## 5 Verification and Sensitivity Analysis  
In a first step, a set of numerical analyses was carried out on a limited number of macro-elements of the construction and compared with the analytical results. A sensitivity analysis was then carried out considering three different sizes of rigid blocks, to validate the assumptions made for the discretization of the whole 3D model. Therefore, in the first phase, the four facades of the castle were considered as independent macro-elements and composed of walls with two leaves without transversal connections between them, as in the real building. Each facade was composed by a set of regular rigid blocks characterized by a depth of 1050 mm and a height of 750 mm. For each course, the block thickness corresponded to the overall thickness of a single leaf of the real structure, while the width and length were three times larger than the real elements. To ensure proper support around the windows, each lintel was modeled as a single rigid block  
Figure 6: The numerical model of the castle: (**a**) exterior north-east view with labeled facades; (**b**) interior south-east view; (**c**) a sample of the adopted rigid block model and loading condition. The block type “\(i\)” presents six interfaces \(J_{i,1-6}\) of four contact points \(k_{j,1-4}^{i}\) each. Normal forces \(n_{j,1-4}^{i}\) and two shear forces \((t_{j,1-4}^{i},t_{j,1-4}^{i})\) act at each contact point along the local block axis. The self-weight \(W_{m}\) and the live loads \(\alpha W_{m}\) are applied at the centroid of the block. (**d**) A voussoir block type; (**e**) details of the rigid block shapes for the rigid blocks supporting the floor joists. Figure 7: Details of the rigid block model. extending a half-block around the openings (with an overall depth given by the sum of the opening and the length of a half-block). The four facades were analyzed with LiABlock_3D for the live loads active along the in-plane and out-of-plane directions. For this purpose, a friction coefficient of 0.577 (which is the value of friction coefficient recommended by Reference [33]) and a block unit-weight of 19 kN/m\({}^{3}\) were considered. As expected, the most vulnerable mechanisms were the ones activated for out-of-plane loading actions. A global overturning mechanism was generally observed, due to the lack of transversal connections between the leaves. For in-plane loads, the mechanisms were triggered due of the presence of openings or following the variation of the wall thickness due to the presence of the buttress (see Figure 8). It is worth noting that a major benefit provided by LiABlock_3D is to immediately return the first local mechanisms that are activated by live loads acting in the wall plane. Conversely, analytical methods would require several hypotheses to be formulated concerning the slope of the failure plane, thus requiring a huge number of calculations that are not necessary when the LiABlock_3D software is used. Table 1 reports the comparison between the load factors for the out-of-plane mechanisms, calculated by applying LiABlock_3D according to both the associative and the non-associative friction behavior, and by carrying out hand-made calculations according to a conventional linear kinematic analysis. It is interesting to note that the analytical solution was included within the two load factors given by the software in the cases of associative and non-associative behaviors. This was mainly due to the fact that the numerical models took into account the friction behavior on the vertical contacts between the two leaves, which is usually neglected in analytical calculations, leading to an overall increase of resistance.