Relating Single Crystal Rheology to Polyphase Aggregate Rheology – the Importance of Stress Percolation

Abstract:

Percolation theory is used to describe the behavior of a large number of disordered systems including the passage of fluid through porous materials, the spread of forest fires, and the mechanical behavior of granular materials. By virtue of both variations in elastic and plastic properties between different rock forming minerals as well as the plastic and elastic anisotropy of individual mineral grains, polycrystalline rocks are elastically and plastically disordered systems. Using 2D finite element models I have shown that stress transmission in rocks can also be described as a percolation problem and that the modulation of stress states within a rock can in some cases, reach levels comparable to the differential load on the rock. The presence of such modulations in the internal stress state of a rock has many implications for understanding how the rock’s rheology arises from the rheology of its constituent crystals. A first order result of stress percolation is the formation of shear localization. Depending on the degree of mechanical heterogeneity of the rock’s mechanical components (including grain interiors and grain boundaries), the nature of the shear localization may be highly concentrated – and therefore observable or widely distributed and “cryptic” in nature. The modulations in stress states created by stress percolation create small regions (yield nuclei) distributed throughout the rock that yield well before the bulk of the rock has reached the yield criterion. Local yielding leads to percolation of yielded regions and shear localization. Whether the shear localization remains cryptic or is observable by virtue of the development of large offsets, is a function of the density and distribution of yield nuclei. The spatial distribution of yield nuclei is a function of the nature of the stress percolation pattern, the variation in yield strength of the mechanical components and their spatial distribution. The presence of shear localization changes the relationship between single-crystal rheology and bulk rock rheology and therefore must be taken into account when modelling bulk rheology based on single-crystal rheology.

Figure: a) FE model mesh b)-e) Plastic strain b) Young’s modulus, E = 500 to 0 GPa with v=0.1 to 0.4, c) E= 500 to 0 GPa with v=0.3 d) E= 200 to 20 GPa with v=0.3 and e) E =120 to 100 GPa with v=0.3.