Effect of stress interactions on anisotropic P‐SV‐wave dispersion and attenuation for closely spaced cracks in saturated porous media

Abstract

Generally, local stress induced by individual crack hardly disturbs their neighbours for small crack densities, which, however, could not be neglected as the crack density increases. The disturbance becomes rather complex in saturated porous rocks due to the wave‐induced diffusion of fluid pressures. The problem is addressed in this study by the comparison of two solutions: the analytical solution without stress interactions and the numerical method with stress interactions. The resultant difference of effective properties can be used to estimate the effect of stress interactions quantitatively. Numerical experiments demonstrate that the spatial distribution pattern of cracks strongly affects stress interactions. For regularly distributed cracks, the resulting stress interaction (shielding or amplification) shows strong anisotropy, depending on the arrangement and density of cracks. It has an important role in the estimation of effective anisotropic parameters as well as the incident‐angle‐dependency of P‐ and SV‐wave velocities. Contrarily, randomly distributed cracks with a relative small crack density generally lead to a strong cancellation of stress interactions across cracks, where both the numerical and analytical solutions show a good agreement for the estimation of effective parameters. However, for a higher crack density, the incomplete cancellation of stress interactions is expected, exhibiting an incidence‐angle dependency, slightly affecting effective parameters, and differentiating the numerical and analytical solutions.

Roughness Effects of Crack Surfaces on the Elastic Moduli of Cracked Rocks

“…This kind of difference are also observed in previous studies, (e.g. Guo et al, 2018a;Guo et al, 2018b;Cao et al, 2019;Cao et al, 2020).…”

“…The comparisons between the results of FEM simulation (circle) and the Gassmann equation (square) show that the bulk moduli calculated by FEM simulation are less than those from Gassmann equation with a constant value. This kind of difference may be caused by the interaction between the fractures, which is as also observed by Zhao et al (2016); Guo et al (2018a); Guo et al (2018b); Cao et al (2019); Cao et al (2020); Zhao et al (2020) have also used the stress amplification and stress shielding to explain the influence of the interaction.…”

Anisotropic Effective Elastic Properties for Multi-Dimensional Fractured Models

“…In this part, we apply Rubino's 2D method to a 3D cracked medium [30]. The governing Equations ( 1)- (11) would remain the same.…”

“…Rubino et al [25,26] employed 2D numerical oscillatory relaxation experiments to study the frequency-dependent effective stiffness matrix using the least-squares optimal approach. The method is used to characterize the frequency-and incidence-angle-dependent attenuation and velocity dispersion in cracked porous media for the P wave [27][28][29] and P-SV wave [30]. Jian et al [31] expanded Rubino's relaxation tests to a three-dimensional (3D) case for computing the equivalent stiffness matrix.…”