Full Equations Utilities (FEQUTL) Model for the Approximation
of Hydraulic Characteristics of Open Channels and Control
Structures During Unsteady Flow
Determining the boundaries of a regulatory floodway is difficult because, although the floodway definition is simple, the floodway may be established in many ways. The floodway is that portion of the available flow cross section that cannot be obstructed without causing an increase in the water-surface elevations resulting from a flood with a 100-year average return period of more than a given amount. The Federal Emergency Management Agency (1995, p. 5-3) establishes the amount to be 1.0 ft, but States can require a smaller amount of increase and, as an example, the State of Illinois requires that the increase be 0.1 ft or less. This definition allows great freedom in the establishment of the actual boundaries of the floodway.
Various auxiliary requirements have been imposed in FEQUTL to more closely define the floodway. The main flow channel, if such can be defined, is generally required to be in the floodway. Thus, the hypothetical obstruction must not affect the lower flows in the stream. Furthermore, the obstruction usually is allocated between the left and right banks of the flood plain so as to reduce the hydraulic capacity of each by about the same amount. Cases can result where only one streambank includes a flood plain, and then all the obstruction must be placed on only one side of the main channel. In other cases, the total capacity of one side of the flood plain may be inadequate for the planned reduction in capacity, and the other side must then have a greater reduction. A mixture of hydraulics and regulatory convenience combine to provide the tools and rules for establishing the boundaries of a regulatory floodway.
The loss of capacity for flow is computed in terms of conveyance, but a hydraulic problem is immediately encountered. Conveyance is an aggregate quantity that can only be computed meaningfully for complete channels or subdivisions of a channel with a shape such that the hydraulic radius properly reflects the frictional characteristics of the channel boundary. Thus, for the typical natural channel with a flood plain on the right and left, three subchannels are present: left overbank, main channel, and right overbank. A value of conveyance may be computed for each subchannel, and then the three subchannel conveyances are added to estimate the conveyance of the entire cross section. The manner in which the subchannels are defined is subject to some uncertainty, as is the best way to treat the interactions across the hypothetical boundaries between the main channel and the flood-plain channels. The hypothetical boundaries are assumed to be vertical and frictionless in most steady-flow and unsteady-flow models. Thus, no interaction is computed between the flow in the main channel and the flood-plain channels. Flow interaction does happen in nature, but the approximation is simple and no convenient, well-established alternative is available. More complex assumptions have been developed from laboratory studies, but too few field studies have been completed to make conclusions concerning the validity of the assumptions.
To compute a trial floodway, a rule of equal reduction of conveyance on the left and right of the channel is applied in FEQUTL by using the following steps.
Another type of problem in the determination of a floodway is that the concept of a floodway, at least as implemented in practice, is unequivocally a steady-flow concept. A floodway is defined in terms of the reduction in flow capacity only, and any changes in storage are ignored. This greatly simplifies the analysis and may be adequate in many cases. The true efficacy of this simplification is unknown because no detailed study of the effects of storage change has been completed. The steady-flow concept is simple because a unique meaning can be assigned to the average 100-year return-period flow, and all that is required for a steady-flow analysis is a flow rate. However, for unsteady-flow analysis, further requirements include one or more hydrographs to determine the water-surface elevation that will be exceeded on the average only once in 100 years. In principle, no single hydrograph can be utilized to determine the 100-year water-surface elevations everywhere in the watershed. The assumption made in the steady-flow analysis is that the flows used represent all possible flow interactions; therefore, a simple analysis can be made. The problem in unsteady-flow analysis is that it is unlikely that an observed hydrograph is available for which the peak or volume approaches a reasonable range for the 100-year flood level.
The logistical aspects of applying FEQUTL and FEQ to define a floodway are now considered. The shape of the cross section is not considered in FEQ. The shape and size of the cross section are only considered in FEQUTL. Only a table of the cross-sectional characteristics for the entire section as a function of the maximum depth in the section is considered in FEQ simulation. Thus, an encroachment into the channel can only be defined with any precision in FEQUTL. Two sets of function tables must be input to FEQ: one set for the stream channel without a floodway and another set for the stream channel with a floodway. Furthermore, FEQUTL must be run for each change in the floodway. Therefore, the user should develop a structure of files that will simplify these operations.
All function tables that do not represent cross sections should be placed in one or more files distinct from the cross-section tables. Also, all the bridge and culvert definitions and the associated cross sections should be in distinct files so they can be run separately. Finally, the remaining cross sections not related to bridges should be in a distinct file. Any closed-conduit sections should also be in distinct files because these will not be involved in floodway changes. Thus, five or six files of input to FEQUTL and the same number of output files containing the function tables for use as input to FEQ may be needed. A well-thought-out naming convention should be established to keep track of the various files. Directory structure also is important for keeping track of the files.
The floodway specification, described in section 5.12, was designed to eliminate the need for making changes to the cross-section descriptions. Thus, the floodway specification consists of a table, with one line in the table used for each cross section to be modified, giving (1) a description of the method to apply in defining the floodway and (2) key items of information required to implement that method. The table number of the cross- section description is utilized to associate the floodway information with the cross-section description. If no floodway information is given in the floodway table for a cross section that appears in the subsequent input, then the cross-section table is computed unchanged. Conversely, floodway information given in the floodway table for a cross section not in the subsequent input is read in FEQUTL but not used. Thus, only those tables for which floodway information is given and that also appear in the subsequent input are changed. However, the complete input should always be processed to simplify the bookkeeping for files because the time taken in FEQUTL computations of the function tables is minimal.
The floodway table is stored in a distinct file and is referenced with the FLOODWAY command. In this way, only one copy of the floodway table is needed for a stream system. This reduces errors and helps maintain consistency. Only two lines must be added to the input files for FEQUTL to invoke the floodway option. Details for the floodway table and the FLOODWAY command are given in section 5.12.
Once the modified set of cross-section tables has been computed and the input to FEQ modified to reference the file containing the modified tables, FEQ can be run with the flood hydrograph or hydrographs selected for defining the floodway. It is unlikely that the first trial to determine floodway limits will be successful. The maximum values for water-surface elevation from FEQ simulation need to be reviewed, and adjustments should be made in the floodway table accordingly. A revised set of modified cross-section tables are then computed and the process is repeated. The process is usually started with a floodway defined in steady-flow analysis. This gives an immediate indication of the significance of the loss in flood-plain storage because steady-flow analysis does not include storage effects, whereas the initial unsteady-flow simulation includes storage effects.
If the cross sections close to bridges and culverts are extensively modified, the flow tables for these structures may need to be recomputed. This complication results because in FEQ simulation the hydraulic characteristics of certain structures must be precomputed to avoid the time and the potential for computational failure of computing them "on the fly" together with the flow computations in the branches. The large number of culverts and bridges in streams in urban areas requires that they be represented carefully to develop a meaningful and useful model of the stream system. The effect of these structures and their mutual interaction on the floodway may be more important than the representation of the branches.