Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

The complex variables boundary element method (CVBEM) is used to study inte raction between a circular opening and fractures originating from its bound ary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The eq uation is solved using the CVBEM technique with circular and straight bound ary elements and polynomial approximations (with square root asymptotics fo r crack tip elements) for the unknown functions. The algorithm is verified through comparison with known semi-analytical and numerical solutions that involve interaction between a circular opening and specific systems of crac ks or other openings. New numerical results concerning the interaction of t he circular opening with the cracks and circular inclusions are presented, The method is applied to an important problem in the petroleum industry: mo delling propagation of hydraulic fractures in the vicinity of a borehole. C opyright (C) 2000 John Wiley & Sons, Ltd.