E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
ASSESSMENT OF VIDEO IMAGING AND PARTICLE COUNTING TECHNIQUES FOR CALCULATION OF
BEDLOAD FLUXES
RUI ALEIXO(1,2), LUÍS MENDES(1), FEDERICA ANTICO(1), PEDRO SANCHES(1), FRANCISCO ALEGRIA(2,3) & RUI M.L. FERREIRA(1)
(1)
CEris – Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
e-mail: ferreira_aleixo@yahoo.co.uk, luis.mendes@ist.utl.pt, {federica.antico; pedro.sanches}@tecnico.ulisboa.pt
(2)
(3)
Instituto de Telecomunicações, Lisboa, Portugal
e-mail falegria@lx.it.pt
Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal
e-mail ruimferreira@civil.ist.utl.pt
ABSTRACT
Sediment transport is a fundamental process of Nature. It is studied by different areas of knowledge such as geology and
civil engineering. In particular it is an important process in fluvial hydraulics as it is associated to morphological changes in
the fluvial basin and thus impacting many human activities such as river management and dam operation. It is a process
that has different spatial and time scales associated with it, from the small scales of the sediment to the larger scales of
the river basin. When studying sediment transport one normally separates suspended and bedload. In the present paper
only bedload will be analyzed. Even in laboratorial environment, bedload fluxes measurements are usually hard to perform
since one needs to calculate the number of particles that cross a given section per time unit. Previous studies used a
devices based on a metallic plate and accelerometers to count the particles impact on the plate; high-speed video
recording was also used to count individual particles.
In this paper a technique is presented to measure the bedload flux based on the particles impact on a sensitive surface.
This technique allows for counting the number of particles’ impacts in a given time interval, which is directly comparable
with the number of particles that cross a certain cross-section in the same interval, quantified by digital image acquisition
and analysis. The advantages of the impact surface technique, like high-frequency acquisition (virtually continuous
measurements), no need for optical access and low amount of digital data (allowing real-time analyses) are discussed and
presented alongside with its limitations.
Keywords: bedload, measurement, bead counter, imaging techniques
1.
INTRODUCTION
Given the right conditions, fluvial bed sediments will move. The beginning of motion is a function of different parameters,
e.g., Shields (1936) explained it as a function of the shear stress. It is known that turbulence plays an important role in
sediment motion (Nelson et al. 1995, McEwan et al. 2002, others?) as well. Once the sediments leave their initial position
in the bed they will be transported by different mechanisms like suspension and bedload. Transport by suspension means
that, like its name suggests, that the sediments are transported the core of flow, whereas bedload regards the sediment
transport in a fine layer close to the bed. In this layer three types of motion are identified: rolling, sliding and saltation. In
this paper the only the bedload transport will be considered.
Sediment discharge determination is important in order to correctly model and predict the fluvial bed evolution. The works
of Einstein (1937, 1950) and Meyer-Peter and Muller (1948) took different approaches in this matter. Einstein used
analytical methods to derive expressions for solid discharge whereas Meyer-Peter and Muller (1948) used experimental
data, for very specific conditions, to obtain their expression for solid discharge; this has limited the range of application of
latter expression. The analytical approach taken by Einstein was focused on the sediment scale and it was based on the
probabilistic and statistical analysis of the sediments. Although innovative, Einstein’s approach was not immediately
recognized as useful, as pointed out by Meyer-Peter (Ettema and Muttel 2004). However recent studies (e.g. Furbish et al.
2012) have brought back the probabilistic approach to the bedload sediment solid discharge analysis.
Bedload solid discharge has to be directly measured to provide much needed information to be used for practical
application as well to validate existing expressions. Measurement techniques exist to measure it and they are based in
different physical principles (Ferreira et al., 2015, van Rijn, 2007). Such techniques like bottle and trap samplers (van Rijn,
2007) work on the principle of collecting sediments during a certain time interval. This type of probes is often used in field
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
experiments (Hassan, others). In laboratory imaging methods have been increasingly used (Furbish, ballio et al, 2010?…).
