1. Introduction
Masonry structures and architectural heritage undergo several decay processes due to exposure to aggressive environmental conditions that threaten its durability and mechanical properties [
1]. Recently, atmospheric pollution (acid deposition) on masonry materials has been recognized as one of the most important and common reasons of decay endangering the built heritage [
2,
3,
4]. High acid rain concentration caused masonry materials to dissolve and form harmful salts, which leads to a significant reduction in the mechanical properties of masonry material and the structural service life [
5,
6]. At the present, there are a large number of masonry structures and cultural heritage of brick masonry worldwide, and they have been exposed to an acidic atmospheric environment for a long time. Therefore, it is necessary to evaluate the degradation of mechanical properties in the acid rain area, which allows more effective restoration works.
For the past few years, the impacts of acid deposition on the weathering of masonry building material (stone) have been discovered and examined. Many researchers have focused on the identification of the different processes responsible for stone dissolution [
7], the influences of acid deposition on the decay of stones, and the quantitative relationships between climatic variables [
8,
9]. The chemical analysis of the run-off solutions, direct measurement of recession, the surface modifications of building stone with an electron scanning microscope, and the X-ray diffraction analysis of stone in response to environmental aggressiveness were studied with consideration of the important role of stone characteristics, weight loss measurements, and the forecast of stone [
10,
11,
12]. Furthermore, the correlation between stone microstructural characteristics and material degradation was investigated [
13].
Additionally, several aspects of mortar and bricks under simulated acid rain conditions were evaluated. The change in mineralogical composition and chemical behavior, as well as the strength, phase, and internal structure of the mortar, were studied in a previous publication [
14,
15,
16,
17]. The effects of acid rain corrosion on the appearance, and the quality of masonry mortars, were studied [
18]. The effect of low-calcium fly ash on mortar strength under simulated acid rain conditions was studied, and the flexural strength of cement-fly ash mortar specimens was lower than that of pure cement mortar specimens after acid rain corrosion [
19,
20]. J.A. Larbi described the integrated microscopic method for diagnosing the causes and the degradation extent of fired clay brick masonry under atmospheric environment [
21]. The damage mechanisms of building materials (stones, mortars) after acid rain corrosion were described. The degradation degree of mortar was higher than that of stone [
22,
23].
The main ion components in acid rain are SO
42−, NO
3−, Ca
2+, NH
4+, Mg
+, H
+, and H
+. SO
42− leads to serious corrosion damage to mortar [
17,
24,
25]. The acid rain corrosion mechanism of masonry material is a complex process, including acid corrosion (dissolved corrosion) and salt corrosion (expansion corrosion) in precipitation.
In conclusion, many research studies have been devoted to chemical components, density, porosity, vapor permeability, water absorption, and the acid rain corrosion mechanism in materials (such as natural stone, brick, mortar, and concrete). However, the effect of an acidic atmospheric environment on the mechanical performance of masonry has not been fully elucidated. Therefore, the aim of this paper is to evaluate the mechanical behavior of a masonry building in an acidic atmospheric environment, including the mechanical characteristics of the masonry unit, mortar, unit-mortar bond, and masonry prism. Thus, simulated acid rain corrosion tests and mechanical performance tests on standard mortar prisms, bricks, masonry shear specimens, and masonry compression specimens were conducted. Furthermore, mathematical strength degradation models for masonry were established.
4. Degradation Model for Compressive Strength
This section provides an overview of the proposed models that were established to describe the test results of the mechanical properties for brick masonry subjected to different acid rain corrosion cycles. Through the comparison and statistical analysis of test data, it can be seen that the compressive strength of the cement mortar prism, cement-lime mortar prism, cement-fly ash mortar prism, brick unit, and acid rain corrosion cycle approximated a quadratic function relationship. The variations of the normalized compressive strength compared to their initial values are plotted in
Figure 16. The analytical expressions of the compressive strength attenuation model for mortars and brick units are given in Equations (7) to (10).
Brick unit:
where
is the compressive strength of the mortar prism and the brick subjected to
n acid rain corrosion cycles.
is the compressive strengths of un-corrosion mortar prism and brick.
