E3S Web of Conferences 415, 03023 (2023)
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https://doi.org/10.1051/e3sconf/202341503023

Experimental study of seismo-acoustic frequency and flow
velocity of debris flow
Sudhan Regmi1*, Ko-Fei Liu1, and Shih-Chao Wei2
1Department of Civil Engineering, National Taiwan University, Taipei, Taiwan (R.O.C.)
2Feng Chia University, Taichung, Taiwan (R.O.C.)

Abstract. Seismo-acoustic wave radiated from debris flows motion is one of the main properties used forits monitoring and detection. Understanding the Seismo-acoustic wave using geophone recordings may give
us great insight into the physical process of debris flows such as flow velocity and flow rate. To connect theseismo acoustic observation to the debris flows motion, vibration signal recorded from fixed geophones
were analysed. In this study, a small-scale granular flow of volume 0.2 m3 consisting of material withaverage particle diameter 3.34 mm was simulated in a hydraulic flume with cross section of 0.5 m X 0.5 m
through granular bed to simulate the debris flow. A series of three-axis geophones were buried along channel
bed to record the vibrations produced by granular flows. The discrete Fourier transform was used todecompose vibrations into frequency spectrum and the weighted non-linear least square regression wasadopted to isolate the dominant frequency functions and peak frequency. Meanwhile, the physicalparameters including front profile, surface velocity, flow depth and discharge were tracked through video
recordings and were compared with respect to isolated peak frequency. Assuming the radiated peakfrequency in the moving granular flow is within 20-50 Hz and normally distributed, the isolated peakfrequency shift in the fixed geophone location was analysed with the tracked flow parameters. Results showsthat the peak frequency shift seems to have a non-linear relation with the surface velocity.

1 Introduction
Heterogeneous and non-uniform flow conditions of thedebris flows possess one of the greatest challenges inunderstanding the characteristics and nature of such flow
conditions. Field conditions of debris flows add a lot of
unpredictable circumstances which makes it a lot difficult
to improve their understanding. Albeit the unpredictable
nature of these flows, idealized laboratory experiments
and large number of monitoring data have vastly helped
to improve the current understanding of these flows.
At present, several techniques exist to monitor,
detect, and define debris flow events. These techniques
include the use of ground vibrations, image acquisitionand hydrological models. However, the warning systemof debris flow is significantly based on rainfall thresholds[1] as there is a substantial gap in the theoretical model
governing acoustic and image-based systems. Existingstudies provide adequate evidence of high correlationbetween flow condition and energy of ground vibration
but falls short to explain the flow mechanism [2]. Present
acoustic based monitoring models can successfully detect
debris flows after it initiates, but is lacking to define theactual flow characteristics. Nevertheless, detection alone
does not correspond to a warning system due to the shorttime between detection and disaster.

2 Experimental Methodology
This study is based on the detecting and analysing
frequencies of acoustic vibration induced by moving
debris (granular mass) over a finite media and the flowvelocity of the moving debris source. To simulate thedebris flow, 0.2 𝑚3 ± 10% of debris material withapproximate average diameter (𝑑𝑎𝑣𝑔 ) of 3.34 mm wasallowed to flow through a flume with cross section of
0.5 𝑚 × 0.5 𝑚, inclined at an angle of 24°, underinfluence of gravity assisted by constant flow of water.
Simple illustration of experimental setup is shown in Fig.
1 and Fig. 2.

Fig. 1. Semantic sketch for experimental Setup describing theoverall setup including the locations of geophones and videocameras* Corresponding author: sudhan.regmi@gmail.com© 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, 03023 (2023)
DFHM8

https://doi.org/10.1051/e3sconf/202341503023

water discharge. However, the final experiment wasconducted as a dam overflow experiment. In this lastexperiment, a 300 mm high dam was placed at 2.4m fromthe start of the granular bed, being all other conditionssame as the previous three experiments.

