*3.2. Rate of Mass Change, Relative Dynamic Modulus of Elasticity and Corrosion Resistance Coefficient of Strength*

According to Formulae (1) and (4)–(6), the relationships among the rate of mass change, relative dynamic elastic modulus, and corrosion resistance coefficient of strength of concrete specimens under the action of sulfate erosion and erosion time were obtained, as shown in Figure 7.

**Figure 7.** Testing results. (**a**) Variation of mass; (**b**) variation of *E*r(*n*); (**c**) variation of *k*c; and (**d**) variation of *k*t.

The change law of the rate of mass change, relative dynamic elastic modulus, and corrosion resistance coefficient of strength of different erosion times of sulfate attack are shown in Figure 7. It can be seen from Figure 7 that with an increase of erosion time, the rate of mass change, relative dynamic elastic modulus, and corrosion resistance coefficient of strength of concrete specimens with different fly ash contents all initially increase and then decrease. When the fly ash content was 10%, concrete had the best resistance to sulfate attack [42]. The reason for this is that the active substances in fly ash reacted with the Ca(OH)2 in concrete, which reduced the content of Ca(OH)2 in the concrete, reduced the production of gypsum and ettringite, and also alleviated the expansion of crystals. At the same time, because of the micro-aggregate effect of fly ash, fly ash particles filled the space between the unhydrated cement particles, which reduced the internal porosity of

concrete, improving the pore structure and compacting the internal structure of concrete; this improved the durability of concrete [43]. At 30 d of sulfate attack, the mass of concrete, relative dynamic elastic modulus, corrosion resistance coefficient of compressive strength, and corrosion resistance coefficient of the split tensile strength with 10% fly ash increased by 2.17%, 10%, 1.0%, and 3.0%, respectively, compared to uncorroded concrete. The mass of concrete, relative dynamic elastic modulus, and corrosion resistance coefficient of strength decreased gradually after 60 d of erosion. The mass of concrete, the relative dynamic elastic modulus, and corrosion resistant coefficient of strength increased with the extension of the first corrosion time after decreasing initially. The reason being that early sulfate, ettringite, gypsum, and other products are produced by the reaction of sodium sulfate solution with hydration products of concrete. At the same time, sulfate intrudes into the concrete specimen, which fills and compacts the pores and cracks within the concrete. The concrete specimen is more compacted than before the erosion and the mass of concrete, relative dynamic elastic modulus, and corrosion resistance coefficient of strength of the concrete are increased. With the continuation of sulfate erosion and the continuous accumulation and expansion of products, micropores and microcracks inside the concrete expand and extend. At the same time, the concrete surface mortar peels off, and the mass of concrete, relative dynamic elastic modulus, and corrosion resistance coefficient of strength gradually begin to decrease.

#### **4. Establishment of Evolution Model of Sulfate Erosion Damage**

#### *4.1. Model of Erosion Damage Based on Each Evaluation Index*

It can be seen from the sulfate attack test that the mechanical properties of concrete changed with the increase in erosion time, and the changes in the macrophysical properties can reflect the degree of internal changes in concrete materials. In order to quantitatively reflect the change law of the mechanical properties of concrete under the action of sulfate erosion, and comprehensively evaluate the state of concrete change, using damage mechanics, the corrosion resistance coefficient of compressive strength (*kc*), the corrosion resistance coefficient of splitting tensile strength (*kt*), and longitudinal wave velocity (*v*) were selected as damage variables. The damage caused by sulfate attack is shown by Equations (7)–(9).

$$D\_1 = 1 - k\_c \tag{7}$$

$$D\_2 = 1 - k\_t \tag{8}$$

$$D\_3 = 1 - \upsilon\_n / \upsilon\_0 \tag{9}$$

where *D*1, *D*2, *D*<sup>3</sup> are the sulfate erosion damage variables and are the corrosion resistance coefficient of compressive strength, the corrosion resistance coefficient of splitting tensile strength, and the longitudinal wave velocity, respectively.

When the times of sulfate attack of concrete are 0 to 30 d, the sodium sulfate solution reacted with hydration products in concrete to produce ettringite, gypsum, and other products, which filled the initial holes in concrete, causing the concrete to be more compact. However, when the erosion time exceeded 30 d, that is, after 60 d of sulfate attack in this experiment, as the erosion time increased, the erosion intensified, and the damage evolution process of concrete changed with length of time. According to Equations (5)–(7), the amount of erosion damage under each evaluation index was calculated, as shown in Figure 8. The established equation in Figure 8 is only valid for concrete composed of polypropylene fiber, basalt fiber, and fly ash subjected to sulfate attack for 60–150 days.

