PHYSICAL MODELING OF SEDIMENT DEPOSITS IN A RIVER DELTA CASE STUDY: THE ALPENRHEIN DELTA IN LAKE CONSTANCE

M. Roth, M. Weber and G. R. Bezzola

Laboratory of Hydraulics, Hydrology and Glaciology (VAW)
Swiss Institute of Technology, Zurich, Switzerland

(Phone: +41-1-632 4091; Fax: +41-1-632 1192; E-mail: mroth@vaw.baug.ethz.ch)

Abstract: The Alpenrhein River has been artificially extended into Lake Constance through the lengthening of its levees. The goal of this extension is to prohibit the premature sedimentation of the bays surrounding the delta. Currently, an investigation on how during floods a part of the flow and transported sediment can be diverted through levee breaches in a controlled manner is under way. These breaches would allow for a more natural delta development. The processes at such a breach were studied with a physical model. For the sediment in the model, an expandable polystyrene grain material with a density of 1030 kg/m³ was used. This density is far smaller than that of the actual sediment found in nature (Lightweight Model). The horizontal model scale was 1:70 and the vertical scale was 1:32, such that the model was geometrically distorted by a factor of approximately 2.2. Only the sand portion of the total suspended sediment load was modeled. Sand is the bed material of the Alpenrhein channel extension and also comprises the most important depositional zones on the lake side of the levee breaches.

Keywords: river deltas, sediment transport, physical models, river restoration

1    INTRODUCTION

The Alpenrhein, which is the name given to the Rhine River above Lake Constance, drains an area of 6100 km² of the northern Alps of Switzerland and Austria. Its flow regime is complex and affected by glacial, nival, and pluvial influences. It has a mean annual flow of 230 m³/s, with summer floods (May-October) that can have peak flows of up to ten times this mean.

The reviewed investigation is concerned with the delta of the Alpenrhein in Lake Constance. The Alpenrhein delivers an annual mean suspended sediment load of approximately 3 million m³, resulting in an extended deposition in the lake. In the past, this has repeatedly resulted in sedimentation problems for the bays and harbors surrounding the delta. Because of this, the “Levee-Extension Project” was proposed in 1972, which involved the extension of the Alpenrhein’s levees, built on the deposits, a maximum of 5 km into Lake Constance. The goal of the project was to transport the sediment to a deeper part of the lake, so to decrease the rate of sedimentation of the shallow areas surrounding the river mouth. The current status of the project is shown in Figure 1. Due to topographic and ecological reasons, the levees were built with a meandering form. Currently, the left levee is almost complete, while the right levee is at about 2/3 of its design length. The channel extension has a width of about 180 m, and a slope of approximately 0.0003 m/m.

Recent discussions have been concerned with the lowering of local stretches of the levee crests, so that during high lake levels and river flows, localized overtopping will occur. With this, a portion of the flow and sediment of the Alpenrhein will be laterally diverted from the channel, flowing into the surrounding area. The breaches will allow for limited and controlled sediment deposition on the lake side of the levees. The goal of this is to optimize the use of Lake Constance’s available depositional areas, as well as to add ecological value to the levee-extension project by creating a natural delta-like morphology.

A 270 m breach has already been built on the left levee (see Figure 1), with a fixed crest elevation between 396.5 and 397.0 m amsl. The bed elevation of the extended channel in the area of the levee breach is approximately 393.0 m amsl, while the lake bed elevation in the same area is about 394.0 m amsl. During the extremely long flood period of 1999, the levee was overtopped at the man-made breach, which resulted in a tongue-formed sediment deposit in the lake. The reviewed physical modeling had the objective of properly simulating this event.

2    BACKGROUND INFORMATION

Sedimentology

Upstream of its mouth area in Lake Constance, the Alpenrhein is a typical gravel-bed river. At the beginning of the channel extension, 40000-50000 m³ of gravel is annually deposited and then dredged. The bed material in the extended channel itself consists primarily of sand. Some sediment probes, which were taken in the stiller areas at the edges of the channel, also contained a bit of silt. The sandy bed material is just a small part of the entire suspended sediment load that the Alpenrhein transports to Lake Constance. Müller and Förstner (1968) showed that the suspended sediment consists of 10% clay, 70% silt, and 20% sand. Clay and silt, however, are rarely deposited in the channel extension and are normally transported to the deeper parts of the lake.

