and height and when present they change the hydraulics conditions. Up to now there are few .... at the border of the uplands (14% of the catchment is situated in ...
River Flow 2006 – Ferreira, Alves, Leal & Cardoso (eds) © 2006 Taylor & Francis Group, London, ISBN 0-415-40815-6
Field investigations of sand-gravel bed forms within the Raba River, Poland Artur Radecki-Pawlik Agricultural University of Krakow, Poland
Paul A. Carling Southampton University, UK
˛zek Ewa Słowik-Opoka & Leszek Ksia˙ Agricultural University of Krakow, Poland
Richard Breakspeare Southampton University, UK
ABSTRACT: The paper presents the important, both from practical and theoretical reasons, problem of forming river bed forms within sand-gravel mixtures. In natural rivers, due to the complicated nature of the discharge and changes in the water level, the bed forms are quite complicated structures. These features are changing in length and height and when present they change the hydraulics conditions. Up to now there are few papers concerning gravel bed forms found in rivers. Most of scientific papers focus only on sand riverbed forms. The present paper concentrates on the field measurements of sand-gravel bed forms found in the Raba River in Polish Carpathians. The research focuses here mostly on the geometrical parameters of these bed forms such as height, length, as well as granulometric characteristics of the sediment. Based on in-site measurements different hydraulics parameters were also determined. Special attention was given to the roughness coefficient, which is very important from a practical point of view for engineers working with river training works and hydraulics structures.
1
INTRODUCTION
Gravel sub aqueous bed forms (those with a median grain size greater than 2 mm), such as dunes and bed load sheets, which occur on river beds which are composed of sand and gravel mixtures are reported very rarely within the world literature. There is even less information on the hydrodynamic development of such gravel features. Reviewing the literature, equilibrium and non-equilibrium gravel dunes range in length from less than 0.6 m to greater than 100 m. Their heights range from less than 0.1 m to 16 m (Carling 1999). In general terms dunes have lengths that scale primarily with boundary layer thickness or water depth (Best 1996). Height (H) and length (L) data for the gravel dunes reported by some researchers (Carling 1999) are consistent with the H:L function reported by Ashley (1990) for equilibrium dunes developed in sand. Using Ashley’s (1990) dune form criteria of height (>0.1 m) and length (>0.6 m) as a general guide it can be shown that gravel dunes have been correctly identified in the number of studies (e.g. Galay 1967,
Dinehart 1992 and Carling et al. 2005). As far as gravel bed forms hydrodynamics is concerned, gravel dunes are suppose to develop for a range of Froude numbers up to 0.75. For the non-dimensional mean shear stress = 0.25 they should reach their maximum height and start to reduce in height at Shields parameter value = 0.30 (Carling 1999). The other bed forms which develop on the river bed are ripples. Their length is proportional to the grain size. They have heights up to a few tens of millimeters and lengths less than 0.6 m (Allen 1984). The reports from the literature about ripples which are developed in gravel are controvertible, being based mostly on length:height criteria. However ripples are suppose to develop only in the bed sediments not coarser than about 0.6 mm (D50 < 0.6 mm) in hydraulic smooth flow (U ∗ D < 10) which is not associated with mobile gravel. However Gomez et al. (1989) reported some gravel bed forms which he called ripples, but Carling (1999) suggests that they were bed load sheets. Finally some scientists (e.g. Kuhnle 1986, Iseya and Ikeda 1987) report bedload sheets and define them as low-relief bedforms,
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that develop in mixture of coarse sand and gravel (D50 from 2 mm to 5 mm).These features are one or two grains in height and share some characteristic of incipient dunes (e.g. Bridge 1993). What is worthy of notice is that no bed load sheets developed in 100% gravels in experiments described by Iseya and Ikeda (1982) as well as Dietrich et al. (1989). At the same time in a mixture of gravel and sand, Whiting et al. (1988) describes bed sheets as stable bed forms, which could grow in thickness giving asymmetric dune like forms up to 0.10 m height, and that such bed forms give the bed instability from which incipient dunes can develop. The main objective of the present work is to understand how riverbed forms developed in the mixture of sand and gravel develop. The study site was in the upland part of the the Raba River below the Dobczyce Water Reservoir and close to the confluence with the Vistula River. The study is important firstly because of the need for a better understanding of the process of formation such features like sand-gravel bed forms. Secondly, dunes are responsible for flow resistance, which is significant, for example, when designing hydraulics structures or calculating flow residence times for water supply or pollutant dispersion. Thirdly, understanding of bed form forming process is important for geologists to interpret how sedimentary rocks were deposited, where ancient sedimentary assemblages are believed to be of alluvial origin. 2 2.1
