Experiments and numerical modeling of wave overtopping and overflow on dikes

Earthen levees are designed for little wave overtopping during a design storm but excessive overtopping and overflow can occur due to the combined effects of an extreme storm, sea level rise and land subsidence. The transition from little wave overtopping to excessive wave overtopping and overflow on an impermeable smooth levee is examined in wave-flume experiments consisting of 107 tests. A numerical model based on time-averaged continuity, momentum and wave action equations is developed to predict the cross-shore variations of the mean and standard deviation of the free surface elevation and depth-averaged fluid velocity of irregular waves in the presence of onshore steady flow. An empirical formula is proposed to express the wave overtopping and overflow rate in terms of the computed variables on the seaward slope of the levee. The formula is shown to predict the measured overtopping and overflow rates within a factor of about 2. The numerical model is applied to an earthen levee in Louisiana to show its practical utility but will need to be verified using field data if available. Furthermore, the numerical model will need to be extended to predict levee erosion and breaching.