Fracture mechanics and subcritical crack growth approach to model time-dependent failure in brittle rock

Abstract

Subcritical crack growth (SCG) takes place when a crack is stressed below its short-term strength. This slow fracturing process may lead to an accelerating crack velocity and to a sudden unstable failure event. SCG is thought to play an important role in long-term rock stability at all scales, ranging from laboratory samples to earthquake-generating faults. SCG can be detected as rock loosening or as sudden rock movements around excavations. A time-dependent crack growth model is developed to evaluate the delayed failure of a loaded rock. It is based on brittle fracture mechanics principles and the theory of subcritical crack growth (stress corrosion). The SCG model was incorporated in the Boundary Element (DDM) software FRACOD. The fracture mechanics code with the SCG model provides a reasonable description of the failure process. New crack formation, slow and fast fracture propagation, stress relaxation and time-dependent failure are considered both in tensional and compressive loading conditions. For brittle rock material the model suggests that stable wing-crack propagation takes place under an increasing uniaxial load prior to crack coalescence and extensive unstable fracture propagation. The rupture of a rock specimen is dominated by the formation of large shear fractures. Fracture dilation occurs in the late post-peak phase of failure. The modelled post-peak axial stress-strain response of brittle rocks shows Class II behaviour and it is explained by the Griffith locus. The effect of time on the load-bearing capacity of the Äspö diorite has been investigated in the laboratory by slow-rate loading experiments (SRS tests). Modelled time-dependent failure behaviour agrees well with laboratory findings. The modelling suggests that negligible amounts of SCG are involved in standard uniaxial and triaxial compressive strength tests, while for the SRS tests the time-dependent effects are significant. The modelled long-term load-bearing capacity is not decreased severely when the applied load is below 80% of the short-term peak strength. The confinement increases the required stress/strain level for failure but do not affect the shape of the time-to-failure curve.