They are robust and efficient. However, the need for optical access and limited buffer size for image acquisition are some
of the drawbacks associated to this technique.
In this paper a prototype device to measure the bedload sediment transport is proposed. This device works by detecting
the particles’ impact in a sensitive surface. An algorithm of signal processing and pattern recognition is implemented to
detect and count the number of particles. The performance of this device is compared with the results obtained using
image processing to determine the solid discharge.
2.
BEDLOAD: DEFINITION AND MEASUREMENT TECHNIQUES
The bedload sediment flux is defined as the solid volume of bedload particles crossing a vertical surface per unit time and
unit width. Several different relations of bedload sediment flux emerge from the literature. Theoretically the solid discharge
can be defined by the following classic expression:
q𝑠 = ∫ 𝒖𝑝 𝒌𝑑𝑆
[1]
𝑆
where S is a cross section of unit width, up, the particle velocity field and k the unit vector normal to S (Ancey 2010).This
definition, suitable for continuous sediment flows, but impractical for discreet solid flows. According to recent studies
(Schmeeckle and Furbish, 2007; Ancey, 2010), the continuum assumption is rarely valid for bedload, particularly at low
transport rates (Roseberry et al., 2012). The majority descriptions of the solid discharge assume that the transported
particles are uniformly distributed: for instance, for one- dimensional transport in the flow direction, with quasi-steady bed
and transport conditions, the “entrainment form”, introduced by Einstein (1950) and recently elaborated by other authors
(Wilcock, 1997a, Parker et al, 2000, Seminara et al. 2002, Wong et al. 2007, Ganti et al. 2010) identified the solid
discharge as:
q𝑥 = 𝐸 λ̅
[2]
Where qx is the one-dimensional, E is the volumetric rate of particle entrainment per unit streambed area and λ is the
mean particle hop distance, measured start to stop. Assuming quasi-steady bed and transport conditions another common
expression used to define the sediment flux is the so-called “flux form”:
q𝑥 = 𝜎𝑈𝑝
[3]
where Up is the mean particle velocity and σ is the bedload particle activity, namely the volume of particles in motion per
unit streambed area. It must be noted, again, how the conventional descriptions of the solid flux, as those presented, are
not applicable in discrete fields. Hence the need to devise a more convenient technique capable of counting individual
particles that cross a section S over an established period of time, to obtain an accurate estimation of the solid discharge.
Having a device capable of doing so, the sediment flux can be easily calculated by the relation:
q𝑥 =
𝑉𝑛0
𝑏
[4]
where V is the volume of the particles, n0 is the number of particles that cross a certain cross-section S in an interval time
of one second and b is the width of S. Note that the definitions (2) and (3) are consistent with the first one inasmuch as
active particles are at any instant uniformly distributed over the streambed and the flux normal width is sufficiently large to
smooth over instantaneous small-scale variations in the particle activity along the width of the section considered (Furbish
et al. 2012a).
2.1 Bedload measurements: imaging methods
Imaging methods can be used to measure discrete fluxes. This is made by acquiring images of the flow and processing
them to identify the particles that cross a given section in a certain time interval. Figure 1 a) depicts a raw image of the
flow and Figure 1 b) depicts the identified moving particles.
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E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
Figure 1. Example kfa) raw image of moving sediments; b) identified moving sediments.
After identifying and counting the particles the flux can be computed. However this method is not very practical if long
period experiments have to be performed. Main reasons are the huge amount of images generated and the time
consuming processing those images. A more practical approach to count individual sediment particles is proposed on the
next section.
