Wave overtopping and crown wall stability of cube and Cubipod-armored mound breakwaters

[EN] The influence of the type of armor on wave overtopping on mound breakwaters is usually represented by the roughness factor. However, different values of roughness factor for the same armor unit are given in the literature. Thus, the roughness factor depends not only on the type of armor, number of layers and permeability but also on the formula and database considered. In the present thesis, a new methodology based on bootstrapping techniques is developed and applied to characterize the roughness factors for different armor units. Differences up to 20% appeared when comparing the optimum roughness factors with those given in the literature. Armor porosity greatly affects the roughness factor and the armor stability: higher armor porosities reduce wave overtopping as well as hydraulic stability. Therefore, armor porosity values usually recommended in the literature should be used to avoid damage during lifetime. Formulas with few variables are easy to apply but they allow the roughness factor to absorb the information not explicitly included in the formula. However, the CLASH neural network avoids this problem and gives excellent estimation for wave overtopping on mound breakwaters. In this thesis, a new formula which emulates the behavior of the CLASH neural network is developed. The new formula has 16 parameters, six dimensionless input variables (Rc/Hm0, Ir, Rc/h, Gc/Hm0, Ac/Rc and a toe berm variable based on Rc/h) and two reduction factors (¿f and ¿ß). The new formula is built-up after systematic simulations using the CLASH neural network and provides the lowest prediction error. Wave overtopping on mound breakwaters can be minimized by increasing the crest freeboard, usually with a concrete crown wall. Crown walls must resist wave loads and armor earth pressure to be stable. In the present study, small-scale test results with cube- and Cubipod-armored mound breakwaters are used to develop a new estimator for calculating horizontal and up-lift forces from waves. The new formulas include four dimensionless input variables (¿f Ru0.1%/Rc, (Rc-Ac)/Ch, ¿(L_m/G_c ) and Fc/Ch) and the crown wall geometry. The roughness factor selected for overtopping prediction is used to consider the type of armor. Up-lift forces decreased sharply with increasing foundation levels. The new formulas provide the lowest error when predicting wave forces on crown walls.[ES] La influencia del tipo de elemento del manto sobre le rebase de diques en talud se caracteriza habitualmente mediante el factor de rugosidad (¿f). Sin embargo, en la literatura existen diferentes valores del factor de rugosidad para el mismo tipo de elemento. El factor de rugosidad no depende solo del tipo de elemento, número de capas y permeabilidad del núcleo sino también de la formulación y de la base de datos empleada. En la presente tesis se desarrolla y aplica una nueva metodología basada en técnicas de bootstrapping para caracterizar estadísticamente el factor de rugosidad de diferentes elementos (entre ellos el Cubípodo) sobre diferentes formulaciones de rebase. Se observan diferencias de hasta el 20% entre los factores de rugosidad óptimos y los que se proporcionan en la literatura. La porosidad del manto afecta notablemente al factor de rugosidad pero también a la estabilidad del manto; mayores porosidades proporcionan menor rebase pero también menor estabilidad hidráulica. Por ello, las porosidades de diseño recomendadas deben emplearse para evitar daños durante la vida útil. Fórmulas con pocas variables de entrada son sencillas de emplear pero absorben a través del factor de rugosidad toda la información que no se incluye explícitamente en las variables de entrada. En cambio, la red neuronal de CLASH evita en gran medida estos inconvenientes y al mismo tiempo proporciona excelentes para estimar el rebase sobre diques en talud convencionales. En la presente tesis se ha desarrollado una fórmula explícita que permite emular el comportamiento de la red neuronal de CLASH. La nueva fórmula posee 16 parámetros, seis variables de entrada (Rc/Hm0, ¿0,-1, Rc/h, Gc/Hm0, Ac/Rc y una variable para representar a la berma de pie basada en Rc/h) y dos factores de reducción (¿f y ¿ß). La nueva