Simplified methods of static free head stiffness of the semi-rigid foundation under lateral loads were limited to flexible or rigid behavior by the critical length of piles. This would lead to errors when predicting the static or dynamic performance of their upper structures in OWT Systems. This paper presents a comprehensive analysis of the head static stiffness of the semi-rigid pile without considering the critical length. Firstly, case studies using the energy-based variational method encompassing nearly twenty thousand cases were conducted. These cases involved different types of foundations, including steel pipe piles and concrete caissons, in three types of soil: homogeneous soil, linearly inhomogeneous soil, and heterogeneous soil. Through the analysis of these cases, a series of polynomial equations of three kinds of head static stiffness, containing the relative stiffness of the pile and soil, the slenderness ratio, and Poisson’s ratio, were developed to capture the semi-rigid behavior of the foundations. Furthermore, the lateral deflection, the rotation for concrete caissons in the bridge projects, and several natural frequencies of three cases about the OWT system considering the SSI effect were carried out. the error of high-order frequency of the OWT system reached 13% after considering the semi-rigid effect of the foundation.

Current calculation methods for the vertical bearing capacity of steel pipe piles are predominantly designed for smaller diameters and do not account for the soil inside the pile. This necessitates an evaluation of their applicability to piles with diameters exceeding 2.0 m. This study aims to refine the existing formula for calculating vertical bearing capacity, as outlined in the Port Engineering Foundation Code of China, by investigating the vertical bearing capacity of large-diameter steel pipe piles through numerical simulations. By analyzing the relationship between the internal friction resistance of the soil core within the pipe and the bearing capacity for diameters ranging from 2 m to 10 m, this paper proposes a revised formula specifically tailored for steel pipe piles with diameters greater than 2 m, incorporating the effect of the soil core. The validity of the proposed formula is then confirmed through comparison with field data from four large-diameter steel pipe piles. The results demonstrate that the modified method proposed in this study performs better than the original formula when compared with the measured data.

In various analytical models, modeling the behavior of large-diameter monopiles and piles can be challenging due to these foundations with huge body sizes carrying mechanisms of lateral loads to the surrounding soils. In this paper, the transfer matrix method with the Timoshenko beam theory was used to modify the shear rotation of pile sections under different loading stages, including serviceability limit stages and the ultimate loading stage. In this transfer matrix method, a large-diameter pile is considered according to the Timoshenko beam theory, and the recurring variables in the matrix equation are replaced with constants to simplify the calculation steps. Two model test cases were used to verify the accuracy of the method. Then, a series of comparisons between the Timoshenko beam and the Euler–Bernoulli beam theories, with the relative pile–soil stiffness being equal to 0.15, 0.45, and 0.75, was conducted to investigate the differences in pile response after considering the shear deformation. The results show that the effect of shear deformation of large-diameter piles changes with different loading levels. The values of the pile deformation based on the Timoshenko beam theory divided by those of that based on the Euler–Bernoulli beam theory were in the range of 1.0 to 1.10, and they increased slightly with increasing loads, reaching their maximum value, and then rapidly decreased to 1.0 when close to the ultimate lateral load; the maximum value was influenced by the relative pile–soil stiffness. Furthermore, the ratio of the shear rotation of the pile section to the slope of the deflection curve was in the range of 1.0 to 1.10; these also showed similar but more moderate trends compared with the values of pile deformation based on the Timoshenko beam theory divided by those of that based on the Euler–Bernoulli beam theory.