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erosion parameters
André Paquier
To cite this version:
André Paquier. Dam breaching models: testing the influence of the erosion parameters. 36th IAHR
World Congress, Jun 2015, The Hague, Netherlands. pp.4. �hal-01271788�
DAM BREACHING MODELS: TESTING THE INFLUENCE OF THE EROSION PARAMETERS
ANDRE PAQUIER(1)
(1) Irstea, UR HHLY, Villeurbanne, France, [email protected]
ABSTRACT
Earthen dams can be overtopped during extreme events that reach flow discharges above the design discharge.
Breaching models can simulate the erosion of the embankment and can be coupled with 1-D or 2-D shallow water equations for propagating the dam break wave. Alternatively, sediment transport models can be used for both processes.
In order to evaluate the influence of the choice of the model and of the main parameters of each model, two series of tests are used. The first ones concern one field test including a 6 m high embankment; the second ones deal with laboratory experiments in which the embankment height is about 0.6 m. Comparing the flow hydrograph at breach site, the higher differences come from the calculation method of the erosion rate or more simply from the value of the erosion coefficient. However, for the selected experiments, these differences are essentially outside the period with high velocities which means that the peak discharges are very similar and that the main differences are found in the evolution of the breach shape leading, for instance, to very different final breach widths.
Keywords: Overtopping; breach model; shallow water equations; breaching experiments; erosion rate.
1. INTRODUCTION
Earthen embankments can be overtopped during extreme events that reach flow discharges above the design discharge.
Then, the erosion processes start on the downstream side of the embankment and propagate to the crest creating a breach that will expand in the lateral and the vertical directions. The main parameters that control the opening of the breach are the availability of water upstream from the breach (which maintains high flow discharges) and the erodibility of the embankment material (which determines the rate of erosion). The erosion processes can be represented in various ways in breaching models. The main differences concern the erosion equations (local equation or sediment transport capacity for the whole breach section) and the evolution of the breach shape (parametric section or full 3-D representation). However, one question for the user of any model is the assessment of the parameter(s) directly related with erosion rate.
In order to evaluate the influence of the choice of these parameters, two series of tests are used. The first one concerns field experiment and the second one laboratory experiments at scale 1/10 to the field experiment. After a description of these experiments and the models used, results of some numerical tests are provided and discussed.
2. DESCRIPTION OF THE EXPERIMENTS
2.1 Field experiment
The field experiment used here below was the first experiment of a series of five experiments carried out in a valley of Norway by SWECO during the Impact European project (Morris et al., 2007). A 6 m high embankment was built to cross the valley (about 36 m wide). Water to fill the reservoir upstream of this dam came from a large dam a few kilometres upstream. The control of the openings of the gates of this large dam permits to regulate the discharge sent to the experiment site. In the experiment 1, the embankment was homogeneous made of clay and silt with median diameter (D50) of about 0.01 mm (and standard deviation σ of 3). The upstream water level is first raised and maintained a little below the embankment crest in order to initiate the erosion process along a 5 m wide opening of which the bottom is a few centimetres below the crest elevation. Then, the upstream discharge is reduced to model the effect of a limited water volume with constant water elevation upstream the embankment. When erosion started, the discharge at the large dam is increased in order to model a flood wave entering the reservoir and to keep a sufficient erosion rate for the whole period of measurements. Available data are the inflow and outflow discharge hydrographs, the upstream water elevation and the evolution of the width of the breach. Observations showed that the breach remained quite rectangular with steep banks and that erosion was quite irregular with sometimes blocks of clay detached because of the formation of cracks in the embankment (Fig.1).
28 June – 3 July, 2015, The Hague, the Netherlands
Figure 1. Field experiment 1. View from downstream after a few minutes of erosion (photo: A. Recking, Irstea).
2.2 Laboratory experiments
The experiments were carried out at the Hydraulics Laboratory of Hydraulics Research Wallingford (U.K.). A series of 22 experiments was set during the Impact European project (Morris et al., 2007). The two experiments used here below are experiments 10 and 17 that are performed on the same shape of embankment but with different sediment material and consequently different erosion rates For experiment 10, the sediment was clay with a mean diameter (D50) of 0.004 mm (and standard deviation σ of 3.1) while for experiment 17, the sediment was a mixture of moraine material with a mean diameter (D50) of 0.715 mm (and standard deviation σ of 9).
