Dam break
modelling can be carried out by either i) scaled physical
hydraulic models or ii) mathematical simulation using a
computer. A modem tool to deal with this problem is the
mathematical model, which is most cost effective and
approximately solves the governing flow equations of continuity
and momentum by computer simulation, as shown in Fig. 1.
Mathematical modelling of dam breach floods can be carried out
by either one dimensional analysis or two dimensional analysis.
In one dimensional analysis, the information about the magnitude
of flood, i.e., discharge and water levels, variation of these
with time and velocity of flow through breach can be obtained in
the direction of flow. In the case of two dimensional analysis,
the additional information about the inundated area, variation
of surface elevations and velocities in two dimensions can also
be predicted. Onedimensional analysis is generally adopted
when valley is long and narrow and the flood wave
characteristics over a large distance from the dam are of main
interest. The basic theory for dynamic routing in
onedimensional analysis consists of two partial differential
equations originally derived by Barre De Saint
Venant in 1871. The equations are:
Conservation
of mass (continuity) equation
(∂Q/∂X) +∂(A + Ao)
/ ∂t  q = 0(2.1)
Conservation
of momentum equation
(∂Q/∂t) + {∂(Q^{2}/
A)/∂X } + g A ((∂h/∂X ) + Sf
+ Sc ) = 0(2.2)
where Q =
discharge, A = active flow area, Ao = inactive
storage area, h = water surface elevation, q= lateral outflow, x
= distance along waterway, t = time, Sf
= friction slope, Sc = expansion contraction
slope, and g = gravitational acceleration.
2.0
MODEL SELECTION
Selection
of an appropriate model to undertake dam break flood modelling
is essential to ensure the right balance between modelling
accuracy and cost in terms of time spent developing the model
setup. In the present study, HECRAS version 4.1.0 model
developed by Hydrologic Engineering Center of U. S. Army Corps
of Engineers has been selected. HECRAS is an integrated system
of software, designed for interactive use in a multitasking
environment. The system comprises a graphical user interface,
separate hydraulic analysis components, data storage and
management capabilities, graphics and reporting facilities. The
model contains advanced features for dam break simulation.
The present
version of HECRAS system contains two onedimensional hydraulic
components for: i) Steady flow surface profile computations; ii) unsteady
flow simulation. The steady/unsteady flow components are capable
of modelling sub critical, super critical, and mixed flow regime
water surface profiles. The system can handle a full network of
channels, a dendric system, or a single river reach. The basic
computational procedure is based on the solution of
onedimensional energy equation. Energy losses are evaluated by
friction(Manning's equation) and
contraction/expansion (coefficient multiplied by the velocity
head). The momentum equation is utilized in situations where the
water surface profile is rapidly varied.
The
graphics include X Y plots of the river system, schematic cross
sections, profiles, rating curves, hydrographs, and many
other hydraulic variables. Users can select from predefined
tables or develop their own customized tables. All graphical and
tabular output can be displayed on the screen, sent directly to
a printer, or passed through the Windows clipboard to other
software's, such as word processor or spread sheet. Reports can
be customized taking into account the amount and type of
information desired.
2.1
MODEL STABILITY DURING UNSTEADY FLOW SIMULATION
HECRAS
uses an implicit finite difference scheme. The common problem of
instability in the case of unsteady flow simulation can be
overcome by suitable selection of following:
Crosssection
spacing along the river reach
Computational
time step
Theta
weighing factor for numerical solution
Solution
iterations
Solution
tolerance
Weir
and spillway stability factors
2.1.1
Crosssection spacing
The river
crosssections should be placed at representative locations to
describe the change in geometry. Additional crosssections
should be added at
locations where changes occur in discharge, slope, velocity and
roughness to describe the change in geometry. Crosssections
must also be added at levees, bridges, culverts, and other
structures. Bed slope plays an important role in deciding the
crosssection spacing. Streams having steep slope require cross
sections at a closer spacing say 100 m or so. For larger uniform
rivers with flat slope, the cross section spacing can vary from
200 m to 500 m.
2.1.2
Computational Time Step
Stability
and accuracy can be achieved by selecting a computational time
step that satisfies the Courant condition: Cr = Vw(Δt/Δx) ≤ 1.0.
Therefore, Δt ≤Δx/Vw), where V w =
flood wave speed, V = average velocity of flow, Δx = distance
between cross sections, and Δt = computational time step. For
most of the rivers, the flood wave speed (Vw) can be calculated
as: Vw = dQ/dA,where dQ is the
change in discharge with change in crosssectional area (dA).
However, an approximate way of calculating flood wave speed (Vw)
is to multiply the average speed (V) by a factor. Factors for
various channel shapes are shown in Table 2.1 below:
Table 2.1 Ratio of wave speed (V w) to average velocity
(V) for various channel shapes
Channel Shape
Ratio (Vw/V)
Wide rectangular
1.67
Wide parabolic
1.44

Triangular
1.33
Natural Channel
1.50
2.1.3 Theta
Weighing Factor
Theta is a
weighing factor applied to the finite difference approximations
when solving the unsteady flow equations using an implicit
scheme. Theoretically,
Theta can vary from 0.5 to 1.0. Theta of 1.0 provides most
stability, while Theta of 0.6 provides most accuracy.
2.1.4
Solution Iteration
At each
time step, derivatives are estimated and the equations are
solved. All the computational nodes are then checked for
numerical error. If the error is greater
than the allowable tolerances, the program will iterate. The
default number of iterations in HECRAS is set to 20. Iterations
are for improving the solution.
2.1.5
Solution tolerances
Two
solution tolerances can be set or changed by the user: i) water
surface calculation and ii) storage area elevation. Making the
tolerance larger can reduce the stability problem. Making them
smaller can cause the program to go to the maximum number of
iterations every time.
