Is the widely used relation between mechanical and hydraulic apertures reliable? Viewpoints from laboratory experiments

Fluid flow through rock masses is a critical issue in rock engineering and geoscience in general, from shallow to great depths. The hydraulic aperture (e) of a single joint under stress is a key variable for simulating the fluid flow through rock masses. Because prediction models for the mechanical aperture (E) of different rock joints under different normal stresses are available, the hydraulic aperture at different depths can be readily estimated using numerous E−e relations. However, experimental hydromechanical studies frequently use the normal displacement method (ND method) for determining the mechanical aperture, for which the initial aperture needs to be “estimated”. This uncertainty can propagate to the E−e relation. In this study, we conducted high-quality laboratory measurements of mechanical/hydraulic apertures of saw-cut, polished aluminum samples, which are comparable to smooth rock joints, using the YOKO 2 system under confining stresses from 3 to 120 MPa. We measured the mechanical aperture directly from the joint volume (JV method); this method differs from the widely adopted ND method for measuring joint closure. The experimental results show that the estimation uncertainty of initial aperture, which is required for converting the joint closure curves into mechanical aperture, reduces the reliability of the existing E−e relations. Using ΔE−e relations for hydromechanical coupling analysis is suggested to avoid errors due to the initial aperture estimation based on the ND method. When the JV method is used to reduce the influence of initial aperture estimation, it is important to note that the contribution of the matrix pore volume of intact rock to the mechanical aperture measurement is not negligible even when the porosity of the matrix is less than 0.1%. Contrary, the matrix permeability of impermeable rock is negligible for laboratory measurements. Finally, neglecting the quadratic Forchheimer term leads to an underestimation of hydraulic aperture.