel of the retaining wall to the crest of the backfill. Based on the experimental findings, a rigorous analytic derivation using a variational limit equilibrium method is conducted to determine the governing equation for the shape of the slip surface in the narrow backfill soil. The analysis reveals that the active failure plane of the narrow soil behind a rigid retaining wall agrees well with a logarithmic spiral plane. The derived log-spiral slip-surface plane is further verified by experimentally observed slip surface and measured active lateral earth pressure. Substantial discrepancy was observed in the lateral earth pressure distribution between the logarithmic spiral slip surface and the assumed linear planar slip surface, indicating that the assumption of a linear planar slip surface in narrow backfill may result in significantly erroneous estimation and lead to an overly conservative and uneconomical design. Furthermore, a threshold value of 0.5 is identified for the backfill width/height ratio that distinguishes the narrow backfill from a sufficiently wide backfill.