Probabilistic modelling of the armour damage of cube-armoured mound breakwaters along their design life using experimental data

Abstract

Field data of armour damage in mound breakwaters is scarce, and experimental testing methods usually neglect the influence of pre-existing damage on subsequent damage increments. This study proposes a probabilistic framework, based on a dataset of 44 cumulative damage experiments, to estimate long-term damage progression in a full-scale, non-overtopped, cube-armoured mound breakwater located in the depth-induced wave breaking zone. A Gaussian copula-based Bayesian network is constructed to model the multivariate relationships between existing armour damage (S_e), the increment of armour damage (ΔS_e), the dimensionless water depth at the toe of the structure (h_s/H_m0), wave steepness (H_m0/L_0p), and the stability number (N_s). Each variable is modelled with a univariate parametric distribution, enabling inference of probabilities for values not directly observed in the experimental dataset. Model validation includes testing the Gaussian copula assumption, which is deemed a reasonable model, and assessing the defined graph with satisfactory results. The model is conditionalized using a historical wave dataset to generate synthetic damage curves, which are subsequently used to quantify a gamma process to model the survivability of the structure along its design life. A case study of a hypothetical breakwater with D_n=2 m close to the port of Tarragona (Spain) illustrates the methodology. According to the results of the model, the probability of observing a dimensionless damage S_e>5 corresponding to Initiation of Destruction after 10 years is 0.29. Overall, the obtained results are deemed conservative; this could be caused by the use of data from 2D experiments which do not take into account oblique wave attack. However, the approach is adaptable to other datasets with additional variables, breakwaters in different conditions or with other configurations, and can also be used in combination with simulations of synthetic wave data, making it relevant under changing climate conditions.