Behavior of Salt Transport in Concrete Structures Under Temperature and Moisture Gradients

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Concrete is a widely applied material around the world in structural projects. Since the 19^th century, when the first iron-reinforced concrete structure was used in the suburbs of Paris, its features, such as high strength, hardness, durability, and moldability, provided extensive application [1].

The useful life of concrete structures is directly related to environmental conditions. During this period, mechanical stresses [2], thermal stress caused by the hydration process [3], high temperatures due to fire [4], climatic changes [5], and chemical attacks [6] can deteriorate the concrete and its steel reinforcement, which is used for added strength, particularly for tensile stresses, which is defined as the maximum mechanical pulling or stretching force by area unit that a material can withstand before failure. Thus, understanding the deterioration mechanisms of reinforced concrete is necessary because it is used in most construction projects.

The integrity of concrete is significantly influenced when subjected to chemical phenomena such as carbonation and the infiltration of sulfate and chloride ions, as emphasized by the presence of sulfate or chloride salts. Sulfate predominantly impacts the hydration reaction mechanism and the formation of its resultant products, whereas chloride salts primarily influence the corrosion processes within reinforced concrete [7]. Salt transport in concrete is a complex phenomenon influenced by pore structure, moisture content, and environmental conditions. It occurs through diffusion and capillary suction, but diffusion is the primary mechanism for chloride ion penetration, driven by concentration gradients [8–10]. The penetration of salts into concrete can lead to deterioration mechanisms such as chloride-induced corrosion and sulfate attack [11, 12]. Various strategies have been proposed to mitigate salt transport in concrete, including using corrosion-inhibiting admixtures [13], surface coatings, and sealants. Proper concrete mix design and construction practices are crucial for minimizing salt ingress [14]. Computational models and simulation techniques are employed to predict salt transport in concrete and assess the effectiveness of mitigation measures, considering factors such as pore structure, material properties, and environmental conditions [15].

The chloride ion is formed when the element chlorine picks up one electron to form an anion Cl^– or when a compound such as hydrogen chloride is dissolved in water. The primary sources of chloride ions are the concrete mix components and the surrounding environment, such as sea salt spray and direct seawater wetting [16]. The oxide resulting from the corrosion takes up the volume of the steel, which causes cracks and fissures, making it more susceptible to other agents.

Some works can be found in the literature that describes models for analyzing salt transport within concrete. Yang and Knight [17] determined the critical chloride level that causes reinforcing and prestressing steel depassivation in concrete mixes under various exposure conditions. They observed how the environment influences corrosion initiation and propagation. For indoor exposure without moisture, the corrosion stopped after 5–6 months, while the corrosion did not stop with moisture. Tu et al. [18] proposed a multiscale modeling to analyze the diffusion of chloride ions within concrete, encompassing the interfacial transition zone (ITZ). An innovative two-phase integrated model comprising a core component and a compensatory element was proposed. These phases were linked through an overlapped region known as the interfacial transition layer. The finite element (FE) model was enriched by incorporating nodes and elements of the ITZ, which are constructed by extending the outlines of aggregates generated randomly. Němeček et al. [19] explored a diffusion–convection problem applied to chloride migration in reinforced concrete using a model based on the Nernst–Planck equation and Gauss’s law of electrostatics. They used a three-stage approach to demonstrate an example of a reinforced concrete beam. Their work showed the effective removal of chloride ions from concrete using electrochemical chloride extraction (ECE).

