## 5 Finite Element Code
### Basic Characteristics of Finite Element Code
established a range of acceptability limits of physical, chemical and mechanical characteristics that should be fulfilled by the restoration mortars, deriving from the evaluation of historical mortars, for different mortar types (Tables 7 and 8) [233]. The use of acceptability limits to assess restoration mortars can be found in [69], while it should be noted that mechanical strength compatibility is linked with the requirement that the restoration mortar is not stronger than the historical building units, in order to avoid failure of the historical materials. Aesthetic compatibility is achieved when the restoration mortar has the same appearance as the authentic mortar. The color, texture, symbolisms, and aesthetic must create an overall appearance similar to the original [6]. The shape and design, materials used, and workmanship are often addressed as key heritage values [234]. An issue which is also widely discussed nowadays is the design and production of environmentally friendly mortars, aiming towards sustainability [235]. The use of traditional materials is in accordance with this tendency, as they are non-toxic, and have lower firing temperatures and a more sustainable life cycle, especially concerning CO\({}_{2}\) emissions. Thus, fragility curves can serve as a tool to evaluate the contribution of restoration mortars on the response of the monument under dynamic stresses, which, coupled with a compatibility assessment and the fulfillment of the above principles, can lead to the selection and application of the optimum material, preserving masonry historic structures for centuries to come. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Mortar Type**} & **Hygroscopic Water (\%)** & **Hydraulic Water (\%)** & **CO\({}_{2}\) (\%) Bound in** & **Tensile Strength** \\  & **Water (\%)** & **Bound in Hydraulic Compounds** & **Calcareous Compounds** & **CO\({}_{2}\)H\({}_{2}\)Ohydraulic \({}^{*}\)** & **Strength (MPa)** \\ \hline \multirow{2}{*}{Crushed brick-line} & c1 & 2–4 & \textgreater{}30 & \textgreater{}8.5 & \textless{}0.35 \\  & 1.5–4.5 & 2.3–5.3 & \textgreater{}20 & 3.2–6.5 & 0.5–1.2 \\  & 0.7–1.5 & 2–4.6 & \textgreater{}25 & 6–15 & 0.8–1.5 \\  & Hydraulic & 1–2.5 & 4–7.2 & \textgreater{}25 & 1.8–6.1 & - \\  & 2–4 & 3.3–5.4 & \textgreater{}22 & 1.3–5.1 & - \\  & - & 5.6–5.9 & \textgreater{}30 & 3.36-5.13 & - \\ \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 7: Range of acceptability limits for different types of restoration mortars through thermal analysis results (TG/DTA) (physicochemical compatibility) and tensile strength measurements (mechanical compatibility) [233].