Boudinage as a material instability of elasto-visco-plastic rocks

Abstract

Pinch-and-swell structures are commonly interpreted to evolve out of viscosity contrasts, which are induced by geometric interactions and material imperfections. From materials science an additional localization phenomenon is well established, where localization emerges out of steady state for critical material parameters and/or loading rates. Here we investigate the conditions under which this second type of instabilities prevails and whether geological materials necessarily require a trigger by imperfections in order to generate instability. We focus on imperfections in terms of grain size variations embedded in a deformation environment controlled by thermo-mechanical feedbacks. We introduce a random distribution of grain sizes over two orders of magnitude in a central layer embedded in a matrix with a diffusion creep rheology. The rheology of the layer evolves with dislocation and diffusion creep as end-member deformation mechanisms. Applying pure shear extension, the 3-layer model is subjected to natural deformation conditions. The central layer quickly establishes a viscous steady state as a natural response of the system due to relaxation and energy optimization. Upon continued loading, localization then intriguingly arises out of a homogeneous state. We present an analysis which confirms that this type of instability is indeed physically admissible. Using vibration analysis, we verify the robustness of the numerical solution by first identifying the natural mode shapes and frequencies of the simulated structure and material parameters, including geometric imperfections. In a second step, the eigenmodes are perturbed and superposed to the initial conditions. We conclude that this pattern of perturbations guides the onset of strain localization. Boudinage can therefore be seen both as a geometric problem and/or a material bifurcation, which evolves out of homogeneous state. The latter class offers the great possibility of extracting fundamental material parameters out of localized structures directly from field observations.