## 2 Simplified Vulnerability Assessment Methods for Masonry and RC Building Structures
### Methods Belonging to Group B
#### 2.2.2 Azizi Method  
In [PERSON] et al. [8] a method for assessing the seismic vulnerability of masonry structures, i.e., in particular schools, through the definition of a vulnerability index \(R\), is presented. The following three intervals of variation of the index are defined:  
* \(R\leq 25\) Low seismic vulnerability: it is not necessary to carry out further assessments or retrofitting the building;
* \(25<R<75\) Moderate seismic vulnerability: the building needs to be assessed with a more refined method;
* \(R\geq 75\) High seismic vulnerability: it is necessary to demolishnd rebuild the structure.  
The index \(R\) is calculated as:  
\[R=R_{i}\cdot k_{4} \tag{4}\]  
\[k_{4}=3.4\cdot a-0.43 \tag{5}\]  
being \(a\) the expected ground acceleration in the site, i.e., PGA\({}_{d}\), and  
\[R_{i}=(L_{1}+L_{2}+L_{3}+L_{4}+L_{5})\cdot k_{1}\cdot k_{2}\cdot k_{3} \tag{6}\]  
The values of the parameters in Equation (6) are directly given in Tables 6 and 7, while the parameter \(k_{1}\) was evaluated as the sum divided by 100 of the four parameters \(k_{11}\), \(k_{12}\), \(k_{13}\), \(k_{14}\) whose values depend on the topics listed in Table 8.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Vulnerability Parameters**} & \multicolumn{4}{c}{**Current Condition**} & \multirow{2}{*}{**Description**} \\ \cline{2-4}  & **Good** & **Fair** & **Poor** & \\ \hline \(L_{1}\) & 10 & 15 & 20 & Local site condition and foundation \\ \hline \(L_{4}\) & 0 & 5 & 10 &
\begin{tabular}{c} Building plan and elevation \\ configuration \\ \end{tabular} \\ \hline \(L_{5}\) & 0 & 5 & 10 & Symmetry of building plan \\ \hline \(k_{2}\) & 1 & 1.1 & 1.2 & Wall openings condition \\ \hline \hline \end{tabular}
\end{table}
Table 6: Values of parameters \(L_{1}\), \(L_{4}\), \(L_{5}\), and \(k_{2}\)[8].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Vulnerability Parameters**} & \multirow{2}{*}{**Topic**} & \multicolumn{2}{c}{**Current Condition**} & \multirow{2}{*}{**Description**} \\ \cline{3-3} \cline{5-5}  & & **Good** & **Fair** & **Poor** \\ \hline \multirow{3}{*}{\(k_{11}\)} & Masonry materials & & 7 & 8 & Quality of masonry units \\ \cline{3-5}  & & 10 & 11 & 12 & Quality of mortars \\ \cline{3-5}  & & 22 & 26 & 30 & Walls density \\ \hline \multirow{3}{*}{\(k_{12}\)} & \multirow{3}{*}{Load-bearing walls} & 6 & 7 & 8 & Walls height/thickness ratio \(\leq 10\) \\ \cline{3-5}  & & 4 & 5 & 6 & Maximum height of the walls \(\leq 4\) m \\ \cline{3-5}  & & 4 & 5 & 6 & Maximum length of the walls \(\leq 5\) m \\ \cline{3-5}  & & 6 & 7 & 8 & Construction quality \\ \cline{3-5}  & & 4 & 5 & 6 & Roof weight \\ \hline \multirow{3}{*}{\(k_{13}\)} & \multirow{3}{*}{Building roof configuration} & 4 & 5 & 6 & Enough supporting length for roof joists \\ \cline{3-5}  & & 4 & 5 & 6 & Roof stiffness \\ \cline{3-5}  & & 6 & 7 & 8 & Roof opening area \(\leq 50\)\% of roof area \\ \cline{3-5}  & & 8 & 9 & 10 & \begin{tabular}{c} Connection between load-bearing walls \\ and roof \\ \end{tabular} \\ \hline \multirow{3}{*}{\(k_{14}\)} & \multirow{3}{*}{Other parameters} & 3 & 4 & 5 & \begin{tabular}{c} Connection between load-bearing and \\ partition walls \\ \end{tabular} \\ \cline{3-5}  & & 10 & 11 & 12 & \
\begin{tabular}{c} Continuity of loading path along the \\ walls \\ \end{tabular} \\ \cline{3-5}  & & 3 & 4 & 5 &
\begin{tabular}{c} Distance from adjacent building \(\leq 0.01\) \\ of building height \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 8: Values of coefficients \(\text{k}_{1i}\)[8].  
Once the \(R\) index is known, the following correlations provide the values of the vulnerability index according to the different masonry typologies reported in Table 9.  
\(I_{0}\)\(=0.3337\cdot R_{i}-0.1342\) for M1 class;  
\(I_{0}\)\(=0.2555\cdot R_{i}+15.572\) for M2 class;  
\(I_{0}\)\(=0.1456\cdot R_{i}+29.713\) for M3 class.