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

Abstract

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.

Cubipod® Armor Design in Depth-Limited Regular Wave-Breaking Conditions

“…The design water depth (h) is calculated at a distance three times the water depth at the toe of the structure (hs), h = hs(1 + 3m). This approximation is reasonable for gentle bottom slopes (m ≤ 0.02); for steep bottom slopes (e.g., m = 0.10), the toe berm design is critical, and armor layer and toe berm must be studied simultaneously (see Herrera and Medina 2015 [22] or Herrera et al 2016 [23]). Small-scale models are The highest wave heights measured in the model area were approximately 60% of the water depth, H max /h s ≈0.60 with a horizontal seafloor (m = 0).…”

Toe Stability in Very Shallow Water Combined With Steep Sea Bottom

“…7 can be used to determine a more stable position if the toe of the structure is moved shoreward or seaward in the range -0.5≤hs/Dn50≤5.0. When it is not feasible to move the toe position of the structure due to environmental, economic or operational constraints, a sacrificial toe berm can be considered following the methodology proposed by Herrera et al (2016).…”

“…6 was proposed to estimate Nod, where Hs0 is the significant wave height in deep water conditions. Herrera et al (2016) analyzed the influence of toe berm width (Bt=ntDn50) on the hydraulic stability. Small-scale tests were conducted in the LPC-UPV wave flume with m=1/10 and 7.7≤hs(cm)≤10.6.…”

“…When considering wider and/or higher toe berms, common damage parameters (Nod, N%) are not recommended since larger toe berms require more rocks displaced from the toe (N) to be damaged; rocks situated in the most seaward part of the toe berm do not contribute to support the armor, but only to protect the most shoreward part of the toe berm. Thus, Herrera et al (2016) proposed a new methodology to design wide toe berms (3Dn50≤Bt≤12Dn50) placed on a m=1/10 sea bottom, based on the damage to the nominal toe berm (Nod*) which actually supports the armor layer. When designing with Nod*, common values for acceptable damage (Nod*<0.5-no damage; Nod*≈1−significant movements; Nod*≈2−moderate damage; Nod*>4−failure) can be directly applied.…”

Mound Breakwater Design in Depth-Limited Breaking Wave Conditions

“…Small-scale tests were conducted with double-layer cube armored breakwaters and rock toe berms with different widths (Bt) and thicknesses (tt). Firstly, a new equation is proposed to design emerged and submerged standard rock toe berms (Bt=3Dn50 and tt=2 Dn50) using three parameters: (1) deep water wave height, Hs0, (2) deep water wave length, L0p, and (3) water depth at the toe, hs. Secondly, the influence of toe berm width (Bt) on toe berm stability is analyzed introducing two new concepts to characterize wide toe berms (Bt>3Dn50): (1) the nominal toe berm or the most shoreward toe berm area conducted by Markle (1989 Figure III.14.…”