The cement used for practical experimentation was 42.5R general-use Portland cement. Crushed granite with nominal particle sizes of 5 mm–40 mm and Weihe river sand with a fineness modulus of 2.35 were used as the coarse and fine aggregates, respectively. The dosage of Grade Π fly ash used was 20% by mass of binder. The air-entraining agents (AEAs) and the superplasticiser (SP) with a water-reducing rate of 20% by weight were used in the concrete mixtures. Table 1 lists the detailed properties of sand and coarse aggregates.

Three concrete mixtures were developed with water–binder (w–b) ratios of 0.35, 0.40 and 0.45. A total water content of 129 kg/m³ was used. Table 2 presents the details of mix proportions and the concrete properties.

All specimens were cured under the standard curing condition. The preparation steps for concrete material are as follows. (i) Add cement, fly ash, gravel and sand into the concrete mixer and mix for 30 s. (ii) Add water together with the given concrete admixture and mix for 3 min. (iii) Pour the fresh concrete into steel moulds and then vibrate for 30 s on the vibrating table. (iv) Cure each specimen under 20 °C and 95% relative humidity.

UV radiation is intense at high elevations. For example, UV radiation can reach 356–444 MJ·m⁻²·a⁻¹ in Xinjiang, China. Therefore, the considered radiation intensity in this investigation was 365 MJ·m⁻²·a⁻¹ (i.e. 1 MJ·m⁻²·d⁻¹). In this test, UVA-340 UV lamps were selected to simulate UV radiation in sunlight due to their consistency with the UV spectrum of sunlight. The UV intensity of UVA-340 UV is 200 W·m⁻², which can be calculated as follows [1]:

where T is the radiation intensity at L from the lamps, W·m⁻²; T’ is the theoretical radiation intensity, 0.5 W·m⁻²; L is the distance from the surface of specimens to UV lamps, 0.05 m; and L’ is the distance corresponding to the theoretical intensity, 1 m.

On the basis of T calculated by Eq. [1], the value of UV radiation that can be calculated by Eq. [2] was 17.3 MJ·m⁻² per day in the test box (i.e. specimens exposed in the test box for 1 day is equal to 17.3 days under natural conditions).

where Q is the UV radiation, J·m⁻²; and t is the UV exposure time, s.

The concrete was exposed to the UV radiation during the curing period and subjected to F–T cycles during the operation period. On this basis, the specimens were UV-treated for 5 days (approximately 90 days under natural conditions) before the F–T test. Figure 1 illustrates the UV radiation equipment for achieving UV exposure.

In this study, six groups (three experimental groups and three control groups) of specimens were prepared. For the experimental groups (A(E), B(E) and C(E)), 100 mm × 100 mm × 400 mm specimens were cured for 23 days and then UV-treated for 5 days. For the control groups (A(C), B(C) and C(C)), the same specimens were cured for 28 days. The mass and initial transverse frequencies of the specimens were measured after curing or exposing to UV radiation.

Sequentially, a rapid F–T test was conducted in an F–T apparatus according to the Chinese standard GB/T50082-2009 (similar to ASTM C666/C666M-03). These specimens were immersed in clean water to investigate their frost resistance. Afterwards, they were placed in the F–T apparatus and subjected to F–T cycles. In each cycle, the specimens were frozen at 5 °C to −20 °C and thawed at 5 °C for 4 h. This process was repeated 275 times. Mass and initial transverse frequencies were measured to calculate mass loss ratio and RDME.

Finally, a flexural test was conducted to investigate the difference of flexural strength among groups. Figure 2 shows the loading equipment for bending loads.

Mass loss ratio and RDME were selected to measure the frost resistance of concrete. Both were calculated by using Eqs. [3] and [4], respectively.

where W is the mass loss ratio at n F–T cycles, %; G_n is the mass after n F–T cycles, N; and G₀ is the mass at the beginning of the F–T cycle test, N.

where RDME is the RDME at n F–T cycles, %; f_n is the initial transverse frequency at n F–T cycles, Hz; and f₀ is the initial transverse frequency at the beginning of the F–T cycle test, Hz.

To understand the significance level of UV radiation for the frost resistance of concrete, a two-way ANOVA was applied to analyse the effect of UV radiation on the test results.

