Cam-Clay plasticity. Part IX: On the anisotropy, heterogeneity, and viscoplasticity of shale

We investigate three aspects of material behavior in this ninth installment of the Cam-Clay series, namely, anisotropy, heterogeneity, and viscoplasticity. The main focus of the paper is creep in shale and how this time-dependent deformation behavior may be quantified across the scales, from nanometers to millimeters. Recognizing the highly heterogeneous nature of shale, we adopt a simplified representation of this material as a mixture of softer matter representing organics and clay, and harder matter representing the inorganic rock matrix. Due to the presence of bedding planes in the rock matrix, anisotropy in both the elastic and inelastic responses is assumed; however, the superimposed softer matter may be taken to be isotropic unless experimental evidence indicates otherwise. Viscoplasticity is considered for the first time in this series of work, in which both the Duvaut–Lions and Perzyna formulations are utilized. The two viscoplastic formulations are shown to predict very similar time-dependent deformation responses. The framework is used to interpret the results of multiscale triaxial laboratory creep tests in organic-rich Barnett shale. Time-dependent strain localization in the form of dilative shear bands is also shown to result from loading with varying strain rates, as well as from creep processes that accommodate the multiscale heterogeneity of shale.