###### Abstract  
Using ultrasonic pulse velocity (UPV) testing has long been regarded as an effective approach for evaluating concrete strength; however, because of the influence of numerous factors (e.g., mixture proportion, type of coarse aggregate, pozzolanic admixture, and age of the concrete), the relationship between UPV and concrete strength cannot be conclusively determined, thus hindering the application of this approach. The objective of this paper is to develop a unified equation for prediction of concrete strength at various ages using the ultrasonic pulse velocity. Firstly, this study investigated the relationship between the UPV evolution index and the strength evolution index of normal concrete with various mixture proportions, coarse aggregate types, and ages. Subsequently, the influence of adding pozzolanic materials on this relationship was considered. The experimental results showed that excellent correlation between the UPV evolution index and the strength evolution index was found and a unified equation was established in this study through regression analysis to represent the relationship between the UPV and the strength evolution index. Finally, the applicability of the unified equation was verified by data obtained from different studies. The results indicated that for all concrete specimens more than 3 days old, the error of the strength estimation decreased to within \(\pm 15\%\), demonstrating that this unified equation has substantial value for application in decision-making processes for major construction procedures (e.g., applying post tensioning or removing formwork supports). unified equation; ultrasonic pulse velocity (UPV); concrete strength; nondestructive evaluation +
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coarse aggregate, then, for a specific cement paste volume and single-type coarse aggregate (i.e., with a similar UPV), the relationship between the UPV and strength of hardened concrete can be simplified as subject to only the influence of coarse aggregate content. However, this relationship does not apply to early-age concrete, primarily because considerable differences can be observed in concrete with various water-to-cemeentitious-material ratios in terms of UPV and strength growth rate. Coarse aggregate type is another unneglectable factor because different aggregate types can substantially affect the UPV of concrete but exert a nonsignificant influence on the strength of normal concrete. Comprehensively considering the influences of concrete mixture proportion, age, and pozzolanic material content can render the relationship between concrete UPV and strength rather complicated, which is why the application of UPV nondestructive testing methods in estimating concrete strength has remained limited. In particular, concrete at an early age exhibits a high level of hydration, further complicating the investigation of the relationship between UPV and concrete strength [17; 18]. A multivariate model treating UPV and curing age as variables was proposed and used to estimate the strength of concrete at various ages and the results showed that the corresponding 95% prediction limits were determined as \(\pm 11.8\) MPa [19]. In this study, the testing results of the UPV and strength of concrete that had set for various ages and had different water-to-cemetitious material ratios (w/cem), paste content, pozzolanic material content, aggregate content, and coarse aggregate type were compiled and analyzed to obtain a simplified and functional relationship between the UPV and strength development of concrete at different ages. Based on the idea that differences in mixture proportion and material type are eventually reflected in the final properties of hardened concrete, this study proposes a method for characterizing the relationship between the evolution index of UPV and strength in an attempt to clarify the complex relationship between UPV and strength in concrete. This study aims to establish a unified equation to represent the relationship between the UPV and the strength evolution index.