Overtopping at Xbloc-armoured Breakwaters with a Berm

Abstract

Traditional rubble mound breakwaters are increasingly designed with lower crest heights, utilizing a berm to dissipate wave energy. Single-layer interlocking concrete units, such as Xblocs, are frequently applied to steep slopes. However, existing empirical models for wave overtopping are primarily calibrated for traditional rock armour on milder slopes. The specific overtopping performance, concerning both mean overtopping discharge (q) and maximum individual wave volumes (V_max), of steep-sloped, Xbloc-armoured breakwaters with a berm remains largely unknown.

To address this knowledge gap, 2D physical model tests were conducted on steep-sloped (cot(α) = 1.33) Xbloc-armoured breakwaters. The experimental program investigated the influence of berm width, berm elevation, and wave steepness under constant relative freeboards (R_c/H_m0 = 0.67 - 1.68). Two berm widths were tested, yielding dimensionless relative widths of B/H_m0 = 1.05 - 4.20 and B/L_m-1,0 = 0.06-0.12. Berm elevations were positioned at the Still Water Level (SWL) or emerged, resulting in relative levels of B_L/H_m0 = 0.40 - 1.69 (relative to crest height) and h_b/H_m0 = 0 - 0.67 (relative to water level). These configurations were subjected to low and high wave steepnesses (s_m-1,0 = 0.025 - 0.028 and 0.038 - 0.046). Furthermore, a reference case without a berm was tested to establish a baseline.

The results demonstrate that berm elevation is the dominant structural factor in reducing overtopping discharge. Berms positioned at the Still Water Level (SWL) proved inefficient at dissipating wave energy, particularly for low-steepness waves. Under these conditions, the relative wave run-up (R_u2%/H_m0) reaches its maximum due to the the very steep slope angle; since the SWL berms fail to disrupt this run-up, adding a small or wide berm yields no significant overtopping reduction compared to a straight slope. Conversely, emerged berms significantly reduced overtopping discharges compared to SWL.

A comparison with existing literature revealed that standard models cannot be directly applied to predict overtopping discharges for this specific steep-sloped, Xbloc-armoured configuration. For the mean overtopping discharge, an optimal constant friction factor of γf= 0.40 was established within the baseline framework of Van Gent et al. (2022) Additionally, the berm influence factor (γ_b) was recalibrated. In this new formulation, the berm level is incorporated using its elevation above the water level scaled by the wave height (h_b/H_m0), instead of its height below the crest scaled by the armour crest height (B_L/A_c).

Regarding individual overtopping volumes, the standard Weibull distribution already provided an accurate baseline prediction. However, it inherently lacked the capability to differentiate between geometric configurations. Specifically, for test series containing approximately 1000 waves, it systematically overestimated V_max for bermed profiles by failing to account for the berm's dampening effect, and underestimated V_max for the steep straight slope (cot(α) = 1.33) by failing to capture severe surging. To resolve this, a new empirical expression for the Weibull shape parameter (b) was formulated, which integrates the surf-similarity parameter (ξ_m-1,0) alongside the relative berm dimensions (B/L_m-1,0 and h_b/H_m0). While this recalibrated formula successfully reduces the prediction error and captures the underlying physics more accurately, the absolute gain is relatively modest. Consequently, despite this theoretical improvement, the added complexity may not be necessary for design practices.