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Real time instability of flow close to a scour affected abutment

Abstract

For centuries, the interaction between the transport and hydrographic networks represents a significant issue in a country such as France. For example, the French railway network includes 1700 river-crossing structures and an important length of embankments either forming river banks or adjacent to watercourses exposed to scouring processes. Recently, various cases highlight the importance and vulnerability of civil transport works in relation to their environmental hazards, e.g. floods, and therefore the need to develop integrated observation tools and warning systems in the aim both of optimizing the management system and of increasing the knowledge on real scour processes. This paper relies to a French research project named SSHEAR which objective is to improve understanding of the scouring process through the use of innovative observation tools and physical and numerical hydraulic modelling. This part of the project aims at improving continuous monitoring in order to follow the evolution of the scour processes of a given bridge or abutment. After a presentation of the experimental site, the instrumentation is described as well as its in situ implementation. The data analysis process is given and results are commented before the presentation of some perspectives part.

Highlights

  • Field study,

  • Scour,

  • Experience feed back.

Introduction

Civil transport works are highly affected by environmental hazards and one of the major one is scour both worldwide and for centuries. Guidelines have been published to explain the phenomenon, provide design rules and dimensioning laws to engineers and practitioners [1,2,3,4,5,6]. However, in France, there are mostly decades-old structures to be maintained. As an example, the National railways Company (SNCF) has to maintain 7500 bridges with foundations in aquatic sites. Civil engineering structures on river sites benefit from a monitoring of their structural health by their managers, generally with regular and exceptional inspections [7, 8]. With variable frequencies depending on the structure type (dams, levees, bridges, weirs, …) and importance (or size). These inspections are most often visual, sometimes underwater and/or associated with specialized survey (geotechnical, geophysical, bathymetric, etc.). The complex context of structures in contact with watercourse (water speed and sediment mobility) makes continuous measurement rare. An effective continuous, detailed and optimized monitoring of these structures can allow a prediction of the state of damage.

The reaction of any work to scour is also highly dependent of structural parameters. Samizo et al. [9] investigated those aspects using micrometers. Schall and Davies [10] proposed a magnetic system. Prendergast et al. [11] focused on bridge natural frequency, Chang et al. [12] presented a major feedback campaign in Korea. Boujia et al. [13] proposed a Scour Depth Sensor that was tested in another site of the current research project Lararrte et al. [14]. [15,16,17,18,19,20,21] have made recent points of available technics and proposed more global views and recommendations, the last authors giving also clear information about the deployment and maintenance costs. Kang [22] developed a scour meter, De Falco and Mele [23] reported about the bathymetry and water levels from a field study in Italy, Hayden et al. [24] only gave bathymetric data from a case in the USA. Tapia Rodriguez et al. [25] presented cases study within a review of velocity measurement devices. However there are few published measurements of this parameter even though, as indicated by Laursen and Toch [26], the key the incoming water depth and velocity are among the parameters influencing the scour phenomenon. More recently, Barbhuiya and Dey [27] did a large review of the available literature, proposed a classification of the parameters related to scour at abutments and concluded « that the exact scour mechanism and effects of different parameters on scour depth are yet to be fully understood or explored». In continuity, Dey and Barbhuiya [28] presented a study showing the influence of the vortex on the scour hole. In its presentation of scour phenomenon, Dey [29] indicated that the upstream water level and velocity are influencing parameters of scour at abutment.

In order to improve scour related knowledge, the presented study aimed at providing an insight into the global monitoring of scour affecting an abutment, Chevalier et al. [30]. Larrarte et al. [31] have presented the instrumentation approach developed in the framework of the SSHEAR project [30]. This paper explains the statistical analysis that can be made of the data. Results, and feedback after some months of instrumentation, will finally conclude this paper.

Site description and instrumentation

Experimental site selection was an important first part of SSHEAR project. Several criteria were defined to select the ones that would be monitored during either brief campaigns or for some longer continuous periods (as the site presented in this paper). If all the details of the site selection process and instrumentation choice are presented in Larrarte et al. [31], the main points are summarized here after.