fórmula se construye en base a simulaciones controladas empleando la red neuronal de CLASH y proporciona el menor error en la predicción de rebase sobre diques en talud de entre los estimadores estudiados. Una de las maneras más efectivas de disminuir el rebase sobre diques en talud es incrementar la cota de coronación mediante un espaldón de hormigón. Estas estructuras sufren el impacto del oleaje y deben ser diseñadas para resistirlo. En la presente tesis se han empleado ensayos de laboratorio de cubos y Cubípodos para desarrollar una nueva fórmula que permita calcular las fuerzas horizontales y verticales del oleaje sobre el espaldón. Las nuevas fórmulas incluyen la influencia de cuatro variables adimensionales (¿f Ru0.1%/Rc, (Rc-Ac)/Ch, ¿(L_m/G_c ) y Fc/Ch) y de la geometría del espaldón. Incluyen la influencia del tipo de elemento mediante el factor de rugosidad al igual que las fórmulas de rebase. Las fuerzas verticales disminuyen significativamente con el aumento de la cota de cimentación. Las nuevas fórmulas proporcionan el menor error de predicción sobre los registros de laboratorio analizados.[CA] La influència del tipus d'element del mantell principal en l'ultrapassament dics en talús és caracteritza habitualment mitjançant el factor de rugositat (¿f). En canvi, en la literatura existeixen diferents valors del factor de rugositat per al mateix tipus d'element. Així doncs, el factor de rugositat no depèn només del tipus d'element, nombre de capes i permeabilitat del nucli però també de la formulació i de la base de dades utilitzada. En la present tesi es desenvolupa i aplica una nova metodologia basada en tècniques de bootstrapping per a caracteritzar estadísticament el factor de rugositat de diferent elements (entre ells el Cubípode) utilitzant diferents formulacions d'ultrapassament. S'observen diferències fins al 20% entre els factors de rugositat òptims i els que apareixen en la literatura. La porositat del mantell afecta notablement el factor de rugositat però també a l'estabilitat del mantell; majors porositats proporcionen menor ultrapassament però també menor estabilitat hidràulica. Per això, les porositats de disseny recomanades deuen emprar-se per a evitar danys durant la vida útil. Formules amb poques variables d'entrada són senzilles d'utilitzar però absorbeixen mitjançant el factor del factor de rugositat tota la informació que no s'inclou de manera explícita en les variables d'entrada. D'altra banda, la xarxa neuronal de CLASH evita en gran mesura aquests inconvenients i al mateix temps proporciona excel·lents resultats per a estimar l'ultrapassament sobre els dics en talús convencionals. En la present tesi s'ha desenvolupat una formulació explícita que permet emular el comportament de la xarxa neuronal de CLASH. La nova formulació té 16 paràmetres, sis variables d'entrada (Rc/Hm0, Ir, Rc/h, Gc/Hm0, Ac/Rc i una variable per a representar la berma de peu basada en Rc/h) i dos factors de reducció (¿f y ¿ß). La nova fórmula es construeix mitjançant simulacions controlades amb la xarxa neuronal de CLASH i proporciona el menor error en la predicció de l'ultrapassament sobre dics en talús de entre els estimadors analitzats. Una de les maneres més efectives de disminuir l'ultrapassament sobre dics en talús és incrementar la cota de coronació mitjançant un espatller de formigó. Aquestes estructures sofreixen l'impacte de les ones i deuen ser dissenyades per a resistir. En la present tesi, s'utilitzen assajos de laboratori de cubs i Cubípodes per a desenvolupar una nova formulació per a calcular les forces horitzontals i verticals causades per l'onatge en l'espatller. Les noves fórmules inclouen la influència de quatre variables adimensionals (¿f Ru0.1%/Rc, (Rc-Ac)/Ch, ¿(L_m/G_c ) y Fc/Ch) i de la geometria de l'espatller. Inclouen la influència del tipus d'element mitjançant el factor de rugositat al igual que les fórmules d'ultrapassament. Les forces verticals disminueixen significativament amb l'augment de la cota de cimentació. Les noves fórmules proporcionen el menor error en la predicció sobre els registres de laboratori analitzats.Molines Llodra, J. (2016). Wave overtopping and crown wall stability of cube and Cubipod-armored mound breakwaters [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/62178TESI

