Solving stress tensor fields around multiple pressure-loaded fractures using a linear superposition method (LSM)

The present paper presents the key steps to model internally pressurized fractures in a homogeneous elastic medium. Internal pressure in the cracks transforms the displacement field, which alters the associated stress concentration. The displacements are solved analytically using a Linear Superposition Method (LSM), and stresses are solved under the assumption of linear elasticity. The method allows for the fractures to have any location, geometry, and orientation. Additionally, each crack may be pressurized by either equal or individual pressure loads. Solution methodology are explained, and results are generated for several cases. Selected LSM model results show excellent matches against other independent methods (photo-elastics for multiple crack problems, and prior analytical solutions for single crack problems). The grid-less, closed-form LSM solution is able to achieve fast computation times by side-stepping adaptive grid-refinement, while achieving high target resolution.