The chosen site is located in a rural wooded lowland area representative of the countryside of the western part of metropolitan France (western Europe) with an oceanic climate (the site is at about 200 km from the Atlantic coast).The railway bridge over the Aurence is a characteristic arch bridge built on the banks of the channels. The river is located into the oceanic climate zone with high flow rates in winter and low flow rates in summer. Strong variations with lower values in summer can be observed as well as inter annual ones. In this small catchment, whose area equals 87 km2, the highly rainy month of January 2018 can also be seen. The Aurence catchment it is very reactive with a flood duration of approximately 24 h. The peak discharge of the highest floods that appeared on the river during the last 25 years was about 28 m3/s in February 2003. The return period of those floods is estimated at twenty years. The river is 5 m wide and less than a meter deep in 95% of the annual water levels as obtained from the 4 previous hydrological years on the Banque Hydro data base presented by Larrarte et al. [31]. Samplings have shown that 95% of the bed materials have a diameter smaller than 5 mm.

This site is affected by scour on the abutment. Larrarte et al. [31] reported that, at the foot of the abutment, a scour of 1.7 m long and 0.5 m deep has been measured. A bathymetric campaign has confirmed that an eroded area exists under the bridge with an even deeper part at the extrados of the bridge (dark blue part on Fig. 1). It has thus been decided to implement the sensors on that area (red circle on Fig. 1).

Fig. 1
figure 1

Bathymetric survey made in 2018. Red circle: place of the monitoring set-up (Larrarte et al. [31])

The objective of the monitoring was to have continuous measurements of both hydraulics properties and bathymetry. These include: water level, velocity profile, and sediment level or bathymetry. The following devices were implemented:

  • an Ijinus LNU06V3-82-3G ultrasonic water level gauge to measure the water level, using the transit time principle,

  • an ultrasonic Ub-flow UBF156 by Ubertone to measure the velocity profile and the water depth,

  • a HIK Vision 4MP WDR fixed network camera to watch the sensors periodically in order to identify any emergency situation.

The great challenge was to be able measure the velocities to evaluate the shear velocity u*. In order to minimize the perturbations generated by the set-up on the bottom, the Ub-flow has been located on a raft (Fig. 2) that is fixed to the abutment.

Fig. 2
figure 2

Monitoring set-up installed on the abutment site

Data processing

The ultrasonic water level gauge allows measuring the free surface position relatively to a fixed reference on the bridge. At any time later, using the UB-flow transducer 2 (that has an inclination angle of 97°), it is possible to measure the water depth (Fig. 3) and then to determine the scour depth using Eq. (1):

$$ {\text{h}}_{{\text{s}}} \left( {\text{t}} \right) \, = {\text{ h}}_{{\text{p}}} \left( {\text{t}} \right) \, - {\text{ h}}_{{\text{l}}} \left( {\text{t}} \right) $$
(1)
Fig. 3
figure 3

Definition of the various heights

where hp(t) is the water depth measured with Ub-flow and hl is the water level obtained with the limnimeter

$$ {\text{h}}_{{\text{l}}} \left( {\text{t}} \right) \, = {\text{ h}}_{{{\text{ref }} - }} {\text{d}}_{{\text{l}}} \left( {\text{t}} \right) $$
(2)

where dl(t) is the distance between the limnimeter and the free surface and href is the reference height given by Eq. (2):

$$ {\text{h}}_{{{\text{ref}}}} = {\text{ h}}_{{\text{p}}} \left( {{\text{t}} = 0} \right) \, + {\text{ d}}_{{\text{l}}} \left( {{\text{t}} = 0} \right) $$
(3)

where t = 0 correspond to the instant t when we implement the set-up.

In order to minimize the perturbations generated by the set-up on the bottom, the UB Flow was set on the free surface The Ub-flow profiler is designed to simultaneously measure the streamwise and vertical velocities. This sensor is made of two transducers: the first one has an inclination angle of 65° with regard to the Ub-flow base and an emission frequency centered on 1.5 MHz. The second transducer has an inclination angle of 97° with an emission frequency centered on 3 MHz (Fig. 4).

