抄録
New cracks are formed in a rock around Griffith cracks or Griffith inclusions with various aspect ratios and various mechanical characteristics. Parabolic Griffith-type criteria for fracture can be derived from the analysis of the condition for formation of new cracks from the penny-shaped cracks or inclusions. The parabolic criteria for fracture for the incompressible Griffith inclusions become more flattened as they are less sensitive to compressive stress. The closure of Griffith cracks with various aspect ratios leads to the linear Coulomb criteria for brittle fracture.
However, the effect of intermediate principal stress is neglected in the conventional theory of generalized Griffith fracture criteria, although it is against the recent results of general triaxial compression experiments of rocks. The statistical distributions of aspect ratio and orientation of Griffith cracks or Griffith inclusions should be considered in order to explain the effect of intermediate principal stress on the fracturing of rocks. The von Mises criteria and Mogi criteria are derived as the special cases of the statistical generalized Griffith theory.
