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).

For the last two decades, significant damage to groyne structures has been observed in the German Elbe estuary. The main reason is the generation of primary ship-induced wave loading. The stern wave of the primary wave system appears as an overflowing over groyne, leading to damage at the crest and lee side of the structure due to the presence of high overflowing flow velocities (Melling et al., 2020). Therefore, overflowing flow velocities and damage were quantified by means of two different experimental setups; the flow experiments and the damage experiment.

The flow experiment involved testing scaled physical models under continuous free-flow conditions. A Particle Image Velocimetry (PIV) setup was used to capture flow velocities at the crest and lee side slope. A dimensionless flow velocity equation is obtained for overflowing flow over groyne structures. The damage experiment assessed the impact of overflowing waves at the crest and lee side on one of the scaled physical models. Measurements were conducted via Structure from Motion principles (SfM) and the damage is expressed in damage parameters S for varying wave heights and freeboard levels. This parameter describes the damage by width-averaged eroded area made dimensionless by the squared nominal stone diameter. Furthermore, the assessment considered the determination of the damage limits (initiation, intermediate, and failure) of a groyne structure for these waves.

The results revealed the relation between the wave height and the freeboard and damage. Furthermore, by regarding the flow velocity explicitly a more fundamental understanding, and more generally applicable design approach might be obtained. The insights gained from this research contribute to an enhanced understanding of groyne behaviour under overflowing long- period ship-induced waves. By highlighting the significance of the flow velocities for waves and freeboard levels, this study provides valuable information for optimizing the design and maintenance of estuarine groynes that are prone to these types of wave-induced loads.

During the last two decades, increasing vessel size in major German estuaries has led to the significant change of the local loading regime i.e. increased importance of ship-induced waves and currents. As a consequence, the intensity of ship-induced loads has increased considerably, resulting in damage to rock structures such as revetments, training walls, and groynes. Research into the causes of rock structure deterioration by the Federal Waterways Engineering and Research Institute (BAW) has shown that for large ships in relatively narrow waterways, the long-period primary ship wave loading has become the most prescient factor for rock structure damage. Looking into the future, it can be expected that the increase in the vessel dimensions will lead to an increase in the ship-wave loading. For this reason, analysing long-term changing trends of long-period ship waves and vessel speed to understand the wave-structure interaction is of significant importance. In this study, the stochastic characterization of long-period primary wave height, drawdown, and speed of the vessel through the water at Juelssand in the Lower Elbe Estuary was analysed via extreme value analysis and copula modeling, and the bivariate return periods were calculated. The one-parameter bivariate copula was utilized to analyse the data. The dependence pattern between the variables was investigated using five parametric copula families: Gaussian, Gumbel, Clayton, Frank, and student's t.