DAM

S. Soares Frazão^1,2, M. POncin¹, V. Paquier¹, B. Spinewine^1,3, Y. Zech¹

Abstract: Numerous catastrophic events in recent history showed that the exceptional flood ensuing a dam-break is associated with strong bed- and bank erosion, and intense sediment transport. Those rapid geomorphic processes in turn may significantly influence the flow behaviour. The resulting dramatic changes in the valley geometry may increase enormously the human and environmental impact.

The present investigation attempts to reproduce both experimentally and numerically the rapid morphologic changes caused by a dam break in a straight valley reach. At this exploratory stage, simplifying assumptions were taken such as an initially prismatic valley and the choice of non-cohesive uniform material for the banks. An accurate topographical survey of the valley after the dam-break was obtained by digital imaging measurement of the cross sections.

Based on these experimental observations, a one-dimensional finite-volume numerical scheme was developed, including a simple bank-erosion mechanism. The encouraging qualitative agreement with the measured data opens motivating perspectives for the numerical modelling of severe transient geomorphic flow.

1 INTRODUCTION

Dam-break flows are currently broadly studied in a pure hydrodynamic context. However, numerous catastrophic events showed that there is a strong interaction between the flow structure and the intense solid transport. Dramatic changes in the valley geometry may result, increasing the human and environmental impact.

The present investigation attempts to reproduce both experimentally and numerically the rapid morphologic changes caused by a dam break in a straight valley reach. At this exploratory stage, simplifying assumptions were taken such as an initially prismatic valley and the choice of a non-cohesive uniform material for the banks. At the end of the experimental simulation, several cross sections were measured, leading to an accurate topographical survey of the valley after the dam-break wave. Based on these experimental observations, a one-dimensional finite-volume numerical scheme was developed including a simple bank erosion mechanism.

2 EXPERIMENTAL SET-UP

Figure 1 shows a sketch of the installation, located in the Laboratory of the Civil Engineering Department, Université catholique de Louvain, Belgium.

The considered reach is 4m long. A 0.20m wide gate separates the valley from the reservoir filled with 0.20m water, initially at rest. No sediment supply comes from the reservoir.

The initial shape of the reach is sketched in figure 2. The sand used in the experiments has an almost uniform granulometry with grain sizes comprised between 1 and 2 mm. At the beginning of the experiment, the bed is saturated while the banks are humid but not saturated, which allows their quite steep slope. Angles of repose j_s were measured and the following values were obtained : j_s between 40° and 45° for the dry sand, j_s between 30° and 35° for the wet sand under water and j_s of about 85° for the humid unsaturated sand.

Figure 3 shows the flow in the valley reach, a few seconds after the dam break. Both bed and banks are heavily eroded, clearly showing the two-dimensional behaviour of the flow just behind the dam. However, those two-dimensional effects remain symmetrical, which is consistent with the design of the experiments. Indeed, the intention here is not to study the initiation of meanders, but rather the heavy erosive effects of a dam-break wave.

The most important effects, like the rapid widening of the valley, occur during the first seconds of the experiments. It was thus chosen to close the gate 10 s after its opening. The drainage process is then slow enough for the valley topography not to be disturbed. Finally, a survey is done by means of digitised pictures of the cross sections at various locations along the valley : a black rigid panel is inserted in the valley, and the valley cross-section appears on the pictures as a clear transition between black panel and white sand (see figure 4). This latter digital imaging process has been automated in such a way that a complete accurate survey could be obtained in a reasonable time.

Figure 5 shows a resulting topographical survey, in the form of a three-dimensional reconstruction of the valley. The symmetrical widening at the upstream end of the valley can be clearly identified, while the important bed erosion at the toe of the dam appears better on figure 6 where the initial and final bed elevation along the thalweg is represented.

Figure 7 shows a series of cross sections from the topographical survey. The intense bed- and bank erosion at the upstream end of the channel slows down the flow (Figure 7a), causing an immediate deposition downstream (Figure 7b). Then, the flow regains erosive power (Figure 7c), and the subsequent downstream deposition is observed again (Figure 7d). This process repeats with decreasing intensity as can be observed on the bed profile in figure 6. Figures 7a, 7c and 7e with a deeper cross-section correspond to an erosive phase, while Figures 7b, 7d and 7f with a trapezoidal cross-section shape correspond to a deposition phase.




Fig. 7 Cross-sections survey at various locations

3 NUMERICAL MODEL

A finite-volume numerical scheme with separate hydrodynamic and solid-transport routines was chosen. This choice is justified by the following reasons : 1) this kind of flow is of severe transient nature, which implies the presence of discontinuities, shocks and transcritical transitions that are best reproduced by a finite-volume scheme, stable in such situations, 2) besides the strong debris flow in the very first moments after the gate opening, the sediments seem to be transported significantly slower than the water velocity, making the de-coupled model choice acceptable.

3.1 Hydrodynamic flow routine

The hydrodynamic finite-volume scheme (Soares and Zech, to be published) solves the one-dimensional Saint-Venant equations written for an arbitrary cross section. Those read, in vector form,

where (see Figure 8) A is the cross-section area, Q the discharge and S_f the friction source term, calculated by the Manning formula.

