Scaling Laws Linking Particle Size Fractality to Contact and Force Chain Networks in Sheared Granular Media: A Discrete Element Study

Sheared granular media—fault gouges, landslide shear zones—develop power-law grain size distributions whose fractal dimension D saturates near 2.5–3.0, a limit classically attributed to the geometric postulate that a grain breaks only when loaded by neighbours of comparable size. That postulate has never been reduced to scaling laws. We therefore prescribe D rather than generate it: six truncated fractal gradings (D = 1.0–3.5, 0.4–4 mm) are sheared to a strain of 80 in three-dimensional discrete-element ring shear simulations at 100 kPa. The grain fractality propagates into the contact network with an amplified exponent, N(≥R*) ∝ R*−αc with αc = 1.25D, bounded between the faithful inheritance and random-pairing limits; the exponential force tail narrows linearly, β = 0.139D + 0.43; and the like-size coarse contacts vanish as fLL ∝ e−4.23D, decaying as the cube rather than the square of the coarse number fraction, which quantifies the cushioning by the fine matrix. The box-counting dimension of the strong force skeleton is near-universal (Df ≈ 1.64–1.80). Combining these laws, a breakage opportunity index Θ ∝ exp(−4.65D) collapses by three orders of magnitude between D = 1 and D ≈ 2.6; the contact topology outweighs the force redistribution ten-fold. The comminution is self-arresting: the terminal fractal dimension is a topological, not an energetic, limit.