Flood event of 1999

The hydrologically rare event of 1999 was simulated with the physical model. The elevation of Lake Constance was for about 71 days higher than the crest of the levee breach. During this period of levee overtopping, between May and July, sediment deposition occurred in the lake outside the breach. During the modeled period, multiple flow peaks occurred. The highest of these was measured at about 1800 m³/s, which is considered to be a 5 to 10 year event. Water probes were taken every 3 to 4 days during the floods in the Alpenrhein and their suspended sediment concentration measured. The mean mass concentration was about 1200 mg/l, while the maximum was approximately 6300 mg/l. As this is a relatively low mass concentration, its possible effects on the fluid rheology can be neglected.

3    PHYSICAL MODEL

Model development

The physical model encompassed a limited section of the area surrounding the levee breach, thus not simulating the entire Alpenrhein mouth in Lake Constance (see Figure 1). This modeled section covered a 600 m long reach of the extended channel, including only 1/3 of the channel width. A 420 × 420 m section of the lake outside the levee breach was represented. The model was equipped with a self-contained water circulation system, with a maximum pump capacity of about 150 l/s. The water, along with the sediment material, was pumped into the model at the upper end of the simulated channel reach. The lower boundary of the model consisted of an adjustable weir, which allowed for sediment to pass through without deposition, and created the proper backwater situation in the channel. The modeled lake surface elevation could be set with adjustable sharp-crested weirs along the outside of the basin. After a model run, the water was drained and the sediment deposits measured with an automatic self-positioning laser measuring device.

Model scales

Sediment transport in a physical model is given through five dimensionless products (Kamphuis, 1991):

                        (1)

with

= grain size Reynolds number

= dimensionless shear stress

= relative density

= relative length

= relative fall speed

where d is the sediment grain size, g is the acceleration due to gravity,  is the kinematic viscosity of water,  is the water density (prototype and model: 1000 kg/m³),  is the sediment density (prototype: 2650 kg/m³),  is the shear velocity, and  is the settling velocity of a sediment grain.

For perfect model similitude, the five dimensionless products must be exactly the same in the model as in the prototype. It has been shown, however, that this is fundamentally impossible. In practice, partial similitude is satisfactory and thus there are different model classes. Scaling effects, which must be considered for the different model classes, were described by Oumeraci (1984).

Analyses showed that for this project, the best model type would be the “Lightweight Model”, which satisfies the similitudes of grain size Reynolds number and dimensionless shear stress. A series of pre-experiments were performed on different substitute sediment material. From these, an expandable polystyrene grain material with a density of 1030 kg/m³ and a grain size of 0.7-0.9 mm was chosen. This approximated a single grain size sediment in the field. Based on the similitude laws of Gehrig (1980), the model was designed in accordance with the chosen sediment material. The resultant scale ratios are listed in Table 1. The scale ratio represents the relationship of the physical dimensions between the prototype and the model. The horizontal scale ratio was 70, while the vertical was 32. Therefore, the model was geometrically distorted by a factor of approximately 2.2. The model grain size represented a prototype grain size of 0.18-0.23 mm.

Table 1 shows that the adopted scale ratios are in agreement with the rounded calculated values. Exceptions are the scale ratios for morphological time-scale and sediment concentration. Based on Gehrig (1980), the morphological time-scale is calculated with:

  Table 1    Calculated and adopted scale ratios (l) for different physical characteristics based on Gehrig (1980).

                                (2)

Other similitude laws for the morphological time-scale were also found in the literature. Assuming that the porosity of the material in the prototype is the same as that in the model, Dou (1999) found that:

                           (3)

With the chosen scale ratios for the horizontal and vertical dimensions, as well as with the submerged sediment specific weight, equation (2) yields a morphological time-scale of 2240, while equation (3) yields a value of 681. Theoretically, the establishment of the morphological time-scale yields highly uncertain results. In the current project, however, it was shown that the deposits resulting from a levee breach are only minimally influenced by the choice of the morphological time-scale. A scale ratio of 1000, based primarily on model operation factors, was thus chosen.

