Engineers require estimates of tolerable overtopping limits for grass-covered levees, dikes, and embankments that might experience steady overflow. Realistic tolerance estimates can be used for both resilient design and risk assessment. A simple framework is developed for estimating tolerable overtopping on grass-covered slopes caused by slowly-varying (in time) overtopping discharge (e.g., events like storm surges or river flood waves). The framework adapts the well-known Hewlett curves of tolerable limiting velocity as a function of overflow duration. It has been hypothesized that the form of the Hewlett curves suggests that the grass erosion process is governed by the flow work on the slope above a critical threshold velocity (referred to as excess work), and the tolerable erosional limit is reached when the cumulative excess work exceeds a given value determined from the time-dependent Hewlett curves. The cumulative excess work is expressed in terms of overflow discharge above a critical discharge that slowly varies in time, similar to a discharge hydrograph. The methodology is easily applied using forecast storm surge hydrographs at specific locations where wave action is minimal. For preliminary planning purposes, when storm surge hydrographs are unavailable, hypothetical equations for the water level and overflow discharge hydrographs are proposed in terms of the values at maximum overflow and the total duration of overflow. An example application is given to illustrate use of the methodology.
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