## 5 Safety Assessment
### Structural Assessment
#### 5.2.2 Numerical Analysis
The tensile response is characterized by a linear part until reaching the peak strength and the post-peak part is defined by an exponential softening law. For the compressive damage, the constitutive law presented in [38] is adopted, allowing for a parabolic hardening-softening part followed by exponential softening. The value of the fracture energy in tension (G\({}_{\rm ft}\)) and compression (G\({}_{\rm fc}\)) is obtained from Equation (2) and Equation (3), respectively [35]. \[\rm G_{ft}=0.04f_{t}^{0.7} \tag{2}\]  
\[\rm G_{fc}=1.6f_{c} \tag{3}\]  
Damage Assessment  
In order to investigate the cause of the existing structural distress, the original un-damaged structure was simulated by a model without any cracks, and uniform material properties corresponding to the \"original masonry\" type presented in Table 2 were assigned to all the walls. The rear wall of the tower was found to be the most vulnerable element in three out of the four directions under analysis, dictating the failure in the pushover analyses. However, the most significant cracks observed during the visual inspection were located on the outer walls of the tower. Therefore, the rear wall was removed from the model to focus on the effect of a horizontal seismic load on the outer walls. To determine if the existing damage was caused by past seismic events, nonlinear static pushover analyses were carried out (Figure 23 top). Damage at the top corner between the northern walls, at the location corresponding to the low-quality masonry that currently shows an existing crack, occurred early on in all the analyses. This crack propagates towards the base of the wall in a fashion very similar to the existing crack at the structure. In general, the investigated loading directions show that the existing damage in the tower would correlate very well with the damage caused by an earthquake with a principal component in the east-west direction. For the rest of the loading directions, the northern part of the structure also developed significant cracks. It is noted that all studied cases exhibit early horizontal cracking at the base of the external walls, which was not observed during the visual inspection. The cracking at the base also appeared in the fundamental load combination with wind, soil, dead and live loads, which led to the conclusion that the assumed foundation level was overly conservative, as the damage observed in the model was not observed in the real structure. Two scenarios for differential soil settlements were considered by applying incremental vertical (Figure 23 bottom) and diagonal displacements over a portion of the base of the eastern walls of the tower that is separated from the rest of the structure by two existing rock joints. Displacements were imposed at the base of the easternmost wall. In both loading scenarios, the cracking pattern was similar to that observed in the real structure. Based on the above analyses, it can be concluded that a large part of the existing damage is due to a differential soil settlement at the base of the eastern walls. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **E** & **f\({}_{\rm c}\)** & **f\({}_{\rm t}\)** & **G\({}_{\rm fc}\)** & **G\({}_{\rm ft}\)** & **\(\rho\)** \\  & **(N/mm\({}^{2}\))** & **(N/mm\({}^{2}\))** & **(N/mm\({}^{2}\))** & **(N/mm\({}^{2}\))** & **(N/mm\({}^{2}\))** & **[kg/m\({}^{3}\)]** \\ \hline Masonry 1 \"Original\" & 2600 & 4.70 & 0.240 & 7.6 & 0.015 & 2100 \\ Masonry 2 \"Medium\" & 1400 & 2.55 & 0.130 & 4.1 & 0.009 & 2000 \\ Masonry 3 \"Low\" & 700 & 1.27 & 0.065 & 2.0 & 0.006 & 1900 \\ Masonry 4 \"Restored\" & 3600 & 6.55 & 0.320 & 10.5 & 0.018 & 2100 \\ Masonry 5 \"Rear Wall\" & 2200 & 4.00 & 0.200 & 6.4 & 0.013 & 2000 \\ Cracks 1, 3, 4 & 0.4 & - & - & - & - & 1000 \\ Crack 2 top & 0.4 & - & - & - & - & 1000 \\ Crack 2 bottom & 2.0 & - & - & - & - & 1000 \\ Crack 5 top & 100 & - & - & - & - & 1900 \\ Crack 5 bottom & 700 & - & - & - & - & 1900 \\ \hline \hline \end{tabular}
\end{table}