Numerical modeling of caldera formation using Smoothed Particle Hydrodynamics (SPH)

Calderas are kilometer-scale basins formed when magma is rapidly removed from shallow magma storage zones. Despite extensive previous research, many questions remain about how host rock material properties influence the development of caldera structures. We employ a mesh-free, continuum numerical method, Smoothed Particle Hydrodynamics (SPH) to study caldera formation, with a focus on the role of host rock material properties. SPH provides several advantages over previous numerical approaches (finite element or discrete element methods), naturally accommodating strain localization and large deformations while employing well-known constitutive models. A continuum elastoplastic constitutive model with a simple Drucker-Prager yield condition can explain many observations from analogue sandbox models of caldera development. For this loading configuration, shear band orientation is primarily controlled by the angle of dilation. Evolving shear band orientation, as commonly observed in analogue experiments, requires a constitutive model where frictional strength and dilatancy decrease with strain, approaching a state of zero volumetric strain rate. This constitutive model also explains recorded loads on the down-going trapdoor in analogue experiments. Our results, combined with theoretical scaling arguments, raise questions about the use of analogue models to study caldera formation. Finally, we apply the model to the 2018 caldera collapse at Kilauea volcano and conclude that the host rock at Kilauea must exhibit relatively low dilatancy to explain the inferred near-vertical ring faults.