Crown Wall Stability of Cube and Cubipod Armored Mound Breakwaters

[EN] Mound breakwaters usually have a concrete crown wall to reduce the amount of quarry material and to improve accessibility. Popular methods to design crown walls consider the same value of the horizontal pressure in the lower edge of the vertical wall and the seaward edge of the crown wall base. Up-lift forces are calculated assuming a triangular pressure distribution with a value given by pressures in the vertical wall. This assumption is reasonable in structures where the foundation level is below the sea water level, but may significantly differ from reality in crown walls with foundation levels above the sea water level. This study focuses on the influence of the foundation level on the crown wall stability analyzing 2D physical tests of cube and Cubipod armored breakwaters with crown wall.The authors acknowledge the financial support of FEDER, Spanish Ministerio de Ciencia, Innovación y Universidades (Grant RTI2018-101073-B-100), SATO (Grupo OHL), Universitat Politècnica de València (Grant SP20180111, Primeros Proyectos de Investigación (PAID-06-18),Vicerrectorado de Investigación, Innovación y Transferencia de la Universitat Politècnica de València) and Generalitat Valenciana (Grant AEST/2019/004)Molines, J.; Medina, JR. (2019). Crown Wall Stability of Cube and Cubipod Armored Mound Breakwaters. Bundesanstalt für Wasserbau. 1-7. https://doi.org/10.18451/978-3-939230-64-9_001S1

Estimations of wave forces on crown walls based on wave overtopping rates

[EN] In this study, seven input variables are used to estimate wave forces on the crown wall, and explanatory variables are ranked using neural network techniques. 274 small-scale 2D tests, including both wave overtopping and pressure on crown-wall measurements, were used to calibrate the wave force predictors. Wave overtopping (log Q) was the most relevant variable to estimate horizontal wave forces and overturning moments, while the relative foundation level (F-e/L-0p) was the most relevant variable to estimate wave up-lift forces. The new wave force estimators showed prediction errors slightly higher than the formulas given in the literature, but using fewer parameters and explanatory variables. The range of application of the new formulas is 1.67 < R-c/(gamma(f) H-m0) < 6.55, 1.39 < xi(0p) < 7.77, 0.36 < gamma(f) R-u0.1%/R-c < 1.41, 0.00 < (R-c-A(c))/C-h < 0.59, 2.64 < root L-m/G(c) < 6.54, 0.00 < F-c/ L-0p < 0.03 and -6.00 < logQ < -2.78. Compared to pressure on crown walls, the mean wave overtopping rate is relatively easy to measure in small-scale tests and prototypes. The new estimators of wave forces on the crown wall can be used to indirectly calculate forces on models when only overtopping rates are measured. If wave overtopping is one order of magnitude higher, the wave forces and overturning moments on the crown wall increase between 11% and 60%, considerably reducing the crown wall stability.The authors acknowledge financial support from European FEDER and Spanish Mirtisterio de Economia y Competitividad (Grant BIA2015-70436-R), SATO (OHL Group) and CDTI. The second author was funded through the FPU program (Formacion del Profesorado Universitario, Grant FP2013/01872) by the Spanish Ministerio de Educacion, Culturay Deporte. The authors thank Debra Westall for revising the manuscript.Molines, J.; Herrera Gamboa, MP.; Medina, JR. (2018). Estimations of wave forces on crown walls based on wave overtopping rates. Coastal Engineering. 132:50-62. https://doi.org/10.1016/j.coastaleng.2017.11.004S506213

Hydraulic stability of nominal and sacrificial toe berms for mound breakwaters on steep sea bottoms

