Abstract / Summary
Abstract A mechanical representative elementary volume (REV) is commonly inferred from stabilization of a mean property, although uncertainty and failure behavior may converge at different scales. We tested this assumption using 240 field-constrained three-dimensional discrete fracture networks for weakly weathered and fresh basalt at six sizes (5–50 m). DFNLab quantified freely slipping-joint lower-bound directional compliance for every realization. Orthogonal sections from one calibrated network per rock-population-scale cell produced 72 finite-discrete element responses; stochastic evidence is therefore limited to elasticity. Fracture count and surface-area intensity became ensemble-stationary at 10 m, but the prescribed 30 m maximum fracture length made 30 m the first boundary-admissible scale. Between 40 and 50 m, direction-mean lower-bound modulus changed by less than 0.7%. Its coefficient of variation nevertheless remained 2.21% and 1.44% for weakly weathered and fresh rock. Fitted self-averaging exponents of 0.43 and 0.47 were far below the ideal three-dimensional value of 1.5. In the tested finite-discrete element networks, direction-mean E₅₀ changed by only 3.6%-4.0% from 5 to 50 m, whereas peak strength and pre-peak energy decreased by 26.7%-30.0% and 47.3%-55.3%. The factor η = 2E₅₀Wₚ r ₑ/σₚ² remained near 1.21; grouped cross-validation predicted energy with R² = 0.912 and 8.1% mean absolute percentage error. The near-constant η identifies the squared strength decline, rather than stiffness change, as the dominant energy-scaling mechanism. Representative model size should therefore distinguish ensemble stationarity, boundary admissibility, elastic uncertainty and conditional failure behavior.