**Figure 8.** Relationship between damage variable of different evaluation indexes and erosion times. (**a**) Results of *D*1; (**b**) results of *D*2; and (**c**) results of *D*3.

It can be seen from Figure 8 that, with the increase in the time of sulfate attacks, the erosion damage defined by the three indexes of the corrosion resistance coefficient of compressive strength, the corrosion resistance coefficient of splitting tensile strength, and the wave velocity increased continuously. The erosion damage and damage degradation rate of concrete specimens with 10% fly ash content were significantly lower than those without fly ash content. The reason for this was that an appropriate amount of fly ash can fully react with the internal components of concrete to generate a C-S-H gel and other substances, enhance the internal cohesion of concrete, reduce the porosity of concrete, improve its compactness, improve its ability to resist sulfuric acid erosion, and improve the ability to resist spallation [44]. However, when the fly ash content was 20%, the erosion damage and damage degradation rate of concrete specimens were higher than those without fly ash content. The reason for the erosion damage to ash was that an appropriate amount of fly ash can consume a certain amount of Ca(OH)2, which reduces the content of substances that react with SO4 <sup>2</sup>−, thereby reducing the generation of erosion products [35,37]. Under the same sulfate attack, the damage defined by the wave velocity index was less than the damage defined by the strength corrosion resistance coefficient index. The reason being that the damage of concrete from sulfate erosion is gradually weakened from the outside to the inside, and the longitudinal wave propagation velocity changed insignificantly, so the erosion damage defined by the wave velocity was relatively small [11,45].

At the same time, it can also be seen from Figure 8 that the correlation coefficients of the fitting formulas of the sulfate erosion damage variables are relatively high, which can better fit the damage evolution law of concrete specimens over time under the action of sulfate erosion. After data fitting, the erosion damage evolution of each performance index showed a more obvious exponential function relationship, and the general fitting function formula is shown in Formula (10).

$$D\_{\rm ll} = a\mathfrak{e}^{bn} + c \tag{10}$$

where *n* is the erosion time; *a*, *b*, and *c* are the coefficients in the fitting formula, as shown in Figure 8a–c.

The relationship between the sulfate erosion variables *D*<sup>2</sup> and *D*<sup>1</sup> is established, as shown in Equation (11).

$$D\_2 = a\_1 \mathfrak{e}^{b\_1 D\_1} + c\_1 \tag{11}$$

where *a*1, *b*1, and *c*<sup>1</sup> are the coefficients in the fitting formula, as shown in Figure 9a.

**Figure 9.** Relationship between different evaluation indexes of sulfate erosion damage. (**a**) Relationship between *D*<sup>2</sup> and *D*<sup>1</sup> and (**b**) relationship between *D*<sup>3</sup> and *D*1.

There is also a good exponential relationship between damage amount *D*<sup>1</sup> of the corrosion resistance coefficient of compressive strength and ultrasonic velocity damage amount *D*<sup>3</sup> of the non-destructive testing, as shown in Figure 9b. Thus, the longitudinal wave velocity of the non-destructive testing can be used to predict the strength performance of and damage to the concrete structure.

### *4.2. Erosion Damage Model of Corrosion Resistance Coefficient of Compressive Strength Based on the Erosion Time and Fly Ash Content*

To better study the influence of sulfate attack times and fly ash content on the corrosion coefficient of concrete's compressive force, a sulfate damage prediction model using both sulfate attack time factors and fly ash content was examined. The scatter diagram results of sulfate erosion times, the amount of fly ash, and the corrosion resistance coefficient of compressive strength of the concrete specimens are shown in Figure 10. The mathematical model of sulfate damage established based on regression analysis is shown in Formula (12). The correlation coefficient of data regression analysis was 0.919, the fitting coefficient was relatively high, and the fitting surface can be in good agreement with the experimental value. This shows that this model can be used to predict the quantitative relation between concrete erosion damage and the amount of sulfate attack and the amount of fly ash after sulfate attack, so as to evaluate the corrosion resistance of concrete under sulfate attack. The model is only established based on the experimental data; hence, the model is not universal. It can, however, provide some calculation methods and data references for actual projects.

$$k\_c = 1.014 - 0.00112n + 0.00379\psi - 2.844 \ast 10^{-6}n^2 - 1.992 \ast 10^{-4}\psi^2 - 1.476 \ast 10^{-6}n\psi \,(\mathbb{R}^2 = 0.919) \tag{12}$$

