# Evaluation of Early Age Concrete Pavement Strength by Combined Nondestructive Tests
## 2 Materials and Methods
### Maturity-Strength Relationship  
The procedure to determine the maturity curve is briefly detailed below and should be conducted in accordance with ASTM C1074 [14]. Relationships are mixture-specific and separate maturity testing must be performed for different mixture designs.  
The process includes monitoring concrete specimen temperatures while regularly measuring concrete strength using destructive testing. ASTM C1074 highlights five days of testing, 1, 3, 7, 14, and 28, but additional times can be added if necessary [14]. At least 15 cylinder or beam specimens are needed, so three specimens are tested at each time increment to establish the average compressive or flexural strength, respectively, for that day. Temperature sensors are placed at the center of at least two cylinder and two beam specimens. These specimens are monitored as strength testing continues on other specimens and are tested for strength on the final day. The Nurse-Saul method is commonly used in the maturity-strength relationship by computing the concrete maturity index or time-temperature factor (TTF) using laboratory temperature data and the following equation:  
\[\mathrm{TTF}=\sum(\mathrm{T}_{\mathrm{PCC,m}}-\mathrm{T}_{0})\Delta\mathrm{t}, \tag{1}\]  
where TTF is the temperature-time factor at age t in degree-days or degree-hours; \(\Delta\mathrm{t}\) is the time interval in days or hours; \(\mathrm{T}_{\mathrm{PCC,m}}\) is the mean concrete temperature during the time interval \(\Delta\mathrm{t}\) in \({}^{\circ}\mathrm{C}\); and \(\mathrm{T}_{0}\) is the datum temperature in \({}^{\circ}\mathrm{C}\) (standard values are 14 \({}^{\circ}\mathrm{F}\) or \(-\)10 \({}^{\circ}\mathrm{C}\)).  
The temperature and strength data are correlated to create a unique maturity-strength relationship for the mixture. The following relationship between strength and maturity is assumed:  
\[\mathrm{M}_{\mathrm{r}}=\mathrm{M}_{\mathrm{rue}}\mathrm{e}^{-(\frac{\Delta \mathrm{m}}{\mathrm{T}\mathrm{T}})^{\mathrm{b}\mathrm{m}}} \tag{2}\]  
\[\mathrm{f}^{\prime}_{\mathrm{c}}=\mathrm{f}_{\mathrm{c}\mathrm{u}}\mathrm{e}^ {-(\frac{\mathrm{G}\mathrm{m}}{\mathrm{T}\mathrm{T}})^{\mathrm{d}\mathrm{m}}} \tag{3}\]  
where \(\mathrm{M}_{\mathrm{r}}\) is the flexural strength (modulus of rupture) in MPa (psi); \(\mathrm{M}_{\mathrm{r}\mathrm{u}}\) is the ultimate expected flexural strength in MPa (psi); \(\mathrm{f}_{\mathrm{c}}\) is the compressive strength in MPa (psi); \(\mathrm{f}^{\prime}_{\mathrm{c}\mathrm{u}}\) is the ultimate expected compressive strength in MPa (psi); and \(\mathrm{a}_{\mathrm{m}}\), \(\mathrm{b}_{\mathrm{m}}\), \(\mathrm{c}_{\mathrm{m}}\), and \(\mathrm{d}_{\mathrm{m}}\) are maturity calibration coefficients.  
To utilize maturity in the field, temperature sensors are placed in the pavement during pouring in a position where they are fully surrounded by concrete to monitor temperature and calculate the maturity index. The maturity of the concrete pavement is then compared in the maturity-strength relationship to determine the estimated strength of the pavement at that time.