Related Experiment Video
Updated: Sep 6, 2025

Determination of the Friction Coefficients of Icy Pavements Under Different Amounts of Snowfall
Published on: January 6, 2023
Reliability of Calculation of Dynamic Modulus for Asphalt Mixtures Using Different Master Curve Models and Shift
Hao Chen1, Diego Maria Barbieri1,2, Xuemei Zhang1
1Department of Civil and Environmental Engineering, Norwegian University of Science and Technology, Høgskoleringen 7A, 7491 Trondheim, Norway.
Abstract:
To develop a mechanistic-empirical pavement design system for Norwegian conditions, this paper evaluates the influence of the adoption of different models and shifting techniques on the determination of dynamic modulus master curves of asphalt mixtures. Two asphalt mixture types commonly used in Norway, namely Asphalt Concrete (AC) and Stone Mastic Asphalt (SMA) containing neat bitumen and polymer-modified bitumen, were prepared by the roller compactor, and their dynamic moduli were determined by the cyclic indirect tensile test. The dynamic modulus master curves were constructed using the standard logistic sigmoidal model, a generalized logistic sigmoidal model and the Christensen-Anderson-Marasteanu model. The shifting techniques consisted of log-linear, quadratic polynomial function, Arrhenius, William-Landel-Ferry and Kaelble methods. The absolute error, normalised square error and goodness-of-fit statistics encompassing standard error ratio and coefficient of determination were used to appraise the models and shifting methods. The results showed that the standard logistic sigmoidal model and the Williams-Landel-Ferry equation had the most suitable fits for the specimens tested. The asphalt mixtures containing neat bitumen had a better fit than the ones containing polymer-modified bitumen. The Kaelble equation and log-linear equation led to similar results. These findings provide a relevant recommendation for the mechanistic-empirical pavement design system.
Related Concept Videos
Dynamic Modulus of Elasticity of Concrete
The sonic test is a common method to determine the dynamic modulus. In this test, a concrete beam, sized either 6 x 6 x 30 inches or 4 x 4 x 20 inches, is clamped at its center. Vibrations are initiated at one end of the beam by an electromagnetic exciter unit powered by...
Elasticity in Concrete
Moisture Content and Bulking of Aggregate
When aggregates are exposed to rain or sit in stockpiles, they absorb moisture, which must be...
Elastic Curve from the Load Distribution
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments.
Design Example: Managing Concrete Workability
Design Example: Aggregate Gradation
The grading, or particle-size distribution, of sand is determined using sieve analysis, with standard sizes ranging from 150 μm to 10 mm (ASTM No. 100 sieve to 3⁄8 in. sieve). Sand is...

