Afflux Advisor: User Guide and Technical Reference

Afflux Advisor: User Guide and Technical Reference
Defra / Environment Agency
FCERM Joint Science Programme
SC030218/PR
Afflux Estimation System
August 2007
AFFLUX ADVISOR
User guide and technical reference
This document provides guidance and
background information for users of the Afflux
Advisor spreadsheet method.
JBA Consulting
South Barn
Broughton Hall
SKIPTON
North Yorkshire
BD23 3AE
UK
t: +44 (0)1756 799 919
f: +44 (0)1756 799 449
www.jbaconsulting.co.uk
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
REVISION HISTORY
Revision Ref./
Amendments
Issued to
Date Issued
Initial Draft, 2 December 2004
Revised 11 May 2005
Andrew Pepper
Following Technical Reviewers
meeting.
Andrew Pepper
CONTRACT
This report describes work commissioned by The Environment Agency under Science Group contract Ref.
SC030218. The Environment Agency’s representative for the contract is Andrew Pepper of ATPEC.
Prof. Peter Mantz, Dr. Serter Atabay, Dr. Rob Lamb, Steve Rose, Claire Packett and Jeremy Benn of JBA
Consulting carried out the work.
Prepared by:
=
=
......................................................................................... Peter Mantz, BSc, MSc, PhD,
CEng, CPhys, MICE, MASCE
=
=
=
=
=
=
=
mêáåÅáé~ä=^å~äóëí=
Reviewed by:
=
=
......................................................................................... Rob Lamb, MA, PhD
=
=
=
=
=
=
=
qÉÅÜåáÅ~ä=aáêÉÅíçê=
Approved by:
......................................................................................... Jeremy Benn, MA, MSc,
CEng, FICE, FCIWEM, MASCE
=
=
=
=
=
=
=
j~å~ÖáåÖ=aáêÉÅíçê=
=
=
Date :
11 May 2005
© Jeremy Benn Associates Ltd
DISCLAIMER
This document has been prepared solely as a research report for The Environment Agency. JBA Consulting
accepts no responsibility or liability for any use that is made of this document or associated software other
than by the Client for the purposes for which it was originally commissioned and prepared.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
i
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
ACKNOWLEDGMENTS
We are grateful to the Defra/Environment Agency joint flood management research programme (Engineering
Theme) for funding this study. In particular, we would like to acknowledge the support given to the project
by Dr Mervyn Bramley OBE (formerly Theme Leader) and Andrew Pepper (External Theme Advisor).
We are grateful for expert comment and review by Prof. Donald Knight, Dr Les Hamill, Dr Nigel Wright, Dr
Paul Samuels and Dr John Riddell. We are also grateful to the above for helping with the provision of data
on afflux, and for having the opportunity to support a number of MSc laboratory projects at Birmingham
University through this project. We would also like to thank Dr Galip Seckin for assistance with data.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
ii
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
EXECUTIVE SUMMARY
Background
Afflux is an increase in water level that can occur upstream of a
structure at high flows (see right). More formally, afflux can be
defined as the maximum difference in water level, for a specific
flow, if the structure were to be removed. It is caused by energy
losses at high flows through bridges and culverts, and it is made
worse by blockage. Afflux can be physically significant in terms
of flood levels and leads to a potential for increased losses due
to blockage. It therefore needs to be represented in river
modelling tools and understood by river engineers and other
professionals.
The Afflux Estimation System
Accurate estimation of flood water level underpins almost all sectors of flood risk management. A new
support tool - the Afflux Estimation System (AES) for bridges and culverts - has been commissioned by the
Environment Agency as part of the joint Defra/EA flood research programme to ensure that best available
methods relevant to conditions in the UK are used for flood risk management.
The Afflux Estimation System will comprise two main outputs:
•
a simple Afflux Advisor providing quick, approximate calculations and guidance in an accessible
spreadsheet form
•
more rigorous Afflux Estimator algorithms, produced as open source code, and available to be
implemented as a software application or a component of existing river modelling packages.
This report is a user guide and technical report for the Afflux Advisor spreadsheet tool.
The Afflux Advisor
The Afflux Advisor allows users to calculate rating curves with and without a structure for a single cross
section in a river. The Advisor represents arch and beam bridges (including simple treatment of multiple
arches and piered beam bridges). It also calculates water levels for the main classes of culverts described
in the current CIRIA culvert design manual.
The Afflux Advisor models flows ranging continuously from free surface subcritical flow below the soffit of
the bridge or culvert to totally drowned flow. Uncertainty is quantified as a function of method choice and
roughness values.
The Afflux Advisor manual
This report introduces the Afflux Advisor and provides a summary of the background research that
underpins the application. It describes how to use the Advisor and includes a number of worked examples.
The report is also available as an on-line help page within the Advisor itself.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
iii
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
This page is intentionally left blank.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
iv
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
CONTENTS
Page
REVISION HISTORY
CONTRACT
EXECUTIVE SUMMARY
CONTENTS
LIST OF FIGURES
LIST OF TABLES
ABBREVIATIONS
NOTATION
1
i
i
iii
v
vi
vii
viii
viii
INTRODUCTION----------------------------------------------------------------------------------- 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2
Background....................................................................................................................................1
What is afflux?................................................................................................................................1
Why do we need an Afflux Advisor? ..............................................................................................2
What is in the Afflux Advisor? ........................................................................................................3
What are the limitations of Afflux Advisor?....................................................................................4
What’s new about Afflux Advisor?.................................................................................................4
How does Afflux Advisor link with other related Defra/Environment Agency research? ..............4
How do I use this Afflux Advisor Manual? .....................................................................................5
TECHNICAL BACKGROUND --------------------------------------------------------------------- 7
2.1
2.2
2.3
3
The River application .....................................................................................................................7
The Bridge Application...................................................................................................................8
The Culvert Application................................................................................................................20
TESTING AFFLUX ADVISOR -------------------------------------------------------------------- 27
3.1
3.2
3.3
3.4
4
How was Afflux Advisor tested? ..................................................................................................27
How was the River Application tested?.......................................................................................27
How was the Bridge Application tested? ....................................................................................29
How was the Culvert Application tested?....................................................................................39
WORKED EXAMPLES---------------------------------------------------------------------------- 43
4.1
4.2
4.3
Worked example for the River Application ..................................................................................43
Worked examples for the Bridge Application ..............................................................................45
Worked examples for the Culvert Application .............................................................................49
APPENDIX A:
ROUGHNESS COEFFICIENTS
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
v
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
LIST OF FIGURES
Figure 1-1: Side elevation at a bridge contraction .............................................................................................1
Figure 2-1: Subdivision method of area (A) for the River Main ..........................................................................7
Figure 2-2: Minimum and maximum Manning’s n values as a function of ‘normal’ values...............................8
Figure 2-3: Bridge types included in Afflux Advisor...........................................................................................9
Figure 2-4: Nine afflux modes through a bridge structure (modes 1 to 4 are sub-soffit, modes 5 to 9
are super-soffit).......................................................................................................................10
Figure 2-5: Correlation of University of Birmingham afflux data for sub-soffit flows ......................................14
Figure 2-6: Profile of a bridge constriction at the stream centreline (after USBPR, 1978) ..............................15
Figure 2-7: Base curve coefficient design curves (from USBPR, 1978) ..........................................................16
Figure 2-8: Discharge coefficient curve for sluice gate flow (from USBPR, 1978) ..........................................18
Figure 2-9: Chart for converting bridge headloss to upstream depth (from USBPR, 1978)............................18
Figure 2-10: Discharge reduction factor (DRF) for submerged weir flow (from USBPR, 1978).......................19
Figure 2-11: Culvert types modelled in the Afflux Advisor...............................................................................20
Figure 2-12: Eight flow modes for a culvert structure......................................................................................22
Figure 2-13: Nomenclature for culvert hydraulics ............................................................................................25
Figure 2-14: Minimum and maximum culvert roughness against ‘normal’ roughness....................................26
Figure 3-1: Comparison of rating curves using CES and AA for the River Main .............................................28
Figure 3-2: Comparison of rating curves using CES and AA for the River Dane.............................................29
Figure 3-3: River cross section, bridge sketch and river rating for the UB Arch bridge model (main
channel friction, nmc = 0.010, floodplain friction, nfp = 0.009)..............................................30
Figure 3-4: Afflux and rating comparisons for the Arch bridge type................................................................31
Figure 3-5: Afflux and rating comparisons for the Multiple Arch bridge..........................................................32
Figure 3-6: Afflux and water level comparisons for all Beam bridges, and afflux and rating
comparisons for the Beam bridge type of span 0.598 m.......................................................33
Figure 3-7: Afflux and water level comparisons for all Piered Beam bridges, and afflux and rating
comparisons for the Piered Beam bridge type of span 0.598 m ...........................................34
Figure 3-8: Afflux versus skew angle and discharge, University of Birmingham data.....................................35
Figure 3-9: Afflux and Rating comparisons for the Arch bridge type with skew .............................................36
Figure 3-10: Cross section plot, calibrated rating curve and Afflux Advisor bridge rating for the Bogue
Chitto.......................................................................................................................................38
Figure 3-11: Comparison of ‘measured’ and Afflux Advisor afflux estimates for the USGS data (see
Table 3-3) ................................................................................................................................38
Figure 3-12: Comparison of AA and HEC-RAS ratings for shallow culverts. (The blue line is the
undisturbed river rating, brown line is the culvert rating and black line is the HEC-RAS
culvert rating). .........................................................................................................................40
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
vi
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Figure 3-13: Comparison of AA and HEC-RAS ratings for deep culverts. (The blue line is the
undisturbed river rating, brown line is the culvert rating and black line is the HEC-RAS
culvert rating). .........................................................................................................................41
Figure 4-1: River application worksheet...........................................................................................................44
Figure 4-2: River Data worksheet.....................................................................................................................44
Figure 4-3: The Bridge Application worksheet.................................................................................................46
Figure 4-4: Bridge data entry for the Arch type ...............................................................................................47
Figure 4-5: Bridge sketch on the River cross section plot...............................................................................48
Figure 4-6: The Culvert Application worksheet................................................................................................49
Figure 4-7: Culvert data entry for the Pipe type...............................................................................................50
Figure 4-8: Inlet and edge types for culverts (after CIRIA, 1997).....................................................................51
LIST OF TABLES
Table 1-1: Afflux methods which appear in models commonly used by the EA ...............................................3
Table 2-1: Recommended methods for hand/spreadsheet calculation or 1D modelling..................................9
Table 2-2: Computational limits for bridge modes of flow...............................................................................12
Table 2-3: Summary of University of Birmingham afflux data and dynamic similarity analysis ......................13
Table 2-4: Base curve design formulae............................................................................................................16
Table 2-5: Summary of eight culvert flow modes used in the Afflux Advisor ..................................................21
Table 2-6: Summary of the CIRIA (1997) design method for culvert hydraulics..............................................24
Table 3-1: Manning’s friction coefficients used for estimating rating curves ..................................................28
Table 3-2: Number of experimental discharges tested for normal bridge flows .............................................30
Table 3-3: Comparison of measured and AA afflux estimates for the USGS data..........................................37
Table 4-1: Inlet structure design coefficients (from CIRIA, 1997) ....................................................................51
Table A-1: Roughness coefficients for natural channels (after CIRIA, 1997) ...................................................60
Table A-2: Roughness coefficients for culvert barrels (from CIRIA, 1997) ......................................................61
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
vii
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
ABBREVIATIONS
AD
CES
CESM
CIRIA
Defra
EA/Agency
FHWA
HEC-RAS
HR
HRC
ID
ISIS
JBA
LOB
MC
Mike11
ROB
USBPR
UK
US
WSPRO
Above Datum. The Datum may be at any minimum elevation (including Ordnance
Datum), and all elevations are given as metres above Datum throughout.
