Analysis of Expansion Stress Evolution of Concrete Erosion Products for Ocean Engineering

Abstract

With the deployment of China's “Maritime Power” strategy and the continuous development of ocean engineering, the safety and sustainability of concrete materials in ocean engineering need to be resolved urgently. In this paper, aiming at the concrete erosion caused by sulfate in marine environment, the evolution analysis of the expansion stress of the erosion products is carried out based on the principles of thermodynamics and crystallography. The results show that there is a liquid film between the ettringite and the pore wall during sulfate erosion in marine environment. The interfacial energy between reactants of different phases should not be neglected, and the liquid film thickness is negatively correlated with the expansion stress. The radial stress on concrete microstructure is composed of expansion stress, seawater pressure and interfacial energy between the concrete pore wall and the seawater. The trends of radial stresses in micro-voids and micro-cracks are basically similarly, both of which are negatively correlated with pore size and positively correlated with erosion time. In addition, the radial stresses in micro-cracks are generally greater than those in micro-voids. During the erosion process, the radial stress is positively correlated with the expansion extend of ettringite.

1 Introduction

Recently, with the rapid development of the ocean engineering, the safety and sustainability of concrete materials in marine environment attract more and more attention. In a complex and harsh marine environment, concrete materials will be corroded by various harmful ions such as sulfate ions, chloride ions and magnesium ions [1, 2]. Sulfate attack will generate harmful products (e.g., ettringite), which would result in serious deterioration of the concrete due to the expansion and cracking [3, 4]. Subsequently, it would have a significant negative impact on safety and economy of structures and materials in ocean engineering. Unfortunately, the current state-of-the-art research on expansion stress of sulfate erosion products in marine environment is far from adequate.

The problem of sulfate attack in concrete material involves complex reactions between sulfate ions and cement hydration products. Considering the different sources of sulfate ions, sulfate attack can be divided into external sulfate attack (ESA) and internal sulfate attack (ISA) [5]. The sulphate attack of concrete in marine environment mentioned in this paper is an ESA problem. The expansion caused by the sulfate attack is mainly attributed to the formation of ettringite, but the mechanism causing the expansion is still controversial [6]. Regarding the expansion of ettringite, there are two mainstream theories [7]: the crystal growth theory and the water swelling theory. Richards and Helmuth [8] suggested that with the start of the erosion, the surface of expanded particles C4A3S and C3A would be covered by ettringite. When the thickness of ettringite exceeds a certain range, it will push other particles away and cause expansion. Kalousek [9] suggested that the expansion of ettringite is due to the positive relative ratio of hydrate volume to anhydrous volume, which means that the increase in anhydrous volume will generate expansion stress acting on the pore walls. Mehta [10] proposed a mechanism hypothesis for the expansion caused by ettringite. There are two types of ettringite, one is a strip crystal with a size of 10 ~ 100 µm, which is formed when the hydroxide concentration is low and usually does not expand. The other is small rod-shaped crystals with a size of 1 ~ 2 µm, which is formed when the hydroxide concentration is higher, and the damage is often caused by this kind of ettringite [11]. Power [8] showed that the adsorbed water on the surface of ettringite may trigger surface tension, making the surface stretched while the rest is in a compressed state. Therefore, the reason for the expansion of ettringite can be attributed to the reduction of van der Waals force, and the shrinkage caused by the surface tension of ettringite is compensated by the volume expand.

This paper focused on the evolution of radial stresses in concrete during sulfate erosion. A microstructural model of concrete has been developed to consider the interfacial energy between the liquid film and the different phase reactants during the expansion of ettringite. Moreover, the time-varying equations between ettringite content and expansion stress in the microstructure of concrete were established based on thermodynamic and crystallographic principles.

2 Expansion Stress of Erosion Products in Marine Environment

2.1 Theoretical Model of Sulfate Attack

Seawater contains a large amount of sulfate ions, which will continuously be able to corrode the concrete materials. The sulfate attack of the concrete materials can be regarded as the effect of a mixed system with multi-phase coexistence in marine environment. Interfacial energy exists between different phases of reactants and needs to be considered during erosion, whether it is between the ettringite and the seawater or between the seawater and the pore walls. The sulfate erosion reaction is characterized by the following three features: Firstly, although the ettringite and the pore wall are not in direct contact (the gaps between the two are fully filled with seawater, i.e., the liquid film), the pore wall will still be subjected to the expansion stress from the ettringite. Secondly, the pressures on different reactants are not the same (no longer a standard atmosphere). Thirdly, the pore wall is subject to a combination of ettringite expansion stress, seawater pressure and interfacial energy (not just expansion stress).

