Elastoplastic Damage Modeling of Rock Spalling/Failure Induced by a Filled Flaw Using the Material Point Method (MPM)

The spalling/failure of rocks often occurs at the underground opening surface during excavation activities, which may also be seriously affected by geological conditions such as joints and cracks. The nearby joints are usually filled with materials such as mortar or concrete to improve the stability of the opening surrounding rocks. To study the rock spalling/failure induced by a filled flaw, we adopt the weighted least squares material point method framework where a coupled Drucker-Prager plasticity and Grady-Kipp damage model is used to capture the mixed tensile-shear failure, and a particle-to-surface contact formulation is employed to model the contact interaction between the filled flaw and surrounding rocks. The framework is benchmarked using a series of cases involving circular opening, penny-shaped crack, and crack propagation, which shows a good agreement between the analytical, experimental, and numerical results. Simulations of plane strain compression tests for an arch-shaped tunnel opening under different geological conditions are also performed, where the rock spalling process is numerically reproduced by the sequential appearance of multiple cracks initiated from the opening surface. We show that the filling exacerbates the spalling at the tunnel left spandrel and induces new mixed shear-tensile cracks connected from the flaw toe to the tunnel corner, and massive collapse could occur at the tunnel left waist when the area formed by the spalling and band failure at the tunnel left spandrel and corner is connected to the filler. Our results suggest that our proposed MPM framework is an attractive alternative for the study of rock spalling/failure for underground openings.