Degradation of the River Bed after Building of Groynes

 

M. SPANNRING

 

Lehrstuhl für Wasserbau und Wasserwirtschaft, Technische Universität München,

80290 München, Germany

Phone: 0049/89/289-23162

e-mail: spannring@.wb.bauwesen.tu-muenchen.de

 

 

ABSTRACT

In this paper a concept is introduced to predict the erosion of the river bed after the building of non submerged groynes. An extensive parameter study was carried out on a numerical model. The analysis of the results shows, that the cross section of the river bed ‑ after the river bed has reached a state of eqilibrium ‑ can be approximated by a parabola of 4^th order. Assuming that the river is straight and groynes are arranged on both sides of the river, the parabola can be determined by the knowledge of two characteristic values:

 

·      maximum erosion in the middle of the river;

·      position of the point in the cross section where erosion is setting in.

 

The maximum erosion in the middle of the river can be estimated by the use of analytical relations for the calculation of bed degradation due to a long contraction, while the groyne effect is taken into account by introducing a groyne coefficient. Approximating the shape of the bottom shear stress in the cross section, the spot where erosion is setting in is determined by that point where the critical shear stress is reached.

This paper concentrates on investigations concerning maximum degradation in the river axis in case of non submerged groynes.

 

Keywords: Groynes, Sediment Transport, Numerical Simulation

 

INTRODUCTION

Groynes are old and traditional elements of river engineering. Besides the protection of river banks, groynes are built for low-water training. By narrowing down the cross-sectional flow area the flow depth can be raised. Due to the production of turbulence in the transition zone between the groyne fields and the undisturbed part of the river there is a further concentration of the discharge towards the middle of the river. The influence of groynes on flow pattern in a river reach involves a change of the corresponding sediment balance. The displacement of the flow towards the river axis is followed by increasing velocities of flow and thus higher bottom shear stresses. Hence bed load transport increases (suspended load is neglected in this investigation) and on the assumption that the considered river reach was in balance before the building of groynes the river bottom will adapt to a new equilibrium state. Several further questions are based on the knowledge of the new equilibrium state of the river bed, e.g. the calculation of water level in case of high water.

Founded on the results of an extensive parameter study a concept was developed to predict the cross-sectional profile of the new river bed while hydraulic (discharge), geometric (width and distance of groynes) and sedimentological (grain size) input is known. This paper concentrates on non submerged groynes. Relating to the influence of submerged groynes must be referred to SPANNRING (1999). Local scours at the first groyne in the flow direction or at the tip of the groynes are not subject of the presented investigations.

The investigations were carried out on a hydrodynamic numerical model (HN-Model) which was extended to appropriate equations to calculate bed load transport and a mobile bed.

 

SHORT DESCRIPTION OF THE HN-MODEL WITH MOBILE BED

The HN-Model is based on the steady depth integrated continuity equation and momentum equations for the horizontal velocity components. Together with the boundary conditions (upstream: discharge; downstream: water level) these equations are solved by the finite-element method. The influence of turbulence on mean flow quantities is simulated with Prandtl's mixing length concept. The mixing length is estimated for free shear layers after RODI (1980). The non submerged groynes are modelled by the impermeable boundary, the slopes are neglected. The comparison of measurements in a rectangular flume with an immobile bed and non submerged groynes on both sides with results of appropriate simulations correspond very well (SPANNRING, 1999).

The coupling of results of the HN-Model (horizontal velocity components and flow depth) and a mobile bed follows with the bed shear stress, whose components are calculated with the quadratic friction law. The bed roughness is considered by Strickler's friction factor. To estimate bed load transport the modified formula of Meyer-Peter and Müller (Hunziker, 1995) is used, based on a characteristic grain size. The direction of bed load at every knot of the computing area follows basically the direction of the bottom shear stress. Additionally the gravitational forces due to bed slope are considered in a relation which is taken from Struiksma et al. (1985).

 

Solving the two-dimensional continuity equation for sediment (SPANNRING, 1999) the change of bed level at every knot of the calculation area within a given time step is determined. The new bed level as a result of the first time step is the basis for solving the shallow water equation in the next time step. In an iterative method this process is repeated until there is only a negligible change in the river bed during a given time step and thus an equilibrium state of the river bed for a special discharge is reached.

 

PARAMETER STUDY

The definition sketch in Fig. 1 contains most of the necessary geometric input data. The indices of the abbreviations are taken over from the German terms, e.g. b_B stands for the width of groynes (German: 'Buhnenbreite'). Invariable quantities are provided with the special values in Fig. 1. In a rectangular flume with a width of b₀ = 40 m groynes are installed with a width of b_B = 6 m, 8 m and 10 m. The distance between the groynes l_Bf varies between 4 m and 20 m in steps of 4 m. In order to keep useful distances between groynes existing literature was evaluated and own investigations were made (see SPANNRING, 1999). The discharge amounts to 160 m³/s, 200 m³/s and 228 m³/s.

Further invariable quantities are the bed slope at the beginning of the simulation (I_S = 0,2 ?), the characteristic grain size (d_m = 10 mm) and Strickler's friction factor (k_St = 40 m^1/3/s).

