Study on the failure envelope of tripod pile foundations under H-M-T combined loading mode

To further explore the bearing capacity limit and failure characteristics of a tripod pile foundation in offshore wind farms under dynamic environmental conditions, a 3D finite element limit analysis model was established using OPTUM^G3. The study systematically investigates the failure envelope characteristics under unidirectional loading, H-T bidirectional loading, and the more complex H-M-T triaxial combined loading mode. Special attention is given to the effects of two key parameters, depth-to-diameter ratio (L/D) and center-to-diameter ratio (s/D), on the failure envelope of the tripod pile foundation. Based on MATLAB, the ultimate bearing capacity of the tripod pile foundation is predicted, and an Artificial Neural Network (ANN) model is established to provide a predictive equation. The results show that: (1) The application of torsional load causes the failure envelope in the H-M plane to shrink but does not change its position in the plane. The failure mode of the pile-soil system shifts from overturning failure to torsional extrusion failure, and the distribution of shear dissipation is direction-dependent; (2) The ultimate bearing capacity of the three-pile foundation increases with the increase in L/D and s/D. However, the effect of these parameters on enhancing the normalized ultimate bearing capacity under H-M combined loading conditions is limited; (3) The ANN predictive model effectively estimates the ultimate bearing capacity of the tripod pile foundation under the combined loading mode. This study provides a reliable basis for accurately assessing the ultimate bearing capacity of tripod pile foundations under complex loading conditions.