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The rockfill toe structure situated within the downstream slope of rockfill dams is an integral part of a defense mechanism safeguarding the dam structure in throughflow situations. Recent studies have concluded that the rockfill toe structure can have significant impacts on throughflow development and stability of rockfill dams under scenarios of accidental throughflow caused by overtopping of the dam core. The ability to numerically model the effect of various toe configurations on flow through rockfill dams can support the design of effective toe drainage structures for rockfill dams. Development and calibration of a reliable numerical modeling tool in this regard has been challenging owing to lack of availability of extensive datasets from physical modeling investigations. This study further employs datasets gathered by a recent physical modeling study investigating the effects of various toe configurations on throughflow development in rockfill dam models. A commercial numerical seepage modeling tool with an option for non-Darcy flow was calibrated against the datasets with good calibration metrics. The study is novel in providing a rare report on the usage of this option. The calibrated tool can further be employed to carry out a wide array of simulations to arrive at an ideal design for a toe structure for rockfill dams and for assessment of hydraulic performance of toe structures.

Reshaping berm breakwaters have been mainly designed and built for water depth less than 20 m. In such conditions, a toe structure may be needed to reduce bottom settlements and increase geotechnical stability in the loose subsoil condition. Also, a toe berm can be deployed to reduce the berm recession and increase the stability of the Reshaping berm breakwater, especially in deep water. Although many studies have been conducted to study the effects of toe berms on stability of conventional breakwaters, investigations on the influence of a toe berm on stability of reshaping berm breakwaters are rare. This paper presents results of an experimental work that has been carried out to investigate the influence of a toe berm on the hydraulic stability of reshaping berm breakwaters. In a 2D physical test setup in a wave flume, a total of 207 tests were conducted to systematically examine the effects of toe berm configuration on the reshaping of berm breakwaters with three types of armor stones. The experimental program covers the influence of different geometrical parameters of the toe berm on the berm recession under various sea state conditions. Comparing results of berm recession of the cases having a toe structure with the cases without a toe berm shows that the amount of berm recession with toe berm is considerably less than the analogous amount for without toe structure. It is observed that an increasing toe berm width and thickness both have considerable influence on recession reduction. However, the toe depth has a relatively larger influence on recession than the toe width, and the influence is larger for higher stability numbers. It is concluded that a toe berm in front of reshaping berm breakwater not only does have influence on recession due to the depth influence and the changing wave conditions, but also the toe depth has a direct influence on the reshaped profile by preventing the displaced rocks to fall down to deeper parts. Using the test results, a new formula is developed for estimation of berm recession by taking into account the influence of the toe berm configuration. Given an acceptable stability number (Ho) as a design criterion for reshaping berm breakwaters, the present method predicts that the recession can be reduced up to 35% by the application of a toe berm. Thus, the main berm width can be shortened, resulting in reduction of the required armor stones volume. So, by using a smaller stone size for the toe berm, the stability of the structure is secured and also the total cost of the breakwater can be reduced.

The toe structure of a breakwater provides support to the armour layer and protects the structure from damage due to scour at the toe. Often a toe structure consists of rock material. Several design formulae exist to predict the amount of damage to the toe structure under wave loading. These design formulae for the required rock size include effects of the wave height and the water depth above the toe structure. Here, rock toe stability has been studied by means of physical model tests to provide information on the required rock size in the toe structure. The tests and analysis are focussed not only on the influence of the wave height and the water depth above the toe structure, but also on the influence of the width of the toe structure, the thickness of the toe and the wave steepness. The wave steepness, width of the toe and the thickness of the toe appear to affect the damage to the toe; these parameters need to be taken into account in order to derive accurate predictions of the damage to the toe structure. Based on the test results a prediction formula has been derived including these effects. The formula can be used to determine the required rock size in the toe of rubble mound breakwaters within the ranges of the performed tests.

Toe structures are a common feature in coastal rock armoured structures, both safeguarding the structure against scour at the toe and providing support to the armour layer. The toe structure itself is often comprised of rocks as well. Hence, generally some form of scour protection, such as a filter layer or a geotextile, is applied underneath the toe structure. Currently, there is a lack of available methods to judge the necessity of these kinds of costly scour protection measures underneath the toe structure. In this paper, a unique data set from physical model tests of scour at the toe of rock armoured structures is presented. The bed level change is measured by a laser scanner across the entirety of the sand bed, including underneath the structure. Additionally, the temporal development of the scour at the glass wall of the flume is measured using an innovative combination of video imagery and a deep learning algorithm. The sand diameter is not varied in the physical model tests. In all tests, scour was observed both in front of the structure and underneath the structure. Two expressions have been derived that give estimates for both kinds of scour, and thus can give insight into the necessity of scour protection underneath the toe structure.

In this work, a CFD model (OpenFOAM) is extended to allow for the exchange of sediment between the inside of porous structures and the outside. This exploratory extended model is applied to simulate the morphological change around and under toe structures, as are often used in rock armoured coastal structures. Both the dimensions of the toe structure and the hydraulic loading are varied to investigate their effect on the simulated scour.

A beach profile equilibrium model for perched beaches is presented. The model assumes that wave reflection at the seaward and leeward sides of the breakwater is the most important process that modifies Dean's equilibrium profile model for non-perched beaches. The influence of wave breaking over the submerged structure is also discussed. Several laboratory data sets are used to analyze the merit of the proposed model for describing the equilibrium condition of a perched beach. A good comparison is obtained. Results show that if the ratio between the water depth above the submerged structure, d , and the water depth at the toe of the structure, h e , is large, d / h e >0.5, only minor advance of the shoreline is achieved with the construction of a toe structure. A considerable advance is obtained for d / h e less that 0.1. In these situations, however, resonant effects may result in an inefficient structure. The proposed model is used to provide an estimation for the required sand volume and the associated beach advance for the case of narrow breakwaters.