Laboratory investigation of the effects of grain size on the dynamics of debris flows: Measurement of pore fluid pressure in an open channel

. The dynamics of debris flow depend on internal stress components, such as particle–particle stress, the stress exerted by pore water, and interactions between particles and pore water. Although dominant internal stress components depend on the grain size composition, the effects of grain size on the dynamics of debris flow are not fully understood. To investigate the effects of grain size on the dynamics of debris flows, pore fluid pressures were measured in an open channel experiment. In the experiment, monodisperse debris flows were triggered for five different grain sizes: 0.2, 0.8, 1.3, 2.2, and 2.9 mm. The pore fluid pressures in debris flows of 0.2 mm grains had larger excess pressures over the hydrostatic pressure, and were close to the total normal stress, while those of other grain sizes had smaller excess pressures and were relatively close to the hydrostatic pressure. Comparing the measured friction factors and theoretical ones for stony debris flows, particle–particle stress dominated in debris flows, except for 0.2 mm grains, and the measured excess pore pressures could be explained by the Reynolds stress of pore fluid due to shear by particles in laminar motion. By contrast, particle–particle stress did not dominate in debris flows of grain size 0.2 mm, and a large portion of the particles was in suspension affected by turbulence. These differences in flow dynamics may correspond to the flow transition from laminar to turbulent flow described by the threshold of relative flow depth, which is the ratio of the flow depth to grain size.


Introduction
To mitigate disasters caused by debris flow, it is important to understand the flow dynamics of debris flows. The stress observed for sediment-water mixtures include particle-particle interactions, the stress exerted by pore water, and interactions between particles and pore water [1]. The dynamics of debris flows vary by grain size, changing dominant stress components. For flows containing mainly coarse grains (coarse-grained debris flows), which are called stony debris flows, particles are in laminar motion, i.e., a small fluctuation of the vertical velocity component, and particle-particle stress dominates [2]. For flows with largely noncohesive fine grains (fine-grained debris flows), called turbulent-muddy debris flows or turbulent mud flows, particles are suspended by turbulence and turbulent stress dominates [3]. Physical models have been proposed for each flow type [1,2,4,5].
The dynamics of debris flows have been investigated by comparing observed and theoretical values using velocity profiles [6] and friction factors [7], which reflect internal stress. The theoretical model of stony debris flows describes coarse-grained debris flows with a relative flow depth (the ratio of the flow depth to grain size) less than about 30 well [3], while debris flows with a relative flow depth over 30 gradually deviate from * Corresponding author: sakai@cc.utsunomiya-u.ac.jp stony debris flows to turbulent-muddy debris flows [8,9]. Thus, the relationship between grain size composition and flow dynamics is important.
Direct investigations of the internal stress of debris flows involve measuring the total normal stress and pore fluid pressure of debris flow. Since the total normal stress is the sum of the pore fluid pressure and effective normal stress associated with particle-particle contact, measuring pore fluid pressure is important for investigating the internal stress of debris flows. The pore fluid pressure of natural debris flows measured at several sites exceeded the hydrostatic water pressure [10,11]. These excess pore pressures have been considered to be related to the long-runout distance of debris flows. Several mechanisms for the observed excess pore fluid pressures have been proposed based on grain size composition, e.g. the pressure gradient in the infiltration flow in the pore spaces [10] and the suspension of fine grains in pore fluid [12]. In the former, the existence of silt-and mud-sized particles may delay the dissipation of excess pore fluid pressure due to the low permeability of the pore space [13]. In the latter, fine grains may be kept suspended by the turbulent pore fluid due to strong shear caused by coarse particles in laminar motion [14].
Although the importance of the effects of grain size on the dynamics of debris flows has been reported, they are not fully understood due to limitations in natural flow conditions. Laboratory experiments may be an effective way to investigate the effects of grain size under a wide range of experimental conditions. Several studies have measured pore fluid pressures in experimental debris flows using rotating drums [14,15]. However, since rotating drums induce inherent internal flows that differ from the flow field of actual debris flows [14], the pore fluid pressure should be measured in an open channel. The measurement system Hotta (2012) [16] developed for the pore fluid pressures of debris flows in an open channel can be applied for this.
This study investigated the effects of grain size on the dynamics of debris flow by measuring pore fluid pressure in an open channel experiment.