MATERIALS AND METHODS Study location
The Raba River – Figure 1 – (137 km long with a catchment area of 1537 km2 ) is mostly (86%) situated in the Polish part of the Eastern Carpathian Mountains
(the Wyspowy Beskid and the Zywiecki Beskid) which are Carpathian flysh. Its streambed, along the alluvial part, consists mostly of sandstone and mudstone bed-load pebbles and cobbles (from Magurian nappe). The typical structure of the lower Raba River alluvial plain, from the beginning of the 20th century consists of normally loose pebble gravels, open work pebble gravels, dilated framework pebble gravels, trough cross-stratified and parallel laminated medium to very coarse grained sands, massive find sands and muds (Wyzga 1993). The coarser grains which collect as armour on the river bed, also form a framework, the interstices of which are filled by a matrix of finer sediment. The Raba River, during the spring and early summer floods, experiences frequent bed load movement, which is reflected in many mobile gravel bars which form along the margins and centre of the river channel. The research region of the Raba River (reach 700 m long, close to the Uscie Solne municipality), where the Raba joins the Vistula River, is situated at the border of the uplands (14% of the catchment is situated in Carpathian intramontane and submontane depressions). The river loses here its mountainous character and is alluvial. The river bed sediment here is the mixture of sand and gravel. The river bed usually is characterised by an armour layer where the range of sediment is from 0.4 mm to 50 mm, with sand and gravel moving above it. In low to medium flows the water is very clear making the sediment transport processes visible to the eye. On the armouring layer sand and sand-gravel bedforms appear under certain range of hydraulics conditions. These bedforms are built up with sediment of the range from D50 = 0.5 mm up to 11 mm. The average slope of the whole Raba River is 0.00443, the slope of the whole lower part of the Raba is 0.00198 whereas the slope of the research reach, at the confluence, is 0.0006. The river channel at the research reach averages 50 m wide. According to Krzanowski (1972) the average annual flow is here 20.86 [m3 · s−1 ] and the minimum annual flow is 2.71 [m3 · s−1 ]. 2.2 Methods
Figure 1. The location of the research region.
The research location was safely accessible from the Raba River banks on foot under low discharge and from a rubber boat under mean discharge conditions. The location was being visited daily during several sampling periods between 2001 and 2005. The work within the research reach concentrated on surveying the migration of several ripples, dunes and other sand and sand-gravel structures, measuring the water depth and the speed of the flow with a NAUTILUS 2000 magnetic current meter. Velocities of running water were recorded above all characteristic points of the bed-forms: crest, trough, along the stoss and lee slopes and finally above the flat bed. Such
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hydraulics parameters as Froude number, Reynolds number, shear velocity, shear stresses and drag coefficient were calculated. For sediment sampling the technique described by Church, McLean and Wolcot (1987) was applied. Samples were collected from a homogeneous body of sub-armour sediment, so as not to combine them with the distinct surface material. The sieving analysis for coarse grains was carried out by hand in the field using round-mesh sieves (Michalik 1990). Fine material was sieved in the laboratory. Water velocity measurements were based on Jarrett’s (1990) recommendations regarding the taking of velocity profiles in river cross-sections. Bergeron and Abraham’s (1992) methods were then applied to the field data, and shear velocity V∗ values were calculated from the velocity profiles obtained near to the river-bed. Finally, shear stress τ values were calculated from:
where: V∗ – shear velocity [m s−1 ], ρ – water density [kg m−3 ]. To calculate various flow resistance coefficients the methods given by Wijbenga (1990) and Przedwojski et al. (1995) were used. The Darcy-Weisbach flow resistance coefficient was obtained from:
where: V – average cross-section velocity [m s−1 ]. The Strickler formula for the roughness is as follows (Sobota 1994):
where: x = v0.8 /v0.2 , y – maximum water depth in the cross section [m], ν0.2 – velocity value measured at 0.2y [m s−1 ], ν0.8 – velocity value measured at 0.8y [m s−1 ].
