Analysis of the notional permeability of rubble mound breakwaters by means of a VOF model

Abstract

When designing a rubble mound breakwater, one would like to predict the stability of the armour layer of the breakwater. For this purpose several armour layer stability formula are developed. The most reliable is considered to be the stability formula of Van der Meer (1988). With this method, the armour layer stability is predicted based on several parameters. One of these parameters is the so-called notional permeability, P. The definition of the word notional is important to keep in mind; existing as or based on a suggestion, estimate, or theory; not existing in reality. Or, in other words, the notional permeability is not a physical description of the real permeability of a breakwater. Furthermore, there are no methods to calculate the notional permeability. This makes it difficult to estimate a safe and reliable P-value for an arbitrary structure. The definition of the notional permeability suggests that a single P-value can be attributed to a structure. However, previous research has suggested that the notional permeability is not only dependent on structural parameters, but also on hydraulic parameters. This makes the assumption of a single P-value for a particular structure under arbitrary hydraulic conditions invalid. The P-value should therefore vary under varying hydraulic conditions. This thesis aims for a better understanding of the physical processes the notional permeability. Some of the original physical model tests of Van der Meer (1988) are selected for analysis to achieve this goal. As a tool the numerical model IH2VOF is used. This 2D vertical model is able to simulate flow interaction with porous media. And makes it possible to measure pressures and flow velocities at any point within a breakwater. In this way physical processes can be described as functions of pressures and flow velocities. The model is able to simulate porous flows by Volume Averaging the Reynolds Averaged Navier Stokes equations. This Volume Averaging introduces a porosity into the equations. Furthermore, the extended Forchheimer equation is needed to close the equations. This additionally introduces the laminar and turbulent Forchheimer coefficients and added mass coefficients to the equations. These four variables describe the porous media and are required as input to the model. Based on a literature study a hypothesis is made about the variables on which the notional permeability is dependent. The Buckingham PI theorem is applied to these variables, resulting in four dimensionless PI terms. Eventually it is concluded that the PI terms are best measured 0.5 times the significant wave height below the initial water level, inside the armour layer and in a normal direction to the front slope of the structure. With this approach, all four PI terms show a positive correlation with P.