E3S Web of Conferences 415, 01022 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341501022

Laboratory investigation of the effects of grain size on thedynamics of debris flows: Measurement of pore fluid pressurein an open channel
Yuichi Sakai1*, and Norifumi Hotta2
1School of Agriculture, Utsunomiya University, Utsunomiya, Japan

2Graduate School of Agricultural and Life Sciences, The University of Tokyo, Tokyo, Japan

Abstract. The dynamics of debris flow depend on internal stress components, such as particle–particlestress, 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 thedynamics of debris flow are not fully understood. To investigate the effects of grain size on the dynamics ofdebris 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 hydrostaticpressure, and were close to the total normal stress, while those of other grain sizes had smaller excesspressures and were relatively close to the hydrostatic pressure. Comparing the measured friction factors andtheoretical 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 flowsof 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 describedby the threshold of relative flow depth, which is the ratio of the flow depth to grain size.

1 Introduction
To mitigate disasters caused by debris flow, it isimportant 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 andpore water [1]. The dynamics of debris flows vary bygrain size, changing dominant stress components. For
flows containing mainly coarse grains (coarse-graineddebris flows), which are called stony debris flows,
particles are in laminar motion, i.e., a small fluctuationof 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 investigatedby comparing observed and theoretical values using
velocity profiles [6] and friction factors [7], whichreflect internal stress. The theoretical model of stonydebris flows describes coarse-grained debris flows witha relative flow depth (the ratio of the flow depth to grainsize) less than about 30 well [3], while debris flows witha relative flow depth over 30 gradually deviate fromstony 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 forinvestigating the internal stress of debris flows. The pore
fluid pressure of natural debris flows measured atseveral 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 fluidpressures 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 finegrains in pore fluid [12]. In the former, the existence ofsilt- and mud-sized particles may delay the dissipationof excess pore fluid pressure due to the low permeabilityof 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 sizeon the dynamics of debris flows has been reported, they
are not fully understood due to limitations in natural* Corresponding author: sakai@cc.utsunomiya-u.ac.jp© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0(https://creativecommons.org/licenses/by/4.0/).

E3S Web of Conferences 415, 01022 (2023)
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flow conditions. Laboratory experiments may be aneffective way to investigate the effects of grain size
under a wide range of experimental conditions. Several
studies have measured pore fluid pressures inexperimental 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 ofdebris 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 fluidpressure in an open channel experiment.

sampling time was also obtained, and the depthaveraged flow velocity (𝑢𝑢𝑚𝑚 ) was calculated from therelationship 𝑞𝑞 = ℎ𝑢𝑢𝑚𝑚 .

Fig. 1. Experimental setup [16].
2.2 Analysis
The pore fluid pressures and friction factors of thedebris flows sampled in the steady-state section wereanalysed. The friction factors of the observed debris
flows were calculated as

2 Method
2.1 Laboratory experiment𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒 =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 channelbottom of the lower 4.5 m was raised to 0.10 m, and 2.9mm-diameter sediment particles were glued to thechannel bottom to ensure bed roughness. Sedimentparticles for debris flow materials were deposited in theupper section of the channel at a height of about 0.10 m.
Water was supplied from the upstream end at a constantflow rate, to trigger a debris flow by eroding sedimentdeposits 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 sedimentdeposits. The mean particle sizes (𝑑𝑑) were 0.2, 0.8, 1.3,2.2, and 2.9 mm. The mass density (𝜎𝜎) and interparticle
friction angle (𝜙𝜙𝑠𝑠 ) of the sediment particles were 2.6
g/cm3 and 34°, respectively. For each grain size, theslope of the channel ( 𝜃𝜃 ) and water supply from theupstream 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 channelbottom was measured at the same position as theultrasonic 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 headto 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 wasrecorded. The unit width flux (𝑞𝑞) and mass density ofthe debris-flow sample ( 𝜌𝜌𝑚𝑚 ) were obtained using adebris-flow sample. The depth-averaged sedimentconcentration (𝐶𝐶) was calculated from the relationship𝜌𝜌𝑚𝑚 = (𝜎𝜎 − 𝜌𝜌𝑤𝑤 )𝐶𝐶 + 𝜌𝜌𝑤𝑤 , where 𝜌𝜌𝑤𝑤 is the mass density ofwater. The time-averaged flow depth ( ℎ ) for the2𝑔𝑔ℎ sin 𝜃𝜃2𝑢𝑢𝑚𝑚(1)