Conveyance Estimation System
Conveyance Estimation System User Manual
Construction Industry Research and Information Association
Department for Environment, Food and Rural Affairs
The Environment Agency
Federal Highways Administration, US
Hydrologic Engineering Centre – River Analysis System (developed by the US Army
Corps of Engineers)
HR Wallingford Ltd.
Hydraulics Research Wallingford method for computing afflux, as amended herein for
compound channels.
Identifier
Hydrology and hydraulic modelling software
JBA Consulting – Engineers & Scientists
HEC-RAS term for left bank of the channel
HEC-RAS term for the main channel
Danish Hydraulic Institute Modelling System for Rivers and Channels
HEC-RAS term for right bank of the channel
United States Bureau of Public Roads
United Kingdom
United States of America
Water Surface PROfile computation code, US
NOTATION
This report cites a range of sources to develop formulae for estimating afflux. Mathematical symbols and
notation have been used in the same way as in the original publications and are introduced in the text at
each relevant equation. Since there is considerable variation in the notation used by different authors and
organisations, this report uses the original notation in all places. Some symbols therefore have different
meanings in different parts of this report.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
viii
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
1
INTRODUCTION
1.1
Background
This document is the first interim report for the project ‘Afflux at Bridges and Culverts’
commissioned under the Engineering Theme of the Defra/Environment Agency joint flood and
coastal defence research programme. The project follows on from an earlier scoping study that
identified the need for improved and more accessible methods for modelling afflux. The scoping
study has been published on the Environment Agency’s web site as ‘Hydraulic performance of
bridges & other structures at high flows - Phase I (W5A-061)’. The URL is as follows:
(http://www.environment-agency.gov.uk/subjects/flood/896276/211195/264395/914216/?lang=_e)
This report describes the development of a spreadsheet-based application, called ‘Afflux Advisor’,
for calculating afflux at bridges and culverts. It also serves as a user manual for the Afflux Advisor.
1.2
What is afflux?
Afflux is defined as the maximum increase in water surface elevation above that of an undisturbed
stream, due to the presence of a structure such as a bridge or culvert in the stream.
Figure 1-1: Side elevation at a bridge contraction
Afflux is illustrated in Figure 1-1 for a bridge structure located in a stream of uniform slope. The
dashed line represents the normal water surface for the undisturbed stream. The solid line
represents the water surface when the structure is present. Afflux is shown as the maximum
increase of water level above the normal depth (Y1) of the undisturbed stream. Note that the afflux
differs from the headloss across a structure, as the latter is a variable depending on the upstream
and downstream locations of measurement.
When a structure such as a bridge or culvert is placed in a stream, there is a local loss of stream
energy. This is due to the fluid friction in contact with the structure, and the stagnation zones that
border the contracting (Sections 4 to 3) and expanding (Sections 2 to 1) flow reaches upstream and
downstream of the structure. To maintain a steady flow, this local loss of energy is compensated
by an increase in stream potential energy immediately upstream of the structure. A backwater is
thus created which begins at the afflux location.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
1
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Structures are usually designed so that the afflux is kept to a minimum, as it can increase flood risk.
However, the design conditions may no longer prevail when extreme floods are encountered or
structures become blocked. The afflux increases under these conditions. Afflux can raise water
levels by something of the order of a metre or more under extreme conditions.
1.3
Why do we need an Afflux Advisor?
Afflux is difficult to estimate, since it depends upon many structural and flow variables. Important
structural variables are:
• Opening ratio, which is the ratio of the structure’s open area to the flow area at a particular
water level;
• Skew, which is the angle normal to the structure’s axis with the incident flow direction;
• Eccentricity, which is the offset of the structure’s centre line from the flow centre line;
• Surface roughness, which determines the frictional energy loss by the flow;
• Bridge Piers, for which the number and streamlining are important.
Important flow variables are:
• Froude number, which determines whether the flow is easily disturbed. As the flow is
increased, the Froude number increases and the water surface is less easily disturbed. When
the Froude number is unity, the flow becomes supercritical and the afflux is theoretically zero;
• Choking, which occurs when the flow depth at the structure is at a condition of minimum
energy, and thus any discharge increase must cause the afflux to increase;
• Sediment transport, which leads to scour at the structure and reduces afflux;
• Debris transport, which leads to the blockage of the structure and increases afflux.
There are several manual methods available for calculating bridge afflux using simple equations
(Hamill, 1999). These methods are specific to a type of structure. For example, bridge types may
be classified as:
• Pier bridges, usually situated in rural areas and crossing an entire flood plain. Afflux equations
have been proposed by D’Aubuisson (1840), Nagler (1917) and Yarnell (1934).
• Embankment bridges, which are flow contractions usually situated in urban areas crossing the
main flow channel. Afflux equations have been proposed by Kindsvater et al. (1953), and
Bradley (1978) proposed equations for Embankment bridges with and without piers.
• Arched bridges, which are usually multiple arched in rural areas and sometimes single arched in
urban areas. Afflux equations have been proposed by Biery and Delleur (1962) and HR
Wallingford (1988).
There are several methods published in classical hydraulic textbooks for calculating the afflux at
culverts of simple geometry (for example, Henderson, 1966, Chow, 1973, French, 1986). More
recently, these hand calculation methods have been updated in the form of culvert design manuals
(FHWA, 2001, CIRIA, 1997).
All of the above methods are too complex for rapidly producing a desired rating curve (water
surface elevation versus flow discharge) upstream of the structure at the afflux location. They have
therefore become incorporated into recent computer codes which model both the stream and
structure hydraulics. Table 1-1 provides a summary of afflux methods in the one-dimensional (1D)
models used by the Environment Agency.
The scoping study carried out prior to this research showed that there has often been confusion
over the choice of method for modelling afflux. It was apparent that a full 1D code must be enabled
before an afflux rating curve may be estimated, and several different codes must be run to estimate
the degree of uncertainty for this rating curve. For this reason, a simple and rapid Afflux Advisor
(AA) was developed for use with uniform flows and several types of bridge and culvert structures.
The AA provides a bridge or culvert afflux rating curve together with an estimate for the uncertainty
of the curve.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
2
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Table 1-1: Afflux methods which appear in models commonly used by the EA
HEC-RAS
ISIS
MIKE 11
Yarnell (1934)
Bradley (1978) - USBPR
D’Aubuisson (1840)
Schneider (1977)- WSPRO
HR, Wallingford (1988)
Nagler (1917)
Energy method
ISIS Energy method
Yarnell (1934)
Momentum method
High flow methods
Bradley (1978) - USBPR
High flow methods
Culvert methods
Schneider et al. (1977) - WSPRO
Culvert methods
Biery and Delleur (1962)
HR Wallingford (1988)
High flow methods
Culvert methods
1.4
What is in the Afflux Advisor?
The Afflux Advisor is a Microsoft Excel project coded in Visual Basic for Applications (VBA). It works
with Microsoft Excel 97 and later versions. The Afflux Advisor consists principally of three
applications as follows:
• River Application, in which a single stream geometrical section (up to 30 coordinates) and
bedslope (or friction slope) are entered together with known coordinates (up to 12 coordinates,
if available) of the stream rating curve. The river rating curve is computed upon data entry and
may be visually calibrated for channel and floodplain friction, if flow gaugings are available.
Otherwise, the friction may be estimated using a design table. If flow gauging data is available,
the energy slope may be further calibrated as the friction slope for flows that are not normal.
• Bridge Application, in which one of four bridge types may be selected (namely an arch,
multiple arch, beam or piered-beam bridge). A data entry table is then accessed to enter the
bridge abutment type, springer elevation, soffit elevation, road elevation and bridge span (five
parameters). The bridge afflux rating curve with uncertainty is computed upon data entry, and
this may be interpolated for particular design discharge magnitudes. The application includes
code to adjust the rating curve for skew and eccentricity.
• Culvert Application, in which one of four culvert types may be selected, namely a pipe, box,
arch or multiple-barrel (pipe, box or arch) culvert. A data entry table is then accessed to enter
the culvert barrel roughness description, span, rise, length, inlet shape, inlet material, inlet type,
inlet edge type, outlet invert elevation and road elevation (10 parameters). The culvert afflux
rating curve with uncertainty is computed upon data entry, and this may be interpolated for any
particular design discharge.
The Afflux Advisor computes afflux for all elevations within the stream section entered in the River
Application. This includes both sub-soffit and super-soffit flows for bridges, and under road and
above road flows for culverts. Calculation of the sub-soffit bridge flows utilises both the USBPR
(1978) and the HRC (2004) methods (the latter method is a new development of the HR Wallingford
(1988) method, and is applicable for compound channels.) Calculation of the under road culvert
flows utilises the CIRIA (1997) and FHWA (2001) methods for analysis. When flow overtops the
bridge or culvert then the Afflux Advisor uses the USBPR (1978) modular and non modular weir flow
model, with iteration for the contemporaneous flows through the structure.
When to use the Bridge Application and when to use the Culvert Application
For simplicity, a structure can be defined as a culvert rather than a bridge if the ratio of its
streamwise length to the height of its opening is greater than about 5, or the opening width (or
span) is less than about 2m. A short structure that is at the arbitrary size limit of 2m span may be
modelled by either application.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
3
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
1.5
What are the limitations of Afflux Advisor?
The AA has been designed towards simplicity in use. There are therefore some limitations; the
major ones are listed as follows:
• The River Application assumes a subcritical, normal flow in a natural channel of uniform cross
section. For such a case, the energy slope is taken as that of its bedslope. For subcritical
cases where the flow is not normal and therefore gradually varied, the energy slope may be
approximated by the average friction slope of the channel. This may occur, for example, if the
water level downstream of a bridge is subject to backwater from a control further downstream.
(The average friction slope may be estimated in Afflux Advisor by visually calibrating the river
rating curve with any known rating curve data.)
• The bridge and culvert types used in Afflux Advisor have been chosen to represent those
commonly found in the UK.
• Multiple arched and piered bridges are simply modelled as single, composite bridges with
reduced openings. The Afflux Advisor therefore becomes inaccurate for such structures that
extend across the entire floodplain.
• The Bridge Application assumes a horizontal roadway (i.e. overtopping level) across the bridge
that extends for the physical limit of the river cross section. The Afflux Advisor is therefore only
approximate for extreme flows where there is an arched roadway crossing or adjacent bridge
approach roadways.
