Micromechanical modelling of bituminous materials' complex modulus at different length scales

The aim of this work is to establish a multi-scale modelling technique usable in the study of the complex viscoelastic properties of asphalt mixes. This technique is based on a biphasic approach. At each scale, the heterogeneous media is considered as a two-phase material composed of granular inclusions with linear elastic properties and a matrix of bituminous materials exhibiting linear viscoelastic behaviour at small strain values. In this approach, the homogeneous equivalent properties of biphasic composites are transferred from one scale of observation to the next, higher scale of observation. The viscoelastic properties of the matrix and the elastic properties of the aggregates serve as the input parameters for the numerical models. The generalised Maxwell rheological model is used to describe the viscoelastic behaviour of the matrix. Thanks to the rheological properties of bitumen and the elastic properties of the aggregates, the viscoelastic properties of mastic, mortar and hot mix asphalt (HMA) as bituminous composites can be, respectively, estimated using a micromechanical finite element model. Random inclusions of varying sizes and shapes are generated in order to construct the granular skeleton. A cyclic loading was imposed on the top layer of the digital model. The dynamic modulus of the pre-cited bituminous composites, obtained from the presented multi-scale modelling process while passing from the bitumen to the HMA scale, is validated by comparison with experimental measurements when possible. Concerning our results, we have found that at low temperature (-10 degrees C), the predicted dynamic modulus is satisfactorily comparable to the experimental measurements. On the other hand, an acceptable gap between predicted numerical results and experimental data takes place when the temperature increases.