3
RESULTS AND DISCUSSION
For the reasons of brevity all results of investigations and calculations are presented in tabular and graphic manner. Every time the research reach in the field was visited geometrical survey of bedforms were conducted, velocity profiles were obtained close to the bed as well as higher within the flow and sediments samples for granulometric analysis were obtained (Figure 2). Every time after major flooding (it has happened twice during the measuring campaign) a geodetic survey was made to get the river bed altitude details (Figure 3). Under low discharges (up to 3.9 m3 /sec) we noted that only sand ripples of heights (H) up to tens millimetres were developing and moving along the full width of the research reach, whereas pre-existing sand-gravel bedforms were immobile on the armoured bed. When the discharge was larger (up to 11.4 m3 /sec) coarser bed load was moving, including overpassing coarser grains over the crests of the sand-gravel features which then began to migrate. Under the latter conditions sand ripples only developed close to the river banks where the flow velocity was lower than in the centre of the channel, whereas sand-gravel barchanoid dunes were developing along the whole width of the channel although predominantly in the centre. Figure 4 presents measured heights (H) of the investigated bedforms against their lengths (L).
where: k – Strickler coefficient, d – the roughness height which could be a grain dimension (e.g., D50 ) or the height of the bed form [m], n – roughness coefficient. The roughness given by Chézy with Manning’s n could be written as follows (Sobota 1994):
where: C – Manning coefficient, Rh – hydraulic radius [m], n – roughness coefficient[–]. The equation for roughness according to the findings of Chow (1959), which could be determinated after field measurements, is as follows:
Figure 2. Examples of representative grain-size curves taken from different bedforms.
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1.0
H/L [-]
0.8
y = 0.104x-0.63
0.6
y = 0.052x-0.62
0.4 y = 0.074x-0.23
0.2
c
0.0 0.0
0.1
1.0
10.0
L [m]
The Raba River Allen 1968
Carling et al. 2000
Figure 5. Steepness index (H/L) of the Raba River bedforms against their lengths (L).
Figure 3. Examples of changes in the riverbed configuration after major flooding.
Figure 4. Height-length relation for the Raba River bedforms.
The Raba data are compared with Fleming (1988) central tendency and limit lines as well as with bigger sand dunes found on the bed of the River Rhine (Carling et al., 2000). The Raba data we divided in Figure 3 into two groups: Type 1 with the 1 < D50 < 2.4 mm and L < 0.6 m which are here termed bed forms I and the second, Type 2 which are longer with 4 < D50 < 11 mm which are termed bed forms II. The relation between Raba features describes the relation: H = 0,05 L0,35 (r 2 = 0.47; F0.05 (1;55) = 3.95; α = 0.05; n = 57). The Raba type 1 bedforms are much shorter and smaller than the Rhine features and are also mostly below the upper limit given by Flemming (1988). Type 2 bedforms are steep and lie above Flemming’s curve.
