A. Paquier
Cemagref, Research Unit Hydrology – Hydraulics
3 bis, quai Chauveau, CP220, F69336 LYON CEDEX 09
Tel.: +33 472208775, Fax: +33
478477875, E-mail:andre.paquier@cemagref.fr
Abstract: Because of the uncertainties linked with the hypothesis concerning the initial conditions and the breaching, the calculation of the propagation of a dam-break wave is generally performed using 1-D model, even for large dams. A 2-D model provides detailed velocity field and water levels which may be useful locally. The cases of three dams in the Southern France show that the combined use of a 1-D and of a 2-D models is sometimes necessary to assess the risks in a suitable way: neither over estimate nor under estimate, a reduction of uncertainty which may be important in an inhabited area. In both cases of 1-D model upstream or downstream from the 2-D model, the discharge hydrograph calculated by the upstream model is used as the upstream boundary condition for the downstream model. Without the introduction of complementary data, global results provided by 1-D and 2-D models are generally similar. Thus, the more frequent case of combined use will be a general 1-D model and local detailed 2-D models in areas with high vulnerability.
Keywords: shallow water equations,
de Saint Venant equations, numerical modelling, dam break wave, emergency
planning
The damages induced by the
failure of a dam may be very high. Most of the countries around the world
enacted some laws in order to take this risk into account. In France, for large
dams (> 15 millions m3 and > 20 m), an emergency plan is compulsory. This
plan should consider the warning of all the people in the valley downstream from
the dam up to the point in which flooding is not dangerous, which has been
transformed in a discharge corresponding to a natural flood of a return period
less than 10 years or in a water depth over the banks less than one metre. Thus,
to draw up this plan, it is necessary to model the possible propagation of the
dam-break wave in the valley. Physical modelling is kept only for difficult
cases (very steep slopes for instance) and the choice stands generally between
1-D and 2-D numerical models. The first step of a dam-break wave computation is
to fix the hypothesis concerning the hydrological conditions and breaching
features. The uncertainties are such in this first step that generally 1-D model
is selected for the calculation of the propagation. The present paper shows how
it is useful to combine a 1-D model which is thus sufficient to provide the main
results along the whole valley with a 2-D model which provides detailed results
in a few places. Three cases located in Southern France are described and the
numerical codes used are presented.
Code Rubar 20 has been developed by Cemagref since 1988. It solves 2-D shallow water equations by an explicit second order Godunov-type finite volume scheme on a grid formed by triangles and quadrilaterals (Paquier and Farissier,1996). An hydraulic structure is defined as a set of a few cells where fluxes through one edge are computed from the relations for the hydraulic structure linking discharge and water levels upstream and downstream. These relations may be a weir type relation but also some more complicated relations such as a breaching in an embankment dam modelled in a simplified way (Paquier et al., 1998).
Code Rubar 3 solves 1-D de Saint Venant equations using an explicit finite volume scheme similar to the one used by code Rubar 20 (Paquier, 1996);(Paquier, 1998). Similar hydraulic structures (including breaching in a dam) may be modelled.
The use of both codes for simulation of dam-break
waves has been carefully controlled in the framework of the IAHR working group
(Goutal and Maurel, 1996;
Soares
and Alcrudo,1997) and the European Concerted Action CADAM about dam-break
waves. During the two years of the CADAM project, benchmarking was performed on
several cases
(Paquier
and Haider, 1999;
Paquier, 1999)
.
Results of the project are available on web site “www.hrwallingford.co.uk/projects/CADAM/”.
For smaller dams, Cemagref developed a 1-D code Castor
which is extensively used in France. The simplified method consists in an
estimate of peak discharge from which other hydraulic variables are deducted
using uniform flow equations
(Paquier and Robin, 1997)
.
Sainte Cécile d’Andorge dam is 40-m high. Maximum
volume of the reservoir is 16 millions m3. A 1-D computation using Rubar 3
simulated the propagation of the flow along the 100 kilometres of the valley
between the dam and Rhone River in case the dam breaks by piping.