In marine environment, the liquid film always exists between the ettringite and pore wall during the erosion process. It is assumed that the liquid film is elastic, and the thickness becomes smaller and smaller as the ettringite grows. Figure 1 shows the diagram of liquid film.

Fig. 1

The diagram of liquid film

The interfacial energy between the ettringite and the liquid film, between the liquid film and pore wall, and between the ettringite and pore wall are defined as $\gamma_{{{\text{CL}}}}$, $\gamma_{{{\text{WL}}}}$ and $\gamma_{{{\text{CW}}}}$, respectively. Correns suggested that the interface energies can satisfy the following relation when the ettringite exerts expansion stress on the pore wall [13]:

$$\Delta \gamma = \gamma_{{\rm{CW}}} - \gamma_{{\rm{CL}}} - \gamma_{{\rm{WL}}} > 0$$

(1)

When $\Delta \gamma > {0}$, ettringite will exert expansion stress on the pore wall. Conversely, when $\Delta \gamma < {0}$, ettringite could reduce the system energy by contacting the pore wall, meaning there is no crystallization pressure generated during the ettringite growth process.

The stress applied on the pore wall during the ettringite growth process is P_d, thickness of liquid film is $\delta$, the relationship between P_d and $\delta$ is [14]:

$$P_{{\text{d}}} = {\text{P}}_{0} \cdot e^{{ - \frac{\delta }{\lambda }}}$$

(2)

where P₀ and $\uplambda$ are constants, P₀ represents the maximum expansion stress of ettringite, $\uplambda$ is the proportional coefficient. There is a negative correlation between the expansion stress and the liquid film thickness. The smaller the thickness of the liquid film is, the greater the expansion stress will be. Therefore, the liquid film between ettringite and pore wall should not be neglected.

2.2 The Relation Between Interfacial Energy and Surface Curvature of Ettringite

The relation between multi-component chemical potential, the system entropy, volume, temperature, and the pressure can be obtained by Gibbs–Duhem equation [15]:

$$\sum\limits_{i = 1}^{N} {x_{i} } {\text{d}}\mu_{i} = V_{{\text{s}}} {\text{d}}P_{{\text{S}}} - S_{{\text{S}}} {\text{d}}T$$

(3)

where $\mu_{i}$ is the chemical potential of component i, x_i is the mass fraction of component i. The reaction system for sulfate attack of concrete in the ocean consists of ettringite in the solid phase and seawater in the liquid phase. The mass concentration of ettringite is c_e, according to Gibbs–Duhem equation [16]:

$$\left( {1 - c_{{\text{e}}} } \right) \cdot {\text{d}}\mu_{{\text{L}}} + c_{{\text{e}}} \cdot {\text{d}}\mu_{{\text{C}}} = V_{{\text{S}}} {\text{d}}P_{{\text{S}}} - S_{{\text{S}}} {\text{d}}T$$

(4)

where $\mu_{L}$ and $\mu_{C}$ are the chemical potentials of seawater and ettringite, respectively, and P_S is the pressure of seawater. The chemical potential is a function of temperature and pressure, so the chemical potential of ettringite can be expressed as, $\mu_{{\text{C}}} = \mu_{{\text{C}}} \left( {T,P_{{\text{C}}} } \right)$ and P_C is the pressure on the ettringite. According to the definition of Gibbs free energy and chemical potential, the differential of chemical potential of ettringite is expressed as:

$${\text{d}} \mu_{{\text{C}}}=V_{{\text{C}}} \cdot {\text{d}} P_{{\text{C}}}-S_{{\text{C}}} \cdot {\text{d}} T$$

(5)

since the seawater can be taken as a dilute solution, then the ions in seawater would obey Henry's law. The chemical potential of seawater is expressed as:

$$\mu_{{\text{L}}} = \mu_{{\text{L}}}^{\vartheta } \left( {T,P_{{\text{S}}} } \right) + R_{{\text{g}}} T\ln \left( {1 - c_{{\text{e}}} } \right)$$

