Reliability-based dynamic damage modelling for monopile scour protection under combined waves and currents

Abstract

Scour around monopile foundations presents a critical risk to the structural stability and serviceability of offshore infrastructure. Traditional deterministic models often fail to capture the inherent uncertainties and non-linear dynamics of scour progression and protection system degradation. This study develops a probabilistic framework to evaluate dynamic scour-induced damage functions using three complementary modeling techniques: the Model Tree (MT), Bayesian Regression (BR), and Explanatory Regression (ER). These models incorporate environmental and structural variables, account for epistemic uncertainties, and generate damage estimates expressed via the three-dimensional damage index (S_3D). 160 experiments from six independent sources were used to train and validate the models, incorporating both wave and current effects. The damage evolution is quantified probabilistically across storm durations using a normalized damage function with wave number (N), S_3D/N^0.243. In this study, to evaluate the probability of failure and generate the Exceedance Probability curves, 1,000,000 (one million) iterations of Monte Carlo simulation were used for each of the three models (MT, Bayesian, and Explanatory) and for each wave number scenario (N = 1000, 3000, 5000). This high number was selected to ensure statistical accuracy in the probability estimates, particularly for low-probability damage levels (the tails of the distribution). Results demonstrate that the ER model yields the highest predictive accuracy (Coefficient of Determination [R²] = 0.7534), followed by BR and MT. Importance analysis reveals that U_C/w_s (ratio of the depth-averaged flow velocity [U_C] to sediment particle fall velocity [w_s]), associated with hydrodynamic forcing, is the dominant contributor to scour damage. The probabilistic approach effectively captures the spatial and temporal variability of damage, offering enhanced insight into risk-informed design and maintenance of monopile scour protection systems. By integrating data-driven and interpretable regression methods into a unified reliability framework, the study advances the assessment and forecasting of dynamic scour impacts in offshore environments.