## 2 Materials and Methods  
For the development of this study, a comprehensive review of previous research on jacket-type fixed offshore platforms, as well as the current regulations applicable to the Gulf of Mexico, was conducted. To define the case study, a drilling platform was considered, featuring a 50,400 m tie-back and the capacity to accommodate 12 conductors. These conductors will be drilled using fixed equipment, and the platform will include two decks for production and drilling operations. The structural components of fixed offshore platforms comprise piles, the jacket, and the topside. The primary loads acting on these structures include gravity and environmental loads, as illustrated in Figure 1 and detailed in Table 1.  
Environmental loads are dependent on the meteorological and oceanographic conditions of the region, with waves, currents, and wind being the most significant factors. The characteristics of these loads are defined according to the guidelines provided in API RP 2A-WSD 22 nd Edition [35] and supplemented by the environmental parameters established in the Pemex technical specification P.2.0130.01-2015 [36]. The generated loads are static forces applied to the structure in eight directions, spaced at 45\({}^{\circ}\) intervals. Table 2 presents  
Figure 1: Components and loads of a jacket-type marine platform. the environmental parameters considered for operational and storm conditions, as well as for ultimate surge resistance. The values in Table 2 are based on the selection of an appropriate stream function, which is generally assumed according to the stream function defined by Equation (1). \[\psi(x,y)=Cz+\sum_{n=1}^{N}x_{n}sinh\big{[}nk(z+d)z+d\big{]}cos(nkx) \tag{1}\]  
where \(N\) represents the order of the stream function and \(k\) denotes the wave number. In the case of regular stream function theory, the input parameters include wave height, period, and water depth, similar to other wave theories. Conversely, for irregular stream function theory, the free surface profile over a single wave cycle serves as a constraint. Specific solutions to Equation (1) are employed depending on the analytical approach. Linear wave theory is applied to steady-state wave analysis, fatigue assessments, and conditions involving regular and uniform waves, particularly for floating and fixed struc \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Description**} & \multicolumn{2}{c}{**Operation**} & \multicolumn{2}{c}{**Extreme**} & \multicolumn{2}{c}{**Pushover**} \\ \cline{2-7}  & **Parameter** & **Reference** & **Parameter** & **Reference** & **Parameter** & **Factor** & **Total** \\ \hline Maximum wave height (m): & 7.60 & * Figure 20 & 16.20 & * Figure 13 & 16.20 & 1.38 & 22.36 \\ Wave period (s): & 8.20 & * Table 17 & 12.18 & * Section A.1.1 & 12.18 & 1.12 & 13.64 \\ Astronomical tide (m): & 0.76 & * Table 17 & 0.76 & * Section A.1.1 & 0.76 & 1.00 & 0.76 \\ Tide storm (m): & 0.30 & * Table 17 & 0.62 & * Figure 15 & 0.62 & 1.51 & 0.94 \\ Water depth (m): & 50.40 & & 50.40 & & 50.40 & & 50.40 \\ Water depth including tides (m): & 51.46 & & 51.78 & & 51.78 & & 52.10 \\ Wave theory & & & steam function 3 & steam function 5 & & steam function 7 \\ Current speed (cm/s): & & & & & & & \\ At 0\% depth: & 30.00 & & 125.00 & & 125.00 & 2.04 & 255.00 \\ At 50\% depth: & 25.00 & * Figure 17 & 112.00 & * Figure 16 & 112.00 & 2.04 & 228.48 \\ At 95\% depth: & 18.00 & & 100.00 & & 100.00 & 2.04 & 204.00 \\ Maximum wind speed at 10 m & 14.00 & * Figure 17 & 31.00 & * Figure 14 & 31.00 & 1.40 & 43.40 \\ SNMM (m/s), 1 h average: & & & & & & \\ \hline \hline \end{tabular}  
* Values taken from the Specification of Pemex “P2.0130.01:2015” [36].  
\end{table} 
Table 2: Environmental parameters. tures where inertial effects predominate. Second-order Stokes theory is recommended for analyzing tendons in Tension Leg Platform (TLP) structures, while stream function theory or fifth-order Stokes theory is applicable to storm wave conditions.