Effect of Including Sand Component in a Debris Flow on Concentration of Coarser Particles at the Flow Front

. We conducted flume experiments for a debris flow consisting of coarser particles, finer particles and sand, focusing on the concentration of coarser particles at the flow front. Our experimental results revealed that the concentration of coarser particles at the flow front using sediment mixture with sand was less than that without sand. This may be because including of sand component in the material contributed to be a smaller averaged interstice between particles in the flow layer and a smaller averaged particle size. These may lead to reduce the falling volume of sand or finer particles and dispersion pressure for the rise of coarser particles, respectively, resulting in the inhibition of inverse grading formation. Our experimental results also suggested that the changing trend in the proportion of finer particles depended on the relationship between their particle size and the average particle size of the flow. These are consistent with our previous experimental results using material without sand. This consistency suggested that for the concentration of coarser particles at the flow front, the behavior of the sand component can be considered in the same manner as other coarser-sized components.


Introduction
A debris flow is composed of sediment particles of various sizes. During its flowing down, particle size segregation occurs in the flow layer by interacting of these particles, resulting in a concentration of coarser particles at the flow front. This tendency is particularly pronounced for a debris flow that includes many boulders, as reported in many studies [1][2][3]. Therefore, many flume experiments and theoretical considerations have been conducted by many researchers to elucidate their mechanisms [3][4][5][6]. We too investigated their mechanisms for debris flows composed of several particle sizes by measuring the proportion of their particles at the flow front using many flume experiments [7][8][9]. These experimental results suggested that the "falling of finer particles through the interstices between particles toward the lower flow layer" proposed by Middleton [4] is the primary mechanism of an inverse grading. This led to relatively faster transport of coarser particles and their concentration at debris flow's front under various particle size compositions. In addition, we developed a one-dimensional (1-D) numerical model to describe this mechanism in a debris flow layer and to be able to estimate the sediment sorting at the flow front [9].
The finer component, whose diameter is approximately 0.01 times a debris flow depth, is often included in debris flow material. Therefore, it is necessary to investigate how these components affect the particle size segregation. In a flume experiment scale where a debris flow depth is approximately 0.01 times than that in a real scale, these components correspond to the sand component with a diameter of 0.1 mm order. * Corresponding author: wada-t@tottori-u.ac.jp Takahashi et al. [10] developed the numerical model illustrating the particle size segregation of a debris flow. In their model, they considered that the behavior of the sand components with a diameter of 0.1 mm order is the same as that of other coarser-sized components. Their experiments for their model validation were conducted with only one particle size composition of the debris flow material. Therefore, it is necessary to verify whether the behavior of sand component can be considered similar to other coarser-sized components for particle size segregation of a debris flow with various compositions of the material.
In this study, we conducted flume experiments on a debris flow composed of three-sized particles, including the sand component, under various compositions of the material. We compared these results with those of our previous experiment under the same conditions without the sand component [8,9], to investigate the effect of the sand component in a debris flow on the concentration of coarser particles at the flow front. Figure 1 shows the experimental setup consisting of two tilted straight flumes, a movable sampler with four boxes, and a digital video camera for measuring sampling time. The movable bed lengths of flumes A and B were 90 cm and 300 cm, respectively, and the widths of flumes A and B were 7 cm and 10 cm, respectively. The intent for using these two types flumes was to investigate the effect of including sand The supplied flow rate per unit width was 0.67 cm²/s, initial sediment thickness was 5 cm, and flume gradients was set to 15°. These quantities were common to both flumes.

Setup and Conditions of Flume Experiment
The sediment materials were composed of sand with a diameter of 0.6 mm, and two particles (referred to as coarser and finer particles, respectively) were chosen from four particles with diameters in the range of 1.4-10.7 mm. The proportions of coarser particles, finer particles, and sand in the materials was 1:4:1.25. The averaged mass density of these materials () was 2.695 g/cm 3 , averaged internal friction angle of these materials () was 31.6°, and their concentration in the static sediment bed (C*) was 0.557. The folloing discussion defines PC, PF, and Psand as the proportions of the three particles to the total material volume, respectively.
The experiments combined various conditions based on the coarser and finer particle sizes of the material and flow length (i.e., the experimental flume). Table 1 lists the experimental cases and their corresponding conditions. The experimental procedure is described as follows. After the materials were placed on the flume bed, water was supplied at the default flow rate at the upstream end of the flume. The supplied water eroded the materials as flowing down the flume, and a debris flow was generated. When the debris flow arrived at the downstream end of the flume, the flow front was separated into four parts by the sampler, which moved at a constant speed in the transverse direction with respect to the flow direction. The time interval during flowing the flow material into each box was measured using a digital video camera. Each sample's total flow volume, all particle volume, and each sized particle volume were measured to investigate the temporal changes in the sediment flux concentration and each particle's proportion. The above processes and measurements were repeated thrice for each material composition and each flume. The above setting and procedure are the same as the authors' previous experiment using debris flow material composed of the two particles without sand component [8,9]. In the following discussion, we compared these experimental results with our previous ones to investigate the effect of sand component in a debris flow on the proportion of coarser and finer particles at the flow front.   Figure 2 shows the temporal changes in PC and PF at the debris flow front in Case 2 B. The figure also shows the PC and PF for our previous experiment in which sand in the materials for Case 2 was excluded [8,9]. The concentration of coarser particles at the flow front using the material with sand was less than that without sand. The possible reason for this is that the including of sand contributes to a smaller averaged interstice between particles in the debris flow layer. This made difficult for particles to fall through the interstice toward the lower flow layer, resulting in the inhibition of inverse grading formation. In addition, the decrease in the averaged particle size of a debris flow caused by including sand component also may contribute to reduce the dispersion pressure owing to particle collisions for the rise of coarser particles in the flow layer.

