Formulating wave overtopping at vertical and sloping structures with shallow foreshores using deep-water wave characteristics

The state-of-the-art formulas for mean wave overtopping (q) assessment typically require wave conditions at the toe of the structure as input. However, for structures built either on land or in very shallow water, obtaining accurate estimates of wave height and period at the structure toe often proves difficult and requires the use of either physical modeling or high-resolution numerical wave models. Here, we follow Goda's method to establish an accurate prediction methodology for both vertical and sloping structures based entirely on deep-water characteristics—where the influence of the foreshore is captured by directly incorporating the foreshore slope and the relative water depth at the structure toe (htoe/Hm0,deep). Findings show that q decreases exponentially with htoe/Hm0,deep due to the decrease of the incident wave energy; however, the rate of reduction in q decreases for structures built on land or in extremely shallow water (htoe/Hm0,deep = 0.1) due to the increased influence of wave-induced setup and infragravity waves—which act as long-period fluctuations in mean water level—generated by nonlinear wave transformation over the foreshore.This work is part of the Perspectief research program All-Risk with Project No. B2 which is (partly) financed by NWO Domain Applied and Engineering Sciences, in collaboration with the following private and public partners: the Dutch Ministry of Infrastructure and Water Management (RWS); Deltares; STOWA; the regional water authority, Noorderzijlvest; the regional water authority, Vechtstromen; It Fryske Gea; HKV consultants; Natuurmonumenten; and waterboard HHNK. Dr. Corrado Altomare acknowledges funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie, Grant No. 792370Peer ReviewedPostprint (published version