Modeling of Stress-Dependent Properties During the Closure of Prestressed Elliptical and Nonelliptical Fractures

Elliptical fractures are often used to characterize the deformation of real fractures; however, their deformation responses do not accurately align with those of actual fractures. Nonelliptical fractures shorten by closing near the fracture tips under compression, demonstrating significant advantages in accurately capturing fracture closure characteristics. This warrants investigation of the elastic response of rocks containing nonelliptical fractures. Focusing on single-fracture closure, this study verifies the accuracy of the numerical simulations for elliptical and nonelliptical fractures. A dynamic numerical simulation for crack deformation under compression is proposed to simulate crack closure. The stress-dependent fracture parameters are collected for models consisting of the two fracture types. Then, the pressure-dependence of wave velocities is fitted using an empirical relationship. Under initial compression (<10 MPa), the velocity increase in the elliptical fracture model is just 14.45% of that in the nonelliptical fracture model, displaying a three-stage stress-dependent behavior. The nonelliptical model follows a more realistic two-stage trend, which is more consistent with empirical observations. Moreover, the differences between microscopic parameters are negligible for the models containing elliptical and nonelliptical fractures with a small aspect ratio (≈0.003). This research lays a theoretical foundation for future inversion of fracture distributions using nonelliptical fracture models.