Dam-Break Wave-Front Celerity
João Gouveia Aparício Bento Leal
1
; Rui Miguel Lage Ferreira
2
; and António Heleno Cardoso
3
Abstract: This work is concerned with the role that friction and inertia effects can play on the magnitude of dam-break wave-front
celerity. Classic analytical solutions are presented. A large collection of experimental data is used, covering a wide range of different initial
conditions: fixed bed or mobile bed five types of bed material, dry or wet bed downstream, and with or without bed step. To overcome
the limitations of analytical solutions, a numerical model is used. The model is based on the shallow-water approach with contact-load
dominated sediment transport, and it makes use of developments recently made in the study of sheet flows. The analytical and numerical
results are compared with experimental data. It was found that the celerity is mainly dictated by the friction coefficient, by the sediment
inertia, by the initial downstream water depth, and by the initial bed step height. For good data fitting, the friction coefficient must be
influenced by the type of bed, fixed or mobile. In the latter, the coefficient must vary with the bed material characteristics. The
dissimilarities between the experimental, analytical, and numerical results are interpreted.
DOI: 10.1061/ASCE0733-94292006132:169
CE Database subject headings: Dam failure; Waves; Risk management; Numerical models.
Introduction
The study of dam-break waves DBW is extremely important in
providing the information needed for risk assessment and man-
agement of river valleys. That information must include the influ-
ence of initial conditions such as the initial downstream water
depth or the type of bed fixed or mobile on the DBW flow
variables. One of the most important of such variables is the
wave-front celerity. In the present work, the influence of friction
and inertia on the wave-front celerity is studied by an exhaustive
comparison of experimental data with analytical and numerical
solutions.
The experimental data for fixed boundary conditions were
gathered from the following studies: U.S. Army Corps of
Engineers 1960, Bell et al. 1992, Franco 1996, Lauber and
Hager 1998, Stansby et al. 1998, Leal 1999, Briechle and
Kötenger 2002, and Leal et al. 2002. Only a small amount of
experimental results are available for mobile bed conditions, yet
some data were collected from the following studies: Capart and
Young 1998, Khan et al. 2000, Spinewine and Zech 2002,
and Leal et al. 2002.
Concerning the analytical solutions, Ritter’s 1982 solution
for a dry frictionless horizontal channel of rectangular cross sec-
tion is used as a referential, where the solution is not contami-
nated with friction effects. The influence of friction is studied
based upon a perturbation solution derived by Dressler 1952.
The influence of the initial downstream water depth is investi-
gated taking Stoker’s 1957 solution as a referential for wet bed
conditions downstream from the dam site.
Fraccarollo and Capart 2002 computed a semianalytical so-
lution of DBW on mobile bed but, due to the complexity of the
Riemann quasi-invariants, they could not provide an explicit ex-
pression for the wave-front celerity. In order to overcome the lack
of analytical expressions for mobile bed situations, a numerical
model was developed. The numerical model was presented by
Leal et al. 2003a; it is based on a 1D depth-averaged shallow-
water approach with contact-load dominated sediment transport
and makes use of some developments recently made in the study
of sheet flows. The numerical model is also used for fixed bed
situations allowing the study of friction’s role on DBW beyond
the limits of Dressler’s solution.
Experimental Data
Most DBW experiments have been carried out in straight rectan-
gular flumes equipped with a lift gate. The gate is removed rap-
idly, thus simulating an instantaneous and complete dam failure.
The DBW experiments present initial conditions as sketched in
Fig. 1, where h
u
and h
d
are, respectively, the initial water depth
upstream and downstream, and z
u
and z
d
are, respectively, the
initial bed elevation upstream and downstream.
The main features of the fixed bed experimental tests, whose
results are used in the present work, are summarized in Table 1. In
this table, = h
d
/ h
u
is the dimensionless initial downstream water
depth and R is a Chézy dimensionless friction coefficient defined
as R = C
f
2
/ g, where C
f
= Chézy friction coefficient and
g =9.8 ms
-2
is the gravitational acceleration.
The main features of the mobile bed experimental tests are
presented in Table 2. In this table, s =sediment specific gravity,
d = sediment mean diameter, w = sediment settling velocity,
1
Research Assistant, Civil Engineering and Architecture Dept., Univ.
of Beira Interior, Calçada Fonte do Lameiro, 6201-001 Covilhã, Portugal.
2
Research Assistant, Civil Engineering and Architecture Dept.,
Superior Technical Institute, Av. Rovisco Pais, 1049-001 Lisbon,
Portugal.
3
Associate Professor, Civil Engineering and Architecture Dept.,
Superior Technical Institute, Av. Rovisco Pais, 1049-001 Lisbon,
Portugal.
Note. Discussion open until June 1, 2006. Separate discussions must
be submitted for individual papers. To extend the closing date by one
month, a written request must be filed with the ASCE Managing Editor.
The manuscript for this paper was submitted for review and possible
publication on January 22, 2004; approved on March 10, 2005. This
paper is part of the Journal of Hydraulic Engineering, Vol. 132, No. 1,
January 1, 2006. ©ASCE, ISSN 0733-9429/2006/1-69–76/$25.00.
JOURNAL OF HYDRAULIC ENGINEERING © ASCE / JANUARY 2006 / 69