1. Introduction
Concrete is one of the most commonly used building materials in civil engineering. As the urban population continuously increases, the amount of industrial waste is increasing year by year. China, for instance, generates 600 million tons of industrial waste residue and waste ore each year. One promising way to recycle industrial waste in construction is to add the waste during concrete production [
1,
2,
3,
4,
5]. However, the heterogeneity of the waste is an obstacle to elucidating the durability of waste-containing concrete, resulting in difficulties in predicting the service life of concrete. The service life of concrete structures over time is closely related to interactions with the environment. Extreme environments, for example, those with freeze–thaw cycles, greatly influence concrete construction integrity and thus impair concrete’s service life. The addition of industrial waste during concrete production provides a better intrinsic system of voids in the concrete, leading to better durability to freeze–thaw, since the extra voids can ease the hydraulic pressure. However, the effect of industrial waste on improving freeze–thaw resistance is still not clear since the results often diverge due to the different kinds of waste or different experimental methods [
6,
7].
The mechanism responsible for concrete damage under freeze–thaw is hydraulic pressure. The water in the capillary pores begins to freeze during freezing, resulting a 9% volume increase [
8,
9]. The formation of ice forces the unfrozen water to move to the nearby pores. The movement causes hydraulic pressure on the capillary walls, which will result in micro-cracks when the pressure increases beyond the tensile strength [
10,
11]. The appearance of micro-cracks will destroy the integrity of the concrete and reduce its service life.
Considering the concrete deterioration mechanism, scholars have found ways to enhance concrete’s freeze–thaw resistance during concrete production [
12,
13]. Falchi found that the addition of silane in concrete preparation did not influence the hydration reaction, and it induced good concrete freeze–thaw resistance [
14]. Liu added denitrifying bacteria during concrete production and found that bacteria bonded the ITZ, resulting in enhanced resistance to freeze–thaw [
15]. On the other hand, for existing concrete construction, surface protection can provide excellent water-repellent performance and freeze–thaw resistance in concrete. In general, surface protection methods can be classified into two groups: (1) hydrophobic protection, which produces a water-repellent surface and has no pore-filling effect; and (2) filling protection, which fills the cracks and capillaries and thus reduces surface porosity. Hydrophobic protection can alter the concrete surface to make it water-repellent. Under this circumstance, water can be prevented from penetrating the surface of the concrete. In the latter, surface protection material can penetrate the concrete through pores, capillaries, and micro-cracks and react with hydration products to fill in the cracks and pores, thus reducing the porosity and increasing the strength.
The deterioration of concrete structures is caused by chemical attack, environmental effects (such as freeze–thaw), and service loads. Therefore, accurately assessing the service life of concrete is important. Testing methods (such as ultrasonic velocity and fundamental transverse frequency) have been adopted to assess concrete durability [
16]. The destructive testing method always causes a reduction of the load-bearing area and is cost-consuming. On the other hand, the nondestructive testing method is easy to conduct. Shang utilized nondestructive testing technology to establish the relationship between the mechanical properties and ultrasonic velocity. The results predicted the service life of existing concrete structures such as offshore platforms and concrete dock walls [
17]. Yan compared the service life of concrete predicted using the fundamental transverse frequency method, the ultrasonic velocity method, and the shear wave velocity method. The results showed that all three methods could predict the service life of concrete [
18].
Several models have been suggested to determine the resistance of concrete specimens to freeze–thaw. Fagerlund proposed a method to analyze the relationship between the degree of saturation and freeze–thaw deterioration [
19]. Cho conducted a regression analysis to predict the freeze–thaw damage of concrete based on the limit state function of the response surface method [
20]. Yu set up a new equation aimed at determining the freeze–thaw damage caused by different freeze–thaw media and systems through rigorous theoretical derivation [
21]. Chen applied MINITAB to perform a nonlinear regression analysis for fracture energy, and the three-parameter Weibull distribution model was used to predict the service life of the concrete specimens [
22]. However, measuring fracture energy is relatively complicated and costly, thus there are few studies that have published freeze–thaw fracture energy damage models. The limited models affected the prediction accuracy of the service life of concrete. Therefore, more research should be conducted to establish damage models for concrete freeze–thaw and to predict the service life of concrete using different damage criteria. The aim of this study was to propose a new way to predict the service life of concrete with high prediction accuracy by creating a two-segment damage model according to the tendencies of the fundamental transverse frequency and ultrasonic velocity.
