Journal of Waterway, Port, Coastal, and Ocean Engineering

The numerical simulations of wave interactions with armor blocks on rubble-mound breakwaters will enable a stronger understanding of breakwater failure and therefore increased malfunction prevention. This paper presents a two-dimensional (2D) SPH-DEM model, which combines smoothed particle hydrodynamics (SPH) and the discrete-element method (DEM) to simulate the wave-structure interaction on a slope and predict the hydraulic stability of the 2D structure. A particle method combined with a Riemann solver evaluates the hydrodynamic loads on the discrete blocks, while a multisphere DEM describes the movement of the solids from the wave attacks. An interfacial force-balance condition enables coupling between the fluids and the solids. A series of experimental tests were conducted to validate the SPH model. The simulation of water entry of the wedge was compared with previous experiments. The wave interactions with massive cross-shaped blocks on a slope were also simulated in 2D. Numerical results are presented showing the details of large deformations of the free surface on the slope, the velocity field, and the hydraulic pressures on the armor units, and the nature of the changes in position of the blocks near the toe of the slope during the wave attack. These results facilitate an improved understanding of the interaction between waves and breakwaters.

Sediment spillage from hopper overflow constitutes a source for sediment plumes and can also impact the turbidity of aquatic environments. The overflowing mixture is often different from the mixture pumped into the hopper (the inflow), because the mixture undergoes compositional transformation as a result of different timescales in the segregation of the various sediment fractions. The heavier constituents in a mixture will have had time to settle, and overflowing sediments are therefore primarily composed of the finer and lighter constituents, whose concentrations potentially exceed those at the inflow. The hopper constitutes a complex system despite its geometrical regularity; the complexities are largely from the settling processes in concentrated polydisperse mixtures. These settling processes can, however, be captured by employing available settling formulas applicable for multifractional sediment mixtures (i.e., polydispersions). Strictly speaking, these formulas have been validated for homogeneous and unenergetic mixtures only, but the hopper system fulfills these criteria reasonably well. A proper description of the compositional transformation during filling and subsequent overflow stages can be captured using a sediment budget approach, i.e., by using continuity equations for water and sediment phases. In this study, the compositional transformation and the bed height inside the hopper are obtained by solving these equations, considering monodisperse, bidisperse, and polydisperse mixtures, the former analytically. Although assumptions tied to the mathematical model are fulfilled best for hoppers rigged with a multiple-inflow system, the model accurately predicts measured concentrations in the final stage of overflow for single-inflow systems. The model can be used as a preprocessing tool for engineering plume models, providing source specifications for overflow spill and for the subsequent dumping of hopper loads.

This paper presents the results of an experimental study of the influence of clay content (CC) on liquefaction of seabed beneath progressive waves. Experiments were, for the most part, conducted with silt and silt-clay mixtures; in supplementary tests, sand-clay mixtures were used. Two types of measurements were carried out: (1) pore-water pressure measurements across the soil depth and (2) water-surface elevation measurements. These measurements were synchronized with video recordings of the liquefaction process from the side. The ranges of the various quantities in the experiments were wave height $H=7.6-18.3\hspace{0.17em}\text{cm}$, wave period $T=1.6\hspace{0.17em}\text{s}$, and water depth $h=55\hspace{0.17em}\text{cm}$. The experiments showed that the influence of CC on wave-induced liquefaction is very significant. Susceptibility of silt to liquefaction was increased with increasing CC up to $\text{CC}\approx 30\%$ (which is clay-specific), beyond which the mixture of silt and clay was not liquefied. Sand may become prone to liquefaction with the introduction of clay, contrary to the general perception that this type of sediment is normally liquefaction-resistant under waves. For instance, sand with $d_{50}=0.4\hspace{0.17em}\text{mm}$ was liquefied with $\text{CC}=10.8\%$, whereas sand with $d_{50}=0.17\hspace{0.17em}\text{mm}$ was partially liquefied with CC as small as 2.9%. Remarks are made as to how to check for liquefaction of clayey soils exposed to waves in real-life situations.

Mean wave overtopping discharge is a key design parameter for many coastal structures, typically designed to limit overtopping discharge to below a chosen admissible value. Dutch, German, and British design guidance from the 1990s was updated using results of research projects supported by the European Commission, and subsequently unified with the publication of the European Manual for the Assessment of Wave Overtopping, or EurOtop [EurOtop. (2007). European Manual for the Assessment of Wave Overtopping, T. Pullen, et al., eds.], now used all over the world. This paper explores five technical issues that were not well covered in the unified manual. (1) For sloping structures, overtopping at low and zero freeboard conditions: new analysis brings together the conventional exponential formulas with the few reliable datasets including very low and zero freeboard. In doing so, early Dutch work from the 1970s was revisited. Weibull-type formulas are proposed, describing wave overtopping at slopes for the whole range $R_c/H_{m0}\ge 0$. (2) For vertical walls, the manual distinguishes overtopping responses depending upon whether wave breaking occurs, with nonbreaking and breaking conditions described by exponential and power law formulas, respectively. Here, the governing equations are manipulated in such a way as to reunify the methods, enabling direct and intuitive comparison. (3) For overtopping at vertical walls under nonimpulsive conditions, early Italian/Dutch and British formulas of the 1990s diverge significantly for higher freeboards. This paper explores why these two reliable studies arrived at two such different predictors. By reanalysis of the original datasets augmented by further data drawn from the international database on wave overtopping, a physical distinction based on the nature of the foreshore is proposed and tested. (4) The prediction method for overtopping at composite vertical structures is reworked to enable the influence of the mound to be apparent and to align with plain vertical wall formulas for smaller mounds. A new scheme is proposed that treats composite structures via a small adjustment to the new vertical wall approach proposed earlier. (5) There is vast literature on overtopping response at mildly sloping structures and substantial literature on vertical walls, but in the intervening range (approximately $1V:1.5H$ to $5V:1H$), there is a paucity of reported tests. Recently published Belgian data have enabled the development of a continuous prediction scheme spanning mild slopes, steep slopes, and vertical structures without foreshore.

An experimental study of two model-scale lens-shaped vertical gates consisting of a truss and plate is presented. Experimental results are applied to the design of the new Nakdong River gates in Busan, South Korea, for flood and irrigation control. Experimental models are developed using finite-element (FE) analysis. A 1:31 scale model is constructed for the short gate (47.5 m wide, 8.5 m high at full scale) using acrylic, and a 1:61 scale model is constructed for the long gate (95 m wide, 8.5 m high at full scale) using an acrylic truss and acrylonitrile butadiene styrene plate. Natural frequencies of the model gates are measured and calibrated with FE predictions. Dynamic characteristics of the flow-induced vibration are compared for two gate orientations. Vibrations of the model gates in Orientation 1 (plate convex in the upstream direction) and Orientation 2 (plate convex in the downstream direction) are measured for various flow conditions. A combination of bottom opening heights and upstream and downstream water levels is tested in an experimental 1.6-m-wide channel. Hydrodynamic vibrational characteristics of the two experimental gate models are analyzed and compared as a function of upstream (river) level, downstream (sea) level, and bottom opening height. Results from the analysis are used to determine the appropriate gate orientation and incorporated into the final design of the bottom shapes of the prototype gates. The test results also provide a basic dataset for development of operations guidelines to minimize flow-induced vibrations of the gates.