The effect of solidification on fluid-driven fracture, with application to bladed dykes

We consider fluid-driven fracture of an elastic solid, with solidification of the injected fluid. In particular: we consider buoyancy-driven horizontal propagation of a crack through a density-stratified solid at the level of neutral buoyancy of the fluid. Each part of the perimeter of the crack is in one of two regimes: at short times and far from the source, fluid reaches the tip of the crack and is able to fracture the solid and cause propagation; at longer times and closer to the source, the tip of the crack has become blocked by solidified fluid, preventing further fracture. A simple criterion for the boundary between these regimes is derived and the blocking of the perimeter is argued to be analogous to the channelling of lat a flows by solidified levees at the edges. We; present a model of crack propagation that combines the effects of viscous fluid flow, elastic deformation, linear fracture mechanics and buoyancy-limited vertical extent with those of fluid solidification. This model has particular relevance to the evolution of volcanic edifices, where hot magma is transported in cracks through the crust, eventually solidifying to form large planar intrusions known as dykes.