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This study extends the theoretical approach developed by JUMELET [2010] to acquire a physical description of the notional permeability coefficient applied in the VAN DER MEER stability formulae [1988]. Van der Meer introduced this coefficient to ensure that the permeability of the structure is taken into account, however due to the empirical character of Van der Meer equations and because prior to Jumelet's research there was not an available physical description of the notional permeability factor, the determination of this factor was rather vague. Because of the fact that the stability relationship includes the P-coefficient, it has to be estimated somehow and, therefore, the research carried out by JUMELET [2010] is, to some extent, the starting point to achieve the required physical description of the notional permeability coefficient. To obtain this physical description, the volume-exchange model is introduced, in which the external and internal processes that take place within a breakwater are coupled. The external process is described by a wave run-up model while the internal process is described by the „Forchheimer‟ equation for the water flow through a porous medium. According to JUMELET [2010], the notional permeability parameter P is highly related to the run-up reduction coefficient from the volume-exchange model, and thus Jumelet defines an expression for this coefficient by means of coupling the notional permeability factor with the volume-exchange model. Because of the simplicity of the notional permeability coefficient formula developed by JUMELET [2010], further research is required to analyze the actual correlation between the notional permeability factor and the so-called run-up reduction coefficient (obtained from the volume-exchange model). This study focuses on developing a general formula for the notional permeability coefficient based on JUMELET [2010] and analyzing the real influence of the hydraulic parameters and structural properties on the P-factor. As stated by JUMELET [2010], the permeability of the structure depends not only on the structural properties but also on the hydraulic parameters. In this way, a physical description of the notional permeability coefficient is given and can be applied in Van der Meer stability equations to design breakwaters. Moreover, a damage level analysis has been performed to compare the observed damage by VAN DER MEER [1988] with the estimated damage through the combined method of Jumelet's model, the generalized formula for the notional permeability coefficient and Van der Meer stability equations, which leads to introducing the combined method as a tool to determine the maintenance policies in breakwaters by taking into account the damage that waves causes on them.

This study extends the theoretical approach developed by JUMELET [2010] to acquire a physical description of the notional permeability coefficient applied in the stability formulae of VAN DER MEER [1988]. Van der Meer introduced this coefficient to ensure that the permeability of the structure is taken into account, however due to the empirical character of Van der Meer equations and, until Jumelet.s research, there was not an available physical description of the notional permeability factor; hence, the determination of this factor was rather vague. Because of the fact that the stability relationship includes the P-coefficient, it has to be estimated somehow and, therefore, the research carried out by JUMELET [2010] is, to some extent, the starting point to achieve the required physical description of the notional permeability coefficient. In order to get this physical description, it is introduced the volume-exchange model where the external and internal processes that take place within a breakwater are coupled. The external process is described by a wave run-up model while the internal process is described by the .Forchheimer. equation for the water flow through a porous medium. According to JUMELET [2010], the notional permeability parameter P is highly related to the run-up reduction coefficient from the volume-exchange model, and so that Jumelet defines an expression for this coefficient by means of coupling the notional permeability factor with the volume-exchange model. Because of the simplicity of the notional permeability coefficient formula developed by JUMELET [2010] further research is required so as to analyze the actual correlation between the notional permeability factor and the so-called run-up reduction coefficient (obtained from the volume-exchange model). This study focuses in developing a general formula for the notional permeability coefficient based on JUMELET [2010] and analyzing the real influence of the hydraulic parameters and structural properties on the P-factor. As stated by JUMELET [2010], the permeability of the structure not only depends on the structural properties but also on the hydraulic parameters. In this way, a physical description of the notional permeability coefficient is given and is ready to be applied in Van der Meer stability equations to design breakwaters. In addition, the combined method of Jumelet.s model, the generalized formula for notional permeability coefficient and Van der Meer stability equations should be introduced as a tool to determine the maintenance policies in breakwaters by taking into account the damage that waves causes on them.

In de Van der Meer formulas for armour stability the Notional Permeability is used as a parameter. Unfortunately the physical basis of this parameter is weak. It is therefore suggested to use a relation between the Notional Permeability P and the reduction of wave run-up due to infiltration into the breakwater. The advantage is that the latter can be computed with VOF models. This makes is possible to estimate the value of P from mathematical models. Also the run-up reduction can be measured in a physical model, which has the advantage that physical tests for run-up are much faster to execute than models for armour stability.