2.2 Bedload measurements: the bead counter
The bead counter is a prototype device developed to count individual sediment particles (beads). This device is based on
counting impacts on a sensitive prismatic element as depicted in Figure 2. The sensitive element is composed of a hollow
box filled with air at a certain pressure, P, connected to a pressure transducer. The upward face of this prism is made of a
rubber membrane. Sediments hitting the rubber surface will cause a pressure variation that will be measured by the
pressure transducers. The pressure signal is converted into an electrical signal (Figure 3) by the transducer. It is then
sampled and analyzed with Digital Signal Processing and Patten Recognition techniques to be validated as a particle
impact. The digital sampled signal is then processed with Digital Signal Processing techniques to extract the relevant
signal characteristics that define a bead impact on the membrane box surface. Those characteristics are then fed to a
pattern recognition algorithm to identify the presence of the impact pattern. If an impact is identified then the instant of the
impact detection is recorded and sent to the client terminal connected through the RS-232 interface, the LCD is also
updated with the number of impacts detected. The LCD also displays a graphic that allows monitoring the digitally
processed real-time signal. The block diagram of Figure 4 depicts the working principle of the bead counter device. The
processing board is named MiCas.
Figure 2.Scheme of the bead counter. These elements are placed side by side along the channel width.
Figure 3.Measured signal of a bead impact in the membrane.
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
Figure 4. Block diagram of the bead counter.
This device was tested in the channel under different flow conditions, to test the turbulence effect over the membranes.
The moving sediments were counted using imaging methods for results comparison.
3.
EXPERIMENTAL SETUP
3.1 Channel and bed configuration
The experimental work was carried out in a 12.5 m long and 40.8 cm wide recirculating tilting flume of the
Laboratory of Hydraulics and Environment of Instituto Superior Técnico. The flume has glass side walls,
enabling flow visualization and laser illumination. The flume bed was divided in a fixed and a mobile reach.
The fixed reach starts with a length of 1.5 m of large boulders with an average dimension of 5.0 cm followed
by 3.0 m of one layer glued gravel with 5 mm of average dimension. After, a 2.5 m of one layer glued
spherical beads, also with 5 mm of diameter. Then, the mobile reach was created with beads with 5.0 mm of
diameter, making 2.5 cm of thickness along 4.0 m of length. The bed is elevated 7.5 cm of the channel
bottom. After the mobile bed, a PVC step with 7.5 cm of height was created to accommodate the bead
counter. Experimental tests were performed with a main pump with a flow rate of 27.0 L/s and a secondary
pump recirculating the beads with a flow rate of 2.2 L/s. The flow from the secondary pump enters the flume in
the third meter of the channel. The flume was also tilted to have a slope of i = 0.0027. Figure 5 depicts the
channel (not at scale).
Figure 5. Scheme of the channel used in the experiments.
3.2 Imaging methods
A high speed camera MotionScope M5 with a maximum resolution of 2336 x 1728 pixels is positioned above the channel
to be able to see the particles hitting the bead counter. The camera resolution is adjusted to 2288 x 200 pixels for an
acquisition frequency of 300 Hz. The camera lens is a 50 mm f0.95 TV LENS-NAVITAR. The camera acquisition is
synchronized with the bead counter. The camera positioning relatively to the channel is depicted in Figure 6.
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E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
Figure 6. Placement of the camera in relation to the moving bed, buffer plate and bead counter’s membrane.
3.3 Bead Counter Configuration
The bead counter is a pair of hollow and sealed PVC triangular prismatic boxes with a rubber membrane connected to two
rubber tubes that allow registering pressure differences caused by the impacts of the beads that fall after the PVC step
described before. These boxes have a rectangular base of 10.0 cm by 5.0 cm and a height linearly decreasing from 3.0
cm along its length. The rubber membrane is glued on the decreasing top surface in order to create a ramp that allows the
beads to roll down. The placement of the bead counter inside of the channel is depicted in Figure 7.
Figure 7. Placement of the bead counter prototype in the channel downstream of the moving bed. A: moving bed. B: buffer
plate. C channel bottom. D1 and D2: bead counter membranes. 425-210 = 215
4.
