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Revisiting fundamental concepts of continental extension |
1 School of Mathematical Sciences, Building 28, Monash University Clayton, Victoria 3800, Australia (e-mail: louis.moresi{at}sci.monash.edu.au)
2 Department of Earth Sciences, University of Queensland, St Lucia, Queensland 4072, Australia
In models of crustal deformation at a scale of a few tens of kilometres, it is appropriate to use a Mohr–Coulomb yield criterion for lithospheric failure based on the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favourably oriented with respect to the stress field. The Drucker–Prager yield criterion has very similar characteristics to the Mohr–Coulomb criterion but is more straightforward to implement, particularly in the context of large-scale fluid-mechanical deformation of the coupled system of mantle, lithosphere and crust. As such models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr–Coulomb failure within the mathematical framework used by mantle-convection fluid dynamics codes.
The new formulation is based on the conceptual picture of lithospheric failure incorporated in the Anderson model of fault development and reproduces shear band angles predicted by this model. We use an transversely isotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a preferred plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We assume the Boussinesq approximation can be applied in the model – neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation.
We compare the behaviour of this formulation to the Drucker–Prager failure model for two-dimensional (2D) layered brittle–ductile systems. The pattern of shear bands is found to be quite similar from each model, although some differences are seen in the characteristic spacings for ‘equivalent’ values of the material properties. In 3D similar patterns are seen but are modulated by additional 3D structure.
