Mechanical interaction of geometrically linked cracks and faults

Abstract. Understanding how macroscopic fractures develop from interacting cracks is essential for describing brittle deformation in upper-crustal rocks. Although empirical failure criteria successfully describe fracturing in laboratory experiments, they do not explain how microcracks distributed within deforming rocks interact, coalesce and organize into through-going fracture networks. In this study, we examine how the geometrical distribution of pre-existing cracks controls the local stress perturbations that may influence fracture formation. We use two-dimensional Finite Element Method-based numerical simulations to quantify the elastic stress field around isolated cracks, en echelon crack arrays and randomly distributed crack systems undergoing simple shear. The results show that crack orientation, and spacing strongly control the distribution of reduced compression, effective cohesion, and localized strain around crack tips, and determine whether local stress perturbations may promote or inhibit crack linkage. Favorably arranged crack arrays produce overlapping lobes of reduced compression and local principal stress trajectories that effectively connect neighboring crack tips, defining potential linkage paths oblique to the far-field maximum principal stress. These findings suggest that shear fractures primarily develop from the overlap of tensile stress perturbation regions around pre-existing cracks rather than being controlled solely by the far-field stress or the geometry of mode I cracks formed during early stages of deformation. In highly anisotropic crack configurations, the distribution forces shear fracture evolution and fault configurations along limited paths. Conversely, rocks with isotropic crack distributions tend to preferentially activate en echelon arrays oriented approximately at 30° relative to the far-field maximum principal stress, as predicted by the Coulomb criterion. This research demonstrates that the distribution, and orientation of the pre-existing cracks exert a first-order control over the mechanical evolution of shear fractures and faults, as well as the impact of crustal and hydrostatic pressure variations on the conditions for failure and crack opening in upper-crustal rocks.