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Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
615
DOI: 10.4408/IJEGE.2011-03.B-067
MONITORING NEAR-RIVERBED SEDIMENT BEHAVIOR
OF DEBRIS FLOWS USING HYDROPHONES
t
akuRo
SUZUKI
(*)
, y
uJi
HASEGAWA
(**)
, H
ideaki
MIZUNO
(*)
& n
obutomo
OSANAI
(*)
(*)
Erosion and Sediment Control Division, Research Center for Disaster Risk Management, National Institute
for Land and Infrastructure Management, Japan - Email: suzuki-t92te@nilim.go.jp - Phone: +81-29-864-4372
(**)
Civil Engineering Research Laboratory, Japan - Email: hasegawa@crl.or.jp - Phone: +81-29-847-3781
els of interactions among particles. Thus, many consti-
tutive equations have been proposed (e.g., t
akaHasHi
,
1980; s
Hen
et alii, 1982; t
subaki
et alii, 1982; d
Rew
,
1983; e
GasHiRa
et alii, 1989). However, in these equa-
tions, the influence of riverbed roughness has not been
taken into consideration. s
uzuki
et alii (2003) and s
u
-
zuki
& H
otta
(2006) confirmed that the coefficient of
resistance increases as riverbed roughness increases
with larger riverbed particles. Thus, the coefficient of
resistance is large when the sediment concentration is
large or the relative flow depth is small. Therefore, it is
necessary to construct a flow model that can evaluate
the influence of riverbed roughness. To do so, the near-
riverbed sediment behavior of debris flows must be
clarified. Unfortunately, there is no established method
to measure this behavior because it is generally very
difficult to measure sediment concentration and sedi-
ment load. There is no sensor that can measure sedi-
ment concentration or sediment load directly. Moreo-
ver, a direct sampling measurement method requires
a huge amount of effort and is tremendously costly,
and long-term continuous measurement is impossible.
Therefore, sediment concentration and load are esti-
mated indirectly by measuring other physical quanti-
ties. One class of methods for the indirect estimation
involve the use of hydrophones (microphones within
steel pipes), and their effectiveness in the measurement
of bedload transport intensity has been verified (b
aR
-
zinGeR
& b
uRCH
, 1990; H
eGG
& R
iCkenmann
, 1998;
R
iCkenmann
, 1998; m
izuyama
et alii, 2002). An exam-
ABSTRACT
Hydrophones are steel pipes containing a micro-
phone, and they can be used to measure bedload trans-
port intensity. Bedload discharge and average grain
diameter can be calculated analytically using sound
pressure data. In this study, hydrophones were used to
identify debris flows. The proportional relationship be-
tween the output voltage corresponding to a grain col-
lision and its momentum was used to analyze electric
pressure distribution, which was then used to calculate
the mean diameter of colliding grains. Flume experi-
ments were conducted to verify the effectiveness of this
method in recognizing the time change of the near-river-
bed sediment discharge from debris flows and low con-
centrated flows, including their transition ranges. Total
sediment discharge can also be calculated if the collision
rate upon the hydrophones is evaluated by setting the in-
terface. In addition, the time change of the average grain
diameter can be calculated. Large grains were detected
in the debris flow surge, and the analytic values were in
rough agreement with the experimental values.
K
ey
words
: debris flow monitoring, hydrophone, sound pres-
sure
INTRODUCTION
The flow characteristics of debris flows are de-
termined by the balance between external forces and
shear stresses. Research on the constitutive equations
of debris flows has been carried out to construct mod-
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t. SUZUkI, y. HASEGAwA, h. MIZUNO & N. OSANAI
616
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
pling time was measured. The debris flow discharge,
Q, was calculated by dividing the sample volume,
Vlm, by the sampling time. The sediment concentra-
tion,
c
, was calculated as follows:
In Eq. (1), V
s
is the sediment volume in the sam-
ple and V
w
is the water content. The passing time of a
large grain was measured with high-speed video (500
frames per second) installed 1 m above the lower end.
