Sediment sorting as result of river bed erosion

 

Anna Lenar-Matyas, Jerzy Ratomski, Hanna Witkowska

 

Institute of Water Engineering and Management, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Tel/fax +48 12 633 10 83, e-mail hwitkows@lajkonik.wis.pk.edu.pl

 

 

ABSTRACT

In the paper riverbed degradation downstream a hydraulic structure is discussed. As the major issue is considered sediment sorting which occurs during this process. Sediment sorting is obtained by computation by of sediment transport by size fractions with the use of sediment transport formula specially worked out for Carpathian rivers. The AR formula was prepared for a sediment mixture with taking into account a possibility of blocking in grains. The existence of armour coat and its removal by flood waves is included into computation. The method is tested on a case of riverbed erosion downstream Dobczyce Dam on Raba River. The computations are done for simplified prismatic channel and for natural cross-sections and longitudinal profile. The results showed the importance of sediment sorting - the significant changes of sediment distribution curves were observed. Therefore the influence of sediment sorting is important for the riverbed degradation.

 

Keywords: Sediment transport, River bed degradation, Dams, Sediment sorting.

 

INTRODUCTION

Erosion downstream of a dam is composed by two phenomena - local scour and river bed degradation on a long reach. The latter one is of long time duration and on a long river reach. Very often, this erosion, is due to complete or partial cessation of sediment transport by hydraulic structure [12]. The degradation processes lasts to the emergence of a new dynamic equilibrium characterised by a new bed slope and change in grain distribution. River bed degradation depends on the river hydraulic and morphologic characteristics and extents over many kilometres of river lengths and has a depth of a few meters [5,6,7,10]. In the present paper the case of riverbed erosion is studied on the example of degradation downstream of Dobczyce Dam on the Raba River. The Raba River is a mountainous tributary of the Wisla River and its catchment is 1537.1 km². Slow degradation was observed during the last 100 years [8,9]. The peak floods of exceptional magnitude and engineering structures accelerated this process. In 1974-87 ^{years the Dobczyce Dam was constructed at the km 60 of the river. The main purpose of the construction was water supply for Kraków. The dam cut off completely bed load transport from upstream.}

 

main objectives and methodology of the study

In the present paper the authors attempt to establish computation methods for the degradation process joined by sediment sorting in a case of cutting off the sediment transport by a dam. The following course of calculation was proposed:

·      sediment transport ( G_r ) calculations for given cross-sections and slopes in between;

·      estimation of sediment mass changes by the continuity equation which gives a certain layer thickness Dh, then the new channel dimensions and a new slope are established;

·      establishment of the new grain distribution curves based on sediment transport for different sizes;

The computation was carried on for time divided into steps DT for the whole sequence of flows from flood waves to low flows. The calculation procedure is shown in the diagram below.

For sediment transport the Agriculture University of Cracow (AR) formula was used. The AR formula was tested for Carpathian mountain rivers [3]:

 

 

Q - water discharge,

q_r - bed load transport,

h - water depth,

J - slope,

r- density,

d - sediment diameter,

b -river bed width,

f_i - sheer stress for i -index diameter,

Dp_i - % percentage of a given diameter.

 

In the AR formula the Bartnik's modifications [2] were included, which allow treat sediment as a mixture of different sizes and possibility of grain blocking.

 

 

Fig.1 Computation diagram

 

Characteristics of calculated example

The Raba River downstream of Dobczyce River Dam was taken to study [4]. On the 6km reach of Raba River there is no tributaries, so there is no additional sediment inflow. The cross-sections, slopes, sediment grain distribution [1] and flows were obtained by field measurements made previously (in 1958, 1984, 1986) and by the authors in year 1997. The field measurements were not complete, the cross-sections were from1985 and grain distribution from 1958. Therefore the computations did not exactly correspond to the reality.

In order to verify the proposed mathematical model the calculation were carried out in a few steps.

 

1.      Prismatic channel

The first stage consisted on verification of the computation method and of the sediment transport formula. To decrease the number of parameters a prismatic channel with slope varying from one to other cross-section was taken into consideration. The channel reach was divided into 10 segments represented by one cross-section. The computation were done for a sequence of two flood waves with peak discharges 655m³/s and 304m³/s represented by hydrograph divided into increments of 10m³/s. The bed sediments were divided into armour coat and substrata. The flow was considered as gradually varied. The sequence of computations was following:

·      channel bed degradation after the first flood wave;

·      sorting of bed sediments;

·      channel bed degradation after one year sequence of low flows;

·      new size distribution

·      repetition for the second flood wave.

