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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.

Since 1977 dedicated studies are made to the stability of rubble mound break-water toes under wave attack. A large number of stability methods is available, but prediction accuracy is low and validity ranges are too small for use in prac-tice. In this research the decoupled model approach is used to evaluate predic-tion capacity of existing toe stability methods. The approach uses numerical model IH-2VOF for a prediction of stability. Review of the model showed that it is highly sensitive to stone properties and that turbulence was not modelled. Un-der the assumption that the latter is not of major importance, calibration of mo-tion formulae against physical measurements and evaluation of the stability methods was performed. The decoupled model approach appeared to give good stability predictions. Validity limits of the stability methods seemed to be too strict. A ranking of stability methods was made. Future validation should con-firm the results before incorporation in design manuals.

Since 1977 dedicated studies are made to the stability of rubble mound break-water toes under wave attack. A large number of stability methods is available, but prediction accuracy is low and validity ranges are too small for use in prac-tice. In this research the decoupled model approach is used to evaluate predic-tion capacity of existing toe stability methods. The approach uses numerical model IH-2VOF for a prediction of stability. Review of the model showed that it is highly sensitive to stone properties and that turbulence was not modelled. Un-der the assumption that the latter is not of major importance, calibration of mo-tion formulae against physical measurements and evaluation of the stability methods was performed. The decoupled model approach appeared to give good stability predictions. Validity limits of the stability methods seemed to be too strict. A ranking of stability methods was made. Future validation should con-firm the results before incorporation in design manuals.

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.

Present design tools, as found in the Rock Manual or Coastal Engineering Manual, for the determination of toe rock size for rubble mound breakwaters are based on test data with a large spread: data is relatively dispersed around the centre and descriptive equations have limited applicability ranges. New research has been undertaken to contribute to a more accurate description of toe rock stability. Flume tests have lead to an empirical design criterion for toe bunds in very shallow water based on the Hudson-type stability number. Herein the foreshore slope turns out to have an important influence. An approach with theoretical background has been used for toe bunds in surging wave conditions. The resulting stability description, based on local flow velocities, has been verified with existing data sets. Additional flume tests were performed to measure flow velocities at the toe bund. Results are used to calibrate the velocity-approach, providing an improved design criterion.

Hydraulic model studies were conducted to aid in ascertaining the technical feasibility and optimum design factors of the perched beach concept. Among these were two-dimensional, movable-bed studies to determine an estimate of the amount of sand which would be lost seaward over the submerged toe structure by normal and storm wave action, the optimum elevation of the submerged toe structure, and the length of a stone blanket required to reduce seaward migration of sand to a minimum. The model beach was subjected to test waves until equilibrium was reached for a wide range of wave conditions for both the existing beach and the perched beach. Test results indicate that (a) little or no beachfill material will be lost seaward of the toe structure for normal wave conditions but the larger storm waves may cause erosion of the perched beach, (b) the installation of a stone blanket shoreward of the toe structure will reduce the amount of beach erosion, (c) if the beach fill is extended a sufficient distance seaward, the toe structure serves no useful purpose, and (d) a three-dimensional movable-bed model study is feasible and is necessary to determine the final design features of a perched beach.