Fig. 4
figure 4

Lateral sketch of the profiler

This sensor configuration allows making a velocity profile with a spatial discretization up to 5 mm below the dead zone that is 5 cm long. On one hand, in contrast to ADCP (Acoustic Doppler Current Profiler), the UB Flow cannot measure the 3 components (streamwise, transverse and vertical) of the velocity but, as shown by Le Barbu et Larrarte [32], those measurements are meaning a spacial averaging which is not compatible with the potential spatial variation of the velocity and bathymetry in this channel which width is about 5 m. On the other hand, the Ub-flow is quite light (less than 1 kg) so the structure of the set-up can be light and not too invasive for the countryside where the measurements are made. Moreover, the Ub-flow allows us to select various configurations in order to obtain the best compromise between water level variations, quantity of data, quality of those data. Four configurations were programmed to be scanned every 5 min:

  • Configuration 1 that used transducer 2 (almost vertical): the backscattered amplitude presents a peak (Fig. 5) that is due to a change in the propagation medium and then is assimilated to the bottom of the river. This gives the water depth hp (see Fig. 3).

  • Configuration 2 that used transducer 1: it was used to measure 200 instantaneous profiles of the velocity close to the sensor and to average, this give the upper part of the velocity profile that was also used to obtain a typical velocities that will be precised later. A fitting by the power law proposed by Cheng [33] could be done.

  • Configuration 3 that used transducer 1: it was used to measure an instantaneous profile every 5 min on the greatest part of the water column.

  • Configuration 4 that used transducer 1: the priority is given to the measurements far from the sensor for the water levels greater than 0.85 m, that means during floods on the farthest part of the water column.

Fig. 5
figure 5

Amplitude of the backscattered signal and bottom location, between June 21st and July 4th of 2019, the black line represent the free surface position

Figure 3 presents the variation of the backscattered amplitude for a 2 weeks period. A high amplitude means the presence of an “acoustic obstacle” like the sediment surface. The sediment surface is interpreted as the first jump of amplitude. The black line indicates the water level measured with the limnimeter. Even after the rain events of June 22nd and July 3rd, the location of the bottom does not change, meaning they did not generate erosion processes.

The configurations 2 to 4 were selected to take account of a specificity of velocity measurement by coherent pulsed Doppler. Using repetition of the ultrasonic beam, very accurate measurements can be obtained in a small cell but only within an exploration depth. All the echoes originating from this exploration depth need to come back from the medium before the next pulse is sent. When the interval between two successive pulses is too long, the measurement suffers from a phase jump inducing an ambiguity. On a frequency point of view, this is equivalent to overstepping the limit given by the Nyquist-Shannon theorem [34, 35]. On one hand, for configuration 2, the depth is small and so the measurements are not affected by the phase jump. On the other hand, for configuration 3 and 4, the measurements can be affected by the Nyquist jump that has to be corrected profile by profile, making more complex any averaging.

The rough data profiles present an inflexion on the upper part, close to the sensor. This aspect ratio, defined as the ratio of the river width on river depth, is close to 5 that means that the river is at the limit of what is considered as a narrow channel. Moreover, profiles obtained with flowmeters have not presented this shape. So we assume this inflexion was not due to a dip phenomenon but to the presence of the raft that created a boundary layer similar to the situations observed by Nyantekyi-Kwakye et al. [36] for partially covered channels. Those parts of the profiles were considered as non representative of the physics of the flow and so not processed in the following analysis.

Figure 6 presents how the data given by the profiles were used obtain a vertical distribution of the streamwise velocity.

Fig. 6
figure 6

Contribution of the various configuration to obtain a velocity profile: a rough data given by the sensor; b after validation process and Nyquist correction

Results

Using the data processing method presented here above, it has been possible to analyse the 9 months data obtained before the set-up failed [31]. Figure 7 presents some zooms on the chronicles at various seasons. The high reactivity of the river can be seen as the water level can increase fast (peak about 0.6 m/hour) as soon as a rain event occurs. In the same time, the maximum velocity at about 1.5 m/s at the free surface is associated with this peak, that means 3 times the velocity observed before the rain event. It is interesting to notice that the velocity increases in all the water column, this will be discussed later.