In both cases, the embankment was built in a flume about 50 m long and 10 m wide. The embankment was set across the flume about 40 m from the upstream end. It was 0.6 m high with side slopes of 2H/1V and was designed to be at scale 1/10 of the field experiments in Norway. Similarly to field experiment, the upstream water level was first kept constant and a little lower than the crest and a little higher than the bottom of a trapezoidal opening dug in the crest of the embankment (0.05 m deep and 0.54 to 0.74 m wide). After the erosion was started, the inflow discharge at the upstream end of the flume was increased in order that the water level upstream of the embankment did not lower too rapidly. The erosion was limited to a 4m wide central part of the embankment. Measurements permitted to follow inflow and outflow hydrographs as well as the evolution of the shape of the breach.
3. DESCRIPTION OF THE MODELS
Two types of erosion models are used: a simplified erosion model of an earthen embankment (Rupro model) coupled with shallow water equations or a sediment transport model that includes one additional equation and shallow water equations. The advantage of the second model type is the integration of the sediment transport downstream the embankment and eventually from upstream in case of sediment inflow. However, for the experiments described here above, there was no sediment from upstream and the sediment downstream was rapidly evacuated by the flow
Rupro model (Paquier, 2007) simulates the evolution of a rectangular cross section that is supposed to be the control section for the breach evolution (both for outflow and for erosion). The embankment is supposed to be of trapezoidal shape and of homogeneous material. To compute average flow variables within the channel, Bernoulli equation is used between upstream and downstream water elevations, the linear head loss being computed using Manning equation. The sediment discharge from which the erosion rate is deduced is computed from the hydraulic variables using equation from (Meyer-Peter and Müller, 1948). Depending of the option selected by the user, either the breach is first deepening and then widening or is together deepening and widening till reaching the foundation and then widening. The second calculation can reduce the rate of erosion because the water head is lower. This simplified erosion model can be coupled with either 1-D shallow water equations (RubarBe software) or 2-D shallow water equations (Rubar 20 software). The Godunov type explicit finite volume solvers are described in (Paquier, 1998; Mignot et al., 2006) and permit to propagate dam break wave along the flume or the valley. In case of 2-D modelling, Rupro model is established on several cells (Fig.2) that are operating together or successively. The erosion process can start over a given width and then pass to a widening that progressively concern cells far from the initial breaching point. For the laboratory experiments, the 2-D cells are generally 0.1 m x 0.2 m while for the field experiment they are more irregular with an area of less than 1 m2 up to100 m2.
Figure 2. Mesh used for the field experiment. Zoom to the embankment. In the red area covered by the breaching model, shallow water equations are not used. This area goes from the upstream toe of the embankment to the downstream toe of the embankment.
The 1-D sediment transport model RubarBE (El Kadi Abderrezzak and Paquier, 2009) includes also the use of the equation from (Meyer-Peter and Müller, 1948) to calculate the sediment transport capacity. The erosion rate of the wetted perimeter is set proportional to the difference between the bed shear stress and the critical shear stress at the power 3/2 (similarly to the calculation of the sediment transport capacity). Bed shear stress is calculated locally which permits an evolution of the shape of the breach. An option of the model adds a bank erosion when side slope is too steep.
The 2-D sediment transport model Rubar 20 TS includes an advection diffusion equation for the concentration of sediment. The source term for erosion is a term proportional to the difference between the ratio of shear stress and a critical shear stress (set to 0.047 as not dimensional value, similarly to (Meyer-Peter and Müller, 1948)) and 1. The coefficient is set to 0.1 mm/s as an usual value. The critical shear stress is reduced on steep slope but only areas under water can be eroded except when adjacent to water, which means that the bank erosion of the breach cannot be easily simulated.
