# Hygro-Thermo-Mechanical Analysis of Brick Masonry Walls Subjected to Environmental Actions
## 3 Hygro-Thermal Simulations and Discussion
### Hygro-Thermal Behavior of a Brick Masonry Wall  
#### 3.2.1 Steady-State Analysis (SS)  
The temperature and relative humidity profiles obtained for the steady-state analyses are shown in Figures 3 and 4, respectively. The results show only minor differences between the two studied cases: namely, the wall with lime mortar (LM) and the wall with cement mortar (CM). This was expected considering that the stationary analysis focuses on the final equilibrium state, which is mostly dependent on the external boundary conditions. Moreover, any difference observed in the response of the wall stems from the different behavior of the selected type of mortar, which ultimately accounts for less than 26% of the total cross-sectional area. It is noted that the temperature and relative humidity values obtained at the external and internal surfaces do not reach the values defined for the boundary conditions: namely, 13.5 \({}^{\circ}\)C and 74% RH for the exterior and 20 \({}^{\circ}\)C and 50% RH for the interior. This is due to the kind of boundary conditions imposed on the model, i.e., convective flux or Neumann boundary conditions. Therefore, the convective heat transfer and the convective mass transfer coefficients induce, respectively, a temperature and a relative humidity exchange between the environment and the surface of the wall. Regarding the thermal field (see Figure 3), the temperature profiles for both cases show an overall linear distribution across the thickness of the wall. In a multi-layered material, the transition between adjacent layers with dissimilar thermal conductivity translates into a change of slope in the temperature profile before and after the interface. For the LM case, the presence of mortar joints is barely noticeable since the thermal conductivity properties of bricks and lime mortar are similar. On the contrary, the presence of joints is clearer for the CM case due to the more dissimilar thermal conductivity of bricks and cement mortar. Therefore, for the CM case, it is possible to perceive slight changes in the slope of the temperature profiles at the location of the vertical head joints. Regarding the hygric response (see Figure 4), the relative humidity profiles for both models show a nearly linear distribution between the two faces of the wall. As was mentioned for the temperature, slight disturbances in the moisture profiles reveal the presence of mortar joints. It is noted that the CM case shows a somewhat less linear trend and slightly higher values of relative humidity across the wall thickness. Moreover, the presence of vertical head joints is clearer for the CM case as well. These aspects can be explained by the marked hygroscopic nature of cement mortar, which contrasts with the less hygroscopic behavior of lime mortar and the barely hygroscopic behavior of bricks. Considering the results of the hygro-thermal steady-state analysis, rather homogeneous temperature and moisture distributions are obtained for the studied wall configuration. Moreover, the differences between the two types of mortar are not significant. Thus, a macro-modeling approach with equivalent masonry properties could be used instead of the presented detailed micro-modeling. It is recalled that macro-modeling assumes