# 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
The compressive stresses in bed mortar joints follow a similar trend with values around \(-0.13\) MPa near the wall boundaries. On the other hand, the results of \(\sigma_{3}\) in head mortar joints show lower compression levels, with values around \(-0.05\) MPa and \(-0.04\) MPa for the vertical joints located closer to the external and internal surfaces, respectively. Finally, the bricks show the same trends observed for the gravitational case: namely, lower compressive stresses in the areas aligned with the vertical joints and higher concentration of stresses near the vertical edges adjacent to mortar head joints. Figure 12: Hygro-thermo-mechanical analysis of the three-wythe brick masonry wall with natural hydraulic lime mortar. Principal stress distribution obtained for the gravitational loads alone: minimum principal stress, \(\sigma_{3}\) [MPa], in (**a**) bricks and (**b**) mortar joints; maximum principal stress, \(\sigma_{1}\) [MPa], in (**c**) bricks and (**d**) mortar joints. The distribution of maximum principal stresses for the LM case (see Figure 14c,d) presents a relatively uniform gradient across the wall thickness with negligible negative values near the external surface and higher tensile stresses close to the internal side of the wall. In fact, the  
Figure 13: Hygro-thermo-mechanical analysis of the three-wythe brick masonry wall with cement mortar. Principal stress distribution obtained for the gravitational loads alone: minimum principal stress, \(\sigma_{3}\) [MPa], in (**a**) bricks and (**b**) mortar joints; maximum principal stress, \(\sigma_{1}\) [MPa], in (**c**) bricks and (**d**) mortar joints. highest positive values are detected in the outermost layer of the elements facing the interior: namely, 0.06 MPa for bricks and 0.05 MPa for bed mortar joints. The maximum principal stresses for vertical head joints depend on the location: namely, 0.01 MPa and 0.04 MPa for the joints closer to the exterior and the interior faces, respectively. The HTM results for the CM wall are depicted in Figure 15. As happened with the gravitational loads, the overall stress distribution is analogous to the one obtained for the LM case. This was expected since the deformed shape is similar for both cases. Nonetheless, several differences can be pointed out. The minimum principal stresses for bricks (see Figure 15a) present a non-uniform distribution with lower values in the middle section, ca. \(-0.07\) MPa, and higher stress concentration near the external and internal faces: namely, \(-0.14\) MPa and \(-0.12\) MPa, respectively. A similar distribution is found in the bed joints (see Figure 15b), with greater compressive stresses near the outer surface, ca. \(-0.15\) MPa. On the other hand, the head joints show values around \(-0.07\) MPa and \(-0.04\) MPa for the vertical joints located closer to the external and internal surfaces, respectively. As for the previous cases, the bricks present lower compressive stresses in the areas aligned with the vertical joints and a higher concentration of stresses near the vertical edges adjacent to the head joints. The maximum principal stresses obtained for the CM case (see Figure 15c,d) present a relatively uniform gradient across the thickness of the wall. The \(\sigma_{1}\) results for bricks (see Figure 15c) show generalized tensile stresses with increasing values for areas closer to the internal surface, around 0.06 MPa. Furthermore, significant concentrations of tensile stresses (values up to 0.12 MPa) appear on the brick corners adjacent to horizontal joints near the external face. Additionally, the \(\sigma_{1}\) results for bed joints (see Figure 15d) show a rather uniform stress gradient through the wall thickness, with negative values near the external surface, ca. \(-0.07\) MPa, and a transition towards tensile values on the internal side, up to 0.02 MPa. It is noted that the maximum principal stress in the bed joints drops to negligible values in the regions near the external and internal faces of the wall.