# Evaluation of Early Age Concrete Pavement Strength by Combined Nondestructive Tests
## 3 Results
\[\text{SWV}_{0}=\frac{1}{\text{a}_{\text{s}}}\ln\frac{\text{M}_{\text{r0}}}{ \text{M}_{\text{ru}}}-\frac{\text{b}_{\text{s}}}{\text{a}_{\text{s}}} \tag{6}\]  
\[\text{SWV}_{0}=-\frac{1}{\text{a}_{\text{s}}}\left(\left(-\ln\frac{\text{f}^{ \prime}_{\text{c0}}}{\text{f}_{\text{c0}}}\right)^{\frac{\text{b}_{\text{m}}} {\text{d}_{\text{m}}}}\left(\frac{\text{a}_{\text{m}}}{\text{c}_{\text{m}}} \right)^{\text{b}_{\text{m}}}\right)-\frac{\text{b}_{\text{s}}}{\text{a}_{ \text{s}}} \tag{7}\]  
_Step 6: Using SWV Field Shift Factor_  
Linear array ultrasonic testing devices are affected by specimen size, which results in higher beam shear wave velocities when compared to velocities of a slab with the same concrete mixture and age. Since this procedure uses beam wave velocities to develop strength correlation factors, shear wave velocities measured on the slab estimate lower  
Figure 1: Test section maturity–strength relationships for (**a**) compressive strength and (**b**) flexural strength. Figure 2: Test section SWV– strength relationships for (**a**) compressive strength and (**b**) flexural strength. strengths. The discrepancy between laboratory and field measurements has been identified in previous studies [19; 31; 32; 33]. [PERSON] et al. (2022) used field maturity data to adjust field velocity measurements, which resulted in an accurate correlation shift [19]. However, with this procedure, field maturity testing is no longer required, since field strength could be estimated by a more reliable ultrasonic test. Although maturity can be used to find the field shift if sensors are used in the field, an alternative shift factor is introduced. The difference between beam and slab velocities remains relatively consistent. The ages of testing were 1, 3, 5, 7, and 14 days, and the differences between slab and beam shear wave velocities were 108, 121, 64, 107, and 99, respectively. This resulted in an average difference of 100 m/s and a standard deviation of 19 m/s. Full data such as this would be unavailable at the time this procedure is needed. Using the difference between the first field wave velocity measurement and the laboratory velocity at the same age provides a reasonable shift factor for the remaining data points (Figure 3). [PERSON] et al. (2020) also used the first wave velocity field measurement as a shift factor for their relationship between wave velocity and temperature, which provided accurate property predictions for the considered field material [31]. When using this procedure, wave velocity measurements should be taken at the earliest age to be tested in the laboratory. The difference between the field wave velocity and the laboratory wave velocity is determined at this age. This value can be subtracted from SWV\({}_{0}\), which allows the user to look for this velocity as it is read on the device in the field and obtain the corresponding strength. For the test pavement, the earliest time of testing was 1 day, where the average laboratory shear wave velocity measurement was 2622 m/s. In the field, the average shear wave velocity measurement was 2513 m/s. This leads to a difference of 108 m/s to be subtracted from SWV\({}_{0}\), providing the immediate device velocity. Figure 4 shows how the field shift factor adjusts the field strength gain rate to better correspond to strengths measured in a laboratory. The dashed line represents a 1:1 ratio between beam and slab shear wave velocity and the shifted slab data is clearly closer to representing beam velocities. Figure 3: Differences between beam and slab velocities before and after shifting. For the test section, the previous step determined that at a compressive strength of 20.7 MPa (3000 psi), the SWV would be 2647 m/s. Applying the field shift factor of 108 m/s, the value to be expected in the field would be 2539 m/s. _Step 7: Calculating Relative Maturity_  
The strength chosen in Step 4 must be converted to maturity. Equations (2) and (3) can be rearranged to find the maturity relative to the chosen flexural or compressive strength, respectively.