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.