Smoothed Particle Hydrodynamics Simulations of Wave Run-Up over Hexaloc Armour on Rubble-Mound Breakwaters

Indonesian beaches are increasingly vulnerable to abrasion and erosion, requiring reliable protection such as breakwaters. Since crest freeboard determines the level of safety, wave run-up predictions must be accurate. This study evaluates run-up on a 1:2 rubble-mound breakwater slope armored with Hexaloc using SPH (DualSPHysics) to improve design accuracy and efficiency. The geometry was constructed in AutoCAD and SketchUp. The simulation covered wave heights of 0.05-0.13 m, periods of 1.1-1.5 s, and single-layer and double-layer armor configurations. The numerical results were validated against analytical-empirical formulations, particularly the Ahrens relation. Ru/H increases with rising Iribarren number and then tends to plateau at high values. SPH produces Ru/H 0.538-1.076 (single-layer) and 0.588-1.216 (double-layer), while theoretical predictions are higher: 1.616-2.299 and 1.59-2.30. In the test range, single- and double-layer Hexaloc produced comparable run-ups; two layers were equivalent or slightly higher. The SPH-Ahrens fit was highly linear (R² = 0.9999 single-layer; 0.9948 double-layer), but SPH still predicted lower Ru/H than Ahrens.