A comparison of plasticity regularization approaches for geodynamic modeling

The emergence, geometry and activation of faults are intrinsically linked to frictional rheology. The latter is thus a central element in geodynamic simulations which aim at modeling the generation and evolution of fault zones and plate boundaries. However, resolving frictional strain localization in geodynamic models is problematic. In simulations, equilibrium cannot always be attained and results can depend on mesh resolution. Spatial and temporal regularization techniques have been developed to alleviate these issues. Herein, we investigate three popular regularization techniques, namely viscoplasticity, gradient plasticity and the use of a Cosserat continuum. These techniques have been implemented in a single framework based on an accelerated pseudo-transient solution strategy. The latter allows to explore the effects of regularization on shear banding using the same code and model configuration. We have used model configurations that involve three levels of complexity: from the emergence of a single isolated shear band to the visco-elasto-plastic stress buildup of a crust. All considered approaches allow to resolve shear banding, provide convergence upon mesh refinement and satisfaction of equilibrium. Viscoplastic regularization is straightforward to implement in geodynamic codes. Nevertheless, more stable shear banding patterns and strength estimates are achieved with computationally more expensive gradient and Cosserat-type regularizations. We discuss the relative benefits of these techniques and their combinations for geodynamic modeling. Emphasis is put on the potential of Cosserat-type media for geodynamic applications

Resolving hydromechanical coupling in two and three dimensions: spontaneous channelling of porous fluids owing to decompaction weakening

International audienceFingering, veining, channelling and focussing of porous fluids are widely observed phenomena in the Earth’s interior, driving a range of geo-processes across all scales. While observations suggest fairly localized flow patterns induced by fractures, the classical Darcian model predicts diffusive behaviour that leads to never-ending spreading and delocalization. We here investigate an alternative physical mechanism without the need to involve fractures. Decompaction weakening leads to the formation and propagation of localized flow-pathways in fluid-saturated porous media. We numerically solve the coupled equations using high-resolution 2-D and 3-D numerical modelling to predict non-linear porous flow in a non-linearly viscously deforming matrix. We show that high-porosity channels may be a dynamic and natural outcome of sufficiently resolved hydromechanical coupling and decompaction weakening. We propose an efficient solution strategy that involves an iterative pseudo-transient numerical method to solve the coupled system of equations in a matrix-free fashion. We discuss benefits and limitations of this approach that performs optimally on hardware accelerators such as graphical processing units and is well-suited for supercomputing. We benchmark the pseudo-transient routines against commonly used direct-iterative solving strategies and show convergence towards identical results. Furthermore, we use the fast solver to systematically study in 2-D the high-porosity channel propagation velocity as a function of bulk and shear viscosity ratios and report discrepancy between 2-D and 3-D configurations. We conclude that the fluid-flow rate in the channels is up to three orders of magnitude higher than expected by pure Darcian flow regimes and show that the high-porosity channels occurrence remains with strain rate dependant shear viscosity. We provide both the 2-D MATLAB-based direct-iterative and pseudo-transient routines for full reproducibility of the presented results and suggest our model configuration as a key benchmark case to validate the implementation of hydromechanical coupling in 2-D and 3-D numerical codes. The routines are available from Bitbucket and the Swiss Geocomputing Centre website, and are also supporting information to this pape

Resolving thermomechanical coupling in two and three dimensions: spontaneous strain localization owing to shear heating

International audienceNumerous geological processes are governed by thermal and mechanical interactions. In particular,tectonic processes such as ductile strain localization can be induced by the intrinsiccoupling that exists between deformation, energy and rheology. To investigate this thermomechanicalfeedback, we have designed 2-D codes that are based on an implicit finite-differencediscretization. The direct-iterative method relies on a classical Newton iteration cycle andrequires assembly of sparse matrices, while the pseudo-transient method uses pseudo-timeintegration and is matrix-free. We show that both methods are able to capture thermomechanicalinstabilities when applied to model thermally activated shear localization; they exhibitsimilar temporal evolution and deliver coherent results both in terms of nonlinear accuracyand conservativeness. The pseudo-transient method is an attractive alternative, since it candeliver similar accuracy to a standard direct-iterative method but is based on a much simpleralgorithm and enables high-resolution simulations in 3-D. We systematically investigate thedimensionless parameters controlling 2-D shear localization and model shear zone propagationin 3-D using the pseudo-transient method. Code examples based on the pseudo-transientand direct-iterative methods are part of the M2Di routines (R¨ass et al., 2017) and can bedownloaded from Bitbucket and the Swiss Geocomputing Centre website

Pegmatites as geological expressions of spontaneous crustal flow localisation

International audienceAmongst the silicate-rich crystalline rocks that are produced in the continental crust, pegmatites are characterised by their large crystals which give them both an aesthetic and economic interest. Pegmatites crystallise either from fractionated magma derived from a parent granitic body or from the partial melting of metasediments or meta-igneous rocks (e.g. amphibolite). The mechanism of residual magma (or fluid) extraction from the parent granitic body has been thoroughly studied, but pegmatitic melt extraction after partial melting has received less attention. We present here a series of non-dimensional numerical experiments using a twophase flow formulation that couples the Stokes problem to/with non-linear Darcy flow. This approach makes it possible to predict the movement of fluid inclusions (named porosity) in a deformable of a viscous rocks (named porous matrix). We find that the simulation produces either clusters or an isolated body of fluid inclusion depending on the compaction/decompaction ratio of the effectively viscous matrix in which they rise. Using a review of pegmatite natural properties, we propose a scaling of our numerical simulations that describes the ascent of a pegmatite-forming melt produced by partial melting. We then discuss possible travel distances and temperature effects. To discuss our results in light of field observations, we assume that the compactiondecompaction ratio is an accurate proxy for the influence of brittle processes at a scale smaller than the representative volume element, and therefore corresponds structural level variations at which pegmatites are emplaced. We find that our numerical simulation explain the statistical organisation, in terms of level of emplacement, of real fields of pegmatites possibly derived from partial melting of meta-sediments. Pegmatites in fact tend to organise as clusters around brittle faults in upper crustal levels, whereas they present a scattered distribution at mid to lower crustal levels. Our results therefore show that porosity waves are a possible mechanism for rapidly extracting and transporting pegmatite melts formed during low-degree (ca. 10%) partial melting at distances up to a few kilometres in the crust