## 2 Materials and Methods
A subset of these mixtures could also represent potential mixture proportioning variability during production with regards to water-to-cement ratio. The concrete ingredients included a 0.78 mm trap rock #57 aggregate and fine aggregate--meeting ASTM C33, Type I cement, water, and admixtures such as air-entraining admixture (AEA)--and high-range water reducer (HRWR), meeting AASHTO M 154 and M194, respectively. Air-entraining admixtures provide resistance to freeze-thaw, although they lead to a reduction in strength. High-range water reducers provide the desired concrete strength at a lower water content with acceptable workability [7]. Cylinders with diameters of D = 100 mm and heights of L = 200 mm were prepared from each mixture and tested with UPV and RFT and for compressive strength at different hardening ages. The samples were kept in a water bath at room temperature during curing. Button sensors were embedded in companion samples for each mixture for recording the  
Figure 1: NDT on concrete cylinders, (**a**) UPV and (**b**) RFT testing setup. temperature history during hydration. The temperature history was then used to calculate the temperature-time factor using the Nurse-Saul maturity function [35]:  
\[MI(t)=\sum(T_{a}-T_{o})\Delta t \tag{4}\]  
where \(MI(t)\) is the temperature-time factor at age \(t\), degree days or degree hours; \(\Delta t\) is time interval, days or hours; \(T_{a}\) and \(T_{o}\) are the average concrete temperature during the time interval \(\Delta t\) and the datum temperature, respectively, in \({}^{\circ}\)C. The datum temperature is the temperature below which the chemical reaction between cement particles and water ceases. It is the theoretical temperature below which concrete ceases to gain maturity. Even though a procedure is available in ASTM C1074 to determine such temperature experimentally, the standard recommends a datum temperature of 0 \({}^{\circ}\)C for concrete with no special admixtures or supplemental cementitious materials, as is the case in this study. Thus, the datum temperature was assumed to be zero [25; 26]. The samples were tested with UPV and RFT 1, 3, 7, 14, and 28 days after casting, and compressive strength was tested for three specimens at each age. Once concrete mixing is complete, the hydration chemical reaction takes place between concrete ingredients. More specifically, during the initial mixing phase, a reaction takes place when cement and water particles come into contact [6]. The aluminate compounds react with water molecules to form ettrinigite. The energy released from such exothermic reaction causes an initial peak in temperature at early ages and, depending on the mixture, as early as a few minutes to hours depending on the mixture and concrete ingredients [14; 25; 26]. During the next hydration phase, a surface coating of the cement particles occurs. As this coating keeps increasing, it slows down the hydration reaction. The amount of hydrated concrete keeps increasing steadily while it stays in a fluid form. The length of time for this phase depends on the specific concrete mix. In the next phase of hydration, the tricalcium and dicalcium silicates react, producing an increase in internal temperature and the formation of silicate hydrate (CSH), associated with strength gain. This phase is followed by a reduction of unhydrated free particles and thus a slowdown in temperature increase. After this stage, the hydration process continues to slow until complete hydration of the remaining unhydrated cement particles is achieved. Hydration is often not complete when the concrete reaches the desired strength, but it continues--if curing conditions are favorable--in some cases for more than a year, and under unfavorable conditions, it stops before reaching completion. Based on the maturity modeling testing outlined in ASTM C1074 [35], concrete hydration and the development of the Maturity Index, are monitored by using the standard laboratory curing conditions (i.e., 20 \(\pm\) 2 \({}^{\circ}\)C, and relative humidity of 100%). As identified