(6)

where $\mu_{{\text{L}}}^{\vartheta } \left( {T,P_{{\text{S}}} } \right)$ represents the standard chemical potential of seawater under pressure P_S. Substituting the differential of the chemical potential of the ettringite and the seawater into Eq. (4), and assuming the reaction happens at a constant temperature, i.e., dT = 0.

$$\left( {1 - c_{{\text{e}}} } \right)\left( {V_{{\text{L}}} \cdot {\text{d}}P_{{\text{S}}} - R_{{\text{g}}} T \cdot \frac{1}{{1 - c_{{\text{e}}} }}{\text{d}}c_{{\text{e}}} } \right) + c_{{\text{e}}} \cdot V_{{\text{C}}} \cdot {\text{d}}P_{{\text{C}}} = V_{{\text{S}}} \cdot {\text{d}}P_{{\text{S}}}$$

(7)

where P_C and P_S are the pressures of ettringite and seawater, respectively. According to the Laplace equation [17]:

$$P_{{\text{C}}} = P_{{\text{S}}} + \gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}}$$

(8)

where $\gamma_{{{\text{CL}}}}$ is the interfacial energy between the ettringite and liquid film, and $\kappa_{{{\text{CL}}}}$ is the surface curvature of ettringite. The relation between the molar volume of seawater and the partial molar volume of the components can be expressed as [14]:

$$V_{{\text{S}}} = \left( {1 - c_{{\text{e}}} } \right)\overline{V}_{{\text{L}}} + c_{{\text{e}}} \cdot \overline{V}_{{\text{C}}}$$

(9)

substituting Eqs. (8) and (9) into Eq. (7), and that $\overline{V}_{\rm{L}} = V_{\rm{L}}$:

$$R_{{\text{g}}} T \cdot \frac{1}{{c_{{\text{e}}} }}{\text{d}}c_{{\text{e}}} = - \left( {\overline{V}_{{\text{C}}} - V_{{\text{C}}} } \right){\text{d}}P_{{\text{S}}} + V_{{\text{C}}} \cdot {\text{d}}\left( {\gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}} } \right)$$

(10)

The reaction is carried out under the condition of pressure change in this paper, i.e., PS ≠ P0. Integrating Eq. (10) and expressing the seawater pressure through Laplace equation, the relation between the surface curvature of ettringite and the interfacial energy can be obtained:

$$\gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}} = \frac{{R_{{\text{g}}} T}}{{V_{{\text{C}}} }} \cdot \ln \left( {\frac{{c_{{\text{e}}} }}{{c_{{{\text{e}}0}} }}} \right) + \left( {\frac{{\overline{V}_{{\text{C}}} - V_{{\text{C}}} }}{{V_{{\text{C}}} }}} \right) \cdot \gamma_{{{\text{LV}}}} \cdot \kappa_{{{\text{LV}}}}$$

(11)

2.3 Time-Varying Equation of Liquid Film Thickness

The seawater filled between the gap of the ettringite and the pore wall is defined as the liquid film. Assuming that the micro-voids is a shell with a certain thickness, and the ettringite is a solid sphere in the micro-voids. The micro-voids and ettringite are concentric spheres (as shown in Fig. 1). The ettringite expands only in the radial direction while it always maintains a spherical shape during the expansion, so the center of the sphere does not move. The time-varying equation of liquid film thickness can be expressed as:

$$\delta (t) = r_{{\text{p}}} - r_{{\text{ett }}} (t)$$

(12)

where r_p and r_ett(t) are the radius of the micro-voids and the ettringite. The radius of ettringite is related to the volume, which is related to the content of ettringite. Therefore, the relation between liquid film thickness and ettringite content can be established:

$$\frac{4}{3} \pi r_{{\text{ett}}}^3(t)=\frac{\Delta c_{{\text{e}}}(t) \cdot V_{{\text{P}}} \cdot M_{{\text{ett}}}}{\rho_{{\text{ett}}}}$$

(13)

where $\Delta c_{{\text{e}}}$ is the variation of ettringite content within a certain time interval, V_P is the volume of micro-voids, M_ett and $\rho_{{\rm{ett}}}$ represent the molar mass and density of ettringite, respectively. Substituting the ettringite radius obtained from Eq. (13) into Eq. (12), the time-varying equation of liquid film thickness can be obtained as:

$$\delta (t) = r_{{\text{p}}} - 0.0899r_{{\text{p}}} \cdot \sqrt[3]{{\Delta c_{{\text{e}}} (t)}}$$

(14)

2.4 Expansion Stress of Corrosion Products

3 Microstructure Model of Concrete.

Based on the evolution process of concrete micro-voids [18], a concrete microstructure model was established. The microstructure model consists of micro-voids and micro-cracks. Assuming that the micro-voids and the micro-cracks are spheres and cylinders, respectively. Besides, the size of micro-cracks is much smaller than micro-voids. The micro-voids and micro-cracks model are shown in Fig. 2.

