A coupled elastic constitutive model for high porosity sandstone

An elastic constitutive model is developed to predict the mechanical unloading response for high porosity sandstone. The resulting model is sufficiently complex to represent known mechanical response, yet reasonably straightforward to calibrate. A mechanical dataset from a suite of true triaxial tests on Castlegate sandstone is used to develop, calibrate, and validate the model, which incorporates the experimentally observed evolutions of the elastic bulk and shear moduli with stress and plastic strain. Furthermore, to properly represent the hydrostatic unloading response, a coupled term is required, in which the plastic volume strain (accumulated during both hydrostatic and deviatoric loading) modifies the nonlinear stress dependence of the bulk modulus. Omission of this coupling term causes significant over prediction of the plastic volume strain and bulk modulus after complete unloading. However, the coupled term is not required to model deviatoric response and shear modulus evolution. While a suite of 28 tests was used to develop the model, only one carefully controlled test is required to calibrate the model for a chosen high porosity sandstone.