A simplified three-dimensional crack growth model to simulate the deformation of brittle rock under true triaxial stresses

Abstract

Under the influence of self weight stress and tectonic stress, most of the underground rocks are in the true three-dimensional unequal stress state. True three-dimensional unequal stress makes the extension and opening of cracks in rock directional. Therefore, it is necessary to study the crack growth model of rock material under the influence of three-dimensional stress, which can better simulate the deformation characteristics of rock material under compression condition. Considering the effect of σ1, σ2 and σ3 on the crack growth, a simplified three-dimensional crack growth model is introduced in this paper. The peak strength increase caused by an increase in σ2 and σ3 are successfully simulated. Meanwhile, the peak strain decrease caused by an increase in σ2 and decrease in σ3 also can be simulated. Through the three-dimensional crack growth model, the influence of the three-dimensional stress and crack orientation on the stress intensity factor are analysed. The results show that the stress intensity factor at the crack tip increases with the increase of σ1, which promotes the crack propagation in rock. With the increase of σ2 and σ3, the stress intensity factor at the crack tip decreases, which inhibits the crack propagation in rock. Crack in brittle rock is more likely to grow when the inclination angle between the crack surface and σ1 is larger than 30°. The larger the σ2 is, the more the crack tends to open along the σ3 direction.