The effect of debris-flow sediment grain size distribution on fan forming processes

Knowledge of the processes driving debris-flow fan evolution are critical in the support of efforts to mitigate related hazards, reduce risk to populations and infrastructure, and reconstruct the history of sediment dynamics in 10 mountainous areas. Research on debris-flow fan development has focused on topographic controls, debris-flow volume and rheology, and the sequence of occurrence of debris flows. While these items have explained a great deal about fan formation and specifically avulsion and runout mechanisms, there is a need to further investigate other properties as they relate to debris-flow fan formative process. Here, we examined the role of debris-flow grain-size distribution on fan formation. Flume experiments were employed to examine the morphology of debris-flow fans that resulted from flows with monoor multi15 granular sediment composition with the same average grain size. All other flow characteristics were held constant. The mono-granular flows formed a symmetric-like fan morphology because there was little avulsion during the formation process. The multi-granular flows produced fans with an asymmetric morphology. Avulsions occurred on both lateral extents of the fan during the early stages of fan development and caused the runout direction to shift produce the fan asymmetry. Grain-size distribution was closely related to spatial diversity in fan morphology and stratigraphy. 20

grain-size distributions. The grain-size distribution has been shown to affect the properties of the released granular flows, such as the flow depth and velocity (Egashira et al., 2001;Kaitna et al., 2016;Sakai et al., 2019). The experimental conditions were designed to purposely avoid unexpected changes in the flow state caused by very large and small sediment 65 particles by adjusting the mixing ratio of sediment particles used in the flume tests but maintaining the same average grain size (D50) between the mono-granular and multi-granular flows ( Fig. 1c and Table 1).

Measurement and analysis
The flow depths and arrival times of the granular flows were monitored and compared as sediment was released to the deposition area in the various simulations. The flow depth of a generated granular flow cannot be measured in the flume 70 because the thickness of the erodible bed decreases sequentially in response to the sediment entrainment. Therefore, the displacement of the flow surface at three positions in the flume (upper,middle,and lower,Fig. 1a) was measured to account for this shortcoming, using ultrasonic displacement meters (described in Sect. S1 in the Supplement).
Four digital cameras installed above the deposition area (Fig. 1a) observed the fan-formation processes (Tsunetaka et al., 2019). Three of these cameras were automatically synchronized using the external shutter and captured images at 1-s 75 intervals. Using a photogrammetry software, we produced digital elevation models (DEMs) and orthophotos that were georeferenced by the coordinates of visible (exposed) intersections of the grid lines on the deposition area (i.e., at the intersections of the grid lines that were not concealed by deposited sediment) from respective sets of three synchronized images (Sect. S2). Deposit depths were measured at the intersections of the grid lines when the fans formed, and compared the measurements with the deposition depths extracted from the generated DEM. The measured elevations corresponded to 80 the DEM-extracted elevations, thereby indicating that the DEMs approximated well to the fan morphology (Fig. S1).
The fourth camera recorded a video of the fans as they formed at a frame rate of 60 fps. Paired image sets were extracted from two images at a 1/60-s time resolution from the video. The paired image sets were processed by a particle-imagevelocimetry (PIV) algorism to show the vectors of the flow velocity at the surface of the deposition area (Sect. S2). During the inundation of sediment at the deposition area, the SfM-MVS photogrammetry could not measure locations where 85 granular flows descended, which resulted in holes of DEMs due to lacking topographic data (e.g., Fig. 5). The vectors of the flow velocity projected by the PIV analysis could compensate for the holes of DEMs, allowing for the investigation of changes in flow direction caused by avulsions. The used videos were acquired from an almost-vertical direction against the area with a 9° slope. It is worth noting that the shooting depth varied spatially in the angle of view because the camera was not strictly vertical to the whole of the deposition area and spatiotemporal changes in fan morphology, which means that the 90 velocity projected by the PIV analysis was not strictly accurate. The measurements of the flow-velocity vectors were useful to investigate changes in the flow direction that occurred during the fan development, rather than measure flow velocity.

Flow state in the channel
Both mono-granular and multi-granular flows descended to the lower position in the flume ~6-7 s upon leaving the arrival 95 point at the upper position (Fig. 2). Given an initial erodible bed thickness of approximately 0.2 m, the peak of the monogranular flows ranged from ~0.03 to 0.07 m for the test runs, while, apart from run 1, those of the multi-granular flows were around ~0.03 m (Fig. 2). The thickness of the erodible bed decreased monotonically with time, probably because the entrainment rate was the same in all the test runs, irrespective of the grain-size distribution of the granular flows ( Fig. 2), which confirms that the released granular flows had reached a steady state. Overall, the results from the flume experiment 100 showed that the difference in the grain-size distribution did not lead to substantial changes in the hydrograph and arrival time of the granular flows.
Exact replication of the dynamic conditions of natural debris flows was not possible in our reduced-scale flume tests, as reported in other similar flume experiments (e.g., De Haas et al., 2015b). The ratios between the flow depth of the front in the channel to the average grain size (i.e., 2.6 mm; Table 1) were between ~10-30, which confirms that the released granular 105 flows that were experimentally modelled as so-called boulder debris flow could be explained as steady laminar flows in terms of their dynamic similarity (Hotta and Miyamoto, 2008).

Runout of surge front
While the mono-and multi-granular flows in the flume were similar, their runout characteristics differed. The fronts of the mono-granular flows travelled faster and further downstream than those of the multi-granular flows ( Fig. 3a, b). 110 Consequently, the velocities of the multi-granular flows from the start to the end of the runout of the front were about ~0.1 m/s less than those of the mono-granular flows (Fig. 3c). Analysis of the grain-size distribution from the center of the multigranular fans (Figs. S2 and S3) shows that particles were segregated by grain sizes and relatively large particles accumulated at the downstream edge of the flow fronts (Figs. S2f and S3f). The difference in the grain-size distribution of the released flows did not affect the flow in the flume but may have changed the flow velocity and frictional resistance in the deposition 115 area where the grains were segregated by size.