In addition to salt diffusion, some studies also analyzed the influences of the region where the reinforced concrete structure was exposed to the environment. Meira et al. [20] developed a model representing marine aerosol behavior in marine atmosphere zones. The main variables considered were the distance from the sea and wind speed. This model was verified with published data, and results showed consistency for zones close to the shoreline. Zuquan et al. [21] also studied the chloride ion transport and binding capacity of different concrete samples in the marine atmosphere, splash, tidal, and submerged zones. They observed that chloride ion content in separate concrete samples exposed to splash and atmosphere regions was lower than in the other zones. However, when the whole concrete sample was exposed to all the zones, the atmosphere and splash regions showed the highest chloride concentrations. This phenomenon was explained by the capillarity absorption that occurs from the submerged zone to the others induced by the difference in moisture. Medeiros et al. [22] analyzed the chloride-ion contents from pillars of a reinforced concrete structure in a marine environment and showed the effects of the height and the positioning of the pillars around the coastline; furthermore, they also verified the strong effect of the wetting and drying cycles on the chloride ion content. The results showed that the higher the concrete is, the less chloride the pillar will have; the same can be said about distance. However, tests about the orientation of the structure of the sea showed no influence on the content. They also conclude that chloride concentrations were about 3–8 times higher in cases where the pillar was exposed in a zone where wetting and drying cycles exist due to mechanisms such as capillary absorption or diffusion. These phenomena will be explored in this work. Sun et al. [23] developed a prediction model for chloride transport in unsaturated concrete. The moisture transport model considered the diffusion of water and vapor and the seepage of liquid water under drying-wetting conditions. To validate the model, they developed a device that simulates a marine environment’s tidal and splash zones. The results demonstrated that chloride transport depends mainly on diffusion; furthermore, the wetting and drying cycles can increase the chloride content, accelerating this process. Like Medeiros et al. [22], this work exposed that the height where the concrete is located influences the content of the salt.

Few studies have considered the effects of temperature on salt transport. Derluyn et al. [16] and Poupeleer [24] presented a computational model coupling heat, moisture, salt ion transport, crystallization, deformation, and damage in porous materials. They concluded that the effective stress caused by salt crystallization depends on the crystallization pressure and the amount of salt crystals in the porous material. Water–cement ratio, time, bonding effect, temperature, relative humidity, and concrete deterioration are the parameters considered by Jin et al. [25] to predict a long-term migration for chloride transport in concrete. Using an empirical model, they noted that temperature and humidity can highly modify chloride diffusion; beyond that, the diffusion is enhanced with the rise of the water–cement ratio.

Temperature plays a critical role in salt transport mechanisms within concrete, influencing the physical properties and the chemical processes. The diffusion coefficient for chloride ions typically increases with temperature. Higher temperatures enhance the kinetic energy of ions, leading to more rapid movement through the concrete matrix. High temperatures can also lead to increased evaporation of surface moisture, potentially concentrating salts within the pore structure. On the other hand, in colder conditions, the movement of ions slows down, but salt can still migrate through capillary action if moisture is present. These effects can increase the corrosion rate of reinforcing steel due to enhanced chloride penetration and the increased activity of corrosion processes.

To consider the temperature effects on salt transport within concrete pores, in most of the numerical works found in the literature, the solution of the governing equations is uncoupled, which may require a substantial computational effort. Furthermore, adding the energy conservation equation to analyze the effects of temperature in chloride transport can generate instabilities in the solution of the equations, depending on the numerical method used. Therefore, this work presents a one-dimensional (1D) mathematical model to analyze the coupled transport of heat, moisture, and salt in concrete structures. The governing equations are solved using the finite volume method [26], and a fully implicit scheme is adopted for the time derivatives. At each iteration level, the multi-tridiagonal matrix algorithm (MTDMA) [27] simultaneously solves the three driving potentials, avoiding numerical divergence caused by the evaluation of coupled terms from previous iteration values.

2. Mathematical Model

According to dos Santos and Mendes [28], the transport of water in the porous media can be divided into two fluxes (liquid and vapor): $$\begin{array}{}\text{(1)}& j=j_l+j_v\end{array}$$where $j$ is the total water mass flux (kilograms per square meter per second), and the contributions of the liquid and vapor phases are $j_l$ and $j_v$, respectively.

