The analog model, the numerical model and the Piton de la Fournaise : tale of a propagating dike

The transport of magma through the crust may sometimes result in volcanic eruptions at the surface, feeding a central conduit, opening fissures on the volcano flank, or at new locations in a volcanic field. Magma travels in the brittle crust by opening its way through the surrounding rock. In addition to the fracturation of the medium, the process of diking is also controlled by the magma flow, fluid-gas phase transitions, and the heat exchange. Representing the propagation of magmatic intrusions using analog and numerical model is essential to understand the physical processes occurring in nature and to mitigate the volcanic hazard linked to the emplacement of magmatic intrusions.

In this context, we performed analog experiments of air and silicon oil injections in a solidified gelatin block. Using three cameras, we monitored the propagation of the oil-filled cracks from the front, side and top views of the tank. The processing of time lapsed pictures enables to access the crack shape (dimension and orientation), trajectory and velocity. This analog modeling technique is routinely used to simulate magmatic dike propagation in the crust. Then, taking advantage of these well constrained experiments, we could validate a novel 2D boundary element model for crack propagation coupling brittle-elastic and fluid-dynamic equations. To do so, we initiate the input and boundary conditions of our numerical simulations, using gelatin and oil parameters from the analog experiments. The outputs of the model include the crack shape, trajectory, and velocity, that is computed according to an energy conservation equation, under the assumption that fluid viscous forces are limiting the crack propagation velocity. Numerical simulations are faced with the observations from our air and oil-filled crack propagation experiments. Eventually, we applied the numerical model to the 1998 magmatic intrusion at Piton de la Fournaise volcano (La Réunion Island), confronting the timing of the of the propagation with the migration of volcano-tectonic events.