Numerical simulations of the propagation path and the arrest of fluid-filled fractures in the Earth

We use a boundary element method to study the growth and quasi-static propagation of fluid-filled fractures in regions with inhomogeneous and deviatoric stresses. The wholesale migration of fractures due to their opening at one end and closing at the other can be simulated when using a finite fluid mass contained in a fracture and considering fluid compression or expansion with changing fracture volume; these fractures are driven by stress gradients and by the density differences between the fluid and the surrounding rock. Contrary to commonly held beliefs, the fracture growth and the propagation directions are not controlled only by the direction of the principal stresses, but also by tectonic stress gradients, apparent buoyancy forces and the length of the fractures themselves. The models help to explain the formation of sills, the lateral migration of magmas under volcanoes and the absence of volcanoes under the shallow parts of the Nazca plate.