Modeling the Shape and Velocity of Magmatic Intrusions, a New Numerical Approach

Dykes are magma-filled fractures propagating through the brittle crust. Understanding the physics of dyking process is essential to mitigate the volcanic hazard associated with the opening of new eruptive fissures at the surface. Often, physics-based models view either fracturing of the host rock or viscous flow of the magma as the dominating energy sink during dyke propagation. Here, we provide a numerical model that captures the coupling of fracturing at the crack tip and the transport of a viscous fluid. Built with the boundary element technique, our model allows for computation of the shape and velocity of a growing fluid-filled crack accounting for the viscosity of the fluid: the fluid flow induces a viscous pressure drop acting at the crack walls, and modifies the shape of the crack. The energy conservation equation provides the constraints to solve for the crack growth velocity, assuming that brittle fracturing and viscous flow are the main processes that dissipate energy. Using a parameter range that represents typical magmatic intrusions, we obtain crack shapes displaying some typical characteristics, including a tear-drop head and an open tail that depend on rock rigidity, magma viscosity, and buoyancy. We show that viscous forces significantly contribute to the energy dissipated during the propagation of magmatic dykes. Applied to the 1998 intrusion at Piton de la Fournaise (La Reunion Island), we provide ranges of dyke lengths and openings by adjusting the numerical velocity to the one deduced from the migration of volcano-tectonic events.