We combine a power-law microfracture size distribution function with an expression for fracture propagation rate derived from subcritical fracture propagation theory and linear elastic fracture mechanics, to derive a geomechanically-based deterministic model for the growth of a network of layer-bound fractures. This model also simulates fracture termination due to intersection with perpendicular fractures or stress shadow interaction. We use this model to examine key controls on the emergent geometry of the fracture network.
First, we examine the effect of fracture propagation rates. We show that at subcritical fracture propagation rates, the fracture nucleation rate increases with time; this generates a very dense network of very small fractures, similar to the deformation bands generated by compaction in unconsolidated sediments. By contrast at critical propagation rates, the fracture nucleation rate decreases with time; this generates fewer but much larger fractures, similar to the brittle open fractures generated by tectonic deformation in lithified sediments. We then examine the controls on the rate of growth of the fracture network. A fracture set will start to grow when the stress acting on it reaches a threshold value, and it will continue to grow until all the fractures have stopped propagating and no new fractures can nucleate. The relative timing and rate of growth of the different fracture sets will control the anisotropy of the resulting fracture network: if the sets start to grow at the same time and rate, the result is a fully isotropic fracture network; if the primary fracture set stops growing before the secondary set starts growing, the result is a fully anisotropic fracture network, and if there is some overlap but the secondary set grows more slowly than the primary set, the result is a partially anisotropic fracture network. Although the applied horizontal strain rates are the key control on the relative growth rates of the two fracture sets, we show that the vertical effective stress, the initial horizontal stress, the elastic properties of the rock and inelastic deformation processes such as creep, grain sliding and pressure solution all exert a control on fracture growth rates, and that more isotropic fracture networks will tend to develop if the vertical effective stress is low or if the fractures are critically stressed prior to the onset of deformation.