Bearing capacity analysis of a full-scale 3D jack-up rig by the implicit elastoplastic FE method incorporating the skew-boundary condition and consistent tangent algorithm

The prediction of the bearing capacity of a three-dimensional (3D) jack-up rig is of vital importance for the safe exploration of offshore hydrocarbon resources. Existing numerical approaches mainly rely on explicit formulations which require the use of very small time increments or artificial stabilization techniques to maintain numerical stability and accuracy, especially when approaching failure. This study presents a novel computational framework that integrates a consistent tangent-stiffness-based implicit elastoplastic finite element (FE) method with a skew-boundary-condition-based interface model to analyse the bearing capacity behaviour of full 3D jack-up rig foundation systems. The structural components are treated as linear elastic, whereas the soil is modeled by the Mohr–Coulomb (MC) failure criterion. The proposed implicit formulation guarantees the consistency condition of the yield surface which sustains the numerical accuracy and stability without the need to use extremely small time increments and incorporate material viscosity artificially to suppress the numerical instability, thereby avoiding the dependency of simulation results on material viscosity as commonly encountered in explicit elasto-viscoplastic approaches. The method is verified by comparing the computed bearing capacity factor ( N c ) of a wedge-shaped footing and a single spudcan with those predicted by established design methods and other numerical methods. The framework is further applied to simulate the full-scale 3D jack-up rig system, capturing the progressive development of soil yielding and foundation failure. Results show that the numerically predicted N c value is slightly higher than those recommended by Society of Naval Architects and Marine Engineers (SNAME) and International Organization for Standardization (ISO) guidelines, suggesting the possibly conservative nature of these simplified approaches.