# Hygro-Thermo-Mechanical Analysis of Brick Masonry Walls Subjected to Environmental Actions
## 1 Introduction  
Ancient and contemporary buildings use masonry as one of the most common construction materials for both structural and non-structural applications. As an integral part of the building envelope, masonry walls are exposed to environmental actions, such as direct solar radiation, wind-driven rain, thermal and hygric variations, moisture condensation, and rising damp. The continuous exposure to environmental loads affects the mechanical response of the material and leads to long-term weathering and degradation, e.g., strength loss, damage (cracks) due to induced dimensional changes and internal stresses, and spalling caused by salt crystallization and freeze-thaw [1, 2]. The mechanical behavior of masonry structures has been well-documented in the literature under bothstatic and dynamic loading scenarios [3; 4; 5]. However, the structural assessment usually neglects the influence of hygro-thermal loads and assumes ideal conditions. As a result, there is still a limited understanding of the hygro-thermo-mechanical (HTM) behavior of masonry. For the analysis of coupled hygro-thermal phenomena in masonry structures, it is necessary to first define a multi-physics model to describe heat and mass transfer in porous materials and multi-layered components. Several hygro-thermal models for porous building materials are available in the literature, e.g., [6; 7; 8]. Their application to multi-layered cases, however, demands specific requirements: namely, the need to use a driving potential continuous across the interfaces or the consideration of interfacial effects on the heat and mass transfer mechanisms. Perfect contact is usually assumed for heat conduction through the interface. Consequently, the hygro-thermal models commonly disregard interfacial effects on heat transfer. On the other hand, the simulation of moisture transport in multi-layered cases still presents some challenges. Only a few investigations have focused on interface modeling for mass transfer problems in masonry, e.g., [9; 10; 11; 12], and a unified methodology to characterize the effect of brick-mortar interfaces has not been achieved yet. [PERSON] and [PERSON] [13] proved that masonry can be modeled as a homogeneous continuum with brick properties to simulate certain water absorption scenarios. Other authors have employed a similar approach for one-dimensional (1D) simulations, e.g., [14; 15]. Conversely, for two-dimensional (2D) analyses, the most common approach is still the differentiation of brick units and mortar joints, although the interfacial effects are usually neglected [14; 16; 17]. Nonetheless, several experimental studies have proven the impact of interfaces on water absorption in masonry [9; 10; 11; 12; 18]. Thus, further research on the modeling of hydraulic interfaces is required. Most of the scientific advances in heat and mass transfer in porous building materials have come from the disciplines of Material Sciences and Building Physics. In this context, the improvement of hygro-thermal models and the development of new numerical tools have allowed for more complex and detailed hygro-thermal simulations. Nonetheless, the link between the heat and moisture fields and solid mechanics has not been exploited yet. On one hand, experimental studies on structural elements are normally conducted under controlled, standard laboratory conditions. On the other hand, numerical simulations usually neglect the influence of hygro-thermal loads and assume ideal conditions. The study of HTM effects has received more attention in concrete structures, e.g., curing of concrete for application in dams [19; 20]. For masonry, some research has been devoted to the mechanical behavior of walls under extreme scenarios such as high temperatures during fire, e.g., [21; 22]. However, the influence of temperature and moisture actions caused by normal environmental conditions are usually disregarded and so are the hygro-thermally induced stresses.