Dense granular materials under low confining stress and low shear velocity—conditions relevant to low-pressure powder handling, near-surface transport, and the upper layers of stored bulk solids—remain insufficiently characterized at the microstructural level. We perform three-dimensional discrete element method (DEM) simulations of annular shear of monodisperse glass spheres at σ = 1 kPa and v = 0.01 m/s, corresponding to an inertial number I ≈ 1.06 × 10−3 at the quasi-static limit of the dense flow regime. The steady-state friction coefficient stabilizes at μss ≈ 0.78, consistent with the quasi-static limit of the μ(I) framework. The solid volume fraction decreases monotonically from φ ≈ 0.50 at the base to φ ≈ 0.35 near the top, while the tangential velocity decays exponentially with depth (decay length δs ≈ 10 mm). Particle trajectory tracking reveals a sharp kinematic transition near z ≈ 5–6 mm separating a quasi-rigid basal layer (z ≲ 5 mm) from an upper shear-active zone (z ≳ 6 mm). The contact force distribution follows an exponential decay P(f/⟨f⟩) ∝ exp(−β·f/⟨f⟩) with β ≈ 0.45, with strong force chains selectively concentrated in the upper zone. Together, these four microstructural descriptors co-locate within a single transition band, providing quantitative benchmarks for material characterization and constitutive modelling at the lower boundary of dense flow.
Luo et al. (Tue,) studied this question.