Abstract
Borehole failure under anisotropic stresses in a sandstone is analyzed numerically for various borehole
sizes using a nonlinear elastic–plastic constitutive model for a Cosserat continuum. Borehole failure is
identified as macroscopic failure of the borehole through the development of shear bands and breakouts.
The results compare well both qualitatively and quantitatively with experimental results from polyaxial tests
on Red Wildmoor sandstone. They show that the hole size effect of the borehole failure strength is
independent of the far-field stress anisotropy and follows a 2/5 power law of the hole size. A similar scale
effect equation with a 4/5 power law is proposed for the scale effect of the maximum plastic shear strain
at failure. This equation can be useful for better predicting hole-size-dependent failure with standard
codes based on classical continua. The effect of stress anisotropy on the borehole failure stress is found
to be independent of the hole size. The failure stress decreases linearly to 40% as the stress anisotropy
increases. However, the maximum plastic shear strain at failure is stress anisotropy independent and
therefore the critical plastic shear strain for failure is only hole-size dependent.
sizes using a nonlinear elastic–plastic constitutive model for a Cosserat continuum. Borehole failure is
identified as macroscopic failure of the borehole through the development of shear bands and breakouts.
The results compare well both qualitatively and quantitatively with experimental results from polyaxial tests
on Red Wildmoor sandstone. They show that the hole size effect of the borehole failure strength is
independent of the far-field stress anisotropy and follows a 2/5 power law of the hole size. A similar scale
effect equation with a 4/5 power law is proposed for the scale effect of the maximum plastic shear strain
at failure. This equation can be useful for better predicting hole-size-dependent failure with standard
codes based on classical continua. The effect of stress anisotropy on the borehole failure stress is found
to be independent of the hole size. The failure stress decreases linearly to 40% as the stress anisotropy
increases. However, the maximum plastic shear strain at failure is stress anisotropy independent and
therefore the critical plastic shear strain for failure is only hole-size dependent.
