Monodisperse material
The run-outs of the monodisperse materials increased with the inclination of the lower slope (Figure 4). It is easy to understand that the materials had a higher mobility on steeper slopes. However, it is surprising that the run-outs of the three monodisperse materials were almost identical on the slope with the same inclination. Coarse materials would move farther than fine materials due to less energy consumption caused by intergranular friction.
The morphology of the main part of the deposit for the three monodisperse materials on the slope of 0°, 5°, 10°, and 15° are shown in Figure 5, 6, 7 and 8, respectively. The deposit morphology of the three monodisperse materials was similar on the slope with the same inclination.
The mass of each material (i.e. gravel, coarse sand, and fine sand) into the second part of the deposit was weighed. The coarser the particles, the more particles accumulated on the second part of the deposit (Figure 9). This means that coarse particles were easier to travel a long distance. The mass of the fine sand accumulated on the second part of the deposit was 1.0 g regardless of the inclination of the lower slope. With the increasing angle of the lower slope, more coarse sand and gravel moved far and deposited on the second part, especially for the gravel. This implies that coarse particles were prone to travel farther than fine particles on the steep slope.
A polydisperse material with the same mass of gravel, coarse sand, and fine sand
A polydisperse material was used, which consisted of 1.0 kg gravel (Mg = 1.0 kg), 1.0 kg coarse sand (Mc = 1.0 kg), and 1.0 kg fine sand (Mf = 1.0 kg). The run-out of this polydisperse material is shown in Figure 10, combined with those of the three monodisperse materials. The mobility of the polydisperse material was significantly higher than the monodisperse materials. This implies that the interactions between coarse and fine particles were helpful to enhance the mobility of granular flows.
Figure 11 shows the deposit morphology of this polydisperse material (Mg = Mc = Mf = 1.0 kg) on the 0°, 5°, 10°, and 15° slope, respectively. Comparing with the monodisperse materials, the deposit shape of this polydisperse material was low and long.
Each case was repeated three times with this polydisperse material (Mg = Mc = Mf = 1.0 kg), and the second part of the deposit were weighted for each time (Figure 12). Less than 100 g of the materials accumulated on the second part of the deposit, and a majority of particles travelled a long distance.
Polydisperse materials with various fractions of fine sand
In order to further confirm the effect of the interactions between particles on enhancing the mobility of granular flows, polydisperse materials with various fractions of fine sand were released. In each series, the mass of the gravel was maintained (1.0 kg, 1.4 kg, or 1.8 kg), and the rest consisted of coarse sand and fine sand at different mixing proportions. Fine sand mass fraction F
f
was defined as the proportion of fine sand in total mass. For example, when the mass of the gravel was 1.0 kg, the mass of the fine sand was 0, 0.4 kg, 0.8 kg, 1.2 kg, 1.6 kg, and 2.0 kg, respectively. Thus, F
f
ranged from 0 (no fine sand) to 0.67 (all fine sand) when the mass of the gravel was 1.0 kg.
Figure 13 shows the run-outs of flows on the 15° slope, which were consisting of coarse and fine particles: gravel as coarse particle, and coarse and fine sand as fine particle. The mobility was enhanced due to the interactions between particles on the 15° slope, except in the case with 1.0 kg gravel and 2.0 kg fine sand where the run-out of this polydisperse material was significantly smaller than that of the three monodisperse materials.
The trend of run-outs for the polydisperse materials in the three series was similar. The run-outs increased with F
f
until reaching a peak, and then decreased with further increasing F
f
. This suggests that a certain amount of fine sand advanced the mobility of granular flows, and excessive amount of fine sand obstructed their propagation. The reason might be that a thin layer of fine sand acted as rollers for the rolling of the gravel, leading to the reduction of effective friction resistance during the movement; the interactions between particles became more complicated than they just acted as a single-row roller to lubricate the gravel when excessive amount of fine sand was involved. These rollers threw into disarray so that the particles might be either blocked or forced into sliding. Furthermore, from the point of view of energy, the energy was consumed significantly due to interegranular friction when excessive amount of fine sand was involved that the gravel was embedded in a matrix of fine sand.
