Erosional equivalences of levees: Steady and intermittent wave overtopping

Present criteria for acceptable grass covered levee overtopping are based on average overtopping values but do not include the effect of overtopping duration. This paper applies experimental steady state results for acceptable overtopping to the case of intermittent wave overtopping. Laboratory results consisting of velocities and durations for acceptable land side levee erosion due to steady flows are examined to determine the physical basis for the erosion. Three bases are examined: (1) velocity above a threshold value, (2) shear stress above a threshold value, and (3) work above a threshold value. The work basis provides the best agreement with the data and a threshold work value and a work index representing the summation of the product of work above the threshold and time are developed. The governing equations for flow down the land side of a levee establish that the flows near the land side levee toe will be supercritical. Wave runup is considered to be Rayleigh distributed with the runup above the levee crest serving as a surrogate for overtopping. Two examples illustrating application of the methodology are presented. Example 1 considers three qualities of grass cover: good, average, and poor. The required levee elevations for these three covers differ by 1.8 m. The results for Example 1 are compared with the empirical criteria of 0.1 liters per second per meter (l/s per m), 1.0  l/s per m, and 10.0  l/s per m. It is found that the required crest elevation by the methodology recommended herein for the “poor” cover is only slightly lower than for the criterion for average overtopping of q=10.0  l/s per m but significantly lower than for the overtopping criterion of 1.0 and 0.1 m/s per m. Example 2 considers two durations of the peak surge with the result that the longer duration peak surge requires a levee that is higher by approximately 0.8 m.