Fig. 7
figure 7

Some zooms on the temporal chronicle, the black line represent the free surface position

Using those data, we look after the potential hysteresis between water level and velocity. As presented above, the instantaneous data can present high fluctuation so we have defined the U2c velocity that is the mean velocity of the measured values between 70 and 80% of the water column (from the bottom). Figure 8a and b presets all the values obtained for a 2 weeks period. Figure 8a details the data points as a function of the height variation whereas Fig. 8b presents a statistical analysis of the data (grey points): the red circles (and lines) represent the mean (and standard deviation) per value packet of constant height intervals. A good linear variation can be noticed for this water level range. Moreover, Fig. 9 shows that linear behavior remains valid whatever the number of days within the observed period and whatever the season was, except for the very little water levels observed at the end of summer (where strong decrease of the mean velocity is expected as the water height is decreasing). One interesting point here is that we do not observed any hysteresis (see Fig. 8a), giving an answer to Muste et al. [37] wondering “Where and when does hysteresis occur and how significant it is?”.

Fig. 8
figure 8

Characteristic U2c velocity as a function of the water level hl from 14th of June to 4th of July (14 days): a all data function of height variation, b statistical analysis

Fig. 9
figure 9

Characteristic U2c velocity as a function of the water level hl for various periods

Going back to erosion aspects, the vertical distribution of the streamwise velocity can be presented and used. Using the data, we can rebuilt a full profile. Moreoever, the configuration 2 data gives us the maximal velocity along a profile.

Cheng [33] proposed a power law (log law) to describe the vertical distribution of the primary velocity (Eq. 4):

$$\frac{U}{{U}_{max}}={(\frac{z}{h})}^{1/m}$$
(4)

where U(z) is the streamwise velocity measured at a distance z from the bottom, h the water depth and 1/m the power law index.

Using Cheng [33] power law, we can fit the experimental data and compare them to the vertical distribution given by the law proposed by Coles [38] (Eq. 5):

$$ \frac{U}{{u_{ * } }} = \frac{1}{\kappa }\ln \left( {\frac{z}{{k_{s} }}} \right) + B_{s} + w\left( \xi \right)\quad {\text{with}}\quad w\left( \xi \right) = \frac{2\Pi }{\kappa }\sin^{2} \left( {\frac{\pi }{2}\xi } \right) $$
(5)

where w(ξ) is the wake function and Π the wake parameter proposed by Coles who introduced an additive correction to the log-law, U(z) is the streamwise velocity measured at a distance z from the bottom, h the water depth, ξ = z/h the dimensionless distance from the bottom, Bs the integration coefficient equal to 8.5 and Nikuradse [39] logarithmic law that uses the u* the shear velocity, κ the Von Karman constant equal to 0.4, ks the equivalent sand grain roughness (5 mm).

Figure 10 presents some vertical distributions of the streamwise velocity for various water levels. The instantaneous profiles present large fluctuations as those observed by Despax [40]. Notwithstanding the dispersion of the instantaneous velocity values, they can be well smoothed by a Cheng’s law (with m = 3.5) or a Coles law, giving the capability to estimate the shear velocity u*. Parameters of Eq. 4 (Umax, h) or 5 (u*, h) were determined with curve_fit function of SciPy Python library that uses non-linear least squares to fit a function to data.

Fig. 10
figure 10

Examples of 5 dimensionless velocity profiles acquired with 5 min. interval. Fits are done with Cheng (left) or Coles (right) law either on each profile (colored curves) or on all the 5 profile data (black curve)

Figure 11 presents the evolution of adjustment parameters for Cheng or Coles fit: (fitted) water heights and mean velocities Umean (instead of Umax or u* for comparison purpose) as a function of the (limnimeter) water height hl and U2c velocity for a period of 14 days from 14th of June to 4th of July. Whether it is for instantaneous profiles or the average over 5 profiles spaced of 5 min, we obtain a cloud of points which presents an increasing linear evolution. On Fig. 9a, the water levels go to an asymptotic behavior for the higher water levels where this is not observed for the velocities (Fig. 11b).

