The objectives of this paper are twofold. First to evaluate the extent, or shadowing, of the stresses and displacements resulting from an internally pressurized crack and second to show how a creative testing apparatus can model the interaction of multiple fractures and display the influence of stress shadowing.
The solution for 2-D planar crack in elliptical-cylindrical coordinates was used to evaluate the stress and displacement shadowing. This analysis indicated that the compressive stresses for a pressurized crack of length H, will dissipate by 100% within a distance d/H = 3/4. The analysis also showed that the shear stresses and displacements are concentrated in a small area around the crack tip of radial distance equal to d/H = 0.05. H is crack length and d is distance from the crack. Following this analysis, the mechanical apparatus was used to visualize the influence of the stress and displacement shadows in the propagation of multiple fractures.
The example that validated the application of the apparatus consisted of modeling the merging of two fractures observed in the 2017 Puebla, Mexico earthquake. In this case, both the testing apparatus and the numerical results given by a two dimensional Finite Element (FE) code closely reproduced the field observations. Following this validation, the application of the testing apparatus was extended to model the propagation and interaction of multiple fractures. Three cases were considered. Case 1, consisted of a main fracture propagating between pre-existing fracture-pockets filled with fluid (pressurized pockets). Case 2, included the propagation of multiple parallel fractures. Case 3, considered hydraulic fractures propagating through zones populated with micro-fissures.
Case 1, showed how a hydraulic fracture can activate and propagate pre-existing frac-pockets. This example could explain how some frac-hits occur. Case 2, illustrated that from a cluster of several parallel fractures that are close to each other (D/H < 1), only one or two dominant fractures will propagate. D is distance between parallel fractures. The experimental results for Case 3 indicated that the micro-fissures diverted the direction of fracture propagation and also increased the tortuosity. The extent of departure and degree of tortuosity depended on the orientation of the micro-fissures. Micro-fissures normal to the crack resulted in more diversion and more tortuosity compared to the diversion and tortuosity resulting from micro-fissures parallel to the crack. Further the tests also showed that the micro-fissures not aligned with the fracture also suffered significant dilation.