# Seismic Assessment of Historical Masonry Buildings at Different Scale Levels: A Review
## 3 Small-Scale Approaches
### Finite Element Methods
#### 3.2.1 FEM Modelling: Strategies and Issues Applied to Cultural Heritage  
The application of the FE method to the engineering field has been widely debated [144; 145; 146; 147], and three different strategies are currently available (see, for instance, [PERSON], [PERSON] [3], [PERSON] and [PERSON] [148]) for modelling and analysing structures with an increasing level of detail and accuracy, i.e., micro-modelling, simplified micro-modelling and macro-modelling. First FEM attempts for masonry structures are due to [149]; the FEM micro- or block-by-block modelling [123] represents the more detailed approach, individually modelling the three masonry components (i.e., blocks/element, mortar, interface) through continuum finite elements for units and mortar and discontinuous elements for the interface, accounting for potential cracks or slip planes. The in- and out-of-plane orthotropic masonry behaviour is well reproduced without needing interpretation, and the anisotropy of the material, as characterised by experimental tests, is directly accounted for. The counterpart is the relevant computational burden, bounding the method's applicability to the analysis of material local responses or small structural components. The computational effort is partially reduced by adopting the simplified micro-modelling [123], where only the unit is modelled as a FEM continuum, whereas the mortar and the interface are smeared at the vertical and horizontal joints, which are represented by a discontinuous element. Even if succeeding in simplifying the numerical problem, this approach has shown relevant errors when applied to nonlinear analysis and is therefore seldom used for complex structural analysis [148; 149; 150; 151]. More information can be found in [PERSON] [152]. The macro-models (see [PERSON] and [PERSON] [148] for numerical and theoretical background) have found a wider application at the building-level analysis thanks to the highly reduced calculation demand. A fictitious homogeneous material is generated by adopting a suitable relationship between average masonry strains and stresses, allowing mesh dimensions higher than the single unit. For historical buildings, the adoption of a macro-model is nearly mandatory due to the presence of multi-leaf irregular randomly assembled masonry, almost impossible to be represented through micro-modelling and difficult to be accurately characterized due to the limitations concerning the execution of destructive tests on cultural heritage [117]. Hereinafter, only the FEM macro-models will be thoroughly analysed. Modelling of Geometry  
The determination of building geometry is fundamental for a reliable FEM model. Indirect survey techniques, including photogrammetry and terrestrial laser scanning (TLS), are mainly used when the building's size and scale of representation require a high density of point capture and need post-processing. Direct survey techniques, including the total station theodolite (TST), the global positioning system (GPS) or measured drawing, represent less 'automatic' procedures since they are dependent on the surveyor's skills. Recently, mainly the former typology was adopted in the field of historical constructions thanks to the increasing technology capability and the high accuracy granted. Particularly, the use of a terrestrial laser scanner (TLS) has been demonstrated to be a valid tool for accurately detecting the external geometry (including permanent deformations, out of plumbs, local deviations, misalignments etc.) and the inner morphology (presence of cavities, thicknesses, etc.). TLS succeeds in describing the geometry of hardly accessible areas and can even be adopted in poorly lit environments such as churches [153; 154; 155]. TLS allows the contemporary survey of the geometrical position of a huge number of points (the so-called 'point cloud model'), which can be elaborated in different ways to provide the structural model.