• Although the River Application has two dimensional data (offset and elevation), the code is
principally a one dimensional model. The Afflux Advisor cannot therefore estimate two
dimensional effects such as varied water levels across a river cross section that are caused by,
say, a skewed bridge or floodplain flow to the main channel.
• The Afflux Advisor does not explicitly model the effects of structural blockage by sedimented or
floating debris. These effects may however be simulated in Afflux Advisor by decreasing the
height or span (as relevant) of the structure’s opening area.
• The River Application code consists of about seven subroutines, including an estimate for
uncertainty. The Bridge application models nine modes of flow at a structure for four bridge
types; it therefore contains 36 core algorithms. The culvert application computes eight modes
of flow at a structure for four culvert types; it therefore contains 32 core algorithms. It is
possible that this first version of Afflux Advisor might fail for certain untested structures. Users
are therefore requested to return a runfile of any failed examples to allow improvements to be
made.
1.6
What’s new about Afflux Advisor?
The Afflux Advisor includes a new model for bridge afflux, based on entirely new laboratory data
and a new analysis of existing field data. The analysis covers a wide range of hydraulic conditions
in a general model. The Afflux Advisor also includes a simplified analysis for culvert ratings,
synthesising existing methods. There is an estimate of uncertainty for both bridges and culverts.
The Afflux Advisor is innovative in all these respects. The background analysis is largely
transparent to the user. A brief summary of the research and data analysis is given in this manual;
further detailed progress notes have been prepared as part of the project record.
1.7
How does Afflux Advisor link with other related Defra/Environment Agency research?
The Afflux Advisor is the first of two planned software outputs from this project. The second
software application will be the ‘Afflux Estimator’. This will be a more detailed modelling tool, and
will be incorporated within the Conveyance Estimation System (CES), recently developed in a
related research project through the Engineering Theme of the Defra/Environment Agency research
programme. The Conveyance Estimation System calculates the relationships between flow, depth
and slope in a river channel and flood plain system, but not the effects of bridges or culverts.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
4
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Although the methods used to model river flow in the CES are more detailed than the methods in
the Afflux Advisor, this report makes use of data sets and test results produced using CES for
comparison purposes. =
1.8
How do I use this Afflux Advisor Manual?
This manual is comprised of four sections:
• Introduction, which is very brief yet sufficient for a user to begin using the Afflux Advisor as
described in the Worked Examples section.
• Technical Background, which describes the theory and algorithms used for the River, Bridge
and Culvert Applications. The development of the code for nine afflux flow modes through and
over a bridge and eight afflux modes through and over a culvert is detailed. This section is
relevant for a technical user.
• Testing the Afflux Advisor, which gives a detailed account of the methods used in testing the
Afflux Advisor using both field and other computer models. The interpretation of results is
described, and details of future possible options are listed. This section is for the general
reader.
• Worked Examples, in which the data entry for two river applications are demonstrated (the
River Main and River Dane; these are chosen from the Conveyance User Manual, CES 2004,
since they represent a fairly uniform river reach). Data entry and computation for all of the
bridge and culvert types are then demonstrated using uniform flow for the River Main.
The Afflux Advisor Manual is structured using a ‘Question and Answer’ approach. The manual is
also available in the Online Help of Afflux Advisor.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
5
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
This page is intentionally left blank.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
6
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
2
TECHNICAL BACKGROUND
2.1
The River application
2.1.1
What is the River application?
This application is a simple flow discharge estimator for a single stream cross-section with varied
flow depths. The depths are varied according to the smallest elevation of the side points of the
cross-section. This elevation is equally divided into 30 increments, and a rating curve (water
surface elevation versus flow discharge) is computed using Manning’s equation for uniform flow.
The flow cross section is divided into a main channel, left and right floodplains, and a Manning’s
friction coefficient may be assigned to each panel. The method is therefore similar to that used in
HEC-RAS (2004). Note however that river discharge is estimated in more detail by the Conveyance
Estimation System (CES, 2004).
2.1.2
How does the application compute a river rating curve?
Figure 2-1 illustrates a channel cross-section similar to that given in the Conveyance User Manual
(CESM, 2004) for the River Main in Northern Ireland. Eight offset-elevation points are used to draw
the geometry, and the cross-section may be vertically subdivided into seven areas for any of the 30
incremental depths from zero to 5.01 m. (The smaller of the cross section, side boundary
elevations is chosen as the limit). The wetted perimeter (P) and top width (T) are also assigned to
each of these areas.
Figure 2-1: Subdivision method of area (A) for the River Main
The locations of the left overbank (LOB) and right overbank (ROB) of the main channel (MC) are
entered in the application, and a Manning’s friction coefficient (n) is assigned to the left floodplain,
main channel and right floodplain. The friction coefficient may be derived from the CES, or from
tabulated values available in Afflux Advisor, as shown in Table A-1, in Appendix A of this report. In
addition, the average slope (S) for the channel must be entered.
The River application sums A, P and T for each of the sub areas at each flow depth, and computes
A, P and T for each of the left floodplain, main channel and right floodplain panels. Manning’s
equation is then used to compute the discharge for each flow panel as follows:
0.667
Q = (1/n) * A (A/P)
S
0.5
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
7
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Where n is the friction coefficient for each panel and S is the average bedslope (or friction slope) for
the stream. The stream or river rating curve is thus derived as the sum of the panel discharges
versus the flow elevations. Additionally, the kinetic energy coefficient (α) is computed for use in the
USBPR bridge afflux method as:
2
α = Σ Qi Vi / Σ Qi
Where the subscript i refers to each of the floodplain and main channel panels, and V is the
computed average panel velocity.
2.1.3
How is the uncertainty of the rating curve estimated?
The major uncertainty for estimating the flow discharge is that of the Manning’s n value. A plot of
the minimum and maximum n values from Table A-1 is shown in Figure 2-2. The minimum n values
for both natural streams and floodplains are close; they approximate to about 0.73 of the normal
value. Likewise, the maximum n values approximate to about 1.37 of the normal value.
Since the flow discharge (Q) is inversely proportional to n, a maximum n value will give a minimum
discharge of about 0.63Q, and a minimum n value will give a maximum discharge of about 1.27Q.
The discharge uncertainty for a rating curve may thus be estimated using this roughness coefficient
error. To find the uncertainty of elevation for these discharges, the mean rating curve was linearly
interpolated between each depth increment. The elevation uncertainty for a given mean discharge
can then be plotted as an envelope around the river rating curve; this is done in Afflux Advisor.
Figure 2-2: Minimum and maximum Manning’s n values as a function of ‘normal’ values
2.2
The Bridge Application
2.2.1
What is the Bridge application?
This application computes a rating curve for four bridge types that are typical in the UK (Figure 2-3).
These are arch, multiple arch, beam and piered beam bridges. Arches are modelled as parabolic
curves throughout. For simplicity, the multiple arch and piered beam bridge are modelled by
reducing the bridge opening to that of a single composite bridge.
The cross section at which the rating is located is the position of afflux (or maximum backwater), as
illustrated in Figure 1-1. This new rating curve is called the bridge rating curve, and afflux may be
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
8
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
interpolated for different discharges by subtracting the river rating for that discharge. The
subtraction of the total bridge rating curve from the river rating curve is therefore called the afflux
rating curve.
Road
elevation
Soffit
elevation
Water
level
Span
Road
elevation
Soffit
elevation
Springer
elevation
Water
level
Span
Span
Springer
elevation
+
Combined span
Datum
Datum
Arch
Road
elevation
Soffit
elevation
Water
level
Datum
Multiple Arch
Road
elevation
Soffit
elevation
Water
level
Span
Pier width
Span
Datum
Beam
Piered Beam
Figure 2-3: Bridge types included in Afflux Advisor
2.2.2
What methods are used to compute afflux?
In Phase 1 of this Research study (JBA, 2004), several methods were recommended towards
calculating afflux at bridges using hand or spreadsheet calculation (Table 2-1). These methods
have now been reduced to the HR, 1988 method (Brown, 1988) adapted for compound channels
herein (called the HRC, 2004 method), and the USBPR (1978) method. Both of these methods are
applicable to both arch and beam bridges, and are derived from a similarity model of the physical
process. They are for use with sub-soffit flows (flows beneath a bridge opening). For super-soffit
flows (flows above overtopping level), the USBPR (1978) methods were used since they are also
used in recent codes such as WSPRO (1986) and HEC-RAS (2004).
The HRC method uses a small velocity scale relevant to the undisturbed flow without a structure,
whereas the USBPR method uses a larger velocity scale relevant to the contracted flow through the
bridge structure. It is therefore expected that the USBPR method will give higher estimates than
the HRC method, especially when exponents of the velocity enter the equations. For this reason, a
mean value is used in AA, and each method is considered as a limit of uncertainty.
Table 2-1: Recommended methods for hand/spreadsheet calculation or 1D modelling
Class
Methods
Pier bridges
Yarnell (1934)
Embankment bridges
Kindsvater (1953) - USGS
Arched bridges
HR, Wallingford (1988)
High flow methods
Orifice flow (USBPR, 1978)
USBPR (1978)
Weir flow (USBPR, 1978)
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
9
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
The two remaining methods in Table 2-1 were eliminated for the following reasons:
• The Yarnell (1934) method applies uniquely to momentum losses at bridge piers in rectangular
channels (that is, piered beam bridges) and cannot therefore be used for embankment beam
bridges without piers (with large abutments) and arch bridges in compound channels.
• The Kindsvater (1953) method applies uniquely to embankment bridges (that is, flow through
contractions), and cannot be used for beam (with piers) and arch (and multiple arch) bridges.
2.2.3
How does afflux vary with flow depth?
A least nine modes of flow may occur through a bridge structure, depending on the flow depth at
the bridge. This requires at least nine types of afflux calculation. The modes are described below
and illustrated in Figure 2-4.
Mode
9
8
Water level
Flood
Bridge flow
Flow
Flooded
Actual
Submerged
Actual
7
Normal
6
Actual
Weir and
orifice
BRIDGE
Actual
Orifice
5
Normal
Sluice
Actual
4
Normal
Subcritical
Critical
Actual
2/3
Normal
Critical (with/
without jump)
Critical
Critical
1
Supercritical
Actual
Upstream
River bed
Downstream
Gap between arrowheads
represents the afflux
Figure 2-4: Nine afflux modes through a bridge structure (modes 1 to 4 are sub-soffit, modes 5 to 9
are super-soffit)
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
10
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
The modes are generally subdivided as sub-soffit flows (‘low flow’ is the term used in US textbooks
and software such as HEC-RAS) and super-soffit flows (‘high flow’ is used in HEC-RAS). For the
case where a bridge deck has an underlying girder, the soffit is taken as the elevation at the bottom
of this girder. And for the case where a bridge deck has an overlying parapet, the ‘road’ elevation is
taken as that at the top of the parapet. (These overtopping elevations may also be called the relief
elevation.)
