Armor layers of mound breakwaters are usually designed with empirical formulas based on small-scale tests in non-breaking wave conditions. However, most rubble mound breakwaters are constructed in the depth-induced breaking zone, where they must withstand design storms having some percentage of large waves breaking before reaching the structure; in these cases, the design formulas for non-breaking wave conditions are not fully valid. To characterize double-layer rock armor damage in breaking wave conditions, 2D physical model tests were carried out with a bottom slope m=1/50. In order to develop a simple method to determine the wave parameters in the depth-induced breaking zone, experimental wave measurements were compared to the numerical estimations given by the SwanOne model. An analysis was conducted to select the best characteristic wave height to estimate rock armor damage when dealing with depth-induced breaking waves; the spectral significant wave height, H m0 , estimated at a distance of 3h s seaward from the structure toe, was found to be the most adequate. 2 A new hydraulic stability formula is proposed for double-layer rock armors in breaking wave conditions, considering the observed potential 6-power relationship between the equivalent dimensionless armor damage and the H m0 at 3h s seaward distance from the structure toe.
The toe berm is a relevant design element when rubble mound breakwaters are built on steep sea bottoms in breaking conditions. Different design formulas can be found in the literature to predict the damage caused to submerged toe berms placed on gentle bottom slopes. However, these formulas are not valid for very shallow waters in combination with steep sea bottoms where toe berms receive the full force of breaking waves. To guarantee breakwater stability in these conditions, new design formulas are needed for toe berms. To this end, physical model tests were carried out and data were analyzed to characterize rock toe berm stability in very shallow water and with a bottom slope m = 1/10. Based on test results, a new formula was developed with three parameters to estimate the nominal diameter (D n50 ) of the toe berm rocks:water depth at the toe (h s ), deep water significant wave height (H s0 ) and deep water wave length (L 0p ).
distribution, utility function, number of overtopping waves -New 2-parameter Weibull and Exponential distributions are proposed with unbiased estimations of Vmax* with rMSE=10.4% and 10.6%, respectively.-Using the quadratic utility function and the estimated q and Now, Vmax* was estimated by the Weibull and Exponential distributions with rMSE=31.6% and 33.3%, respectively.
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.
Although little attention is usually given to the armor porosity and armor randomness 5 of randomly-placed concrete armor units in mound breakwaters, significant model effects may 6 occur if armor porosity and randomness are different for prototype and small-scale models. 7Armor randomness and porosity are easier to control in small-scale models because they are 8 generally constructed by hand in dry and perfect viewing conditions; equipment and 9 environmental constraints make control at prototype scale more difficult. Results from 3D 10 small-scale placement tests are analyzed when cube and Cubipod units are placed with a small-11 scale crawler crane and pressure clamps. Armor porosity was not workable below 37% for cubes 12 and 35% for Cubipods; placement grids were obtained for feasible armor porosities, considering 13 row settlements during construction as well. A methodology to measure armor randomness 14 using high-precision laser scanning, similar to terrestrial LIDAR, was tested with small-scale 15 cube and Cubipod armor. Three armor randomness indexes (ARIs) measured the randomness 16 of cube and Cubipod armor; the values for ARIs were higher for Cubipod armor than for cube 17 armor. 18
Armor stability formulas for mound breakwaters are commonly based on 2D small-scale physical tests conducted in non-overtopping and non-breaking conditions. However, most of the breakwaters built around the world are located in breaking or partially-breaking wave conditions, where they must withstand design storms having some percentage of large waves breaking before they reach the structure. In these cases, the design formulas for non-breaking wave conditions are not fully valid. This paper describes the specific 2D physical model tests carried out to analyze the trunk hydraulic stability of single- and double-layer Cubipod® armors in depth-limited regular wave breaking and non-overtopping conditions with horizontal foreshore (m = 0) and armor slope (α) with cotα = 1.5. An experimental methodology was established to ensure that 100 waves attacked the armor layer with the most damaging combination of wave height (H) and wave period (T) for the given water depth (hs). Finally, for a given water depth, empirical formulas were obtained to estimate the Cubipod® size which made the armor stable regardless of the deep-water wave storm.
Armor porosity and armor unit randomness are much easier to control in small-scale models constructed by hand than in prototype. Differences between design and prototype armor porosities and design and armor unit randomness can generate significant model effects. This paper describes realistic 3D placement tests with cube and Cubipod CAUs, using a small-scale crawler crane and pressure clamps. This research aims to estimate workable armor porosities at prototype scale and to determine the prototype placement grids to obtain the armor porosities commonly tested in laboratories. A new methodology based on laser scanning was developed to measure armor unit randomness. This methodology can be applied to both small-scale models and prototypes. Armor Randomness Indexes (ARIs) are proposed to measure the randomness of cube and Cubipod armor units. The ARI values were higher for Cubipods than for cubes.
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