Application of Particulate-Filled Composite (PFC) Theory to Hot-Mix Asphalt (HMA) Mixtures

Dynamic modulus (|E*|) of HMA mixtures is one of the fundamental engineering properties measured by the Simple Performance Tester (SPT) and has been incorporated as a basic input parameter in the American Association of State Highway and Transportation Officials (AASHTO) 2002 Mechanistic-Empirical (M-E) Design Guide for flexible pavement design. Although direct laboratory testing and empirical equations (such as the Witczak model and the Hirsch model) provide two ways to obtain the values of dynamic modulus of HMA mixtures, a predictive model based on the microstructure of HMA mixtures is more desirable. HMA mixtures consist of three phases: aggregate, asphalt binder (or mastic), and air voids. During the blending process of HMA mixtures, every aggregate particle, regardless of its size, is coated with a thin film of asphalt mastic. Therefore, the resulting mixture can be considered as a particulate-filled composite (PFC) with aggregate particles dispersed in the asphalt matrix. Consequently, the theoretical approaches for PFC can be applied to HMA mixtures. This study presents an attempt to apply PFC models to predict the dynamic modulus of HMA mixtures. A three-dimensional two-layered model and several models from the differential method were developed and formulated. These PFC models have the ability to take into account the particular characteristics of HMA mixtures: the viscoelastic nature, aggregate gradation, and air voids. Laboratory experiments were conducted to evaluate the applicability of the newly developed and some currently existing PFC models to HMA mixtures. Dynamic shear rheometer (DSR) testing was conducted on asphalt binder and mastic for their dynamic shear moduli. HMA mixture was tested for its dynamic modulus. PFC models were first applied to predict dynamic shear modulus of asphalt mastic with the measured dynamic shear modulus of asphalt binder as input parameter. The predicted dynamic shear moduli of asphalt mastic from all PFC models were fairly close to the measured results. Then, the PFC models were used to predict the dynamic modulus of HMA mixtures with dynamic shear modulus of asphalt binder or mastic as an input parameter. The predicted dynamic modulus values of HMA mixtures were found to deviate from the measured data to varying degrees. The reasons for the discrepancy between the predicted and measured dynamic moduli were analyzed. Sensitivity analysis was conducted to explore the effects of different factors on dynamic modulus of HMA mixtures

A further characteristic of abstract convexity structures on topological spaces

AbstractIn this paper, we give a characteristic of abstract convexity structures on topological spaces with selection property. We show that if a convexity structure C defined on a topological space has the weak selection property then C satisfies H0-condition. Moreover, in a compact convex subset of a topological space with convexity structure, the weak selection property implies the fixed point property

Generalized Chiral Kinetic Equations

We derive the generalized chiral kinetic equations which are applicable to the fermions with arbitrary mass. We show how the dynamical magnetic-moment distribution function could lead to spin polarization and electric charge separation. We also show how the electric/magnetic moment distribution and pseudoscalar distribution could be induced by vorticity and acceleration in global equilibrium.Comment: 6 pages, no figure