3 Analysis
The frequency analysis part in this study comprises of
estimating the frequency response of the flow using thedata acquired by geophones. The first step for geophonedata preparation is to identify the acquisition parameters.
This includes the sampling rate and the unit of samplingof the sampled data. For this study, the sampling rate was5000 Hz, i.e. a data is sampled every 0.0002 Seconds.
After identifying the acquisition parameters, time for theopening of the gate was identified based on the highest
peak observed in time series data. When the gate isopened, it hits the flume bed at high force which creates alarge peak in the time series data. This large peak also
creates additional interfering frequencies undermining thefrequencies produced by actual event. Hence, the data for
analysis is selected 0.5 seconds after opening of the gatewith an assumption that the frequency of the events
overpowers the frequency from the gate opening after 0.5
seconds based on observations.
The key characteristic component of the vibration
recorded by the geophone can be extracted using
appropriate analysis technique. Among various tools
available for interpretation of such signals, variants ofFourier transform are used. As the data recorded by thegeophone are of discrete nature, discrete Fouriertransform (DFT) of overall event duration was performed
using the Fast Fourier Transform (FFT) algorithm [3]. In
this study the DFT on the event data was performed using
Python library, SciPy and NumPy [4].
Similarly, Short-time Fourier transform (STFT), avariant of DFT was used to compute the discrete Fourier
series for a short period to analyse the change in frequency
spectrum overtime. For this study, STFT we computed for
1 sec data at a time with 96.667% overlap, resulting intime resolution of STFT of 0.033 seconds to be consistent
with time resolution of image analysis (i.e. 30 fps).
DFT resolves the frequency in both positive andnegative domain, the maximum frequency resolved is halfof the sampling frequency call Nyquist frequency. For thisstudy, the sampling frequency is 5000 Hz, hence themaximum frequency resolved is 2500 Hz. Since, we areconcerned with the lower frequency range for debris flow,frequency up to 100 Hz is only considered for analysis.
Seismo-acoustic frequency induced by debris flow
normally ranges from 10-80 Hz, with lower frequency
observed at surge front and higher frequency towards theend [5]. The dominant frequency induced by the flow is
generally between 20-50 Hz [6] and higher frequency isnormally attributed to water flow. Similar trend wasobserved from the DFT analysis of experimental data.
Hence, to develop an appropriate model for nonlinear regression, the frequency spectrum was expected to
be normally distributed among these three frequency
clusters. Again, superposition principle of these threenormally distributed frequency ranges were presumed toFig. 2. Stages of flume bed preparation with geophones
locations, fine granular material, coarse granular material, final
stage with very thin layer of fine granular material on top ofcoarse material, and the completed flume (right)

The flow region for the simulated debris flow can beseparated into three main sections. Initial 2.3 m section
after the quick-release gate holding the source material islined with smooth PPMA material which allows thesource material to accelerate before passing through thegranular surface. This section can be labelled as theacceleration zone. The granular section after theacceleration zone is constructed to simulate the granular
bed surface for debris flow. This section is laid out for theremaining 4.8 m and is constructed in three layers, handcompacted after each layer. The first layer consisted offine granular material same as the source material withapproximate 𝑑𝑎𝑣𝑔 of 3.34 mm, laid at a thickness of 70mm throughout. The second layer consisted of coarse
granular material with approximate 𝑑𝑎𝑣𝑔 of 11.65 mm,laid at a thickness of 30 mm on top of the fine material.
This layer of coarse material acts as erosion barrier for thefine material underneath. The third layer consists of verythin layer of fine granular material, same as the first layer
on top of the coarse material to reduce the surface frictionof the bed. Although, all the 4.8 m section after theacceleration zone is constructed the same, it can still be
divided into two sections. The first 3 m section can belabelled as granular-flow zone, where the source material
flows freely over the granular bed, deaccelerating
constantly due to the surface friction. The remaining 1.8
m section can be labelled as the accumulation zone, where
the source material may accumulate at the end of theflume. As the experiment progresses, the accumulation
zone may extend to the granular-flow zone based on thevolume of source material used.
The acoustic signals/vibrations induced by the moving
debris mass is detected and recorded by three geophones,
completely buried under the fine granular material, andfixed to the bottom of the flume. These geophones areplaced approximately 1.5 m apart from each other withthe first one at 3 m from the gate (0.74 m from the end ofPPMA surface). The thickness of bed material above thegeophones is maintained at 30 mm throughout. In
conjunction with geophones video cameras are used torecord the progression of the experiment to track the phasespeed of the flow front.
In total 4 sets of experiments were performed, with thefirst three having similar flow conditions but varying

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E3S Web of Conferences 415, 03023 (2023)
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be valid and could be summed together. Hence, a model
for linear summation of three Gaussian distribution wasadopted for the non-linear regression analysis. This model
can be described as:

location of each point on the frame for all images. Fig. 4
shows the side profile of the flow during one of theexperiments:

31 𝐹 − 𝜇𝑛 2𝑓(𝐹) = ∑ 𝛼𝑛 exp [− () ]2𝜎𝑛𝑛−1(1)Where, 𝐹 is the frequency range for analysis, 𝛼𝑛 isthe amplitude of the function, 𝜇𝑛 is the location of thepeak and 𝜎𝑛 is the spread of the distribution.
The Gaussian function have three unknown variables,
which results in nine variables considering all threefunctions. This study is focused on the location of thepeak. Although, using weighted non-linear least square
regression method, all nine variables are computed.
Detection of peak frequencies for one of the experimentsfor one instant is shown in Fig. 3.

Fig. 4. Side profile of the experiment. The dashed outline
indicates ROI for image analysis and the dot indicates theparticle being tracked.

