DOI: https://doi.org/10.14710/kapal.v23i1.78197

Numerical Simulation of Wave Run-Up on Coastal Structure with Hexaloc Armour Units based on the SPH Method

Muhammad Brilliant Danu Ghazali Hafiz  -  Institut Teknologi Sepuluh Nopember, Indonesia
*Haryo Dwito Armono orcid scopus  -  Institut Teknologi Sepuluh Nopember, Indonesia
Muhammad Zikra orcid scopus  -  Institut Teknologi Sepuluh Nopember, Indonesia
Received: 2 Oct 2025; Published: 20 Dec 2025.
Open Access Copyright (c) 2025 Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Citation Format:
Abstract
Coastal abrasion and erosion pose a threat to shoreline stability in Indonesia, necessitating the implementation of reliable coastal protection structures, such as breakwaters. Accurate prediction of wave run-up is essential, as crest elevation is crucial, as it directly determines structural safety and the level of protection provided. This study aims to analyse wave run-up on rubble-mound breakwaters with Hexaloc armour units using the Smoothed Particle Hydrodynamics (SPH) method in DualSPHysics, to improve the accuracy and efficiency of design. The numerical model was developed using AutoCAD, SketchUp and simulated under varying wave heights (0.05 – 0.13 m), periods (1.1 – 1.5 s), and one versus two layer armour configurations. Validation was carried out by comparing simulation results with analytical and empirical formulations, particularly Ahrens’ equation. The results indicate that relative run-up ( ) increases with the Iribarren number but tends to stabilize at higher values. Numerical simulations produced run-up ratios ranging from 0.56 – 1.66 for a single layer and 0.63 – 0.86 for a double layer, while theoretical predictions yielded higher values of 1.59 – 2.39. The comparison demonstrates that single-layer Hexaloc arrangements produced slightly higher run-up than double layers, due to increased permeability. A strong correlation was obtained between SPH results and Ahrens’s theory, with a coefficient of determination of  for a single layer,  for a double layer, confirming that both approaches yield consistent outcomes.
Fulltext
Keywords: Run-up, Coastal Structure, Smoothed Particle Hydrodynamics, Hexaloc, Breakwater
Funding: Ministry of Higher Education and Research under contract Master Thesis Research Grant No 017/C3/DT.05.00/PL/2025

Article Metrics:

