SPH–porous media modelling of wave overtopping at rubble-mound revetments

This study presents a comprehensive validation and application of an advanced Smoothed Particle Hydrodynamics (SPH) method for investigating wave overtopping at rubble-mound coastal revetments. The numerical framework is based on the SPH–porous media model developed by Jandaghian et al. (2025), incorporating volume-adaptive particle formulations and enhanced stabilization techniques. We evaluate the performance of this model in simulating long-duration breaking-wave interactions with permeable coastal revetments under regular and irregular wave conditions across multiple structural designs. A theoretical benchmark case of seepage flow through multi-layer porous media with distinct porosity and grain size is first considered to assess numerical accuracy and convergence. The model is then applied to simulate monochromatic wave overtopping of a permeable revetment protecting a vertical seawall, including calibration of drag force parameters and particle resolution. Subsequently, a systematic validation and application study is conducted for irregular wave overtopping at rubble-mound revetments under three scenarios with multiple rock-armoured layers. Results demonstrate that the model accurately reproduces wave propagation and overtopping processes across all cases, supported by qualitative and quantitative analyses of wave characteristics and discharge rates, while also identifying model limitations. The findings emphasize the importance of calibrating empirical drag coefficients for physically consistent overtopping estimates. Overall, this work provides the first comprehensive evidence of the reliability and robustness of the SPH–porous media model for wave overtopping performance, supporting design optimization and risk assessment of coastal protection structures.