Predicting Threshold Entrainment Mass for a Boulder Beach

Mark S. Lorang


The critical threshold mass for boulders composing a beach is the mass of the largest stone entrained by the hydraulic forces associated with wave breaking and swash run-up. For any given storm event there is a maximum boulder mass that can be moved and another slightly larger boulder that has the minimum mass necessary to remain stable. Two equations are derived: one to estimate critical threshold mass and another to estimate minimum stable mass for boulders on a beach. The equations incorporate: stone density, beach slope, breaking wave height, water depth, wave period, run-up height, maximum swash velocity and average swash velocity. In both equations the wave force applied to the beach face is scaled relative to the elevation that wave energy raises the water surface. Scaling the wave force relative to the run-up elevation results in a critical threshold formula. This is given as equation (45). Its predictions accurately match field data giving the largest boulder transported on a beach during storm events. Scaling the wave force relative to the breaking wave height at the toe of the beach results in a stability formula. This is given as equation (46). It predicts stable mass in the range defined by the Hudson formula. Equation (46) has an advantage over the Hudson formula by incorporating the physically important parameters of wave period and swash velocity. Both equations could be useful in the initial evaluation and design of dynamic revetments constructed with quarry stone.


Wave runup; swash velocity; coastal engineering; dynamic revetment; gravel beach

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