For one-way ANOVA, three important measures of variability similar to regression theory were applied to test the population means (28).

where y_ij represents the jth observation from the ith treatment; y.. is the mean of all nk observations (n: number of samples per treatment; k: number of treatments); y_i. is the mean of all observations in the sample from the ith treatment; SST is the ‘total sum of squares’; SSA is the ‘treatment sum of squares’; and SSE is the ‘error sum of squares’.

The sum of squares can be conveniently identified by Eq. [8], which expresses how the between-treatment (SSA) and within-treatment (SSE) variations added up to the total sum of squares.

For two-way ANOVA, Eqs. [5] and [8] can be directly used. However, Eqs. [6] and [7] must be modified to characterise the responses correctly (29). Specifically, the treatment (level) component of variance was broken down into sums of squares for each factor and can be calculated by Eq. [6]. The modified SSA for two-way ANOVA is the sum of the separate sums of squares for each factor, and the modified SSE can be deduced by Eq. [8] only if SSA is replaced by modified SSA.

To quantify the idea of statistical significance of evidence, the significance of UV radiation for two-way ANOVA was determined on the basis of associated p-values. For the statistical significance level of all analyses, the p-value of 0.05, which is mostly offered for experimental analysis, was selected (28). If the p-value was less than or equal to 0.05, then the means of two or more independent groups were statistically significantly different from each other for the two-way analysis. Therefore, the null hypothesis that all the group population means of cooperation are equal was rejected. Otherwise (i.e. if the p-value is greater than 0.05), the means were not statistically significant. For convenience, F-ratio (i.e. ratio of between-group variability to within-group variability) was compared with F_0.05 to determine whether the p-value was greater than 0.05. If the F-ratio was greater than or equal to F_0.05, then the p-value was less than or equal to 0.05. Otherwise, the p-value was greater than 0.05. Mean square represents an estimate of population variance. This estimate was calculated by dividing the corresponding sum of squares by the degrees of freedom (DF).

Specimens in group C(C) were selected to illustrate the surface changes of concrete specimens. Figures 3(a)–3(g) show the concrete deterioration in group C(C) under the cyclic F–T condition. The surface of concrete specimens significantly changed with the increase of F–T cycles. The surface mortar of specimens showed gradual stripping, and the coarse aggregates were exposed after 100 cycles. Thus, serious F–T damage occurred.

Specimens in groups A(C), B(C) and C(C) were selected to illustrate the influence of w–b ratio on the frost resistance of concrete. As shown in Figures 3(g)–3(i), the surface damage of specimens in group A(C) with the lowest w–b ratio (0.35) was the lightest when subjected to 275 F–T cycles. The surface damage of specimens in group C(C) with the highest w–b ratio (0.45) was the most serious. Therefore, under the same conditions, the higher the w–b ratio, the more serious the F–T damage. Moreover, w–b ratio had a great influence on pore structure (30). Furthermore, high w–b ratio led to poor compactness and internal bond of concrete. Thus, the ratio had a significant effect on the frost resistance of concrete.

Specimens in group C(C) and C(E) were selected to illustrate the influence of UV radiation on the frost resistance of concrete. Figures 3(c) and 3(j) show the specimen deterioration after 50 cycles. The surface damage of group C(E) was more serious than that of group C(C) after 50 F–T cycles. However, the surface damage of both groups gradually increased with the number of F–T cycles. Moreover, the difference in surface damage between groups C(E) and C(C) was gradually reduced. After 150 F–T cycles, the surface damage of the two groups were the same (Figures 3(d) and 3(k)), which could be attributed to the UV radiation only affecting a certain depth of concrete surface. Therefore, in the early stage of F–T cycle test, specimens in group C(E) more likely suffered from F–T damage, and the surface damage of group C(E) was more serious than that of group C(C). As the number of F–T cycles increased, the surface mortar of specimens showed gradual stripping. Furthermore, the effect of UV radiation gradually disappeared. Afterwards, the damage of the two groups gradually approached the same level.

