## 5 Finite Element Code
### Basic Characteristics of Finite Element Code
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Mortar Type**} & **Cumulative** & **Apparent Density** & **Average Pore** & **Specific Surface** & **Total Porosity** \\  & **Volume (mm\({}^{2}\)/g)** & **(g/cm\({}^{3}\))** & **Radius (um)** & **Area (m\({}^{2}\)/g)** & **(\%)** \\ \hline \multirow{2}{*}{Lime} & 170–320 & 1.5–1.8 & 0.8–3.3 & 1.3–3.3 & 30–45 \\  & crushed & 170–290 & 1.5–1.9 & 0.1–0.8 & 3.5–15 & 32–43 \\  & brick-line & 110–180 & 1.7–1.9 & 0.3–0.8 & 2.5–4.7 & 20–30 \\  & Hydraulic & 90–230 & 1.7–2.1 & 0.1–3.5 & 2.5–15.5 & 18–40 \\  & lime-Pozzolan & 160–265 & 1.6–1.9 & 0.1–1.5 & 3–14 & 30–42 \\  & bubble masonry & 117–220 & 1.8–2.1 & 0.2–20.6 & 1.2–4.7 & 25–39 \\ \hline \hline \end{tabular} \({}^{*}\)CO\({}_{2}\)/H\({}_{2}\)O: Inverse hydraulicity ratio, representative of a mortar’s hydraulicity. It is calculated as the ratio of CO\({}_{2}\) (\%) loss during thermal analysis and attributed to calcareous compounds and the H\({}_{2}\)Ohydraulic (\%) loss, attributed to water bound to hydraulic compounds (CSH, CASH, etc.). Low values (\(<\)10) are representative of mortars with hydraulicity, such as lime–poszzolan, natural hydraulic lime and lime–crushed brick mortars, while high values (\(>\)10) are representative of mortars with no hydraulicity, such as aerial lime mortars.

\end{table} 
Table 8: Range of acceptability limits for different types of restoration mortars through mercury intrusion porosimetry results (MIP)—microstructural compatibility [233]. ## 7 Case Studies

Aiming to assess the proposed methodology, its implementation is presented in this section both on theoretical, as well as on actual masonry structures. ### 2D Masonry Walls

The behavior of four 2D masonry walls, with square openings, as presented in Figure 36, was studied. The values of the percentage of the openings (surface of the opening/wall surface) were 0%, 16%, 36% and 64%. The mechanical characteristics of the masonry material are presented in Table 9. It should be noted that the data used were considered as typical and are stated in the experimental study of [PERSON], conducted in 1981 [236], the results of which have been widely utilized by the majority of researchers investigating the behavior of masonries, on both experimental and numerical levels. In Figure 37, the failure areas of 2D masonry wall L50H100 are presented. This wall has two openings reaching a total opening percentage of 16% and two different failure criteria are utilized, with three different values of Peak Ground Acceleration (0.24, 0.32 and 0.40 g). These diagrams are especially

Figure 36: Cases of 2D masonry walls examined. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Elasticity modulus in x direction (GPa) & 4.3625 \\ Elasticity modulus in y direction (GPa) & 7.5550 \\ Compressive strength in the x direction (MPaa) & 4.3625 \\ Compressive strength in the y direction (MPa) & 7.5550 \\ Tensile strength in the x direction (MPa) & 0.40 \\ Tensile strength in the y direction (MPa) & 0.10 \\ Poisson ratio in the xy plane & 0.20 \\ Poisson ratio in the yx plane & 0.20 \\ Specific weight (kN/m\({}^{3}\)) & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Mechanical characteristics of masonry (Page 1981) [236]. useful for the determination of failing areas of the structure, as well as for the selection of the optimum repair measures aiming to their repair. More specifically, the failure areas are marked with different colors highlighting in distinct ways the kind of stress underpinning the failure. As can be easily perceived, different repair measures are demanded when failure occurs under biaxial compression, biaxial tension and heterosemous biaxial stress state (tension/compression).