Sub-soffit modes
The following sub-soffit modes may occur in order of increasing water level at the bridge structure:
• Mode 1: Supercritical flow occurs when the upstream Froude number (F) is greater than unity.
(It is named Class C flow in HEC-RAS, 1995). Since F = velocity / (gravitational acceleration *
0.5
flow depth) , supercritical flow occurs at shallow flow depths on steep slopes. For this flow,
the afflux is theoretically zero since no backwater can exist. There will however be a local
bridge energy loss due to form drag. The AA first computes the Froude number rating, and if
F ≥ 1 then the afflux is set to zero.
• Modes 2 and 3: When critical flow occurs at the structure, the flow is said to be choked. This
is because critical flow is a condition of minimum energy at constant discharge, and any
increase in potential energy upstream will increase the upstream water level but not increase
the critical flow level. This may occur, for example, when the bridge entry becomes partially
blocked by debris. The critical flow may change gradually downstream (Mode 2), or rapidly
(Mode 3 as a hydraulic jump). The choking condition is not included in AA for simplicity. (It is
modelled in HEC-RAS as a Class B flow).
• Mode 4: The flow throughout is subcritical. (It is named Class A flow in HEC-RAS). This is the
appropriate condition for the HRC and USBPR similarity methods.
Super-soffit modes
The following super-soffit modes may occur in order of increasing water level at the bridge
structure, and are derived from USBPR (1978); they are common to WSPRO (1986) and HEC-RAS
(2004):
• Mode 5: Sluice gate flow occurs when the upstream water level is greater than the soffit depth
and the downstream soffit level is unsubmerged. The upstream soffit is effectively acting as a
sluice gate, and associated sluice gate equations are used.
• Mode 6: When the downstream soffit level is submerged, the flow under the bridge becomes
fully pressurised. Since the distance between upstream and downstream faces is usually much
less than the soffit depth, the pressurised flow acts more like a submerged orifice than a closed
conduit. The flow is therefore described by orifice flow equations.
• Mode 7: Once the upstream water level is above the road or parapet, a weir flow will ensue. If
the weir flow submergence (downstream water level above road level divided by upstream
water level above road level) is less than about 85%, then the weir flow is modular, and its
discharge coefficient is determinable (Ackers et al., 1978). Note that pressure flow is still
occurring beneath the bridge (provided it is not totally obstructed), and this is calculated in the
AA computations using an iterative procedure.
• Mode 8: As the downstream flow level increases, the weir becomes submerged and the flow
becomes a non-modular weir flow. This occurs for a submergence of between 85% and 95%,
and the discharge coefficient is accordingly reduced. Note that flow is still occurring beneath
the bridge (provided it is not totally obstructed), and this is calculated in the AA using an
iterative procedure.
• Mode 9: When a submergence of about 95% is reached, the weir is drowned and the mode
returns to that of uniform river flow. Inevitably, the friction for this condition will increase above
that for the undisturbed stream (due to the presence of the drowned structure), but this is
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
11
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
neglected in the AA computation. Note that flow is still occurring beneath the bridge (provided it
is not totally obstructed), and this is calculated in the AA using an iterative procedure.
In summary, AA first checks for Mode 1, omits Modes 2 and 3 and computes the remaining six
modes. A summary of the above computational limits for each mode is given in Table 2-2.
Table 2-2: Computational limits for bridge modes of flow
Afflux
mode
Bridge flow
Start condition
Finish condition
Constraints
1
Critical
F>1
F<1
dh = 0
4
Subcritical
F<1
y+dh > ySF
M > 0.1
5
Sluice gate
y+dh > ySF
Cd ≥ 0.5
Yd < ySF
6
Orifice
Cd > 0.5 ; y+dh > ySF
Yu > yRD
Yd > ySF
7
Weir and orifice
Yu > yRD
S > 0.85
Iterated flow
8
Submerged weir
and orifice
Drowned weir and
orifice
S > 0.85
S ≥ 0.95
Iterated flow
9
hÉóW=
F
dh
Y
ySF
M
2.2.4
S > 0.95
Cd
yRD
Yu
Yd
S
Q
Froude number
Afflux
Normal depth
Soffit elevation
Opening ratio
Maximum river
Iterated flow
elevation
Sluice gate discharge coefficient
Road elevation
Upstream flow depth for super-soffit flow
Downstream flow depth for super-soffit flow
Submergence
Total flow discharge
How is the sub-soffit Mode 4 computed?
The HRC and USBPR methods are computed separately in AA, since there are no common
variables i.e. they use different length and velocity scales for the same physics. Note that the
original nomenclature for each method is used here. The HRC method is the simplest and most
direct method, and is described first.
HRC (2004) sub-soffit method
The HRC method uses the HR Wallingford (Brown, 1988) similarity method to analyse a recent
laboratory data series from the University of Birmingham and also field data from rivers with wide,
vegetated floodplains (USGS, 1978). The HR (1988) method involves expressing bridge afflux (dh) in
dimensionless terms as follows:
dh/D3 = f (F3, J3)
where D3 is the normal flow depth without the presence of the structure (Figure 1-1), F3 is the
Froude number of the flow without the presence of the structure, and J3 is a blockage ratio to the
flow caused by the structure, and is given by the quotient:
J3 = flow area blocked by downstream bridge section ÷ total flow area in the undisturbed channel
a~í~ ~å~äóëáë
Two recent series of laboratory experiments concerned with the measurement of bridge afflux have
been conducted at the University of Birmingham (UB) using a compound channel (Atabay and
Knight, 2002, Seckin et al., 2004). In the first series, a total of 145 afflux measurements were made
for bridge types of single semi-circular openings (20 experiments, designated ASOSC), multiple
semi-circular openings (15 experiments, designated AMOSC), single elliptical openings (15
experiments, designated ASOE), straight deck beam bridges without piers (45 experiments,
designated BEAM) and with piers (50 experiments, designated BEAMP). All bridges were located
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
12
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
normal to the flow direction, and five cases of bed roughness (designated Case 1, Case 2, Case 3,
Case 4 and Case 5) were used. The experimental data set is summarised in Table 2-3.
Table 2-3: Summary of University of Birmingham afflux data and dynamic similarity analysis
AMOSC
ASOE
ASOSC
BEAM
BEAMP
Total
Coefficient of
Determination
in HRC model
15
42
52
57
37
15
42
52
57
42
20
42
52
62
62
45
52
52
97
97
50
47
52
97
97
145
225
260
370
335
0.98
0.93
0.93
0.94
Number of experiments
Bridge Type
First series
Second series
Skew series
All series
Sub-soffit series
In the second series, a total of 225 afflux measurements were made for bridge types of single semicircular openings (42 experiments, designated ASOSC), multiple semi-circular openings (42
experiments, designated AMOSC), single elliptical openings (42 experiments, designated ASOE),
straight deck beam bridges without piers (52 experiments, designated BEAM) and with piers (47
experiments, designated BEAMP). This series was designed to test afflux magnitudes for a bridge
located at an angle to the flow direction (named a skew bridge, for which there were 180
experiments), and three cases of bed roughness (designated Test A, Test B and Test C) were used.
Note that the Test A and Test B roughness conditions were the same as those of the Case 1 and
Case 2 roughness conditions used in the first series.
The data of the first series were analysed using the HR (1988) similarity model with quadratic
trending to give a unique correlation model with a 98% coefficient of determination. The data for
the second series was combined with some of the data of the first series which had the same
roughness conditions for normal flow incidence (Table 2-3, skew series), and was used to examine
the influence of skew on the similarity model. It was found that the skew bridge data could be
represented adequately by the same model provided the bridge opening width was simply reduced
by the cosine of the skew angle. (The coefficient of determination for model correlation reduced to
a value of 0.93, compared with 0.98 for the first series data.)
It followed from the above that a new similarity model could be derived from the entire first and
second series data set, with the skew variable represented by the reduced bridge opening width.
Subsequent analysis gave a unique correlation for all bridge types and all skew angles, with a
coefficient of determination of 0.93 (Table 2-3, all series). Further analysis indicated that some of
the data scatter was associated with increased afflux due to the flow submerging the bridge soffit.
The data was therefore reduced to all sub-soffit flows (Table 2-3, sub-soffit series), and the
coefficient of determination increased to 0.94. This final similarity equation can be used in design
for all bridge types at skew angles up to ~60°, and would give a statistical afflux estimate with a
95% confidence limit of about ±3%.
kÉï=Úeo`Û=ëáãáä~êáíó=ãçÇÉä=
The similarity equation with quadratic trending that was derived for AA is:
5
4
3
2
2
2
dh/D3 = (84.661J3 - 209.1J3 + 189.11J3 - 79.78J3 + 16.314J3)*F3 + (5.0498J3 2.2691J3)*F3
Figure 2-5 illustrates the data correlation for each bridge type and that for all types. It was noted
that the correlation is least accurate for low afflux values at which F3 < 0.25. A new correlation was
derived for this condition:
5
4
3
2
2
6
dh/D3 = (78.438J3 - 205.06J3 + 178.79J3 - 55.375J3 + 4.9695J3)*F3 + ( -84.452J3
5
4
3
2
+ 212.64J3 - 190.59J3 - 72.949J3 - 10.649 J3 - 0.4551 J3)*F3
=
Ñçê=cP=Y=MKOR
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
13
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
The USGS (1978) field data series consisted of 13 floods with detailed flow and river cross section
measurements. The data were modelled using HEC-RAS (2004) and the results are summarised in
Section 3, Table 3.3 of this manual. All of the data were for flows with F3 < 0.1, and a new
correlation for this data was prepared as:
3
2
dh/D3 = (4.6627J3 - 3.6975J3 + 2.3326J3) * F3
Ñçê=cP=Y=MKN
Since the data were derived from natural field conditions, the 67% confidence level was only about
12% of the measured values.
100
100
UB sub-soffit afflux data
90
80
70
60
50
AMOSC y = 0.9233x
R2= 0.91
40
ASOE
30
y = 0.9927x
R2 = 0.91
ASOSC y = 1.009x
20
BEAM
10
R2 = 0.95
y = 1.0282x
R2 = 0.95
BEAMP y = 1.0413x
R2 = 0.95
0
10
20 30 40 50 60 70 80
Measured afflux (mm)
90 100
Trended afflux (mm)
Trended afflux (mm)
80
0
UB sub-soffit afflux data
90
70
60
50
40
30
20
All bridge types
y = 1.009x
2
R = 0.94
10
0
0
10
20
30 40 50 60 70 80
Measured afflux (mm)
90 100
Figure 2-5: Correlation of University of Birmingham afflux data for sub-soffit flows
USBPR (1978) sub-soffit method
The first edition of the USBPR method (Bradley, 1960) was based on a large number of model
studies (Liu et al., 1957) and field data from 12 short, beam bridges. In 1970, the second edition of
the method was extended with field data from 43 beam bridges; this lead to improvements for the
design coefficients. This edition was later published electronically by the Federal Highway
Administration (FHWA), and has become known as the USBPR (1978) bridge afflux method. A brief
description of the method follows. Note that the nomenclature and cross section numbering are
not always the same as used earlier in this report.
