## 3 FEM Model Validation
### Material Properties  
The mechanical properties of the materials for the church were determined based on bibliographic sources and in situ experimental tests carried out by the University of Minho in April 2024 [19]. As depicted in Figure 7, material assignments in the model correspond to their observed location on site: rubble stone masonry for the foundation; adobe masonry for the walls, buttresses, and triumphal arch pilasters; timber for the lintels and tie beams. Young's modulus values for the adobe and rubble stone masonry were obtained from the sonic tests. Sonic testing is a non-destructive method used to estimate certain elastic properties by measuring the speed of stress waves (P-waves, S-waves, and R-waves) through the material. The method involves placing piezoelectric sensors on a wall to record the travel time of wave pulses between two points, either on the same surface (indirect test) or across the wall's thickness (direct test). Wave velocity is a function of the material's density, dynamic Young's modulus, and Poisson's ratio [23; 24; 25]. Studies on the indirect sonic testing of masonry walls have shown that the resulting dynamic Young's modulus values are often close to those obtained from static tests [25]. However, due to the inherent heterogeneity and anisotropy of masonry, the results depend strongly on the direction of wave propagation relative to the mortar joints. Direct sonic tests are generally preferred, as they allow for more accurate detection of the P-waves, which are the first to arrive [26]. In contrast, indirect sonic tests are more challenging to interpret, but they allow for the estimation of Young's modulus in the vertical direction [27] and are relatively easy to perform. When the adobe masonry is uniform and in good condition, as in this case, a combination of direct and indirect tests is typically employed, with the results processed statistically. Accordingly, both methods were used here to estimate the Young's modulus of the two masonry types. For adobe, the average modulus was found to be 340 MPa, with a coefficient of variation (CoV) of 29%, while rubble stone masonry exhibited an average of 1080 MPa, with a CoV of 12%. These values fall within the ranges identified in the nearby Church of K\(\ddot{\text{u}}\)ntotambo [28], where the modulus for rubble stone masonry ranges from 190 MPa to 1600 MPa, and between 200 MPa and 450 MPa for adobe. Both masonry types were assigned a Poisson's ratio of 0.2 and a density of 1900 kg/m\({}^{3}\)[19; 29; 30]. A homogeneous isotropic material model was adopted for the adobe masonry, as this approach is well suited for large structures [1]. Given the similar material composition of adobe blocks and mortar, cracks tend to develop independently of the unit layout, thereby supporting the use of isotropic modeling for such constructions [6]. Masonry is a quasi-brittle material exhibiting high compressive strength but limited tensile and shear capacity. Under compressive loading, masonry undergoes an initial hardening phase, followed by a softening branch after peak strength. Even before reaching peak stress, materials such as concrete, brick, mortar, soils (including adobe blocks), and rocks exhibit nonlinear compressive behavior, which is driven by internal progressive damage and microcrack development [1; 31; 32; 33]. Under tension, the material response is characterized by a rapid softening branch initiated by microcrack formation [1]. The total-strain rotating-crack model is well suited for describing this nonlinear behavior, as it captures the transition from the initial microcracking to the development of localized macrocracks. For the numerical model, a parabolic hardening-softening law was adopted to represent the compressive response, while tension behavior was described by an exponential softening in strength, as depicted in Figure 8[20].