Theoretical And Computational Studies Of Hydraulic Anisotropy In Shear Fractures With Self-Affine Surfaces
Mallikamas, Wasin 1 ; Rajaram, Harihar 2
1 University of Colorado
2 University of Colorado
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. 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 found that generating these 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) led to better agreement with theoretical variograms than the standard approach, which uses a single FFT and discretizes the continuous theoretical spectrum.