In this study, the effect of the surface treatment material lithium silicate (LS) on concrete freeze–thaw resistance was determined using water absorption and rapid freeze–thaw tests. In the water absorption test, the weight gain was measured during the test, and the moisture uptake and coefficient of water absorption were calculated to clarify the effect of LS on preventing water from penetrating the concrete specimens. For the rapid freeze–thaw test, the relative dynamic modulus of elasticity was calculated by the fundamental transverse frequency (Er) and ultrasonic velocity (Ev), respectively, in order to evaluate the concrete damage due to the conducted freeze–thaw cycles. In addition, a two-segment damage model was adopted to predict the service life of concrete. The model for predicting concrete’s service life was verified by comparing the service life results calculated by Er and Ev, which provided an effective calculation basis for the design of freeze–thaw resistant concrete.
3. Results
3.1. Results of the Water Absorption Test
Figure 3 presents the results of water absorption uptake against time. According to
Figure 3, the variation in the water absorption trends of the two types of concrete specimens (0.35–1, 0.55–4.5) increased in a similar manner. The water absorption curve comprised two distinguished polynomial patterns: the first pattern was a rapid and linear increase, while the latter was a smooth transition. The rapid increase part was attributed to rapid capillary absorption, while the soft transition part was the result of slow uptake by diffusion [
28].
Table 3 displays the coefficient of water absorption and the total water absorption of the two types of concrete specimens. In the first pattern, the values of the initial coefficient of water absorption (
Bini) of the four concrete groups (0.35–1–NO, 0.35–1–LS, 0.55–4.5–NO, 0.55–4.5–LS) were 1.16, 0.75, 1.80, and 1.40, respectively. The
Bini values of the LS-sprayed specimens were smaller than those of the unsprayed specimens for both the 0.35–1 and 0.55–4.5 specimens. In addition, the total water absorption amounts of the four concrete groups were 1.69%, 1.40%, 2.84%, and 2.34%, respectively. As exhibited in
Figure 3, at the same condition, the amount of absorbed water for the LS-sprayed specimens was smaller than that for the unsprayed specimens. This phenomenon was evident in the 0.55–4.5 specimens. This may have been due to the low w/b ratio of the 0.35–1 specimens and thus their lower porosity. The results were consistent with the results reported by Baltazar [
28].
One significant implication of the differential water absorption coefficient and total water absorption amount is that the filling of the cracks and air pores was governed by the chemical product of LS reacting with cement hydration products (CHs). Theoretically, the chemical reaction between the LS surface protection material and CHs is expressed as Li2O∙nSiO2 + mH2O + nCa(OH)2→nCaO∙SiO2∙(m + n−)H2O + 2LiOH. LS reacts with part of the CHs to form new C-S-H, which densifies the concrete surface. Therefore, a slow water absorption coefficient, Bini, and a lower total water absorption amount was found in the specimens coated with LS.
3.2. Results of the Relative Dynamic Modulus of Elasticity
Figure 4a,b exhibits the change in
Er with freeze–thaw cycles, assuming a 60% cut-off limit. It can be seen from
Figure 4a that the
Er of the 0.35–1–NO specimens decreased slowly before 50 cycles and then displayed a rapid decrease afterwards. At 150 freeze–thaw cycles, the
Er of the 0.35–1–NO specimens was 46.06%, surpassing the failure criterion according to Chinese specification GB/T 50082-2009. On the other hand, the
Er of the 0.35–1–LS specimens showed a similar tendency compared to the 0.35–1–NO specimen, reaching the failure criterion of 48.62% at 200 freeze–thaw cycles. The LS-coated specimens showed better freeze–thaw resistance.
Figure 4b demonstrates the
Er tendency of the concrete specimens (0.55–4.5–NO, 0.55–4.5–LS). The
Er of the 0.55–4.5 specimens increased slightly in the early stage of the freeze–thaw cycles. This was because concrete is a heterogeneous composite material with many inherent defects and high porosity. According to Powers’ hydrostatic pressure theory [
27], part of the solution in the pores freezes and expands during freezing, forcing the unfrozen solution to migrate out of the pores, therefore discharging the air in the micro-pores. However, external water solution enters the micro-pores and circulates within them when the temperature is positive. The air in the micro-pores is gradually replaced by the water solution. Thus, the mass of the concrete increases and the specimen seems to be denser. This results in a slight increase in the
Er, especially for air-entrained specimens. As shown in
Figure 4b, the tendency of the 0.55–4.5–LS specimens was similar to that of the 0.55–4.5–NO specimens before 100 cycles. However, after that, an obvious decrease was found in the 0.55–4.5–NO specimens. The 0.55–4.5–LS specimens displayed more negligible attenuation than the 0.55–4.5–NO specimens. The
Er of the 0.55–4.5–LS specimens at 300 freeze–thaw cycles was 62.23%, while the
Er of the 0.55–4.5–NO specimens at 250 freeze–thaw cycles was 49.32%, which had already reached the damage criterion. Therefore, LS could improve the freeze–thaw resistance in both kinds of concrete specimens.
