Constitutive model for shale

Presented is a new spherocylindrical microplane constitutive model that can capture the inelastic fracturing behavior of orthotropic materials, and particularly the shale. The basic idea is to couple a cylindrical microplane system to the classical spherical microplane system. Each system is subjected to the same strain tensor while their stress tensors are superposed. The spherical phase is similar to the previous microplane models for concrete and isotropic rock. The cylindrical phase, which is what creates the transverse isotropy, involves only microplanes that are normal to plane of isotropy, or the bedding layers, and enhance the stiffness and strength in that plane. This new model can reproduce all the five independent elastic constants of transversely isotropic shales, which are all positive if the elastic in-to-out-of plane moduli ratio is < 3.75 (this applies to all shales). Vice versa, from these constants, one can easily calculate all the microplane elastic moduli. Oriented micro-crack openings, frictional micro-slips and bedding plane behavior can be modelled more intuitively than with the spectral approach. Data fitting shows that the microplane resistance depends on the angle with the bedding layers non-monotonically, reaching a minimum at 30° to 60°. Finally, comparisons with extensive test data for shale validate the model.