HR: 0800h
AN: H11D-1304    [Abstracts]
TI: Theoretical and Computational studies of Hydraulic Anisotropy in Shear Fractures with Self-Affine Surfaces
AU: * Mallikamas, W
EM: wasin.mallikamas@colorado.edu
AF: Department of Civil Engineering, University of Colorado, Campus Box 428, Boulder, CO 80309-0428
AU: Rajaram, H
EM: hari@colorado.edu
AF: Department of Civil Engineering, University of Colorado, Campus Box 428, Boulder, CO 80309-0428
AB: We present theoretical and computational analyses of the anisotropy of the aperture correlation structure and effective transmissivity in fractures generated by sliding between identical self-affine surfaces. Quite surprisingly, the anisotropy resulting from shear has been overlooked in most previous analyses. Expressions are derived for the aperture correlation function in different directions, highlighting longer persistence and a larger integral scale normal to the shift than parallel to it. A stochastic perturbation analysis of the Reynolds equation leads to an effective transmissivity tensor with higher transmissivity normal to the shift. The hydraulic anisotropy depends on the coefficient of variation of the aperture field and the Hurst exponent, and is also influenced by the geometry of contact areas. Numerical simulations are presented to evaluate the above theoretical predictions. The numerical simulations required generation of self-affine fields and other random fields with unbounded integral scales. We present some of the computational issues that arose in the context of generating these fields using FFT spectral methods. Specifically, better accuracy was obtained by generating fields using a pair of discrete FFTs: the first to obtain a numerical representation of a discrete spectrum based on the theoretical autocorrelation function and the second to generate the field based on the discrete spectral representation. This approach led to better agreement with theoretical variograms than the standard approach, which uses a single FFT and discretizes the continuous theoretical spectrum. A second issue was related to the rapid variation of the spectra near zero wavenumber. Adequate resolution of the spectrum in this region required generation of the fields as large as 16 times the desired domain size, followed by extraction of the central portion for flow simulations.
DE: 1829 Groundwater hydrology
DE: 1859 Rocks: physical properties
DE: 3265 Stochastic processes (3235, 4468, 4475, 7857)
DE: 4440 Fractals and multifractals
DE: 5104 Fracture and flow
SC: Hydrology [H]
MN: Fall Meeting 2005