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Federal Highway Administration Research and Technology
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Publication Number: FHWA-RD-98-085
Backcalculated asphalt moduli can be adjusted for temperature by using the following formula:
ATAF = 10slope(Tr-Tm)
Slope = Log(Mr) = intercept + slope T
Tr = Reference Temperature, °C
Tm = Measured Temperature, °C
The relationship between the asphalt moduli and its temperature, as defined by the slope in the above equation, is dependent on the individual characteristics of the mix, including the binder properties and aggregate characteristics. The slopes range from the low teens (such as -0.013) to the low 30's (such as -0.032), depending on the individual characteristics of the mix.
The slopes are negative since the moduli of the asphalt mix goes down as the temperature goes up, on a semi log basis (Log modulus). The slope of the semi-log varies by the mix and binder properties, as would be expected. The range encountered in the LTPP SMP study is roughly bounded by -0.015 to -0.030. A typical default value that can be used is -0.021 if there is no other data available.
The calculation of the adjustment factor (ATAF) is based on the temperature at the time the pavement was tested. This can be determined by direct measurement, typically by a hole in the pavement, or with the use of the BELLS3 equation in the case of routine testing, or the BELLS2 equation if the testing was done according to LTPP Protocol. The backcalculated asphalt moduli can be adjusted what the moduli is expected to be at another mid-depth temperature with the above equation. For example, if the mid-depth temperature at the time of testing was 10 °C and the backcalculated moduli was 9,770 MPa. To estimate what the moduli would be at 21 °C, the above equation is used. The Tr in this case is 21 °C and Tm is 10 °C. Using the default slope of -0.021, the ATAF is calculated to be 0.587. Multiplying 9,770 MPa by 0.587 provides an estimated moduli of 5,740 MPa for the asphalt at 21 °C.
Source code for implementing this equation as a function in MS Excel VBA is available here.
Sample data for checking code is available here.