[EN] When mound breakwaters are placed on steep sea bottoms in combination with very shallow waters, the design of the toe berm becomes a relevant issue. Toe berms built close to the water surface on a steep sea bottom must withstand such high wave loads that their design may not be feasible with available quarrystones. In this study, a new design method was developed to reduce the rock size by increasing the toe berm width. The analysis involved specific 2D small-scale tests with toe berms of different rock sizes and widths, placed on a m = 1/10 bottom slope with the water surface close to the toe berm crest. Two new concepts were introduced to better characterize damage to wide toe berms: (1) the most shoreward toe berm area which effectively supports the armor layer, in this study referred to as the primary or nominal toe berm and (2) the most seaward toe berm area which serves to protect the nominal toe berm, in this study called the secondary or the sacrificial toe berm. Damage to the nominal toe berm was used to describe hydraulic stability of wider toe berms. Given a standard toe berm of three rocks wide (nominal toe berm), an equivalent toe berm with damage similar to the nominal toe berm was defined by increasing the berm width and decreasing the rock size. The reduction in rock size showed an inverse 0.4-power relation with the relative berm width.Herrera Gamboa, MP.; Molines, J.; Medina, JR. (2016). Hydraulic stability of nominal and sacrificial toe berms for mound breakwaters on steep sea bottoms. Coastal Engineering. 114:361-368. https://doi.org/10.1016/j.coastaleng.2016.05.006S36136811

Armor Porosity and Hydraulic Stability of Mound Breakwaters

Armor porosity significantly affects construction costs and hydraulic stability of mound breakwaters; however, most hydraulic stability formulas do not include armor porosity or packing density as an explicative variable. 2D hydraulic stability tests of conventional randomly-placed double-layer cube armors with different armor porosities are analyzed. The stability number showed a significant 1.2-power relationship with the packing density, similar to what has been found in the literature for other armor units; thus, the higher the porosity, the lower the hydraulic stability. To avoid uncontrolled model effects, the packing density should be routinely measured and reported in small-scale tests and monitored at prototype scale.The authors are grateful for financial support from the Spanish Ministerio de Economía y Competitividad and FEDER (Grant BIA2012-33967) and CDTI (CUBIPOD and CLIOMAR Projects). The second author was funded through the FPU program (Formación del Profesorado Universitario, Grant AP2010-4366) by the Spanish Ministerio de Educación, Cultura y Deporte

Estimation of layer coefficients of cubipod homogeneous low-crested structures using physical and numerical model placement tests

[EN] Homogeneous low-crested structures (HLCSs) on hard seabed are designed to protect beaches and regenerate coral reefs. The height of a HLCS depends on the placement grid which determines the crest freeboard, wave transmission and concrete consumption. In real seafloor conditions, it is not easy to define feasible placement grids for HLCSs on uneven sea bottoms. In this study, the parameters of the numerical model Bullet Physics Engine (BPE) are calibrated and validated using the results of small-scale physical model placement tests of fivelayer Cubipod HLCSs on horizontal rigid bottom. The BPE model showed a low sensitivity to variations in the calibrated parameters; the numerical model estimated the layer coefficients with global mean relative errors of 1.04% and 1.39% in the triangular and rectangular placements grids, respectively. Once the numerical model was calibrated, new numerical and physical model tests on a 4% rigid bottom slope were compared for validation. A five-layer Cubipod HLCS on a 4% bottom slope was simulated using the BPE numerical model showing a global mean relative error of 2.75% compared to the small-scale physical model tests. A good agreement was found between numerical and physical model tests of five-layer Cubipod HLCSs on both horizontal as well as 4% rigid bottom slope. The BPE numerical model was found a suitable tool to estimate the structure height of HLCSs and to optimize placement grids of HLCSs on real cases with hard sea bottom.The authors thank the two anonymous reviewers for their constructive comments and suggestions, the financial support of the Spanish Ministerio de Ciencia, Innovacion y Universidades (Grant RTI 2018-101073-B-I00) and also Karel De Keyser and Elias Jacobs for conducting the physical placement test.Molines, J.; Centi, R.; Di Risio, M.; Medina, JR. (2021). Estimation of layer coefficients of cubipod homogeneous low-crested structures using physical and numerical model placement tests. Coastal Engineering. 168:1-11. https://doi.org/10.1016/j.coastaleng.2021.103901S11116

