## 5 Finite Element Code
### Basic Characteristics of Finite Element Code
In Figure 38, the failure areas of 2D masonry wall L100H100 are presented for three different opening percentages (0%, 16% and 36%) using two different failure criteria and for a PGA = 0.32 g.

In Figures 39 and 40, the damage indices of 2D masonry walls L50H100 (Figure 36a) and L100H100 (Figure 36b), both without any opening (total opening percentage of 0%), are presented. These diagrams are especially useful for the assessment of the seismic vulnerability in a preliminary stage. Namely, we can see that for both masonry walls the determined damage indices are under the lower limit of heavy damage of 25% for values of peak ground acceleration up to 0.24 g. Furthermore, a comparison between these two 2D masonry walls depicts that damage indices of the \"shear\" wall L100H100 are much less than the damage indices of the \"cantilever\" wall L50H100 something that is expected. Such diagrams are of great interest and extremely useful for the assessment of more complicated structures. In Figure 41, the development process of fragility curves is presented. Namely, having determined the damage indices for the case of the 2D masonry wall L50H100 (Figure 36a) with opening percentage of 16% for a set of masonry tensile strengths ranging from 0.0650 to 0.4350 MPa using a step of 0.0465 MPa (response parameter) and for values of Peak Ground Acceleration (intensity measure (IM)) from 0.00 to 0.80 g using a step of 0.08 g, the probability of exceeding a damage limit state is determined. Based on these probabilities, the results for values of PGA equal to 0.00, 0.24, 0.48 and 0.72 g are presented in the four smaller images and the fragility curves are derived and presented in the larger image of Figure 41.

In Figure 42, the fragility curves of the current condition of wall L50H100 are presented, using the [PERSON] modified failure criterion and for an opening percentage of 16% for normal and lognormal distribution. In Figure 43, the fragility curves of the current condition of wall L50H100 are presented, using the Kupfer and Girstle failure criterion [160], four different opening percentages (0%, 16%, 36% and 64%), lognormal distribution and moderate damage performance level. In Figure 44, the fragility curves of the current condition of three different walls with percentage openings of 16% are presented, using the [PERSON] et al. (1995) failure criterion [8; 25], lognormal distribution and heavy damage performance level. This particular figure is indicative of the potential of fragility curves in quantifying the vulnerability of structures and especially in classifying structures according to their vulnerability. In Figure 45, the fragility curves for the case of wall L50H100 are presented, using the [PERSON] et al. (1995) failure criterion [8; 25], regarding the current state of the wall, as well as the repaired states in the cases of using three different repair mortars M5, M10 and M15, of compressive strength 5, 10 and 15 MPa, respectively, using lognormal distribution and moderate damage performance level. These three types of restoration mortars were evaluated to cover the whole range of mechanical properties presented by restoration mortars, which have been assessed to be compatible for use in monuments and historical buildings ([PERSON] et al., 2005 [61]). In Table 10, the values of the tensile strengths (response parameter) for existing structures as well for the repaired ones used for the development of fragility curves are presented. \begin{table}
\begin{tabular}{c c} \hline
**Structure** & **Tensile Strengths in MPa** \\ \hline Existing 2D masonry walls & 0.065 to 0.435 by step 0.0465 \\ Repaired 2D masonry walls with mortar M5 & 0.117 to 0.467 by step 0.0438 \\ Repaired 2D masonry walls with mortar M10 & 0.142 to 0.566 by step 0.0530 \\ Repaired 2D masonry walls with mortar M15 & 0.158 to 0.634 by step 0.0595 \\ \hline \end{tabular}
\end{table} 
Table 10: Values of tensile strength (response parameter) of 2D masonry walls examined.