CONDITIONS
Four tests were performed. In all cases, the chan-
nel slope θ was set to 13°. The supplied sediments in
the upstream part of the channel had different grain
distributions. In two cases, a uniform grain size was
used, with d = 0.294 cm and σ = 2.65 (σ is the specific
gravity of the sediment) (Case-Uni.). In the other two
cases, together with a sediment of d = 0.294 cm, larger
grains were used with d = 1.76 cm and located at 15
cm intervals on the surface (Case-Large). The total
number of larger sediment grains was 10, one grain per
15 cm interval. The supplied water discharges were 1
and 3 L/sec under each grain distribution condition.
NUMERICAL SIMULATION
A continuous sequence of sediment discharge can-
not be identified through experimental measurements
alone. Therefore, a one-dimensional numerical simula-
ple of such a method is the “pulse” method, in which
the sound of sand colliding with the steel pipe contain-
ing the microphone is analyzed and transformed into
a pulse; this pulse represents the number of times the
sound level crosses a certain threshold. Thus, the sedi-
ment transport intensity is estimated on the basis of the
premise that it is positively correlated with the pulse.
However, this method has some problems. For exam-
ple, when the sediment rate is high, the sound level
is continuously high. Thus, the number of pulses de-
creases or becomes zero (m
izuyama
et alii, 2008).
On the basis of the above information, s
uzuki
et
alii (2010) attempted to use an analytical method in-
volving the use of sound pressure data. According to
these researchers, bedload discharge and average di-
ameter can be obtained by considering the reduction
in sound pressure caused by the interference of sound
waves. While hydrophones can be used to evaluate de-
bris flow, the method of s
uzuki
et alii (2010) has meas-
urement limitations with regard to the number of grain
collisions. Thus, this method needs to be modified be-
fore it can be used for debris flow measurements. The
aim of this paper is to develop a method for calculating
the mean grain diameter by analyzing the electric pres-
sure distribution and to apply it to debris flows. The
method was verified by performing flume experiments.
EXPERIMENTS
EXPERIMENTAL DEVICES
The variable slope channel of the Civil Engineer-
ing Research Laboratory was used for the experiment.
The channel is 9 m long and 10 cm wide, with glazed
sides (Fig. 1). The sides in the downstream part of the
channel (4.5 m) are as high as 10 cm. A sand rough-
ness was positioned at the downstream part (4.5 m);
the upstream part (1.8 m) was filled with sediment.
Water was regularly supplied from the upper end and
a debris flow was generated.
MEASUREMENT METHOD
An ultrasonic sensor was used to measure the time
change of the flow surface level. This sensor was in-
stalled 1 m above the lower end. A hydrophone was
installed at the lower end of the channel, as shown
in Fig. 2. The output voltage of the microphone was
amplified to the range of ±10 V.
Around the surge front, a sample of the debris
flow was taken at the downstream end and the sam-
Fig. 1 - Experimental setup
Fig. 2 - Schematic design of the hydrophone setup
(1)
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MONITORING NEAR-RIVERBED SEDIMENT BEHAVIOR OF DEBRIS FLOWS USING HYDROPHONES
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
617
specified as 0.0828, e is the coefficient of restitution,
and k
f
is an experiment constant of 0.16.
Substituting Eq. (8) with c = c
e
, h = h
e
, and u = M/h
e
into the following Eq. (12), h
e
is obtained,
Numerical simulations were conducted using the
above- mentioned method.
Model parameters were calibrated to obtain the
best match between simulation and experimental re-
sults in terms of time-series variation of h and sedi-
ment concentration around the surge front.
In Figs. 3 and 4, the experimental and simulation
results are compared; c-Exp and h-Sensor refer to the
measured c and h, and c-Cal. and h-Cal. refer to the
simulation results of c and h using calibrated param-
eters. From 72 to 85 sec of the 1 l-case and from 31 to
34 sec of the 3 l-case, the h-Sensor decreased drasti-
cally. These changes were due to the transition from
debris flow to low concentrated flow after most of the
grains were eroded. Thus, the simulation results agree
well with the experimental results. Therefore, these
simulation results are useful as comparison values for
hydrophone measurements.