The expression for afflux (h*1) upstream from a bridge which constricts the flow (Figure 2-6) is given
in terms of the USBPR nomenclature as:
2
2
2
2
h*1 = K*α2V n2/2g + α1[(An2/A4) – (An2/A1) ] V n2/2g
The expression may be considered as an initial estimate to which is added a kinetic energy
correction. The coefficient K* is a total backwater coefficient given by:
K* = Kb + ∆Kp + ∆Ke + ∆Ks
The variable K* represents the effect of the flow constriction (Kb); it is incremented with the effects
of pier type and number (∆Kp), bridge eccentricity (∆Ke) and skew (∆Ks). The parameters α1 and α2
are velocity coefficients defined below, An2 is the water area in the constriction below normal stage,
A4 is the water area at section 4 where normal stage is re-established, and A1 is the water area at
section 1 and includes the afflux.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
14
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Figure 2-6: Profile of a bridge constriction at the stream centreline (after USBPR, 1978)
The velocity coefficient, α is a weighting factor caused by the velocity distribution across a river
section; it is classically defined as:
2
α = ∑(qv )/QV
2
where v is the average velocity in a subsection of the river section, q is the discharge in the same
subsection, Q is the total river discharge and V is the average river velocity at the section. The
value α1 at section 1 (upstream of the bridge) can be computed by measurement at high flows, but
the value α2 at the bridge is not readily available. A field study by USBPR estimated α2 as a function
of α1 thus:
α2 = 1 - M + α1*M
where M is defined as a bridge opening ratio, and is expressed as the ratio of the flow which can
pass unimpeded through the bridge constriction (Qb) to the total river flow (M = Qb/Q). This α2
estimate is however considered as a guide only, and field measurements are recommended.
Since both K* and α2 are a function of M, the above afflux equation may be divided by the
downstream depth (y4) and written:
2
h*1/y4 = K*α2V n2/2gy4 ≈ f(M, Fr4)
where Fr4 is the Froude number at the downstream section. It is thus seen that the USBPR method
is the same type of equation as the three dimensional similarity method used for the HRC analysis.
The major difference between the methods is the different velocity scale. The choice of a velocity
scale is however arbitrary, since the velocity varies throughout the flow profile.
The base coefficient has greatest weight in the USBPR method; it is caused by the flow constriction
at a bridge (Figure 2-7). Note how the coefficient increases with the decrease in the opening
ratio, M.
The curves are also influenced by the shape of the abutment wingwalls as shown in the figure. This
abutment influence only occurs for small bridges less than about 60m in length however, since
abutment geometry only becomes important at this smaller scale. Table 2-4 enumerates the design
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
15
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
formulae represented by the three design base curves, and these were coded into AA. These
curves apply for normal sub-soffit flows to the bridge.
Figure 2-7: Base curve coefficient design curves (from USBPR, 1978)
Table 2-4: Base curve design formulae
Abutment type
Design formula
o
Kb = -1.9024Ln(M) - 0.043
30 Wingwall
o
Kb = -1.8007Ln(M) - 0.0662
All bridges with length > 60m
Kb = -1.5735Ln(M) - 0.0324
90 Wingwall
The USBPR pier type and skew coefficients were not used in AA, since the HRC method simply
reduced the bridge opening area for a given pier width and applied a cosine reduction for skew.
The same method was therefore used for the USBPR analysis. However, the USBPR eccentricity
coefficient was applied to both methods since no data were available for the HRC calibration.
Eccentricity (e) is defined using the ratio of the smaller bridge abutment length (x) and the larger
bridge abutment length (y) across the flow area. To indicate maximum eccentricity when the bridge
opening is at the channel side, this ratio is subtracted from unity. Thus eccentricity is equal to
1 - y/x. The eccentricity range is therefore from zero (for which abutment lengths are equal) to unity
(for which one abutment length is zero at the channel side). Note that afflux is only increased when
the eccentricity is greater than 0.8 or less than -0.8, and the following relation was derived from the
USBPR design curves:
2
2
∆Ke = 1.4540 + 0.6825M - 4.1436e - 0.1293M + 2.8688e - 0.6750Me
The straight deck, beam bridge laboratory data (Atabay and Knight, 2002) were compared with the
USBPR method for afflux calculation. It was found that the USBPR method could predict the afflux
to within about 7% of the laboratory data. This accuracy was of the same order of prediction
accuracy as the HRC method. AA was therefore coded to use both methods, and the mean value
from each method was used as the final afflux estimate.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
16
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Since it has been shown that the USBPR method provides systematically lower afflux estimates for
the USGS (1978) field data (Kaatz and James, 1997), only the HRC method was used in AA for
these field bridge types at low Froude numbers (F < 0.1).
2.2.5
How is the sluice gate Mode 5 computed?
Sluice gate flow begins at a bridge when the upstream water level reaches the soffit. A commonlyused sluice gate equation is given by USBPR (1978) as:
2
Q = CdbNZ [2g (Yu –Z/2 + α1V1 /2g) ]
0.5
where Q is the total discharge, bN the net width of waterway (excluding piers) and Yu the upstream
water depth above the mean river bed at the bridge (Figure 2-8).
The discharge coefficient (Cd) varies with the ratio Yu/Z, where Z is the soffit depth; it is computed
from Figure 2-8 as the relation:
4
3
2
Cd = -2.5 Yu/Z + 15.722 Yu/Z - 36.983 Yu/Z + 38.616 Yu/Z - 14.623
The sluice gate discharge equation is solved iteratively in AA for the upstream depth. The
downstream USBPR water depth (Y3) is also solved iteratively using Figure 2-8 and the Yu/Y3 curve.
Thus Y3 can be tested for submergence.
The flow mode is terminated when Cd exceeds 0.5 in the computation. At this stage, the orifice flow
computation begins (Mode 6).
2.2.6
How is the orifice Mode 6 computed?
Orifice flow begins at a bridge when both the upstream and downstream water levels are above the
soffit and finishes when the upstream water level reaches the road or parapet level. The orifice
equation in USBPR (1978) is given as:
0.5
Q = CdbNZ [2g∆h ]
where Q is the total discharge, bN the net width of waterway (excluding piers), Z is the water depth
at soffit level and ∆h is the difference in water surface elevation across the bridge (preferably
across the bridge embankments). From USBPR (1978) the discharge coefficient is approximately
constant at 0.8. The major uncertainty in the computation was thus the orifice coefficient error.
This equation is solved explicitly for ∆h in AA for the above start and finish conditions. A chart
given in USBPR (1978) was then used to estimate Yu. The chart is reproduced in Figure 2-9; it non
dimensionalises the depths using Ybar, the normal flow depth at the bridge.
2.2.7
How is the weir and orifice Mode 7 computed?
Weir flow begins at a bridge when the upstream water level is above the road or parapet level. The
standard weir flow equation is given as:
Q = CLH
1.5
where Q is the total discharge, C the discharge coefficient, L the road length across the bridge (the
span), and H the total head upstream measured above the road. Orifice flow through the bridge
occurs during weir flow, and AA iterates both the weir and orifice flow equations so that both
solutions provide the same upstream water level.
The major unknown variable in the weir equation is the weir coefficient C. The coefficient varies
according to the weir type (broad crested or rectangular) and increases with L. Values are
summarised in HEC-RAS (2004), and vary from about 1.5 to 1.7. In AA, the roadway length is taken
as the span of the bridge for simplicity, and no allowance is made for additional approach roadway
and embankment overtopping. The weir coefficient was therefore taken as 1.6 ±0.1, and the
associated uncertainty of about ±6% was called the weir error.
The modular weir flow coefficient is used until the submergence (the ratio of upstream and
downstream water levels above the overtopping level) exceeds 85%.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
17
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Figure 2-8: Discharge coefficient curve for sluice gate flow (from USBPR, 1978)
1.8
Yu
Ybar
1.6
y = 0.5595x2 + 0.4845x + 0.9938
R2 = 0.99
1.4
1.2
1
0.8
-0.2
0
0.2
0.4
0.6
0.8
∆h 1
Ybar
Figure 2-9: Chart for converting bridge headloss to upstream depth (from USBPR, 1978)
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
18
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
2.2.8
How is the submerged weir and orifice Mode 8 computed?
Submerged or non-modular weir flow begins for a submergence of 85% and ends at 95%. The
same weir flow equation and iterative method is used as for the modular flow, but the discharge
coefficient is reduced by a discharge reduction factor (DRF) as given in Figure 2-10.
1.2
1
DRF
0.8
0.6
y = -0.0025x2 + 0.429x - 17.422
0.4
R2 = 0.998
0.2
0
85
90
95
100
% Submergence
Figure 2-10: Discharge reduction factor (DRF) for submerged weir flow (from USBPR, 1978)
2.2.9
How is the drowned weir and orifice (flooded) Mode 9 computed?
The drowned (flooded) mode begins for a submergence that exceeds 95%, in accord with the
USBPR default. The flow now returns to the uniform flow condition. Although the river roughness
will increase with the submerged bridge obstruction, this is neglected as it is likely not to be
significant.
2.2.10 How is the uncertainty of the bridge rating curve estimated?
The sub-soffit and super-soffit estimates for afflux uncertainty differ. For sub-soffit flows, the limits
of uncertainty are taken as the HRC (lower) and USBPR (higher) estimates. These estimates usually
vary by a few percent, but can be higher for uncalibrated deep flows. For flows of low Froude
number (F < 0.1), the HRC method is used alone with a 12% error (67% confidence level) in afflux
elevation.
For super-soffit weir flows, the two major errors are the estimate of the weir coefficient (about 6%
of the flow discharge) and the contemporaneous orifice flow through the bridge. The major
uncertainty for the latter is the discharge coefficient. It is considered below that for culvert
hydraulics, the major uncertainty in computing culvert flows is the wall roughness error of about
8%. This value was therefore assigned to the bridge opening flow, giving a total super-soffit weir
flow error of about 14% in flow discharge. For simplicity, this 14% discharge error was also
assigned to the sluice and orifice modes. These discharge uncertainties were linearly interpolated
from the mean rating to give the elevation uncertainties. Note that the super-soffit uncertainties
were not applied to the drowned (flooded) flow mode, since the flow contained the original river
roughness error.
The uncertainty in water level elevation was finally computed as the addition of the afflux and river
uncertainties.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
19
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
2.3
The Culvert Application
2.3.1
What is the Culvert application?
This application computes a rating curve for three different culvert types, typical of UK
watercourses, namely pipe, box and arch culverts of uniform cross section (Figure 2-11). Multiple
identical culverts are also modelled. The flow is then divided by the number of culverts, and the
divided flow is applied to each culvert (note that the roadway length is also divided for overtopping
flows).
The cross section at which the rating is located is assumed to be the position of afflux (or maximum
backwater), as illustrated in Figure 1-1. This new rating curve is called the culvert rating curve, and
afflux may be interpolated for different discharges by subtracting the river rating for that discharge.
The subtraction of the total culvert rating curve from the river rating curve is the afflux rating curve.