Numerical Study of Wave Forces on Crown Walls of Mound Breakwaters with Parapets

[EN] The influence of parapets on crown walls of mound breakwaters on wave forces has not been extensively analyzed in the literature. In this study, numerical experiments were carried out using the open-source platform OpenFOAM(R) to evaluate the influence of nine crown wall geometries with and without parapets. The OpenFOAM(R) model was validated with laboratory experiments. Dimensionless horizontal forces and overturning moments due to horizontal forces increase when there is a parapet. Dimensionless up-lift forces provide similar results, regardless of the existence of a parapet. Crown walls with parapets increase the horizontal wave forces and overturning moments due to horizontal wave forces by a factor of two.This research was funded by (1) Universitat Politecnica de Valencia (Grant SP20180111, Primeros Proyectos de Investigacion (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia) and (2) Spanish Ministerio de Ciencia, Innovacion y Universidades (Grant RTI2018-101073-B-I00).Molines, J.; Bayón, A.; Gómez-Martín, ME.; Medina, JR. (2020). Numerical Study of Wave Forces on Crown Walls of Mound Breakwaters with Parapets. Journal of Marine Science and Engineering. 8(4):1-15. https://doi.org/10.3390/jmse8040276S11584Molines, J., Bayon, A., Gómez-Martín, M. E., & Medina, J. R. (2019). Influence of Parapets on Wave Overtopping on Mound Breakwaters with Crown Walls. Sustainability, 11(24), 7109. doi:10.3390/su11247109Martinelli, L., Ruol, P., Volpato, M., Favaretto, C., Castellino, M., De Girolamo, P., … Sammarco, P. (2018). Experimental investigation on non-breaking wave forces and overtopping at the recurved parapets of vertical breakwaters. Coastal Engineering, 141, 52-67. doi:10.1016/j.coastaleng.2018.08.017Nørgaard, J. Q. H., Andersen, T. L., & Burcharth, H. F. (2013). Wave loads on rubble mound breakwater crown walls in deep and shallow water wave conditions. Coastal Engineering, 80, 137-147. doi:10.1016/j.coastaleng.2013.06.003Molines, J., Herrera, M. P., & Medina, J. R. (2018). Estimations of wave forces on crown walls based on wave overtopping rates. Coastal Engineering, 132, 50-62. doi:10.1016/j.coastaleng.2017.11.004Van Gent, M. R. A., & van der Werf, I. M. (2019). Influence of oblique wave attack on wave overtopping and forces on rubble mound breakwater crest walls. Coastal Engineering, 151, 78-96. doi:10.1016/j.coastaleng.2019.04.001Castellino, M., Sammarco, P., Romano, A., Martinelli, L., Ruol, P., Franco, L., & De Girolamo, P. (2018). Large impulsive forces on recurved parapets under non-breaking waves. A numerical study. Coastal Engineering, 136, 1-15. doi:10.1016/j.coastaleng.2018.01.012Issa, R. . (1986). Solution of the implicitly discretised fluid flow equations by operator-splitting. Journal of Computational Physics, 62(1), 40-65. doi:10.1016/0021-9991(86)90099-9Patankar, S. ., & Spalding, D. . (1972). A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15(10), 1787-1806. doi:10.1016/0017-9310(72)90054-3Jacobsen, N. G., van Gent, M. R. A., Capel, A., & Borsboom, M. (2018). Numerical prediction of integrated wave loads on crest walls on top of rubble mound structures. Coastal Engineering, 142, 110-124. doi:10.1016/j.coastaleng.2018.10.004Jensen, B., Jacobsen, N. G., & Christensen, E. D. (2014). Investigations on the porous media equations and resistance coefficients for coastal structures. Coastal Engineering, 84, 56-72. doi:10.1016/j.coastaleng.2013.11.004Hirt, C. ., & Nichols, B. . (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201-225. doi:10.1016/0021-9991(81)90145-5Berberović, E., van Hinsberg, N. P., Jakirlić, S., Roisman, I. V., & Tropea, C. (2009). Drop impact onto a liquid layer of finite thickness: Dynamics of the cavity evolution. Physical Review E, 79(3). doi:10.1103/physreve.79.036306Jacobsen, N. G., van Gent, M. R. A., & Wolters, G. (2015). Numerical analysis of the interaction of irregular waves with two dimensional permeable coastal structures. Coastal Engineering, 102, 13-29. doi:10.1016/j.coastaleng.2015.05.004Higuera, P., Lara, J. L., & Losada, I. J. (2014). Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part II: Application. Coastal Engineering, 83, 259-270. doi:10.1016/j.coastaleng.2013.09.002Higuera, P., Lara, J. L., & Losada, I. J. (2013). Realistic wave generation and active wave absorption for Navier–Stokes models. Coastal Engineering, 71, 102-118. doi:10.1016/j.coastaleng.2012.07.002Higuera, P., Lara, J. L., & Losada, I. J. (2013). Simulating coastal engineering processes with OpenFOAM®. Coastal Engineering, 71, 119-134. doi:10.1016/j.coastaleng.2012.06.002Higuera, P., Lara, J. L., & Losada, I. J. (2014). Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part I: Formulation and validation. Coastal Engineering, 83, 243-258. doi:10.1016/j.coastaleng.2013.08.010Bayon-Barrachina, A., & Lopez-Jimenez, P. A. (2015). Numerical analysis of hydraulic jumps using OpenFOAM. Journal of Hydroinformatics, 17(4), 662-678. doi:10.2166/hydro.2015.041Bayon, A., Valero, D., García-Bartual, R., Vallés-Morán, F. ​José, & López-Jiménez, P. A. (2016). Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environmental Modelling & Software, 80, 322-335. doi:10.1016/j.envsoft.2016.02.018Bayon, A., Toro, J. P., Bombardelli, F. A., Matos, J., & López-Jiménez, P. A. (2018). Influence of VOF technique, turbulence model and discretization scheme on the numerical simulation of the non-aerated, skimming flow in stepped spillways. Journal of Hydro-environment Research, 19, 137-149. doi:10.1016/j.jher.2017.10.002Romano, A., Bellotti, G., Briganti, R., & Franco, L. (2015). Uncertainties in the physical modelling of the wave overtopping over a rubble mound breakwater: The role of the seeding number and of the test duration. Coastal Engineering, 103, 15-21. doi:10.1016/j.coastaleng.2015.05.00

