Conflict Between Fracture Toughness and Tensile Strength in Determining Fracture Strength of Rock Samples with a Circular Hole

Abstract In this article, using a two-dimensional numerical model based on the finite element method, the fracture pressure of rock samples with a circular hole in the center is obtained. In this model, a mixed criterion is used to determine the fracture pressure, which is a combination of the tensile strength criterion and the fracture toughness criterion. The superiority of this model over the tensile strength criterion or the fracture toughness criterion is that it shows well the effect of the size of the hole in the middle of the sample on the fracture stress. The main and innovative finding of this article is that if the radius of the hole in the center of the sample is more than 70 mm, the fracture strength of the sample is dependent on the tensile strength of the rock material, and if the radius of the hole is less than 70 mm, the fracture strength is dependent on the fracture toughness. According to other results, the fracture strength decreases with the increase of the radius of the hole in the center of the sample, the decrease rate is high at first and then decreases with the increase of the radius of the hole.