Modeling dike trajectories in a biaxial stress field with coupled magma flow, fracture, and elasticity

Because dike propagation depends on stress state, the geometry of dikes can be used to make inferences about crustal stress conditions during emplacement. Early work relied on analytical solutions for stress in a two-dimensional elastic medium with a pressurized circular magma chamber and biaxial far-field stress. The principal stress trajectories in this classical model depend on the ratio of deviatoric stress magnitude to chamber pressure. Assuming dikes follow principal stress trajectories and bounding plausible magma chamber excess pressures lead to estimates of deviatoric stress magnitudes from the map pattern of dikes. Mériaux and Lister (2002) pointed out that this approach ignored stresses due to the magma-filled dikes themselves, which significantly alter predicted dike trajectories. They estimated deviatoric stresses 2 to 5 times previous estimates. However, Mériaux and Lister (2002) assumed the pressure distribution within the dike rather than computing it from viscous magma flow. We revisit this simplification using a 2D model which fully couples a linear elastic host rock with a pressurized chamber and a fluid-filled dike, assuming the lubrication approximation for viscous flow. This model is solved using the finite element method (FEM). Ensuring that dike propagation is stable limits the dike-tip cavity pressure for realistic fracture toughness. We find that computed trajectories fall between the classical principal stress and Mériaux and Lister (2002) trajectories for given regional stress and chamber pressure conditions. This leads to deviatoric stress magnitude estimates that are 1 to 2 times the classical estimates, and 1/2 to 1/3 the Mériaux and Lister (2002) estimates. We also explore the consequences of chamber depressurization due to magma outflow during dike propagation. For a given melt compressibility, the resulting trajectories align more closely with those obtained from the classical model, compared to those obtained assuming a constant chamber pressure. At higher ratios of tectonic stress to chamber pressure, the trajectories are nearly identical. In both the constant pressure and depressurizing chamber cases, our results suggest that realistic magma pressure profiles within a dike lead to smaller estimated ratios of deviatoric stress to chamber pressure than found by Mériaux and Lister (2002). Future work should extend dike propagation models to three dimensions, and more thoroughly explore effects of magma compressibility.