Advance in wave reflection estimation for rubble mound breakwaters: The importance of the relative water depth

Investigation on the Reflection Coefficient for Seawalls Protected by a Rubble Mound Structure

“…Furthermore, it can be observed that the role of the surf similarity parameter is larger if compared to the role of relative water depth. Equation ( 8) was tested against other widely used formulas for the estimation of the reflection coefficient, which take into account the dependence of K r from the surf similarity parameter ξ m −1,0 [63,64] and the relative water depth [66]. Figure 11 shows a satisfactory agreement between the experimental points and those calculated using Equation ( 8), as also confirmed by the accuracy assessment estimated using the statistical parameters reported in Table 7.…”

“…More recently, Diaz-Carrasco et al [66] proposed a new formula to estimate K r in a wider range of variation of the relative water depth [66]. The reflection coefficients are estimated exploiting a sigmoid function depending on the relative water depth and front slope d/(L tan α) (Equation ( 4))…”

“…As already observed in other formulas depending on the relative water depth, the sigmoid function must be fitted for each tested front slope, since the lower asymptotic value K r0 clearly depends on the front slope angle, whereas K r1 , a, and γ could be considered as constants [66]. Diaz-Carrasco et al suggested K r1 = 0.8, a = 0.18, and γ = 3.5 for all slopes, whereas K r0 ranges from 0.2 (for a 1:3 slope) to 0.27 (for a 1:1.5 slope) [66].…”

“…Figure 9 shows that the experimental data are well represented by a sigmoid function, and, as expected, the lower asymptotic value K r0 (=0.30) assumes a higher value than those estimated for milder front slopes. The coefficients a and γ were also refitted (Table 6), and the estimated values are lower than those estimated by Diaz-Carrasco et al [66]. The influence of the surf similarity parameter upon the reflection coefficient K r was also investigated.…”

“…The formal definition of the functional dependence of K r from the identified dimensionless groups can be a hard and complex task. Indeed, it should depend on physical reasoning (as the formulation proposed by Diaz-Carrasco et al [66]) and must reveal the main feature of the phenomenon to be described.…”