Article Info
Section: Research Articles
Language : EN
Recent articles
Numerical Simulation of Wave Run-Up on Coastal Structure with Hexaloc Armour Units based on the SPH Method Quantitative Analysis of Macro Foam Integration in Non Pressurized Manned Submersibles (NPMS): A Comprehensive Study of Buoyancy Management and Operational Performance More recent articles
Most cited articles
PENGARUH BENTUK LAMBUNG KAPAL TERHADAP POLA ALIRAN DAN POWERING PADA KAPAL PERAIRAN SUNGAI DAN LAUT HIGH SPEED SHIP TOTAL RESISTANCE CALCULATION (AN EMPIRICAL STUDY) PEMANFAATAN TENAGA ANGIN DAN SURYA SEBAGAI ALAT PEMBANGKIT LISTRIK PADA BAGAN PERAHU Karakteristik Geometri dan Pengaruhnya Terhadap Stabilitas Kapal Ferry Ro-Ro Indonesia ANALISA GERAKAN SEAKEEPING KAPAL PADA GELOMBANG REGULER More cited articles
  1. A. Muchlisin, W. Gathot, and P. Teguh, “Kajian Perubahan garis pantai menggunakan data satelit landsat di Kabuaten Kendal,” Penginderaan Jauh, vol. 8, no. 8, pp. 71–80, 2011
  2. P. Aryastana, I. G. A. P. Eryani, and K. W. Candrayana, “Perubahan Garis Pantai Dengan Citra Satelit Di Kabupaten Gianyar,” Paduraksa, vol. 5, no. 2, pp. 70–81, 2016
  3. N. Fadilah, Suripin, and D. P. Sasongko, “Identifikasi kerusakan pantai Kabupaten Bengkulu Tengah Provinsi Bengkulu,” in Prosiding Seminar Nasional Pengelolaan Sumberdaya Alam dan Lingkungan, 2013, pp. 337–341
  4. M. A. Marfai, L. King, J. Sartohadi, S. Sudrajat, S. R. Budiani, and F. Yulianto, “The impact of tidal flooding on a coastal community in Semarang, Indonesia,” Environmentalist, vol. 28, no. 3, pp. 237–248, 2008, doi: 10.1007/s10669-007-9134-4
  5. J. W. van der Meer, Conceptual Design of Rubble Mounds. Delft, The Netherlands: Delft Hydraulics, 1995
  6. X. Chen, B. Hofland, and W. Uijttewaal, “Maximum overtopping forces on a dike-mounted wall with a shallow foreshore,” Coast. Eng., vol. 116, pp. 89–102, 2016, doi: 10.1016/j.coastaleng.2016.06.004
  7. J. Yuan Li, Q. He Zhang, and Y. Jun Lu, “Numerical Simulation of Random Wave Overtopping of Rubble Mound Breakwater with Armor Units,” China Ocean Eng., vol. 35, no. 2, pp. 176–185, 2021, doi: 10.1007/s13344-021-0016-1
  8. B. Triatmodjo, Teknik Pantai. Yogyakarta, Indonesia: Beta Offset, 1999
  9. H. Schüttrumpf and M. R. A. Van Gent, “Wave overtopping at seadikes,” Coast. Struct. 2003 - Proc. Conf., vol. 40733, no. June, pp. 431–443, 2003, doi: 10.1061/40733(147)36
  10. T. Pang, X. Wang, R. A. Nawaz, G. Keefe, and T. Adekanmbi, “Coastal erosion and climate change: A review on coastal-change process and modeling,” Ambio, vol. 52, no. 12, pp. 2034–2052, 2023, doi: 10.1007/s13280-023-01901-9
  11. R. Vallarino Castillo, V. Negro Valdecantos, and J. M. del Campo, “Understanding the impact of hydrodynamics on coastal erosion in Latin America: a systematic review,” Front. Environ. Sci., vol. 11, no. October, pp. 1–24, 2023, doi: 10.3389/fenvs.2023.1267402
  12. J. Van der Meer and S. Sigurdarson, “Geometrical Design of Berm Breakwaters,” Coast. Eng. Proc., vol. 1, no. 34, p. 25, 2014, doi: 10.9753/icce.v34.structures.25
  13. J. J. Monaghan, “Smoothed Particle Hydrodynamics,” Proc. - Front. Educ. Conf., pp. 388–392, 1994, doi: 10.1109/fie.1994.580564
  14. A. J. C. Crespo et al., “DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics (SPH),” Comput. Phys. Commun., vol. 187, pp. 204–216, Feb. 2015, doi: 10.1016/j.cpc.2014.10.004
  15. C. Altomare et al., “Long-crested wave generation and absorption for SPH-based DualSPHysics model,” Coast. Eng., vol. 127, no. August 2016, pp. 37–54, 2017, doi: 10.1016/j.coastaleng.2017.06.004
  16. Z. Wei and R. A. Dalrymple, “SPH modeling of short-crested waves,” arXiv preprint arXiv:1705.08547, 2017
  17. J. W. Kamphuis, Introduction to Coastal Engineering and Management, vol. 11, no. 1. 2000
  18. R. A. Jackson, Design of Cover Layers for Rubble-Mound Breakwaters Subjected to Nonbreaking Waves. Vicksburg, MS: U.S. Army Engineer Waterways Experiment Station, Corps of Engineers, 1968
  19. M. Muttray, B. Reedijk, P. Bakker, and A. Van Den Berge, “Development of concrete breakwater armour units,” Proceedings, Annu. Conf. - Can. Soc. Civ. Eng., vol. 2003, pp. 331–342, 2003
  20. C. Irawan and H. D. Armono, “Numerical Study of the Proposed Hexaloc Concrete Armor Units under Static Loading,” IOP Conf. Ser. Earth Environ. Sci., vol. 1250, no. 1, 2023, doi: 10.1088/1755-1315/1250/1/012005
  21. M. Kreyenschulte, D. Schürenkamp, B. Bratz, H. Schüttrumpf, and N. Goseberg, “Wave run-up on mortar-grouted riprap revetments,” Water (Switzerland), vol. 12, no. 12, 2020, doi: 10.3390/w12123396
  22. H. Schuutrumpf, “Wave Run-Up and Wave Overtopping at Armored Rubble Slopes and Mounds,” pp. 383–409, 2009
  23. J. P. Ahrens, “Irregular wave runup on smooth slopes.” U.S. Army Coast. Eng. Res. Center, Coast. Eng. Tech. Aid, vol. 81–17, 1981
  24. J. De Rouck et al., “Wave run-up on a rubble mound breakwater,” Proc. Fifth Int. Conf. Mediterr. Coast. Environ. Oct. 23-27, 2001, Hammamet, Tunis, no. 1, pp. 1153–1164, 2001
  25. H. Mase, “Random Wave Runup Height on Gentle Slope,” J. Waterw. Port, Coastal, Ocean Eng., vol. 115, no. 5, pp. 649–661, 1989, doi: 10.1061/(asce)0733-950x(1989)115:5(649)
  26. S. L. Douglass, “Estimating extreme values of run-up on beaches,” Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 118, no. 2, pp. 220–224, 1992
  27. J. P. Ahrens, “Approximate upper limit of irregular wave runup on riprap,” Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 114, no. 4, pp. 614–635, 1988
  28. G. Argente, M. E. Gómez-Martín, and J. R. Medina, “Hydraulic stability of the armor layer of overtopped breakwaters,” J. Mar. Sci. Eng., vol. 6, no. 4, pp. 1–13, 2018, doi: 10.3390/jmse6040143
  29. R. Vacondio et al., “Grand challenges for Smoothed Particle Hydrodynamics numerical schemes,” Comput. Part. Mech., vol. 8, no. 3, pp. 575–588, 2021, doi: 10.1007/s40571-020-00354-1
  30. J. M. Domínguez et al., “State-of-the-art SPH solver DualSPHysics: from fluid dynamics to multiphysics problems,” pp. 1–43, 2021, doi: 10.1007/s40571-021-00404-2
  31. Ferryanto, O. Setyandito, Nizam, N. Yuwono, and W. Trihadi, “Wave run-up characteristic on armour layer breakwater using the smoothed particle hydrodynamics (SPH) method,” in IOP Conference Series: Earth and Environmental Science, Institute of Physics, 2024. doi: 10.1088/1755-1315/1324/1/012031
  32. M. A. Losada and L. A. Giménez-Curto, Mound Breakwaters Under Wave Attack. Santander, Spain: Dept. of Oceanographical and Ports Engineering, University of Santander, 1979

Last update:

No citation recorded.

Last update: 2025-12-20 19:26:13

No citation recorded.