Laboratory Experiments on the Influence of the Wave Spectrum Enhancement Factor on a Rubble Mound Breakwater
Abstract
:1. Introduction
2. Materials and Methods
2.1. Model Set-up
2.2. Wave Spectrum
- α: Phillips constant
- fp is the frequency which corresponds to the peak value of the spectral density function
- σ = (σa if f ≤ fp; σb if f ≥ fp)
- γ varies from 1 to 7
- H1/3: Significant wave height
- T1/3: Significant wave period
- Tp: Peak period.
2.3. Wave Conditions
2.4. Measurements of Damage, Pressure on the Crown Wall and Overtopping
- Beginning of damage: Corresponds to the displacements of the armour blocks over a distance greater than or equal to D50 (mean diameter of armour blocks);
- Irribaren damage: Holes created in the armour surface cause the exposure of the sub-layer;
- Beginning of destruction: Corresponds to the beginning of damage to the sub-layer;
- Destruction: the sub-layer is exposed to the effect of incident waves.
- V: Total of the overtopping volume measured at the end of the test
- B: Width of the receptacle
- T: Test duration.
3. Results
3.1. Overtopping
- The measured average overtopping rate (q) for a spectrum with γ = 3.3 is 35% to 100% greater than with the spectrum with γ = 1.
- For a wave spectrum generated with γ = 1, the measured average overtopping has almost the same value for the two peak periods Tp = 16 s and Tp = 18 s.
3.2. Water Pressure on the Crown Wall
- For a given value of the peak period (Tp), the measured maximum pressure for a spectrum with γ = 3.3 is 20% higher than the spectrum with γ = 1.
- For a given value of the PEF, the maximum peak period generated the higher value of maximum wave pressure.
3.3. Armour Block Stability
- For the first tests established for waves with Hs varying from 4 to 5 m, the variation of the PEF parameter has no consequence on armour stability. This is mainly due to the fact that the structural response is below the threshold of the damage beginning level;
- For the rest of the tests where we approached the destabilization limits (Hs varying from 5 to 6 m), we noted that the influence of the PEF becomes more meaningful for higher peak periods.
4. Discussion
5. Conclusions
- The PEF variation has a significant effect on the pressure exerted on vertical structures and on mean overtopping flow;
- The stability of the armour layers is not sensitive to the variation of the PEF for intermediate wave periods (12 to 14 s). This observation is consistent with the results of armour stability tests conducted by Van der Meer and Pilarczyk [36] for narrow and wide wave spectra. However, for longer waves, higher values of the PEF lead to more severe damage levels. The influence of the PEF on armour layer response is therefore highlighted for long period ocean waves.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Notation | Unit | Scaling Factor |
---|---|---|
Length, width, wave height | m | N |
Surface | m2 | N2 |
Volume | m3 | N3 |
Time | s | N1/2 |
Velocity | m/s | N1/2 |
Mass | kg | N3 |
Density | kg/m3 | 1 |
Test Reference | Density (kg/m3) | Full-Scale Median Weight (kg) | Modelled Median Weight (kg) |
---|---|---|---|
Front armour layer | 2.4 | 7200 | 0.267 |
Rear armour layer | 2.4 | 3600 | 0.133 |
