Study on the stress field concentration at the tip of elliptical cracks

The holes and defects in rock materials have a great impact on the mechanical properties and failure mechanism of rock, cracks often appear in the form of flat ellipses in natural rock mass, and the current research is still insufficient. For this purpose, based on the Particle Flow Code (PFC) of discrete element particle flow program, the numerical prefabricated fractured rock samples with the ratios of the long and short axes of the elliptical fractures being 5, 7.5, 10, 12.5, and 15 were simulated in order to obtain the strength and failure characteristics, stress concentration characteristics at tips of numerical rock samples in uniaxial compression test. The results of the numerical test simulation show that: (1) When the rock models with prefabricated elliptical crack were damaged, the initial cracks occurred at the end of the short axis of the elliptical crack, and penetrated up and down from the surface of the elliptical crack, the wing cracks occurred at both ends of the long axis, gradually formed a macro-crack, and the secondary cracks extended near the wing crack. (2) With the increase of the ratios a:b of long and short axes of the elliptical fracture, the strength and elastic modulus of the numerical rock samples gradually decreased, Poisson’s ratio gradually increased, and the total number of micro-cracks in the rock models decreased. (3) The numerical solutions of stress concentration factor k obtained by numerical simulations at the tip of the elliptical crack increased with the increase in the ratio of a:b; it was highly consistent with the variation law of the analytical solution of the stress concentration factor calculated by the theory of flat ellipse. The stress concentration is an important reason for failure of rock with elliptical cracks. Study on the crack tip will be very useful and significant.