Figure 4 shows the concrete deterioration in the mass loss ratio under F–T cycles. As shown in Figure 4, the testing data reveal that mass loss was strongly reduced and was consistent as the w–b ratio decreased. In the three control groups, the mass loss ratio of group A(C) was the lowest, whereas that of group C(C) was the highest. Specimens in group A(C) began to lose mass after 100 F–T cycles, whereas the mass loss ratios of specimens in groups B(C) and C(C) were 0.56% and 1.21%, respectively. After 200 F–T cycles, the mass loss ratios of specimens in groups A(C), B(C) and C(C) were 0.58%, 1.72% and 3.56%, respectively. When subjected to 275 F–T cycles, the mass loss ratios of specimens in groups A(C), B(C) and C(C) were 0.88%, 2.88% and 4.72%, respectively. Thus, under the same F–T cycles, high w–b ratio resulted in high mass loss and poor frost resistance of concrete. This result was consistent with the conclusions in Section 3.1.

The mass of specimens in group A increased at the beginning of the F–T test because these specimens had good frost resistance, and the surface damage was extremely low that it was negligible. In addition, a certain level of moisture could be absorbed into the specimens in the early F–T test. Therefore, the mass of specimens in group A slightly increased initially and then decreased. In each group, the mass loss ratio gradually increased with the number of F–T cycles. Nevertheless, the increase rate of the mass loss ratio in different groups had minimal difference. The increase rate in the mass loss ratio of the specimens in group C(C) initially accelerated and then decelerated. However, the mass loss ratio of the specimens in group C(E) initially reached a high level and then slowly increased during the early stage and quickly increased in later F–T cycles. This occurrence might be due to the UV radiation affecting the surface mortar of the concrete specimens in group C, thereby resulting in F–T damage at the early stage of F–T cycles.

For the mass loss ratio of groups A(E) and A(C), no evident difference was found before 125 F–T cycles and after 200 F–T cycles. From 125 to 200 F-T cycles, the mass loss ratio of group A(E) was higher than that of group A(C). The mass loss ratio of group B(E) was also higher than that of B(C) before 175 F–T cycles and was the same after 175 F–T cycles. In addition, the mass loss ratio of group C(E) was higher than that of C(C) before 150 F–T cycles and was the same after 150 F–T cycles. The largest difference of mass loss ratio between experimental and control groups was 0.49% in group C at 50 F–T cycles. The effect of UV radiation on the frost resistance of high w–b ratio concrete was reflected in the early stage of F–T test, whereas that of low w–b ratio concrete was reflected after a certain number of F–T cycles. This result might be due to the adverse effect of UV radiation on the concrete surface, which accelerated the surface mortar stripping at the beginning of F–T damage. The F–T damage of high w–b ratio group occurred later than the low w–b ratio group.

Table 3 shows the results of two-way ANOVA of mass loss ratio. The analytical method mentioned in Section 2.4 demonstrated that UV radiation statistically significantly affected the mass loss ratio (p < 0.05). The mass loss ratio primarily reflects the surface damage. Therefore, UV radiation significantly affected the concrete surface. As discussed in Section 3.5, the microstructure of the surface mortar was analysed by SEM to verify the reliability of the analysis.

Figure 5 illustrates the concrete deterioration in the RDME under F–T cycles. From the figure, the testing data indicated that RDME slightly decreased with the increase of w–b ratio. In the three control groups, the RDME of group C(C) was the lowest, whereas that of group A(C) was the highest. After 25 F–T cycles, the RDME of specimens in group A(C) only began to decrease, whereas that of specimens in group C(C) had already decreased to 92.25%. When subjected to 150 F–T cycles, the values of RDME of specimens in groups A(C), B(C) and C(C) were 90.41%, 84.9% and 84.32%, respectively. After 275 F–T cycles, the values of RDME of specimens in groups A(C), B(C) and C(C) were 84.5%, 75.32% and 67.32%, respectively. In summary, under the same F–T cycles, high w–b ratio resulted in low RDME and poor frost resistance of concrete. This result was consistent with the previously mentioned conclusions.

