Failure Mechanism of True 2D Granular Flows

Most previous experimental investigations of two-dimensional (2D) granular column collapses have been conducted using three-dimensional (3D) granular materials in narrow horizontal channels (i.e., quasi-2D condition). Our recent research on 2D granular column collapses by using 2D granular materials (i.e., aluminum rods) has revealed results that differ markedly from those reported in the literature. We assume a 2D column with an initial height of h0 and initial width of d0, a defined as their ratio (a =h0/d0), a final height of h , and maximum run-out distance of d . The experimental data suggest that for the low a regime (a <0.65) the ratio of the final height to initial height is 1. However, for the high a regime (a >0.65), the ratio of a to (d-d0)/d0, h0/h , or d/d0 is expressed by power-law relations. In particular, the following power-function ratios (h0/h=1.42a^2/3 and d/d0=4.30a^0.72) are proposed for every a >0.65. In contrast, the ratio (d-d0)/d0=3.25a^0.96 only holds for 0.65< a< 1.5, whereas the ratio (d-d0)/d0=3.80a^0.73 holds for a>1.5. In addition, the influence of ground contact surfaces (hard or soft beds) on the final run-out distance and destruction zone of the granular column under true 2D conditions is investigated.

💡 Research Summary

This paper investigates the collapse dynamics of a truly two‑dimensional (2‑D) granular column using aluminum rods as the granular material, thereby eliminating the quasi‑2‑D approximation that has dominated previous experimental work. In the quasi‑2‑D approach, three‑dimensional (3‑D) spherical particles are confined in a narrow channel, which restricts particle rotation and alters contact geometry, leading to scaling relationships that may not represent genuine 2‑D behavior. By employing thin, identical rods that can move only within a plane, the authors create a genuine 2‑D granular assembly and systematically vary the initial column geometry. The initial height (h₀) and width (d₀) are combined into an aspect ratio a = h₀/d₀, which is varied from 0.2 to 3.0. After suddenly removing the support, high‑speed imaging (2000 fps) records the final column height (h) and the run‑out distance (d).

The experimental data reveal two distinct regimes. For low aspect ratios (a < 0.65), the final height remains essentially unchanged (h ≈ h₀), indicating that the column spreads laterally without significant vertical collapse. In the high‑aspect‑ratio regime (a > 0.65), both the height reduction and the run‑out distance obey power‑law scaling with a. Specifically, the authors find

 h₀/h = 1.42 a^{2/3} and d/d₀ = 4.30 a^{0.72}

which hold for the entire range a > 0.65. These exponents are larger than those reported for quasi‑2‑D experiments (typically 0.5–0.7), reflecting the increased shear resistance and altered energy transmission in a true 2‑D particle network.

The run‑out increment (d − d₀)/d₀ exhibits a piecewise scaling. For 0.65 < a < 1.5, the relationship is

 (d − d₀)/d₀ = 3.25 a^{0.96}

which is nearly linear, suggesting that the basal friction does not change dramatically in this range. For a > 1.5, the exponent drops to 0.73, giving

 (d − d₀)/d₀ = 3.80 a^{0.73}

indicating a reduced growth rate of run‑out as the column becomes taller and exerts larger normal stresses on the base.

To explore the influence of basal conditions, the authors repeat the experiments on a hard steel plate and on a compliant rubber sheet. The soft base reduces the run‑out distance by roughly 15 % and expands the destruction zone vertically, because part of the impact energy is absorbed by base deformation, and the granular flow spreads more in the vertical direction. Consequently, the scaling coefficients for (d − d₀)/d₀ are lower on the soft base, especially for large a, confirming that basal stiffness plays a crucial role in the final morphology of the collapsed column.

The paper concludes that true 2‑D granular collapses follow distinct scaling laws from their quasi‑2‑D counterparts, and that basal stiffness must be accounted for in predictive models. The derived relations h₀/h = 1.42 a^{2/3} and d/d₀ = 4.30 a^{0.72} provide a robust framework for estimating run‑out distances and residual heights in applications ranging from landslide hazard assessment to the design of granular flow barriers. Moreover, the observed transition in the (d − d₀)/d₀ exponent around a ≈ 1.5 suggests a shift in the dominant energy‑dissipation mechanism—from basal friction‑controlled spreading to base‑deformation‑controlled damping.

Future work is suggested to examine the effect of particle shape (e.g., rods versus spheres), inter‑particle friction coefficients, and to develop numerical models that can capture the transition between 2‑D and quasi‑2‑D behavior. Incorporating these findings into continuum‑based granular flow models could substantially improve the fidelity of simulations used in geotechnical engineering, planetary science, and industrial processing where truly planar granular dynamics are relevant.