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3D simulation of overtopping erosion on embankments by shallow-water
approximation
Simulation en 3D d'une érosion par débordement sur des remblais, avec approximation
en eau peu profonde
Fujisawa K., Murakami A.
Graduate School of Agriculture, Kyoto University, Kyoto 606-8530, Japan
ABSTRACT: Recently, the failure of embankments, such as levees and small embankment dams for irrigation reservoirs, has
occurred more frequently because of a greater chance of severe typhoons and localized heavy rains. Overflow, a phenomenon in
which the water level exceeds the height of the embankments, is known as a primary cause of embankment breaks. The purpose of
this study is to develop a numerical method which can predict the breach process of an embankment caused by overflow. This paper
presents the three-dimensional numerical analysis of embankment breaching. The finite volume method, with a Riemann solver, is
applied to numerically solve shallow water equations for computing the overflow onto the embankments and the changes in
configuration of the embankment profiles are successively calculated in accordance with the erosion rates of the embankment
materials as a function of the bed shear stress exerted onto the embankment surface. In order to achieve a stable computation, the
surface gradient method is incorporated into the finite volume discretization. The proposed method has enabled three dimensional
breaching of embankments to be stablely computed.
RÉSUMÉ : Récemment, les défaillances des remblais comme les digues et les petits barrages en remblais pour les réservoirs
d'irrigation, se produisent plus fréquemment en raison d'une augmentation des typhons violents et de fortes pluies localisées. Le
débordement, phénomène dans lequel le niveau d'eau dépasse la hauteur des remblais, est connu comme étant la principale cause de
rupture des remblais. L'objectif de cette étude est de développer une méthode numérique qui permette de prédire le processus d'une
rupture de remblai causée par débordement. Cet article présente l'analyse numérique tridimensionnelle d'une rupture de remblai. La
méthode des volumes finis, avec un solveur de Riemann, est appliquée pour résoudre numériquement des équations en eau peu
profonde pour le calcul du trop-plein sur le remblai, et les changements dans la configuration du profil du remblai sont
successivement calculés selon les taux d'érosion des matériaux de remblai en fonction de la contrainte de cisaillement exercée sur la
surface du remblai. Afin de réaliser un calcul stable, la méthode du gradient de surface est incorporée dans la discrétisation par les
volumes finis. La méthode proposée a permis d'effectuer des calculs très stables de ruptures de remblais en trois dimensions.
KEYWORDS: embankment, overtopping, overflow, erosion, numerical simulation, shallow water equations
1 INTRODUCTION
Recently, the failure of embankments, such as levees and small
embankment dams for irrigation reservoirs, has occurred more
frequently because of a greater chance of severe typhoons and
localized heavy rains. Overflow, a phenomenon in which the
water level exceeds the height of the embankments, is known as
a primary cause of embankment breaks. Actually, Foster et al.
(2000) statistically investigated the failure and the incidents
involving embankment dams around the world, and reported
that such failure accounted for approximately 50% of these
incidents. Overflow is a major threat to embankments made of
earth materials; and thus, interest in the failure of embankments
triggered by overflow has been growing. Visser (1998) and
Coleman et al. (2002) investigated the breaching process of
cohesionless embankments during overtopping failure, while
Zhu (2006) focused his investigation on the failure process of
cohesive embankments. Hanson et al. (2005) conducted large-
scale overflow-embankment tests using silty sand and a clayey
material, and Hanson et al. (2011) integrated the material
properties for embankment breach.
This paper is dedicated to develop a tool to compute the
three dimensional breaching process of embankments caused by
overflow, since it enables the damage to the earth structure and
the time up its break to be predicted in advance of severe
events, such as typhoons, floods and tsunamis. This paper
presents a numerical analysis of embankment erosion using
shallow water equations, which are often applied to the
computation of overland flows. The finite volume approach,
combined with the surface gradient technique (Zhou et al.
2001), is applied to numerically solve shallow water equations
for computing the overflow onto the embankment, and the
changes in configuration of the embankment profiles are
successively calculated in accordance with the erosion rate of
the embankment material as a function of the bed shear stress
on the embankment surface.The results of three dimensional
analysis of embankment erosion due to overflow are presented
in this paper.
2 GOVERNING EQUATIONS
The following shallow water equations are used to describe the
behaviour of overflowing water onto an embankment:
S G F U
y x t
(1)
in which
vh
uh
h
U
,
uvh
gh hu
uh
2/
2
2
F
,
2/
2
2
gh hv
uvh
vh
G
,
fy
fx
f
ghS
ghS
y z gh
x z gh
0
/
/
0
0
S S S
(2)
where
U
is the state variable vector,
F
and
G
are the flux
vectors,
S
is the source term vector,
h
is the flow depth,
u
and
v
are the flow velocities along the
x
and
y
directions, respectively,
g
is the acceleration due to gravity,
z
is the height of the flow
bed, respectively, and
S
fx
and
S
fy
are the energy slopes in the
x