Rise
Soffit Water
elevation level
Road
elevation
Span
Datum
Datum
Road
elevation
Span
Datum
Span
Pipe
Rise
Soffit
elevation
Road
elevation
Rise
Soffit
elevation
Road
elevation
Rise
Soffit
elevation
Springer
elevation
Arch
Box
Span
Datum
Multiple Box
Figure 2-11: Culvert types modelled in the Afflux Advisor
2.3.2
What methods are used to compute afflux?
In Phase 1 of this Research study (JBA, 2004), the CIRIA method was recommended for calculating
afflux at culverts using a spreadsheet application. The method is intended for hand calculation, and
is detailed in a publication entitled ‘Culvert design guide’ (CIRIA, 1997). The method is
supplemented herein with overtopping weir flows similar to the bridge afflux weir flows used in the
Bridge Application. The AA is thus relevant to the hydraulic performance of culvert structures for
unsubmerged and submerged flows. To better understand the methods used for unsubmerged
flows, a brief primer in culvert hydraulics follows.
In open channel hydraulics, there are 12 possible stable, water surface profiles for a given channel
geometry (Montes, 1998). These depend on five types of channel slope (horizontal (H), mild (M),
critical (C), steep (S) and adverse (A)) and three zones of controlling water depth, y (y > yn and yc
(1), y between yn and yc (2), y < yn and yc (3), where yn is the normal depth and yc the critical
depth). The profiles are abbreviated by slope letter and zone number as follows:
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
20
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
H2, H3; M1, M2, M3: C1, C3: S1, S2, S3: A2, A3
Six of the profiles are subcritical with y > yc (H2, M1, M2, C1, S1, A2) and the remainder are
supercritical. There therefore exists the possibility of at least 12 profiles in free culvert flow.
Culvert flow may be controlled by high friction at the inlet structure, or high friction at the outlet due
to a long barrel. If the inlet structure allows the least discharge for the same upstream energy as
applied to the outlet, then the culvert is under inlet control and the flow is usually supercritical. If
the culvert outlet allows the least discharge for the same upstream energy as applied to the inlet,
then the culvert is under outlet control and the flow is usually subcritical. Since the flow control
determines the computation of a water surface profile, it must therefore be first determined for both
free and full flow conditions.
The CIRIA (1997) procedure begins by calculating the inlet control energy using the FHWA (2001)
method. The latter estimates the inlet energy for either an unsubmerged or submerged inlet
condition. (Note that if both the inlet and outlet are submerged for inlet control, a hydraulic jump
and possible instability may occur in the culvert. This detail is ignored in AA for simplicity). The
CIRIA method then calculates the outlet control energy (for the same discharge) using the standard
step method for water profile analysis. The higher of these energies determine the control of the
culvert flow.
When the culvert outlet is nearly submerged under outlet control, the culvert flow becomes
equivalent to that of full conduit flow. The FHWA (2001) approximate backwater method is used
prior to tailwater submergence. The full flow hydraulic computations differ to that of free flow. And
when the culvert inlet water level reaches that of the road or overtopping level, the conditions of
modular weir flow, submerged and drowned weir flow occur sequentially with increased flow
elevation. The AA thus computes a total of eight flow modes, as detailed below.
The CIRIA (1997) procedure applies to culverts which are less than 100m in length, since UK
culverts of greater length are usually non uniform. However, AA will compute afflux for a uniform
culvert of any length. A minimum culvert rise or span of 0.45m is recommended to avoid blockage
(this limitation is coded in AA), and the design manual assumes that the culvert invert slope is equal
to the river channel slope.
2.3.3
How does afflux vary with flow depth?
Figure 2-12 illustrates that at least eight modes of flow may occur through a culvert structure, thus
requiring at least eight types of afflux calculation, summarised in Table 2-5. The modes are
subdivided into five below road flows (low flows) and three above road flows (high flows). All of the
modes depend on whether the culvert is in inlet or outlet control.
Table 2-5: Summary of eight culvert flow modes used in the Afflux Advisor
Mode
Control
Flow
Description
Profile
Method
1
Inlet
Supercritical
Unsubmerged
Usually S2
FHWA
2
Inlet
Supercritical
Submerged
Usually S2
FHWA
3
Outlet
Subcritical
Drawdown
H2, M2, or A2
Direct step
4
Outlet
Subcritical
Backwater
M1, C1, or S1
Direct step
5
Outlet
Subcritical
Full
Pressurised
Conduit
6
Road
Supercritical
Weir
Modular
USBPR (1978)
7
Road
Subcritical
Submerged weir
Non modular
USBPR (1978)
8
Channel
Subcritical
Drowned weir
Open channel
Open channel flow
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
21
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Figure 2-12: Eight flow modes for a culvert structure
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
22
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
The eight culvert flow modes computed in Afflux Advisor are described below.
Under-road (not overtopping) flow modes
• Mode 1: Unsubmerged inlet control condition. The high friction at the culvert entry causes a
high energy loss and water level fall. Flow may pass beneath the critical flow depth for the
culvert, but usually attains an S2 profile to normal depth downstream for a long culvert. This
profile is not modelled in AA since the FHWA (2001) equations enable the energy loss at the
inlet to be calculated directly.
• Mode 2: Submerged inlet control condition. The same comments as Mode 1 apply.
• Mode 3: Drawdown outlet control condition. The outlet water level is below the culvert normal
depth, and thus an H2, M2, or A2 drawdown profile is developed within the culvert to normal
depth upstream for a long culvert. In AA, the water surface profiles are computed using the
Direct Step method (Sturm, 2001). This method is used in HEC-RAS (2004), and is favoured
because it is faster than Standard Step method detailed by CIRIA (1997).
• Mode 4: Backwater outlet control condition. The outlet water level is above the culvert normal
depth, and thus an M1, C1, or S1 backwater curve is developed within the culvert to normal
depth upstream for a long culvert. The Direct Step method is used for computation of this
profile.
• Mode 5: Full flow outlet control condition. It has been empirically shown by FHWA (2001) that
when the outlet water level is greater than (dc + D) / 2 (where dc is the culvert critical depth and
D is the culvert height), the culvert friction loss is the same as if it were in full flow. This criterion
is therefore used as an outlet condition in AA if the associated outlet depth is less than D
and (dc + D) / 2. It is known as the backwater approximation.
Over-road (overtopping) flow modes
The following above road modes may occur in order of increasing water level at the culvert
structure, and are derived from USBPR (1978); they are common to WSPRO (1986) and HEC-RAS
(2004):
• Mode 6: Once the inlet water level is above the road a weir flow will ensue. If the weir flow
submergence (downstream water level above road level divided by upstream water level above
road level) is less than about 85%, then the weir flow is modular, and its discharge coefficient is
determinable (as for the bridge flow). Note that pressure flow is still occurring within the culvert
(provided it is not totally obstructed), and this is calculated for each discharge rating in the AA
computations using an iterative procedure.
• Mode 7: As the downstream flow level increases, the weir becomes submerged and the flow
becomes a non-modular weir flow. This is assumed to occur for submergence between 85%
and 95%, and the discharge coefficient is accordingly reduced (as for the bridge flow). Note
that pressure flow is still occurring within the culvert.
• Mode 8: When submergence of about 95% is reached, the weir is drowned and the mode
returns to that of uniform river flow. Inevitably, the friction for this condition will increase above
that for the undisturbed stream (due to the presence of the drowned structure), but this is
neglected in the AA computation. Note that pressure flow is still occurring within the culvert.
In summary the AA computes eight flow modes which include roadway overtopping, as opposed to
the five under road modes calculated in CIRIA (1997). Since the AA Bridge Application represents a
single upstream bridge section, the Culvert Application also computes afflux for a section upstream
of the culvert. The computation is however started downstream of the culvert (adjacent to the
outlet), and the river normal depth is used at this boundary condition.
2.3.4
How are the under-road Modes 1 to 5 computed?
The CIRIA (1997) design method for under road modes is summarised in Table 2-6 and the
nomenclature it uses is explained in Figure 2-13. For inlet control, the inlet structure design table
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
23
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
given in CIRIA (Table D1) was simplified for an Arch culvert by averaging the two given design
conditions (that is, the 450 mm and 790 mm corner radius conditions). This was done because the
design coefficients were similar for each corner radius condition. A pipe arch culvert may thus be
approximated in AA by using an arch culvert with a representative springer elevation. (The
simplified design table is reproduced in Table 4-1 of this report.)
2.3.5
How are the over road Modes 6 to 8 computed?
The design methods used for above road modes were the same as used in the Bridge Application.
The super-soffit bridge design methods of sluice gate and orifice flow were not used for culverts as
they are included in the FHWA (2001) inlet design equations. Note that the roadway (i.e.
overtopping level or ground level) in AA is assumed to be horizontal, and the overtopping length
along the road is taken as the length between points at the floodplain intersection. That is, the
effective weir crest length is the river channel width at the single roadway elevation.
Table 2-6: Summary of the CIRIA (1997) design method for culvert hydraulics
Symbol
Free flow
Full flow
Inlet control
HWLic
An inlet structure design table (Table 4-1) is used to calculate the headwater elevation under
inlet control.
Outlet control
yo
ho
The tailwater depth (TW) is calculated as the
normal depth for the downstream flow.
If TW > critical depth (yc) then yo = TW
Else yo = yc
The tailwater depth (TW) is calculated as the
normal depth for the downstream flow.
If TW > culvert height (D) then yo = TW
If TW<D and TW > (yc+D)/2 then yo=TW
Else yo = (yc+D)/2
The outlet headloss is calculated as the difference in velocity heads between the culvert barrel
and the downstream channel.
hb
yi
hi
The headloss due to culvert bends; it is omitted herein for simplicity.
The water depth at the culvert barrel entrance
The culvert friction headloss (hf) is calculated
is calculated by backwater analysis.
using Manning’s formula.
The inlet structure design table (Table 4-1) is used to calculate the inlet head loss.
hs
HWLoc
The headloss due to trash screens; it is omitted here for simplicity.
The headwater elevation under outlet control
is calculated as:
HWLoc = ILo + yi + hi
If HWLoc > HWLic then use outlet control, else
use inlet control.
The headwater elevation under outlet control
is calculated as:
HWLoc = ILo + yo + ho +hf + hi
If HWLoc > HWLic then use outlet control,
else use inlet control.
kçíÉëW=
1. Inlet control is computed for the entire discharge rating.
0.5
2. For inlet control, if the discharge ratio value 1.811Q/AD is between 3.5 and 4, then the HWLic rating
is linearly interpolated.
3. Free flow begins at the lowest flow elevation and ends when yi > ySF (where ySF is the soffit depth at
the culvert inlet).
4. For Full flow, if TW > D then yo = TW, else the FHWA (2001) approximate backwater assumption that
yo is the larger of (yc+D)/2 or TW is used.
5. The Full flow rating begins when free flow is ended.
6. The larger of HWLic and HWLoc for free and full flow at a particular discharge is the rating elevation
(HWL).
7. When HWL > RD the flow is computed sequentially as a modular weir, submerged weir and a
drowned weir, each with the appropriate inlet or outlet controlled culvert flow. The weir elevation is
computed iteratively since flow continues through the culvert.