The liquid mass flux ($j_l$) occurs by the gravity effect and by the transport of the condensed phase through capillarity, described by Darcy’s equation, adapted for unsaturated media. $$\begin{array}{}\text{(2)}& j_l=K\nabla P_{\text{suc}}-{\rho }_{l}g\end{array}$$where $K$ is the hydraulic conductivity (seconds), $P_{\text{suc}}$ is the suction pressure (Pascal), ${\rho }_l$ is the liquid density (kilograms per cubic meter), and $g$ is the gravity acceleration (meter per second squared).

The suction pressure gradient can be described as a function of temperature T (Kelvin) and vapor pressure P_v (Pascal) gradients as follows: $$\begin{array}{}\text{(3)}& \nabla P_{\text{suc}}=\frac{\partial P_{\text{suc}}}{\partial T}\nabla T+\frac{\partial P_{\text{suc}}}{\partial P_v}\nabla P_v\end{array}$$where $$\begin{array}{}\text{(4)}& \frac{\partial P_{\text{suc}}}{\partial T}=-{\rho }_l{R}_v\ln \varphi +\frac{T}{\varphi }\frac{\partial \varphi }{\partial T}\text{(5)}& \frac{\partial P_{\text{suc}}}{\partial P_v}=-\frac{{\rho }_l{R}_{v}T}{P_v}\end{array}$$and Equations (4) and (5) were derived from Kelvin’s law. $$\begin{array}{}\text{(6)}& \ln \varphi =-\frac{P_{\text{suc}}}{{\rho }_l{R}_{v}T}\end{array}$$where $R_v$ is the gas constant for water vapor (Joules per Kelvin per kilogram) and $\varphi$ is the relative humidity.

In the case of vapor mass flux ($j_v$), it occurs in a diffusive way as follows: $$\begin{array}{}\text{(7)}& j_v=-{\delta }_v\nabla P_v\end{array}$$where ${\delta }_v$ is the diffusive vapor permeability (seconds).

Thus, in the present model (PM), the moisture conservation can be described as follows: $$\begin{array}{}\text{(8)}& \frac{\partial w}{\partial t}=-\nabla ·j\end{array}$$where $w$ is the mass moisture content (kilogram per cubic meter). The robustness of the solution method (MTDMA) is increased considering that the transient term is defined as a function of temperature and partial vapor pressure: $$\begin{array}{}\text{(9)}& \frac{\partial w}{\partial t}=\frac{\partial w}{\partial \varphi }\frac{\partial \varphi }{\partial T}\frac{\partial T}{\partial t}+\frac{\partial w}{\partial \varphi }\frac{\partial \varphi }{\partial P_v}\frac{\partial P_v}{\partial t}=\nabla ·-\frac{\partial P_{\text{suc}}}{\partial T}\nabla T-\frac{\partial {\text{P}}_{\text{suc}}}{\partial P_v}-\frac{{\delta }_v}{K}\nabla P_v+{\rho }_{l}gK\end{array}$$where the derivatives $$\begin{array}{}\text{(10)}& \frac{\partial \varphi }{\partial T}=-\frac{P_v}{P_{\text{sat}}^2}\frac{\partial P_{\text{sat}}}{\partial T}\text{(11)}& \frac{\partial \varphi }{\partial P_v}=\frac{1}{P_{\text{sat}}}\end{array}$$are obtained from the relative humidity definition: $$\begin{array}{}\text{(12)}& \varphi =\frac{P_v}{P_{\text{sat}}}\end{array}$$where $P_{\text{sat}}=P_{\text{sat}}T$ is the saturation pressure (Pascal).

The heat flux $q$ can be attributed to the effects of conduction and convection: $$\begin{array}{}\text{(13)}& q=q_{\text{cond}}+q_{\text{conv}}\end{array}$$where $$\begin{array}{}\text{(14)}& q_{\text{cond}}=-\lambda \nabla T\text{(15)}& q_{\text{conv}}=j_l{c}_{pl}+j_v{c}_{pv}T\end{array}$$where $\lambda$ is the thermal conductivity (Watts per meter-Kelvin) and the specific heat at a constant pressure (Joule per Kelvin per kilogram⁠) of liquid and vapor are $c_{pl}$ and $c_{pv}$, respectively.

