A review of mechanical models of dike propagation: Schools of thought, results and future directions

Magma transport in brittle rock occurs by diking. Understanding the dynamics of diking and its observable consequences is essential to deciphering magma propagation in volcanic areas. Furthermore, diking plays a key role in tectonic phenomena such as continental rifting and plate divergence at mid-ocean ridges. Physics-based models of propagating dikes usually involve coupled transport of a viscous fluid with rock deformation and fracture. But the behavior of dikes is also affected by the exchange of heat with the surroundings and by the interaction with rock layering, pre-existing cracks, and the external stress field, among other factors. This complexity explains why existing models of propagating dikes are still relatively rudimentary: they are mainly 2D, and generally include only a subset of the factors described above. Here, we review numerical models on dike propagation focusing on the most recent studies (from the last 15 to 20 years). We track the influence of two main philosophies, one in which fluid dynamics is taken to control the behavior and the other which focuses on rock fracturing. It appears that uncertainties in the way that rock properties such as fracture toughness vary from laboratory to field scale remain one of the critical issues to be resolved. Finally, we present promising directions of research that include emerging approaches to numerical modeling and insights from hydraulic fracturing as an industrial analog.