PRELIMINARY RESULTS
Different tests were made with the bead counter: in air, in still water and inside the channel. The results here presented
are referred to the tests inside the channel. In the spectrogram of Figure 8 it is possible to see that an impact is clearly
identified by the high energy patches. Comparing the imaging technique with the bead counter it was possible to observe
that observed beads in the camera corresponded to detected impacts. These results are promising however some
attention has to be given the following factors: particles rebounds interpreted as new particles, simultaneous impacts in the
same membrane interpreted as just one particle.
Figure 8. a) Spectrogram from the sampled signals showing the impacts; b) Spectrogram with detected impact instants
shown as overlapped vertical red lines
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
5.
CONCLUSIONS AND FUTURE WORK
A prototype for a bead counter was presented. The preliminary tests have shown promising results. However attention has
to be given to the signal analysis in order to avoid false positives and to correctly interpret rebounds. Also if a bead hits in
between the membrane boxes no impact is detected. Improvements in the setup have also to be made in the bead
counter to be useful in different environments.
ACKNOWLEDGMENTS
This work was partially funded] by FEDER, program COMPETE, and by national funds through Portuguese Foundation for
Science and Technology (FCT) project RECI/ECM-HID/0371/2012.
REFERENCES
Ancey, C. (2010). Stochastic modeling in sediment dynamics: Exner equation for planar bed incipient bed load transport
conditions, Journal of Geophysical Research, 115, F00A11.
Einstein, H. A. (1950). The bed-load function for sediment transportation in open channel flows, Tech. Bull. 1026, Soil
Conserv. Serv., U.S. Dep. Of Agric., Washington, D. C.
Ettema, R. and Mutel, C. (2004). Hans Albert Einstein: Innovation and Compromise in Formulating Sediment Transport by
Rivers. J. Hydraul. Eng., 130(6), 477–487.
Furbish, D.J., Haff, P.K., Roseberry, J.C., and Schmeekle, M.W. (2012). A probabilistic description of the bed load
sediment flux: 1. Theory, Journal of Geophysical Research, 117, F03031.
Ganti, V., M. M. Meerschaert, E. Foufoula-Georgiou, E. Viparelli, and G. Parker (2010). Normal and anomalous diffusion
of gravel tracer particles in rivers, Journal of Geophysical Research, 115, F00A12.
Meyer-Peter, E., and Müller, R. (1948). Formulas for bed load transport. Proceedinds of the 2nd IAHR Congress,
Stockholm, June.
Parker, G., C. Paola, and S. Leclair (2000). Probabilistic Exner sediment continuity equation for mixtures with no active
layer, J. Hydraul. Eng.,126, 818–826.
Roseberry, J. C., M. W. Schmeeckle, and D. J. Furbish (2012). A probabilistic description of the bed load sediment flux: 2.
Particle activity and motions, Journal of Geophysical Research, 117, F03032.
Schmeeckle, M. W., and D. J. Furbish (2007). A Fokker-Planck model of bedload transport and morphodynamics, paper
presented at the StochasticTransport and Emerging Scaling on Earth’s Surface (STRESS) work group meeting, Natl.
Cent.for Earth-Surf. Dyn ., Univ. of Ill. and Desert Res. Inst., Lake Tahoe, Nev.
Seminara, G., L. Solari, and G. Parker (2002). Bed load at low Shields stress on arbitrarily sloping beds: Failure of the
Bagnold hypothesis, Water Resour. Res., 38(11), 1249.
van Rijn, L.C. (2007). Manual Sediment Transport Measurements in Rivers, Estauries and Coastal Seas. Online version:
http://www.vliz.be/wiki/Manual_Sediment_Transport_Measurements_in_Rivers,_Estuaries_and_Coastal_Seas.
Wilcock, P. R. (1997a), Entrainment, displacement and transport of tracer gravels, Earth Surf. Processes Landforms, 22,
1125–1138.
Wong, M., G. Parker, P. DeVries, T. M. Brown, and S. J. Burges (2007). Experiments on dispersion of tracer stones under
lower-regime plane bed equilibrium bed load transport, Water Resour. Res., 43, W03440.
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