The energy balance is described by the divergent heat flux plus a source term due to the phase transition as follows: $$\begin{array}{}\text{(16)}& c_m{\rho }_0\frac{\partial T}{\partial t}=-\nabla ·q+S\text{(17)}& c_m=c_0+c_l\frac{w}{{\rho }_0}\end{array}$$where $c_0$ and ${\rho }_0$ are the specific heat capacity (Joule per Kelvin per kilogram) and density (kilograms per cubic meter) of the dry material, and $c_l$ is the specific heat capacity of liquid water (Joule per Kelvin per kilogram).

In the case of the term source, attributed to the phase change, it was quantified by the latent heat of transition through the vapor mass flux as follows: $$\begin{array}{}\text{(18)}& S=-L\nabla ·j_v\end{array}$$where $L=LT$ is the latent heat of vaporization (joules per kilogram).

Considering the reference temperature of 273 K, the energy conservation equation can be described as [28] $$\begin{array}{}\text{(19)}& c_m{\rho }_0\frac{\partial T}{\partial t}=\nabla ·-\frac{\partial P_{\text{suc}}}{\partial T}{c}_{pl}T-\frac{\lambda }{K}\nabla T-\frac{\partial P_{\text{suc}}}{\partial P_v}{c}_{pl}T-\frac{{\delta }_v{c}_{pv}T}{K}\nabla P_v+{\rho }_l{c}_{pl}Tg-\frac{L}{K}{J}_{v}K.\end{array}$$

Salt transport has been attributed to two phenomena, as described by van der Zanden et al. [29]. Convective transport occurs when water carries dissolved salt through pores. On the other hand, diffusion occurs due to the difference in salt concentration between the pores. The chloride binding significantly influences chloride penetration because only free chloride can diffuse into bulk concrete [30]. However, a cement with a lower binding capacity was adopted, and the bound porous effects were not considered in the PM. Therefore, 1D salt transport can be defined as follows: $$\begin{array}{}\text{(20)}& \frac{\partial C_s}{\partial t}=\frac{\partial }{\partial x}D\frac{\partial w}{\partial x}\frac{C_s}{w}+D_s\frac{\partial C_s}{\partial x}\end{array}$$where $C_s$ is the salt concentration (kilogram per cubic meter), $D$ is the water diffusion coefficient in concrete (square meter per second), and $D_s$ is the salt dispersion coefficient in concrete (square meter per second), given by $$\begin{array}{}\text{(21)}& D_s=\frac{D_m}{\tau }+\frac{1}{2}{\frac{D}{w}\frac{\partial w}{\partial x}}^2\frac{r^2}{D_m}\end{array}$$where $D_m$ is the diffusion coefficient of salt in water (square meter per second), $\tau$ is the media tortuosity, and $r$ is the pore radius (meters).

The three governing equations were discretized using the finite volume method [26]. The well-known Thomas algorithm or TDMA (tridiagonal matrix algorithm) could be used to solve the tridiagonal system of linear equations. However, a more robust algorithm may be necessary for strongly coupled equations of heat transfer problems to achieve numerical stability. In this case, the MTDMA provides the three potentials simultaneously at a given time step, avoiding numerical divergence caused by the evaluation of coupled terms from previous iteration values [27]. Therefore, for the PM represented by three dependent variables, the discretization of the differential equations leads to the following system of algebraic equations: $$\begin{array}{}\text{(22)}& A_i·x_i=B_i·x_{i+1}+C_i·x_{i-1}+E_i\end{array}$$where $x$ is a vector containing three dependent variables ($T$, $P_v$, and $C_s$), described as $$\begin{array}{}\text{(23)}& x_i={T{P}_v{C}_s}^T.\end{array}$$

Coefficients $A$, $B$, and $C$ are $3\times 3$ matrices in which each line corresponds to one dependent variable. The elements not belonging to the main diagonal are the coupled terms for each conservation equation. $E$ is a 3-element vector.

