On the critical value of asphalt binder’s rheological index controlling the sign of the ΔTc parameter

The current Performance Grading system for asphalt binders in the USA determines limiting temperatures for binder selection. In practice, values of the creep modulus and/or its slope versus loading time, measured with the Bending Beam Rheometer (BBR), are used to determine the lowest acceptable temperature to avoid thermal cracking. However, current specifications are being challenged, and a new criterion, ΔT c , has been proposed to better predict binder resistance to thermal cracking. A recent study showed that ΔT c relates to other binder rheological properties, particularly the rheological index R defined in the Christensen–Anderson model. A theoretical critical value R c = 1.94 was predicted to control ΔT c : values above R c produce a negative ΔT c , while values below produce a positive one. Experimental data confirmed that R governs the sign of ΔT c , but the observed threshold was closer to 1.82. This discrepancy was attributed to the theoretical assumption of a constant glassy modulus of 3 GPa, which is known to be somewhat inaccurate. This short communication examines the mathematical origin of R c = 1.94 for a glassy modulus of 3 GPa and how the actual value of the glassy modulus affects the critical value R c of the rheological index.