Analytical study of subcritical crack growth under mode I loading to estimate the roof durability in underground excavation

Abstract The long-term stability of the roof is particularly important in designing underground rock structures. To estimate the durability of roof strata in underground excavation, a computation scheme of subcritical crack growth is proposed in this study. By adopting the proposed method (1) the potential collapse location of strata is derivable in accordance with a static model, (2) the durability of roof strata can be estimated, (3) a dynamic time step control strategy is achieved to balance the accuracy and speed of computing and (4) the initial crack size of rock can be estimated. In addition to the above, a mechanical model of underground excavation with non-uniformly distributed loads and partially yielded foundation is presented as the prototypical case. A set of case studies is carried out that showcase a power correlation between applied stress and roof durability. The allowable applied tensile stress for a 100-year life cycle is about 76% of the tensile strength. By using the proposed subcritical crack growth computation scheme, the roof stability in an underground excavation can be identified not only from the spatial view but also from the temporal perspective.