## 3 Relationship between UPV and Strength Evolution Index of Concrete
### Influence of the Proportion of Coarse-to-Fine Aggregates  
This section explores the influence of differences in the content of coarse and fine aggregates on the relationship between concrete UPV and strength under the condition of a fixed volume of paste. The specimens were prepared according to the mixture proportions listed in Table 2; specifically, the V\({}_{\text{paste}}\) was 36%, the S/A were 30, 45 and 60%, and the specimens were tested at 1, 3, 7, 14, and 28 days. Figure 4a presents the relationship curves of UPV and strength for concrete specimens with different sand-aggregate ratios. Noticeable variation was apparent among these relationship curves; specifically, increases in the S/A caused the relationship curves to move to the right. The results indicated that the relationship curves of specimens with different sand-aggregate ratios were fairly scattered and that no simplified single relationship curve could be obtained.  
When the UPV and strength data of specimens with different mixture proportions and at different ages in Figure 4a were converted into UPV and strength evolution index, a  
Figure 4: Relationship between the UPV and strength of normal concrete specimens with various coarse-fine aggregate mixture proportions: (**a**) UPV and strength, (**b**) UPV and strength evolution index.  
Figure 3: Relationship between the UPV evolution index and the strength evolution index of normal concrete.  
relationship curve could be replotted (Figure 4b). This figure reveals that the distribution of data points for the UPV and strength evolution index is highly concentrated. An exponential function could then be employed for regression analysis. The optimal curve was determined to be \(S_{g}=0.0612\text{e}^{(0.0740\cdot V_{g})}\), where R\({}^{2}\) = 0.966. The regression results of Figure 4b again indicate that the UPV and strength evolution index of the concrete specimens with various S/A and at different ages, which were obtained with reference to the terminal UPV and strength evolution index, exhibited strong correlation. Thus, the relationship between concrete UPV and strength evolution index could be simplified into a single regression curve.  
Regarding the possible influence of different sources of coarse aggregate on the relationship between concrete UPV and strength, the testing results of two concrete groups, namely NC1-NC5 listed in Table 1 and NC11-NC1 listed in Table 2, were adopted for comparison and analysis. Even though these two groups of concrete had identical mixture proportions, they exhibited dissimilar UPV values because of their different coarse aggregate sources. Figure 5a presents the relationship curves of UPV and strength for concrete with different sources of coarse aggregate. A significant difference can be observed in the relationship curves of the two groups; the increase in the UPV of coarse aggregate (Type 2) leads the relationship curve to move to the right.  
The UPV and strength data presented in Figure 5a of specimens with different mixture proportions and at different ages were again converted into UPV and strength evolution index to construct relationship curves, as depicted in Figure 5b. Figure 5b reveals that the distribution of data points for the UPV and strength evolution index of the specimens with different mixture proportions and at different ages is again highly concentrated. Inputting the data into an exponential function for regression analysis yielded an optimal curve, \(S_{g}=0.0649\text{e}^{(0.0734\cdot V_{g})}\), where R\({}^{2}\) = 0.967.  
The results presented in this section with respect to differences in aggregate proportion and source of coarse aggregate revealed that the regression relationship between concrete UPV and the strength evolution index remained satisfactory. The following sections investigate whether the addition of pozzolanic materials and changes in paste volume ratio exert significant influence on the relationship between concrete UPV and the strength evolution index.