# Hygro-Thermo-Mechanical Analysis of Brick Masonry Walls Subjected to Environmental Actions
## 1 Introduction
To date, few studies have approached the mechanical response of masonry as affected by this type of environmental conditions, e.g., [23; 24; 25]. [PERSON] and [PERSON] [24] developed a one-way coupled HTM model to analyze the behavior of a limestone masonry wall subjected to environmental loads. The authors created a 2D finite element model and performed a series of non-isothermal, non-isohygral, steady-state analyses while isolating and combining the different physics. From a comparison between the mechanical, thermo-mechanical, and HTM results, they were able to identify the contribution of each field to the overall response. Moreover, it was shown that the distribution of stresses in the wall was geometry-dependent, and the highest tensile values were concentrated in the vertical head joints and the corners of the masonry units. Transient analyses were also performed to analyze the evolution of the moisture and temperature distributions from the initial condition to the steady-state equilibrium. The authors did not perform transient HTM analyses for variable environmental conditions and this type of analysis is still missing in the literature. Some authors have dealt with independent thermo-mechanical or hygro-mechanical problems in masonry. For the former, most research is devoted to the mechanical response of structural elements under high-temperature conditions. Among the hygro-mechanicalstudies, [PERSON] et al. [16] developed a multi-scale numerical framework for the analysis of masonry walls subjected to water absorption, e.g., rising damp. In particular, the authors employed a two-dimensional discrete coupled hygro-mechanical model to assess the influence of the moisture field on the structural response as well as to incorporate the effect of mechanical degradation on the moisture transport process. In line with the hygro-mechanical studies, research on salt transport and crystallization in porous materials has received more attention in recent years, e.g., [25; 26; 27; 28; 29; 30; 31]. The proposed models have been proved able to predict the transport of salts and subsequent crystallization under different environmental scenarios. An all-encompassing analysis considering the additive effects of thermal dilation, hygric swelling, and crystallization pressure is still missing. On the other hand, scientific works on fully coupled HTM problems in masonry are notably scarce. Regarding this aspect, further investigation is needed to determine the influence of moisture on the mechanical performance of the material, including linear and non-linear behavior as well as damage. Similarly, more research is necessary to quantify and reproduce the reverse coupling, that is, the mechanical effects (stress variation, creep, volumetric changes, damage, cracking) on moisture transport. The studies developed by [PERSON] [32] and [PERSON] [33] are worth mentioning, and they focused on the non-linear hysteretic behavior of quasi-brittle porous materials. Different finite element computational strategies have been developed for the mechanical analysis of masonry: namely, micro- and macro-modeling approaches [34]. These strategies can be further extended to hygro-thermal analyses as presented in Figure 1. In the case of micro-modeling, which is the focus of this work, the constituent materials (brick units and mortar) and brick-mortar interfaces are modeled separately. On the other hand, macro-modeling approaches assume a homogenized continuum material. This paper presents a hygro-thermo-mechanical (HTM) model to simulate the impact of hygro-thermal loads on the structural response of masonry walls. Moreover, this paper provides a new insight into the HTM behavior of masonry when subjected to normal environmental actions, considering both constant and variable temperature and relative humidity conditions. These aspects are usually disregarded in experimental and simulation works, and therefore, there is an evident lack of scientific knowledge. This paper is structured as follows.