Analysis of Channels With

ANALYSIS OF CHANNELS WITH

COMPOUND CROSS SECTIONS FOR

CHANNEL RESTORATION DESIGN

Final Report, October 2000

Principal Investigator: Colin R. Thorne

Research Associate: Philip J. Soar

School of Geography

University of Nottingham

University Park

Nottingham, U.K.

NG7 2RD

FINAL REPORT

Submitted to

U.S. Army Research, Development and

Standardization Group-U.K., London

Contract No. N68171-00-M-5506

Project No. W90C2K-8913-EN01

October, 2000

The research reported in this document has been made possible through the support and sponsorship of the United States Government through its European Research Office of the United States Army. This report is intended only for the internal management use of the contractor and United States Government.

Final Report – October 2000

CONTENTS

List of Figures......

List of Tables......

Summary......

Keywords......

Conversion of SI to US Customery Units......

1.Introduction: Lateral Momentum Loss in Compound Channels......

2.Preliminary Guidelines for Determining Lateral Momentum Losses......

3.Curve-Fitting Approach......

4.Matrix Visualisation Approach......

4.1Constructing 3-D Plots......

4.2Risk Assessment......

4.3nx – Manning n Multiplier Software......

5.Recommendations for Further Analysis on Compound Channels......

6.Channel Design Software......

7.Channel Restoration Design in Braided Rivers......

8.References......

Followed by:

nx User’s Guide

Final Report – October 2000

LIST OF figures

Figure 1Predicted roughness multiplier from multiple regression analysis versus calculated roughness multiplier based on the hydraulic equations and method adopted by Copeland (1999). / 4
Figure 2Confidence limits applied to the n multiplier as a function of the Wetted Perimeter Ratio (total channel perimeter to wetted channel perimeter), Curves apply to both smooth and rough floodplains. / 6
Figure 3Confidence limits applied to the n multiplier as a function of the dimensionless Velocity Differential (ratio of the difference in calculated channel and floodplain average velocities to the channel velocity, ignoring lateral momentum loss), *Curve applies to ‘smooth’ floodplains. / 7
Figure 4Confidence limits applied to the n multiplier as a function of the dimensionless Velocity Differential (ratio of the difference in calculated channel and floodplain average velocities to the channel velocity, ignoring lateral momentum loss), *Curve applies to ‘rough’ floodplains. / 7
Figure 5Risk assessment of n multiplier as a function of Wetted Perimeter Ratio (P Ratio) and Velocity Differential (V Differential) parings in channels with hydraulically ‘rough’ floodplains. / 11
Figure 6Risk assessment of n multiplier as a function of Wetted Perimeter Ratio (P Ratio) and Velocity Differential (V Differential) parings in channels with hydraulically ‘smooth’ floodplains. / 11
Figure 7Threshold of specific energy between single thread and multi-thread flows as a function of width to depth ratio. Test data from Jamuna River in Bangladesh. / 17

LIST OF tables

Table 1Values of the parameters in Equation 1 for confidence limits applied to the n multiplier (Y) as a function of i) Wetted Perimeter Ratio (total channel perimeter to wetted channel perimeter),  and; ii) Velocity Differential (ratio of the difference in calculated channel and floodplain average velocities to the channel velocity, ignoring lateral momentum loss), *, and floodplain type, where: s = smooth floodplain; r = rough floodplain. / 6

SUMMARY

River restoration projects often require the design of a stable channel with a compound, or multi-stage cross section when it is necessary to preserve flood defence and land drainage functions. The restored design incorporates an inner channel with the attributes of a natural, regime channel and a significantly larger channel that surrounds it which is able to convey flood flows without causing property damage on the surrounding floodplain. However, the existence of significant shear stresses at the interface between over-bank flow and main channel flow due to lateral momentum exchange presents a challenge to river engineers as the resultant energy losses are not accounted for in existing channel restoration design approaches. This report extends earlier research by Copeland (1999) in the development of a method to calculate a Manning n multiplier applied to the channel roughness coefficient from cross section dimensions and velocity data. The preferred approach is a 3-D plot of n multipliers as a function of two dimensionless parameters which account for both morphology and flow influences: a Wetted Perimeter Ratio and a dimensionless Velocity Differential. At present, the method is only applicable to straight channels.

