We introduce a higher-order indirect boundary element method in a traction-free
half-plane known as semi-infinite displacement discontinuity method. The method is
modified to use the linear elastic fracture mechanics principles for radial crack
analysis in brittle materials like rocks. In this numerical method there is no need to
discretize the traction-free boundary of the half-plane into higher-order elements thus
decreasing the number of elements without affecting the accuracy of the
solution to the desired problems. The use of higher-order elements increases the
accuracy so that it is possible to discretize both the boundary of the body and
radial cracks by the same higher-order elements, therefore there may be
no need to use the more complicated hybrid methods. A special crack tip
element is added for each crack tip to increase the accuracy of displacement
discontinuities near the crack ends due to their singularities. Based on the brittle
behavior of most rocks, linear elastic fracture mechanics principles have been
used to find the fracture mechanics parameters (mode-I and mode-II mixed
mode stress intensity factors) of radial cracks occurring in common blasting
operations. Arbitrary fracture criteria can be implemented in this code, but here a
simple maximum tangential stress criterion is used to predict the angle of
deviation (initiation) of radial cracks. Although this code is specially designed to
include the traction-free half-plane problems, it is somewhat comprehensive so
that any number of radial cracks with any length in the finite, infinite and
semi-infinite planes can be treated easily. The validity of the method is proved
by solving simple examples and some previously solved problems in the
literature.