In each group, RDME gradually decreased with the increase in the number of F–T cycles. At the beginning of the F–T test (0–50 cycles), the reduction rate of the decreased RDME in group C was faster than that in groups B and C. However, no difference was evident in the reduction rates among the groups after 75 F–T cycles. For the RDME of groups A(E) and A(C), no difference was observed in the early and late stages of the F–T test. The RDME of group A(C) was also slightly higher than that of group A(E) in the middle stages. For groups B and C, the RDME of the control group was higher than that of the experimental group in the early stage of F–T test. The result was the same for the later stage. The largest difference of RDME between experimental and control groups was 2.8% in group C at 150 F–T cycles.

Table 4 shows the results of two-way ANOVA of RDME. As shown in the table, UV radiation statistically insignificantly changed the RDME of concrete (p > 0.05) because the RDME is a measurement of the inner compact degree (31, 32). Moreover, given that the specimens were UV-treated after they were moulded, only the surface of specimens was exposed to UV radiation. As a result, UV radiation had difficulty in affecting the interior of specimens. Ultimately, UV radiation insignificantly affected the RDME. The results of RDME were consistent with those of previous works (33, 34). However, these previous studies have not considered the effect of UV radiation.

Figure 6 demonstrates the flexural strength of the concrete after 275 F–T cycles. As shown in Figure 6, no evident difference was observed in the flexural strength between the control and experimental groups after 275 F–T cycles. The largest difference of flexural strength between control and experimental groups was 0.04 MPa. Therefore, UV radiation showed no evident effect on the flexural strength of concrete after F–T cycles.

Table 5 presents the results of two-way ANOVA of the flexural strength of concrete. As shown in the table, the effect of UV radiation on flexural strength was insignificant (p > 0.05).

Figure 7 presents the specimen microstructure in group B characterised by SEM. The concrete specimens without damage history (i.e. Figure 7(a)) were smooth and dense, whereas varying degrees of damage were observed on concrete after UV radiation and F–T cycles (i.e. Figures 7 (b)–7(g)). As the number of F–T cycles increased, the surface of mortar was no longer smooth. Moreover, the number of cracks and pores increased. This result explains the damage degree increment and RDME reduction. For example, Figures 7(f) and 7(g) show that specimens after 275 F–T cycles seemed rough and uneven, accompanied by several microcracks and pores.

As shown in Figures 7(b)–7(e), no evident difference was found between Figures 7(c) and 7(e), whereas slight differences were observed between Figures 7(b) and 7(d). In Figure 7(b), the particle fraction of concrete was more uniform and compact than that in Figure 7(d) because UV radiation had certain hindrances to the hydration reaction. The comparison of Figures 7(b) and 7(d) demonstrated that the damage degree of surface mortar of the specimens exposed to UV radiation followed by 100 F–T cycles was slightly higher than that of the specimens subjected to 100 F–T cycles without UV radiation. UV radiation could only affect the surface mortar of specimens, and this phenomenon was consistent with the results of mass loss ratio and RDME. No difference was observed between Figures 7(f) and 7(g). Thus, the effect of UV radiation on concrete could be ignored at 275 F–T cycles because of the increased damage degree of concrete with the increased number of F–T cycles. Moreover, the effect of UV radiation on concrete could eventually be negligible.

On the basis of damage theory, various microcracks and microdefects in concrete structures can be regarded as a continuous distribution of damage field in a material. RDME is easy to measure and analyse in F–T cycle test. Moreover, RDME is an important index to describe the internal damage of concrete materials (35). In addition, RDME can be used to analyse the internal damage degree of concrete materials quantitatively. Therefore, damage degree is defined as follows:

where D_n is the damage degree after n F–T cycles, E_n is the dynamic modulus of elasticity after n F–T cycles and E₀ is the initial dynamic modulus of elasticity.

Table 6 shows that the F–T damage model of each group was obtained by linear regression analysis of the experimental data. Moreover, the model fitted by each group was in good agreement with the experimental results. In addition, the coefficient of determination of each model was all above 0.92. On this basis, the models and experimental results had a high-fitting accuracy. Therefore, the damage model of F–T cycles was reasonable for the experimental results. Figure 8 the comparison of the fitting curves of the groups with the experimental data. The damage degree of group A initially accelerated and then decelerated as the number of F–T cycles increased, whereas that of group C rapidly developed at the beginning of the test. The reason for this difference might be that the surface of specimens in group C was significantly affected by UV radiation. Furthermore, the surface mortar was rapidly damaged at the beginning of F–T cycles.