2.1.6
Weir and spillway stability factor
Weirs and
spillways can often be a source of instability in the solution.
During each time step, the flow over a weir/spillway is assumed
to be constant. This can cause oscillations by sending too much
flow during a time step. One solution is to reduce the time
step.
'
2.2
MODEL LIMITATIONS
The water
in HECRAS modelling has been assumed to flow in the
longitudinal direction only, i.e. the flow is onedimensional
implying that there is no direct modelling of the hydraulic
effects of crosssection shape changes, bends, and other two and
threedimensional aspects of flow. It represents the terrain as
a sequence of crosssections and simulate flow to estimate the
average velocity and water depth at each crosssection. The uncertainties
associated with the breach parameters, specially breach width,
breach depth and breach development time may cause uncertainty
in flood peak and arrival time. Further, the high velocity flows
associated with dam break floods can cause significant scour of
channels. This enlargement in channel crosssection is neglected
since the equations for sediment transport, sediment continuity,
dynamic bed form friction etc. are not included in the governing
equations of the model. The narrow channels with minimal flood
planes are subject to overestimation of water elevation due to
significant channel degradation. The dam breach floods create a
large amount of transported debris, which may accumulate at very
narrow cross sections, resulting in water level variation at
downstream locations. This aspect has been neglected due to
limitations in modelling of such complicated physical process.
2.3
INPUT DATA REQUIREMENT
In general,
the data required for dam break analysis can be categorized as
described below.
2.3.1
Reservoir data
To predict
the flood hydrograph from the reservoir, it is necessary to have
either of the following along with details of typical flow
through the reservoir and normal retained water level.
A
elevation storage relationship for the reservoir, or
Bathymetric
data for the reservoir
Provision
of just an elevationarea or elevationvolume relationship
limits the extent of modelling possible to predict flood flow
out of the reservoir. Under these conditions, only a simple
'flat pond' can be modelled which does not take into
consideration the time taken for flow to exit the reservoir.
This may be significant if the reservoir is relatively long and
narrow or has number of branches.
2.3.2
Catchment hydrology
Inflow into
the reservoir, reservoir condition at the time of failure and
base flow conditions in the river valley downstream may combine
to have a significant effect on the predicted flood conditions,
depending on the size and nature of the reservoir and dam.
Potential reservoir inflow and river base flow data should be
collected to allow a sensitivity analysis to be undertaken as
part of the dam break analysis. For highrisk sites, it is
likely that the flow conditions assumed for the sensitivity
analysis would range from normal low flow operating conditions
to a probable maximum flood (PMF).
2.3.3
Structural data
A minimum
of information is required to allow a reasonable prediction of
breach size, and hence, potential flood flow in the event of
structure failure. Regardless
of structure type, it is necessary to outline structure
dimensions and levels. Details of gates, valves, and spillways
will be required, if partial failure modes are to be considered,
and as part of a sensitivity analysis when considering different
reservoir/ river water levels and base flow conditions at the
time of failure. Techniques for the prediction of breach
formation through embankment dams are more advanced than
techniques for the prediction of concrete or masonry structure
failure. For embankment dams, details of core and layer geometry
(including any surface protection) along with respective
material sizes will be required. For concrete and masonry
structures, the potential failure mechanisms will be based
either on potential maximum breach dimensions or failure of
single units such as buttresses or spillways. General
arrangement drawings ror the structure should provide sufficient
information to allow such an analysis.
2.3.4
Topographic data
Topographic
data representing the whole area potentially liable to flooding
is required. The extent of this data should not be
underestimated. Floods resulting
from dam failure can be significantly larger than natural
floods meaning that flood flow is often through areas
considered safe from flooding viewpoint. Required topographic
data will therefore extend widely across floodplains and
upvalley slopes well above normal flood levels.
Details of
major structures that may form an obstruction to flow are also
required, such as road and railway embankments and bridges
andmajorriver control structures. Contrary
to river modelling studies, smaller structures that may be
completely inundated, and therefore, washed away, may be ignored
for dam break modelling purposes.
The accuracy of a dam break study is different from that of a
river modelling study. Traditional river modelling simulates
natural floods that occur within defined floodplain areas. Our
knowledge of typical flow conditions and modelling parameters
such as channel and floodplain roughness for these events is
relatively good. Equally, there is likely to be a range of data
available with which the model may be calibrated. For a dam
break model the flow conditions typically exceed natural events
by a large margin meaning that there is little calibration data
and the flooded terrain is outside of the normal floodplain
areas making the estimation of channel roughness difficult.
Equally, there is uncertainty in prediction of the failure
mechanisms leading to the initial flood hydro graph, in
understanding 3D flow effects and in predicting the movement and
impact of debris and sediment. With this range of uncertainty,
it is inappropriate to attempt flow modelling to the same level
of accuracy as for normal river flow modelling. The accuracy of
topographic data collected should also relate to the location
within the area at risk.
Thus, in
brief, the following data are required for a typical dam break
analysis:
Salient
features of dam and other hydraulic structures in study
reach of the river.
Rating
curves of all the hydraulic structures in the study reach of
the river
Design
flood hydrograph.
Spillway
rating curve.
Crosssections
of the river from dam site to the most downstream location
of interest.
Elevation
 storage/area relationship of the reservoir.
Stagedischarge
relationship at the last river crosssection of the study
area, if available.
Manning's
roughness coefficient for different reaches of the river
under study.
Topographic
map of the downstream area at a scale of 1:15000 to 1:25000,
with a contour interval of 2 to 5 m for preparation of
inundation map for dam break flood.
Breach
Geometry.
Time
taken for Breach formation.
Reservoir
elevation at start of failure and initial water elevation.
Description
of d/s flow condition, i.e. subcritical and supercritical.