Anisotropic Effective Elastic Properties for Multi-Dimensional Fractured Models

The size, distribution, and orientation of fractures are generally multiscale and multi-dimensional in nature, leading to complex anisotropic characteristics. Theoretical or semi-analytical methods to determine the effective elastic properties depend on several assumptions, including the absence of the stress interaction and idealized fractures. On the basis of finite-element models, we conduct numerical oscillatory relaxation tests for determining the effective elastic properties of fractured rocks. The numerical approach for calculating equivalent stiffness tensors in two-dimensions is compared to the theoretical models for different fracture densities. Due to fracture interactions at high fracture densities, the suggested model makes a physical prediction. The effective elastic properties obtained from the application to a real fractured model, established from an outcrop, obviously disperse at different frequencies, which can be used to investigate fracture interactions and dynamic stress disturbances. The algorithm is extended to three-dimensional cases and also validated by using conventional effective medium theories. It is found that the fracture density obviously impacts the effective anisotropy properties, and the proposed method gives a reasonable prediction for high-fracture density. This work is significant because it enables the calculation of effective elastic properties of multi-dimensional fractured models and the fracture interaction mechanism.