Mechanisms of creep in shale from nanoscale to specimen scale

Creep in shale is a multiscale deformation process across both space and time. In this paper, we propose a scale-bridging technique linking creep phenomena in shale from nanometer scale to specimen scale, and explore the mechanisms of creep at different scales. To this end, we simulate indentation tests on Woodford shale at the nanometer and micrometer scales using an incremental frictionless multi-body contact algorithm based on the Lagrange multipliers method, along with a recently developed Cam-Clay IX constitutive framework that explicitly recognizes the inherent heterogeneity of the rock material. Simulation results suggest that creep of the sample is mostly attributed to the viscoplastic deformation of the material away from the indenter tip, and that such response is highly dependent on the stress rate during the loading stage. Furthermore, simulations of triaxial creep indicate that creep behavior of the bulk sample is dominated by the presence of organics and clay constituents, and that such behavior follows a widely used logarithmic law. Throughout this work, we address the issues of heterogeneity across scales, anisotropy arising from the presence of bedding planes, and viscoplasticity of the individual constituents as they relate to the time-dependent properties of the bulk shale sample.