 

 

Fig. 1 Definition sketch for a river reach with groynes

 

EVALUATING THE RESULTS OF THE PARAMETER STUDY

45 simulation runs were carried out until the equilibrium state of the river bed was reached. In order not to cause confusion, a selection of five cross-sectional profiles as a result of the simulations are shown in Fig. 2. Dz is the difference between the level of the river bed at the end of the calculation and the starting conditions. Standardising the axis of ordinates with the corresponding maximum erosion in the river axis Dz_max and the abscissa with the position y_N,S of the point in the cross section where erosion is setting in, the different profiles can be brought to coincidence (Fig. 3). The standardised profiles can be approximated by parabola of 4^th order. Using the symmetric characteristic it is possible to specify the parabola in dependence on Dz_max and y_N,S (y_N,S is zero position and local maximum at the same time).

 

(1)

 

The further evaluation of the results of the parameter study concentrates on the determination of the two characteristic values Dz_max and y_N,S. In this paper only the investigations concerning the maximum degradation in the river axis can be introduced.

 

 

Fig. 2 Cross-sectional profiles as a result of five selected simulation runs

 

 

Fig. 3 Cross sectional profiles after standardising both axis and approximation with a parabola of 4th order

 

MAXIMUM EROSION Dz_max

The maximum erosion Dz_max of every simulation run is displayed in Fig. 4. An increasing discharge as well as the extension of the groyne width involve greater erosion which is evident and does not require further explanation. The connected points in Fig. 4 mark values Dz_max that come off by identical discharge and groyne width, the groyne distance is variable. A growing distance between the groynes causes a reduction of Dz_max. This phenomenon can be explained by the fact that an increasing groyne distance allows the line of flow to expand into the groyne fields. Thereby the partcipation of the discharge in the groyne fields increases and the remaining area of flow is relieved.

 

 

Fig. 4: Maximum erosion Dz_max in the axis of the flume for different discharges Q, groyne distances l_Bf and widths of groynes

 

GROYNE COEFFICIENT l

In order to predict the bed degradation Dz_max a concept is taken over from SUZUKI et al. (1987) who introduced a groyne coefficient l.

 

 

Fig. 5: Bed Degradation due to the building of groins or smooth vertical walls respectively

 

Bed degradation due to a long constriction with smooth walls can be determined analytically (e.g. KOMURA, 1966). For that purpose one must distinguish between a static and a dynamic state of equilibrium. In the following expositions only the static state of equilibrium is considered, what means that there is no transport of bed load in case of equilibrium in the river reach. Neglecting the concentration of the discharge to the river axis (groyne effect) the degradation Dz is constant and can be determined with Eq. (2).

 

(2)

 

where h₀ is the flow depth and t₀ the bottom shear stress upstream the groyne area, t_cr is the critical shear stress of the bed material, b₀ is the river width, b₁ is

the restricted width of the river between the corresponding groyne heads. With the groyne coefficient l it is possible to separate the groyne effect from the pure effect of contraction. With l<1 and an imaginary further contraction of the river width to l b₁ the degradation assuming smooth walls is Dz_max (Eq. 3)

 

(3)

 

With known values Dz_max as a result of the simulation (Fig.4) the corresponding values for l can be determined after rearranging Eq. (3). The resulting groyne coefficients (Fig. 6) are in a narrow range with a mean value of  = 0,78 and a standard deviation of s_l = 0,02.

 

 

Fig. 6: Groyne coefficient l for different discharges Q, groyne distances l_Bf and widths of groynes

 

In an extension of the presented parameter study the bed slope I_S and the characteristic grain size d_m were varied. Furthermore calculations were carried out where conditions in a river reach of the Bavarian Danube were simulated. For all further simulation runs the groyne coefficient l was in the range of 0,76<l<0,80.

 

CONCLUSION

An extensive parameter study was carried out to investigate the influence of the building of groynes on the erosion of the river bed in a river reach. This paper is focused on part of these investigations concerning the maximum degradation of the river bed in the river axis. For the application in practice several further questions must be discussed, among others which discharge is to be chosen for the calculation - keyword bed forming discharge.

 

ACKNOWLEDGEMENT

Finally I would like to express my appreciation to Prof. Günther J. Seus, who has initiated the research project and who's support through the more difficult stages of the project proved invaluable.

 

REFERENCES

HUNZIKER, R.P.: Fraktionsweiser Geschiebetransport. Mitteilungsheft der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie der ETH Zürich, Heft 138, 1995.

KOMURA, S.: Equilibrium Depth of Scour in Long Constrictions. ASCE, Journal of the Hydraulics Devision, Vol. 92, No. HY4, 1966.

RODI, W.: Turbulence and their Application in Hydraulics. A state of the art review. IAHR, Delft 1980.

SPANNRING, M.: Einfluß von Buhnen auf Strömung und Sohle in einem Fließgewässer - Parameterstudie an einem numerischen Modell. Lehrstuhl für Wasserbau und Wasserwirtschaft der Technischen Universität München, 1999.

STRUIKSMA, N.; OLESEN, K.W.; FLOKSTRA, C.; DE VRIEND, H.J.: Bed Deformation in Curved Alluvial Channels. IAHR, Journal of Hydraulic Research, Vol. 23, No. 1, 1985.

SUZUKI, K.; MICHIUE, M.; HINOKIDANI, O.: Local Bed Forms around a series of Spur-Dikes in Aluvial Channels. 22. IAHR Kongreß, Lausanne, 1987.