Hydraulic stability of cube-armored mound breakwaters in depth-limited breaking wave conditions

[EN] Armor erosion due to wave attack has been studied intensively since it is considered the main failure mode of mound breakwaters. Cube-armored mound breakwaters in depth-limited breaking wave conditions are common in practice but have received limited attention in the literature. In this study, 2D physical tests were performed on non-overtopped double-layer randomly-placed cube-armored mound breakwater models with armor slope cot¿ = 1.5 and bottom slope m = 2% in breaking wave conditions. Using the experimental results, a new hydraulic stability formula was derived with a coefficient of determination R2 = 0.85 based on a power relationship between the armor damage and the stability number and the dimensionless water depth. A lower hydraulic stability was found for the front slope of non-overtopped cube-armored structures in breaking wave conditions when compared to formulas given in the literature.The authors acknowledge the support from grant RTI2018-101073B-I00 funded by MCIN/AEI/10.13039/501100011033 and "ERDF A way of making Europe", the Spanish Ministry of Economy and Competitiveness under grant BIA2012-33967, the Generalitat Valenciana under the grant AEST/2021/045 and FEDER. The authors thank Debra Westall for revising the manuscript.Mares-Nasarre, P.; Molines, J.; Gómez-Martín, ME.; Medina, JR. (2022). Hydraulic stability of cube-armored mound breakwaters in depth-limited breaking wave conditions. Ocean Engineering. 259:1-13. https://doi.org/10.1016/j.oceaneng.2022.11184511325

