Formulating Wave Overtopping at Vertical and Sloping Structures with Shallow Foreshores Using Deep-Water Wave Characteristics

Christopher H. Lashley*, Jentsje Van Der Meer, Jeremy D. Bricker, Corrado Altomare, Tomohiro Suzuki, Katsuya Hirayama

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
17 Downloads (Pure)


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.

Original languageEnglish
Article number04021036
Number of pages13
JournalJournal of Waterway, Port, Coastal and Ocean Engineering
Issue number6
Publication statusPublished - 2021


  • Dike
  • Emergent toe
  • Infragravity waves
  • Shallow foreshore
  • Vertical wall
  • Wave overtopping
  • Wave transformation


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