## 4 Finite Element Modeling Approach  
### Modeling Approach  
Various methods are commonly applied for the evaluation of masonry structures using numerical models. Masonry as a building material comprises a combination of bricks and mortar, with each element being equally important to the composition. Individual units generally make up the majority of masonry, while the mortar fills in the gaps between the units. Thus, the models used to represent masonry vary in their treatment of the interface and interaction between these elements. Detailed micro-modeling represents all elements individually using continuum elements to model the masonry units and mortar and introducing a discontinuous element as an interface between these units. This allows for the detailed application of mechanical and constitutional models to all of the  
Figure 10: Overview of results from dynamic identification: (**a**) spectral density for west wall setups with estimators; (**b**) first three mode shapes for the fundamental frequencies of a fixed string.  
material types individually. A more simplified approach can be adopted in simplified micro-modeling, in which the masonry units are geometrically expanded to contact one another using continuum elements, and the mortar and unit-mortar interface are modeled together using discontinuous elements [6]. For the application of both these methods, knowledge about the exact geometry and composition of not only a structure, but also the individual masonry elements that comprise it, is required. This is often extremely difficult to apply in a historical context, especially where very irregular and random arrangement and size of units is expected as in the case of the castle. These approaches are also very computationally expensive, requiring much greater computational time and storage capabilities [29]. Macromodeling was therefore used for the purpose of this study, in which the masonry units and mortar interface are all treated wholistically as a homogenous anisotropic material. This homogenized approach is well supported by the application of non-destructive tests where little additional information about the nature of a site can be gathered, further increasing the efficiency of the methods. Sonic testing and modal analysis, therefore, are complimentary approaches in ascertaining homogenous material properties [6].  
A 3D finite element model was prepared using DIANA Finite Element Analysis (DIANA FEA) 10.8 for numerical simulations [30]. The model considered the extent of the masonry elements comprising the castle in three dimensions, based on an existing photogrammetric survey of the site (available in Supplementary Materials). The exterior walls were modeled from the foot of the wall outside the castle to the height of the masonry, disregarding railings or the infill of the soil inside the enclosure. The walls were then extruded inwards. The faces of the underside of the model were considered with translationally fixed boundary conditions. For this study, a separate model considering the large western wall of the enclosure was also prepared. The locations of the accelerometers from dynamic identification were also imprinted on the model to directly compare the models (Figure 9) and calculate the MAC later.