Unified Nonlinear Elasto-Visco-Plastic Rheology for Bituminous Rocks at Variable Pressure and Temperature

Abstract

To address nonlinear constitutive relations of rocks containing soft matter such as bitumen, a rigorous rheological model based on Lagrangian mechanics is proposed. The model is general and applies to arbitrary quasi-static deformations in poroelastic or viscoelastic materials. As an application to bitumen-rich rock, the model is used for detailed modeling and inversion of laboratory measurements of linear and nonlinear creep in asphalt mastic. Several physically meaningful, loading-stress and temperature-dependent material properties are identified and inverted from laboratory observations. By presenting the data on the (strain, strain rate) plane, three distinct regimes of deformation are differentiated: viscoelasticity, linear plasticity (Newtonian viscous flow), and nonlinear plasticity (non-Newtonian flow). The model accurately predicts all measured creep data from which it was derived without hypothesizing empirical time-dependent properties of the material. In addition, the model predicts results of several new experiments: rapid unloading, measurement of effective time-dependent compliance, stress relaxation under static strain, and arbitrary controlled-strain or constant-strain-rate deformations. In constant-strain-rate experiments, peak stresses are measured and used as indicators of the onset of nonlinear creep. For a fixed temperature, these peak stresses fall on the same line in the strain-stress plane, and they are strongly related to rock properties.