 # Assessing the Stability of Masonry Structures (part 2): Numerical and Physical Modeling

QUICK UPDATE:  Demi just had her paper published ‘Assessing the Stability of Unreinforced Masonry Arches and Vaults: A Comparison of Analytical and Numerical Strategies’, in the Journal of Architectural Heritage.  You can find it here

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This post is second in a series covering different assessment methods for stability of masonry structures. Part 1 covered classical and equilibrium methods; this post covers suitable numerical modeling techniques as well as different examples of physical modeling for masonry stability.

#### 4. Numerical modeling

Several methods of numerical modeling for masonry structures exist, as demonstrated by the flowchart in Fig. 10. Figure 10: Overview of numerical modeling methods for masonry structures, adapted from  with As the first level of Fig. 10 suggests, numerical modeling of masonry structures can be divided into four main categories: macro-modeling, homogenized modeling, simplified micro-modeling, and detailed micro-modeling. Asteris et al.  provide discussions, summarized below with some additions where noted, on the differences between these modeling approaches. Fig. 11 also depicts the different numerical modeling approaches. In this section, macro-modeling and simplified micro-modeling are the focus. Figure 11: Illustration of different strategies for modeling true masonry sample (a): (b) one-phase macro-modeling, (c) two-phase micro-modeling, and (d) three-phase micro-modeling 

#### 4.1 Macro-modeling: masonry as a one-phase material

The macro-modeling approach models both bricks and mortar (or all bricks, in the case of dry masonry) as a homogeneous continuum as in Fig. 11(b). As the subsets under macro-modeling in Fig. 10 suggest, these numerical models are typically finite element models.