This article discusses the rheological tests and analyses based on the Schapery non-linear viscoelasticity model that were performed to study asphalt mastic behaviour under high shear stresses. Seven mineral filler types were applied in this study, including a mixed filler with hydrated lime and fillers derived from dust extraction systems. Determination of basic properties of the fillers was followed by creep and recovery tests (DSR) at different levels of shear stress conducted in accordance with a modified MSCR procedure. The first stage in the analysis was the identification of linear viscoelastic region and the non-linear viscoelasticity model parameters such as the length of the loading period, the temperature and the stress level using TTSSP (Time-Temperature- Stress Superposition Principle). Subsequent numerical simulations of strain variation with respect to stress confirmed a high degree of agreement between the non-linear viscoelasticity model and mastic sample behaviour. A strong correlation was found between the non-linear viscoelasticity parameters and mastic properties. The proposed methodology is able to quickly identify and eliminate the fillers that may contribute to HMA deformations.

A one-dimensional (1D) analytic example for dynamic displacement tracking in linear viscoelastic solids is presented. Displacement tracking is achieved by actuation stresses that are produced by eigenstrains. Our 1D example deals with a viscoelastic half-space under the action of a suddenly applied tensile surface traction. The surface traction induces a uni-axial shock wave that travels into the half-space. Our tracking goal is to add to the applied surface traction a transient spatial distribution of actuation stresses such that the total displacement of the viscoelastic half-space coincides with the shock wave produced by the surface traction in a purely elastic half-space. We particularly consider a half-space made of a viscoelastic Maxwell-type material. Analytic solutions to this tracking problem are derived by means of the symbolic computer code MAPLE. The 1D solution presented below exemplifies a formal 3D solution derived earlier by the present authors for linear viscoelastic solids that are described by Boltzmann hereditary laws. In the latter formal solution, no reference was made to shock waves. Our present solution demonstrates its validity also in the presence of singular wave fronts. Moreover, in our example, we show that, as was also indicated in our earlier work, the actuation stress can be split into two parts, one of them producing no stresses, and the other no displacements in two properly enlarged problems.