Richards Bay Port, located in the East Coast of South Africa, was built during the 1970s. Two rubble mound breakwaters were constructed to protect the deep-water entrance channel and create a sheltered area for the vessels. Since the completion of these breakwaters in 1976, they have withstood several major storms, including cyclones that have caused significant damage to the dolos armour layers. To restore their functionality, two major reparations were carried out in 1976 and 1996, respectively. In addition, a severe storm that occurred in March 2007 caused relevant damages to the breakwaters of Richards Bay Port. Their damage level was established after the survey conducted in May 2007. This survey concluded that most of the breakwaters sections had an intermediate damage, except from the South Breakwater’s roundhead, which was in failure and it required urgent repairs. Since then provisional measures have been adopted to avoid the spread of damage along the breakwater while new repair works are designed. The main objective of this thesis was to determine the most suitable design for the repair works that should be applied in the roundhead of the South breakwater at Richards Bay Port through a Quasi Three-Dimensional (3D) model testing. This was achieved by reproducing the observed damage at the structure’s roundhead in one of CSIR’s hydraulic laboratory flumes and testing three repair alternatives. These repair alternatives consisted of covering the damaged structure with new armour units. Dolos, Core-Loc and antifer cubes were the armour units used in this research. The wave basin used to conduct this research had a length of 32m, a width of 4m and an available height of 1m. A transitional slope of 1:15 that extends about 4.5m long was built inside the basin to connect the deep water with the shallower water close to Richards Bay Port. Thereafter, the seabed profile corresponding to the South East direction was constructed along the next 20m of the basin. The structure was placed at a distance of 26m from the wavemaker. Graded gravel was used to construct the core, underlayer and toe protection of the roundhead, with a nominal size of 4.2g, 4.8g and 12.2g, respectively. The existing armour layer was built using dolos of 68g and gravel that represented the broken pieces. Above this damaged armour layer, the new armour units were placed with a nominal size of 82g for the dolos, 102g for the Core-Loc and 100g for the antifer cubes. The new armour units were placed trying to replicate the placement conditions at the roundhead. A total of 8 to 9 tests were conducted per armour unit. Five wave conditions were tested with increasing significant wave heights varying from 7cm to 18cm. Two water levels were set up per wave condition (High Water and Low Water). The tested wave conditions were generated with a JONSWAP spectrum and a duration that corresponded to a 1000 waves approaching the structure. Prior to and after each test, pictures were taken from three fixed positions perpendicular to the roundhead. These images were visually compared with the Armour Track software developed by CSIR to identify and quantify the movement of the armour units. This software is based on the superposition technique and it is useful to determine the stability of the structure. For each test, the stability number and the measured damage within the reference area were estimated. Generally the movements of the units occurred along the water line. However for higher wave heights (return periods of 20, 50 and 100 years), the waves overtopped and the damage started to concentrate in an area located between the angles 120 and 150 degrees from the direction of the incident wave, until failing with the overload condition. From these experiments it followed that the Core-Loc repair alternative does not perform as good as the other two options. Although all the repair options have difficulties to achieve the placement requirements at the roundhead, this phenomenon has a larger impact in the Core-Loc armour layer because it consisted of a single layer and any unit displacement resulted in failure of the structure. Therefore repairs should be undertaken more frequently, which leads to larger maintenance costs. The remaining repair options had a similar performance, even though the resistance mechanism of dolos and antifer cubes is different. The first one resists by the interlocking between the units, whereas the antifer cubes resist by their mass. Both are placed as double armour layers and thus some damage is allowed before carrying new repair works. The main difference between them is the actual feasibility to construct the units. The antifer cubes do not have any size restriction. Therefore heavier units can be manufactured without changing the stability of the unit. However, dolos have a size limitation because of its slenderness, and right now dolos heavier than 30-tonne cannot be built. Overall it could be concluded that the repair alternative consisting of antifer cubes is the one that should be applied at this particular location due to its performance and its construction feasibility.