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					       Comparison of idealised experiments, numerical solutions,
       and field features for dam-break waves over granular beds

                          H. Capart1,2, D.L. Young3, Y. Zech1
             1
               Dept of Civil Engrg, Univ. catholique de Louvain, Belgium.
                2
                  Fonds National de la Recherche Scientifique, Belgium.
    3
      Dept of Civil Engrg and Hydraulic Res. Lab., National Taiwan Univ., Taiwan.


Abstract

To assess the possible consequences of dam-break events, it is in some instances
important to consider the effect of geomorphic interactions between the flood wave and
the valley. A review of recent research performed by the authors to address this issue is
presented. Aimed at identifying the physical processes involved, the work focuses on
idealised conditions. Experiments feature artificial sediment material and simple valley
topographies. Special image analysis algorithms have been tailored to characterise dense
fluid-granular flows. On the other hand a finite volume scheme, in one and two
horizontal dimensions, was developed to seek numerical solutions to a shallow-water,
non-equilibrium transport theoretical framework. Detailed measurements and numerical
results are compared quantitatively with each other, and qualitatively with the available
field observations. Encouraging agreement is obtained. Limitations and perspectives for
future work are sketched.
1) Introduction

It is increasingly being recognised that an evaluation of the hazards associated with
possible dam-break events must include consideration of geomorphic effects. Based on
a review of field data, the following assessment is made by Costa and Schuster (1988):
  "A complicating factor in downstream routing of floods from natural-dam failures is the
  bulking and debulking of flood waters with sediment and debris as the flood moves
  downvalley. (...) Most commonly, flood peak discharges attenuate downvalley.
  Sometimes, however, downstream peaks can be considerably larger because easily
  eroded sediment is incorporated into the flow. So much sediment can be added to the
  flood flow that a debris flow forms. (...) This problem of bulking and debulking of flood
  flows represents a difficult unsolved problem in sediment transport today, and its
  consequences for hazard evaluation are significant."
A number of experimental studies are available on the breach formation process, or on
the purely hydrodynamic consequences of dam-break events (see e.g. Takahashi and
Nakagawa, 1994; Sillen, in preparation). Since the early study of Chen and Simons
(1979), however, little experimental work has been done on the downvalley geomorphic
consequences of dam-break waves. Most of the available information must therefore be
gathered from field studies, generally performed in the aftermath of dam-break events.

In figure 1, data from a number of documented natural and constructed dam failures are
presented (data from various authors gathered in Capart et al., 1999). Estimates are
provided, on the one hand, for the total water volume released from the breached
reservoir, and on the other hand, for the total volume of sediment eroded, transported
and deposited by the water wave. Constituting only rough estimates, these data are
biased towards events which have had important geomorphic consequences (prompting
field work by geomorphologists). Yet they furnish some important information.




       Fig. 1: Released water and transported sediment volumes for documented
                    dam-break cases (natural and constructed dams)
It is seen that the volume of transported sediment can in some instances be extremely
important. The estimates shown cluster around one order of magnitude less than the
water volume in the breached reservoir, with some events leading to very limited
transport (two orders of magnitude lower), and others leading to very high volumes (of
the same order of magnitude than the volume of water). The transported volumes can be
much higher than the sediment volume constituting the body of the initial dam. In the
case of the Klattasine Creek event, for a total volume of transported material of 3.0×106
m3, only 4000 m³ were eroded from the moraine dam itself (Clague et al., 1985).

Regardless of the total transported volume, geomorphic consequences can be quite
important because of highly localised effects. Intense erosion can be limited to steep-
sloped upper reaches in the near-field of the dam, while deposits can concentrate on
alluvial fans and at sudden valley enlargements. Following the 1991 breach of the
Chandora dam on the Tapi River, in India, a 2 m thick layer of soil was stripped from a
very large area immediately downstream of the dam (Kale et al., 1994). While being
limited in comparison with the water volume, dam-break sediment transport can also
amount to a large part of the total sediment yield of the catchment. For the Tsidjiore
Nouve glacier, for example, the sediment output due to the single outburst event was of
the same magnitude as the total annual yield; representing the equivalent of a vertical
lowering of the entire 4.8 km3 glacier catchment by 0.43 mm (Beecroft, 1983).

