Rock groins in the Elbe Estuary are constructed to maintain proper water levels for navigation and for embankment erosion protection. At certain localities, significant damages to rock groins have been observed due to the primary ship-generated waves. Primary waves are generated along the ship's hull and then propagate toward the river banks and groin fields, appearing in the interaction with the structures as a turbulent overflow phenomenon. Eventually, this overflowing may cause damages mainly to the crest and leeward side of the groins. Since this overflowing is the most pronounced with large primary waves at certain water levels, the estimation of the probabilities of extreme primary waves is a key element for a safe and reliable design of groins. For this goal, nonparametric Bayesian networks (NPBNs) are used here to infer the probability distribution function of the extreme primary wave heights at the tip of a groin in the Elbe Estuary. Results demonstrate the suitability of the NPBN in their prediction. The model framework allows the designer to predict the probabilities of primary ship-generated waves at groins when the information of ship dimensions, nautical parameters, and waterway geometry is available. These probabilities can later be used for design purposes for current and future conditions.

The passage of ships in confined waterways creates a stern wave that can overflow bank protection structures such as groins. This overflow, due to the long-period primary ship-induced waves, can be high in velocity, especially at the lee-side slope of groins, potentially causing significant damage to the structure. This study derives an equation to express overflow velocities, intended as a design tool for groins exposed to these types of waves. A detailed experimental investigation was performed on four physical models of groins with different slopes and stone sizes in the armor layer under the influence of different hydraulic heads. Particle image velocimetry (PIV) was used to measure the flow velocities at the crest and lee sides of the structure. All PIV measurements were performed thrice under free-flow conditions with no initial water level at the lee side of the structure. The depth- and time-averaged flow velocities (Uavg) were extracted from four positions along the lee-side slope and accelerated from 0.7 to 2.2 m/s. A dimensionless equation of the overflow velocities was obtained as a function of the hydraulic head (h), slope (θ), freeboard (Rc), and nominal rock diameter (dn50).