As MTDMA is similar to the TDMA, it is necessary to replace Equation (22) with relationships of the following form: $$\begin{array}{}\text{(24)}& x_i=P_i·x_{i+1}+q_i\end{array}$$where $P$ is now a $3\times 3$ matrix and $q$ is a 3-element vector.

In the same way, vector $x_{i-1}$ can be expressed in terms of $x_i$: $$\begin{array}{}\text{(25)}& x_{i-1}=P_{i-1}·x_i+q_{i-1}.\end{array}$$

Substitution of Equation (25) into Equation (22) gives $$\begin{array}{}\text{(26)}& A_i·x_i=B_i·x_{i+1}+C_i·P_{i-1}·x_i+q_{i-1}+E_i\end{array}$$or rearranging $$\begin{array}{}\text{(27)}& A_i-C_i·P_{i-1}·x_i=B_i·x_{i+1}+C_i·q_{i-1}+E_i.\end{array}$$

Writing Equation (27) in an explicit way for $x_i$: $$\begin{array}{}\text{(28)}& x_i={A_i-C_i·P_{i-1}}^{-1}·B_i·x_{i+1}+{A_i-C_i·P_{i-1}}^{-1}{C}_i·q_{i-1}+E_i.\end{array}$$

For consistency of the formulas, Equations (28) and (24) are then compared, leading to the following recursive expressions: $$\begin{array}{}\text{(29)}& P_i={A_i-C_i·P_{i-1}}^{-1}·B_i\text{(30)}& q_i={A_i-C_i·P_{i-1}}^{-1}{C}_i·q_{i-1}+E_i.\end{array}$$

Once those matrix coefficients are calculated, the back substitution provides quite mechanically all elements of vector x_i.

The algorithm improves the diagonal dominance of the systems of equations by increasing the A_i coefficients and decreasing the $E_i$ source terms simultaneously. Therefore, the transient terms of Equation (9) were also written to increase diagonal dominance.

3. Results and Discussion

The PM has been verified through the model proposed by van der Zanden et al. [29] model (ZM), which has not considered the heat transport effects on salt migration. A concrete sample length of 10 cm was used in the comparison, and its hygrothermal properties were obtained from Künzel et al. [31]. The concrete employed in all simulations (comparison and tests) was considered with a water–cement ratio of 0.6, a bulk density of 2300 kg/m³, a specific heat capacity of approximately 0.85 kJ/(kg·K), a thermal conductivity of the dry material of approximately 1.6 W/(m·K), a porosity of 13.5%, and a capillary saturation of 155 kg/m³. The uniform mesh was divided into 20 finite volumes, and a time step of 10,800 s was applied in the simulations. The internal surface was considered impermeable, while the external surface was exposed to environmental conditions. An initial condition was adopted as a mass moisture content (mass water per concrete volume) of 80 kg/m³. In simulations, the mass moisture content varied according to the season. $$\begin{array}{}\text{(31)}& w=70\sin 1.9924\times {10}^{-7}t+80\end{array}$$where $t$ represents the time in seconds.

The salt in the saline mist is composed of chloride ions (Cl^–), which have a diffusion coefficient in the water of $1.26\times {10}^{–9}$ m²/s at 20°C.

In this comparison, no initial amount of salt was considered in the sample, but a salt mist with a chloride concentration in the pore water of 19 kg/m³ was imposed on the external surface. The ions enter the pores of the concrete and remain in the sample; thereby, no salt flows out into the environment. Figure 1 shows the chloride concentration (mass per concrete volume) throughout the sample during 1 year.

