An Extended Hyperbolic Closure Model for Unmated Granite Fractures Subject to Normal Loading

Abstract

The closure behavior of rock fractures subject to normal loading is essential for deformation analysis of fractured rock masses and the modeling of associated coupled processes. Previous studies have mainly focused on characterizing the closure behavior of mated fractures, and the applicability of existing models to unmated fractures and characteristics of involved parameters have not been comprehensively investigated. We conducted normal loading tests on three tensile granite fractures with different mating degrees by dislocating the fracture surfaces with three offsets. A high-resolution contact model was used to simulate the fracture closure behavior, which was validated by comparing the simulated closure curves and the surface damage areas with experimental measurements. After that, it was applied to simulate the closure behavior for nine numerically generated surfaces with different surface roughness characteristics. The experimental and numerical results exhibit a downward bending trend in the stiffness versus stress curves, which existing models cannot accommodate. An extended hyperbolic model was established by introducing an exponent parameter into the classical Barton–Bandis hyperbolic model, which can better represent the experimental data than previous models. Via regression analysis, we found that the exponent parameter has an approximately constant value of 0.3. The maximum normal displacement is about two times of the mean aperture. The initial stiffness is positively correlated with the elastic modulus and the correlation length and negatively correlated with the mean aperture. Parameters involved in the extended model have precise physical meanings, and they are mathematically predictable based on measurable mechanical and geometrical properties of the rock fractures.