Laboratory experiment
The experiments were conducted in a 10-m-long, 0.10m-wide, 0.50-m-high variable slope channel with glazed sides (Fig. 1). During the experiment, the channel bottom of the lower 4.5 m was raised to 0.10 m, and 2.9mm-diameter sediment particles were glued to the channel bottom to ensure bed roughness. Sediment particles for debris flow materials were deposited in the upper section of the channel at a height of about 0.10 m. Water was supplied from the upstream end at a constant flow rate, to trigger a debris flow by eroding sediment deposits in the upper section of the channel; the resulting debris flow descends over the rigid bed of the lower section of the channel.
Monodisperse debris flows were triggered using silica sands of nearly uniform grain sizes at the sediment deposits. The mean particle sizes ( ) were 0.2, 0.8, 1.3, 2.2, and 2.9 mm. The mass density ( ) and interparticle friction angle ( ) of the sediment particles were 2.6 g/cm 3 and 34°, respectively. For each grain size, the slope of the channel ( ) and water supply from the upstream end were varied (13,15, and 17°, and 1, 2, 3, and 3.5 L/s, respectively).
An ultrasonic sensor (E4PA-LS50-M1-N, Omron) was installed 1 m from the downstream end to measure the temporal change in flow surface level at a sampling rate of 20 Hz. The pore fluid pressure at the channel bottom was measured at the same position as the ultrasonic sensor. The system developed by Hotta (2012) [16] for measuring pore fluid pressure in open channel experiments was applied using a differential gas pressure gauge (AP-47, Keyence).
The debris flows observed at the measurement position had three different flow sections from the head to tail, as reported by Hotta (2012) [16]: the front, steady-state, and final sections. The debris-flow sample for the steady-state section was captured using a sampler at the downstream end, and the sampling time was recorded. The unit width flux ( ) and mass density of the debris-flow sample ( ) were obtained using a debris-flow sample. The depth-averaged sediment concentration ( ) was calculated from the relationship = ( − ) + , where is the mass density of water. The time-averaged flow depth ( ℎ ) for the sampling time was also obtained, and the depthaveraged flow velocity ( ) was calculated from the relationship = ℎ .

