Predict the Phase Angle Master Curve and Study the Viscoelastic Properties of Warm Mix Crumb Rubber-Modified Asphalt Mixture

Abstract

To identify the most accurate approach for constructing of the dynamic modulus master curves for warm mix crumb rubber modified asphalt mixtures and assess the feasibility of predicting the phase angle master curves from the dynamic modulus ones. The SM (Sigmoidal model) and GSM (generalized sigmoidal model) were utilized to construct the dynamic modulus master curve, respectively. Subsequently, the master curve of phase angle could be predicted from the master curve of dynamic modulus in term of the K-K (Kramers–Kronig) relations. The results show that both SM and GSM can predict the dynamic modulus very well, except that the GSM shows a slightly higher correlation coefficient than SM. Therefore, it is recommended to construct the dynamic modulus master curve using GSM and obtain the corresponding phase angle master curve in term of the K-K relations. The Black space diagram and Wicket diagram were utilized to verify the predictions were consistent with the LVE (linear viscoelastic) theory. Then the master curve of storage modulus and loss modulus were also obtained. Finally, the creep compliance and relaxation modulus can be used to represent the creep and relaxation properties of warm-mix crumb rubber-modified asphalt mixtures.

Evaluation on the Performance of Hydraulic Bitumen Binders under High and Low Temperatures for Pumped Storage Power Station Projects

“…Frequency sweep test data at other temperatures were shifted horizontally to obtain a smooth master curve of the complex modulus as well as the phase angle [ 28 ]. The shift factors at various temperatures were usually described by using the Arrhenius equation [ 29 ]. where: α T = Temperature shift factor; T = Test temperature, K; Δ Ea = Apparent activation energy, kJ/mol; R = Universal gas constant, R = 8.314 J/(K·mol).…”

“…However, it should be noted that the Arrhenius equation has its limit to fit at a wide temperature range between −10 °C and 70 °C. In particular, a slight deviation between the model prediction and the actual value was found at −10 °C [ 29 ].…”

Reliability of Calculation of Dynamic Modulus for Asphalt Mixtures Using Different Master Curve Models and Shift Factor Equations

“…To construct the master curves deriving from the experimental data, the nonlinear least squares regression analysis was integrated in the Microsoft Excel Solver tool. The Sum of Square Error (SSE) between measured values after shifting, |E*| measured , and predicted values, |E*| predicted , as shown in Equation (10) was used for the fitting procedure.…”

“…The SLS model can more accurately fit the dynamic modulus test data in a wider temperature range than a single polynomial model [7,8]. However, the SLS model is more applicable when test data are symmetrical, whereas the Generalized Logistic Sigmoidal (GLS) model developed by Rowe et al is better employed to fit asymmetric data [9,10]. Moreover, Marasteanu and Anderson proposed a Christensen-Anderson-Marasteanu (CAM) model based on the Christensen-Anderson (CA) formulation [11], which provides a better fit of the dynamic modulus of asphalt mixtures within very low and very high frequencies for unmodified and polymer modified bituminous binders [12][13][14].…”

“…The Arrhenius equation is another popular model used to describe the temperature dependence of viscoelastic properties of materials. The WLF and Arrhenius equations focus on the volume processes and the thermally activated processes, respectively [10,22]. In addition to the above two methods, the log-linear equation can also describe the temperature dependence of asphalt materials [7].…”