Rubar 20 was used in order to simulate the wave
crossing the town of Alès in a better way because the valley is shared into
three parallel parts by the dikes along the main bed. The 1-D topography
constituted of cross sections (Fig. 2) was completed by the ground level contour
lines from the map at scale 1:25,000 and by more precise ground survey in some
specific points (Fig. 2). 2-D computational grid was built from the cross
sections with 31 cells in the cross direction and a total of 3720 cells. Fig. 1
shows the comparison between the maximum water levels in the main bed in 1-D and
2-D. In the upstream (Northern) part, the left flood plain is narrowed by the
hill on which the centre of the town is built: the rise of the water level is
computed by the 2-D model whereas the 1-D model does not take it into account
because of the widening of the right flood plain. In the downstream part, in an
opposite way, the 1-D model provides higher water levels.
The site of the Juanons dam is located close to Rhone
valley in the South Eastern part of France. A 16-m high earthen dam is planned
for storage of irrigation water. The reservoir will have a relatively low volume
(about 600,000 m3) and the valley downstream is dedicated to agriculture.
Moreover, the farm buildings are generally located on the hills, above the
natural flood level. In a first step, considering the a priori low risk, a 1-D
computation using Castor software was performed. Because of the high level of
uncertainty as well in the hypothesis and data as in the calculation method
itself, the results have lead to a forecast of a very large flooded area. A
railway line, about 800 metres downstream the dam, appeared to be overtopped by
several metres. Thus, it was decided to perform some more precise computations
in order to know if the risk was really so high and to propose some measures to
prevent the railway embankment to be broken by the flow. As the dam-break wave
crosses the railway line at several places (the two main hydraulic structures
and the locations of the overtopping flow (Fig. 3)), it appeared that a 2-D
computation was necessary. This computation was performed using a grid of 6375
cells that extended over the reservoir and the valley to 2.5 kilometres
downstream from the railway line in order to assure a suitable computation of
the evacuation for the water downstream from the embankment. Piping was supposed
to occur at the basis of the dam at a time in which the level was exceptionally
high. The evolution of the breach calculated in Rubar 20 using a simplified
erosion model takes into account both the characteristics of the material
constituting the dam and the evolution of the water levels inside the reservoir.
It provided a much lower peak discharge (about 300 m3/s) than the statistical
relation about dam failures used by Castor (> 1,000 m3/s).
Yet, even with this hypothesis of lower peak
discharge, the railway embankment is overtopped by about 20 cm. High velocities
(>2m/s) are computed near the basis of the railway embankment. Building an
embanked diversion of the road between the reservoir and the railway does not
improve the situation clearly. The only possible solution to reduce the risk
consists in lowering the maximum water level of the reservoir. It can be also
noted that using the discharge hydrograph obtained by the 2-D model a few
hundred metres downstream from the railway embankment as input to a 1-D
computation would be enough to provide more relevant water levels in the valley
downstream.
Ganguise dam is 33-m high. The reservoir has a maximum
volume of 50 millions m3. In case of failure, the valley of Hers River is
flooded on to the confluence with Garonne River North from the town of Toulouse.
In the outskirts of this town, the Hers valley is parallel to the Garonne valley
and is separated from it by a line of hills a few metres high (Fig. 4). Two
possibilities for flooding Garonne valley exist: passing over the hills or
flowing by the trench of the highway A612 which is first close to Hers River and
then goes down to the West towards the Lateral Canal before going again up to
the North. Modelling the flow across and along the trench required a 2-D model
which was built on the 25 kilometres of the downstream Hers valley (Fig. 4). The
input to the 2-D model was the discharge hydrograph on the Hers River at a place
in which the flooded area is narrow and the flow is essentially 1-D (no
diversion, no embankment). The 2-D calculation confirms that the trench of the
highway can convey as much as 30% of the discharge (case corresponding to Fig.
4).