8. Energy losses due to flow at culvert bends and at trash screens are omitted for simplicity.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
24
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Free flow
HWLoc = ILo + yi + hi
Road
Embankment
yi
Flow
D
yo
River bed
So
L
Culvert
ILi
ILo
Full flow
HWLoc = ILo + yo + ho + hf + hi
Road
Embankment
ho + hf + hi
HW
Flow
D
yo
River bed
So
L
Culvert
ILo
ILi
Figure 2-13: Nomenclature for culvert hydraulics
Legend for Figure 2-13
HWLoc
Headwater elevation under outlet
control
HWLic
Headwater elevation under inlet
control
HW
Headwater depth
TW
Tailwater depth
ILi
Invert elevation at barrel inlet
ILo
Invert elevation at barrel outlet
D
Barrel depth
yo
Design depth downstream of barrel
outlet
B
Barrel span
hi
Energy loss at culvert inlet
L
Barrel length
hf
Friction loss in barrel for full flow
So
Barrel bedslope
ho
Energy loss at culvert outlet
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
25
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
2.3.6
How is the uncertainty of the culvert rating curve estimated?
The major uncertainty for the under road modes is the culvert friction. Figure 2-14 illustrates the
minimum and maximum Mannings n roughness values for culverts (CIRIA, 1997, Table D2). It is
seen that the error about the normal value is about ±8 %. Although the FHWA (2001) inlet energy
curves used for Mode 1 and Mode 2 do not use Mannings n, the associated roughness error is
assumed to be the same.
Since the discharge (Q) is inversely proportional to Mannings n, the error in discharge (dQ) is given
for maximum roughness by dQ = -0.08Q, and for minimum roughness by dQ = 0.08Q. These error
increments were therefore applied to the under road, culvert rating curve and the associated values
of flow elevation solved by linear interpolation to give the roughness error.
The same uncertainties were used for over road flows as for the Bridge Application. Thus a 14%
discharge error was applied, and this was linearly interpolated to give the elevation uncertainty.
Note that the over road error was only applied for Mode 6 and Mode 7, since Mode 8 contained the
original river roughness error.
Minumum or maximum n in range
0.040
Minimum
0.035
Maximum
0.030
y = 1.0837x
R2 = 0.97
0.025
0.020
y = 0.9163x
R2 = 0.97
0.015
0.010
0.005
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
'Normal' value of n
Figure 2-14: Minimum and maximum culvert roughness against ‘normal’ roughness
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
26
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
3
TESTING AFFLUX ADVISOR
3.1
How was Afflux Advisor tested?
The River, Bridge and Culvert applications in Afflux Advisor were each tested using measured data
where possible. The tests were chosen to represent the extreme range of physical conditions
encountered for the UK. For the River Application, the rating curves were compared with ratings
from the ‘Conveyance Estimation System’ (CES, 2004). For structural cases where no measured
data were available, AA ratings were compared with ratings computed by the HEC-RAS code
(HEC-RAS, 2004).
The rating curve for the River Application was tested using measured data derived from the River
Main (a small river and floodplain in Northern Ireland) and the River Dane (a larger river and wide
floodplain in the Peak District). These data were for straight river reaches, and were detailed in the
Conveyance User Manual (CESM, 2004). After visual calibration of the channel friction, a close
correspondence with rating data was attained for each test. The AA rating was also compared with
the CES rating, and the levels of uncertainty were similar although small differences existed due to
the simplified AA estimate.
For the Bridge Application, very small bridge tests were made using the University of Birmingham
(UB) model bridge data for normal flows (Atabay and Knight, 2002). In contrast, large bridge tests
with wide and densely vegetated floodplains were made using the USGS Hydrologic Atlas data for
13 rivers in the southern US States (USGS, 1978). Both test series computed the measured afflux
data for sub-soffitt flows within the levels of uncertainty (note that the HRC algorithms were
calibrated using the same data). For super-soffit flows for which there was no data, AA was tested
against HEC-RAS models for the UB data, and a close correspondence was obtained since both
codes used the same afflux methods. The HR Wallingford data of Brown (1988) for model and field
arch bridges could not be directly tested with AA, since the data used the headloss at a structure
(see Figure 1-1) for estimating afflux.
Skewed bridges were tested using some of the UB data for bridge types at 30 and 45 degrees of
arc to the flow direction (Seckin et al., 2004). Since no bridge data were available for the USBPR
skewed bridge analysis (USBPR, 1978) the USBPR skewed bridge method was not used in AA.
Although the HRC skew algorithms were derived from the UB data, the uncertainty at the largest
skew (45 degrees) had an error of about 12%.
Shallow culverts were tested using the CIRIA worked example for a box culvert in free flow (CIRIA,
1997). Deep culverts were tested using the Defra/EA Benchmarking example for a deep culvert
(Crowder et al., 2004). Since these examples did not have measured field data, they were modelled
using HEC-RAS and the computed ratings were compared with AA. Close correspondence was
demonstrated for under road flows, but the over road ratings differed slightly. AA gave lower
ratings than HEC-RAS for over road flows of shallow culverts, and higher over road ratings for deep
culverts. Since these errors were similar to the AA uncertainty, the AA was considered satisfactory.
3.2
How was the River Application tested?
The River Main is a straight compound channel with some vegetation and substrate. The study
reach was reconstructed and realigned in the past to form a double trapezoidal channel cross
section (Figure 3-1). The main channel is a trapezoidal shape being 1m deep and about 12m wide,
and the floodplain is a trapezoidal shape being 4m deep and about 40m wide. The regularity of
this cross section produces a simple rating curve, and this is demonstrated in Figure 3-1. The latter
also compares the AA rating with the CES rating. The CES rating method has a more complex
friction distribution as illustrated in Table 3-1, and the method for the estimate of uncertainty differs
to that of the simplified AA method. Nevertheless, the uncertainties are comparable.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
27
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
The River Dane is a natural channel with wide floodplains. The study reach is straight and the main
channel is 4m deep and about 30m wide. The floodplain considered is a rectangular shape being
about 2m deep and about 500m wide (Figure 3-2). The large floodplain promotes energy losses
due to lateral shear and this is demonstrated in Figure 3-2 by comparing the AA rating with the CES
rating. Although the correspondence is close, the CES rating method is more accurate since it
includes a more complex friction distribution (Table 3-1) and the lateral shear. The upper
uncertainty estimates for this river are similar for AA and CES, but the lower uncertainty is smaller
for the CES rating. This is because the CES includes seasonal uncertainty in the roughness
estimate, and this may reduce the vegetation coefficient to zero. Nevertheless, the uncertainties
are comparable, especially at high flows.
Table 3-1: Manning’s friction coefficients used for estimating rating curves
River
Method
Left
overbank
Left
bank
Main
channel
Right
bank
Right
overbank
Main
AA
CES
0.046
0.046
N/A
0.045
0.028
0.025
N/A
0.045
0.046
0.046
Dane
AA
0.083
N/A
0.036
N/A
0.083
CES
0.083
0.151
0.036
0.151
0.083
Cross section
bank markers
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
6.0
Rating curves for the River Main
5.0
4.0
3.0
AA rating
2.0
AA uncertainty
CES rating
CES uncertainty
1.0
Gauged flow
0.0
0.0
100.0
200.0
Discharge
300.0
400.0
500.0
(m3s-1)
Figure 3-1: Comparison of rating curves using CES and AA for the River Main
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
28
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
18.0
bank markers
17.0
16.0
15.0
14.0
13.0
12.0
Cross section
100.0
0.0
100.0
200.0
300.0
400.0
18.0
Rating curves for the River Dane
17.0
16.0
15.0
AA rating
14.0
AA uncertainty
CES rating
CES uncertainty
13.0
Gauged flow
12.0
0.0
50.0
100.0
150.0
200.0
250.0
300.0
Discharge (m3s-1)
Figure 3-2: Comparison of rating curves using CES and AA for the River Dane
3.3
How was the Bridge Application tested?
For the Bridge Application, tests were made for very small bridges using the University of
Birmingham (UB) model bridge data for normal flows (Atabay and Knight, 2002). Skewed bridges
were tested using some of the UB data for bridge types at 30 and 45 degrees of arc to the flow
direction (Seckin et al., 2004). In contrast, tests for large bridges with wide and densely vegetated
floodplains were made using the USGS Hydrologic Atlas data for 13 rivers in the southern US
States (USGS, 1978). For super-soffit flows, for which there was no data, AA was tested against
HEC-RAS models for the UB data.
3.3.1
How were normal bridge flows tested with University of Birmingham data?
The University of Birmingham conducted a series of afflux measurements for model bridges in flows
normal to the bridge axis (UB, 2002, 2004, ibid). They were made for bridge types of single semicircular openings (20 experiments, designated ‘Arch’ in AA), multiple semi-circular openings (15
experiments, designated ‘Arches’ in AA), single elliptical openings (15 experiments, undesignated in
AA) and straight deck beam bridges without and with piers (110 experiments, designated ‘Beam’
and ‘Piered Beam’ in AA). The experiments were conducted for measurable afflux under five
channel roughness conditions and at five discharges for each bridge type. Table 3-2 summarises
the number of experiments available for testing in AA.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
29
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Table 3-2: Number of experimental discharges tested for normal bridge flows
nmc = 0.028 nmc = 0.029 nmc = 0.032
nfp = 0.047 nfp = 0.069 nfp = 0.080
Arch
5
5
Arches
5
Beam (Span = 0.398)
5
5
5
Beam (Span = 0.498)
5
5
5
Beam (Span = 0.598)
5
5
5
PBeam(Span = 0.398)
5
5
5
5
5
PBeam(Span = 0.498)
5
5
5
PBeam(Span = 0.598)
5
5
5
nmc = main channel friction, nfp = floodplain friction, PBeam = piered beam bridge, span in metres
Bridge Type
nmc = 0.010
nfp = 0.009
5
5
5
nmc = 0.015
nfp = 0.030
5
5
5
As detailed above, the River Application was first calibrated to give a rating curve for each
roughness condition. Note that although the Manning’s friction coefficient varied slightly in a
compound channel for a single physical roughness condition at each of the five discharges, an
average representative value was visually calibrated to be within the estimated river uncertainty
(Figure 3-3).
A typical set of results for the testing of the Arch bridge data is illustrated in Figure 3-4. The AA
Afflux and Water level comparisons are demonstrated to be close for both the measured data and
that computed using the HEC-RAS code. The latter computations were also used to compare the
super-soffit afflux estimates, and the HEC-RAS ratings were mainly within the AA estimates of
uncertainty. Similar results were obtained for all bridge types, and examples are illustrated in
Figures 3-5 to 3-7.
