Analytical relationships between normal stress and fluid flow for single fractures based on the two-part Hooke's model

The normal stress-dependent hydraulic properties of single fractures are fundamental in hydro-mechanical coupling for the fractured reservoirs. With increasing normal stress, fluid flow through single fractures de-creases dramatically in the low stress range and then gradually in the high stress range, respectively. In order to describe this heterogeneous hydro-mechanical behavior, analytical relationships between normal stress and fluid flow for single fractures are established based on the two-part Hooke's model (TPHM), in which the fracture aperture is conceptualized into two parts at a macro scale, hard part and soft part. The contributions of soft part and hard part apertures on the hydraulic properties are separately evaluated by the different mechanical properties with normal stress. The validity of the proposed relationships between normal stress and fluid flow is verified by the good agreements between experimental data and theoretical predictions for natural and induced tensile fractures. The significant reductions of permeability and flow rate at low stress are dominated by the soft part and the degree of their nonlinearity highly depends on the spatial correlation of fracture geometry. In addition, the irrecoverable fracture deformation and flow drop between loading cycles are also greatly affected by the soft part while the fracture modulus of the hard part exhibits a weak dependence on loading cycle. The proposed relationships can be used to evaluate the coupled hydro-mechanical processes in fractured rock en-gineering such as geothermal energy development, CO2 geologic sequestration and stability of fractured rock slope.