[figure(s) omitted; refer to PDF]

Figure 1 shows a homogeneous distribution of chloride in 3 months. After this period, a sample dries, and the surface concentration increases in 6 and 9 months (salt water enters the sample, but only sweet water leaves). Between 9 and 12 months, the sample absorbs water and salt, increasing the chloride concentration again. According to the comparison between the PM and ZM [29], a good similarity between the results is observed, presenting the root mean square (RMS) deviation values of 2.94% for 3 months (minimal RMS) and 6.63% for 12 months (maximal RMS). Minor differences can be attributed to the numerical precision and time step used in the two works. A more refined mesh did not cause significant differences in the results presented.

3.1. Effects of Temperature Gradients on Moisture and Salt Transport

Over 1 year, simulations were carried out considering a concrete sample with a length of 20 cm, and its hygrothermal properties were obtained from Künzel et al. [31]. A uniform mesh with 20 volumes and a time step of 30 s. The right surface was adopted as internal, while the left was considered exposed to the environment and affected by a saline mist composed of chloride ions (Cl^–). Hence, nine tests were performed: Tests 1–3 in isothermal conditions; Tests 4–6 in nonisothermal conditions; Test 7 to compare different salt diffusivities; and Tests 8 and 9 to verify the crystallization possibility. The boundary conditions for all the tests are of the first type (Dirichlet), that is, specified values. These tests and their boundary conditions are described in the sequence.

Firstly, the influence of temperature on the diffusion coefficient was verified. This effect was proposed by Dousti et al. [32], as shown in the following equation: $$\begin{array}{}\text{(32)}& D_m=D_{m0}^{E_a/R1/T_0-1/T}\end{array}$$where $D_m$ and $D_{m0}$ are the diffusion coefficients (square meter per second) at $T$ and $T_0$ (Kelvin), respectively, $E_a$ is the activation energy of the substance (kilojoules per kilomole), and $R$ is the ideal gas constant, equal to 8.314 kJ/(kmol·K).

Tests 1, 2, and 3 were performed with uniform temperatures throughout the sample. The inner surface was considered impermeable. As the initial condition, relative humidity and concentration of saline mist of 88% (referring to $w=80$ kg/m³) and 1.52 kg/m³ (both on the external surface, i.e., boundary condition), respectively, and no chlorides were adopted inside the sample for the three tests. Table 1 shows the tests’ temperatures.

Table 1

Conditions of the isothermal tests performed.

Test	Uniform temperature (K)
1	283
2	293
3	303

Figure 2 shows the results obtained for chloride concentration (mass per concrete volume) throughout the sample for Tests 1, 2, and 3 after 6 months.

[figure(s) omitted; refer to PDF]

As observed in Figure 2, a temperature of 283 K caused a higher salt concentration gradient between the two surfaces. On the contrary, the propagation occurred faster in Test 3 due to the higher diffusion coefficient.

Tests 4, 5, and 6 were performed under nonisothermal conditions and are presented in sequence. Both surfaces were considered impermeable to water with different temperatures. Relative humidity and concentration of saline mist of 88% and 1.52 kg/m³ (both on the external surface, i.e., boundary condition), respectively, and internal wall face temperature of 283 K were considered initial conditions. No chloride input or inside the sample was assumed. Table 2 shows the boundary conditions.

Table 2

Conditions of the nonisothermal tests performed.

Test	External wall face temperature (K)
4	293
5	298
6	303

Chloride concentration (mass per concrete volume) and mass moisture content (mass water per concrete volume) throughout the sample are shown in Figures 3 and 4, respectively, after 6 months.

[figure(s) omitted; refer to PDF]

Figure 3 indicated a higher chloride concentration gradient throughout the sample in Tests 6, 5, and 4, respectively, due to the higher difference in temperature between surfaces. Likewise, Figure 4 shows more significant drying on the left side in Test 6, causing the water in the sample to move to the internal surface, reducing the salt concentration, as seen in Figure 3. The same behavior was observed in Tests 4 and 5.

