Prof. B.S. Thandaveswara. The computation of a flood wave resulting from a dam break basically involves two

Transcription

1 41.4 Routing The computation of a flood wave resulting from a dam break basically involves two problems, which may be considered jointly or seperately: 1. Determination of the outflow hydrograph from the reservoir for flow through the breach. 2. Routing of the outflow from the dam in the downstream reach of the channel Input Required (a) Water discharges entering into and flowing along the body of water from which the impound water is released. (b) Water discharges (s) flowing out from the body of water before the sudden release. (c) Water discharges (s) flowing along the bodies of water into which impound water is suddenly received. (d) The flow regime (such as GVF, Uniform) associated with both the bodies which releases and receives. (e) Water surface elevation (f) Submergence effect. (g) Time function of breaching (or closing and opening of gates in canals). The above information may be in the form of parameters or functions Breach Outflow Hydrograph This is the outflow resulting from a dam collapse from the initiation of the breach till the reservoir water level reaches the final breach bottom level, or the contents of reservoir gets exhaused whichever is earlier (as in multiple breaches, the extent of breach could be different). The breach outflow hydrograph may be obtained by using reservoir routing method. In case of a dam break problem, the following functions are required: (a) Inflow hydrograph (f 1 (t)); (b) Outflow hydrograph (Outflow through openings) (f 2 (t));

2 (c) Stage hydrograph (f 3 (h) h is the depth); (d) Outflow rating curve (f 4 (H), H is the head); and (e) Storage function (a function of elevation) Reservoir routing can be accomplished with any one of the hydrologic routing methods (puls, storage indication method) based on the equation ds = I - Q dt in which I is the inflow into the reservoir, Q is the outflow from the reservoir and, ds is the rate of change of storage in the reservoir dt Commonly used method is modified Puls method. The other method for solving equation is Standard Runge - Kutta method, in which the water surface elevation and water spread area are used. This approach does not require the computation of special storage outflow (as in the case of modified Puls method), but is more closely related to hydraulics of flow through the reservoir. The 3 rd Order Runge - Kutta method involves dividing each time step interval into three increments and calculating successive values of water surface elevation and reservoir discharge. This method has proved to be easier for programming and computations as the trial and error procedure is eliminated. Determination of breach outflow hydrograph requires knowledge of rate of breaching. Models for this purpose are available in standard commercial software Channel Routing This is a mathematical procedure used for tracking the flow along the channel. This involves the determination of discharge, water surface elevation, and time of arrival of peak, along the channel reaches, by using St. Venant's equation. i.e. unsteady free surface flow equation. One may note that, kinematic wave approximation also known as

3 lumped method routing will lead to "channel routing". Otherwise the routing using the Saint Venant equations is called the distributed flow routing Boundary Condtions Upstream Boundary: Computed breach outflow hydrograph Downstream Boundary: The stage discharge relationship Internal Boundary Condtions There are many types of internal boundaries and some of them are shown in Figure Rising Flood Falling Flood Main Channel Parallel to Bank Transverse Slope Left Flood Plain Right Flood Plain Meandering

4 Weir Expansion or Contraction Levee Drops or Steps Dam Lock Dam and Lock

5 Bridge Emabankment Bridge Breach Flood Detention Basin Existing Levee Intake River Loop River Flood Plain Formation of Cells 1. Agricultural Land 2. Urban Land (Islands) 2 3 H Intake for detention basin acts as a weir-bi-directional flow Constant Level H Intake Flow Possible Super Critical Flow Figure Some of the Interior Boundaries

6 Information Required for Routing the Dam Break Flow (1) The model and scheme that is to be adopted. (2) Lateral Flow - whether distributed or lumped inflow and outflow and its characteristics with respect to time. The lateral flows include (i) Contribution of rainfall on the free surface (ii) Overland flow (iii) Infiltration (iv) Evaporation (v) Seepage (3) Cross sectional details (a) Prismatics or (b) Non-uniform properties of natural rivers. Following methods are used for representing the cross sections Replacing of actual river by unform channel for total length such as Trapezoidal section. Repacing of actual river by series of prismatic channel. Representing cross sections by Polygonal sections. Replacing of surveyed sections by Polynomials. Interpolation of cross sections. Stochastic generation of cross sections. (4) RESISTANCE PROPERTIES: Any resistance law such as Chezy's, Manning's, Darcy- Weisbach's may be used. The relevant coefficients need to be defined as a function of length (or section) and its variational function with respect to depth should be known. (5) Details of channel network in Flood plains : Numerical Methods for Solving the Governing Equations Any of the following numerical methods may be used for solving the governing Saintvenant equations in conservation form. Many schemes such as Total Variation Diminishing (TVD), Essentially Non-Oscillating (ENO) have been proposed in recent years for correct numerical solution of the governing equations.

7 (i) Explicit - Lax Wendroff (ii) Diffusive scheme (iii) Method of characteristics - irregular grid using predictor - corrector scheme. (iv) Explicit with - Two dimensional characteristic Network model with moving grid - Reservoirs as nodes channels as links. (v) Four point implicit (nonlinear Finite Difference Scheme) (vii) Galerkin Finite element method Steps in Mathematical Formulation 1. To identify the model and technique to be used. 2. INPUT THE DATA regarding (a) Physical system (Figure 41.3) including internal boundaries. Spillway Q t Reservoir Tributary Inflow Hydrograph Bridge Cells Over topping Piping

8 Branched Looped Figure 41.3 Cell groups (Two dimensional) (b) Types of precipitation distribution, Spillway rating curve. (c) Shape, size and progress of breach with time or piping, time of starting of breach. 3. To write the finite difference approximations for all situations that are to be incorporated. 4. To choose the method of averaging the Sf Arithmetic, Geometric, Harmonic). 5. Softwares regarding Newton Raphson technique, Matrix method, Space matrix converter to normal matrix, (if possible) such as Band solver and program for reservoir routing, dynamic channel routing, are required Available Software Two models namely HEC Dam break model and, DAMBRK / DWOPER models developed by Fread for National weather service are available for dambreak flow analysis. A new model FLDWAV has been developed in 1985 by Fread. The FLDWAV model is a system of DWOPER and DAMBRK. This is a generalised dynamic wave model for one dimensional unsteady flows in a single or branched water way. It is based on Four point nonlinear implicit F.D. model. The following special features are included in that model. (i) Variable t and x grid. (ii) Irregular cross sectional geometry. (iii) off channel storage.

9 (iv) Roughness coefficient as a function of discharge on water surface elevation and along the distance. (v) Linearly interpolated cross sections and roughness coefficients. (vi) Automatic computation of initial steady state. (vii) Time dependent leteral flows. (viii) Can account for Supercritical/ Subcritical flows.