Effects of fracture-surface geometries on the third-order acoustoelastic constants for aligned fluid-saturated fractures

Abstract

The pressure sensitivity of stiffness in fractured rocks is closely related to fracture-surface geometries. The resulting stress-dependence of stiffness can be represented by the third-order elastic constants (3oECs). Fracture surfaces are generally rough at various scales, and can significantly affect the 3oECs of pre-stressed fractures as well as the wave-induced fluid flow (WIFF) induced by the Biot slow P-wave between fractures and the background medium. The WIFF usually depends on the fracture width relative to the slow P-wavelength and the fracture-surface roughness. We generate various fracture-surface geometries at different scales of random roughnesses parametrized by the surface standard deviation (SSD) of fracture-surface heights. With theoretical analyses and numerical simulations, we investigate the effect of fracture-surface geometries on the stress-and frequency-dependent stiffness through the 3oECs for pre-stressed rocks with aligned fractures. For the elastic wave in the low-frequency regime of Biot theory with the fracture scale much less than the wavelength, the induced WIFF significantly enhances the effect of fracture-surface geometries on the 3oECs and P-and S-wave moduli. The stiffness of fractured rocks increases with increasing SSDs, yielding a high sensitivity to pre-stresses. Toward the high-frequency limit, however, the fluid diffusion between fractures and the porous background decreases, which reduces the influence of fracture-surface roughnesses with the 3oECs much less than that in the low-frequency regime. The resulting P-wave modulus of aligned fluid-saturated fractures approximates to the background value.