In order for end-users to apply the 3-D plots to channel restoration design and other river engineering applications, the 3-D plots have been made available in a user-friendly software package called ‘nx’ (n multiplier). A built-in interpolation tool yields n multipliers for user-specified floodplain roughness type, sample confidence level and measures of the Wetted Perimeter Ratio and Velocity Differential. The package can be found on the CD-ROM submitted with this report.

This report also presents a windows-driven version of the stable channel design module in the SAM hydraulic design package. The new software has been developed by Colorado State University researchers and aims to make existing channel restoration design approach user-friendly and ultimately more accessible to practitioners.

Finally, at present restoration design is limited to meandering channels. This excludes the possibility of designing a braided channel, which might be desirable in some restoration scenarios. This report provides recommendations for a future restored channel design methodology applicable to rivers with braided or anastomosed planforms.

The research described here carries forward and further develops an earlier programme of research designed to address the design of stable channels with natural attributes (Thorne and Soar, 2000). Any uncorrected errors or omissions in this report remain only the responsibility of the authors.

KEYWORDS

Compound ChannelsChannel Restoration DesignFlood Control Channels

Flow Resistance Lateral Momentum LossManning n Multiplier

Two-Stage Channels

CONVERSION OF SI TO US CUSTOMERY UNITS

The following units are used in this report and may be converted as indicated:

Length1 m = 3.281 ftDischarge1 m3s-1 = 35.32 ft3s-1

Area1 km2 = 0.39 square miles Mass 1 tonne = 1.1 US tons

Final Report – October 2000

1.Introduction: lateral momentum loss in compound channels

The design of stable channels with mobile bed materials and natural attributes poses particular problems in the case of multi-functional restoration schemes. Often, it is desired to restore the natural functions of a river (for example, fisheries, recreation or conservation) while also preserving flood defence and land drainage functions. Under these circumstances, a widely used approach is to design a channel with a compound, or multi-stage cross-section. The smaller, inner channel then has the attributes of a natural, regime channel, while the larger channel that surrounds it is able to convey flood flows without causing property damage on the surrounding floodplain.

A number of recent studies have demonstrated that there are often significant shear stresses at the interface between over-bank flow and main channel flow due to lateral momentum exchange. Failure to account for this momentum exchange, and the resulting energy losses, in discharge calculations may result in considerable overestimation of the channel capacity for a given depth of flow. However, there is a paucity of knowledge concerning the physics of fluid flow in compound channels, the mechanics of sediment transport, and the relationships between flow regime, channel geometry and channel stability of the inner channel and the floodway. Recent studies have shown that the sources of energy dissipation and flow resistance in compound channel flow are very difficult to determine (Ervine et al., 1994; Sellin and Willets, 1996).

A programme of research designed to address the design of stable channels with natural attributes was initiated between the U.S. Army Engineering Research and Development Center (formerly Waterways Experiment Station, WES) and the University of Nottingham in 1996. The research described here further develops that earlier initiative by considering how the results of concurrent research on the analysis of lateral momentum losses in compound channels could be utilised within the Channel Restoration Design approach.

The approaches adopted develop out of the preliminary guidelines for determining lateral momentum losses described in a draft report by Copeland (1999). An objective of this initial study was to develop a method that could be incorporated into existing computer programs and methodologies employed in the U.S. Army Corps of Engineers for channel design and river analysis. These guidelines are based on the results of flume studies from several literature sources. The study demonstrated that hydraulic losses associated with lateral velocity variations are significant in certain cases. However, attempts to provide engineers with definitive guidance to date have been unsuccessful due to insufficient data and scale effects. In light of this, the objective of this research is to develop existing general guidelines to account for lateral momentum losses using a roughness multiplier applied to the main channel roughness coefficient and to assist in establishing a range of uncertainty determinations. Two approaches have been adopted to meet this objective and are described in this report: i) curve-fitting techniques to describe the mean roughness multiplier for a given set of hydraulic parameters, and; ii) fitting 3-D surfaces to the available data using interpolation and matrix visualisation techniques. In both cases, statistical limits of uncertainty have been applied to estimate the most probable range of roughness multiplier based on the variability of the measured data.