ANALYTICAL METHOD
Raw data obtained with a hydrophone are shown
in Fig. 5. To reduce the electrical noise, circumferen-
tial frequency components were extracted with a band-
pass filter (Fig. 6). Sound pressure data correspond to
the line connecting the local maximum points of the
extracted data (Fig. 7), and Sp is the average value.
s
uzuki
et alii (2010) confirmed the relationship
between Sp and bedload discharge, Qs, as follows:
where α is the proportionality coefficient, R is the detec-
tion rate, and N is the number of collisions per second.
Equation (14) indicates that R is a function of N. The re-
lationship between R and N can be obtained from exper-
imental results under a wide range of conditions. How-
ever, it is unrealistic because a tremendous amount of
data is necessary for experimental accuracy. Therefore,
s
uzuki
et alii (2010) proposed a method for estimating
the relationship between R and N using superposition
simulations. Their method is described in the following.
First, a uniform random number, rd(t), is given
every one-millionth of a second, where t is the elapsed
tion was conducted to replicate the flume experiments.
The basic debris flow equations are shown below
(m
iyamoto
& i
to
, 2002). The momentum equation is:
The continuity equation for the total volume of
the debris flow is:
and the continuity equation for the particles is:
Changes in the bed surface elevation can be deter-
mined using the following equation:
For Eqs. (2)-(5), h is the flow depth, u is the flow
velocity, M = uh, g is the acceleration due to gravity,
ρ
m
is the density of the debris flow, H = h + z
b
, z
b
is the
bed elevation, E is the erosion velocity, τ
0
is the river-
bed shear stress, c is the average sediment concentra-
tion, c
t
is the flux sediment concentration, and c
*
is
the sediment concentration of the movable bed layer.
The equations of m
iyamoto
& i
to
(2002) were
applied for τ
0
and c
t
, and the following erosion rate
equation of s
uzuki
et alii (2009) was applied for E:
In Eq. (6), T is the relaxation time of erosion or
deposition, and e is the equilibrium sediment concen-
tration, expressed as follows:
In Eq. (6), h
e
is the equilibrium flow depth when τ
0
is equal to the external force. In the equations of miya-
moto & ito (2002), τ
0
was expressed as the following
equation with the sum of the Coulomb friction shear
stress, τ
0y
, and dynamic shear stress, τ
0D
:
In Eq. (9), f
b
is the coefficient of resistance.
In Eq. (11), k
g
is the empirical constant that is
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(14)
(13)
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t. SUZUkI, y. HASEGAwA, h. MIZUNO & N. OSANAI
618
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
transformed data and m is an arbitrary counting number.
T
2
, second transformed data, is calculated using
T
1
, second original data. The relationship between T
1
and T
2
is expressed as follows:
The original data are divided evenly into m parts,
and the pth part is designated as V
1
(p,t), where p is the
counting number from 1 to m and t is the elapsed time
from the starting point of every part. Transformed data
are designated as V
2
(t) and calculated as Eq. (19),
In Fig. 9, an example with T
1
= 5.0, T
2
= 0.5, and
m = 10 is shown.
With regard to transformed data, Eq. (20) is devel-
oped using a method similar to Eq. (16),
where Sp
tfd
is the sound pressure value of the trans-
formed data. Equations (16) and (20) are solved as a
set of simultaneous equations to calculate Qs and d.
However, this method has measurement limitations
with respect to the number of grain collisions. Thus,
the method needs to be modified before it can be used
for debris flows. In the present study, a new method
was developed to calculate the grain diameter distri-
bution by analyzing the electric pressure distribution.
This new method is detailed in the following.
time (sec). The threshold value, Th, is set at Th =
N/100000 for arbitrary N. When rd(t) is lower than Th,
an individual collision wave datum, which is obtained
by preliminary experiment, is added to the wave data
being produced. R is calculated using Eq. (13) from
the data computed in this way. The relationship be-
tween R and N is obtained when N is changed over a
wide range. Thus, R decreases as N increases due to
the effects of sound wave interference (Fig. 8).
Qs is expressed as
Substituting Eqs. (14) and (15) into Eq. (13), Eq.
