## 4 Nonlinear Pushover Analyses  
A series of nonlinear pushover analyses was conducted to evaluate the global seismic performance of the church and to identify its most vulnerable structural elements. The building was initially subjected to gravity loading, followed by an incremental monotonic lateral load, which represents inertial forces. Due to the geometric and structural complexity of irregular masonry buildings, multidirectional pushover analysis is essential to capture the full range of possible collapse mechanisms [35]. Therefore, the loads were applied in the four principal directions, i.e., along the X and Y axes, in positive and negative directions. The lateral loading was increased until the structure reached its ultimate capacity. Among the various lateral-load distribution patterns available, the mass-proportional distribution was adopted, as this has been recognized as being the most appropriate for complex unreinforced masonry structures [36]. The modal pattern was not considered reliable in this case, as the eigenvalue analysis showed that the vibration modes are predominantly local, involving the response of individual walls with minimal associated mass participation [36]. The convergence criteria were based on energy, set at 0.1%, and force, which was equal to 5%. The standard Newton-Raphson iterative method was applied for a self-weight load (gravitational loading), while a secant method was used for lateral loading [20]. The structural seismic response is given in terms of capacity curves describing the relationship between the load factor (equivalent ground acceleration) and the displacements of control points located at the top of selected walls, depending on the direction of analysis. Damage patterns were identified at the ultimate displacement using principal tensile strains. These analyses were able to reproduce the main observed damage patterns, including the  
Figure 11: Mode shapes of the updated undamaged model (Model-B), assuming a Young’s modulus of 335 MPa for adobe and 1400 MPa for rubble stone masonry. formation of cracks at the corners of the building, thus providing valuable insight into the church's structural vulnerabilities. In the +X direction (positive transverse direction), the structure reached a peak capacity of 0.22 g, with a corresponding displacement of 2.62 cm measured at the top of the south have wall (Figure 12a). Damage started at the intersections between the lateral walls and the facades, with the onset of vertical cracks at the upper corners. As the lateral load increased, diagonal cracks developed, and a horizontal crack opened at the interface between the rubble stone foundation and the adobe masonry. At peak load, the out-of-plane failure mechanism of the south wall was fully developed. In the post-peak phase, buttresses detached from the walls due to shear failure, and cracking also led to partial separation of the gable walls of the sacristy and baptistery (Figure 13a). The maximum displacement recorded at the south have wall in this phase reached 3.90 cm (Figure 12a). This failure mechanism can be attributed to the limited out-of-plane restraint of the wall due to the absence of ring beams, perpendicular walls, intermediate slabs, or a rigid horizontal diaphragm, all of which are typically used to enhance lateral stability. Moreover, the low tensile and shear strength of adobe makes the wall highly susceptible to cracking and detachment under lateral loading. The poor anchorage between the buttresses and the wall led to their detachment once shear forces exceeded the interface shear strength. In the -X direction (negative transverse direction), the building exhibited slightly lower strength (a 10% reduction), with a maximum strength capacity of 0.20 g and a peak displacement of 2.15 cm at the north have wall (Figure 12b). Although the buttress exhibited a stiffer response up to the peak load, its deformation capacity was similar to that of the north have wall by the end of the analysis, both reaching approximately 3.40 cm (Figure 12b).