# Hygro-Thermo-Mechanical Analysis of Brick Masonry Walls Subjected to Environmental Actions
## 6 Conclusions
In the proposed HTM model, the link between the mechanical component and the hygro-thermal fields consists of a one-way coupled relationship. In other words, the hygro-thermal results affect the mechanical response, but mechanical stresses/strains do not influence heat and moisture transport. Additionally, temperature and moisture dependencies of the mechanical properties were not considered. The HTM model was completed withthe implementation of mechanical boundary conditions as well as the initial or free-strain conditions. A careful definition of initial and boundary conditions is of special importance for mechanical analyses since the appearance and distribution of stresses largely depend on these parameters. In particular, when considering the non-linear behavior of the coefficient of hygric expansion, the definition of the initial moisture conditions (and, therefore, the associated free-strain state) greatly affects the stress evolution. The three-wythe brick masonry model defined for the hygro-thermal analysis was further used to study the internal distribution of stresses of the wall subjected to temperature and moisture gradients. In particular, the temperature and moisture results from the time-dependent analysis TD2 were used as input for the mechanical study. The instant of maximum displacement was chosen, and the corresponding stress distribution induced by the hygro-thermal loads was compared with the self-weight scenario. The analysis focused on a section of the mid-portion of the wall in order to avoid disturbances caused by the proximity of loads or boundary conditions. It was proven that temperature and moisture variations change the natural stress distribution of the wall subjected to gravitational loads alone. Moreover, the brick wall with cement mortar underwent higher stress levels in comparison with the wall with natural hydraulic lime mortar. This was caused by the higher thermal expansion and hygric expansion coefficients of cement in comparison with lime mortar. Although the induced tensile stresses were low, they may contribute to crack propagation of existing cracks. Similarly, the hygro-thermally induced deformations may add up to previous damage and magnify existing problems such as tilting in structures with moisture deterioration at the base or soil permanent deformation. Finally, it is noted that the hygro-thermo-mechanical behavior of the brick wall is a 2D phenomenon derived from the multi-layered nature of masonry. The numerical approach presented in this paper can be used to evaluate the hygro-thermal performance of masonry walls as well as to complement the structural assessment when considering other static or dynamic loads. The methodology can be further extended to study the compatibility between masonry units and mortars. Taking into consideration the everyday nature and relevance of hygro-thermo-mechanical problems, the need for further investigation on this topic is evident. Similarly, experimental studies aimed at acquiring data for validation of the corresponding models are needed. Future works should extend the hygro-thermo-mechanical model to incorporate non-linear material behavior, with different constitutive laws for tension and compression and the capacity to reproduce creep. Likewise, improvements could be achieved by extending the simulations to 3D models, which are more suitable to reproduce complex hygro-thermal phenomena such as thermal bridges in envelope walls. Moreover, the study may be expanded to incorporate different heat and moisture regimes according to specific climatic zones. Finally, considering the cyclic nature of hygro-thermal phenomena, the study of material fatigue is strongly recommended. Conceptualization, R.R., B.G., P.P. and P.B.L. ; methodology, R.R., B.G., P.P. and P.B.L. ; software, R.R. ; validation, R.R. ; formal analysis, R.R. ; investigation, R.R. ; writing--original draft preparation, R.R. ; writing--review and editing, B.G., P.P. and P.B.L. ; visualization, R.R. ; supervision, B.G., P.P. and P.B.L. ; project administration, P.B.L.