3.3. Change in the Ultrasonic Velocity
The changes in ultrasonic velocity, also known as P-wave velocity, are exhibited in
Figure 5a,b. According to
Figure 5a, the variation in ultrasonic velocity of the 0.35–1 specimens was slight before 50 freeze–thaw cycles, then it significantly decreased. Compared to the ultrasonic velocity of the 0.35–1–LS specimens, the ultrasonic velocity of the 0.35–1–NO specimens manifested a more pronounced decrease after 50 cycles. In
Figure 5b, the ultrasonic velocities for both the 55–4.5–NO and 55–4.5–LS specimens displayed a slight decline before 100 freeze–thaw cycles. The ultrasonic velocity of the 0.55–4.5–NO specimens decreased dramatically after 100 freeze–thaw cycles. On the other hand, the ultrasonic velocity of the 0.55–4.5–LS specimens manifested a smaller attenuation. The ultrasonic velocity results of the 0.55–4.5 specimens corresponded with those of the 0.35–1 concrete specimens. Applying LS surface coating material could delay the attenuation of the ultrasonic velocity during the rapid freeze–thaw test.
The relationship between the dynamic modulus of elasticity
Mv and the ultrasonic velocity V has been clarified theoretically according to Equation (5):
where
Mv is the dynamic modulus of elasticity calculated by the ultrasonic velocity,
ρ is the specimens density, μ is Poisson’s ratio, and
V is the ultrasonic velocity. Since ρ and μ have negligible change, the relative dynamic modulus of elasticity calculated by ultrasonic velocity (
Ev) [
29,
30] is calculated according to Equation (6):
where
Mv−0 and
Mv−t are the dynamic modulus of elasticity at 0 cycles and after
t cycles, respectively; and
V0 and
Vt are the ultrasonic velocity at 0 cycles and after
t cycles, respectively.
Figure 6 displays the relationship between
Ev, and freeze–thaw cycles. As exhibited in
Figure 6a, the
Ev of the 0.35–1 concrete specimens decreased slowly before 50 cycles and showed rapid attenuation after 50 cycles. The
Ev of the 0.35–1–LS specimens was 67.48% at 200 freeze–thaw cycles, and at 150 freeze–thaw cycles, the
Ev of the 0.35–1–NO specimens was 52.52%. The variation trends of
Ev were similar to those of
Er. Before 100 freeze–thaw cycles, the attenuation of
Ev was small for the 0.55–4.5 concrete specimens, as exhibited in
Figure 6b. Nevertheless,
Ev decreased quickly after 100 freeze–thaw cycles, ending with 52.77% at 300 cycles for the 0.55–4.5–LS concrete specimens and 44.83% at 250 cycles for the 0.55–4.5–NO concrete specimens, respectively. The
Ev and
Er for the 0.55–4.5 specimens exhibited a similar tendency. The
Ev of the concrete specimens coated with LS displayed a slower attenuation.
3.4. Prediction of Relative Dynamic Modulus of Elasticity
Many scholars have analyzed the degree of freeze–thaw damage to concrete by establishing different mathematical models [
31,
32,
33]. A two-segment damage mathematical relationship has been employed to characterize the relative dynamic modulus of elasticity [
34]. The two-segment damage mathematical model comprises a straight line and a univariate quadratic polynomial. The first segment is a straight line and the second segment is a univariate quadratic polynomial. In this model, there is one tangent point, cycle
N12, between the straight line and the univariate quadratic polynomial. The relationship between the relative dynamic modulus of elasticity,
E, and the freeze–thaw cycles,
N, is described below:
where
E1 represents the straight line, and
E2 represents the univariate quadratic polynomial.
Since concrete damage proceeds during the freeze–thaw test,
E also decreases with the freeze–thaw cycles. The univariate quadratic polynomial also exhibits a descending tendency. According to the properties of the univariate quadratic polynomial, the coefficient c should be prior to 0. To better explain the formula, the following derivation is conducted based on Equations (4) and (7). The relationship between the degree of freeze–thaw damage,
D, and the freeze–thaw cycles is exhibited below:
- (1)
In the first segment ①, the velocity and acceleration are shown as follows:
where the velocity is −
a and the acceleration rate is 0, respectively. Thus, the first segment is a uniform damage period.
- (2)
In the second segment ②, the velocity and acceleration rate are exhibited as below:
where the velocity is –(
b + cN), and the acceleration rate is −
c. The second segment is a uniformly accelerated degradation process.
