Analytical solutions of near-borehole stress–strain responses are often based on simple elastic-perfectly plastic constitutive models. However, such models are incapable of capturing rock softening, and thus often disagree with observed failure patterns. Therefore, in this study, we present a set of closed-form solutions to estimate the stress–strain response around a borehole in a finite medium obeying elastic-softening-plasticity. Solutions are presented for material subject to either Mohr–Coulomb (M–C) or Hoek–Brown (H–B) failure criteria. The proposed analytical solutions define two failure surfaces to capture the peak and residual stress states, which are linked by a softening law. We demonstrate how to identify these two surfaces by first conducting a set of triaxial tests on a sandstone sample to differentiate the deformation stages. The proposed methodology provides a practical approach to characterize the strain-softening response with good accuracy. Finally, the proposed analytical solutions are validated through comparisons with (a) numerical simulations and (b) hydrostatic experiments on hollow-cylinder sandstone samples analysed using Digital Image Correlation. The strain development and interfaces calculated from the proposed model are in good agreement with the experimental and numerical data.
- Analytical solution
- Constitutive model
- Digital Image Correlation (DIC)