## 2 Materials and Methods
### Structural and Hydrodynamic Model  
The research conducted considered the development of a MMFAR niche, whose structure was composed of 16 units, each of which occupied a cube with an edge of 65 cm (Figure 6). With a width of approximately 2 by 2 m, the structure represents a bottom projection area of 4.807 m\({}^{2}\) and a total volume of 1.76 m\({}^{3}\)[57]. The full assemblage was numerically studied based on a reticulated model of bars to evaluate the stresses for the structural mechanics analysis. For that, a finite element tool, with a 3D graphical user interface object-oriented, was used for the linear static analysis of the structure. In this process, the 3D elements were transformed into bar elements connected by nodes. The connection zone was not considered by simplification, and the structure was treated as monolithic with a perfect continuity between modules. The base was restricted with double supports, resembling real support conditions. Concrete and steel were considered for the sectional properties.  
The structure was subjected to the self-weight and the hydrodynamic load (dF), which in turn was the result of the environmental actions (E) including waves (Ew), tidal currents (Ec), and marine growth (Em). In this process, the fluid velocities and accelerations were resolved into drag (dP\({}_{\text{D}}\)) and inertial forces (dP\({}_{\text{I}}\)) and applied as distributed loads on the members of the numerical model. The velocities (u\({}_{\text{wave}}\); u\({}_{\text{current}}\)) and accelerations (\(\partial\)u/\(\partial\)t) of the fluid were calculated using the Stokes Wave Theory (Table 2) [62; 63]. The local current profile was combined vectorially with the wave kinematics to determine local fluid velocities and accelerations adopting the Morison Equation (1).  
Figure 5: (**a**) Geographical location of the Littoral North Marine Park in Esposende, Portugal; (**b**) detailed bathymetry distribution, and (**c**) zone with acceptable MMFAR depth [45].  
\[\begin{array}{c}\mathrm{dF}=\mathrm{dF}_{\mathrm{D}}+\mathrm{dF}_{\mathrm{I}}\\ \mathrm{dF}_{\mathrm{D}}=\mathrm{C}_{\mathrm{d}}\times\
icefrac{{1}}{{2}}\times \
icefrac{{}}{{\rho}}\times\mathrm{D}\times(\mathrm{u}_{\mathrm{wave}}+\mathrm{u}_ {\mathrm{current}})^{2}\ \mathrm{d}\mathrm{z}\\ \mathrm{dF}_{\mathrm{I}}=\mathrm{C}_{\mathrm{m}}\times\mathrm{\rho}\times( \pi\times\mathrm{D}^{2})/4\times(\partial\mathrm{u}/\partial\mathrm{t})\ \mathrm{d}\mathrm{t}\end{array} \tag{1}\]  
In Equation (1), \(\mathrm{\rho}\) represents water density, \(\mathrm{dz}\) the depth interval, and \(\mathrm{D}\) the diameter of the bar element. The hydrodynamic drag coefficient (\(\mathrm{C}_{\mathrm{d}}\)) and hydrodynamic inertia coefficient (\(\mathrm{C}_{\mathrm{m}}\)) were adopted following the recommendation of API [63; 64]. The water current velocity profile (\(\mathrm{u}_{\mathrm{current}}\)) assumed a constant velocity of 1.2 m/s between the water surface level and half of the depth (z/2) and a constant velocity of 0.3 m/s between z/2 and the seabed. According to DNV-RP-C205, a value of 0.1 m was assumed for the marine growth [65]. Buoyant loads were also taken into account. The resulting forces were applied in x direction (\(\mathrm{d}_{\mathrm{XX}}\)). The load combinations followed the recommendations of ISO 19903:2006 [66]. The crest wave phase was considered since it corresponds to the maximum positive horizontal velocity and to zero horizontal acceleration. The vertical velocity is zero, and the vertical acceleration is maximum (in negative value).  
For the analysis the characteristic event, the typical storm condition and the extreme storm condition were considered. In addition, abnormal environmental extreme events were also considered as accidental loads.  
Figure 6: MMFAR structure: (**a**) 3D model, (**b**) numerical bar model, (**c**) forces applied to the numerical bar model. The marks “a, b, c and d” show the visual correspondence between the elements of the 3D model and the bar model.