Recently, sediment transport in more intense (sheet- and debris flow), or highly transient
(non-equilibrium) conditions have attracted a lot of scientific attention, leading to
extensive field, laboratory, theoretical and numerical studies. The stage is thus set for
attempts at approaching interaction processes between dam-break wave and downstream
valley in a more quantitative way. Recent laboratory studies have in particular focused
on the near-field morphological evolution. The studies of Amado Mendes et al. (1997),
Tuan and Vander Meerssche (1998), Leal and Ferreira (1999) have dealt with dam-
break waves over natural sediment material. In our research, we have privileged the use
of light sediment analogues in order to magnify the phenomena observed (Capart and
Young, 1996, 1998; Capart et al., 1999). It is these last works which are synthesised in
what follows.

2) Experiments with simple geometries and light grains

Experimental and numerical studies were performed by the authors for two idealised
valley topographies. The first case is that of a dam-break wave flowing over a granular
bed in a prismatic rectangular channel, while the second involves the propagation of a
dam-break induced debris wave past a sudden channel enlargement. In both cases, an
idealised dam is materialised by a sluice gate, and the initial surface of the granular bed
is made horizontal on both sides of this "dam". Before release, water of constant depth
extends upstream, above the granular bed, and the water table downstream rises up to
the granular surface. The set-ups were characterised by small dimensions, spanning a
length of 2 m within a 20 cm wide flume. The flows were filmed from the side and from
above using a high-velocity CCD camera at frame rates of 100 to 200 images per
second.

In both cases also, a light sediment analogue (spherical artificial pearls of relative
density 1.05 and diameter 6 mm) was used. Such a choice was pioneered by Bagnold
(1955), who noted that experiments with light (yet heavier than water) material make it
possible to observe intense sediment transport processes in the laboratory without
resorting to steep slopes and high flow velocities. In our case, additional motivation was
provided by the much greater applicability of digital imaging techniques in the case of
artificial sediment, allowing high-resolution measurements to be made in conditions
currently unattainable with natural material. An original pattern-tracking algorithm
could thus be developed to follow the trajectories of individual particles and acquire
granular velocity fields.




   Fig. 2: Dam-break wave over a granular bed in a prismatic channel: (a) mosaic of
digital images; (b) granular velocities; - - -, initial dam position. Dimensions in meters.


3) Shallow-water, non-equilibrium transport description

To describe the highly transient two-phase flow and its exchanges with the bed, two
main assumptions are made. First, the flow is considered shallow, in order to be able to
reduce the problem to a vertically-averaged one. Secondly, the fluid-granular mixture is
assumed to behave as a single-phase fluid with varying density and rheological
properties. These are the assumptions most commonly made when dealing with debris
flow (see e.g. Takahashi and Nakagawa, 1994; Hungr, 1995; Han and Wang, 1996).
Equations for continuity of the mixture, momentum conservation of the mixture, and
continuity of the transported sediment and bed material can then be written. They
require a description of the mass and inertia exchange between bed and flow, which we
achieve using a non-equilibrium transport formulation (Capart and Young, 1998).
Constitutive relations are required for closure, and these are based on empirical
descriptions of rapid (collisional) flows of fluid-grain mixture in sheet- and debris flow
modes.

In mathematical terms, this description results in a set of Eulerian partial differential
equations with independent variables provided by time and one or two horizontal
dimensions. The system is hyperbolic and can thus lead to the formation of
discontinuities, or shocks, in the flow domain. Solutions are to be constructed
numerically, achieved here using a finite-volume scheme which generalises to two
horizontal dimensions the algorithm of Capart and Young (1998). Details concerning
both the governing equations and their numerical solution will be provided in Capart (in
preparation).




     Fig. 3: Bed interface and free surface profiles: —, computed; - - -, measured.
                                 Dimensions in meters.
                                        0.1


                                         0                                   0.15
                                         0
                                                                      0.25
                                              0.1              0.35
                                                    0.2 0.45
       (a)




                                        0.1


                                         0                                   0.15
                                         0
                                                                      0.25
                                              0.1              0.35
                                                    0.2 0.45
       (b)




                                        0.1


                                         0                                   0.15
                                         0
                                                                      0.25
                                              0.1              0.35
                                                    0.2 0.45
       (c)




                                        0.1


                                         0                                   0.15
                                         0
                                                                      0.25
                                              0.1              0.35
                                                    0.2 0.45
       (d)

  Fig. 4: Propagation of a dam-break wave past a sudden channel enlargement: left,
experimental images; right, computations. Dimensions in meters and time intervals of
                                   0.05 seconds.
4) Results and comparison

In figures 2 and 3, results for the prismatic channel experiments are presented. Figure 2
presents the raw images and granular velocity fields some instants after the dam removal
(located at position X = 0). Figure 3 compares the experimental and numerical results
for the bed interface and flow free surface evolution. At the wave tip, a steep debris flow
front propagates over the initially still bed. Near the initial position of the dam, a scour
hole forms and a hydraulic jump conspicuously appears. These various effects are well
captured by the numerical solutions, even though the jump location and magnitude are
slightly off. This discrepancy is likely due to limitations of the shallow-water
description, as vertical components of velocity are not entirely negligible close to the
jump.

