A phase field model of magma transport in dykes: validation with small-scale experiments

Magma is transported through the Earth’s crust via thin fractures called dykes that cut through layers of bedrock towards the surface to feed volcanic eruptions. Dyke propagation is a multiphase problem where fluid dynamics control propagation velocities and solid mechanics determine dyke pathways. Numerical models are essential tools for understanding the hidden processes of magma transport and interpreting the geophysical and geodetic signals (e.g. earthquakes and surface deformations) that are released during dyke propagation. The complex physical processes governing propagation are challenging to implement in a numerical model, and simplifying assumptions must be made. Common simplifications include neglecting magma flow and assuming that buoyancy drives propagation, or assuming a viscosity-dominant unidirectional flow within a single, vertically oriented dyke. However, such models represent only a small subset of natural cases, and there is motivation for a new model that can simulate a wider range of dyke behaviour. We propose a phase field approach, where a continuous variable (the phase field) denotes the presence or absence of a fracture. Phase field evolution (i.e. dyke propagation) is governed by a simple equation which enables the simulation of nonlinear fracture pathways, whilst the continuous nature of the approach makes it well suited for multiphase fracture problems. We have developed a three-variable φ-p-u model that solves for the phase field φ, magma pressure p, and solid rock displacement u. Real-time simulations of an experimental dyke show promising results, suggesting that the phase field approach could bring significant advancements to models of natural dyke propagation.