Experimental Results and Discussion
The arrival time to the downstream end of the flume using the material with sand was shorter than that without sand. The reason for this is that the decrease in the averaged particle size by including sand reduced the flow energy dissipation owing to the friction and collision of these particles in the flow layer. This increasing in the debris flow velocity also may contribute to the reduction in the falling of sand or finer particles in the flow layer. This is because the migration velocities of particles in the flow direction become more apparent than those in the downward direction. Figure 3 shows the temporal changes in PC, PF, and PSand at the debris flow front in Cases 1 B and 2 B. In these cases, only the finer particle sizes of the materials were different. In Case 1, PSand was almost zero, PC increased, and PF decreased from the initial proportion of the material. These results suggested that the finersized particles had a more significant decrease in the flow front, and that when the finest particles were sufficiently reduced, the proportion of slightly coarser particles than the finest particles were reduced. In Case 2, at the most flow front, PC increased, and PF and PSand decreased from the initial proportion. These tendencies are similar to that in Case 1. However, immediately after the most front, PF became more than the initial proportion. These results suggest that the change in the proportion of intermediate-sized particles (in this paper, we refer to the finer particles) depends on the particle size composition of the debris flow. Specifically, in the case where the intermediate-sized particle is significantly coarser than the average particle size of the debris flow material, it increases from its initial proportion like the coarser particle. Otherwise, in the case where the intermediate-sized particle is nearly equal to or finer than the average particle size, it decreases from its initial proportion like the finer particle. The above inference is   also based on the temporal changes in the relationship between the mean diameter and the diameter of each sized particle in debris flow materials, as shown in Figure 4. This inference corresponds with the inference obtained by the authors' previous experimental results using a material consisted of five or six particles with a   diameter of more than 1.4 mm [7]. Therefore, the behavior of the sand component can be considered similar to other coarser-sized components in the mechanism of particle size segregation for various material compositions. Figures 5 and 6 show the relationship between the PC of the materials flowing into the first box and the initial mean diameter of the material, dm0, and dimensionless shear stress, *, for all cases and previous cases without the sand [8,9]. * was calculated by using the following equation: * = (ghI) 0.5 /{(/ -1)gdm0 (1) where g is the gravitational acceleration, h is the calculated debris flow depth using the cross-sectional averaged flow velocity equation proposed by Takahashi [5] and the equation of continuity for a debris flow, I is the flume gradient,  is the mass density of the materials, and ρ is the mass density of the interstitial fluid. These upper and lower figures suggest that, in both cases with debris flow materials with or without sand, the concentration of coarser particles at the flow front becomes more significantly as the flow distance increases. These also suggest that with or without sand, the relationship between dm0 and PC is a directly proportional, and the relationship between * and PC is an inversely proportional. These suggestions imply that for a debris flow including the sand component with a diameter of 0.1 mm order, the concentration of coarser particles at the flow front can be investigated based on the debris flow hydraulic quantities in the same manner as a debris flow without the sand component. Thus, for the concentration of coarser particles at the flow front, the behavior of the sand component can be considered in the same manner as other coarser-sized components.

Conclusion and Future Works
We conducted flume experiments on a debris flow consisting of coarser particles, finer particles, and sand under various debris flow compositions. And using our experimental results, we investigated the effects of including sand components in a debris flow on the mechanisms of particle size segregation at the flow front.
In the experimental results, the concentration of coarser particles at the flow front using the debris flow material with sand was less than that without sand. This is because including of sand component in debris flow material contributed to decrease in an averaged interstice between particles in the flow's interior, which made it difficult for sand or finer particles to fall through the interstices between particles toward the lower flow layer. In addition, decreasing of the averaged particle size could lead to a reduction in the dispersion pressure for the rise of coarser particles in the flow layer, resulting in the inhibition of the inverse grading formation.
Our experimental results also suggested that the changing trend in the proportion of the intermediatesized particles depended on the relationship between their particle size and the average particle size of a debris flow. This is consistent with previous experimental results using material without a sand component [7]. Furthermore, in both cases with debris flow materials with or without a sand component, the common relationship was observed between the concentration of coarser particles at the flow front and the debris flow hydraulic quantities. These results imply that the concentration of coarser particles at the flow front can be investigated, considering the behavior of the sand component in the same manner as other coarser-sized components.
However, it has not been sufficiently investigated which mechanism is dominant for the coarser particle's concentration at the flow front, the "falling of finer particles toward the lower flow layer," or the "rising of coarser particles by dispersion pressure derived from particle collisions." In our future works, we will investigate whether our numerical model only considered "falling of finer particles" in the flow layer can estimate our experimental results. If it will be difficult for our model to estimate, we will reveal the contribution of "rising of coarser particles by dispersion pressure" for particle size segregation of a debris flow with experimental and numerical approaches.