Effect of Construction Methodology on Uncertainty in Asphalt Concrete Mastercurves

Abstract

Viscoelastic properties [i.e., creep compliance D(t) and relaxation modulus E(t)] are significant input parameters in constitutive modeling of asphalt concrete (AC). Because application of input and recording the response of a smooth function (like sinusoid) is convenient, researchers have resorted to determination of dynamic modulus (|E*|) and phase angle (ϕ) of AC. These |E*| and ϕ values observed over range of temperatures and frequencies are subsequently used in (1) construction of |E*| and ϕ mastercurves, and (2) conversion into D(t) and E(t) mastercurves. Even under strict quality control, specimens prepared with the same AC mixture show significant variation in material response due to specimen fabrication, instrumentation, and testing issues. Further, various numerical approximations arise during usage of interconversion procedures. Thus, it is inevitable to encounter significant scatter in finalized D(t) and E(t) mastercurves. Under these circumstances, uncertainty quantification techniques offer an efficient approach to handle such scatter. This article critically evaluates the effect of (1) various temperature shift factor determination approaches [i.e., free-shifting approach, Arrhenius-type equation, William-Landel-Ferry (WLF) equation, and Kaelble equation], and (2) the functional form of mastercurve (symmetric and asymmetric) adopted on the resulting uncertainty in D(t) and E(t) responses. Uncertainty in finalized mastercurves was quantified using mean, coefficient of variation, percentile, and normalized uncertainty range. The results indicate that uncertainty at any particular reduced time is dependent primarily on the mastercurve construction method. In other words, the temperature shift factor determination approach and functional form of the sigmoid function play important roles in uncertainty quantification. Based on these uncertainty quantification parameters, various mastercurve construction methods were ranked. Based on this ranking, for a given sigmoidal function, use of Kaelble, Arrhenius, WLF, and free-shifting approach results in least to highest uncertainty. Further, for a given temperature shift factor, the symmetric sigmoidal function results in higher uncertainty compared with the asymmetric sigmoidal function. This ranking can be attributed to the flexibility offered by individual construction methodologies.