# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 2 Large-Scale Approaches
### Empirical Methods
#### 2.1.1 Damage Probability Matrix Methods (DPM)
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{4}{c}{**Empirical (Macroseismic) Methods**} \\ \hline
**Damage Probability Matrix** & **Fragility Curves Methods** & \begin{tabular}{c} **Vulnerability Index** \\ **Methods (VIM)** \\ \end{tabular} \\ \hline [PERSON], [PERSON] [12] & \begin{tabular}{c} [PERSON], [PERSON] [22] \\ [PERSON], [PERSON] [23] \\ [PERSON] [24] \\ [PERSON], [PERSON] [25] \\ [PERSON], [PERSON] [26] \\ [PERSON], [PERSON] [27] \\ [PERSON], [PERSON] [28] \\ [PERSON], [PERSON] [18] \\ [PERSON], [PERSON] [19] \\ [PERSON] and [PERSON] [20] \\ [PERSON] and [PERSON] [21] \\ [PERSON], [PERSON] [11] \\ \end{tabular} & \
\begin{tabular}{c} [PERSON], [PERSON] [22] \\ [PERSON], [PERSON] [23] \\ [PERSON] [24] \\ [PERSON], [PERSON] [25] \\ [PERSON], [PERSON] [26] \\ [PERSON], [PERSON] [27] \\ [PERSON], [PERSON] [28] \\ [PERSON], [PERSON] [29] \\ [PERSON] and [PERSON] [30] \\ [PERSON], [PERSON] [31] \\ [PERSON], [PERSON] [32] \\ [PERSON], [PERSON] [33] \\ [PERSON], [PERSON] [11] \\ \end{tabular} &
\begin{tabular}{c} [PERSON] and [PERSON] [34] \\ [PERSON], [PERSON] [35] \\ GNDT-SSN [36] \\ [PERSON], [PERSON] [37] \\ [PERSON], [PERSON] [38] \\ [PERSON], [PERSON] [39] \\ [PERSON], [PERSON] [40] \\ [PERSON], [PERSON] [41] \\ [PERSON], [PERSON] [42] \\ [PERSON], [PERSON] [43] \\ [PERSON] et al. [44] \\ [PERSON], [PERSON] [11] \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of different proposals for the empirical analysis of masonry structures. and Lagomarsino [20], the DPM method was applied to the case of monumental buildings with a knowledge-based approach. Since the EMS 98 scale refers to ordinary buildings, a new vulnerability model was proposed by grouping in class types the monumental buildings with similar use, architecture and, potentially, seismic behaviour, according to the observation of post-earthquake damages described in the available literature. The DPM was, therefore, generally used to describe the damages of a set of buildings with observed homogenous behaviour, leading to defining a discrete number of resulting classes. Due to the frequently limited data availability, not enough for covering all the building typologies and all the intensities required for a complete DPM model, the expert judgment [54], the neural network system [55], or the fuzzy set theory [56] were used as a support or replacing-tool, besides the probabilistic processing of the surveyed data [57]. In Lagomarsino and Cattari [21], binomial intensity coefficients were used to complete the matrix levels of damage with a few data caused by the lack of information concerning damage grades for all levels of intensity at a certain site characterised by a given building type. If we consider the huge variety of historical buildings, even internally differing in materials, construction techniques, geometry, etc., the application of DPM methods--even if thought for single structural units within the aggregate--is not always suitable, and other approaches can be preferred.