Analysis
The pore fluid pressures and friction factors of the debris flows sampled in the steady-state section were analysed. The friction factors of the observed debris flows were calculated as The theoretical friction factors for a stony debris flow were calculated by applying constitutive equations for stony debris flow [2], as follows: Here, ( ) is a function of the local sediment concentration ( ) at the vertical position ( ) and depends on the explicit form of constitutive equations. When the constitutive equations for stony debris flows proposed by Egashira et al. (1997) [4] are applied, ( ) is expressed as follows: where , and are functions of the local sediment concentration that appear in the constitutive equations [4]. In this study, the sediment concentration profiles were assumed to be uniform and the depth-averaged sediment concentration was used for the local sediment concentration .
The average pore fluid pressures of the sampled debris flow at the steady-state section ( ) was calculated as the average of the section. Measured pore fluid pressures was compared with the hydrostatic pressure, = ℎ cos and total normal stress = ℎ cos . The excess pore fluid pressure was calculated as − . The measured excess pore fluid pressures were compared with the theoretical excess pore fluid pressure. The causes of excess pore fluid pressure are diverse [14,15]. Suspension of particles causes excess pore fluid pressure, which increases with the number of suspended particles. In stony debris flows, particles are in contact with each other without being suspended, and excess pore fluid pressure is caused by the Reynolds stress of pore fluid induced by the shear of particles in laminar motion [16], expressed as follows: where is an experimental constant, taking a value of 0.08 here (following Hotta, 2012 [16]). The theoretical excess pore fluid pressure caused by the Reynolds stress of pore fluid at the bottom, , was calculated with Eq. (4), assuming a linear velocity profile / = 2 /ℎ [16]. The pressure gradient due to infiltration flow in pore fluid also causes excess pore fluid pressure, which is dissipated through the diffusion of pore fluid. With the existence of mud-and silt-sized particles, the excess pore fluid pressure due to infiltration flow may be sustained for longer [13]. pressure and total normal stress. In all cases except the 0.2 mm grain size, the pore fluid pressures were relatively close to the hydrostatic pressure, and were lower than the total normal stress. However, the pore fluid pressures for the 0.2 mm grain size exceeded the hydrostatic pressure and were close to the total normal stress, indicating that high excess pore fluid pressures were induced. Since the debris flows in this study lack mud-and silt-sized particles, the excess pore fluid pressures due to infiltration flow may dissipate quickly [6,13]. Thus, the excess pore fluid pressures observed here may be attributed to the suspension of particles or Reynolds stress of pore fluid in stony debris flows. Figure 4 compares the measured excess pore fluid pressures with the Reynolds stress of pore fluid in stony debris flows, . For grain sizes of 0.8, 1.3, 2.2, and 2.9 mm, the measured excess pore fluid pressures were in relatively good agreement with the Reynolds stress of pore fluid, with coarser grain tending to have greater excess pore fluid pressures corresponding to Eq. (4). Since the theoretical lines for stony debris flows described the friction factors for the 2.2 and 2.9 mm grain sizes well, the particles in these debris flows were in laminar motion, and the excess pore fluid pressures of these cases may be attributed to the Reynolds stress of pore fluid. Although the theoretical lines for stony debris flows underestimated the friction factors for 0.8 and 1.3 mm grains, this may be explained by the effect of bed roughness on stony debris flow. When the bed roughness exceeds the grain size of flowing particles, the friction factors become larger than predicted by the theoretical lines for stony debris flow [17,18]. Thus,   debris flows with grain sizes of 0.8 and 1.3 mm may also be considered stony debris flows. As considered above, debris flows with grain sizes of 0.8, 1.3, 2.2, and 2.9 mm are considered stony debris flows, and particle-particle stress dominated.

Results and Discussion
The measured excess pore fluid pressures for the 0.2 mm grain size were significantly underestimated by , indicating that the excess pore fluid pressures for that grain size were induced by a mechanism other than the Reynolds stress of pore fluid. Since the experimental friction factors were far from the theoretical values for stony debris flows, the excess pore fluid pressures for the 0.2 mm grain size may be attributed to particle suspension. This is supported by the reports that debris flows with relative flow depths under 30 are described well by the constitutive equations for stony debris flows, but gradually deviate from stony debris flows to turbulent-muddy debris flows with relative flow depths over 30 [8,9]. Since the debris flows with the grain size of 0.2 mm had relative flow depths of 50~120 (Fig. 2), the particles may be suspended by turbulence. The finding that the pore fluid pressures were close to the total normal stress indicates that a large portion of the particles was kept suspended by turbulence.

Conclusions
To investigate the effects of grain size on the dynamics of debris flows, pore fluid pressures were measured in an open channel experiment. Monodisperse debris flow was triggered in experiments using five different grain sizes: 0.2, 0.8, 1.3, 2.2, and 2.9 mm. The pore fluid pressures measured for the 0.2 mm grains had greater excesses over hydrostatic pressures, and were close to the total normal stress, while those of other grain sizes showed smaller excess pressures and were relatively close to the hydrostatic pressure. Comparing the experimental friction factors and theoretical ones for stony debris flow, particle-particle stress dominated the debris flows, except for 0.2 mm grains, and the measured excess pore pressures may be explained by the Reynolds stress of pore fluid due to shear by particles in laminar motion. By contrast, particle-particle stress did not dominate the debris flows of 0.2 mm grains and most particles were in suspension affected by turbulence.