Mathematical modeling of the fate of beach fill

Abstract

This paper describes mathematical approaches for calculating the fate of beach fill under wave action. General properties of the spatial and temporal behavior of fills under average longshore sand transport conditions are first reviewed through use of simple closed-form solutions of the sediment continuity equation. This well-known solution procedure is then extended to describe the collective movement of sediment or “longshore sand waves”. Because of the increasing use of beach fills as storm-protection barriers, the paper focuses on prediction of storm-induced beach erosion. An empirically based model is described and tested with a high-quality field data set of storm-induced beach erosion. One synthetic tropical storm and one synthetic extratropical storm representing typical mid-Atlantic storms with approximate 2–5-year return period are then used to simulate the erosion of two hypothetical beach fill configurations and the subsequent post-storm recovery process. Eroded volume and contour movement are evaluated as a function of storm type, fill cross section, grain size, and time. Quantitative and qualitative features of storm erosion are reasonably well reproduced, and calculated changes in beach fills impacted by the synthetic storms indicate that little erosion protection benefit is gained for moderate storms (2–5-year return period) by placing fills with grain sizes greater than 0.4 mm. Simulation of post-storm beach recovery is presently limited to qualitative reproduction of observed trends.