Fig. 2

The diagram of micro-voids and micro-cracks model

With the diffusion of seawater, ettringite would be formed in both micro-voids and micro-cracks. It is assumed that the pieces of ettringite formed in micro-voids and micro-cracks are spheres and cylinders, respectively.

4 Expansion Stress Equation of Micro-Voids

By introducing the time variable, the time-varying equation of expansion stress and ettringite content is established. Figure 3 shows the diagram of micro-voids (r_p and r_e represent the radii of micro-voids and micro-cracks, respectively).

Fig. 3

The diagram of micro-voids [14]

Take the point E₁ at the entrance of the micro-voids and any point S₁ inside micro-voids for example (as shown in Fig. 3). The curvature at the two points can be expressed as [14]:

$$\kappa_{{{\text{CL}}}}^{{S_{1} }} (t) = \frac{2}{{r_{{\text{p}}} - \delta (t)}}$$

(15)

$$\kappa_{{{\text{CL}}}}^{{E_{1} }} (t) = \frac{2}{{r_{{\text{e}}} - \delta (t)}}$$

(16)

Since the size of micro-voids is much smaller than that of micro-cracks, the curvature at point S₁ is approximately to zero. The pressures at E₁ and S₁ are as follows:

$$P_{{\text{C}}} (t) = P_{{\text{S}}} + \gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}}^{{E_{1} }} (t)$$

(17)

$$P_{{\text{C}}} (t) = P_{{\text{S}}} + \gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}}^{{S_{1} }} (t) + P_{{\text{d}}} (t) \approx P_{{\text{S}}} + P_{{\text{d}}} (t)$$

(18)

where P_d is the expansion stress produced by ettringite, and PS is the pressure of the solution. From Eqs. (17) and (18), it can be seen that the surface of ettringite inside micro-voids (S₁) is affected by seawater pressure, interfacial energy of ettringite and liquid film, and the expansion stress of ettringite. At the entrance of micro-voids (E₁), ettringite grows freely without any expansion stress along the direction of the micro-cracks. According to the crystallographic theory, if the crystal is stable, the pressure on the surface of the crystal must be equal everywhere, otherwise the crystal will dissolve [14]. Therefore, the pressures at point S₁ and point E₁ are equal:

$$P_{{\text{d}}} (t) = \gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}}^{{E_{1} }} (t)$$

(19)

Equation (19) shows that the expansion stress generated by ettringite in the micro-voids has the same effect of the interfacial energy at the entrance of the micro-voids. According to the relationship between the surface curvature and interfacial energy of ettringite are as follows:

$$P_{{\text{d}}} (t) = \frac{{R_{{\text{g}}} T}}{{V_{{\text{C}}} }} \cdot \ln \left[ {\frac{{c_{{\text{e}}} (t)}}{{c_{{{\text{e}}0}} }}} \right] + \left( {\frac{{\overline{V}_{{\text{C}}} - V_{{\text{C}}} }}{{V_{{\text{C}}} }}} \right) \cdot \gamma_{{{\text{LV}}}} \cdot \kappa_{{{\text{LV}}}}$$

(20)

Equation (20) is the time-varying equation between the expansion stress and the content of ettringite in the micro-voids.

5 Expansion Stress Equation of Micro-Cracks.

The diagram of micro-cracks in concrete is shown in Fig. 4.

