Genetic programming to formulate viscoelastic behavior of modified asphalt binder

The objective of this research was to develop prediction models for complex shear modulus (G*) and phase angle (δ) of bitumens modified with crumb rubber, styrene-butadiene styrene, and polyphosphoric acid at low and moderate temperatures. The experiments consisted of three different dosages of each modifier added to the original bitumen followed by measurement of G* and δ of the original and modified bitumen using the dynamic shear rheometer (DSR) test in frequency sweep mode (21 loading frequencies from 0.1 to 100 Hz) at seven test temperatures: −22, −16, −10, 0, 10, 16 and 22 °C. Having the experimental database, a robust genetic programming (GP) method was used to develop an individual prediction model for each modifier based on temperature, loading frequency, the G* and δ of the original bitumen, and the dosage of the modifier. Results showed that GP successfully developed accurate and meaningful expressions for calculating G* and δ of the modified bitumen as two main constitutive components of the viscoelastic behavior of bituminous composites. Then, a parametric study and sensitivity analysis were performed on the developed models to better understand the effect of variables on the trend of the models. The modifier dosage is the most effective input variable of the model and the amount of G* and δ of the original bitumen accurately reflect the effect of temperature and loading frequency on viscoelastic behavior of the modified bitumen, as they behave linearly at the considered test temperatures.