Registros

In this paragraph an attempt is made to realize formulae in which the influence of the packing density and the influence of the slope are combined. The formulae by Van der Meer are used as a starting point to develop formulae which include the packing density. The formula for a double layer of cubes doesn‟t involve the surf similarity parameter. Therefore no distinguish is made for surging and plunging waves. Looking at the plotted results from the test series this it seems un-justified. Therefore the formulae for loose rock is used as a starting point.

Since we have a different configuration than riprap, the permeability parameter is not applicable here. As well as the form of the damage number. The waves were kept constant in this study. Still the formulae by Van der Meer is used as a starting point to develop formulae which include the packing density and slope variation.

6.4.1 Formulae

Van der Meer used the distinction between surging waves and plunging waves. Therefore, and based on the fact that the stability probably increases when ξ0p > 3, The same is done here. The plotted data does show an increased stability when ξ0p > 3 occurs. The following formulae are developed that can be applied for cubes that are placed in a stretching bond.

For plunging waves



 

c_pl = coefficient for plunging waves depending on packing density [-]

The formulae use different coefficients for different breaker types. The coefficients for different wave conditions are found through curve fitting. For different packing densities different proc-esses play a role. In the next paragraph this will be discussed. For now the different coefficients are presented in the next table.

Table 18. Coefficients for breaker types

Packing density [-] np 0.2 0.28 0.35

Coefficient for plunging waves [-] cpl 8.5 15 10.5 Coefficient for surging waves [-] cs 1.1 1.5 1.25

It must be mentioned that this is a careful estimation in case of test series B and E, since with this packing densities no damage occurred. Similar to Van der Meer‟s equations there is a point of

6 / 7

When applying the formulae on the test serie A, the following results are plotted.

0 1 2 3 4 5 6 7

Figure 33. A Series with formulae

All other test series are plotted using the formulae above and presented in appendix I.

6.4.2 Physical process

In this paragraph an attempt is made to specify the physical processes which form the basis for the behaviour of the different results found in the previous chapters.

For an armour layer basically two different failure mechanism can be distinguished. Those are:

 The situation in which the wave has maximum withdraw.

 The situation in which the wave hits the armour layer.

The first situation, in which the wave has it‟s maximum withdraw is a complex dynamic progress.

This process has it‟s maximum at the lowest point of the waterline. At this point, a flow occurs in the direction of the armour layer elements from within the sub layers and core. The flow will result in a pressure difference that can lift the armour layer elements from the top layer. For the stabil-ity of the armour layer it is important that the water easily flows through the armour layer but, at the same time, it has difficulties flowing through the sub layer.

This process, elevation of the cubes out of the armour layer, happened when the packing density of n = 0.20 was applied. Therefore this mechanism is the cause of failure for this configuration.

The second process is more or less the reverse mechanism. At the moment of impact a pressure peak occurs at the top of the armour layer elements, which subsequently penetrates the sublayer.

Although this happened for all packing densities, the packing density of np = 0.35 suffered the most from this failure mechanism. Due to the large gaps the cubes couldn‟t interlock enough to withstand the wave impact and started to rotate and finally subsided.

Although the packing density of np = 0.20 failed because of the pressure difference which was formed during the wave trough, it was capable resisting the wave force.

Based on the tests it can be said that the packing density of n_p = 0.28 was the most stable con-figuration. It seems to be the optimum packing founded on the facts that is capable of releasing the pressure and withstand the wave attack at the same time.

The test results show that a slope of cotα = 1.5 is more stable than a slope of cotα = 2.0. The steeper slope seems to benefit more from the gravity in the form of friction between the armour elements. When the slope gets steeper the cubes seem to rely more on the neighbouring cubes.

The more gentler slope therefore relies less on the friction between the elements and therefore get lifted easier when packing density of np = 0.20 is applied. Also when a packing density of np = 0.35 was used in combination with a slope of 1:2, the cubes started to rotate sooner than on a slope of 1:1.5.

The findings in this paragraph seem to justify the surging and plunging coefficients found through curve fitting.

7. CONCLUSIONS

The main objectives of this study are to assess the influence of the slope, packing density and wave steepness on the stability of an armour layer consisting of concrete cubes placed in a stretching bond. The study consists of hydraulic testing performed in a wave flume from the Fluid Mechanics laboratory of the Faculty of Civil Engineering and Geosciences at Delft University of Technology. A total of eighteen tests were performed. During these tests three different wave steepness were tested, as well as three different packing densities and two different slopes.

The following test program was realized.

Table 19. Test program of the study

Test series n_p cot α s_0p

A 0.20 1.5 0.02-0.06

B 0.28 1.5 0.02-0.06

C 0.35 1.5 0.02-0.06

D 0.20 2.0 0.02-0.06

E 0.28 2.0 0.02-0.06

F 0.35 2.0 0.02-0.06

Additional, the placement method is an important parameter. The cubes were placed by hand in a stretching bond configuration.