(16) is obtained,
This paper aimed to develop a method for calcu-
lating Qs and d using just sound data obtained with a
hydrophone; this was attempted because it is difficult to
measure the time-series variation of grain size distribu-
tion. Thus, Eq. (16) has two unknown values, d and N,
while Sp is measured variable. Therefore, it is impossible
to obtain Qs from Sp only through Eq. (16). s
uzuki
et
alii (2010) proposed a method for calculating the trans-
formed data that satisfies Eq. (17) by dividing the origi-
nal data equally and summing them linearly as follows:
in which Qs
tfd
is the bedload discharge value of the
Fig. 3 - Experimental and simulation results of flow height, h, and sediment concentration, c (Case-Uni.-1l)
Fig. 4 - Experimental and simulation results of flow height, h, and sediment concentration, c (Case-Uni.-3l)
(15)
(16)
(17)
(18)
(19)
(20)
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MONITORING NEAR-RIVERBED SEDIMENT BEHAVIOR OF DEBRIS FLOWS USING HYDROPHONES
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
619
The grain size accumulation curve is obtained
by accumulating r
i
, and d is calculated as the volume
mean diameter using Eq. (26),
Substitutions allow for the identification of d in
Eq. (16), enabling the value of Nf(N) to be calculated.
The relationship between N and Nf(N) (Fig. 10) was
computed easily from the Nf(N) relationship (Fig. 9).
Nf(N) was substituted into the Nf(N) relationship, and
N was calculated. Finally, substituting d and N into
Eq. (15) allowed Qs to be obtained.
First, output voltage data were divided by 0.0001
V. The voltage of the ith section, V
i
, is
s
uzuki
et alii (2010) confirmed that the maximum
voltage of the individual collision sound, V
max
, was
proportional to the momentum of the grain. Thus, the
relationship between V
max
and d is as follows:
where β is the proportionality coefficient and v is the
velocity of a grain. Assuming that v is constant in cer-
tain durations, the diameter corresponding to the ith
section, d
i
, is given as follows:
where γ is the proportionality coefficient and is found
to have a value of 0.6β from the results of the present
preliminary investigations.
Assuming the number of local maximum volt-
age values in the ith section, Nm
i
, is proportional to
the number of grains in the ith section, the volume of
grains in the ith section, Vol
i
, is expressed as follows:
where k is the proportionality coefficient. Therefore, the
ratio of Vol
i
to the total volume, r
i
, is given as follows:
Fig. 5 - Raw wave data
Fig. 9 - Schematic diagram of the data transformation
Fig. 6 - wave data extracted with a band-pass filter
Fig. 7 - Sound pressure data
Fig. 8 - Relationship between the number of collisions, N,
and the detection rate, R
Fig. 10 - Relationship between the number of collisions, N,
and Nf(N)
(21)
(22)
(23)
(24)
(25)
(26)
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t. SUZUkI, y. HASEGAwA, h. MIZUNO & N. OSANAI
620
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
In this study, Qs and d were calculated every 0.01
sec because the duration of one collision sound was about
0.02 sec. For Qs, a 0.1 sec moving average was computed.
In Figs. 11 and 12, simulation results when IF was
1.7 cm [Qs-Cal(Interface = 1.7)] are shown, and they
are in agreement with the analyzed results.
When c was high, the analytic results of d were
close to 0.294 cm. However, when c was low (low
concentrated), the analytic results of d were lower.
This was due to the noise of the water, and the prob-
lem should be rectified in future studies.
CASE-LARGE
Qs-Hp, d-HP, Qs-Cal., and d-Cal. around the surge
are shown in Figs. 13 and 14, in which pass timings
of large grains determined from high-speed video also
are shown. Qs and d increased instantaneously when
large grains were considered to have collided with the
hydrophone. About five grains in the 1l-case and two
grains in the 3l-case were discriminated. It is presumed
that other grains did not collide with or graze the hy-
drophone. The maximum analysis value of d was about
0.8 cm, which is lower than the actual value of 1.76
cm. This is because the analytic value of d was the vol-
ume mean diameter. The volume mean diameter, d
av
,
when large grains collide is obtained as follows:
RESULTS
CASE-UNI
In Figs. 11 and 12, the analyses and simulation
results are shown and compared, with Qs-Hp and
d-HP referring to the analytic results of Qs and d
(see the previous paragraph), and Qs-Cal. and d-Cal.
referring to the simulation results of Qs and d (see
the section titled “Numerical Simulation”). In the
1l-case, Qs-HP and Qs-Cal. agreed quantitatively.
