Geoscience Reference
In-Depth Information
Simulation of dam-break fluvial
processes
Flood due to dam failure can cause catastrophic damage of properties and loss of life.
Prediction of dam-break flow and the associated sediment transport is very impor-
tant for dam operation, flood control, disaster mitigation, water infrastructure safety
assessment, etc. This chapter covers the numerical algorithms developed for simulation
of dam-break and overtopping flows over fixed and movable beds.
9.1 SIMULATION OF DAM-BREAK FLOW
OVER FIXED BEDS
Although the St. Venant (or shallow water) equations were derived based on the
hydrostatic pressure assumption, many studies have revealed that these equations are
approximately applicable to dam-break flow over fixed beds. The 1-D St. Venant
equations (5.1) and (5.2) are written in conservative form as follows:
∂
∂
t
+
∂
F
(
)
∂
=
(
)
S
(9.1)
x
where
,
F
(
)
, and
S
(
)
represent the vectors of unknown variables, fluxes, and
source terms:
h
q
,
,
q
0
=
F
(
)
=
S
(
)
=
(9.2)
q
2
gh
2
gh
(
S
0
−
S
f
)
/
h
+
/
2
where
q
is the flow discharge per unit channel width;
S
0
is the bed slope; and
S
f
is the
friction slope:
S
f
h
10
/
3
.
The convection term in Eq. (9.1) can be rewritten as
n
2
q
=
|
q
|
/
∂
F
(
)
∂
=
∂
F
(
)
∂
∂
∂
M
∂
∂
x
=
(9.3)
x
x
where
M
is the Jacobian matrix:
0
1
M
=
(9.4)
q
2
h
2
−
/
+
gh
2
q
/
h
