The model for damaged asphalt concrete modulus used in CalME follows the relationship previously given in Equation 1:
Equation 4: Modulus of damaged asphalt concrete.
where the damage, ω, is calculated from:
Equation 5: Damage as a function of load applications, strain, modulus and temperature.
| Where |
MN is the number of load applications in millions,
με is the tensile strain at the bottom of the asphalt layer,
E is the modulus,
Ei is the modulus of the intact material,
tr is reduced time, and
A, α, β, γ, and δ are constants (not related to the constants of Equation 4). |
The constants of Equation 5 were determined from four point bending beam tests, at constant strain at a temperature of 20 °C. The value of γ was fixed at β/2, making the damage a function of strain energy. The parameter δ was based on the parameter for initial asphalt moduli in the Asphalt Institute criterion for asphalt fatigue. With this criterion the damage will be proportional to the initial modulus raised to -α times -0.854 (= 0.854×α). This results in positive values of δ, between 0.3 and 0.5, where the results of fatigue testing at different temperatures indicated a negative value of -1.9. Using the value from fatigue testing done at temperatures different from 20 °C resulted in damage being predicted in the warm periods, where the observed damage occurred mostly during relatively cold periods. The reason for this difference between the laboratory and the in situ damage is not known.
The permanent deformation of the asphalt is partly due to a decrease in air voids caused by post compaction and partly to shear deformation. The average decrease in air voids over the first 12 months of the experiment, ΔAV, for the top and bottom lifts combined based on measurements from cores, was found to be:
Equation 6: Average decrease in air voids.
This decrease was used in the simulations with CalME. It was assumed to occur over the first 60 days with traffic loading and was added to the shear deformation.
The majority of the permanent deformation of the asphalt was due to shear deformation. A shear-based approach, developed by Deacon et al. (2002), was used. The permanent, or inelastic shear strain, γi, is determined from RSST-CH tests as a function of the shear stress,τ, the elastic shear strain, γe, and the number of load repetitions. The best fitting relationship for the materials used was found to be a power function as follows:
Equation 7: Power function for permanent shear strain.
| Where |
γe is the elastic shear strain,
τ is the shear stress,
MN is the number of load repetitions in millions,
τref is a reference shear stress (0.1 MPa), and
A, α, and β are constants determined from the RSST-CH (constants are not related to those in Equation 5) |
The constants should be determined at an air voids content corresponding to post compaction. The permanent deformation of the asphalt is calculated from:
Equation 8: Calculation of permanent deformation.
| Where |
K is a calibration factor (determined from HVS testing or actual field asphalt rutting data),
hi is the thickness of layer i, and
γii is the inelastic (permanent) shear strain in layer i calculated from Equation 7 |
The summation is done for the top 100 mm of the asphalt where the majority of the permanent deformation in the asphalt has been observed to occur.
The permanent deformations of the aggregate base and of the subgrade were calculated using the model described in Ullidtz et al. (2007). The contributions to the permanent deformation from these layers were small and in good agreement with the observations from the WesTrack experiment.
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