When F
f
was small (0 < F
f
≤0.2), the flows with 1.8 kg gravel (blue line, Figure 13) exhibited the highest mobility. This implies that the polydisperse material containing more coarse particles might travel farther than that with less coarse particles at small F
f
. The main cause may be that the gravel typically had a high porosity, and the interactions between particles would be reduced by substituting a coarse particle for the same mass of fine particles. Frictional loss was proportional to the surface area of particles available for the interactions, and thus less energy was consumed by intergranular friction when the mass of the gravel increased.
The flow with 1.8 kg gravel at F
f
= 0.13 (1.8 kg gravel, 0.8 kg coarse sand, and 0.4 kg fine sand) travelled the longest run-out of 109 cm; the maximum run-out of 102 cm was observed for the flow with 1.4 kg gravel at F
f
= 0.27 (1.4 kg gravel, 0.8 kg coarse sand, and 0.8 kg fine sand), and the peak in run-out was 98.3 cm for the flow with 1.0 kg grave at F
f
= 0.27 (1.0 kg gravel, 1.2 kg coarse sand, and 0.8 kg fine sand). For the polydisperse materials with different mass of gravel, the flows exhibited the highest mobility at different F
f
. The interaction of particles with different sizes and shapes became more complicated when internal structure of granular flows was varied. The precise details of interactions among constituent particles are still poorly understood.
The flows containing 1.8 kg gravel show a peak in run-out over a range of F
f
between 0.1 and 0.2. The peak in run-out extended over a greater range of F
f
between 0.1 and 0.3 for the flows containing 1.4 kg gravel, and of F
f
between 0.1 and 0.4 for the flows containing 1.0 kg gravel. The peak was sharper in the experiments with 1.8 kg gravel. This suggests that the mobility was more sensitive to the proportion of fine sand when more gravel was involved.
The run-outs of flows on the slope of 10°, 5°, and 0° are shown in Figures 14, 15, and 16, respectively. The polydisperse materials also travelled farther than the three monodisperse materials on these slopes. The trends of run-outs were similar to that on the 15° slope. However, the run-outs on the gentle slopes were shorter than that on the 15° slope. This indicates that the inclination of the lower slope significantly influenced the mobility of polydisperse materials. The difference in run-out was not significant for a range of F
f
on these gentle slopes, comparing with that on the 15° slope. This implies that the effect of the interactions between coarse and fine particles on enhancing the mobility of polydisperse materials was not fully developed on the gentle slopes, i.e. the rolling motion did not readily occur on the gentle slopes. On the 5° and 0° slope, the run-outs were almost identical at large F
f
(0.3 ~ 0.67) regardless of the mass of gravel. This was because the gravel embedded in a matrix of fine sand and was difficult to move on these gentle slopes.
Figure 17 shows the deposit morphology of the main part of the deposit accumulated on the lower slope with different inclinations. The three flows, consisted of various constitute particles, were selected for comparison. Each of the three flows (Mg = 1.0 kg, Mc = 1.2 kg, Mf = 0.8 kg; Mg = 1.4 kg, Mc = 0.8 kg, Mf = 0.8 kg; Mg = 1.8 kg, Mc = 0.8 kg, Mf = 0.4 kg) typically exhibited the longest run-out in the series on the 15° slope. The deposit morphologies on the steep and gentle slopes significantly departed from each other. This indicates that the deposit morphology of granular flows was also influenced strongly by the inclination of the lower slope. The deposit profile was much flatter and longer on the steep slopes (15° and 10°) than that on the gentle slopes (5° and 0°). This phenomenon implies that there was a critical inclination of the lower slope between 5° and 10° at which particle motion in flows changed in this work. When the slope was steeper than the critical inclination, the particles were prone to rolling. Otherwise, the particles exhibited sliding motion.
For all polydisperse materials used in the experiments, the deposits exhibited some common features as follows. First, coarse particles segregated to the surface of fine particles. This phenomenon is also observed frequently in field investigations. Second, the region of maximum concentration of particles was farther from the flow origin on the steeper slope, that is, more materials were transported a long distance. A broad range of granular materials accumulated from the position 20 cm to 90 cm on the 15° and 10° slopes. On the gentle slopes, however, the deposits concentrated a narrow range from the position 0 cm to the position 40 cm. The materials were prone to contribute to add the deposition height rather than the run-out on the gentle slope. Finally, the deposit morphologies were almost similar on the same slope for the three flows with different polydisperse components. This implies that the mobility of granular flows was more sensitive to the inclination of the lower slope than granular component.