Scale dependency and anisotropy of mechanical properties of jointed rock masses: insights from a numerical study

Affected by discontinuities, the properties of rock masses are characterized by strong scale dependency and anisotropy. Rock mass samples taken at any scale smaller than the representative elementary volume (REV) size could lead to an incorrect characterization and property upscaling. To better understand the sampling problem, numerical tests based on an outcrop-data-based discrete fracture network (DFN) model were conducted, trying to determine the REV size and its anisotropy. The model was validated and subsequently sampled to produce 455 rectangular samples with a width ranging from 0.05 to 21 m and a constant height-to-width ratio of 2. The samples were introduced into a 3D particle flow code model to create synthetic rock mass (SRM) samples. Numerical uniaxial compressive tests at different loading directions were performed to study the scale dependency and anisotropy of mechanical parameters. The results show that the mechanical REV sizes in different directions differ, changing between 7 and 19 m. The mechanical properties of rock mass samples in a REV size exhibit strong anisotropy, with the values of uniaxial compressive strength (UCS) and elastic modulus (E) varying from 5.6 to 10.3 MPa and 3.9 to 8.0 GPa, respectively. The simulated values of UCS were validated based on GSI and the Hoek-Brown failure criterion. The geometrical REV size based on the volumetric fracture intensity was calculated to be 7 m, equal to the minimum of the mechanical REV size; this suggests that the geometrical REV defines the lower bound of the REV size.