The theoretical friction factors for a stony debris
flow were calculated by applying constitutive equations
for stony debris flow [2], as follows:
𝑓𝑓𝑐𝑐𝑐𝑐𝑐𝑐 =25ℎ −2𝐾𝐾(𝑐𝑐) � �2𝑑𝑑(2)Here, 𝐾𝐾(𝑐𝑐) is a function of the local sedimentconcentration (𝑐𝑐) at the vertical position (𝑧𝑧) and depends
on the explicit form of constitutive equations. When theconstitutive equations for stony debris flows proposedby Egashira et al. (1997) [4] are applied, 𝐾𝐾(𝑐𝑐) isexpressed as follows:
𝐾𝐾(𝑐𝑐) =𝜌𝜌𝑤𝑤 (𝑓𝑓𝑑𝑑 + 𝑓𝑓𝑓𝑓 )𝜌𝜌𝑚𝑚 − 𝛼𝛼(𝜎𝜎 − 𝜌𝜌𝑤𝑤 )𝑐𝑐 tan 𝜙𝜙𝑠𝑠 / tan 𝜃𝜃(3)where 𝑓𝑓𝑑𝑑 , 𝑓𝑓𝑓𝑓 and 𝛼𝛼 are functions of the local sedimentconcentration 𝑐𝑐 that appear in the constitutive equations[4]. In this study, the sediment concentration profileswere assumed to be uniform and the depth-averaged
sediment concentration 𝐶𝐶 was used for the local
sediment concentration 𝑐𝑐.
The average pore fluid pressures of the sampleddebris flow at the steady-state section ( 𝑃𝑃𝑒𝑒𝑒𝑒𝑒𝑒 ) was
calculated as the average of the section. Measured pore
fluid pressures 𝑃𝑃𝑒𝑒𝑒𝑒𝑒𝑒 was compared with the hydrostaticpressure, 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 𝜌𝜌𝑤𝑤 𝑔𝑔ℎ cos 𝜃𝜃 and total normal stress
𝑃𝑃𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝜌𝜌𝑚𝑚 𝑔𝑔ℎ cos 𝜃𝜃.
The excess pore fluid pressure was calculated as
𝑃𝑃𝑒𝑒𝑒𝑒𝑒𝑒 − 𝑃𝑃𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 . The measured excess pore fluid pressures
were compared with the theoretical excess pore fluidpressure. The causes of excess pore fluid pressure arediverse [14, 15]. Suspension of particles causes excess
pore fluid pressure, which increases with the number ofsuspended particles. In stony debris flows, particles arein contact with each other without being suspended, andexcess pore fluid pressure is caused by the Reynolds
stress of pore fluid induced by the shear of particles inlaminar motion [16], expressed as follows:2

E3S Web of Conferences 415, 01022 (2023)
DFHM8𝑝𝑝𝑓𝑓 = 𝑘𝑘𝑓𝑓 𝜌𝜌𝑤𝑤 𝑑𝑑 2 �https://doi.org/10.1051/e3sconf/202341501022

1 − 𝑐𝑐 2/3 𝜕𝜕𝜕𝜕 2� � �𝑐𝑐𝜕𝜕𝜕𝜕pressure and total normal stress. In all cases except the0.2 mm grain size, the pore fluid pressures wererelatively close to the hydrostatic pressure, and werelower than the total normal stress. However, the porefluid pressures for the 0.2 mm grain size exceeded thehydrostatic pressure and were close to the total normalstress, indicating that high excess pore fluid pressures
were induced. Since the debris flows in this study lackmud- and silt-sized particles, the excess pore fluidpressures 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 orReynolds stress of pore fluid in stony debris flows.
Figure 4 compares the measured excess pore fluidpressures with the Reynolds stress of pore fluid in stonydebris flows, 𝑃𝑃𝑓𝑓 . For grain sizes of 0.8, 1.3, 2.2, and 2.9mm, the measured excess pore fluid pressures were in
relatively good agreement with the Reynolds stress ofpore 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 werein laminar motion, and the excess pore fluid pressures ofthese cases may be attributed to the Reynolds stress ofpore fluid. Although the theoretical lines for stonydebris flows underestimated the friction factors for 0.8
and 1.3 mm grains, this may be explained by the effectof 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 thetheoretical lines for stony debris flow [17, 18]. Thus,(4)

where 𝑘𝑘𝑓𝑓 is an experimental constant, taking a value of
0.08 here (following Hotta, 2012 [16]). The theoreticalexcess pore fluid pressure caused by the Reynolds stressof pore fluid at the bottom, 𝑃𝑃𝑓𝑓 , was calculated with Eq.
(4), assuming a linear velocity profile 𝜕𝜕𝜕𝜕/𝜕𝜕𝜕𝜕 = 2𝑢𝑢𝑚𝑚 /ℎ[16]. The pressure gradient due to infiltration flow inpore 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 besustained for longer [13].

