## 2 Materials and Methods  
In this study, two NDTs were used: ultrasonic pulse velocity and resonant frequency. While UPV can be used in both lab and field conditions, resonant frequency is primarily for lab samples and is thus a complementary method when further forensic verification may be of interest. UPV transducers measure the wave's propagation time through concrete. Three modes of testing are possible, direct, semi-direct, and indirect transmission. In the direct method used in this study, longitudinal compressive stress waves generated by an electro-acoustic transducer travel through the concrete and are received at the other end by another transducer, Figure 1a. As per ASTM C597, the pulse velocity is independent of the sample dimensions when there are no reflected waves from the sample boundaries [32]. This is assured when the smaller sample dimension exceeds the signal wavelength. With the distance between the two transducers known, the velocity can be calculated. The velocity of compression waves in concrete is related to concrete's elastic properties and density. Equation (1) provides the relationship between concrete properties and compression wave velocity [32], while Equation (2) provides the dynamic modulus, \(E_{d}\), in relation to pulse velocity and concrete properties:  
\[V=\sqrt{\frac{E_{d}(1-\
u)}{p(1+\
u)(1-2\
u)}} \tag{1}\]  
\[E_{d}=\frac{(1+\
u)(1-2\
u)}{(1-\
u)}\rho V^{2} \tag{2}\]  
where \(E_{d}\) is the dynamic modulus of elasticity, \(\mathrm{N/m^{2}}\), \(\
u\) is the dynamic [PERSON]'s ratio, \(\rho\) is the density, \(\mathrm{kg/m^{3}}\), and \(V\) is the ultrasonic pulse velocity, \(\mathrm{m/s}\). The UPV configuration used in this study was in the direct longitudinal mode, Figure 1a. Resonant frequency testing, RFT, involves determining the fundamental resonant frequency of concrete samples. Similarly to UPV, the fundamental longitudinal, transverse, and torsional frequencies can be determined. Two testing alternatives are available--theforced and the impact resonance methods. In this study, the impact resonance method was used in the longitudinal testing mode, in which the specimen is struck with a small impactor at one end and the response is measured with an accelerometer at the other end of the sample. The maximum amplitude observed represents the resonance frequency. RTF is more sensitive to sample size (i.e., cylinders with length-to-diameter ratios equal to 2 are often recommended even though ASTM C215 recommends a higher ratio). The resonant frequency is a function of sample's elastic constants (modulus and Poisson's ratio), geometry, and mass density [14; 33]. The dynamic modulus of a concrete sample in the longitudinal mode used in this study is calculated based on the fundamental longitudinal frequency and a sample shape constant based on Equation (3) [34]:  
\[E_{d}=DM\left(n^{\prime}\right)^{2} \tag{3}\]  
where \(E_{d}\) is the dynamic modulus in Pa; \(n^{\prime}\) is the fundamental longitudinal frequency in Hz; \(D\) is 5.093 (\(\frac{L}{d^{2}}\)) in m\({}^{-1}\) for a cylinder or 4 (\(\frac{L}{\text{Br}}\)) in m\({}^{-1}\) for a prism; and \(M\) is the mass in kg. The configuration of the resonance testing gauge (RTG) used in this study for resonance frequency evaluation is shown in Figure 1b. In this study eleven mixtures were considered, Table 1. Some of these mixtures represent typical concrete used in the construction of infrastructure projects in the region (Mixes 1 to 8), reflecting possible fine-tuning in proportioning that a concrete producer may consider. The remaining mixtures have higher water-to-cement ratios, deviating from a typical concrete in the region (Mixes 9 to 11). The typical mixtures have to meet proportioning and acceptance requirements similar to MD7 (Maryland designation 7). The deviation from MD7 was intentional in order to observe the effect of different parameters on NDT response and assess the feasibility of the \"master curve\" concept.