# Hygro-Thermo-Mechanical Analysis of Brick Masonry Walls Subjected to Environmental Actions
## 5 Hygro-Thermo-Mechanical Simulations and Discussion
### Hygro-Thermo-Mechanical Behavior of a Brick Masonry Wall
distribution in bricks brings to light two aspects: (a) the compression stress is slightly lower, around \(-0.08\) MPa, in the mid-section of the header course bricks, that is, the portion of the brick aligned with the vertical head joints; (b) higher compression values, ca. \(-0.10\) MPa, are found on the vertical edges of the bricks adjacent to mortar head joints. Therefore, the brick-mortar interaction is associated with 2D phenomena that affect the distribution of stresses within the masonry wall. The maximum principal stresses obtained for the gravitational case reveal expected trends as well (see Figure 12c,d). On one hand, the positive component of the principal stress for bricks is practically zero, whereas it presents low positive values for the vertical head joints, around \(5.0\times 10^{-3}\) MPa. Even though the obtained values are not significant, this observation is consistent with the fact that head joints typically act as tension planes within the wall geometry. On the other hand, the results for the horizontal joints show small negative values for \(\sigma_{1}\), around \(-8.0\times 10^{-3}\) MPa, which indicates that the bed mortar joints experience biaxial compression. Moreover, the maximum principal stress in the bed joints drops to zero in the regions near the external and internal faces of the wall. The distribution of stresses for the CM wall under gravitational loads is shown in Figure 13. It is noted that the obtained results are analogous to the ones of the LM case. In this sense, the distribution of minimum principal stresses for bricks and mortar bed joints (see Figure 13a,b) presents the same average compression, i.e., \(-0.09\) MPa. Likewise, the areas of the bricks aligned with vertical joints show lower stresses, ca. \(-0.08\) MPa. Some differences between the two cases can be pointed out as well. For instance, the compression values on the vertical edges of the bricks adjacent to mortar head joints are slightly higher, around \(-0.11\) MPa. Moreover, the vertical joints show less compressive stresses, ca. \(-0.05\) MPa. The distribution of maximum principal stresses for the wall with cement mortar (see Figure 13c,d) shows some differences with respect to the LM case as well. The positive component of the principal stress for bricks is still negligible for most of the wall, but higher values appear close to the brick corners, between \(5.0\times 10^{-3}\) and \(6.0\times 10^{-3}\) MPa. Furthermore, higher \(\sigma_{1}\) values can be found in the vertical head joints, ca. \(7.0\times 10^{-3}\) MPa. Although the obtained tensile stresses are low, they may contribute to crack propagation when cracks are already present. On the other hand, the horizontal joints show lower negative values, around \(-0.01\) MPa; thus, they undergo a biaxial compression state. Finally, the maximum principal stress in bed joints falls to zero in the regions near the faces of the wall. In conclusion, for the two studied models, the outcomes of the gravitational case reveal a complex 2D stress distribution derived from the multi-layered nature of the material. Moreover, the stress distribution results for the LM and CM walls are analogous, although slightly higher stress states are obtained for the wall with cement mortar. Regarding the HTM analysis, the stress distribution results obtained for the LM case are shown in Figure 14. It is recalled that the instant with maximum horizontal displacement is selected for the analysis (see Figure 10). At that moment, the imposed boundary conditions lead to shrinkage of the internal face of the wall. It is noted that the corresponding deformed configuration is intimately linked to the stress distribution. As expected, the distribution of stresses is not uniform across the wall thickness. Considering the minimum principal stresses (see Figure 14a,b), lower compression values are found in the middle portion of the wall, around \(-0.07\) MPa. Conversely, higher stresses appear near the external and internal faces, ca. \(-0.12\) MPa.