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

Abstract

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) the integral form in which damage accumulates, which permits relating its random character to the normal distribution. These four elements are combined to derive a general structure of models for determining the damage produced by any wave history, and to obtain the evolution of densities of cumulative damage with time. Finally, the proposed methods are illustrated by means of a real case example, and one of the models proposed is shown to be convenient in reproducing damage progression in breakwaters. The proposed method is valid not only for breakwaters but to other evolutive processes appearing in the maritime and coastal engineering field.