Distribution of individual wave overtopping volumes on mound breakwaters

[EN] Conventional mound breakwaters are usually designed to withstand low mean wave overtopping discharges and a low proportion of overtopping waves (P-ow). Existing formulas to estimate P-ow, and maximum individual wave overtopping volume are usually based on tests with high P-ow; this study is focused on mound breakwaters subjected to P-ow, < 0.2. The performance of the 2-parameter Weibull and Exponential distributions is examined in order to describe individual wave overtopping volumes of mound breakwaters in non-breaking wave conditions. A new methodology is applied to 164 small-scale 2D physical tests to identify the number of overtopping waves, and the corresponding individual wave overtopping volumes. Utility functions are used to consider the relative relevance of the observed data: in this study, a quadratic utility function depending on all the individual wave overtopping volumes and step utility functions with 10%, 30% and 50% of the highest volumes are used to fit the Weibull and Exponential distributions. In this study, a new estimator of P-ow is proposed to improve the predictions required to estimate the maximum individual wave overtopping volume. Existing estimators of P-ow, underpredict the largest values of P-ow, measured in the physical tests. The parameters fitted to the Weibull and Exponential distributions using the quadratic utility function provide estimations of the dimensionless maximum individual wave overtopping volume with relative mean squared errors rMSE = 10.4% and 10.6%, respectively. When CLASH Neural Network-estimated mean overtopping rates are used to predict the maximum individual wave overtopping with the quadratic utility function, the 2-parameter Weibull and Exponential distributions provide rMSE = 31.6% and rMSE = 33.3%, respectively. The new estimators proposed in this study improve the predictions of P-ow and maximum individual wave overtopping volumes on conventional mound breakwaters designed for low wave overtopping rates.The authors are grateful for financial support from European FEDER and Spanish Ministerio de Economia y Competitividad (Grants BIA2012-33967 and BIA2015-70435-R), SATO (OHL Group), Universitat Politecnica de Valencia (Grant SP20180111, Primeros Proyectos de Investigacion (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia) and CDTI (Centro para el Desarrollo Tecnologico e Industrial). The authors also thank Debra Westall for revising the manuscript.Molines, J.; Herrera, MP.; Gómez-Martín, ME.; Medina, JR. (2019). Distribution of individual wave overtopping volumes on mound breakwaters. Coastal Engineering. 149:15-27. https://doi.org/10.1016/j.coastaleng.2019.03.006S152714

Influence of Parapets on Wave Overtopping on Mound Breakwaters with Crown Walls

[EN] Background literature on the influence of parapets on the overtopping of mound breakwaters is limited. In this study, numerical tests were conducted using computational fluid dynamics (CFD) to analyze the influence of nine crown wall geometries (seven with parapets). The CFD model was implemented in OpenFOAM((R)) and successfully validated with laboratory tests. A new estimator of the dimensionless mean wave-overtopping discharges (logQ) on structures with parapets is proposed. The new estimator depends on the estimation of logQ of the same structure without a parapet. The effects on wave overtopping of the parapet angle (epsilon(p)), parapet width (w(p)), and parapet height (h(p)) were analyzed. Low values of epsilon(p) and w(p)/h(p) approximate to 1 produced the highest parapet effectiveness to reduce the mean wave-overtopping discharges.This research was funded by Universitat Politecnica de Valencia (Grant SP20180111, Primeros Proyectos de Investigacion (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia). The authors are grateful for financial support from European FEDER and Spanish Ministerio de Economía y Competitividad (Grant RTI2018-101073-B-I00), SATO (OHL Group). The authors acknowledge the support provided by the postdoctoral company internship program AEST granted to Jorge Molines by Generalitat Valenciana (Grant AEST/2019/004) and by the postdoctoral program APOSTD granted to Arnau Bayon by Generalitat Valenciana (Grant APOSTD/2019/100).Molines, J.; Bayón, A.; Gómez-Martín, ME.; Medina, JR. (2019). Influence of Parapets on Wave Overtopping on Mound Breakwaters with Crown Walls. 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