An Interesting Look at Multiple Fractures: Stress Shadowing andPropagation

摘要

The objectives of this paper are twofold.First to evaluate the extent,or shadowing,of the stresses anddisplacements resulting from an internally pressurized crack and second to show how a creative testingapparatus 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 stressand displacement shadowing.This analysis indicated that the compressive stresses for a pressurized crackof length H,will dissipate by 100% within a distance d/H = 3/4.The analysis also showed that the shearstresses and displacements are concentrated in a small area around the crack tip of radial distance equalto d/H = 0.05.H is crack length and d is distance from the crack.Following this analysis,the mechanicalapparatus was used to visualize the influence of the stress and displacement shadows in the propagationof multiple fractures.The example that validated the application of the apparatus consisted of modeling the merging of twofractures observed in the 2017 Puebla,Mexico earthquake.In this case,both the testing apparatus andthe numerical results given by a two dimensional Finite Element(FE)code closely reproduced the fieldobservations.Following this validation,the application of the testing apparatus was extended to model thepropagation and interaction of multiple fractures.Three cases were considered.Case 1,consisted of a mainfracture 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 propagatingthrough zones populated with micro-fissures.Case 1,showed how a hydraulic fracture can activate and propagate pre-existing frac-pockets.Thisexample could explain how some frac-hits occur.Case 2,illustrated that from a cluster of several parallelfractures that are close to each other(D/H < 1),only one or two dominant fractures will propagate.D isdistance between parallel fractures.The experimental results for Case 3 indicated that the micro-fissuresdiverted the direction of fracture propagation and also increased the tortuosity.The extent of departure anddegree of tortuosity depended on the orientation of the micro-fissures.Micro-fissures normal to the crackresulted in more diversion and more tortuosity compared to the diversion and tortuosity resulting frommicro-fissures parallel to the crack.Further the tests also showed that the micro-fissures not aligned withthe fracture also suffered significant dilation.