Geometric and Undercutting Controls on the Failure of Steep Scarps in Cohesionless Sand: A Parametric Investigation

ABSTRACT

Steep, unvegetated scarps in cohesionless sand form when waves and elevated water levels cut into the seaward face of beaches and foredunes during storms. These features are short‐lived, are typically one to a few metres high and are geotechnically distinct from the consolidated, weakly cemented coastal bluffs that reach tens of metres in height. The mechanics that determine whether such a scarp slides or topples once its toe is undercut are not well quantified. This study uses the Material Point Method to examine how scarp geometry and progressive toe undercutting jointly control failure mechanisms in cohesionless sand. The model was validated against a wave flume experiment on a 1.0 m scarp, reproducing the measured saturation profile, pore pressure evolution, failure timing and failure mode. Twenty‐eight configurations were then simulated, spanning scarp height 1.0–2.0 m and face slope 60°–85°, with the measured wave forcing and the notch progression from a calibrated empirical relation applied in every case. Three results follow. First, although wave action raises pore pressure and saturation throughout the scarp, failure is initiated by the stress redistribution that accompanies undercutting rather than by moisture infiltration. Notch growth produces a consistent stress signature before failure: Deviatoric stress concentrates along the incipient slip surface, compression builds at the notch root, and confinement is lost above the notch. Second, the transition between failure modes is abrupt in geometric terms. At 75°, raising the scarp from 1.1 to 1.2 m switches the dominant mechanism from toppling to shear. Shear failures occur for 1.2 m and mobilize two to three times the sediment volume of the toppling failures, which are confined to low ( 1.1 m), steep ( 75°) scarps. Third, none of the geometries tested could stand on friction alone, since every face is steeper than the 39° friction angle of the sand. The standing configurations are held by the apparent cohesion that matric suction supplies in the unsaturated zone, and a distinct class of tall, steep configurations collapses before any undercutting is imposed because that contribution can no longer balance the self‐weight moment. The face angle at which this occurs falls as the scarp grows, from 70° at  m to 85° at 1.5 m, with no configuration at or below 1.25 m reaching it. The resulting stability chart separates the slope–freeboard plane into standing, shear‐prone, toppling‐prone and geometrically unstable domains. The scarp heights modelled here span the range these features occupy in the field, so the findings apply directly to storm‐cut scarps in cohesionless beach and dune sand. They are not intended to describe cemented or stratified coastal bluffs, whose stability is governed by cohesion and structure rather than by geometry alone.