# 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
#### 3.2.2 Time-Dependent Analysis with Constant Boundary Conditions (TD1)  
The previous section dealt with the steady-state equilibrium attained by the studied three-wythe brick masonry wall considering an environment with constant boundary conditions. In this section, the first group of time-dependent analyses, labeled TD1, focuses on the process required for the wall to reach the same state of hygro-thermal equilibrium.  
Figure 4: Steady-state analysis (SS). Relative humidity distribution across the studied three-wythe brick masonry wall: (**a**) joints with lime mortar (LM); (**b**) joints with cement mortar (CM).  
The evolution of temperature and relative humidity profiles obtained from the TD1 analysis is shown in Figures 5 and 6, respectively. It is worth noting the time difference needed for both processes to reach equilibrium. On one hand, the thermal field attains the steady-state equilibrium in about 60 h. Conversely, moisture transport is a much slower process and hygric equilibrium is only attained after 450 days (or 11,000 h). Taking this into account, heat transfer can be treated as an immediate process in comparison with mass transport. Furthermore, it is possible to conclude that a real structure will not likely attain a full hygric equilibrium considering the usual variability of environmental conditions and the long time required for the materials to accommodate moisture processes.  
Figure 5: Time-dependent analysis (TD1). Temperature evolution across the studied three-wythe brick masonry wall: (**a**) joints with natural hydraulic lime mortar (LM); (**b**) joints with cement mortar (CM). Lines A–A” (**top**), B–B” (**middle**), and C–C” (**bottom**).  
There are some differences between the wall with lime mortar (LM) and the one with cement mortar (CM). On one hand, the temperature evolution is faster for the CM case. In other words, the wall with cement mortar requires less time to reach thermal equilibrium. This is consistent with the higher thermal conductivity of cement mortar in comparison with lime. Conversely, the relative humidity evolution is slower for the CM case. This can be explained by the transport properties as well: cement mortar has lower liquid diffusivity and higher water vapor resistance than its lime counterpart.  
Figure 6: Time-dependent analysis (TD1). Evolution of the relative humidity across the studied three-wythe brick masonry wall: (**a**) joints with natural hydraulic lime mortar (LM); (**b**) joints with cement mortar (CM). Lines A–A’ (**top**), B–B’ (**middle**), and C–C’ (**bottom**).  
As was pointed out for the SS analysis, the presence of mortar joints can be distinguished by slope changes in the temperature and relative humidity profiles at the location of the brick-mortar interfaces. It is noted that the TD1 results for the CM case show the location of the vertical head joints more evidently. Once again, this can be explained by the more dissimilar properties between bricks and cement mortar in comparison with lime mortar.  
Besides the previous analyses, a parametric study was performed in order to evaluate the influence of the hydraulic resistance on the evolution of relative humidity. In particular, different values of the interface resistance, \(R_{IF}\), were adopted, but the results did not show significant differences. Thus, it was concluded that the impact of the interface resistance was not significant for the moisture conditions considered in this problem. It must be pointed out, however, that the hydraulic resistance may become non-negligible for higher moisture levels.  
Considering the results of the time-dependent analysis TD1 for both LM and CM cases, only slight differences are noticed between the three studied sections of the wall. Therefore, a macro-modeling strategy with equivalent masonry properties could be used as well to simulate the observed temperature and moisture content evolution. Notwithstanding the loss of detail, a simplified 1D model could be considered as well with a minor impact on the overall accuracy.