In figure 4, results for the propagation of the dam-break wave past a sudden channel
enlargement are shown. A steep dam-break induced debris front is seen to radiate from
the enlargement. A good agreement is obtained between the observations and the
computation, with no further tuning of the constitutive parameters derived from the
prismatic experiments. The computed bed dynamics (not shown) indicate that bed
erosion is most intense at two locations: at the initial position of the dam, where the
water-wave loads itself with sediment in the first instants following the dam-break, and
at the corner of the enlargement. Conversely, deposition is most severe in the lateral
dead zone downstream of the enlargement, where the aggraded material forms a levee.
The global effect of the erosion and deposition is to channelise the flow.

In figure 5, a comparison between numerical and experimental results for the surface
velocity field are provided. Again, a good correspondence between the two is obtained.
At a later stage, however, numerical and experimental results begin to diverge. This can
be directly traced to the fact that beyond this point, relative motion between fluid and
grains becomes significant and the single-fluid assumption breaks down. Despite the
high degree of idealisation, the results outlined above correspond to a number of
qualitative features observed in the field. In particular, features such as the bulking and
debulking processes, backwater effects, steep front propagation and channelisation, well
documented for actual dam-break events, were obtained in both our numerical and
experimental results.

5) Conclusions and perspectives

A dam-break wave starting out as clear water is likely to rapidly pick up sediment
material both from the dam body and from the valley floor. Conversely, it can at some
point deposit most of its material and continue as a muddy streamflow. This bulking and
debulking process can significantly affect the flow rheology, the wave hydrodynamics,
and the valley morphodynamics. While each of these processes in itself is difficult to
describe, our research has shown that a first understanding of their interaction can be
derived from idealised laboratory and numerical experiments. The shallow-water, single
fluid description fails however to capture a number of the features observed in the
laboratory. This suggests that further progress will probably require an in-depth look at
the micromechanics of the sediment-water interactions. At the other end of the scale,
considerable work will be needed before modelling approaches can be applied
quantitatively to actual field cases involving natural sediment material and complex
valley topographies.
             0.2




             0.1




               0
               0.1                0.2               0.3                0.4

                       (a)


             0.2




             0.1




               0
               0.1                0.2               0.3                0.4

                       (b)

    Fig. 5 : Horizontal plane (surface) velocity field : (a) measured by digital imaging
  techniques ; (b) computed using a 2DH finite volume scheme. Dimensions in meters


REFERENCES
Amado Mendes, P., Antunes do Carmo, J. S. and Seabra Santos, F. J., 1997: Preliminary
analysis of the morphodynamic processes generated by a dam break. Preprint (in
Portuguese).
Bagnold, R. A., 1955: Some flume experiments on large grains, but little denser than the
transporting fluid and their implications. Proc. Inst. Civ. Engrs, 111, 174–205.
Beecroft, I., 1983: Sediment transport during an outburst from Glacier de Tsidjiore
Nouve, Switzerland. Journal of Glaciology, 29, 185–190.
Capart, H. and Young, D. L., 1996: Dambreak wave over a movable bed. Proceedings
of the Eighth Hydraulic Engineering Conference, Taipei, Taiwan, Chinese Institute of
Civil Engineers, 379–386 (in Chinese).
Capart, H. and Young, D. L, 1998: Formation of a jump by the dam-break wave over a
granular bed. Journal of Fluid Mechanics, 372, 165–187.
Capart, H., Young, D. L. and Zech, Y., 1999: Dam-break induced debris flow.
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press.
Capart, H., in preparation: Dam-break waves over loose granular beds: hydrodynamics,
morphodynamics, and micromechanics of solid-liquid flows. PhD thesis, Université
catholique de Louvain, Belgium.
Chen, Y. H. and Simons, D. B., 1979: An Experimental Study of Hydraulic and
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BEng Thesis, Université catholique de Louvain.

				
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