Moreover, the detailed topography used for the 2-D
model makes possible a flow to Garonne valley even without the trench ; yet, in
any case, this discharge is very low and may be put to zero depending on the
upstream hypothesis. In fact, the input discharge to the 2-D model may be
changed because of the uncertainties concerning the dam failure and the
propagation in the upstream valley. Thus, it was very difficult to conclude in
the flooded area of the Garonne valley because the diverted volume varies
rapidly with the maximum water level in Hers River. In any case, the flow in the
area around the trench is complex because the flow to the West by the trench is
added to a general flow to the North. The 2-D calculation also provided a higher
water level (than 1-D) in the Northern part in which the Canal embankment
prevents the flow to go down to Garonne River.
The three cases described here above show how 2-D
computations may complete 1-D computation by providing detailed velocity field
and water level. In case of Juanons dam, it was the main objective. Generally,
1-D model for dam-break wave includes rather pessimistic hypothesis and thus
provides higher maximum water levels (than 2-D); however, the example of Alès
shows that the opposite situation might occur because of an insufficient
description of the flood plain. In the case of Ganguise dam, a 2-D computation
was necessary to model the flow by the highway although because of the
uncertainties about the upstream hypothesis, the extent of the flooded area in
Garonne valley could not be mapped.
In these three cases, the complementary information
brought by the 2-D model was necessary to plan emergency measures in areas with
dense population. In other cases, an alternative to 2-D computation may be a
model coupling 1-D calculation for the main bed and 2-D calculation for the
flood plain; such a model developed by Cemagref may save computational time but
it meets difficulties to model some situations: for instance, a meandering main
bed or a confluence
(Paquier and Sigrist, 1997)
.
References
Goutal, N., and Maurel, F.,
1996, Proceedings of the second workshop on dam-break wave simulation: Lisbon,
Portugal, Electricité de France, Direction des études et recherches.
Paquier, A.,
1996, Validity of 1-D model for simulating dam-break wave, Hydroinformatics' 96,
Volume 1: Zurich, 9-13 septembre
1996, p. 409-416.
Paquier, A.,
1998, 1-D and 2-D models for simulating dam-break waves and natural floods, in Concerted action on dam-break modelling, 1st CADAM meeting:
Wallingford, United Kingdom, European Commission, Science Research Development,
Hydrological and hydrogeological risks., p. 127-140.
Paquier, A.,
1999, Computations performed by Cemagref on Malpasset test case, in 4 th CADAM
meeting: Zaragoza, Spain, European Commission, Science Research Development,
Hydrological and hydrogeological risks.
Paquier, A., and
Farissier, P., 1996, Use of a 2-D model for simulating the flooding of a plain,
in Muller, A., ed., Hydroinformatics' 96, Volume 1: Zurich, Switzerland, Balkema,
Rotterdam, p. 129-136.
Paquier, A., and
Haider, S., 1999, Computations performed by Cemagref on Toce test case, in Third
CADAM meeting: Milano, Italy, European Commission, Science Research Development,
Hydrological and hydrogeological risks.
Paquier, A.,
Nogues, P., and Herledan, R., 1998, Model of piping in order to compute dam
break wave, in Second CADAM meeting: Munchen, Germany, European Commission,
Science Research Development, Hydrological and hydrogeological risks.
Paquier, A., and
Robin, O., 1997, CASTOR, a simplified dam-break wave model: Journal of hydraulic
engineering, v. 123, p. 724-728.
Paquier, A., and
Sigrist, B., 1997, Coupling 1-D and 2-D models for floods management, 27th IAHR
Congress, Volume A, ASCE, p. 639-644.
Soares, S., and Alcrudo, F., 1997, Proceedings
of the 3rd meeting of the IAHR working group on dam-break modelling: Louvain,
Belgium, Université Catholique de Louvain.
Fig. 1 Alès area. Maximum water levels in main bed.
Fig. 2 Alès area. Cross sections and complementary survey points.
Fig. 3 Juanons dam-break wave. Maximum water depths (darker cells every 0.5 m up to 2 m)
Fig. 4
Ganguise dam-break wave. Ground level contour lines (every 5 m) and maximum
water depths
(darker cells every 0.5 m up to 2m)