N12 is the freeze–thaw cycle number at the tangent point of the straight line and the univariate quadratic polynomial. The first and second segments should have the same damage velocity at the tangent point N12, that is . Therefore, N12 is calculated by the coefficients a, b, and c, respectively. Moreover, the damage acceleration changes from 0 to − at the tangent point N12. Concrete freeze–thaw damage changes from uniform damage mode in segment ① to uniform degradation mode in segment ② at the tangent point N12. Thus, N12 is the damage mode changing point.
3.4.1. Prediction of the Relative Dynamic Modulus of Elasticity Er
According to the two-segment model, the freeze–thaw damage evolution of
Er is fitted by the two-segment damage model, as shown according to Equation (11) below:
The results of the predicted
Er by the two-segment damage model are displayed in
Figure 7a,b. For the 0.35–1 specimens, the tangent freeze–thaw cycle number was set as 50. Meanwhile, for the 0.55–4.5 specimens, the tangent freeze–thaw cycle number was 100.
Er could be well fitted by the two-segment damage model.
Table 4 shows the calculated velocity in segment 1, the velocity and acceleration rate in segment 2, and the goodness of fit (
R2) of the 0.35–1 and 0.55–4.5 concrete specimens. The
R2 values of the specimens were all above 0.97, representing perfect fitness. The velocity in segment 1 and acceleration rate in segment 2 were above zero, indicating that the concrete freeze–thaw damage had been accelerated. The LS-coated specimens showed a smaller velocity than the uncoated specimens in segment 1. As shown in
Figure 7b, the velocity of the LS-coated specimens was 0.0463, while the value of the uncoated specimens was 0.0532. In addition, the damage acceleration was lower for the LS-coated specimens, which verified that LS surface protection could improve freeze–thaw resistance.
3.4.2. Prediction of Relative Dynamic Modulus of Elasticity Ev
The relative dynamic modulus of elasticity
Ev of the two types of concrete specimens (0.35–1 and 0.55–4.5) were also according to the two-segment damage model, as exhibited in Equation (12) below:
Figure 8 shows the calculated results of
Ev.
Table 5 shows the damage velocity, the damage acceleration, and the goodness of fit (
R2). The tangent freeze–thaw cycle numbers for the 0.35–1 and 0.55–4.5 concrete specimens were also fixed at 50 and 100, respectively. According to
Table 5,
R2 was above 0.98, showing an excellent fitting result. It can be seen that the acceleration rate of the two types of specimens were above 0, and the freeze–thaw damage of the specimens was accelerated in the second segment. Only the initial velocity of the 0.35–1–LS specimens was slightly below 0 at −0.0079; the initial velocities of all the other specimens were above 0.
3.5. Calculation of the Service Life by the Two-Segment Damage Model
According to the “Test method for long-term performance and durability of concrete,” concrete is regarded as damaged when the E
r is below 60%. Many scholars have used the
Ev to characterize freeze–thaw damage. Chen found that the relative dynamic modulus of elasticity by ultrasonic velocity (
Ev) could represent the damage caused by the coupled sulphate and freeze–thaw attack [
35].
Similar to the damage criterion defined by the
Er, concrete specimens become deficient when the
Ev is below 60%. The service life results of the concrete specimens calculated by
Er and
Ev are exhibited in
Table 6. As displayed in
Table 6, the service life results calculated by
Er and
Ev were close to each other. Only the error of the 0.35–1–LS specimens was relatively large at 24.28%, while all the other errors were small, at less than 8%. The authors supposed that the freeze-thaw resistance of the 0.35–1 concrete specimens was relatively low. After spraying with LS, the micro-cracks in the surfaces were reduced, making the specimen’s surface denser. A denser specimen surface facilitates ultrasonic transmission, resulting in a higher service life prediction. After spraying with LS, the
Ev of the 0.35–1 specimens increased from 132 to 215, showing a 62.9% increase. However, the increase in concrete surface compactness had a relatively small effect on the overall fundamental transverse frequency. The
Er increased 32%, which was only half of the increase in the
Ev. Therefore, this result showed a larger error in the 0.35–1–LS specimens. However, the influence of LS on the relative dynamic modulus of elasticity (
Ev and
Er) was still not clear and more research should be conducted in the future.
Despite the variations in the 0.35–1–LS specimens, the service life calculated by the ultrasonic velocity using the two-segment damage model was quite close to the standard service life calculated using the fundamental transverse frequency. Therefore, it is feasible to adopt the ultrasonic non-destructive test method and the two-segment damage model to predict the service life of concrete suffering from freeze–thaw, and the results showed relatively high reliability.