Analytical Evaluation of Vertical-Load Effects on the Lateral Response of Semi-Rigid Monopiles in Undrained Clay

Offshore wind turbine monopiles with different pile-soil stiffness characteristics may experience coupled vertical, horizontal and moment loading, but the interaction between the vertical load and the lateral response is still often simplified in practice. For monopiles installed in undrained clay, this interaction is governed by a mechanism different from that in sand: vertical shaft friction alters the local stress state around the pile and rotates the principal stress direction, thereby changing the mobilised lateral soil resistance. This paper develops an analytical framework for evaluating the lateral response of monopiles under combined V-H loading in undrained normally consolidated clay using the Tresca criterion (Mohr-Coulomb criterion with an undrained friction angle φu = 0). The formulation first embeds the P-Δ effect, nonlinear p-y resistance and the restoring moment generated by non-uniform shaft friction into an elastic-foundation beam model. The vertical load-transfer problem is then used to quantify the axial-force distribution and the associated frictional stresses along the pile. To capture the clay-specific coupling mechanism, the strain-wedge model is modified by introducing a stress-rotation-dependent wedge angle, which updates the ultimate soil resistance in the p-y curve. The proposed method is examined against published benchmark data and three-dimensional finite-element simulations. The comparisons show that vertical loading in undrained clay can increase pile-head displacement and reduce lateral capacity by modifying the local stress state and principal stress direction of the surrounding soil. At V = 0.9 Vult, lateral capacity fell by 9.8% at 0.1D, and 16.3% at 0.15D, relative to the uncoupled case. The parametric study reveals that the unfavourable P-Δ and p-y curve effects dominate over the beneficial MR effect, resulting in an overall reduction in lateral capacity across varying slenderness ratios. The method provides a transparent and computationally efficient tool for assessing coupled vertical-lateral monopile behaviour in cohesive seabed deposits.