Fig. 11
figure 11

Evolution of the adjustment parameters from 14th of June to 4th of July (14 days): a water level, b velocities

Figure 12 presents the typical statistical analysis on the mean velocities considering the various fit conditions (Cheng or Coles fit on 1 or 5 profile(s)) for this data. No strong variations are observed between the different fit conditions. Dispersion is reduced considering the fit on 5 profiles as more data points are considered for these adjustments. Similar observations can also be done on the water height data (Fig. 11a).

Fig. 12
figure 12

Statistical analysis on the on the mean velocities considering the various fit conditions from 14th of June to 4th of July (14 days): Cheng (left) or Coles (right) fit on 1 (top) or 5 (bottom) profile(s)

Focusing on the Cheng fit for 5 profiles, Fig. 13 shows that the behavior observed on Fig. 11 for one period of 14 days remains valid whatever the number of days within the observed period and whatever the season was.

Fig. 13
figure 13

Evolution of the adjustment parameters (Cheng fit on 5 profiles) for various periods

To characterize the dispersion of the instantaneous velocity profile measurements from the adjusted profile (Cheng or Coles), we evaluate the standard deviation of the velocity with the following definition (Eq. 6):

$$\Delta U=\sqrt{\frac{1}{number\,of\,data\,points}\sum_{data\,points}{(U\left(z\right)-{U}_{fit}\left(z\right))}^{2}}$$
(6)

where typical data points and fit are depicted of Fig. 10.

Figure 14a presents the evolution of this standard deviation of the velocity divided by the mean velocity Umean as a function of the water level for Cheng or Coles fit on 1 or 5 profile(s). Here again the data represents a cloud but a statistical analysis can be practiced, for example on Cheng fit for 5 profiles as depicted by Fig. 14b. We recall that the red circles (and lines) represent the mean (and standard deviation) per value packet of constant height intervals for the gray data points.

Fig. 14
figure 14

Evolution of standard deviation as a function of the water level from 14th of June to 4th of July (14 days): a all data function, b statistical analysis (Cheng fit on 5 profiles)

Figure 15 allows comparing the evolution of the standard deviation of the velocity for various periods of time. We can thus identify that the standard deviation represents about 25% of the mean velocity, whatever the water level is.

Fig. 15
figure 15

Evolution of standard deviation as a function of the water level (Cheng fit on 5 profiles) for various periods

Conclusion

This paper relies to a project aiming at improving continuous monitoring of scour affecting public transport network [30]. A real site has been selected to follow the evolution of the scour process observed close to an abutment of a bridge. First the main criteria used to select the site were listed. Then, after a presentation of the experimental site, the instrumentation was presented as well as the complete set-up. The analysis method has been developed and was described as well as some of the results obtained during the 9 months during which it was possible to acquire data.

By using the sensor and its configurations, we obtain water levels measurements and velocities that give profiles over the entire water height in the observed range. Those experimental data were compared with usual vertical distribution laws that can be used to estimate the shear velocity. During the 9 months of the experimental campaign, a wide range of hydrological contexts were met but no hysteresis was observed between floods (which are rather fast) and much slower decrescents.

When the raft failure occurred [31] we prepared a modification of the configurations to acquire 200 successive instantaneous profiles and their averages on the different sections (in height) in order to validate the above conclusion and to refine the determination of u*. The winter season should also have allowed us to determine if phenomena more specific to high water heights exist (hysteresis in particular).

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Acknowledgements

The authors thank Hugues Chollet, Louis Battist, Carlos Minatchy, Fabien Szymkiewicz of Université Gustave Eiffel Marne la Vallée (France) for their contribution to the in situ interventions, Mark Cheetham, Yannick Della Longa and SNCF Réseau staff in Limoges (France) for their safety and technical support related to river experiments.

Funding

This research was funded by Agence Nationale de la Recherche (French National Research Agency) within the project SSHEAR ANR-2014-CE03-0011.

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Chevalier, C., Larrarte, F. Real time instability of flow close to a scour affected abutment. Environ Fluid Mech 22, 495–510 (2022). https://doi.org/10.1007/s10652-022-09842-9

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  • DOI: https://doi.org/10.1007/s10652-022-09842-9

Keywords

  • Monitoring
  • Data analysis
  • Hydraulics
  • Instrumentation