As a first step to develop a probabilistic method for the maintenance and repair of breakwaters, one 28.5-h test and two shorter tests, which were repeated twice, were conducted in a wave flume. Damage progression and variability were measured on a conventional rubble mound exposed to depth-limited breaking waves in sequences of storms with varying wave conditions and water levels. Measurements were made of 16 or 32 damage profiles every 30 min of irregular wave action. Each measured profile was characterized by the eroded area, depth and length of the armor layer, and the remaining cover depth. The mean and standard deviation of these statistical variables changed with damage progression, whereas the probability distributions of the normalized variables were practically invariant. The mean and standard deviation of the damage variables are shown to be represented empirically by the mean eroded area alone. The damage variability along the breakwater was significant. Finally, an empirical formula is proposed to predict the mean eroded area in sequences of storms for these three tests.

Progression and Variability of Damage on Rubble Mound Breakwaters

The stability of a cubic armored breakwater head and trunk under monochromatic wave trains is experimentally studied. For the head there is a sector, roughly of 60°, where the unit stability is minimum. The stability function values (similar to Hudson's number) are 1.3‐three times higher there than those obtained from biodimensional tested sections. Head shape, at least for the cases tested, does not exert significant influence on the head stability. Trunk sections tested under long crested waves with a standing longitudinal wave height variation (here called quasi‐three‐dimensional [3D] tests) are less stable than two‐dimensional (2D) tested sections. Furthermore, trunk and head sections show a different behavior as the damage grows; the radio of initiation of damage wave height to destruction wave heights is much lower for head than for trunk sections. Head sections are more brittle than trunk sections. Additionally, exploration was carried out into standing longitudinal variation of wave height along t...

Stability of mound breakwater's head and trunk

Motivated by existing damage accumulation modeling difficulties, some suggestions on how to build consistent stochastic models for damage accumulation in breakwaters are given. The models avoid the selection of easy to use mathematical functions, which are replaced by those resulting from a set of properties that are expected in the model. It is shown how an inadequate selection of damage progression models leads to inconsistencies, which are avoided by using the proposed consistent mathematical structures. Dimensional analysis, compatibility conditions, and the central limit theorem are the bases for building a model aimed at reproducing the stochastic damage progression on breakwater as a result of general random wave actions. Four elements are identified as essential for a damage accumulation analysis: (1) the statistical distribution of the initial damage, (2) the mathematical structure of damage growth curves, (3) the damage function, which accounts for how the variables affect damage, and (4...

Stochastic Model for Damage Accumulation in Rubble-Mound Breakwaters Based on Compatibility Conditions and the Central Limit Theorem

Dolosse: Past, Present, Future?

Nowadays, risk based designs as well as reliable rehabilitation and maintenance strategies are essential when dealing with coastal structures In this sense, the probability of failure due to instability of the armour layer is one of the main issues in rubble mound breakwaters, and so is improving the knowledge on its deterioration rate Both stability and damage progression on rubble mound breakwaters have been studied for more than 80 years, using different approaches, under regular/irregular waves and testing diverse geometries and armor units However, due to the complexity of the processes involved, there are some modelling difficulties and the applicability of the different proposals is usually restricted to the typologies and specific range of the parameters tested in laboratory for deriving their empirical coefficients Also, there are not many experimental results focused on the stochastic nature of damage progression, which is indeed an essential part of the problem Despite being relatively common in coastal laboratories, a lack of standards for damage progression experiments in rubble mound breakwaters has been perceived What is more, the concept of damage itself and how it is measured seems to be a debatable issue, specially taking into account the potential of the recent advances in scanning techniques for monitoring small scale model as well as prototypes Regarding the large amount of information on this topic, part of the present dissertation is focused on stating a discussion on damage definition, describing the parameters influencing armor layer stability and providing a detailed historical overview of the most relevant models and contributions in the study of damage progression on rubble mound breakwaters Also, a methodological approach for damage progression experiments is provided, describing, step-by-step, its main peculiarities and considerations Following this approach, a set of experiments have been carried out in order to characterize the stochastic nature of damage progression in a quarry stone model, in which an innovative post-processing based on the results of a structured light scanner is presented These results, together with the ones from Melby and Kobayashi (1999), are used for accomplishing an initial calibration of the damage progression probability model of Castillo et al (2012), which was fully derived under probabilistic assumptions and following premises of general validity A methodology for calibrating this model is also proposed and some preliminary conclusions derived from the results are proportioned However, further experimentation covering a wider range of design parameters, ideally both in model and prototype, is needed for achieving a fully developed tool for assisting rubble mound breakwater design and conservation

R. Escutia

Papers

Reliability of Breakwater Model Tests