Stability of a single top layer of cubes

Abstract

In an attempt to reduce the cost of breakwaters, several elements have been developed. Examples are Accropodes, Tetrapods and concrete cubes. Previous tests were performed with armour layers consisting of a double layer of cubes. This study is based on a single layer of cubes. The great benefit of a single layer of cubes is that it reduces the total cost of concrete. Another benefit is that because of the shape, cubes are easy to prefabricate. Three important aspects considering the stability of a single armour layer of a breakwater consisting of concrete cubes are addressed: The influence of the wave steepness on the stqbility, the influence of the slope on the stability of the single armour layer, and the influence of the packing density on the stability of the single armour layer. This study is based on a literature study and the results from a test program including a small-scale physical model tests. All conclusions in this thesis have been based on model tests, in which the cubes were placed by hand and placed in a stretching bond (half-steensverband). In total eighteen tests were performed in the wave flume of the Fluid Mechanics Laboratory of the Faculty of Civil Engineering and Geosciences. Two different slopes were tested together with three different packing densities and three different wave steepness. It was found that the gentler slope did not contribute to the stability in this setting using a stretching bond. In fact the model failed earlier than the model with a steeper slope in most cases. The best results were found using a slope of cot? = 1.5. Secondly, the influence of the packing density showed varying failure mechanism. When applying a large packing density (np = 0.20) the damage occurred below SWL. Contrary to small packing densities (np = 0.35) where damage occurred higher than SWL. It was found that, from the tested packing densities, a packing density of 0.28 gives the best results for both slopes. This conclusion is conform the findings of previous tests [Van Gent et al, 1999]. During these tests an optimum packing density of np = 0.25 – 0.30 was found. Although the cubes were placed randomly in the tests of Van Gent. In this study the cubes were placed in a stretching bond. Finally it was found that a wave steepness of s0p = 0.04-0.05 causes minimum stability for the armour layer. The tests with a single armour layer of cubes placed in a stretching bond indicated that high sta-bility numbers (Hs/?Dn) can be reached before failure occurs (Nod > 0.2). the tests show that sta-bility numbers as high as 4.5 can be realized before Nod > 0.2 is reached. This study shows that the use of a single top layer of cubes is feasible. The top layer becomes very stable when placed in a stretching bond. In this configuration it is recommended to use a single top layer of cubes instead of a double top layer of cubes. The results during the tests seem to have a strong correlation with pitched stones. Therefore the black box model as well as the analytical method for pitched stones (6-xi-rule) is treated in an attempt to optimize the design rules for different configurations. Finally, in combination with an adjusted 6-xi-rule and the formulae from Van der Meer for loose rock, formulae were developed based on curve fitting.