Formed fan morphology
The flow direction and deposition range differed between the mono-granular and multi-granular flows. In the first 10 s of the flow, both types of granular flow descended in an approximately straight flow direction, but the locations of the lobe-like deposits generated by the flow fronts differed (Figs. 4 and S4). Between 20 and 50 s after the flow was released, the mono-120 granular flows descended in a straight line through the zone with a 9°-12° slope without substantial avulsion, but then The mono-granular flows had similar profiles and bilaterally symmetrical fan morphologies (Fig. 10a, d, g). Similarly, the 130 multi-granular fans had similar longitudinal profiles, irrespective of the elongated direction (Fig. 10b). However, the multigranular flows were less deep than the mono-granular runs in the area 2 m downstream from the flume outlet (Fig. 10c).
Although the peaks of the deposition depth of the longitudinal profiles were similar between the multi-granular and monogranular flows (Fig. 10a-c), the flows were laterally wider and larger 1 m downstream from the flume outlet (Figs. 10d-f).
There were noticeable differences in the deposition depths of the mono-granular and multi-granular flows at the cross section 135 2.2 m downstream from the flume outlet ( Fig. 10g-i). The deposition depths of the multi-granular flows varied by more than 0.03 m, depending on the direction of the elongated fan (Fig. 10i). The fan widths of the multi-granular flows were notably larger again at 2.2 m (Fig. 10g-i). A larger fan width is an expected consequence of the avulsion observation and PIV support information from the multi-granular flow modelled scenarios.

Discussion 140
The fan-forming processes and the sediment deposition and stratigraphy changed in response to changes in grain-size distribution of the released granular flows, while holding all other conditions constant. Some equations that describe debris flows assume that multi-granular debris flows can be approximated to mono-granular debris flows with the same average grain-size (e.g., Egashira et al., 1997;Takahashi, 2007). However, the mono-granular and multi-granular flows with the same average grain-size produced fans with different morphologies, and the fans that resulted from the multi-granular flows 145 also varied between the test runs (Figs. 9 and 10), which indicates that existing models that assume a mono-granular approximation may provide ambiguous simulations of the debris-flow deposition and inundation ranges.
The fronts of the multi-granular flows were comprised of relatively large sediment particles (Figs. S2 and S3), reflecting grain-size segregation often discussed in the literature (e.g., Johnson et al., 2012) and evidenced in the field. These large particles may increase the flow frictional resistance (e.g., De Haas et al., 2015b;Hürlimann et al., 2015), which may help 150 explain why the runout distance and velocity of the released multi-granular flow fronts were shorter and lower than those of the mono-granular flows, respectively (Fig. 3). The flow rates and arrival times of the mono-and multi-granular runs were almost the same in the flume (Fig. 2). This finding suggests that the thick and short lobe-like deposits of the multi-granular flows reflected the shorter runout distances (Figs. 4 and 10c), which may in turn have triggered the pronounced avulsion further upstream of the deposition area that did not form for the mono-granular flows (Figs. 5-8 and S5-S8).
The thick and short deposits with surfaces comprised of large particles identified in the early stage of the fan-forming processes might facilitate the dispersion and seepage of the pore fluid through the fan because of its high permeability, and lead to unsaturated conditions at the fan surface. Other researchers, through field measurements and flume experiments, have shown that deposition of debris flows may be triggered when the surfaces of channel beds are highly permeable and unsaturated (e.g., Major and Iverson, 1999;Staley et al., 2011;Tsunetaka et al., 2019). As there was little difference between 160 the runout characteristics of the multi-granular test runs (Figs. 3b and 4e-h), the variations in the fan morphology may reflect spatial and temporal variations in the degree of saturation throughout the fan. If this is the case, even processes that drive mono-granular fan formation may vary among test runs, particularly when mono-granular flows comprise large particles that can facilitate the dispersion and seepage of pore-fluid in a formed fan.
This examination of the grain-size distribution of debris flows shows that fan-forming processes are complex and reflect the 165 interactions between their functional and structural characteristics. The differences in the experimental fan morphometries highlight how varying orders of grain-size distribution strongly impact debris-flow fan development and produced varying stratigraphic layers. The findings also considered the moisture regime of the experimental fan evolution, which improves the accuracy and reliability of forecasts of the deposition and inundation ranges of debris flows around channel outlets.

Conclusions
While it is accepted that the morphology of debris-flow fan depends on the characteristics of the debris flow that is released to the fan apex (e.g., flow stage and sediment concentration), there is still considerable debate about how changes in these characteristics impact fan-forming processes. In this study, changes in fan morphology were investigated, with a particular focus on the grain-size distribution of the released debris flow. We carried out reduced-scale flume experiments to model the 175 morphology of debris-flow fans that resulted from flows that were mono-or multi-granular with the same average grain size, but with all other flow characteristics the same. The mono-granular flows formed a symmetric-like fan morphology because there was little avulsion during the formation process. The multi-granular flows produced fans with asymmetric morphology, and had avulsions on both sides during the early stages of the inundation, which caused the runout direction to shift as the topography evolved. Our results show that the grain-size distribution was closely related to spatial diversity in fan 180 morphology and stratigraphy.

Data availability
The data used in this study are freely available from the corresponding author upon request.    In panels c, f, and i, the broken gray line indicates the average value of all the mono-granular flows. The red and black lines indicate the average values of the flows that produced fans that were elongated on the left bank side (i.e., runs 2 and 3) and on the right bank side (runs 1 and 4), respectively.