A time-dependent microplane model for deformation and fracturing of brittle rock

A more comprehensive understanding of the progressive, time-dependent deformation and fracturing of brittle rock is crucial for assessing the long-term integrity of rock masses surrounding engineering structures. In this study, we propose a three-dimensional numerical model that integrates the microplane model and subcritical crack growth to investigate the progressive, time-dependent deformation and fracturing of brittle rock. The model incorporates subcritical crack growth and time-dependent damage evolution constitutive laws into the microplanes. By following the trend of subcritical crack growth observed in previous studies, the model accurately captures the time-dependent propagation of virtual cracks. The cooperative interaction between strain and damage evolution on the microplanes ultimately leads to localized material degeneration over extended time. Moreover, this model effectively characterizes the temporal and spatial distribution of damaged elements during time-dependent deformation and fracturing of brittle rock. The numerical simulations successfully replicate phenomena observed in laboratory experiments performed on brittle rock. Specifically, they demonstrate how different stress levels influence creep strain rate and time-to-failure. Additionally, the simulations reveal that the microscale interaction of potential cracks (microplanes) can effectively describe the complex macroscopic time-dependent behavior of brittle rock. As a result, it becomes possible to predict time-to-failure and rupture patterns using the calibrated model based on laboratory tests. The proposed numerical model holds the potential to be further extended for predicting the long-term stability of larger rock masses.