## 3 Relationship between UPV and Strength Evolution Index of Concrete  
### Relationship between UPV and Strength in Normal Concrete  
Figure 2a shows the testing results of NC1-NC5, which adopted the mixture proportions in Table 1. The UPV-strength curve of concrete with a w/cem of 0.3 is located on the upper end of the curve, followed sequentially by the curves of concrete with w/cem of 0.4, 0.5, 0.6, and 0.7. The measurements were conducted at specimen ages of 1, 3, 7, 14, 21, and 28 days. For the concrete with a w/cem of 0.3, the testing results revealed a relatively high UPV and strength evolution index; nearly all points on the relationship curve became adjacent to each other after 3 days. As the w/cem increased, the various points that comprised the relationship curve gradually became scattered, and the relationship curves moved downwards. In other words, concrete strength decreased in accordance with increases in the w/cem. Figure 2a clearly shows that the relationship curves of concrete with various water-to-cemetitious-material ratios were mutually independent and dispersed.  
Compiling the relationship curves of concrete at different ages yielded Figure 2b, which exhibits that the distribution of the relationship curve between UPV and strength is highly related to the concrete age. Along with increases in the age of the concrete, the UPV and strength relationship curve of the concrete moved to the upper right of the figure. In terms of the shape of relationship curve, a substantial radian change was observed at an age of 1 day; however, the degree of change decreased over time. The curve shapes of all concrete specimens became fairly similar after 14 days. Figure 2b reveals that the increase in UPV due to relatively low w/cem is more apparent when the concrete is at early ages, but the difference in cementitious material content exerts less influence on increases in UPV when the concrete has a longer period of curing time. Figure 2b shows that the relationship curves of concrete specimens at different ages are independent and scattered. In Figure 2a,b, the relationship between concrete UPV and strength is weak; thus, a simple yet general regression curve could not be obtained.  
Dividing the UPV (\(V_{n}\)) and strength (\(S_{n}\)) of specimens at various ages in Figure 2a by their corresponding terminal UPV (\(V_{t}\)) and strength (\(S_{t}\)) of concrete, one can obtain the relationship between the UPV evolution index (\(V_{g}\)) and the strength evolution index (\(S_{g}\)) of concrete with different mixture proportions, as depicted in Figure 3. Figure 3 indicates that, as the w/cem decreased, the UPV and strength evolution index became closer to the top of the figure. In other words, smaller w/cem corresponded to a higher UPV and strength evolution index when the concrete was at an early age, and vice versa. In Figure 3, the distribution of the UPV and strength evolution index data points of specimens with different mixture proportions and at different ages is highly concentrated. By inputting the data into an exponential function for regression analysis, an optimal regression curve,  
Figure 2: Relationship of UPV and strength in normal concrete: (**a**) regression based on water-to-cemetitious-material ratio; (**b**) regression based on the specimen age.  
\(S_{g}=0.0685e^{(0.0728\cdot V_{g})}\), was obtained, where R\({}^{2}\) = 0.968. The regression results for Figure 3 reveal that the UPV and strength evolution index of concrete specimens with different water-to-cemetitious-material ratios at different ages exhibited satisfactory correlation. Therefore, the UPV and strength evolution index of normal concrete with different mixture proportions should be capable of being simplified into a single regression curve.