Fig. 4

The diagram of micro-cracks [14]

Similarly, point E₂ at the entrance of the micro-cracks and any point S₂ in the micro-cracks are taken for analysis. In micro-cracks, the curvatures of these two points are expressed as follows [14]:

$$\kappa_{{{\text{CL}}}}^{{E_{2} }} (t) = \frac{2}{{r_{{\text{e}}} - \delta (t)}}$$

(21)

$$\kappa_{{{\text{CL}}}}^{{S_{2} }} (t) = \frac{1}{{r_{{\text{e}}} - \delta (t)}}$$

(22)

The pressures at S₂ and E₂ are shown in Eqs. (23)-(24):

$$P_{{\text{C}}} (t) = P_{{\text{S}}} + \gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}}^{{E_{2} }} (t)$$

(23)

$$P_{{\text{C}}} (t) = P_{{\text{S}}} + \gamma_{{{\text{CL}}}} \cdot \kappa_{{{\text{CL}}}}^{{S_{2} }} (t) + P_{{\text{d}}} (t)$$

(24)

According to the equal pressure at the S2 and E2, the relation between the surface curvature of ettringite and the interfacial energy is expressed as:

$$P_{{\text{d}}} (t) = \frac{1}{2} \cdot \frac{{R_{{\text{g}}} T}}{{V_{{\text{C}}} }}\ln \left[ {\frac{{c_{{\text{e}}} (t)}}{{c_{{{\text{e}}0}} }}} \right] + \left( {\frac{{\overline{V}_{{\text{C}}} - V_{{\text{C}}} }}{{V_{{\text{C}}} }}} \right) \cdot \gamma_{{{\text{LV}}}} \cdot \kappa_{{{\text{LV}}}}$$

(25)

Equation (25) is the time-varying equation between the expansion stress and the content of ettringite in the micro-cracks.

6 Microstructural Stress of Concrete in Marine Environment

Considering the effect of the liquid film, the pore wall is affected by the expansion stress of the ettringite, seawater pressure and the interfacial energy between liquid film and pore wall. The radial stress on the pore wall is [14, 19]:

$$\sigma_{r} (t) = - P_{{\text{S}}} - P_{{\text{d}}} (t) + \gamma_{{{\text{wL}}}} \cdot \kappa_{{{\text{WL}}}}$$

(26)

where P_S is seawater pressure, P_d(t) is the expansion stress caused by ettringite, $\gamma_{{{\text{WL}}}}$ is the interfacial energy between liquid film and pore wall, $\kappa_{{{\text{WL}}}}$ represents the curvature of pore wall. $\kappa_{{{\text{WL}}}} = {2 \mathord{\left/ {\vphantom {2 {r_{\rm{p}} }}} \right. \kern-0pt} {r_{\rm{p}} }}$ for micro-voids, and $\kappa_{{{\text{WL}}}} = {{1} \mathord{\left/ {\vphantom {{1} {r_{\rm{e}} }}} \right. \kern-0pt} {r_{\rm{e}} }}$ for micro-cracks. In addition to radial stress, the pore wall is also subjected to tangential stress, which can be expressed as follows [19]:

$$\sigma_{\theta } (t) = \gamma_{{{\text{LV}}}} \cdot \kappa_{{{\text{LV}}}} + \gamma_{{{\text{CL}}}} \left[ {\kappa_{{{\text{CL}}}}^{E} (t) - \kappa_{{{\text{CL}}}}^{S} (t)} \right] - \gamma_{{{\text{WL}}}} \cdot \kappa_{{{\text{WL}}}}$$

(27)

When the porosity of concrete is not high, it can be approximated that $\sigma_{\rm{\theta }} \approx - \sigma_{{\text{r}}}$. For most concrete materials with good performance, whose porosities are generally not high, so the radial stress and the tangential stress are equal, and only the radial stresses are analyzed.

6.1 Stress Analysis of Pore Wall in Micro-Voids

Substitute the time-varying equation of ettringite expansion stress and the Laplace equation of seawater pressure into Eq. (26):

$$\sigma_{{\text{r}}} (t) = \frac{0.042}{{r_{{\text{p}}} }} - 10^{5} - 3419060.828 \cdot \ln \frac{{c_{{\text{c}}} (t)}}{6.06} - \frac{0.1038}{{r_{{\text{p}}} - 0.0899r_{{\text{p}}} \cdot \sqrt[3]{{\Delta c_{{\text{e}}} (t)}}}}$$

(28)

Equation (28) is the time-varying equation between the radial stress and the content of ettringite in micro-voids, and the unit is Pa. The radial stress of the pore wall in the micro-voids depends on the aperture of the micro-voids and the content of ettringite. Figure 5 shows the variation surface of the radial stress as a function of aperture and erosion time.

