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.