**Figure 10.** Relationship between fly ash content and erosion time *n* with *k*c.

It can be seen from Table 4 that the error between the calculated values and the measured values of the regression formula is small. Among these, the minimum error without fly ash occurred at 120 d of sulfate erosion, with an error of 0.12%. The maximum error was −3.17% at 30 d of sulfate attack. When the fly ash content was 10%, the minimum error occurred at 120 d of sulfate attack, with an error of 0.59%. The maximum error was −4.23% at 30 d of sulfate attack. When the fly ash content was 20%, the minimum error occurred with a sulfate erosion lasting 30 d, with an error of 0.30%. The maximum error occurred at 150 d of sulfate attack with an error of 4.49%. For engineering practices and measurement errors, this is negligible; hence, the test value and the fitting value are basically the same.


**Table 4.** Comparison of fitting *kc*<sup>1</sup> and measured *kc*.

#### **5. Mechanism Analysis**

When concrete is subjected to sulfate attack, the change in its performance is, not only reflected in the process of macroscopic properties, but also in the process of microstructure changes.

#### *5.1. XRD Analysis*

Figure 11 shows the XRD mineral analysis results of various concretes with different erosion time stages (erosion times of 0 d, 30 d, 150 d). The results show that, when various concretes are not attacked by sulfate, the main components are quartz (SiO2), calcium

hydroxide (Ca(OH)2), and calcium silicate hydrate (C-S-H). In addition to C-S-H, ettringite (Aft) could also be observed in groups FA0, FA10, and FA20 after being eroded for 30 days. At that time, ettringite production was limited, which filled the micro pores and cracks in the concrete specimens, optimizing the pore structure and making the concrete structure more compact. With the increase in erosion time, ettringite, and gypsum generation, when the erosion age reached 150 d, the content of Ca(OH)2 in the pores of concrete decreased continuously, decreasing the alkalinity and causing the erosion degree to intensify. A large amount of gypsum and ettringite was generated in the concrete, which increased in volume and produced expansion stress. When expansion stress exceeds the tensile stress of internal concrete, microcracks will form and the internal pore structure of concrete will be destroyed [11,46]. At the same time, it can be concluded that the amount of gypsum produced in concrete with fly ash is obviously more than that without fly ash, and the amount of gypsum produced increases with the increase in fly ash content [43]. More ettringite and gypsum were produced in specimens with fly ash at 150 days [43]. The product of fly ash concrete under sulfate erosion was similar to the experimental conclusions of Liu et al. [43] and Zhao et al. [11].

**Figure 11.** X-ray diffraction patterns of concrete subjected to sulfate attack. (**a**) FA0 concrete; (**b**) FA10 concrete; and (**c**) FA20 concrete.

#### *5.2. SEM Analysis*

The microstructures of concrete at different time under the action of sulfate attack were observed using SEM, as illustrated in Figures 12–14. It can be seen from Figure 12 that, when the FA0 group concrete was not corroded, there were numerous hydration products and C-S-H gel inside the concrete, with smaller pores and a denser internal structure (Figure 12a). After 90 d of erosion, a small amount of acicular calcium silicate, flaky gypsum, and cracks appeared inside the concrete, making the structure relatively loose (Figure 12b). After 150 d of sulfate attack, the erosion intensified, and more gypsum and ettringite formed in the concrete. During this process, volume expansion occurred, the expansion force increased, and the

concrete cracked and expanded gradually (Figure 12c) [11,41]. Figure 13 shows that there were a large number of hydration products and C-S-H gel in various concretes before sulfate attack, and the internal structures were relatively complete and compact (Figure 13a). After 90 d of sulfate attack, a few new cracks appeared in the concrete from the FA10 group (Figure 13b). After 150 d of sulfate attack, more erosion products were generated, cracks increased and expanded, and the structure was loose. It can also be seen from Figure 14 that a small number of cracks appeared in the internal structure of concrete without sulfate attack. After 90 d of sulfate attack, a large number of new microcracks were generated in the internal structure of the FA20 group concrete, and the cracks crossed each other and the structure was loose (Figure 14b). As the erosion time increased, the microcracks in the concrete specimens expanded and increased, and the internal structure became loose, making the degree of erosion worse. After 150 d of erosion, the internal microstructure of FA20 concrete specimens further loosened, the cracks were interconnected, the internal space increased, and the compactness decreased (Figure 14c).

