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Modeling linear and nonlinear fluid flow through sheared rough-walled joints taking into account boundary stiffness

This study modeled four hundred fluid flow cases through shear-induced aperture fields of a rough-walled joint with self-affine surface characteristics under different boundary stress and stiffness conditions by solving the Navier-Stokes equations. The results show that as the hydraulic gradient increases from 10−8 to 101, the fluid flow experiences changes characterized by a linear regime, a weak nonlinear regime and a strong nonlinear regime. The permeability is a constant in the linear regime and starts to decline when entering the weak nonlinear regime, and the declining rate gradually converges when reaching the strong nonlinear regime. Such transition is poorly indicated by the global Reynolds number alone; it is instead primarily governed by the magnitudes and distribution characters of local Reynolds numbers. The boundary stiffness has linear/nonlinear relations with the permeability, depending on the magnitude of the joint aperture, which is governed by surface roughness, joint compressive strength and mechanical boundary conditions. With increasing boundary stiffness from 0 to 2.0 GPa/m, the ratio of permeability in y-direction to that in x-direction increases from 2.49 to 26.49 by approximately a factor of 10, suggesting that anomalous flow may prevail in sheared zones with stiff surrounding confinements.

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