Three-dimensional BEM analysis of stress state near a crack-borehole system

The paper presents a numerical study of the three-dimensional problem of cracks interacting with a cylindrical uniformly pressurized borehole. The theoretical developments describe general case in which the axis of the borehole can be inclined to the vertical direction, the cracks are either located outside of the borehole or emanate from it, and the in-situ stresses are uniform with major principal stress acting in vertical direction. The tractions are prescribed at the cracks surfaces that includes two limiting cases of traction-free cracks (“fast pressurization”) or cracks subjected to uniform load equal to that applied at the surface of the borehole (“slow pressurization”). The study is based on the complex integral representations for the three-dimensional fields around the borehole-crack system. The boundary surfaces are approximated using triangular mesh and quadratic polynomials are employed for approximating the boundary unknowns. The prescribed boundary conditions are met using “limit after discretization” procedure. The linear algebraic system to find the unknowns is set up by the collocation method. Two numerical benchmarks are presented.