3 Results and Discussion
We conducted 103 experiments and successfullymeasured the pore fluid pressure in 28 of them. The
measured flow depths and sediment concentrations ofdebris flow samples had ranges of 10~30 mm and
0.1~0.3 m3/m3, respectively. Figure 2 shows therelationship between the relative flow depth and friction
factor in all 103 cases, in addition to the data by Hotta& Miyamoto (2008) [8]. The figure plots the theoreticallines for the friction factors of a stony debris flow (Eq.
(2); 𝐶𝐶 = 0.1, 0.2, 0.3 ) and turbulent water flow overrough surfaces. The friction factors for grain sizes of 2.9
and 2.2 mm were in good agreement with the theoreticallines for a stony debris flow, indicating that these cases
are stony debris flows, wherein particles are in laminar
motion. The theoretical lines for stony debris flowunderestimated the friction factors for grain sizes of 1.3
and 0.8 mm. Contrasting with the other grain sizes, thetheoretical lines of stony debris flow significantly
underestimated the friction factors at the grain size of0.2 mm, by more than one order, indicating that the flow
differed from a stony debris flow.
Figure 3 compares the measured pore fluidpressures of debris flow samples with the hydrostatic
𝑓𝑓

35

Pore fluid pressure (mm)1010(a)250.2 mm200.8 mm
1.3 mm152.2 mm

H&M08

2.9 mm

0.2 mm100.8 mm101.3 mm

112.2 mmPore fluid pressure (mm)Turb. flow

−2100.01

1001021000
103ℎ⁄𝑑𝑑30350.2 mm

C=0.310102535

C=0.21120(b)2.9 mm−1100.1

15

Hydrostatic pressure (mm)C=0.1

10−30.001

3010000
104

Fig. 2. Relationship between the relative flow depth ℎ/𝑑𝑑
and friction factor 𝑓𝑓𝑒𝑒𝑒𝑒𝑒𝑒 for all 103 cases. The theoreticallines for stony debris flows (Eq. (2); 𝐶𝐶 = 0.1, 0.2, 0.3)
are shown. The data in the literature [8] and theoreticalline for turbulent water flow over rough surfaces are also
indicated for reference (see Hotta & Miyamoto (2008)[8] for details).

0.8 mm301.3 mm
2.2 mm252.9 mm201510101520253035

Total normal stress (mm)Fig. 3. Comparison between the measured pore fluidpressure and (a) hydrostatic pressure and (b) total
normal stress (presented as hydraulic head). Meanvalues and standard deviations are shown.

3

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Reynolds stress of pore fluid (mm)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.
The measured excess pore fluid pressures for the 0.2
mm grain size were significantly underestimated by 𝑃𝑃𝑓𝑓 ,indicating that the excess pore fluid pressures for thatgrain size were induced by a mechanism other than theReynolds stress of pore fluid. Since the experimental
friction factors were far from the theoretical values forstony 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 toturbulent–muddy debris flows with relative flow depths
over 30 [8, 9]. Since the debris flows with the grain sizeof 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 thetotal normal stress indicates that a large portion of theparticles was kept suspended by turbulence.

These differences in flow dynamics may correspond to
the transition from laminar to turbulent flow describedby the threshold of relative flow depth. The detailed
mechanism for this transition observed in debris flows
should be investigated in the future.
This research was supported by JSPS KAKENHI (grantnumbers 17J08424, 20J00991, and 22K14452).

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0.8 mm61.3 mm
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4 Conclusions

mixture flow in a rotating mill, in Proceedings of the 5thInternational Conference on Debris-Flow Hazards
Mitigation, 319–330 July 2011, Padua, Italy (2011)

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 fluidpressures 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 theexperimental friction factors and theoretical ones forstony debris flow, particle–particle stress dominated thedebris flows, except for 0.2 mm grains, and themeasured excess pore pressures may be explained by theReynolds stress of pore fluid due to shear by particles inlaminar motion. By contrast, particle–particle stress did
not dominate the debris flows of 0.2 mm grains and mostparticles were in suspension affected by turbulence.

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