From the computational results it was seen that the first flood wave caused removal of the armour coat and transport of sediments in the substrata conncted with important changes in river bed - erosion up to 0.8m. The sequence of low flows resulted in an intensive movement of fine material and increase of sediment size. After the second wave the new size distribution curve approached the previous one for the armour coat. The river bed erosion is shown in Fig.2.

 

 

Fig.2 River bed changes after wave I, lower annual flows and next wave II

 

The sorting procedure was simulated under the following assumptions: the erosion value from the first step calculations was taken as a sediment active layer in which the changes of size distribution could take place, this layer was presumed to contain 100% of sediment. From the initial size distribution curve the amount of given size fraction could be obtained, then from sediment transport computation by fractions (for every computational step) the value of flowing out sediment was estimated. The remaining sediment size distribution was found by calculating the transported out sediment. The changes in size distribution curves are presented in Fig.3. The first flood wave after removal of the armour coat did not significantly affected the size distribution, that was done by following low flows.

 

 

Fig.3 Changes of size distribution in cross-section 4 after

the whole computational sequence

 

2.      Natural channel

In the next stage the natural 10 river cross-section downstream Dobczyce Dam were taken. The first cross sections had a small slope and shape close to the prismatic, the following ones were very irregular with marked flood plains. The calculations were done for the same flow sequences and initial sediment distribution curve as in the first stage Fig.4. The riverbed in every cross-section was divided in 3 to 5 bands. The computations were done in following turns:

·      Flow rating curve and the division of river bed into bands for every cross-section;

·      transport of every grain fraction in a band;

·      river bed deformation after the first wave, sequence of low flows and the second wave;

·      changes in grain size distribution.

 

Fig.4 Hydrograph

 

The erosion in the main riverbed is smaller than in prismatic channel, and is equal to 0.03 to 0.3m. But changes in size distribution curves are significant (Fig.5), the fine sediment fractions are removed and near the dam sediment became coarser.

 

 

Fig.5 Changes of size distribution in cross-section 3 of natural channel after

the whole computational sequence

 

Conclusions

1. The river bed erosion due to hydraulic structures is coupled with the important change in the sediment size distribution curve. In the case of mountainous river with differentiated sediments of different shapes, calculation of sediment sorting during the erosion process is crucial.

2. According to the obtained results there is a great importance of sediment transport calculations, not only for the flood waves, but also for the sequences of lower flows which wash out smaller fractions and re-establish a new armour coat.

 

The authors plan to continue their field investigations and computation for the whole period of Dobczyce Dam existance.

 

References

[1] S.Augustyniak, Rumowisko rzeki Raby, praca doktorska 1970 PK

[2] W. Bartnik, Hydraulika potoków i rzek górskich z dnem ruchomym. Poczatek ruchu rumowiska wleczonego, Zeszyty Naukowe AR-Kraków 171/92

[3] W. Bartnik, A. Michalik, T. Bednarczyk, Równanie transportu rumowiska wleczonego dla rzek Podkarpacia. Gospodarka Wodna 7/88

[4] Gospodarka wodna w dorzeczu Górnej Wisly, IIGW PK, ODGW Kraków, RZGW Kraków, Kraków 1995

[5] W. H. Graf, Hydraulics of Sediment Transport MacGraw Hill 1971

[6] A. M. Gurnell, M. J. Clark, C. T. Hill The geomorphological impact of modified river discharge and sediment transport regimes downstream of hydropower scheme meltwater intake structure, Hydrology in Mountainous Regions IAHS Pub.194 Wallingford 1990

[7] W. Parzonka, L. Plywaczyk, S. Serafin Oddzialywanie stopnia wodnego w Brzegu Dolnym na koryto Odry i wody gruntowe ponizej stopnia. Gospodarka Wodna 92

[8] J. Punzet, J. Czulak, Zmiennosc koryt karpackich doplywów Wisly: Soly, Skawy, Raby w XX wieku. Gospodarka Wodna 8/93

[9] J.Ratomski, H. Witkowska, Dyskusja nad teza B. Wyzgi o wplywie regulacji na zachowanie sie koryta rzeki górskiej. Gospodarka Wodna 9/93

[10] Thair M. Al.-Taiee The influence of a dam on downstream degradation of a river bed, Hydrology in Mountainous Regions IAHS Pub.194 Wallingford 1990

[11] F.Y.Wang, Bed load transport in open channels. Proc IAHR.A9/1977

[12] H. Witkowska, Erozja ponizej zapór i stopni wodnych Czas.Techn.1972