Growth of plastic zone around boreholes is described in a model with post-failure non-linear power-like strain softening. The failure itself is defined by conventional Mohr-Coulomb criterion. Growth of plastic zone around the inner opening is considered for a hollow (thick-wall) cylinder geometry. It is found that the growth of plastic zone as a function of the outer load is not unlimited but encounters a terminal instability before reaching the outer boundary of hollow cylinder. Without post-failure softening the plastic zone growth does not encounter that type of instability except for the trivial one when the plastic zone spreads throughout the sample to the outer boundary. This terminal instability is reached at some critical load, and plastic zone cannot grow further at a higher load. Instead the plastic zone experiences a brittle failure, and only after that the entire cylinder collapses. It is shown that the terminal instability is characterized by singular response to the load of Considére type. The critical load and final size of plastic zone depend on the softening parameters. Softening-oriented measurements in triaxial tests on stiff machines can provide parameters of post-failure softening and allows us to predict terminal failure in hollow (thick-wall) cylinder samples under load. The model also provides geometric scaling of the data obtained in hollow (thick-wall) cylinder test, and applied for sand production prediction.
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