Underlayer in front side | 2.6 | 600 | 0.022 |
Underlayer in rear side | 2.6 | 350 | 0.013 |
Core | 2.6 | 500 | 0.018 |
Test Reference | Return Period | Tp (s) | PEF | Hs |
---|---|---|---|---|
DAK21135 | 200 years | 14 | 1 | 6 m |
DAK21136 | 200 years | 14 | 3.3 | 6 m |
DAK21137 | 100 years | 16 | 3.3 | 5.5 m |
DAK21139 | 100 years | 16 | 1 | 5.5 m |
DAK21138 | 100 years | 18 | 3.3 | 5.5 m |
DAK21146 | 100 years | 18 | 1 | 5.5 m |
DAK21154 | 200 years | 16 | 3.3 | 6 m |
DAK21155 | 200 years | 16 | 1 | 6 m |
DAK21156 | 200 years | 18 | 3.3 | 6 m |
DAK21157 | 200 years | 18 | 1 | 6 m |
Test | Return Period | Tp [s] | γ | Hs | Q (L/s/m) |
---|---|---|---|---|---|
DAK21137 | 100 years | 16 | 3.3 | 5.5 | 26 |
DAK21139 | 100 years | 16 | 1 | 5.5 | 19 |
DAK21138 | 100 years | 18 | 3.3 | 5.5 | 46 |
DAK21146 | 100 years | 18 | 1 | 5.5 | 24 |
DAK21154 | 200 years | 16 | 3.3 | 6 | 62 |
DAK21155 | 200 years | 16 | 1 | 6 | 41 |
DAK21156 | 200 years | 18 | 3.3 | 6 | 88 |
DAK21157 | 200 years | 18 | 1 | 6 | 43 |
Water Level [m/Zh] | Hs (In −25 m/Zh) | Tp (In −25 m/Zh) | Observations for γ = 3.3 | Observations for γ =1 |
---|---|---|---|---|
+4.21 | 4 m | 12 s | No damage | No damage |
+3.61 | 4.4 m | 14 s | No damage | No damage |
+4.21 | 5 m | 12 s | No damage | No damage |
+4.21 | 5 m | 18 s | No damage | No damage |
+3.61 | 5 m | 18 s | No damage | No damage |
+4.21 | 5.5 m | 14 s | Oscillation of 2 blocks | Oscillation of 1 block |
+4.21 | 5.5 m | 18 s | Oscillation of 2 blocks | Oscillation of 2 blocks |
+ 3.61 | 5.5 m | 18 s | Oscillation of 2 blocks | Oscillation of 2 blocks |
+ 4.21 | 6 m | 18 s | Extraction of 3 blocks | Oscillation of 3 blocks |
+ 3.61 | 6 m | 18 s | Extraction of 3 blocks | Oscillation of 4 blocks |
+ 4.21 | 6.6 m | 18 s | Extraction of 3 blocks | Oscillation of 4 blocks |
γ =1 | γ =3.3 | Rayleigh Distribution | |
---|---|---|---|
H1/10/Hs | 1.248 | 1.253 | 1.271 |
Hmean/Hs | 0.639 | 0.636 | 0.626 |
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Bakali, H.; Aouiche, I.; Serhir, N.; Zahir, Y.; Ziane, E.h.; Harti, A.; Zerhouni, Z.; Anthony, E. Laboratory Experiments on the Influence of the Wave Spectrum Enhancement Factor on a Rubble Mound Breakwater. J. Mar. Sci. Eng. 2022, 10, 2035. https://doi.org/10.3390/jmse10122035
Bakali H, Aouiche I, Serhir N, Zahir Y, Ziane Eh, Harti A, Zerhouni Z, Anthony E. Laboratory Experiments on the Influence of the Wave Spectrum Enhancement Factor on a Rubble Mound Breakwater. Journal of Marine Science and Engineering. 2022; 10(12):2035. https://doi.org/10.3390/jmse10122035
Chicago/Turabian StyleBakali, Hosny, Ismail Aouiche, Najat Serhir, Youssef Zahir, El hassan Ziane, Abderrazak Harti, Zakariae Zerhouni, and Edward Anthony. 2022. "Laboratory Experiments on the Influence of the Wave Spectrum Enhancement Factor on a Rubble Mound Breakwater" Journal of Marine Science and Engineering 10, no. 12: 2035. https://doi.org/10.3390/jmse10122035
APA StyleBakali, H., Aouiche, I., Serhir, N., Zahir, Y., Ziane, E. h., Harti, A., Zerhouni, Z., & Anthony, E. (2022). Laboratory Experiments on the Influence of the Wave Spectrum Enhancement Factor on a Rubble Mound Breakwater. Journal of Marine Science and Engineering, 10(12), 2035. https://doi.org/10.3390/jmse10122035