Anisotropic microplane constitutive model for coupling creep and damage in layered geomaterials such as gas or oil shale

An anisotropic constitutive model for coupling creep with damage of shale and other anisotropic geomaterials under complex loading paths is formulated. The material damage is described by a previously developed spherocylindrical microplane model, which can simulate not only the stress-induced incremental anisotropy but also the inherent material anisotropy. Like material damage, the creep must be expected to be anisotropic as well. The creep responses of shale with inherent transverse isotropy are first separately constructed for the loading by compressive principal stress oriented either (i) parallel or (ii) normal to the bedding planes, and (iii) for shear stress along the bedding planes produced by the differences of the bedding plane inclination angle. This leads to three elementary linear creep models, which are mathematically formulated based on a continuous retardation spectrum of generalized Kelvin chain. These three creep responses are combined with the spherocylindrical microplane model. This leads to a general anisotropic constitutive creep model for arbitrary three-dimensional applied loading and arbitrary loading path. To achieve high numerical efficiency, a fully explicit numerical algorithm for the microplane constitutive model and finite element analysis is then formulated. Short-time (two-day) creep tests of shale cylinders with multilevel deviatoric stress and various inclinations of bedding planes relative to the axial compressive load are conducted. The numerical simulations by the microplane model are compared with the results of laboratory creep tests. The comparisons demonstrate a linear dependence of creep on the stress and verify the applicability of the anisotropic microplane model for creep and damage. Extensions to multi-year time ranges are in principle possible but will necessitate further calibration and verification.