4. RESULTS OF THE CALCULATIONS
The influence of various parameters is first estimated from the breach discharge hydrograph and secondly from the breach width. If more details are required, one will follow the evolution of the shape of the breach. For the laboratory tests in which the range of sediment sizes is taken into account, the transport of the whole sediment is well described by the transport of the mean diameter.
4.1 Field experiment
All the calculations provide quite a similar discharge hydrograph after the peak and even for the peak (Fig. 3). At the beginning of the erosion, there are more differences. Particularly, the 1D model with simplified erosion model provides a higher peak and a first erosion sooner than the 2D with simplified erosion model; the head loss because of the narrowing of the flow at the breach entrance is not present in the 2-D model oppositely to the 2-D model. If the erosion rate is divided by 10, this first peak disappears and it appears sooner if the critical shear stress is reduced in case of steep slope. In this case, the difference of parameters appears only at the beginning of erosion although two types of calculation of the erosion rate are used. The field observations provide a final breach width of 23 metres while all the models provide a total erosion fo the dam (36 metres) except the 2D with simplified erosion model that gives 31 metres and the 2D with reduced critical shear stress that gives 26 metres.
4.2 Laboratory experiments
The measurements of breach discharge hydrographs for experiments 10 and 17 for which only the sediment is changed (changing from 0.004 mm to 0.7 mm) show completely different shapes although the peaks (0.3 m3/s for experiment 10 and 0.6 m3/s for experiment 17) are finally not so different. Similarly, the final breach widths are close: 2 and 3 m.
Numerical calculations show the same order of difference for peak discharges between the two cases. Similarly to field case, the peak discharges are not changing a lot with value of erosion rate coefficient, the type of calculation of the erosion rate or the modelling of secondary processes. However, calculations have more instabilities, which makes more difficult the comparisons. For breach width, depending of the type of calculations and parameters, the calculation overestimates the final width with often the maximum width of 4 m being reached. This may be due to a set of factors but,
28 June – 3 July, 2015, The Hague, the Netherlands
Figure 3. Discharge hydrograph for field test
5. CONCLUSIONS
Comparing the flow hydrograph at breach site, high differences come from the calculation method of the erosion rate or more simply from the value of the erosion coefficient. However, these differences are essentially at the beginning or the end of the experiments while the velocities are not so high and shear stress only a little above the critical shear stress.
Peak discharges are then not so different even when changing the coefficient of erosion rate by a factor 10. These conclusions should be validated on other test cases with very different upstream conditions and evolution of these conditions because the change in the breach shape (already shown on the selected experiments) could also imply different hydrographs with other boundary conditions. Yet, the numerical results show the influence of the size of the material that can change completely the shape of the discharge hydrograph similarly to what was observed during experiments.
ACKNOWLEDGMENTS
We thank the European Union that funded the Impact research project and all the partners of the project, particularly HR Wallingford and Sweco that carried out the experiments.
REFERENCES
El kadi Abderrezzak, K., Paquier, A. (2009). One-dimensional numerical modeling of sediment transport and bed deformation in open channels. Water Resour. Res., 45, W05404, doi:10.1029/2008WR007134.
Meyer-Peter, E., Müller, R. (1948). Formulas for bed-load transport. Report on second meeting of IAHR. IAHR, Stockholm, Sweden, 39-64.
Morris, M.W., Hassan, M.A.A.M, Vaskinn, K. A. (2007) Breach formation: Field test and laboratory experiments, Journal of Hydraulic Research, 45 (sup1), 9-17.
Mignot, E., Paquier, A., Haider, S. (2006). Modeling floods in a dense urban area using 2D shallow water equations.
Journal of Hydrology, 327, 186-199.
Paquier, A. (1998). 1-D and 2-D models for simulating dam-break waves and natural floods. In: M. Morris, J.-C. Galland and P. Balabanis (Ed.), Concerted action on dam-break modelling, proceedings of the CADAM meeting, Wallingford, United Kingdom. European Commission, Science Research Development, Hydrological and hydrogeological risks., L2985, Luxembourg, 127-140.
Paquier, A. (2007). Testing a simplified breach model on Impact project test cases. In: G.D. Silvio and S. Lanzoni (Ed.), XXXII IAHR Congress. IAHR, Venice, Italy.
