# Parametric Analyses of the Response of Masonry Walls with Reinforced Plaster
## 3 Numerical Simulations
### Unreinforced Masorury--Effect of Weak Bricks  
The quality of the brick in a masonry wall may have a significant effect on its overall response. Several factors influence brick quality: workmanship, the presence of inner cracks due to transportation to the job site, nonuniform heat distribution in the oven during the drying time, damage recorded after seismic events, etc. This section analyzes the effect of the distribution of some of the weak bricks on the overall wall structural response. Three different weak-brick patterns were defined (Figure 13), representing a wall with a random distribution of weak bricks (R1), a wall in which an opening has been closed so that the edges of the former window represent lines of structural weakness (R2), and a wall that shows damage along the diagonal because of an earthquake (R3). The number of weak bricks is constant in the different configurations. The assumed elastic properties of the weak bricks were an elastic modulus E = 500 MPa and a Poisson ratio \(\
u\) = 0.17. The obtained results were compared, and then compared to those of the configuration with no weak bricks (i.e., reference configuration).  
Figure 11: Load vs. displacement curves for different mortar grades.  
Figure 12: Damage distribution for different mortar grades: (**a**) weak; (**b**) modified weak; (**c**) intermediate; (**d**) strong.  
Figure 14 shows the load vs. displacement curves for the different configurations. It is evident that the presence of weak bricks determines a lower peak load and more ductile behavior of the specimen with respect to the reference configuration, but it is interesting to highlight how different distributions of the same number of weak bricks can determine different overall responses. In particular, when the weak bricks are located along the diagonal (i.e., case R3), a significant reduction in terms of the peak load and stiffness is evident with respect to cases R1 and R2. This result confirms the importance of considering the presence of weaknesses (e.g., pre-existing damage) in the modeling of existing masonry structures because they can significantly affect the overall structural response.  
Figure 15 shows the damage distribution for the different configurations at failure. The cracks followed the mortar joints and the bricks were broken only rarely. In the R1 pattern (a), the damage was widespread in a larger area around the compressed diagonal and, even though a main diagonal crack was detected, several minor cracks involved both the mortar joint and the weak bricks. The R2 case (b) showed several diagonal cracks, which were mainly driven by the location of the weak bricks. In the case of R3 (c), the damage was entirely localized on the compressed diagonal, and only a few other cracks were detected in the mortar joints outside the damaged diagonal. The reference configuration without weak bricks (d) mainly shows stair-stepped cracks along the compressed diagonal.  
Figure 14: Load vs. displacement curves for different weak-brick patterns.  
Figure 13: Weak-brick patterns: (a) R1; (b) R2; (c) R3.  
Overall, it is evident that, for all the cases, the damage distribution was strongly influenced by the presence of weak elements, since the load always chose the path that minimized its internal work. When the damage (i.e., weak breaks) was distributed in a larger area, the wall response was more homogenous and the stress peaks, where the cracks usually initiated, reduced.