Rocking Revisited 1

Rocking of a Singe Cube on a Breakwater Slope

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Prototype single layer armour units on a breakwater slope are observed to break. To predict when breakage occurs, the objective of this research project is to obtain knowledge on, and measurements of the rocking behaviour and failure mode of single layer armour units. A single cube on a breakwater slope is subjected to investigations. An analysis of previously conducted research by CUR C70 reveals a number of important weak points. The first point is the assumption for the fixed number of 3 collisions per moving unit. The second point is the deployment of a one-directional accelerometer. Consequently, the impacts, which occurred in different directions relative to the orientation of the accelerometer, were not captured accurately. The third point is the exclusion of the wave steepness during tests for impact velocities. The outcome of the calculation by CUR C70 is largely dependent on the mentioned points. Therefore, it is chosen to take those points into account in the current research. Wave flume tests are conducted, in which a similar set-up as in the theoretical analysis is applied. This is chosen to have a better insight in the physical processes. The tested parameters is: degree of exposure of cube, wave height, wave steepness and position on slope in relation to the water level. It is chosen to measure the accelerations due to movement. A three-axis accelerometer, which is placed in the cube’s centre, is applied during this Master's Thesis. Data processing shows that crosstalk occurs in two accelerometer axes. Therefore, only the accelerometer z-axis is processed. To come to the desired impact velocities, a synthetic model is used, which takes the time period of movement and the angle of the cube before and after movement as input values. Subsequently, the output is the angle of the cube in time. Differentiation of the angle in time results in the angular velocities, in which the impact velocity is taken to be equal to the occurring velocity before collision. Analysing the data shows that the number of collisions is dependent on the wave height, wave steepness, position on the slope and degree of exposure of the cube. Hence, an assumption for a fixed number of 3 collisions by CUR C70 is proven to be inaccurate. Therefore, it is recommended that the amount of collisions of a moving unit is regarded as a function that has dependencies on hydraulic and geometric conditions. For multiple conditions the number of collisions is observed to become very large and hence, concrete fatigue becomes important. Consequently, it is recommended to incorporate fatigue in the calculation procedure by CUR C70. Furthermore, it is concluded that the wave steepness is of influence for the probability distribution functions and hence, the exclusion of the wave steepness by CUR C70 is proven to be incorrect. The wave steepness should be included as a variable parameter in the probability distribution function for impact velocities. In addition, it is observed that the data is described best with a Weibull distribution, which is different from the exponential distribution obtained by CUR C70. However, the two distribution types are from the same family of distributions and hence, the differences between the distribution functions remain small. Next, it is clearly observed that the probability distribution is dependent on the type of movement and therefore, it is advised to consider multiple types of movement to find the governing impacts. Lastly, analysis shows that the analytical model overestimates the impact velocities and therefore, is too conservative. The assumptions made for the analytical model should be further investigated to derive a more accurate calculation method.