Numerical analysis of the Forchheimer coefficients and the maximum pressures for a dike with impermeable core and permeable Elastocoast layer

Abstract

The Van der Meer formula for amour stability takes the Iribarren number, number of waves and damage level into account. It also contains a factor P which describes the “notional permeability” of the breakwater. This factor is based on the fact that a more permeable structure dissipates more energy and hence requires less heavy armouring. Its value depends on the different layer designs of the breakwater. The notional permeability (P) was empirically determined by van der Meer [1988] for three different standard situations, to be exact the P=0,1, P=0,5 and P= 0,6. It is difficult to find the exact value of this parameter. From a physical point of view the value of P should depend on the Forchheimer coefficients. These coefficients describe the permeability of the filter layers and core of the structure. Without these coefficients a breakwater cannot be accurately calculated in a numerical model. The intention of this research is to use the IH-2VOF model and to determine the pressures by the transition zone from the core of the breakwater with impermeable core and permeable layer. In the Großer Wellen Kanal (GWK) in Germany tests were done for a dike with impermeable core and permeable Elastocoast layer with a porosity of 0,388 and a stone diameter of 34mm. The maximum pressure which is measured in the GWK is 5,6 kPa. In this study the results of these GWK tests are compared with the mathematical model. This test is simulated in the IH2-VOF model with non impact regular waves with Hm = 0,18m, Tm = 5,93 sec and a water depth of 3,40 m. For this study 190 combinations of Forchheimer coefficients are run with the VOF model. The Forchheimer coefficient ? is varied between 200 and 2000 and the coefficient ? is varied between 1,0 and 1,9. Finally, twelve possible combinations of the coefficients gave an error less than one percent and two of these combinations gave the smallest error of 0,3 percent. This combinations are ? = 200 and ? = 1,7 and ? = 1700 and ? = 1,7. By the impact regular wave test with Hm = 0,98m and Tm = 2,99 with the same Forchheimer coefficient as above, the model gave an error of approximately 45% in the prediction of the pressures. In the next step of this research it is tried to improve the value of the Forchheimer coefficient by using a constant value ? = 1700 and ? = 1,7 and change the stone diameter and the porosity to find a better agreement with the maximum pressure. The porosity is varied between 0,25 and 0,55 and the stone diameter is varied between 8,5 mm to 136 mm. The results of the tests are close to each other. Only the tests with a porosity of 0,25 and stone diameter of 8,5 mm are not near to the real value of 10,77 kPa. The porosity and the stone diameter have an impact on the maximum pressure. However, after a certain value, the impact is noticeable. Hence it is possible to choose by a porosity of 0,388 a stone diameter between 0,017 m and 0,136 m and by a diameter of 0,034 m a porosity between 0,35 and 0,45. These values have not a big impact on the maximum pressure. The dike is also tested with Irregular waves with number of waves of 400 and the wave height Hm = 0,8 m. Different tests are run with the model for different Iribarren numbers which is varied between 1,0 to 5,0. It is visible that the Iribarren number and the maximum pressure are related to each other for both plunging and surging waves. In contrast to what has been mentioned above, the maximum pressure and the filter velocity for surging waves gave quite irregular results, whereas by plunging waves there is a regularity with the filter velocity and maximum pressure. The main conclusion of this research is that when using a VOF model to predict pressures inside a breakwater, it is essential to have a correct value of the Forchheimer coefficients. Simply using a standard value on the basis of the grain size only is not accurate enough.