Modelling shear bands in a volcanic conduit: Implications for over-pressures and extrusion-rates

Shear bands in a volcanic conduit are modelled for crystal-rich magma flow using simplified conditions to capture the fundamental behaviour of a natural system. Our simulations begin with magma crystallinity in equilibrium with an applied pressure field and isothermal conditions. The viscosity of the magma is derived using existing empirical equations and is dependent upon temperature, water content and crystallinity. From these initial conduit conditions we utilize the Finite Element Method, using axi-symmetric coordinates, to simulate shear bands via shear localisation. We use the von Mises visco-plasticity model with constant magma shear strength for a first look into the effects of plasticity. The extent of shear bands in the conduit is explored with a numerical model parameterized with values appropriate for Soufrière Hills Volcano, Montserrat, although the model is generic in nature. Our model simulates shallow (up to approximately 700 m) shear bands that occur within the upper conduit and probably govern the lava extrusion style due to shear boundaries. We also model the change in the over-pressure field within the conduit for flow with and without shear bands. The pressure change can be as large as several MPa at shallow depths in the conduit, which generates a maximum change in the pressure gradient of 10's of kPa/m. The formation of shear bands could therefore provide an alternative or additional mechanism for the inflation/deflation of the volcano flanks as measured by tilt-metres. Shear bands are found to have a significant effect upon the magma ascent rate due to shear-induced flow reducing conduit friction and altering the over-pressure in the upper conduit. Since we do not model frictional controlled slip, only plastic flow, our model calculates the minimum change in extrusion rate due to shear bands. However, extrusion rates can almost double due to the formation of shear bands, which may help suppress volatile loss. Due to the paucity of data and large parameter space available for the magma shear strength our model results can only allow for a qualitative comparison to a natural system at this stage.