Afterward, Test 7 was carried out and involved different salts in sea salt mist, which can also damage the concrete. Table 3 describes the diffusion coefficients for sodium chloride, magnesium chloride, calcium sulfate, and magnesium sulfate (MgSO₄) at 298 K in water.

Table 3

Diffusion coefficients of salts [33].

Salt	Diffusion coefficient (m 2 /s)
NaCl	$$1.612\times {10}^{–9}$$
MgCl2	$$1.251\times {10}^{–9}$$
CaSO4	$$0.905\times {10}^{–9}$$
MgSO4	$$0.849\times {10}^{–9}$$

Test 7 was carried out at the following boundary conditions: a constant temperature of 298 K and 88% relative humidity, where a sample was subjected to a salt mist with a concentration of 1.52 kg/m³ for each salt for 6 months.

Figure 5 shows the effect of the diffusion coefficient of each salt through the sample. Sodium chloride (NaCl) reached the internal surface more easily due to its higher diffusion coefficient between the salts. On the other hand, MgSO₄, which has the lowest coefficient, takes longer to diffuse throughout the sample.

[figure(s) omitted; refer to PDF]

As NaCl and MgSO₄ are the most abundant in seawater, two more tests (8 and 9) were performed to verify the possibility of crystallization in both salts. This analysis used a sine function as the boundary condition for the mass moisture content. $$\begin{array}{}\text{(33)}& w=0.4\sin 1.9924\times {10}^{-7}t+0.5\end{array}$$

For the initial conditions of Tests 8 and 9, relative humidity of 60% and temperature of 293 K were adopted, in addition to not considering salt in the sample. The external and internal wall face temperatures (boundary conditions) were 308 and 298 K, respectively. Table 4 shows the concentrations of saline mist on the external face, and Figure 6 presents the test results of salt mass per pore water volume.

Table 4

Tests performed for different salts with temperature gradients.

Test	Salt	Concentration of saline mist (kg/m 3)
8	NaCl	19wext/1000
9	MgSO4	2.7wext/1000

[figure(s) omitted; refer to PDF]

Figure 6 shows the capacity of NaCl to crystallize. After a year of the simulation, the NaCl reached the solubility degree in almost the entire sample, unlike the MgSO₄ concentration. This fact occurred due to the higher diffusivity of NaCl concerning MgSO₄. Furthermore, the salts have different concentrations in the seawater, with the NaCl more present. Therefore, NaCl is more dangerous for the concrete structure, being able to cause countless problems, like fissures and cracks, or start the corrosion process in the reinforcement.

4. Conclusions

This work presented a numerical study about the influence of the coupled heat and moisture transport on the salt migration in concrete. From the results obtained, the main conclusion is that heat transport is essential in the modeling because minor temperature differences significantly impact moisture and salt transport. Notably, most of the works in the literature analyzed salt transport in concrete structures in an isothermal manner.

Considering the effects of temperature, the simulations showed that diffusion is faster in warmer places, with increased salt concentration in regions where water content is reduced. Salts can also generate different results, depending on their diffusion coefficient, which directly interferes with salt displacement inside the sample. Furthermore, comparing the crystallization potential of salts found in water sea, NaCl can cause more damage to concrete structures due to high concentration. This salt has a high potential to cumulate and reach the solubility degree, which could cause fissures and cracks in concrete and corrosion in the reinforcement structure. Thus, this work showed the importance of considering the energy conservation equation to analyze moisture and salt transport in concrete structures, providing relevant information to prevent their deterioration. Crystallization models can be incorporated in future works since the PM does not consider the influence of salt growth in the porous media.

Funding

This work was supported by the Brazilian Federal Agency for Support and Evaluation (CAPES) (Finance Code 001) and a Federal University of Technology–Paraná (UTFPR) grant.

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