## 2 Simplified Vulnerability Assessment Methods for Masonry and RC Building Structures
### Methods Belonging to Group A  
#### 2.1.1 Save  
The SAVE method [18] is an improvement of the typological classification provided by EMS-98. Such a method was, indeed, calibrated on the damage observed in the buildings after eight relevant earthquakes occurred in Italy from 1980 (Irpinia) to 2002 (San Giuliano di Puglia). Except the Irpinia earthquake, the considered events are characterized by a macroseismic intensity, evaluated according to the MCS scale, variable from V to VIII. Since all the examined buildings were built before 2003,  
Figure 1: Input parameters for fast vulnerability assessment methods. Figure 2: Vulnerability classes according to EMS-98 [22]. when the first innovative seismic code was introduced in Italy, the method was calibrated on buildings not designed according to the'modern' rules reported in more recent national and international codes. The method provides the estimation of an overall vulnerability of the building, which is indicated by an average synthetic damage index (synthetic parameter of damage, SPD) and depends only on the typology of vertical resistant elements. The following four vulnerability classes are defined, with a decreasing level of vulnerability from class A\({}_{\rm v}\) to D\({}_{\rm v}\):  
\(\bullet\)\(\rm A_{\rm v}=\) Stones, irregular masonry;  
\(\bullet\)\(\rm B_{\rm v}=\) Stones, regular masonry, hollow bricks, mixed (reinforced concrete and masonry on different floors);  
\(\bullet\)\(\rm C_{\rm v}=\) Solid bricks, mixed (reinforced concrete and masonry, both on all floors);  
\(\bullet\)\(\rm D_{\rm v}=\) RC or steel frames. These vulnerability classes can be correlated to the EMS classes as follows:  
\(\bullet\)\(\rm A_{\rm v}=\)\(\rm A_{\rm EMS}\): high vulnerability;  
\(\bullet\)\(\rm B_{\rm v}=\)\(\rm B_{\rm EMS}-\)\(\rm C_{\rm EMS}\): high-medium vulnerability;  
\(\bullet\)\(\rm C_{\rm v}=\)\(\rm C_{\rm EMS}-\)\(\rm D_{\rm EMS}\): medium-low vulnerability;  
\(\bullet\)\(\rm D_{\rm v}=\)\(\rm D_{\rm EMS}-\)\(\rm E_{\rm EMS}\): low vulnerability. Each vulnerability class corresponds to an average value of the SPD index that was calculated for each class of vertical typology for macroseismic intensities variable in the range V-VIII, since this was the range where more numerous and suitable empirical data (damages observed in past earthquakes) were available, as previously discussed. Thus, the following average values of the SPD index for the four macroseismic intensities were provided: 2.3 for A\({}_{\rm v}\), 2.1 for B\({}_{\rm v}\), 1.7 for C\({}_{\rm v}\), and 1.5 for D\({}_{\rm v}\). Successively, depending on the further 11 parameters affecting the seismic behavior of the building, the value of SPD and, thus, the vulnerability class can be modified with an increase or a reduction of the initial value. For whatever building typology, the additional parameters are: vertical structures, horizontal structures, number of floors, regularity in plant and/or in elevation, position of the building in case of aggregates, and building age. For masonry buildings, the following further parameters are considered: roof typology (inclined or plan), roof lightness, the presence of isolated columns, and the presence of ties. For RC buildings, also the regularity of infill walls is taken into account. For'mixed' buildings, the type of mixed structure and the roof typology are considered as additional parameters. Some of these parameters are dependent on others (horizontal structure, roof lightness, number of floors, and building age), while others are independent. Even if the values for each parameter were calculated independently, the analysis of the database evidenced that some of them are dependent on each other. For example, 25% of buildings of class \"A\({}_{\rm v}\)\" have both \"deformable floor\" and were built \"before 1919\". This means that the two features are not independent and the use of coefficients related to both parameters in the scoring of vulnerability would lead to an overestimation of the vulnerability.