The velocity of particles at varying depth wasmeasured for different instances. Due to the varying
depth, the measured velocity couldn’t be considered as therepresentative and was converted surface velocity using
appropriate velocity profile.
Many studies have observed that the velocity of debris
flows is asymmetrical with maximum velocity observedat the surface, decreasing throughout as the flow depth
increases [8]. Following the same principle, a non-linear
velocity profile with maximum share at the base of theflow and no slip condition was adopted [9], andtransformed into non-dimensional flow parameter as:
1𝑧 1−𝛼(2)𝑣 = (2 − 𝛼)𝑣𝑚𝑒𝑎𝑛 [1 − (1 − ) ]ℎFig. 3. Detection of peak frequencies using the Gaussian
regression

Although all three frequencies in low frequency (1020), mid frequency (20-50) and higher frequency (50-100)
are resolved using the three-peak model, only thefrequency in mid-range are considered during the analysis
as this range is considered dominant during the debris
flow events. Lower frequencies are omitted because thenatural frequency of the geophone used in the experiments
is 10 𝐻𝑧 ± 2.5%, this causes maximum resonance in that
range and its amplitude cannot be established exclusively
for the debris flow movement. Also, the higher frequency
is commonly attributed to the water flow, for this reason
this range is omitted as well.
Besides the geophone analysis, this study also focuseson physical characteristics of the debris flow including
flow velocity, flow depth and discharge. To measure these
physical parameters, various image analysis approaches
were used on the video taken during the experiments. All
experiment proceedings were recorded using for video
cameras and recorded at either 60 frames per second or 30frames per second. To maintain consistency with theanalysed geophone data, the time resolution of 30 fps(0.033 sec) was used for image extraction from video
files.
Using MATLAB’s image processing toolbox [7], firstthe video file was separated into individual frames. The
separated images were then converted into grayscale andusing Gaussian filtering lightning inconstancy wasremoved from each frame. Then, using the principle ofperspective projection, the images were transformed into
orthographic projection with known X and Y scales.
Finally, the front location, particle velocity and flowheight were traced on each frame manually, recording theWhere, 𝑧 is the depth of the particle, ℎ is the total
depth of flow, 0 ≤ 𝛼 ≤ 1 controls the shape of the profile
by controlling amount of shear within the greater part of
the flow and 𝑣𝑚𝑒𝑎𝑛 is the depth averaged velocity.
At 𝑧 = ℎ,vsurface = (2 − α)vmean(3)
Hence, equation (2) can be re-written as:
1𝑧 1−𝛼𝑣 = 𝑣𝑠𝑢𝑟𝑓𝑎𝑐𝑒 [1 − (1 − ) ]ℎ(4)To estimate the value of α from the experimental
observations, four sets of data consisting of three velocity
observations each were used. These velocity data wereobserved at different depth at same time for each set ofdata. To analyse different sets of data from different
experiments together, they were normalised for both
depth and velocity with respect to maximum depth andmaximum velocity (near the surface) observed at same
instant. From the analysis, value of α is estimated to be
0.4899 with coefficient of determination (R2) of 0.977.

4 Results and observations
From the recorded seismo-acoustic data and calculated
surface velocity, it was initially observed that therelationship between acoustic frequency of the flow and3

E3S Web of Conferences 415, 03023 (2023)
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5 Conclusions

its surface velocity is nonlinear and to a point evenchaotic. No perceptible linear trend among theexperiments were observed.
However, another plot of normalized velocity squared
to normalized frequency/velocity for all four experiments,
shows a power curve distribution as shown in Fig. 5Comparing these plots, we can observe that the fittingthese data using a power curve in form 𝑌 = 𝑎𝑋 𝑛 shows
an exceptional trend with very little amount of scattering.
The 𝑅2 value as seen in plots suggests that the data is moresuitable for power curve fit than linear fit. Among all thesefour experiments, experiment 4 plots are slightly different
than the rest. This might be due to the different nature of
the last experiment as described in previous section. Thisobservation of the frequency and velocity relation could
not yet be explained and further analysis andinterpretation is necessary.

References
1.
2.

3.
4.
5.

6.
7.
8.

Fig. 5. Normalized frequency/velocity vs velocity squared plot
with power curve fit. a) Shows the distribution of all four
experiments individually, whereas b) shows the power curve fit
for combination of all four experiments.

9.

In the above plot both frequency and velocity arenormalised such that:𝑙(5)𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 = 𝑓𝑐0𝑐
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 =(6)𝑐𝑜Where, 𝑓 is the observed frequency, 𝑙 is the averagelenth of flow, 𝑐0 is the average surface velocity of the flow
ad 𝑐 is the observed instantiations surface velocity of theflow. The average length of flow and the average surface
velocity of the flow is assumed constant for eachexperiment. The coefficients and power fit parameter foreach experiment is listed in Table 1.
Table 1: Constants and coefficients of power curve fit
Exp_1
Exp_2
Exp_3
Exp_4
All

Constant
115.5026
76.061993.1077
587.2582
128.9883

Power-0.42843-0.55847-0.58866-0.51905-0.51925

R20.897
0.973
0.993
0.995
0.996

𝑙22222

𝐶00.65682
1.02158
0.771760.14093
0.60590

4

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