Research on Crack Propagation of Deep Geologic Mass Disturbed by Excavation Based on Phase Field Method

Abstract

In recent years, the phase field fracture model has been widely studied and applied. It has good convergence in crack propagation simulation. Comparing with other methods, the phase field method has advantages in simulating crack intersection, bifurcation, and three-dimensional propagation. Based on the phase field method, the influence of excavation disturbance on crack initiation of rock mass is realized in this paper. The phase field fracture variational model is built by using user-defined element interface (UEL) and user material subroutine (UMAT) in ABAQUS. Firstly, the prefabricated crack propagation simulation is carried out to verify the algorithm. The fracture initiates in a butterfly shape and then expands along the horizontal direction. The results show that the maximum support reaction decreases with the gradual increase of l , which is compared with the results obtained by Miehe et al. The result proved the correctness and reliability of the algorithm. In this paper, the phase field fracture model of a flat plate with a reserved small hole under the upper tension is established. The results show that the crack finally produces a crack in the lower left and upper right directions of the square hole and continues to extend to the model boundary, which proves the feasibility of crack independent initiation and propagation by the phase field method. The stress formed a butterfly region until the fracture occurs. And the butterfly stress distribution was still present at the end of crack propagation. The maximum vertical stress was 1.7 × 103  MPa. Based on the South-to-North Water Transfer Project, the simulation of tunnel crack propagation under excavation disturbance is realized for the first time, which is based on the phase field method. The results show that the influence area of excavation disturbance will increase after considering crack development. Comparing the simulation results without considering crack propagation with the simulation results considering crack propagation, it is found that the stress level in the excavation disturbance area around the tunnel is greatly affected by cracks. When the crack is not considered, the maximum vertical stress is   2.16 × 105  Pa, and the maximum horizontal stress is 9.35 × 105  Pa, which occurs at the waist of the tunnel on the horizontal axis. When the crack is considered, the maximum vertical stress is 2.53 × 105  Pa, and the maximum horizontal stress is 1.10 × 106  Pa. It shows that the stress at the dome increases greatly. The vertical stress reaches 3.68 × 105  Pa, and the horizontal stress is up to 3.07 × 103  Pa. For the rock mass far away from the excavation disturbance area, because part of the elastic strain energy is absorbed by the surface crack, the stress level considering the crack is lower than that without the crack. But it is basically similar, indicating the accuracy of the phase field fracture model. This paper realizes the simulation of crack propagation under excavation disturbance and provides a way for the application of phase field fracture model in rock mechanics. This paper proves that phase field method has broad prospects in simulating rock crack propagation and provides the possibility for the popularization of phase field method.