# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 2 Large-Scale Approaches
### Empirical Methods
#### 2.1.3 Vulnerability Index Methods (VIM)  
VIM, as well as fragility curve methods, try to overcome the limits of DPM by proposing a continuous approach to evaluate the probability of exceeding a certain damage level, given an earthquake characterised by a specific macroseismic intensity, or PGA. The vulnerability evaluation is based on buildings' structural features (instead of typologies adopted in DPM), and the 'vulnerability index' (Iv) provided is the result of the weighted sum of selected parameters. Data related to observed damages are used to calibrate vulnerability functions for buildings belonging to the same typology. The resort to instrumental parameters (e.g., PGA) instead of macroseismic measures allows for easier result comparison even if, as stressed by [PERSON] and [PERSON] [60], the accuracy provided by the correlation between PGA and damages has been recently questioned [61; 62; 63]. The main shortcoming of VIM is the fact that the result is significantly affected by the technician's judgment, as well as the parameters selected, and their weights are affected by a certain degree of uncertainty and related to the analysed building typology [10; 63]. The VIM was introduced in 1984, starting with the elaboration of a huge amount of field survey damage data based on the survey form proposed by [PERSON] and [PERSON] [34] and applied by [PERSON], [PERSON] [35]. A scoring assignment ranging between class A (situation aligned to the Italian code prescriptions) and D (most unsafe condition) qualified each parameter, weighted depending on the relative influence of the accounted structural features on the building vulnerability. The different weighted parameters were finally added up, providing the building vulnerability index (Iv). [PERSON] and [PERSON]'s [34] proposal was the basis of the GNDT II level contribution [36] for existing masonry and ordinary reinforced concrete structures. The form was developed from the post-damage observations for identifying the primary structural system and the relevant deficiencies through visual inspections. Compared to [PERSON] and [PERSON] [34], modifications in the parameters' list--such as the inclusion of the non-structural element parameter--and in the assigned scores--realibrated based on the damage survey performed--were introduced. The GNDT II level was implemented in Puncello, Caprili [64] to fit the case of historical monumental masonry buildings. Assuming to first disaggregate the building into its structural units, a survey form was provided to account for the main structural and geometrical features, determining a score for each unit. As a result, the most vulnerable unit among the aggregate was identified, therefore suggesting the order to follow for a more in-depth investigation and design of retrofit interventions. A significant VIM update was due to [PERSON], [PERSON] [37] and applied in many further works [38; 39; 40; 42; 65]. The issue of masonry building aggregates, reflecting the structural layout of many historic Italian city centres, was first proposed and analysed. Inspired by [PERSON] and [PERSON]'s [66] research, [PERSON], [PERSON] [37] integrated the original form by introducing five parameters that account for the interaction among adjacent buildings. The scores and the weighting factors were determined by realising 3D models of a building, used as a representative sample, through 3 Muri(r) software [67]. The issue of building interaction was even faced by [PERSON], [PERSON] [43], who proposed an updated survey table that rediscussed some existing parameter criteria and introduced new ones that accounted for the interaction among ordinary buildings. Besides somehow quantifying the safety under seismic loads, the Iv can contribute to defining vulnerability functions if related, through stochastic methods, to a global damage index D of buildings having the same typology, in the case of equal macroseismic intensity I (or PGA).