Constitutive Modelling for High Porosity Sandstone: Castlegate Sandstone

Accurate field-scale deformation models require use of a constitutive framework that is capable of representing material behavior, and able to be calibrated using available mechanical response data. This study focuses on the formulation of such a constitutive framework for Castlegate sandstone, a high porosity fluvial-deposited reservoir analog rock. Experimentalists report that for high porosity sandstones, accounting for the evolution of the elastic moduli with stress and plastic strain is essential to properly represent deformation response. Hence, the principles of hyperplasticity (e.g., Houlsby and Puzrin, 2006) were employed to develop a thermodynamically consistent constitutive framework for high porosity sandstone. The mechanical data set of Ingraham et al. (2013) was then used to develop a specific constitutive model for Castlegate sandstone, adapted from that of Zimmerman et al. (1986). This study uses a Gibbs' function to define expressions for the evolution of the elastic moduli, from which recoverable and irrecoverable strain increments are determined. The yield surface in dissipative stress-space is also used to derive the plastic strain increments. Through systematic analysis of stress-strain unloading data for Castlegate, it was found that the bulk modulus evolved with mean stress and plastic volume strain during the hydrostatic portion of the loading. During the subsequent deviatoric loading, the shear modulus evolved with von Mises equivalent shear stress and plastic shear strain. With this understanding, expressions for the elastic moduli were formulated and subsequently assessed for thermodynamic consistency. Once thermodynamic consistency was confirmed, analytical and numerical techniques were applied to the mechanical data set to obtain explicit expressions and material parameters of the elastic moduli. These expressions were used to separate plastic strain from total strain. Yield surfaces were plotted using plastic strain data and expressions were derived for the yield surfaces in true and dissipative stress spaces, thus completing the constitutive framework. The key outcome of this study is a thermodynamically consistent constitutive framework for high porosity sandstone which accounts for the evolution of the elastic moduli with stress and plastic strain.