## 2 Methods
### Time-Domain Multi-Physics Model  
The numerical time-domain tool used in this study is OpenFAST. This is a type of open-source software developed in Fortran 95, used for studying both onshore and offshore wind turbines. It is defined as a numerical model that extends the capabilities of the FAST v8 code, analyzing turbines and wind farms through different modules that define and simulate aerodynamic, hydrodynamic, elastic, and structural characteristics. Being open-source, OpenFAST allows users to access and modify its source code, which facilitates its continuous evolution through modifications and improvements stored on a GitHub repository [24].  
All the simulations presented in this study were performed while taking into account the following considerations: The aerodynamic loads on the blades and tower were calculated using the AeroDyn module [25], which accounts for rotor wake and induction, blade airfoil aerodynamics, the tower's influence on the fluid near the blade nodes, and tower drag. The wind input files were generated with the program TurbSim [26] and computed with InfloWind [27]. The structural dynamic responses of the rotor, drive-train, nacelle, and tower were modeled using the ElastoDyn module, with a modal formulation for the blades and tower and a multi-body approach for the drive-train and nacelle [28]. The control and electrical drive dynamics were modeled using the ServoDyn module, simulating the control and electrical subsystems of the wind turbine. Wave loads and fluid-structure interaction phenomena were simulated using the HydroDyn module [29], which can use a potential-flow theory solution, a strip-theory solution, or a combination of both to calculate the hydrodynamic loads on the submerged part of the substructure. The structural dynamic response of the substructure, from the transition piece to the base, was computed using the SubDyn module, starting with a linear-frame, finite-element beam discretization of the structure. A more detailed explanation of each module can be found in the OpenFAST Documentation [24].  
The SubDyn module [30] was modified to incorporate dynamic soil-structure interaction effects by adjusting the FEM subroutine and the state-space formulation. The implementation developed is described in [31,32], and the code can be found at [[https://github.com/mmc-siani-es/openfast_3.0.0_multisupport](https://github.com/mmc-siani-es/openfast_3.0.0_multisupport)]([https://github.com/mmc-siani-es/openfast_3.0.0_multisupport](https://github.com/mmc-siani-es/openfast_3.0.0_multisupport)) (accessed on 5 February 2025). It uses a lumped parameter model (LPM) at the mudline level to simulate the dynamic interaction between the foundation and soil. The LPM used in this study was initially proposed and validated by [PERSON] et al. [33] and later tested in [34,35]. The LPM configuration, characterized by eccentric elements, allows for the simultaneous modeling and fitting of translational, rotational, and horizontal-rocking coupled impedance functions, while the vertical and torsional impedances are modeled using first-order LPMs because of their lesser influence on the turbine's response [36]. To reduce the discrepancies between the two compared models, the frequency-dependent impedance functions considered to adjust the LPM were obtained from the same numerical model [18] considered for the simplified static-equivalent model.