Fig. 8 Definition of variables

The hydrostatic pressure on the cross-section is represented by the static momentum I₁while

is the joint contribution of the spatial variation of the cross-section I₂ and of the bottom-slope source term S₀.

As outlined by Capart et al. (1996), the conservative formulation (1) of the Saint-Venant equations is well suited for flows on abrupt topographies, where the distinction between spatial variation and bed slope cannot always be clearly defined.

The finite-volume integration of (1) on a discretized domain of computation yields

The numerical fluxes

fluxes are calculated by a characteristics-based flux-predictor scheme (Braschi and Gallati, 1992), comparable to the well-known Roe's scheme.

3.2 Sediment transport

The rate of sediment storage is related to the spatial variation in sediment discharge by the continuity condition for bed sediment (see for example Chang, 1992) :

where l is the porosity, A_b the channel boundary within a reference frame (see figure 9b), Q_s the longitudinal sediment discharge and q_s the rate of lateral sediment inflow coming from the banks. The bank stability criterion is defined as follows (see figure 9a) : above the water free surface, the bank slope corresponds to the angle of repose of humid unsaturated soil (angle of 85°), while under the water surface the angle is 30°. At each time step, the cross section stability is checked and the sediment volume in excess compared to the stable bank slope is removed from the bank to supply a lateral sediment inflow. The cross-section shape is then adapted as sketched on figure 9b where deposition or erosion results from (3).

4 COMPARISON WITH EXPERIMENTAL MEASUREMENTS

The numerical model was run with the initial conditions used for the experiments. The scheme proved to be stable with a CFL number of 0.9. After 10 s, the valley shape and the bed elevation along the thalweg are illustrated respectively on figure 10.

The computed profile, although quite sharp, presents similarities with the observed one. The important erosion at the upstream end of the channel, as well as the deposition zone immediately downstream could be reproduced. At this exploratory stage, such a qualitative agreement can be regarded as encouraging.

5 PROBLEMS AND PERSPECTIVES

Although general qualitative agreement is observed between the experimental and numerical results, several problems and/or limitations can be pointed out.

A first obvious limitation is the fact that a pure one-dimensional model will not be able to simulate the initiation of meanders, which will occur once the water velocity has significantly decreased. This trend to meandering was observed in the experiments, for waves flowing longer than the here-considered 10s.

Also, the highly simplified model used to describe the bank failure constitutes a limit. Indeed, at this stage, only the hydrostatic effects (water level) are taken into account to initiate the failure and feed the flow with the volume of sediments removed from the banks. The model could be improved by including the dynamic effects of the flow velocity. Moreover, to follow closer the natural shell shape of a landslide, the simulated bank failure could be spread over more than just one computational cell. Therefore, a kind of diffusion operator should be introduced in the process.

Finally, the question of coupled or de-coupled model arises. It is clear that the water and sediment flow cannot be regarded as fully independent from each other. Coupled models have been developed to describe the near-field flow (Capart, 2000). However, such an approach still has to be investigated for the far-field modelling.

Despite all those questions and problems, the approach presented here seems promising. A severe transient flow could be simulated, which could not have been the case with a more classical finite-difference model, even coupled.

6 CONCLUSIONS

This paper presents an exploratory investigation on dam-break induced bank erosion. New experimental work has been undertaken to simulate a far field geomorphic flow. The accurate topographical survey provided interesting data that can be used to validate numerical models. A finite-volume model has been developed and tested. The encouraging good qualitative agreement with the measured data opens motivating perspectives for the numerical modelling of severe transient geomorphic flow.

Work is still under progress to refine the numerical model, and get extended measurements from the experiments, such as time evolution of velocities, water depths, bank failure.

Braschi G. and Gallati M. (1992), A conservative flux prediction algorithm for the explicit computation of transcritical flow in natural streams, Hydraulic Eng. Software IV : fluid modelling, Southampton : Comput. Mech. Publication, pp 381-394.

Capart H., Young D.L., Huang S.Y., Pan J.M. (1996), A lateralized flux- predictor scheme for the computation of open channel flow in arbitrary topography, Proceedings of the 20th National Conference on Theoretical and Applied Mechanics, Taipei, Taiwan, pp. 406-413.

Capart H. (2000), “Dam-break induced geomorphic flows and the transition from solid- to fluid-like behaviour across evolving interfaces”, Doctoral thesis, Université catholique de Louvain. Faculté des Sciences Appliquées, Louvain-la-Neuve.

Chang H. (1992), “Fluvial processes in river engineering”, Krieger Publishing Company, Malabar, Florida.

Soares S. and Zech Y. (to be published), 2D and 1D modelling of the Malpasset dam-break test case, Proceedings of the CADAM meeting Zaragoza, Spain, 18 and 19 November 1999, pp 51-61.

DAM-BREAK INDUCED BANK EROSION: EXPLORATORY INVESTIGATION AND PERSPECTIVES