The term “damage” in rubble mound breakwaters is usually related to the foremost failure mode of this kind of coastal structures: their hydraulic instability. The characterization of the breakwater response against wave action was and will be the goal of hundreds of studies. Because of the large amount of information, the present review on damage in rubble mound breakwaters is divided in two papers, which are closely linked but conceptually different; whereas Part II is focused on the various approaches for defining and measuring damage, Part I summarizes the diverse strategies for modelling damage development and progression. The present paper compiles 146 references on this topic, chronologically discussed over almost a century of history: from 1933 to 2020. It includes 23 formulations of hydraulic stability models and 11 formulations of damage progression models, together with main advances and shortcomings up to date. The future of rubble mound design is linked to risk-based tools and advanced management strategies, for which deeper comprehension about the spatial and temporal evolution of damage during the useful life of each particular structure is required. For this aim, damage progression probabilistic models, full-scale monitoring and standardization will presumably be some of the key challenges in the upcoming years.

Damage in rubble mound breakwaters has been addressed for more than 80 years and, as reported in “Part I: Historical review of damage models”, a considerable number of hydraulic instability models have been proposed up to date. Most of them were developed from small-scale physical tests, based on damage descriptors not always parameterized nor measured in the same way, which indeed complicates the comparison and reproducibility from different experimental data sources. The latter is increased by the lack of a standardized methodological approach inside an experimental and measuring process that involves many sources of uncertainty. Currently, the latest innovations applicable to damage measurement, together with the growing demand of reliable decision-making tools for conservation/maintenance strategies and structural/operational risk management, venture an upcoming proliferation of prototype monitoring, as well as new approaches aimed to characterize the stochastic nature of damage evolution. In this context, this paper is meant to review the concept of damage in rubble mound breakwaters, the different proposals for its parameterization, the past and present measuring techniques, and main challenges in the near future.

This paper describes a Long Short-Term Memory (LSTM) neural network model used to simulate the dynamics of the OC3 reference design of a Floating Offshore Wind Turbine (FOWT) spar unit. It crafts an advanced neural network with an encoder–decoder architecture capable of predicting the spar’s motion and fairlead tensions time series. These predictions are based on wind and wave excitations across various operational and extreme conditions. The LSTM network, trained on an extensive dataset from over 300 fully coupled simulation scenarios using OpenFAST, ensures a robust framework that captures the complex dynamics of a floating platform under diverse environmental scenarios. This framework’s effectiveness is further verified by thoroughly evaluating the model’s performance, leveraging comparative statistics and accuracy assessments to highlight its reliability. This methodology contributes to substantial reductions in computational time. While this research provides insights that facilitate the design process of offshore wind turbines, its primary aim is to introduce a new predictive approach, marking a step forward in the quest for more efficient and dependable renewable energy solutions.

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.