The propagation mechanism of radial cracks emanating from the blast holes in any rock blasting operation can be modeled by the displacement discontinuity method which is a version of the broad boundary element method. The stress intensity factors (SIFs) at the crack tips of the radial cracks are related to the displacement discontinuities near the crack ends. The stress intensity factors can be numerically evaluated based on the displacement discontinuity variations near the crack tips. Due to the singularity of the stress and displacement fields at the crack tips a special treatment of the displacement discontinuities near the crack tips can be used to obtain more accurate results of SIFs. In this paper a cubic variation of the displacement discontinuities along the boundaries of the circular blast holes and along the radial cracks have been assumed. For the crack tip treatment, the same cubic variation of the displacement discontinuities is also used but to decrease the singularity effect of the crack tips a special crack tip element variation in the form of the square roof of the crack tip element length multiplied by the general displacement discontinuity variation is formulated and some typical example problems are solved numerically. The numerical results are compared with the corresponding results cited in literature which verify the validity and accuracy of the proposed method.
The displacement discontinuity method is a version of the indirect boundary element method originally developed by Crouch (1976) . The method has been modified for crack analysis of fracture problems in geomechanics by several researches (e.g. [2–4]). Recently, some mixed mode fracture mechanics problems using special crack tip elements and kink elements have been solved for rock mechanics problems [4–7]. Linear elastic fracture mechanics (LEFM) principles have been widely used in rock fracture mechanics (RFM) [8–12]. Based on LEFM principles, a superposition of the three fracture modes describes the general case of loading called mixed mode loading. For a given cracked body under a certain type of loading, the SIFs are known and the displacements and stresses near the crack tip are accordingly determined. Due to brittle behavior of most rocks, the linear elastic fracture mechanics principles have been used to find the fracture mechanics parameters i.e. the mixed mode (mode I or opening mode and mode II or shearing mode of fractures) SIFs of radial cracks occur in the common blasting operations. A general numerical modeling for quasi static crack analysis in infinite plane is given and as a practical problem, the radial cracks around the blast holes are numerically analyzed. Any number of blast holes with any gas pressurization ratios along the emanating cracks can be studied by this model. Suitable normal gas pressurization ratios along the radial cracks are used, to solve the problem.
In this paper, the higher order displacement discontinuity elements is used (i. e linear, quadratic and cubic elements are considered) for analysis of crack problems in finite and infinite bodies.