Reflection cracking damage was calculated using the method developed by Wu (2005). In this method the tensile strain at the bottom of the overlay is estimated using a regression equation. The calculated tensile strain at the bottom of the overlay is used with the fatigue equation to calculate damage in the asphalt layers.
The regression equation for tensile strain at the bottom of the overlay is based on many 2D and 3D finite element calculations, and assumes a dual wheel on a single axle:
Equation 1: Strain, in μstrain, over existing crack
| Where |
Ea is the modulus of the overlay,
Ha is the thickness of the overlay,
Eu is the modulus of the underlayer,
Hu is the thickness of the underlayer,
Eb is the modulus of the base/sub-base,
Es is the modulus of the subgrade,
LS is the crack spacing,
σo is the tire pressure, and
a is the radius of the loaded area for one wheel. |
The following constants were used:
α = 342650, β1 = -0.73722, β2 = -0.2645, β3 = -1.16472, a1 = 0.88432, b1 = 0.15272,
b2 = -0.21632, b3 = -0.061, b4 = 0.018752.
To predict reflection cracking, the resulting strain was used with the model for the master curve of the damaged asphalt, which has the format:
Equation 2: Modulus of damaged asphalt
where δ, α, β, and γ are constants, tr is reduced time in sec and the damage, ω, is calculated from:
Equation 3: Damage as a function of number of loads, strain, and modulus
| Where |
E is the modulus of damaged material,
Ei is the modulus of intact material,
MN is the number of load repetitions in millions (N/106),
με is the strain at the bottom of the asphalt layer in μstrain,
SE is the strain energy, and
A, A’,α, β, μεref, Eref, and SEref are constants |
The initial (intact) modulus, Ei, corresponds to a damage, ω, of 0 and the minimum modulus, Emin=10δ, to a damage of 1. |
