A High-Resolution Contact Analysis of Rough-Walled Crystalline Rock Fractures Subject to Normal Stress

Analysis of rock fracture deformation by normal stress is important for quantifying hydromechanical properties of fractured rocks that are related to a large number of geophysical problems and geoengineering applications. Experimental and numerical results for the closure of crystalline rock fractures subject to normal stress are presented in this study. An efficient high-resolution, half-space elastic–plastic contact model for analyzing the closure of crystalline rock fractures based on the Boussinesq’s solution is validated by high-precision and high-resolution experimental data. Using the validated elastic–plastic model, we investigate the correlation between fracture-specific stiffness and multi-scale surface roughness. The wavelet analysis method and the extended averaged slope magnitude for asperity heights (referred to as \( Z_{2}^{{3{\text{D}}}} \)) are introduced to characterize the multi-scale surface roughness. The results show that the elastic–plastic contact model is effective and precise in modeling the closure of crystalline rock fractures, which matches better with the test results than the elastic model. The multi-scale features of surface roughness can be well characterized by the wavelet analysis and the extended roughness parameter \( Z_{2}^{{3{\text{D}}}} \). The specific stiffness is nonlinearly correlated with the multi-scale surface roughness that possibly follows a power law. The validated elastic–plastic contact model and the multi-scale surface roughness characterization methods, as well as the nonlinear correlation between the specific stiffness and the multi-scale surface roughness presented in this study, are helpful for evaluating the dependence of mechanical behaviors of rock fractures on its multi-scale surface roughness.