## 2 Materials and Methods
### Numerical Model Characteristics  
The geometry of the structure was precisely recreated in both models (Figure 6), paying attention to each structural component and opening. The ground presence on the walls of the ground floor was considered by adding vertical rollers and big blocks adjacent to them in both the CM and DM. Figure 5: Bodies in possible contact in a plane (**a**), the Signorini’s (**b**) and dry-friction Coulomb’s (**c**) laws. Figure 6: Comparison between CM (**a**) and DM (**b**) with zooms on the civic tower and a cross vault. In the DM, the inner core stones are reported in yellow (colors in the online version). On the 3D views of the structure, the control points considered to plot the results are reported. The CM, in which the geometry was discretized with 4-node solid brick elements, had 92986 elements, 23091 nodes, and 69276 degrees of freedom (Figure 6a). In the DM, conversely, the masonry was represented as a blocks' assembly; the size of them was chosen to obtain a fair compromise between computational costs and accuracy of results. The model is composed of 6790 3D rigid blocks, establishing a mutual interaction in normal and tangential directions. The tower walls' thicknesses were split into three measures to distinguish between the external layers, of 0.4 m each, and the inner core, of 0.4 m. The blocks used to simulate the inner core were simply allocated close to the external ones. The masonry panels are characterized by a poor connection between the layers within the wall. For this reason, the numerical simulation is implemented through the distinction between an internal layer and two external layers. In particular, the internal part is modeled by greater blocks than the other layers. Therefore, regarding the masonry damage study, this choice has allowed the investigation of the crumbling phenomenon with focus on the external layers. The wall's layer connection was ensured by means of a through stone each square meter (Figure 6b). This choice could guarantee a limited connection, avoiding a complete independency between the layers. The models require distinct parameters to simulate masonry behavior. Regarding the CM generated with the Midas FEA NX(r) 2022 V1.1, it is necessary to define elastic moduli and masses for the linear response. Conversely, for the nonlinearity, the parameters of the yield surface and the two mono-axial laws in tension and compression, with their respective damage evolutions, are defined. In the DM made with the LMGC90% version 2021, the blocks are characterized by only their density. In addition, to specify the interaction laws, the definition of the friction values is required (see Table 1). According to the survey conditions, the entire structure is conceived with cut regular stone masonry. The only difference is in the tower, which has an inner core made with rubble stones. The materials' parameters are considered as reported in the Italian Code [28; 29]. In the CM, three materials are defined: one for the complex and tower, one for the bell cell, and the last for the roof. There was evidence in observing the structure and the cracks' pattern that the quality of the masonry was good in the Podesta Palace and annex, and also in the tower body, although this latter presented an inner core. For these reasons, the 'Medium-quality masonry properties' (see Table 1) is assigned. However, the bell cell, due to its exposition to the atmospheric agents, showed a mechanical reduction in the mortar in the joints, which is simulated by lowering its nonlinear parameters (\"Low-quality masonry properties\" in Table 1). Finally, the roof is modeled with the elastic parameters of