A comparative study of temperature shifting techniques for construction of relaxation modulus master curve of asphalt mixes
Introduction
Asphalt mixtures are thermorheologically simple materials [1]. In other words, it is possible to utilize the time–temperature superposition principal to determine the viscoelastic behavior of asphalt mixes in a wider range of time and temperature than those used for testing [2]. Several temperature shifting techniques have been developed for asphalt mixes according to the time–temperature superposition principal [2]. Among the most important temperature shifting techniques, used for asphalt mixes, are the Numerical, Log-Linear, Williams-Landel-Ferry (WLF), Modified Kaelble, and Arrhenius methods [2], [3], [4]. The mentioned techniques are empirical in nature, and usually show different results for the asphalt mixes, having the same mix characteristics, under the same testing conditions.
Almost all the earlier researches on characterizing the viscoelastic behavior of asphalt binders and mixes have been conducted using only one of the mentioned temperature shifting techniques [5], [6], [7], [8], [9], [10]. By contrast, comparatively little work has been undertaken for the asphalt binders [11] and no work for the asphalt mixes to compare various shifting techniques and to rank them regarding their relative ability to provide an excellent fitness to the experimental data. Therefore, this research was undertaken to compare and rank the different temperature shifting techniques among various asphalt mixes.
In order to more accurately evaluate and compare the temperature shift factors resulted by the above mentioned techniques, it was first necessary to gather a data base including the tensile relaxation modulus test results for a variety of asphalt mixtures, having different mix characteristics, at various temperatures and different aging conditions. For this purpose, direct tension relaxation modulus tests were conducted on the dense graded asphalt mixtures, commonly used in binder and wearing courses, at different temperatures and aging conditions, and the tensile relaxation modulus master curves of each mixture were constructed using all the mentioned shifting techniques. Finally, the temperature shift factors determined from each shifting technique were compared using both the graphical and statistical approaches.
Section snippets
Temperature shifting techniques
Among the above mentioned temperature shifting techniques, the non-functional Numerical method, having the highest degree of freedom, provides the best fitness to the experimental data; while the other methods, all of which are on the basis of some empirical equations, have lower degrees of freedom. Therefore, they are usually unable to provide an excellent fitness to the experimental data [11].
Numerical technique is a non-functional method in which no equation is used to determine the shift
Material properties
Two aggregate gradations, having the Maximum Nominal Aggregate Sizes (MNAS) of 25 mm and 19 mm, were used to comply with the gradation specifications of the dense graded binder and wearing courses respectively [18]. The gradations used in this study and the gradation limits are plotted in Fig. 1, Fig. 2. The 60/70 penetration bitumen was also used as asphalt binder for preparation of the specimens.
Specimen preparation
Five variables, aggregate gradation, binder content, air void level, aging condition, and
Graphical and statistical representations
Fig. 5, Fig. 6, Fig. 7 graphically compare the shift factors resulted by the Numerical method to those obtained by the Log-Linear, WLF, Modified Kaelble, and Arrhenius techniques for the specimens having different mix characteristics, i.e. aggregate gradation, binder content, and air void level. The same comparisons are also presented on Fig. 8 for the shift factors determined at different reference temperatures, i.e. −7, +4, +14, and +21 °C. In addition, Fig. 9 shows similar comparisons for the
Conclusion
This research was undertaken to investigate the effects of different variables, i.e. mix characteristics, aging condition, and reference temperature, on the rank order of various temperature shifting techniques including the non-functional Numerical, Log-Linear, Williams-Landel-Ferry (WLF), Modified Kaelble, and Arrhenius methods. For this purpose, the relaxations modulus master curves were constructed using the Generalized Logistic Sigmoidal Model, and the temperature shift factors obtained by
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