Size dependency of Castlegate and Berea sandstone hollow-cylinder strength on the basis of bifurcation theory

A theoretical analysis of hollow-cylinder stability on the basis of the bifurcation theory is presented and the predicted scale effect with respect to the hollow cylinder inner-hole diameter is compared with experimental data of initial failure of Berea and Castlegate sandstone hollow cylinders. The two-dimensional analysis employs a Cosserat-Mohr-Coulomb flow theory of elastoplasticity model with friction hardening/cohesion softening calibrated on conventional triaxial compression test data for the two sandstones. The sensitivity of the stability predictions is evaluated by considering: (a) variations in the rate of cohesion softening, (b) two hollow cylinder outer-to-inner diameter ratios, and (c) loading configuration effects, that is external radial stress increase versus internal radial stress decrease under constant external radial stress.