# Hygro-Thermo-Mechanical Analysis of Brick Masonry Walls Subjected to Environmental Actions
## 6 Conclusions  
This paper presents a hygro-thermo-mechanical (HTM) model and its application to simulate how different hygro-thermal phenomena affect the structural behavior of masonry elements. First, the hygro-thermal model was presented together with the coupling assumptions needed to link the temperature and moisture fields. Subsequently, a finite element masonry wall was prepared and different hygro-thermal simulations were performed using COMSOL Multiphysics. In the second stage, the hygro-thermal model was extended to incorporate mechanical effects and a one-way coupled HTM model was presented. The capabilities of the HTM analysis were tested on the same masonry wall studied for the hygro-thermal analyses. The presented work addresses the gap found in the literature regarding the impact of normal environmental actions on the structural response of masonry elements; namely, experimental studies are normally conducted under controlled, standard laboratory conditions, and numerical simulations usually neglect the influence of hygro-thermal loads by assuming ideal scenarios. Thus, the influence of temperature and moisture variations caused by actual environmental conditions are usually disregarded and so are the hygro-thermally induced stresses. Furthermore, examples of transient HTM analyses for variable environmental conditions are still lacking in the literature. A 2D finite element model was prepared to simulate a three-wythe brick masonry wall under different hygro-thermal scenarios. Two types of mortars were considered: namely, natural hydraulic lime mortar (LM) and cement mortar (CM). The corresponding boundary conditions were defined based on the climate records of Guimaraes (Portugal). Subsequently, steady-state (SS) analysis, time-dependent analysis with constant boundary conditions (TD1), and time-dependent analysis with variable boundary conditions (TD2) were performed. The results of these hygro-thermal studies were evaluated in terms of temperature and relative humidity distributions across the thickness of the wall as well as for different points on the external and internal surfaces. It was found that for the SS and TD1 analyses, there were only minor differences between the LM and the CM cases. Thus, for these scenarios, the wall can be simulated following a macro-modeling approach with equivalent masonry properties. Similarly, the system can be simplified into a 1D analysis without compromising the accuracy of results. The evolution of temperature and relative humidity profiles obtained by transient analyses show that heat transfer is significantly faster than moisture transport. In fact, thermal processes can be considered instantaneous in comparison with mass transfer. Considering the transient analysis TD2, the results showed differences in the hygro-thermal performance of the wall depending on the type of mortar. As expected, the LM case showed a more uniform response due to the similar behavior of bricks and lime mortar. On the contrary, the CM case presented localized behavior depending on the material. Thus, the LM case can be simplified to a 1D macro-modeling approach, but the same process applied to the CM wall may result in a loss of detail and accuracy. Finally, the interface hydraulic resistance at the brick-mortar interfaces did not play a role when considering the moisture conditions defined in this study. The mechanical problem was coupled with the thermal and moisture fields through the total strain additive decomposition principle. According to this principle, the total strain can be divided into different components: namely, mechanical strains, temperature-induced strains, and moisture-induced strains. The thermal and hygric strains stem from the presence of a temperature gradient or a moisture gradient, respectively. Moreover, the induced strains are proportional to thermo-mechanical and hygro-mechanical parameters: namely, the coefficient of thermal expansion and the coefficient of hygric expansion.