The time to failure of rocks under load is governed by various factors such as rock structure including voids and fracture, loading rate and magnitude, boundary conditions, environmental conditions, and so on. The lifetime could be predicted by either empirical exponential laws or physical laws based on damage and fracture mechanics but the integration from the characterization to the modeling is not firmly established. The authors developed continuum numerical model with the subcritical crack growth test and acquisition of parameters from the laboratory test. The developed model was based on subcritical crack growth and damage mechanics considering practical applications in 2 and 3-dimensional numerical modeling of time-dependent behavior. The algorithm considers both mode-I and mode-II fracturing. Each zone or element contains a random damage state variable. Damage growth is controlled by the modified Charles equation. Macroscopic failure is the results of the coalescence of growing damaged elements. The proposed model was applied to the mode-I and mode-II subcritical crack growth test carried out in the laboratory. The comparison shows that the model describes the time-dependent behavior well. In addition, the accumulation of damaged element during the loading period can be an indicator for the instability of rock like an AE (Acoustic Emission) in a laboratory test.
The time to failure of rocks under load is governed by various factors such as rock structure including voids and fracture, loading rate and magnitude, boundary conditions, environmental conditions, and so on. The lifetime could be predicted by either empirical exponential laws or physical laws based on damage and fracture mechanics. A few research works on subcritical crack growth (SCG) modelling had been published in spite of its importance (Konietzky et al., 2009; Li and Konietzky, 2015; Potyondy, 2007; Rinne et al., 2004). FRACOD can directly simulate crack initiation and propagation under a subcritical crack growth condition in 2D space (Rinne et al., 2004). Stress-corrosion model implemented using PFC can simulate crack initiation and propagation in 2D and 3D space but the subcritical crack growth is limited within mode-I (Potyondy, 2007). FLAC based subcritical crack growth model can indirectly simulate time-dependent behavior using fictitious crack within each element in 2D space but an extension to 3D space is not straightforward.
The authors developed continuum 2D and 3D model to simulate time-dependent behavior of rock like material under mode-I, mode-II and mixed configurations as well as to apply to engineering problems.
Subcritical crack growth parameters are based on fracture mechanics but there is an equivalent crack concept that describes the incremental damage accumulation based on damage mechanics is equivalent to incremental crack growth based on fracture mechanics as shown in Fig. 1 (Legendre et al. 1984; Xie, 1993). Then, a formulation in 2D and 3D domain is almost same because the damage variable is a scalar.
The formulation of damage model from the subcritical crack growth model is straightforward under the equivalent crack concept.