Fig. 5

Variation surface of radial stress with aperture and erosion time for micro-voids

In Fig. 5, for the same erosion time, the radial stress decreases with the increase of the aperture. While the erosion time lasts, the radial stress will increase accordingly.

In Fig. 6a, the radial stress varies with aperture for different erosion times cases in a relatively consistent trend, which shows that the radial stress decreases with the increase of aperture. When aperture is larger than 100 nm, the radial stress tends to be stable. For the same aperture, the radial stresses with shorter erosion time are larger. After 20 weeks of erosion, the expansion stress tends to be stable, which probably due to the less ettringite content. For smaller apertures, the radial stresses are larger, with the increasement of the aperture, the radial stress increasing velocity changes mildly.

Fig. 6

The curve of radial stress with aperture and erosion time in micro-voids

6.2 Stress Analysis of Pore Wall in Micro-Cracks

Substituting the time-varying equation of expansion stress in micro-cracks into Eq. (26):

$$\sigma_{{\text{r}}} (t) = \frac{0.021}{{r_{{\text{e}}} }} - 10^{5} - 1709530.414 \cdot \ln \frac{{c_{{\text{e}}} (t)}}{6.06} - \frac{0.0819}{{r_{{\text{e}}} - 0.0899r_{{\text{e}}} \cdot \sqrt[3]{{\Delta c_{{\text{e}}} (t)}}}}$$

(29)

Equation (29) is the time-varying equation of the radial stress of micro-cracks and the content of ettringite. The radial stresses of the micro-cracks are affected by the content of ettringite and the aperture of micro-cracks. The variation of radial stresses in micro-cracks with the aperture and the content of ettringite is shown in Fig. 7.

Fig. 7

Variation surface of radial stress with aperture and erosion time for micro-cracks

It can be seen from Fig. 7 that the trends of the radial stress of micro-cracks and micro-voids are very similar. At the same moment, as the aperture increases, the radial stress on the pore wall also decreases. For smaller cracks, radial stresses tend to be higher. As erosion time increases, the radial stress on pore wall will increases. Overall, the trends of radial stresses in micro-voids and micro-cracks are similar, but the radial stress in micro-cracks are greater than those in micro-voids.

In Fig. 8a, for the same micro-cracks, the increase of erosion time will cause a mild increasement of the radial stress. For the same erosion time, the radial stress on small cracks is much greater, and the radial stress tends to be stable while the aperture is greater than 20 nm. The radial stress is less sensitive to the extension of erosion time. Compared with the micro-void cases, radial stress in micro-cracks shows a more moderate trend. The maximum radial stresses in micro-cracks are almost twice those of micro-voids.

Fig. 8

The curve of radial stress with aperture and erosion time in micro-cracks

7 Conclusions

This paper carried out an analysis of the influences of ettringite content on expansion stress in concrete materials in ocean engineering based on thermodynamics and crystallographic theory. By establishing the concrete microstructure model, the time-varying equations of the expansion stress related to the content of ettringite in the micro-voids and micro-cracks were obtained analytically. The evolution analysis of the radial stress of the concrete microstructure was conducted, and the key conclusions are summarized as follows:

• 1 The sulfate attack process in concrete involves complicated interactions of heterogeneous reactants. There are interface energies between reactants of different phases, and the interaction between different phases in the erosion process cannot be ignored. From the generation phase of the ettringite to the destruction phase of the concrete microstructure, there is always a layer of liquid film between ettringite and pore wall. With the growth of ettringite, the thickness of the liquid film becomes smaller and the expansion stress increases.

• 2 The concrete microstructure model is composed of micro-voids and micro-cracks. With the diffusion of sulfate ions in micro-voids and micro-cracks, it will directly lead to the formation of ettringite. Moreover, it develops along the micro-cracks on the micro-voids.

• 3 The trends of radial stress in micro-voids and micro-cracks are similar. It is negatively correlated with aperture and positively correlated with erosion time, respectively. In addition, the radial stress in micro-cracks is greater than that in micro-voids. The radial stress is positively correlated with the expansion extend of ettringite.

Some preliminary research results in this paper provide reference for the subsequent determination of chemical damage variables and the establishment of concrete force-chemical coupling damage model. To understand the concrete erosion products thoroughly and improve of durability and reliability of the concrete materials in marine environment, further quantitative analyses are warranted.