The propagation paths of fluid-driven fractures in layered and faulted rocks

Abstract

Fractures that form when fluid pressure ruptures the rock are referred to as fluid-driven fractures or hydrofractures. These include most dykes, inclined sheets and sills, but also many mineral veins and joints, as well as human-made hydraulic fractures. While considerable field and theoretical work has focused on the geometry and arrest of hydrofractures, how they select their propagation paths, particularly in layered and faulted rocks, has received less attention. Here I propose that of all the possible paths that a given hydrofracture may follow, it selects the path of least (minimum) action as determined by Hamilton's principle. This means that the selected path is that along which the energy transformed (released) multiplied by the time taken for the propagation is a minimum. Hydrofractures advance their tips/fronts in steps, with a time lag between the fracture front and the fluid front. In the present framework, each step is then controlled by Hamilton's principle. The results suggest that when the hosting rock body is regarded as homogeneous, isotropic and non-fractured, hydrofracture paths are everywhere perpendicular to the trajectories of the minimum compressive (maximum tensile) principal stress σ3 and follow the trajectories of the maximum principal compressive stress σ1. When applied to layered and faulted rock body, the results indicate that hydrofracture paths may follow existing faults for a while, depending primarily on (1) the dip of the fault (steep faults are the most likely to be used by vertically propagating hydrofractures), and (2) the tensile strength across the fault compared with the tensile strength of the host rock along a path following the direction of σ 1. The results suggest that hydrofractures may use faults as parts of their paths primarily if the fault is steeply dipping and with close to zero tensile strength.