Development of a Thermodynamically Consistent Constitutive Framework for Castlegate Sandstone

Development of accurate field-scale deformation models requires use of a constitutive framework that is capable of representing material behavior, and can be calibrated using available mechanical response data. This study focuses on the formulation of such a constitutive framework for Castlegate sandstone, which is a high porosity fluvial-deposited reservoir analog rock. In developing a constitutive framework, researchers must balance the complexity of the mathematics required to represent all aspects of mechanical response, with the ease of implementation. Central to this effort is identifying and modeling the most fundamental material behaviors. For Castlegate sandstone, experimentalists (e.g., AGU Abstract 30068, Issen et al.) report three behaviors that are essential in characterizing deformation response: 1) dependence of the moduli on stress (nonlinearity), 2) evolution of the moduli with plastic strain, and 3) non-normality of the plastic strain increment to the yield surface (non-associativity). This work employs the principles of hyperplasticity (e.g., Houlsby and Puzrin, 2006) to develop a thermodynamically sound constitutive framework for Castlegate sandstone. This requires selection of two potentials: 1) a thermodynamic potential (i.e., internal energy, enthalpy, Helmholtz function, or Gibbs' function) and 2) a dissipation function or yield surface. Furthermore, the elastic, plastic, and coupled strain increments are derived from these potentials. This study uses a Gibbs' function to define expressions for the evolution of the elastic moduli, from which elastic and coupled strain increments are determined. The yield surface in dissipative stress-space is used to derive the plastic strain increments. A key result of this formulation is that normality is predicted in dissipative stress space; this result is evaluated against experimental data from work discussed in AGU Abstract 30068, Issen et al.