Unchannelized collapse of wet granular columns in the pendular state: Dynamics and morphology scaling

The unchannelized collapse of wet granular columns in the pendular state is investigated experimentally. Three different collapse regimes are observed in experiments, which are significantly dependent on the particle size as well as the initial aspect ratio of the column, while the water content has a quantitative effect on final deposit morphology. A dimensionless number containing the particle size and the water content is proposed to quantitatively characterize the macroscopic cohesion induced by the presence of water. On this basis, a phase diagram is put forward for describing different collapse regimes of wet granular materials. Furthermore, the dynamics and the resulting deposit morphology after collapse are primarily examined based on a series of experiments, particularly in two typical collapse regimes, where the coupling effects of particle size, water content, and initial aspect ratio of the column are mainly considered. Finally, generalized scaling laws have been developed to characterize the dependency of the deposit morphology on two relevant variables: the initial aspect ratio and the proposed dimensionless parameter. The morphological quantities in the wet case may be determined by respectively adding the variations caused by the cohesion effect to the results of dry granular material. The proposed scaling laws can be well degraded to those obtained in dry granular material when the cohesive effect inside wet granular material is weak enough. This implies that generalized scaling laws can be applicable to the collapse of granular material in a wider range of situations.

Figure 1

Schematic diagram of the experimental setup for the unchannelized collapse of wet granular columns in the pendular state.

Figure 2

Snapshots of the evolution of the collapse flow of granular columns with various particle sizes at an initial aspect ratio of $a=3$. (a) $d=0.5\mathrm{mm}$, $w=0\%$, (b) $d=2.0\mathrm{mm}$, $w=1\%$, and (c) $d=0.5\mathrm{mm}$, $w=1\%$. The yellow dashed line in (c) represents the failure plane obtained from the velocity field in the side view.

Figure 3

Final deposit morphology of the collapsed wet granular column under different experimental conditions. (a) Different $d$ at $a=3$, (b) different $a$ for $d=0.5\mathrm{mm}$, and (c) different $a$ for $d=2.0\mathrm{mm}$. The water content $w=1\%$.

Figure 4

Phase diagrams in phase space $\left(B_o^{-1}{w}^{2/3},a\right)$ for describing the collapse regimes of wet granular material, where red squares ($\blacksquare$), light blue circles ($•$), and dark blue diamonds ($⧫$) correspond to the noncollapse (NC), block collapse (BC), and continuous collapse (CC) regimes, respectively.

Figure 5

Scaled spreading distance on the horizontal surface traveled by the flow front as a function of normalized time in the unchannelized collapse of wet granular materials with different particle sizes at $a=3$. (a) The length along the longitudinal direction. (b) The maximum width along the lateral direction. The dashed lines in different colors correspond to the duration of wet granular flow for different particle sizes, respectively. (c) The variation of normalized flow duration $t_f/{\tau }_c$ with the initial aspect ratio $a$ for different particle sizes.

Figure 6

Velocity field at successive time steps in the BC regime, where the water content $w=1\%$, the particle diameter $d=0.5\mathrm{mm}$, and the initial aspect ratio of the column $a=3$. The colors and arrows in the velocity field are used to visualize the magnitude and direction of the velocity in the collapse flow, respectively.

Figure 7

Velocity field at successive time steps in the CC regime, where the water content $w=1\%$, the particle diameter $d=2.0\mathrm{mm}$, and the initial aspect ratio of the column $a=3$.

Figure 8

The height profile of final deposit morphology after the collapse of a wet granular column for various $a$ for the dry and wet cases. (a) Series of experiments in the BC regime with $d=0.5\mathrm{mm}$; (b) series of experiments in the CC regime with $d=2.0\mathrm{mm}$.

Figure 9

The deposit shape on the horizontal surface after the unchannelized collapse of wet granular columns with different initial aspect ratios (a) $a=1.5$, (b) $a=3$, (c) $a=7$, and (d) $a=10$. The water content $w=1\%$. The blue and red solid lines are the results of the particle size $d=0.5\mathrm{mm}$ and $d=2.0\mathrm{mm}$, respectively, and the gray dashed line is the corresponding circle with the same area for comparison.

Figure 10

The dependences of the runout distance (a), the deposit height (b), the deposit width (c), and the deposit area (d) on the water content for various particle sizes at the initial aspect ratio of the column $a=10.$

Figure 11

The variations of normalized runout distance (a), deposit height (b), deposit width (c), and deposit area (d) with the column initial aspect ratio $a$ for various particle sizes and water contents. The black, red, blue, and green dashed lines represent the fitted curves for wet granular materials with particle sizes of $d=0.5,1.0,2.0,\mathrm{and}5.0\mathrm{mm}$, respectively, while the light gray solid lines are the fitted results for dried particles.

Figure 12

Variations of normalized runout distance (a), maximum deposit height (b), deposit width (c), and deposit area (d) with the dimensionless number $B_o^{-1}{w}^{2/3}$ for various particle sizes and water contents at different initial aspect ratios.

Figure 13

Variations of the relative difference in normalized runout distance (a), deposit height (b), deposit width (c), and deposit area (d) between wet and dry particles with the dimensionless number $B_o^{-1}{w}^{2/3}$ for various particle sizes and water contents at different initial aspect ratios. The results for different column aspect ratios $a=3,5,10,$ and 13 are filled with cyan, orange, magenta, and green, respectively. The gray curve is the fitting result based on Eqs. (7, 8, 9, 10).

Figure 14

Dependences of the rescaled runout distance (a), maximum deposit height (b), deposit width (c), and deposit area (d) on the initial aspect ratio $a$, where the light gray dashed lines represent the results predicted by the generalized scaling laws.