Model calibration

Figure 2 shows the sediment deposits on the lake side of the levee breach at different times during a run with the physical model. The deposits show a tongue-like formation. It can also be seen that the depositional pattern was influenced by the flow momentum in the channel.

The actual sediment deposits in nature were measured about four months after the end of the modeled flood period of 1999. Figure 3 shows the resultant elevations. The physical model was calibrated with these measurements. During the calibration, different parameters such as the morphological time scale, the surface roughness of the levee breach crest, and the input rate of sediment were varied. The calibration showed that the chosen model sediment material adequately represented the sand portion of the suspended sediment. The sand accounted for about 10-20% of the total suspended sediment during the modeled flood period. The model tests showed that sand was not only the bed material for the extended channel, but also for the primary deposit areas in the lake outside the levee breach.

Figure 4 shows the final sediment deposits from the calibrated model. In general, these results are in good agreement with the measured values. The flatter areas at the edges of the deposits could not be adequately simulated, because the involved finer grain sizes were not represented in the model. Analyses of sediment probes showed that these deposits consisted primarily of silt.

4    CONCLUSIONS

The reviewed physical model is able to simulate the deposition of the sand portion of the suspended sediment of the Alpenrhein in its delta in Lake Constance. With the model, future studies on the influence of the levee breach properties (length, crest elevation) on the geometry of the lake deposits can be performed. The physical model, however, can only simulate a limited section of the delta. Also, the silt portion of the suspended sediment cannot be simulated with the chosen model grain material. Further studies with a numerical model are thus under way, so that the transport and depositional processes of the entire delta area with the naturally occurring sediment grain size distribution can be simulated.

Acknowledgement

This study was financed by the Joint Commission for International Rhine Regulation (Gemeinsame Rheinkommission der Internationalen Rheinregulierung). The authors extend to them their appreciation for the support.

References

Dou, G. (1999): “Keynote lecture: Develpment of physical model studies on sediment transport in China”, Proc. 7^th International Symposium on River Sedimentation, Hong Kong, China, 16-18 December 1998.

Gehrig, W. (1980): “River models with movable bed”, in Hydraulic Modelling, H. Kobus, Ed., Bulletin 7, German Association for Water Resources and Land Improvement, Bonn, Germany, pp 49-70.

Hughes, S. A. (1993): “Physical Models and Laboratory Techniques in Coastal Enginering”, Advanced Series on Ocean Engineering, Vol. 7, World Scientific, Singapore, New Jersey, London, Hong Kong.

Kamphuis, J. W. (1985): “On Understanding Scale Effect in Coastal Mobile Bed Models”, in Physical Modelling in Coastal Engineering, R. A. Dalrymple, Ed., A. A. Balkema, Rotterdam, The Netherlands, pp 141-162.

Kamphuis, J. W. (1991): “Physical Modeling”, in Handbook of Coastal and Ocean Engineering, J. B. Herbich, Ed., Vol. 2, Gulf Publishing Company, Houston, Texas.

Müller, G., Förstner, U. (1968): “General relationship between suspended sediment concentration and water discharge in the Alpenrhein and other rivers”, Nature, 217: pp 244-245.

Oumeraci, H. (1984): “Scale effects in coastal hydraulic models”, Proc. Symposium on Scale Effects in Modelling Hydraulic Structures, H. Kobus, Ed., International Association for Hydraulic Research.

Fig. 1    Overview of the existing and planned levee extensions of the Alpenrhein in
 Lake Constance, as well as the area simulated with the physical model.

Fig. 2    Sediment deposits in the lake outside the levee breach in the
calibrated model after (a) 7 minutes, (b) 25 minutes, (c) 68 minutes, and (d) 102 minutes (final status).

Fig. 3    Measured sediment deposits at the levee breach, four months after the modeled flood period.

Fig. 4    Simulated sediment deposits at the levee breach in the calibrated physical model.