2.preliminary guidelines for determining lateral momentum losses

Copeland (1999) assembled an extensive database of compound channel data based on flume experiments on straight channels from eight sources. The method employed by Copeland was to estimate both a channel and a floodplain roughness coefficient, ignoring lateral momentum losses, using standard techniques and then apply a roughness multiplier to the channel roughness coefficient to account for increased energy dissipation from lateral momentum losses. The multiplier is defined as the Manning n value that accounts for momentum loss over Manning n value estimated from the channel boundary only. In this way, the multiplier has a value of unity when the water surface is not above the top of bank of the main channel and varies with water surface elevation above top of bank. The assembled data were used to describe the interrelationships between channel roughness multiplier and several dimensionless hydraulic parameters. Two of the most significant parameters are the ratio of total channel perimeter to wetted channel perimeter (Wetted Perimeter Ratio), , and the ratio of the difference in calculated channel and floodplain average velocities to the channel velocity, ignoring lateral momentum loss (Velocity Differential), *. These two parameters represent the influence of the channel morphology, in terms of the relative portion of the channel boundary subject to apparent shear stress at the channel-floodplain interface, and the flow conditions, expressed in terms of velocity differential between channel and floodplain flows.

The approach adopted by Copeland (1999) is to divide the compound channel into subsections assuming vertical division lines. In this way, average hydraulic parameters are calculated for subsections with an average hydraulic roughness assigned without considering lateral momentum loss. For narrow channels where the main channel bank roughness is significantly different from the bed roughness, it is recommended that the equal velocity compositing method (Horton, 1933; Einstein, 1942, 1950; Einstein and Banks, 1950) should be used to determine average hydraulic parameters for the main channel. Furthermore, if there are significant variations in roughness across the floodplain, then conditions next to the main channel should be used. Velocity and roughness determined from these calculations are designated with an asterisk, *, in this report.

The preliminary guidelines are based on multiple regression analysis conducted on 329 measurements. Three dimensionless parameters were found to be significant for predicting the roughness multiplier, defined as:

Wetted Perimeter Ratio / / (1)
Velocity Differential / / (2)
/ (3)

where:

Pwetted perimeter (does not include interface between channel and floodplain flows)

Nfpnumber of floodplains: 1 or 2

n*assigned Manning n value ignoring lateral momentum loss

V*calculated velocity assuming no lateral momentum loss

Yfpwater depth in floodplain

subscripts

chchannel

fpfloodplain

bphysical surface of the channel

The roughness multiplier values are not measured data but were theoretically derived by Copeland (1999) based on measured variables from flume experiments and standard hydraulic calculations. The derivation is not repeated here and reference should be made to the report by Copeland (1999).

The regression equation yielded an R2 value of 0.63 and is given as:

/ (4)

Figure 1 is a plot of predicted roughness multiplier (from Equation 4) versus calculated roughness multiplier (from 329 measured variables and hydraulic equations used by Copeland, 1999).

Figure 1Predicted roughness multiplier from multiple regression analysis versus calculated roughness multiplier based on the hydraulic equations and method adopted by Copeland (1999).

However, there are three main limitations of this approach which compromise the basic assumptions of the multiple regression model:

i)Plots of the roughness multiplier as a function of the individual dimensionless variables (Copeland, 1999) show that the roughness multiplier is not a linear (or log-linear) function of the variables. Figure 1 also shows that Equation 3 significantly overestimates the calculated n multiplier at high values;

ii)The form of the best fit multiple regression equation includes identical Manning n values on both sides of the equation, indicating significant collinearity between parameters. This can misleadingly produce high R2 values in regression analyses.

iii)The plot of calculated versus predicted data points reveals significant scatter about the regression line.

In light of these limitations, an alternative method is required. The approaches discussed below may be applied to a compound channel in which there is a distinct main channel and a distinct over-bank area on one or both sides of the main channel. It can also be applied to the case of a channel and floodplain. In this report, no distinction is made between over-bank surface in a compound channel configuration and a floodplain and both are referred to as floodplain.

