Statistical design of submerged artificial oyster reefs using Design of Experiments and clustering strategies

The implementation of artificial oyster reefs as a Nature-based Solution to enhance ecological benefits and shoreline protection represents a prominent area of research. Nevertheless, the wave attenuation performance of multiple underwater artificial reefs has yet to be subjected to comprehensive investigation. To address this gap, we investigated numerically the wave attenuation produced by a sequence of submerged artificial oyster reefs, taking into account a range of incoming wave conditions and configurations of the artificial reefs themselves. A large number of simulations have been designed using an approach based on the Design of Experiment theory, namely the D-optimal approach. The large dataset obtained has been analyzed using unsupervised machine learning techniques, i.e. the weighted K-means. The results showed a clear separation of the combinations of physical variables that led to the lowest transmission coefficients. In particular, three dimensionless variables were identified as being of particular significance for minimizing the transmission coefficient, namely the submergence of the oyster reefs, the length of the oyster reef in relation to the incident wavenumber, and the number of oyster reefs. Relative water depth, wave steepness, distance between adjacent oyster reefs, and seabed slope were found to play a minor role. Based on the results, we suggested an optimal statistical design strategy in order to reach a wave transmission coefficient as low as 0.5, provided the specific characteristic of the site (design wave, slope of the shoaling zone, and water depth). These findings will provide guidance for practical application. © 2025 The Authors.