## 1 Introduction  
Over the last few decades, offshore wind energy has experienced significant advancements due to the necessity of alternative energy sources in the transition from fossil fuels to renewable energies. This is motivated by the more favorable conditions offered by the marine environment compared to land. Regarding the current state of offshore wind energy, in 2023, the offshore wind energy sector experienced a significant expansion, marking its second most productive year with the commissioning of 11 GW in new projects. By year's end, the cumulative global capacity soared to 1 TW. Based on the current growth trajectory, projections indicate that the 2 TW threshold could be reached before 2030. The industry's expansion is accelerating, with another annual record shattered in 2024. However, this growth remains heavily concentrated in major markets, including China, the European Union, the United States, India, and Brazil [1]. Nevertheless, to ensure the efficiency of this technology, it is crucial to analyze how structures respond to environmental factors such as wind and waves as it is defined in several standards and design guidelines [2; 3; 4]. This analysis is complex due to the variety of phenomena involved, including aeroelastic effects, fluid-structure or soil-structure interaction (SSI), and the proper modeling of the turbine control system and the uncertainty associated with certain parameters. Regarding wind turbines, the foundation is a crucial element in their design, as it is responsible for transferring the loads from the wind turbine to the ground and depends on both the specifications of the wind turbine and the load-bearing capacity of the terrain. Moreover, additional challenges are present in the marine environment, such as chloride corrosion or the complexities in their installation. The foundations of offshore wind turbines (OWTs) are divided into two main categories: foundations fixed to the seabed and those with floating supports usually anchored with chains. Out of the 68 258 MW in existing offshore wind energy projects, monopiles are the predominant substructure type (55.6%), followed by jackets (13.4%), pile caps (7.6%), tripods (1.6%), and gravity-base (1.3%) designs [5]. In this particular work, monopile foundations are analyzed. They consist of tubular steel structures used to anchor the towers of the wind turbines to the seabed. Although they can be installed up to 40 m deep, their use is more common in shallower waters, and it is the most widespread type of foundation in the offshore wind industry due to its versatility. Monopiles present advantages such as their simple design or their effectiveness in sandy or clay soils without requiring prior preparation of the terrain. However, their disadvantages include the high costs and risks associated with installation and transport, as well as the need for heavy machinery for their placement, which can negatively affect marine life. In terms of their geometry, monopiles are composed of two distinct parts: the monopile itself and the transition piece. Simplified procedures are often used to carry out a preliminary analysis of the structure based on the environmental characteristics of the site. One of the most widely used methods is the one developed by [PERSON] et al. [6], where the design of a monopile is defined in ten steps using an iterative calculation procedure and transferring wind and wave loads in a simplified way to the mudline level. Numerous studies have employed simplified procedures in the design of monopiles. For instance, [PERSON] et al. [7] presented a method for laterally loaded rigid monopiles in cohesionless soil, while [PERSON] et al. [8] applied the PISA design model to marine sand. Additionally, the rapid approach for structural design by NREL [9] provides baseline designs for a 25 MW turbine in a simplified way. These studies, among others, highlight the effectiveness of simplified methods in preliminary design stages.