As can be seen from Figure 15 that SO4 <sup>2</sup><sup>−</sup> entered the concrete and reacted with its internal hydration products to form acicular ettringite crystals and flake-like gypsum, which was continuously generated in the microcracks and pores, thus making the pores inside the concrete compact. However, with the continuous diffusion and reaction of SO4 <sup>2</sup>−, the generated needle-shaped ettringite and flaky gypsum gradually increased and crossed each other to form a network, which caused the pores of the concrete to be subjected to expansion forces. When the expansion forces reached a certain level, the number of microcracks and pores in the concrete specimens increased and expanded continuously [11]. According to the micromorphology of concrete after sulfate erosion, Zhang et al. [47] and Li et al. [9] observed that sulfate ions diffused into concrete and reacted with its internal substances to generate acicular ettringite crystals. With an increase in sulfate erosion time, in concrete, the amount of generated ettringite crystals gradually increased which finally led to the formation of cracks. The obtained microstructures and conclusions in this article are consistent with the results of Zhang et al. [47] and Li et al. [9].

**Figure 12.** Microcrack expansion of FA0 concrete at different corrosion times. (**a**) FA0-D0; (**b**) FA0-D90; and (**c**) FA0-D150.

**Figure 13.** Microcrack expansion of FA10 concrete at different corrosion times. (**a**) FA10-D0; (**b**) FA10-D90; and (**c**) FA10-D150.

**Figure 14.** Microcrack expansion of FA20 concrete at different corrosion times. (**a**) FA20-D0; (**b**) FA20-D90; and (**c**) FA20-D150.

**Figure 15.** Growth and aggregation of products in FA10 concrete. (**a**) FA10-D90 and (**b**) FA10-D150.

#### **6. Conclusions**

According to the results of this paper, the following conclusions can be drawn:

(1) With an increase in sulfate attack time, the change law of concrete mass, relative dynamic elastic modulus, and strength corrosion resistance coefficient are similar, as they all initially increase and then decrease. Compared with other fly ash contents, concrete durability is better when fly ash content is 10%. The reason for this is that fly ash can fully react with the internal composition of concrete to produce C-S-H gel and other substances, enhance the internal cohesion of concrete, reduce the porosity of concrete, improve the density, and improve sulfuric acid erosion resistance.

(2) The corrosion resistance coefficient of compressive strength, the corrosion resistance coefficient of splitting tensile strength, and the change in wave velocity were taken as damage variables. Concrete sulfate erosion damage was comprehensively evaluated using various damage variables. The evolution equation of concrete sulfate erosion damage based on each damage variable was obtained by data regression, and the exponential function relationship between different damage variables was established.

(3) A composite sulfate erosion damage model between the corrosion resistance coefficient of compressive strength as a damage variable, erosion phase, and fly ash content was established. This model was used to predict concrete damage and erosion time after sulfate erosion. The model was used to predict the quantitative relationship between concrete damage, erosion time, and fly ash content after sulfate erosion to evaluate the resistance of concrete to sulfate attack in saline areas. The damage model is only suitable for concrete with a water–binder ratio of 0.6, fly ash dosage range of 0–20%, and mixed with 0.1% basalt fiber and 0.2% polypropylene fiber simultaneously.

(4) Sulfate attack changes the internal microstructure of concrete, and sulfate ions react with hydration products in concrete to produce expansive crystal ettringite and gypsum. With an increase in erosion products and expansion force, microcracks and damage appear inside the concrete, which is aggravated continuously, inducing the expansion and penetration of cracks and pores, and the deterioration of the microstructure reduces the macro performance of concrete.

**Author Contributions:** Conceptualization, Q.W., Q.M. and X.H.; methodology, Q.M. and X.H.; software, X.H.; validation, Q.W., and Q.M.; formal analysis, Q.W. and X.H.; investigation, Q.W.; resources, Q.W.; data curation, Q.M. and X.H.; writing—original draft preparation, Q.W.; writing—review and editing, Q.W., Q.M. and X.H.; visualization, Q.W.; supervision, Q.W.; project administration, Q.W.; funding acquisition, Q.M. and X.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Anhui Province University Leading Talent Team Funding Project (2016-16). The APC was funded by Q.M.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors are grateful for financial support from the School of Civil Engineering and Architecture, Anhui University of Science and Technology and the Engineering Research Center of Underground Mine Construction, Ministry of Education of Anhui Province.

**Conflicts of Interest:** The authors declare no conflict of interest.