However, Qs-HP of the 3l-case was lower than Qs-
Cal. The underestimation of Qs for the 3l-case can
be explained fairly well if one considers that, during
the experimental tests, the grains in the upper layer
likely did not collide with the hydrophone. Assum-
ing that only grains under a certain interface height,
IF, collide with the hydrophone, the collision rate, r
c
,
was evaluated as follows:
where u(z) is the velocity at z. Substituting the typical
velocity distribution of a debris flow [Eq. (28)] into
Eq. (27), r
c
is expressed as Eq. (29),
Fig. 11 - Analytic results of sediment discharge, Qs, and average grain diameter, d (Case-Uni.-1l)
Fig. 12 - Analytic results of sediment discharge, Qs, and average grain diameter, d (Case-Uni.-3l)
(27)
(28)
(29)
(30)
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MONITORING NEAR-RIVERBED SEDIMENT BEHAVIOR OF DEBRIS FLOWS USING HYDROPHONES
Italian Journal of Engineering Geology and Environment - Book www.ijege.uniroma1.it © 2011 Casa Editrice Università La Sapienza
621
lated if the collision rate on the hydrophones is evalu-
ated by setting the interface.
The hydrophone itself has some limitations. For
example, the measurable sound level is limited and
its range depends on the performance of the micro-
phones. Because of this, hydrophones are applicable
within a specific range. The method described in this
study can be used to perform highly accurate meas-
urements of the time change of sediment discharge
within experimental results of this study . However,
this method also has some limitations. For example,
when sediment concentration is low, the values of
the grain diameter obtained are lower than the actual
values. Moreover, it is presumed that the interface
varies with the scale of the debris flows, the condi-
tions under which the hydrophone is installed, and
the terrain conditions at the installation site. There-
fore, further improvement of the method is necessary
to resolve these problems.
In addition, the method described in this study
was developed for flume experiments performed as
part of basic studies of debris flows. However, it may
also be applied to field monitoring. In such cases,
the hydrophone’s steel pipe must be large enough to
endure the impact of realistically scaled debris flows.
Therefore, verification of the applicability of large-
size hydrophones is a necessary next step in the de-
velopment of the method.
where Qs
S
is the sediment discharge of 0.294 cm
grains, d
L
is the diameter of a large grain, and Qs
L
is
the sediment discharge of large grains. Qs
L
was ob-
tained with Eq. (31),
Substituting Eqs. (31) and (32) with d = 0.294, d
L
= 1.76, and the simulation results of Qs
S
into Eq. (30),
d
av
was calculated from 0.82 to 1.14 cm. Therefore,
the analytic values of d
av
were slightly lower than the
actual values, but they are reasonably close.
CONCLUSIONS
In this study, hydrophones, which have been de-
veloped for bedload sediment analysis, were used to
analyze debris flows. An analytical method for calcu-
lating the grain diameter distribution from measure-
ments of the electric pressure distribution was devel-
oped by considering the fact that the output voltage
corresponding to a grain collision is proportional to
its momentum. Also introduced herein was the exist-
ing method of s
uzuki
et alii (2010). Flume experi-
mental and analytical results confirmed that sediment
discharge and the average diameter of near-riverbed
sediment can be measured quantitatively by this
method. Total sediment discharge can also be calcu-
(31)
(32)
Fig. 13 - Analytic results of sediment discharge, Qs, and average grain diameter, d (Case-Large.-1l)
Fig. 14 - Analytic results of sediment discharge, Qs, and average grain diameter, d (Case-Large.-3l)
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t. SUZUkI, y. HASEGAwA, h. MIZUNO & N. OSANAI
622
5th International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment Padua, Italy - 14-17 June 2011
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uRCH
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to
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izuyama
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izuyama
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uzuki
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iyamoto
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uzuki
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otta
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uzuki
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otta
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iyamoto
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izuno
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aseGawa
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