3. Relaxation Modulus and Complex Modulus

The main purpose of this chapter is to relate the relaxation modulus of bitumen through its stiffness modulus with the penetration index and the softening point of asphalt. In this chapter, the equations are derived for numerical and analytical evaluation of relaxation modulus and complex modulus of asphalt based on its stiffness modulus. An enhanced Hopkins-Hamming algorithm was proposed and applied for numerical converting the creep compliance based on stiffness to relaxation modulus of binder. The recursive formula for converting the creep compliance to relaxation modulus was derived which is applicable not only for bitumen but also for polymer modified binders. This chapter also describes the derivation of approximate analytical equation to predict the relaxation modulus of bitumen as a function of its penetration index, softening point, time and temperature. This chapter discusses different equations obtained for evaluation of dynamic modulus and phase angle for asphalt as a function of frequency of loading and temperature based on its penetration and softening point. Good agreement of predicted dynamic modulus, phase angle, and relaxation spectrum of bitumen with test data is illustrated. Method of conversion from the measured dynamic modulus of bitumen to its relaxation modulus was proposed.