Through the comparison and statistical analysis of test data, it can be seen that the shear strength and compressive strength of masonry gradually decreased with the increasing number of acid rain corrosion cycles. The variations of the normalized shear strength and compressive strength compared to their initial values are plotted in
Figure 17 and
Figure 18. The evolution appeared to be quadratic with the number of acid rain corrosion cycles. Therefore, the shear strength attenuation model (Equation (11)) and compressive strength attenuation model (Equation (12)) of brick masonry considering the effect of acid rain corrosion cycles were proposed.
where,
is the shear strength of masonry subjected to
n acid rain corrosion cycles,
is the shear strength of the un-corrosion masonry,
is the compressive strength of masonry subjected to
n acid rain corrosion cycles, and
is the compressive strength of un-corrosion masonry.
5. Damage Constitutive Relationship Model
(1) The initial state of a specimen after maintenance is regarded as the first damage state, and the damage state after acid rain corrosion is regarded as the second damage state. Based on the strain equivalence principle, the following relationship can be obtained.
where
and
are the effective stresses in the initial damage state and, after
n acid rain corrosion cycles, respectively,
is the cross-sectional area in the initial damage state and, after
n acid rain corrosion cycles, respectively,
and
are the elastic moduli in the initial damage state and, after
n acid rain corrosion cycles, respectively, and
is the damage variable after
n acid rain corrosion cycles.
Based on Equations (13) to (15), the relationship between the elastic modulus of the initial damage and the acid rain corrosion damage can be illustrated by Equation (16), and the acid rain corrosion damage constitutive relationship can be illustrated by Equation (17).
(2) According to the variation law of the elastic modulus for brick masonry after acid rain corrosion cycles, the damage evolution equation with the number of acid rain corrosion cycles was established. Similar to the damage evolution of concrete, the following assumptions were made before giving the damage evolution equation: (1) The initial damage value of the masonry was considered to be zero before acid rain corrosion. (2) The masonry corrosion damage was only a function of the number of corrosion cycles, which ignores the influence of other factors. (3) As the number of corrosion cycles increased, the damage value grew gradually and the damage was positive.
According to the basic theory of macroscopic phenomenological damage mechanics, the masonry corrosion damage variable
is defined as follows.
(3) During the uniaxial compression of masonry, macroscopic compressive strain is generated under the action of external compressive stress. According to the equilibrium condition of the pressure direction of the macroscopic unit, the following relationship can be obtained.
where
is a mesoscopic damage variable caused by external pressure.
The state after acid rain corrosion is regarded as the first damage state, and the total damage state caused by the axial pressure after acid rain corrosion cycle is regarded as the second damage state. Again, based on the principle of equivalent strain, the constitutive relationship of the axial compression under an acid rain corrosion cycle is deduced as follows.
where
,
is the total damage of brick masonry under the action of acid rain corrosion and axial compression. The damage caused by an acid rain corrosion cycle as well as the damage caused by axial compression show clear nonlinear characteristics.
(4) A masonry structure is composed of mortar, brick, and the interface. Additionally, the material damage strength for brick masonry obeys the Weibull Distribution from a mesoscopic perspective, which has been proven in Reference [
37]. Therefore, the compression damage variable
D obeys the Weibull statistical distribution, and it can be described by Equation (21).
where
and
represent the scale parameter and the shape parameter, respectively.
The mesoscopic statistical damage model is used to describe the damage constitutive of brick masonry as follows.
Deriving Equation (22) yields the following equation.
From the basic characteristics of the uniaxial compressive stress-strain curve of brick masonry, the peak strain
corresponding to the peak stress
can be obtained by Equation (22).
Taking the natural logarithm twice for Equation (24), the following relationship can be obtained.
The slope of the peak point for the stress-strain curve is zero and the equation
has a unique non-zero solution, which indicates that there is only one peak on the curve and there is a maximum point. Thus, the following equation can be obtained by Equation (23).
Taking the natural logarithm of both sides, it can be determined that
For the simultaneous Equations (25) and (27), the expressions of the shape parameters are as follows.
The expression of the scale parameter can be obtained from Equation (26).
Lastly, the masonry damage model can be obtained as follows.
(5) Based on Equations (18) and (30), the equation of the total damage evolution of brick masonry under uniaxial compression after acid rain corrosion is as follows.
Therefore, the damage constitutive relationship considering an acid rain corrosion cycle can be expressed as follows.
(6)
Figure 19 illustrates the comparison between the deduced damage constitutive model and the experimental data of brick masonry under different acid rain corrosion cycles. As
Figure 19 shows, it was indicated that the uniaxial compression damage constitutive model of brick masonry could objectively reflect the variation of the uniaxial compression performance of brick masonry under different acid rain corrosion cycles.