Three-dimensional elastoplastic modelling for deformation property of sandstone with dilatancy

Abstract

Due to the development of plastic strains, the strain path within the meridian plane deviates from the reference line corresponding to elastic state. Similarly, under true triaxial stress conditions, the strain path within the deviatoric plane deviates from the reference line corresponding to the constant Lode angle. This deviation is attributed to the plastic shear strain associated with the Lode angle. To account for these phenomena, a novel three-dimensional elastoplastic constitutive model incorporating Lode angle is proposed to characterize the deformation behavior of sandstone. The yield and potential functions within this model incorporate parameters that vary with the plastic internal variable, enabling the evolution of the yield and plastic potential surfaces in both the meridian and deviatoric planes. The comparison between experimental data and the analytic solution derived from the constitutive model validates its reliability and accuracy. To examine the differences between yield surface and plastic potential surface, a comparison between the associated and non-associated flow rules is conducted. The results indicate that the associated flow rule tends to overestimate the dilatancy of sandstone. Furthermore, the role of Lode angle dependence in the potential function is explored, highlighting its importance in accurately describing the rock's deformation.