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Federal Highway Administration Research and Technology
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Publication Number: FHWARD98085 
The F1 factor is calculated by dividing the difference between defl_{0} and defl_{24} by defl_{12}. The equation for calculating the F1 factor is:
F1=(defl_{0}  defl_{24})/defl_{12}
The F1 basin shape factor relates to the ratio of bound layer stiffness to the unbound layer and subgrade stiffness. The bound layer stiffness characteristic here is dependent on both the thickness, and on the stiffness of the materials that make up the bound layer. The role that stiffness plays is clearly shown in Figure 19 by the relationship between F1 factor and pavement temperature. Increasing the thickness of the asphalt would decrease the F1 factor, whereas decreasing the thickness would increase the F1 factor. Likewise, if this same pavement structure was placed on a less stiff subgrade, it would decrease the F1 factor, or conversely, if the subgrade was stiffer, the F1 would increase. F1 values can range from about 0.3 for very stiff thick asphalt pavements on soft subgrade soils to the low 2's for thin soft asphalt pavements on stiff subgrade soils. A basin calculated for deflections on a onelayer system about 3.5. If there is a hard bottom, the F1 factor will be higher, increasing as the surface gets closer to the hard bottom.
The F1 basin factor increases with the middepth temperature of the asphalt, that is, as the temperature goes up, the magnitude of F1 goes up. The relationship between the middepth temperature of the asphalt and F1 best follows a semilog relationship. Figure 19 shows three basins measured at the same spot, on the same day as the asphalt temperature rose. Figure 20 shows the F1 factors that relate to the basins in Figure 19 and Figure 21 shows the F1 factors at this same point over one year of testing during the LTPP Seasonal Monitoring Program.
Figure 19. Sample Deflection Basins Measured at the Same Point
Figure 20. F1 Factors of Basins in Figure 17
Figure 21. F1 Factors Versus Temperature at a Single Test Location
The LTPP SMP data was used to develop a regression equation that relates the F1 basin factor to pavement characteristics including the thickness of the asphalt, the temperature at the middepth of the asphalt, the 9 kip deflection at the 36inch offset (which provides a replacement to the subgrade stiffness), and the latitude. (The latitude relates to the stiffness of the asphalt binder used in the mix. Hot southern climates use a stiffer binder than cooler or colder northern climates, which generally results in the asphalt mixes in colder climates being softer than asphalt mixes in warmer climates.)
The resulting regression equation for the F1 basin factor is as follows:
log(F1) = 0.326  0.382*log(ac)*log(defl_{36}) + 0.327*log(lat)*log(defl_{36})  0.004447*T + 0.00555*T*log(ac)
Where:
ac = Total thickness of the HMA, mmlat = Latitude of the pavement section
defl_{36} = Deflection (loadnormalized to 40.5 kN (9 kip)) at 915 mm (36") from the center of the load plate, µm
T = Temperature at middepth of the HMA, °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.
The F1 factor decreases as the log of the thickness of the ac increases; increase as the temperature of the asphalt increases because the second term with T dominates the first term with T. The latitude is a substitute for the stiffness of the binder used in the asphalt mix and the F1 increases as the latitude increases because softer binders are used in north and harder binders are used in the south. The coefficient on the term where the latitude appears is positive, indicating that as the latitude increases, the F1 factor increases which is consistent with the relationship between the F1 factor and stiffness. The defl_{36} variable is in two terms where the net result of an increase in defl_{36} is an decrease in the F1 factor. The delta36 varies inversely with the subgrade stiffness, so as defl_{36} increases, the subgrade stiffness decreases and the ratio of the stiffness of the asphalt layer to the subgrade increases.
Use of the F1 basin factor generally will require that the calculated F1 values be adjusted for temperature. Temperature adjustment factors can be calculated by using the F1 equation to calculate an F1 for the pavement tested using the middepth asphalt temperature at the time of the test (T_{m}). The F1 is then calculated again using the middepth asphalt temperature, or reference temperature (T_{r}) that it is to be adjusted to. The Basin Adjustment Factor for F1, or BAFF1, is the F1 at the reference temperature divided by the F1 at the measured temperature. The functions can be used to build tables of adjustment factors, or to calculate adjustment factors on a casebycase basis.
Source code for implementing BAFF1 as a function in MS Excel VBA is available here.
Sample data for checking code is available here.
Topics: research, infrastructure, pavements and materials Keywords: research, infrastructure, pavements and materials TRT Terms: Pavements, AsphaltUnited StatesTemperature, Pavements, AsphaltPerformanceUnited States, LongTerm Pavement Performance Program (U.S.), Adjustment factors, Asphalt pavements, Backcalculation Updated: 04/07/2011