Raba bedforms are steeper (Figure 5) then dunes described by Allen (1968) but flatter then the Rhine long sand dunes. Their H/L index = 0.0518L0.622 (r 2 = 0.71; F0.05 (1;51) = 7.24; α = 0.05; n = 52). Also plotted are the geometrical lengths and height of the Raba features against water depth (Figure 6 a, b), they lie close to the Yalin (1964) middle curve as far as their length (L) is concerned but some of them are higher (H) than the maximum limitation. This may be because the higher bedforms has formed under a previous discharge when water depths were greater and have not yet fully readjusted their morphology. Table 1 presents examples of hydraulics parameters calculated for sand-gravel dunes we found during the investigations. The shear stresses were not sufficient to disrupt the armouring layer of the sediment river bed. However, under the highest measured values coarse sediment movement occurred over the sand-gravel features and intensive sedimentation occurred at the toes of the bedforms. Also the sand ripples were transported, building and then decaying rapidly in different parts of the flat gravel armoured river bed. The smaller features were moving with a celerity of 5 cm/sec and larger with 2 cm/sec. The Froude number was between 0.238 and 0.678 indicating that they are still in the developing or steady stage, below the transition stage. At the same time the D50 shows that they are fine-gravel to medium gravel (Gordon et al. 1992). Table 2 shows the different roughness coefficient values, for different ways of their calculations. As expected, when using the bed form height in the Strickler formula larger values of roughness values are obtained. Given that all the measurements were for low or medium discharges, it is possible that larger dunes would have developed under higher flows and thus a larger n value for discharge calculation, would be required. Consequently a traditional approach to estimating the roughness coefficient values would be inaccurate.
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Table 1.
Hydraulic parameters of investigated bedforms.
D50 [m]
τ [N m2 ]
f
Re
Fr
0.0070
1.65 1.47 1.12 1.47 1.12 0.88 1.35 2.65 1.41 0.94 1.29 1.94 1.45 6.35 0.38 2.09
0.00131 0.00127 0.00116 0.00160 0.00489 0.00187 0.00060 0.00133 0.00410 0.00170 0.00064 0.00268 0.00338 0.01481 0.00089 0.00060
170800 130000 106400 100000 64600 121500 151800 225000 100800 126400 158400 171600 97500 136000 172200 220000
0.368 0.332 0.410 0.255 0.249 0.668 0.439 0.238 0.274 0.631 0.490 0.289 0.249 0.678 0.571 0.278
0.0110
0.0070
0.0080
Table 2.
Roughness coefficient value (n).
By Strickler
Figure 6. (a,b) Lengths (L) and (b) heights (H) of investigated bedforms against water depth (h).
4
CONCLUSIONS
The following conclusions can be drawn from the analysis of the data: 1. Under the range of low discharges up to 3.9 m3 /sec only sand and very fine sand-gravel bedforms of 1 < D50 < 2.4 mm of heights (H) up to tens millimetres can develop and move, whereas other existed sand-gravel features were preserved, sitting on the armoured bed.
For D50
For H
By Chezy
By Ven Te Chow
0.01308 0.02018 0.01804 0.01804 0.01308 0.02018 0.01804 0.01804 0.01308 0.02018 0.01804 0.01804
0.02200 0.03173 0.02772 0.02200 0.02200 0.03328 0.02772 0.02200 0.02200 0.03762 0.03527 0.02200
0.03410 0.01564 0.01622 0.02418 0.04433 0.01583 0.01822 0.02660 0.03499 0.01511 0.01511 0.02046
0.04214 0.00193 0.00555 0.01439 0.06215 0.00539 0.00714 0.01289 0.04571 0.00635 0.00412 0.01722
2. When the discharge is growing up to 11.4 m3 /sec the sand-gravel dunes start to develop with 4 < D50 < 11 mm. The movement of sediment along such features is under such discharges very low and mostly the crests are mobilized first. 3. The relation between height (H) and length (L) Raba River bedforms describes the relation: H = 0.05 L0.35 (r 2 = 0.47; F0.05 (1;55) = 3.95; α = 0.05; n = 57). The Raba’s bedforms are much shorter and smaller than the features measured at the bed of larger rivers (e.g. the Rhine). They are mostly below the limitation given by Flemming (1988). 4. The Raba bedforms are steeper and flatter then classical dunes described by Allen (1968). Also they are flatter then the features from bigger rivers (e.g.
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the Rhine). Their H/L index is: H/L = 0.0518 L0.622 (r 2 = 0.71; F0.05 (1;51) = 7.24; α = 0.05; n = 52).
ACKNOWLEDGEMENTS Authors would like to thanks the River Water Authority in Krakow for their logistic help they provided, especially to Mr. Stanislaw Kmiec. Also we are thankful for financial support to British Council and Polish Scientific Committee (KBN).
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