Efficient reliability analysis of laterally loaded offshore monopile in spatially variable clays: A DeepONet-based approach

Offshore monopiles in clayey seabed suffer from significant uncertainties from the pile-soil parameters, which influence their bearing performance and necessitate reliability-based design. However, conventional random finite element model (RFEM)-based reliability analyses often prescribe random field parameters as fixed values before training surrogate models, although these parameters are highly uncertain in practice. To overcome this limitation, this study proposes an efficient surrogate modeling framework based on the Deep Operator Network (DeepONet), which learns nonlinear operators in infinite-dimensional spaces without predefining statistical parameters as explicit model inputs. A comprehensive database is established using the results of numerical calculations. Four independent DeepONet models are developed to map stochastic soil strength profiles and pile-soil parameters to nonlinear pile responses. The trained models achieve exceptional prediction accuracy, with median accuracy metrics exceeding 0.96 for lateral deflection, rotation angle, bending moment, and shear force. Blind case studies demonstrate robust extrapolation capability of the model. By leveraging the trained DeepONet as a surrogate, large-scale Monte Carlo simulations (MCS) with 10,000 realizations are completed in about 0.9 s, enabling efficient failure probability estimation and sensitivity analysis. The proposed framework offers a promising and computationally efficient solution for reliability-based design of offshore monopiles in spatially varying clays.