A rigorous tool for evaluating the importance of viscous dissipation in sill formation: it's in the tip
Andrew P. Bunger, 2008. "A rigorous tool for evaluating the importance of viscous dissipation in sill formation: it's in the tip", Dynamics of Crustal Magma Transfer, Storage and Differentiation, Catherine Annen, Georg F. Zellmer
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Crustal magma transport is typically described using a complex, non-linear model associated with fluid-driven fracturing, and therefore fundamentally sound modelling forms the basis for interpretation of magmatic intrusions. One of the most basic considerations is that magma-driven sills can be broadly categorized based on the energy dissipation mechanism that is predominant during intrusion growth. In cases where either viscous flow or overcoming fracture toughness strongly dominates fracture behaviour, it is typical to speak of viscosity-dominated or toughness-dominated regimes, each of which defines a class of fracture propagation with significant implications for modelling. This paper presents a straightforward and geometry-independent means for local determination of the expected propagation regime based on an experimentally verified mathematical analysis of the multi-scale, coupled mechanics that govern the near-tip region. The propagation regime is then related directly to the ratio between a characteristic length associated with the near-tip physics compared with the size of the fracture/sill. Sill growth is shown to be expected in or near the viscosity-dominated regime and hence modelling generally must take into account the complexity of the near-tip region rather than relying solely on the tip behaviour implied by linear elastic fracture, although toughness-dominated mafic intrusions can also be anticipated if fracture toughness increases sufficiently rapidly with the intrusion size.