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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.

This study describes a theoretical approach of a physical description of the notional permeability factor in the stability formulae of Van der Meer [1988]. Caused by the empirical character of these stability formulae a physical description is not available for the notional permeability factor. In practice this leads to ambiguities in determining the value of this factor. To give this factor a physical description a volume-exchange-model was introduced to express the effect of core permeability on the external wave run-up process.

In JUMELET [2010] a method with a physical basis (so called “Volume Exchange model”) to determine the ‘notional’ permeability coefficient P was developed. The ‘notional’ permeability coefficient was previously introduced in the stability formula of the armour layer; see VAN DER MEER [1988]. In this latter study this coefficient was empirically based for three different structures. Due to the limited validity it is difficult to apply a coefficient for different breakwater configurations. The Volume Exchange model determines the influence of the core permeability by computing the difference between the surface wave run-up on an impermeable core and a permeable core. The volume of water that flows into the core causes a reduction of the wave run-up. Reduction of the wave run-up is not only caused by infiltration, but also by the slope surface roughness and energy dissipation inside the pores of the armour layer. To investigate the influence of the above three mentioned factors physical model tests have been conducted. The tests were carried out in the wave flume in the water laboratory at Delft University of Technology. On four different configurations (smooth impermeable slopes, rough impermeable slope, armour layer on an impermeable core and permeable core) tests were conducted. In the analysis of the results the influence of the surface roughness, energy dissipation in the pores of the armour layer and the reduction of the surface wave run-up due to the inflow into the core could be determined. Besides, the surface wave run-up also the wave run-up on the core is measured. The results showed that the slope surface roughness has no influence on the wave run-up, when the waves are of the surging breaker type. Also, the surface wave run-up is not reduced by a permeable core. Wave run-up measurements showed the same wave run-up height for armour layers on an impermeable and a permeable core. Wave run-up on the core showed a considerable difference between run-up on an impermeable core and a permeable core. Therefore, in the Volume Exchange model the wave run-up on the core should be considered. The adjusted Volume Exchange model is used to determine a formula for the permeability coefficient. This has led to the conclusion that the permeability coefficient is dependent on the Iribarren number and the structural configurations and /or properties.

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.