Fracture dimensions, displacements and fluid transport

There is commonly a linear relationship between the lengths of rock fractures and their displacements, but for many fracture populations there is a very large scatter in the data. In the lava flows of the rift zone in Iceland, the displacements on a fracture or fault of a given length may vary by a factor of 2–10. Similar scatter is obtained for the aperture (width)/length ratios of several hundred mineral-filled veins in a major fault zone. I propose that the displacement on a fracture depends mostly on the smaller of its dip and strike dimensions, referred to as the controlling dimension. Thus, in a horizontal outcrop, fractures with the same strike dimension (outcrop length) can have widely different displacements depending on whether the displacements of individual fractures are controlled by strike or dip dimensions. During growth of a fracture, its controlling dimension may alternate between the dip dimension and the strike dimension. The volumetric rate of flow of fluid through a rock fracture with smooth, parallel walls depends on the cube of the fracture aperture. This cubic law implies that when the aperture of a fracture of a given length in a single set or population can vary by a factor of 2–10, the corresponding volumetric rate of fluid flow through that fracture can vary by a factor of 8–1000. A single, wide fracture in a set of as many as several hundred fractures may thus largely dominate the fluid transport through that set. Fracture aperture depends not only on the associated stress field, but also on its controlling dimension.