## 3 FEM Model Validation
### FEM Model Generation  
The FEM model was created in DIANA 10.10 software [20] using a 3D geometry generated with AutoCAD 2024 software [21]. It is based on the geometric survey conducted by CIMS and includes the nave, presbytery, baptistery, and sacristy, as shown in Figure 6. The foundation, considering height variations due to the ground slope (see Figure 6b; highlighted in green), and the timber tie beams were also incorporated into the model (see Figure 6a; red transversal lines in the different church bodies). However, the choir loft and the spandrels of the triumphal arch were excluded, as their influence on the global structural response of the church was considered negligible. Due to limited information on the geometry of the linlets (red parts over openings in Figure 6), those above the doors of the main facade and north wall were assumed to have a thickness of 0.30 m and a bearing length of 0.50 m, while the remaining linlets were assumed to be 0.25 m thick with a bearing length of 0.20 m.  
Figure 5: Intersection of the rear facade with the lateral walls, showing the vertical cracks (in red) at (**a**) the south corner, (**b**) the north corner, and (**c**) the borescopic examination and internal views of the cracks [19].  
Regarding the boundary conditions, all translational degrees of freedom at the bottom surface of the foundation were constrained. The mesh, depicted in Figure 7, consists of 151,257 nodes and 45,557 elements. An average element size of 0.50 m was adopted, enabling the thickness of the walls to be discretized using four elements. The foundation, walls, and lintels were modeled using twenty-node isoparametric solid brick elements with quadratic interpolation (CHX60). Unlike linear elements, which use first-order (linear) shape functions and have nodes only at the ends, quadratic elements incorporate an additional node at the midpoint of each element edge. This allows for the use of second-order polynomial shape functions, which provide a more accurate approximation of the displacement field and internal force distribution within each element [22]. Therefore, they capture curvature more effectively and improve the representation of local deformations, particularly in elements subject to bending. While quadratic elements involve a higher computational cost per element, their improved accuracy often reduces the total number of elements needed compared with elements with linear interpolation.  
Timber tie beams were simulated by two-node truss elements (L2 TRUs), assuming an equivalent circular section with a 0.20 m diameter. To prevent stress concentration in the tie-to-wall connections, the tie beams ends were considered to be embedded within the walls. The embedded portions were modeled using bar reinforcement elements, continuous with truss elements and having the same diameter and mechanical properties.  
The roof system was excluded from the numerical model, as it does not exhibit any significant rigid diaphragm behavior that would contribute to the global structural response of the church. However, its mass was considered by applying an equivalent density to the upper sections of the walls. The equivalent densities accounted for the weight of the timber trusses, cane layer, earthen layer, and roof tiles and the self-weight of the wall sections.  
Figure 6: Three-dimensional geometry used for the FEM model: (**a**) Isometric view and (**b**) south elevation.  
Figure 7: Isometric visualization of the FEM model with assigned material properties.