Abstract

The interplay among mechnical, chemical, hydrological, and thermal processes in the evolution of crustal shear zones makes an analytical approach to their study difficult. As an alternative, a stochastic description (using percolation theory) is used to gain insight into reaction softening and volume loss in ductfle deformation zones. Directed percolation is preferred to ordinary percolation as a model because, in common with natural shear zones, directed percolation clusters have high length/width ratios and anisotropic permeability. In addition, transport along the cluster length (for p > pc is linear with time (modeling fluid advection). The process of strain softening is modeled by subjecting a critical cluster to variable amounts of simple shear, resulting in a geometry similar to that of natural shear zones. A stochastic model for the evolution of porosity with time on a directed lattice displays fixed-point behavior for a range of pore-collapse rates. The observation that natural shear zones from a variety of tectonic settings display mean volume losses of 60%-70%; suggests that the system naturally evolves toward a critical state. This can be explained by assuming that pore collapse is regulated by the tendency for fluid pressure to remain close to lithostatic. Volume loss in crustal shear zones appears to be an example of hydromechanical-chemical self-organized critical behavior.

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