## 5 Safety Assessment
### Structural Assessment
#### 5.2.2 Numerical Analysis  
The geometry of the FE model of the tower was prepared based on the point cloud obtained via laser scanning, while information on the soil strata and properties were obtained from the geotechnical investigations. FE Model Generation  
The walls of the FE model were geometrically defined in terms of: (a) overall geometry of load-bearing masonry walls; (b) subsections of masonry having different material properties; and (c) large existing cracks. The sections of the walls having different material  
Figure 19: Three-dimensional representation of some of the kinematisms studied at the tower. Macro-elements involved in the kinematism are shown in the original position (green) and rotated position (red) for illustrative purposes. properties were defined based on the results of the NDT campaign and in correlation with the in situ visual inspection and aerial photogrammetry. Cracks were incorporated in the model as 10 cm wide full-height solid elements, splitting the walls almost vertically. The geometry of the cracks was simplified to match their predominant direction in the actual structure. The walls were assumed to extend up to the depth of the strata of conglomerate identified in the geotechnical investigations. The model was discretized using 120,389 isoparametric tetrahedral elements based on linear interpolation and Gauss integration, with a maximum size of 0.5 m. The following modifications were made to the geometry to capture a more realistic structural response and shorten the computational time: (a) reduction in the length of wall EW1 and (b) replacement of the small transversal wall between EW1 and RW with the corresponding boundary conditions on the walls adjacent to it. The final geometry of the structure is presented in Figure 20. The base of the model was fixed in all analyses, except for the soil settlement study. The horizontal movement orthogonal to sections of walls EW1 and NW1 was restrained at locations in contact with the neighbouring walls, simulating the boundary conditions imposed by those elements. The calibration of the numerical model is carried out by comparing the natural frequency and modal shape of each mode with the experimental one. Numerical and experimental frequencies are compared in terms of absolute error, while modal shapes are compared using the MAC. The results of the SPV tests were used to categorize the masonry into five different types on a qualitative basis. The zones can be identified in Figure 21. The maximum values of \(\mathrm{E_{d}}\) for each of the above masonry types are shown in Figure 13.  
The following labelling of the cracks is adopted hereafter, with reference to Figure 21:  
* Crack-1: Crack at EW2, with one end at the corner between EW1 and EW2. * Crack-2: Crack at EW2, close to the corner between EW2 and EW3. * Crack-3: Crack at NW1, close to the corner between NW1 and EW3. * Crack-4: Crack at NW2, close to the corner between NW1 and NW2. * Crack-5: Construction joint/crack at NW2, separating NW2 and NW3. All cracks were separated into two segments along their height, with the first corresponding to visible cracks, as identified from the in situ inspection, and the second to the portion of the crack that extends into the base of the wall. Initially, the cracks were assigned the same properties as the adjacent masonry. During the model calibration procedure, the stiffness of the cracks was reduced to calibrate the model based on the recorded mode shapes and frequencies. It is acknowledged that other parameters in addition to the crack stiffness (e.g., soil-structure interaction or Young's Modulus for the different types of  
Figure 20: The finite element model of the investigated tower, where different colours correspond to areas where different material properties were assigned (see Figure 21). masonry) could also be incorporated in the calibration process. However, based on the data gathered from the various in situ tests performed, the influence of the cracks was considered to be the parameter with the highest influence.