## 2 3D FEM Model
### Building Model  
The numerical model of a building is based on detailed architectural drawings of an actual building, as shown in Figure 3. The base plans include a ground floor plan (a), a first-floor plan (b), and a cross-section of the foundations (c). These plans serve as the blueprint for constructing a precise and representative model of the structure. Figure 3: \(Cont.\)  
Figure 4 displays a visualization of a three-dimensional finite element building model (FEM) created in ANSYS, with a finite element mesh applied to the structure. Additionally, Figure 5 illustrates the individual components of the numerical model, broken down layer by layer to show the complexity and detail captured in the FEM analysis. Starting from the top, the model includes the roof (a), knee walls and roof supports (b), first-floor slab (c), the entirety of the first floor including structural elements (d), ground-floor slab (e), the detailed ground floor (f), the surface level or ground level (g), foundation walls (h), and finally, the foundation footings and tie beams (i). Figure 4: 3D FEM model of the building. Figure 5: _Cont._  
Figure 3: Base plans for the numerical model of the building: (a) ground floor plan; (b) first-floor plan; (c) cross-section of foundations. By starting with the roof, the building's topmost structure was composed of prefabricated troughed plates, modeled as a shell using the four-node element SHELL181. This element had six degrees of freedom at each node and was suitable for both linear and nonlinear applications, as well as for analyzing thin to moderately thick shell structures. The supporting knee walls, constructed from brick, were also modeled with SHELL181 and SHELL181. The resulting shell structures were also modeled with SHELL181. Figure 5: Components of the FEM building model: (**a**) roof; (**b**) knee walls and roof supports; (**c**) first-floor slab; (**d**) first floor; (**e**) ground-floor slab; (**f**) ground floor; (**g**) ground level; (**h**) foundation walls; (**i**) foundation footings and tie beams. elements, characterized by a thickness of 0.12 m. For the ceilings of both the ground floor and the first floor, originally cast from reinforced channel slabs, an equivalent thickness of 0.132 m for the first-floor slab and 0.2 m for the ground-floor slab was calculated. These slabs were modeled using SHELL181 elements. The ceiling ties around the floor plates were represented using BEAM188 elements, capturing the dimensions of 0.24 m by 0.24 m. The stairwell, a reinforced concrete structure, was modeled with SHELL181 elements, with a stair thickness of 0.1 m. For the load-bearing walls, three variants of typical materials used in buildings were considered: brick walls with a thickness of 0.25 m, considering an additional mass for the external insulation; reinforced concrete walls with a thickness of 0.15 m; and cellular concrete walls with a thickness of 0.25 m. The partition walls of 0.12 m thickness were built of brick, and the monolithic reinforced concrete foundation walls were 0.25 m thick. All of the walls (load-bearing, partition, and foundation walls) were modeled with SHELL181 elements. Whereas the monolithic reinforced concrete foundation fotiings (with cross-sections of 0.4 m by 0.7 m or 0.4 m by 0.5 m) were modeled using two-node 3D BEAM188 elements, each of which had six degrees of freedom. The foundation tie rods, square in cross-section at 0.3 m by 0.3 m, were introduced to stiffen the foundation due to the building being subject to mining-induced vibrations. This is particularly important in ensuring structural integrity under such conditions. The model assumed a linearly elastic material behavior, a reasonable approximation given that the actual building had shown no signs of damage, suggesting that stress and strain levels had not reached critical limits.