Creep-Life for Brittle Rocks Subjected to Uniaxial Compression: a Theoretical Investigation

The failure and damage of brittle rock is attributed to crack development, there is crack propagation inside the brittle rock even the applied stress is lower than the rock strength. Establishing the theoretical relationship between the external loading and the local stress that around the crack is not only helpful for understanding the mechanisms underlying the creep behavior of brittle rock, but also offers the possibility of theoretically estimating the creep-life of brittle rock. In this paper, the cracks in the cylindrical rock specimen are assumed to be uniformly distributed and penny-shaped with their major axes parallel to the axial direction of the cylindrical rock specimen, the creep-life of brittle rock refers specifically to the total time consumed in the subcritical crack growth stage. The expressions and direction of the local stresses around the crack tips are derived based on dividing the local stress into two parts. The phenomenon of brittle rock exhibiting tensile failure under the uniaxial compression is preliminarily explained. The crack propagation rate that directly related to the local tensile stress is derived. The requirements for subcritical crack growth are theoretically analyzed. A new expression of creep-life of brittle rock with a clear physical meaning and the key parameter “ $$\Psi $$ ” is established. Considering that the theoretical studies on estimating the creep-life of brittle rock are rare, and the experiments related to the creep-life are very time-consuming. Therefore, this study may provide an effective approach for theoretically estimating the creep-life of brittle rock under the given uniaxial compressive stress state.