3.Curve-fitting approach

Initial research focused on the application of curve-fitting software to better represent the non-linear relationships between the roughness multiplier and the two main dimensionless parameters and account for various levels of uncertainty. The approach predicts the likely maximum n multiplier for a given confidence level, rather than some average value as with the regression approach. The data analysis and technical graphics Software Origin V6 (Microcal Software Inc., 1999) includes a non-linear ‘beta’ function which is appropriate for meeting this objectives. The beta function is of the form:

/ (5)

where:

Ydependent variable

Xindependent variable

Y0Y-offset

Xcmode (at Y=Y0+A)

W1, W2, W3shape parameters

Aamplitude

The curve intercepts the line Y=Y0 when X=X1 and X=X2, as given by:

/ (6)

and

/ (7)

X1 and X2 often define fixed lower and upper bounds to the data, for example values of 0 and 1 for certain dimensionless parameters, for which the shape parameters, W1, W2 and W3, must be adjusted accordingly. The coefficient, A, in Equation 5 defines the amplitude of the peak in the beta curve. By calculating the percentage of data points that lie outside of the curve, for a specific A value, a range of A values can be derived for different uncertainty levels, or confidence limits.

This technique is demonstrated in Figures 2-4, which show uncertainty determinations of the n multiplier as a function of: i) Wetted Perimeter Ratio (total channel perimeter to wetted channel perimeter),  (Figure 2) and; ii) Velocity Differential (ratio of the difference in calculated channel and floodplain average velocities to the channel velocity, ignoring lateral momentum loss), * (Figures 3 and 4). The parameters in Equation 5 for each confidence curve in Figures 2-4 are given in Table 1. In a sensitivity analysis, Copeland (1999) found that the Velocity Differential is also a function of the type of floodplain. Copeland classified floodplains in terms of the ratio of floodplain Manning n value to channel Manning n value. Ratios less than or equal to unity are classified as having hydraulically ‘smooth’ floodplain boundaries (327 values) and ratios greater than unity are classified as having hydraulically ‘rough’ floodplain boundaries (98 values). In general, river channels fall into the rough floodplain category. The influence of floodplain type on the distribution of n multiplier is shown in Figures 3 and 4.

A (at specified confidence level)
Xc / Y0 / Xc / W1 / W2 / W3 / 99% / 95% / 90% / 80% / 70% / 60% / 50%
 / 1 / 1.1 / 1.5 / 1.67 / 10.33 / 1.592 / 1.119 / 0.697 / 0.469 / 0.349 / 0.276 / 0.224
/ 1 / 0.3 / 3 / 3 / 19 / 1.273 / 0.794 / 0.611 / 0.468 / 0.376 / 0.335 / 0.304
/ 1 / 0.8 / 1 / 5 / 2 / 1.751 / 1.505 / 1.26 / 0.94 / 0.833 / 0.697 / 0.563

Figure 2Confidence limits applied to the n multiplier as a function of the Wetted Perimeter Ratio (total channel perimeter to wetted channel perimeter), Curves apply to both smooth and rough floodplains.

Figure 3Confidence limits applied to the n multiplier as a function of the dimensionless Velocity Differential (ratio of the difference in calculated channel and floodplain average velocities to the channel velocity, ignoring lateral momentum loss), *Curve applies to ‘smooth’ floodplains.

Figure 4Confidence limits applied to the n multiplier as a function of the dimensionless Velocity Differential (ratio of the difference in calculated channel and floodplain average velocities to the channel velocity, ignoring lateral momentum loss), *Curve applies to ‘rough’ floodplains.

The bell-shaped nature of the distributions in Figures 2-4 can be explained in terms of bank overtopping and inundation of the floodplain during the passage of a flood. Figure 2 indicates that there is an initial increase in the multiplier as flow begins to overtop the banks and flow onto the floodplain between =1.0 and approximately =1.1. The rise in multiplier is due to the increase in the apparent shear stress boundary surface with increasing . This is followed by a gradual decline in the multiplier as  increases beyond 1.1. The decline is associated with the decrease in the relative difference between floodplain depth and channel depth (and their velocities), which decreases the magnitude of apparent shear stress. Therefore, the impact of momentum exchange on the channel velocity is very low during high stage flood flows. Similar reasoning can be used to explain Figures 3 ad 4, although * decreases from 1.0 to 0.0 with increasing stage above the channel’s (inner channel if compound) top of bank.