0.30
0.25
Soffit
Road (overtopping)
level
0.20
0.15
0.10
0.05
0.00
Cross section
0.0
0.2
0.4
0.6
Offset (m)
0.8
1.0
1.2
0.40
0.35
Rating curve
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.00
0.05
0.10
0.15
0.2
0.25
0.30
Discharge (m 3s-1)
0.35
0.40
0.45
0.50
Figure 3-3: River cross section, bridge sketch and river rating for the UB Arch bridge model,
main channel friction (nmc) = 0.010, floodplain friction (nfp) = 0.009
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
30
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Comparison of Afflux values between HECRAS and Afflux Advisor
Comparison of Water Surface Elevations
0.30
70
Road Level
Water Surface Elevation (m)
Computed Afflux using Afflux Advisor (mm)
Soffit level
0.25
60
50
40
AA (nmc=0.01, nfp=0.009)
30
HECRAS
AA (nmc=0.015, nfp=0.030)
HECRAS
20
0.20
0.15
HECRAS
0.10
Afflux Advisor
AA (nmc=0.028, nfp=0.047)
Springer level
0.05
HECRAS
AA (nmc=0.029, nfp=0.069)
10
HECRAS
0.00
0.00
0
0
10
20
30
40
50
60
0.05
0.10
70
0.15
0.20
0.25
0.30
Measured Water Surface Elevation (m)
Measured Afflux (mm)
Rating Curve with Bridge (nmc = 0.010, nfp = 0.009)
Rating Curve with Bridge (nmc = 0.015, nfp = 0.030)
0.60
0.80
Measured
Measured
0.70
HECRAS
0.50
River Rating
0.40
Road Level
0.30
Soffit Level
0.20
0.10
0.00
0.000
Water Surface Elevation (m)
Water Surface Elevation (m)
AA uncertainty
0.50
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
AA uncertainty
0.40
River Rating
Road Level
0.30
Soffit level
0.20
0.10
Springer level
0.050
HECRAS
Afflux Advisor
Afflux Advisor
0.60
Springer level
0.00
0.000
0.500
3
Discharge (m /s)
0.050
0.100
0.150
0.200
3
Discharge (m /s)
Rating Curve with Bridge (nmc = 0.028, nfp = 0.047)
Rating Curve with Bridge (nmc = 0.029, nfp = 0.069)
0.50
0.50
0.45
Measured
0.45
0.30
0.40
Afflux Advisor
AA uncertainty
River Rating
Road Level
0.25
Soffit level
0.20
0.15
Water Surface Elevation (m)
Water Surface Elevation (m)
0.35
Measured
HECRAS
HECRAS
0.40
0.35
0.30
Afflux Advisor
AA uncertainty
River Rating
Road Level
0.25
Soffit level
0.20
0.15
0.10
0.10
Springer level
Springer level
0.05
0.05
0.00
0.000
0.020
0.040
0.060
0.080
0.100
0.120
0.00
0.000
0.020
0.040
3
Discharge (m /s)
0.060
0.080
0.100
3
Discharge (m /s)
nmc = main channel friction, nfp = floodplain friction
Figure 3-4: Afflux and rating comparisons for the Arch bridge type
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
31
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Comparison of Afflux values between HECRAS and Afflux Advisor
Comparison of Water Surface Elevations
0.30
Road Level
0.25
60
Water Surface Elevation (m)
Computed Afflux using Afflux Advisor (mm)
70
50
40
30
20
AA (nmc=0.01, nfp=0.009)
HECRAS
AA (nmc=0.015, nfp=0.030)
HECRAS
AA nmc=0.028, nfp=0.047)
HECRAS_Case 3
10
10
20
30
40
50
Soffit level
0.15
HECRAS
0.10
Afflux Advisor
Springer level
0.05
0
0
0.20
60
70
0.00
0.00
0.05
0.10
Rating Curve with Bridge (nmc = 0.010, nfp = 0.009)
0.25
0.30
Rating Curve with Bridge (nmc = 0.015, nfp = 0.030)
Measured
Measured
0.70
HECRAS
0.50
Water Surface Elevation (m)
0.60
AA uncertainty
River Rating
0.50
0.40
Road Level
0.30
0.20
Soffit Level
0.10
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
Discharge (m3/s)
AA uncertainty
0.40
River Rating
Road Level
0.30
0.20
Soffit level
0.10
Springer level
0.050
HECRAS
Afflux Advisor
Afflux Advisor
Water Surface Elevation (m)
0.20
0.60
0.80
0.00
0.000
0.15
Measured Water Surface Elevation (m)
Measured Afflux (mm)
Springer level
0.500
0.00
0.000
0.050
0.100
0.150
0.200
3
Discharge (m /s)
Rating Curve with Bridge (nmc = 0.028, nfp = 0.047)
0.50
0.45
Measured
HECRAS
Water Surface Elevation (m)
0.40
0.35
0.30
Afflux Advisor
AA uncertainty
River Rating
Road Level
0.25
0.20
Soffit level
0.15
0.10
Springer level
0.05
0.00
0.000
0.020
0.040
0.060
0.080
0.100
0.120
Discharge (m3/s)
nmc = main channel friction, nfp = floodplain friction
Figure 3-5: Afflux and rating comparisons for the Multiple Arch bridge
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
32
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Comparison of all beam bridge Afflux values
Comparison of all beam bridge Water Surface Elevations
0.20
70
Afflux Advisor
50
40
0.16
HECRAS
Water Surface Elevation (m)
Computed Afflux using Afflux Advisor (mm)
0.18
AA (nmc=0.01, nfp=0.009)
HECRAS
AA (nmc=0.015, nfp =0.030)
HECRAS
AA (nms=0.028, nfp = 0.047)
HECRAS
AA (nmc=0.029, nfp-0.069)
HECRAS
AA (nmc=0.032, nfp=0.080)
HECRAS
60
30
20
0.14
0.12
0.10
0.08
0.06
0.04
10
0.02
0.00
0.00
0
0
10
20
30
40
50
60
70
0.02
0.04
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Rating Curve with Bridge (nmc = 0.029, nfp = 0.069, b=598mm)
Rating Curve with Bridge (nmc = 0.028, nfp = 0.047, b=598mm)
0.50
0.50
Measured
0.45
0.45
Measured
0.40
Afflux Advisor
HECRAS
HECRAS
0.40
Afflux Advisor
Water Surface Elevation (m)
Water Surface Elevation (m)
0.06
Measured Water Surface Elevation (m)
Measured Afflux (mm)
AA uncertainty
0.35
River Rating
0.30
Road level
0.25
0.20
Soffit Level
0.15
0.35
AA uncertainty
River Rating
0.30
Road level
0.25
0.20
Soffit Level
0.15
0.10
0.10
0.05
0.05
0.00
0.000
0.020
0.040
0.060
0.080
0.100
0.00
0.000
0.120
0.020
0.040
0.060
0.080
0.100
3
Discharge (m /s)
3
Discharge (m /s)
Rating Curve with Bridge (nmc = 0.032, nfp = 0.080, b=598mm)
0.50
0.45
Measured
0.40
Afflux Advisor
Water Surface Elevation (m)
HECRAS
AA uncertainty
0.35
River Rating
0.30
Road level
0.25
0.20
Soffit Level
0.15
0.10
0.05
0.00
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
0.090
0.100
3
Discharge (m /s)
nmc = main channel friction, nfp = floodplain friction
Figure 3-6: Afflux and water level comparisons for all Beam bridges, and afflux and rating comparisons for
the Beam bridge type of span 0.598 m.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
33
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Comparison of all piered beam Afflux values
Comparison of all piered beam Water Surface Elevations
0.20
70
50
40
Afflux Advisor
0.16
HECRAS
Water Surface Elevation (m)
Computed Afflux using Afflux Advisor (mm)
0.18
AA (nmc=0.010, nfp =0.009)
HECRAS
AA (nmc=0.015, npp=0.030)
HECRAS
AA (nmc=0.028, nfp=0.047)
HECRAS
AA (nmc=0.029, nfp=0.069)
HECRAS
AA (nmc=0.032, nfp=0.080)
HECRAS
60
30
20
0.14
0.12
0.10
0.08
0.06
0.04
10
0.02
0.00
0.00
0
0
10
20
30
40
50
60
70
0.02
0.04
0.08
0.10
0.12
0.14
0.16
0.18
Rating Curve with Bridge (nmc = 0.029, nfp = 0.069, b=598mm)
Rating Curve with Bridge (nmc = 0.028, nfp = 0.047, b=598mm)
0.50
0.50
0.45
Measured
HECRAS
0.45
0.40
Afflux Advisor
AA uncertainty
0.40
0.35
AA uncertainty
River Rating
0.30
Water Surface Elevation (m)
Water Surface Elevation (m)
0.06
Measured Water Surface Elevation (m)
Measured Afflux (mm)
Road level
0.25
Soffit Level
0.20
0.15
0.35
Measured
HECRAS
Afflux Advisor
AA uncertainty
AA uncertainty
River Rating
0.30
Road level
0.25
Soffit Level
0.20
0.15
0.10
0.10
0.05
0.05
0.00
0.000
0.020
0.040
0.060
0.080
0.100
0.00
0.000
0.120
0.020
0.040
0.060
0.080
0.100
3
Discharge (m /s)
Discharge (m3/s)
Rating Curve with Bridge (nmc = 0.032, nfp = 0.080, b=598mm)
Water Surface Elevation (m)
0.50
0.45
Measured
HECRAS
0.40
Afflux Advisor
AA uncertainty
0.35
AA uncertainty
River Rating
0.30
Road level
0.25
Soffit Level
0.20
0.15
0.10
0.05
0.00
0.000
0.010
0.020
0.030
0.040
0.050
0.060
0.070
0.080
0.090
0.100
Discharge (m3/s)
nmc = main channel friction, nfp = floodplain friction
Figure 3-7: Afflux and water level comparisons for all Piered Beam bridges, and afflux and rating
comparisons for the Piered Beam bridge type of span 0.598 m
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
34
0.20
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
3.3.2
How were skewed bridge flows tested with University of Birmingham data?
A skewed bridge has the normal direction to its axis aligned at an angle with the main flow
direction. This skew angle is measured in AA using degrees of arc. The increased afflux due to
skew was simply computed in AA by multiplying the bridge span with the cosine of the skew angle.
(This is the same method as used in HEC-RAS). Since the USBPR (1978) method provides no
measured data for skew analysis, it was not used for skewed bridges. And since the cosine of 10
degrees is 0.985, a skewed computation was arbitrarily started for skew angles greater than this
value.
The single Arch bridge type was used to test AA for the UB model skew data. Figure 3-8 shows
how the UB measured afflux increases with skew angle and discharge. This data was compared
with the AA afflux and water level data and fairly close correspondence was obtained. The 45
degree skew data was however significantly higher for AA, but since it fell at the lower level of
uncertainty (Figure 3-9) it was not corrected.
Q = 0.0382
Q = 0.0332
Q = 0.0297
Q = 0.0239
Q = 0.0210
Q = 0.0181
(m3s-1)
Skew angle (degrees)
Figure 3-8: Afflux versus skew angle and discharge, University of Birmingham data
3.3.3
How were eccentric bridge flows tested with University of Birmingham data?
The UB experiments have not yet been extended to eccentric bridge flows. The USBPR (1978)
method was used in AA, and it was checked manually against USBPR charts for verification.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
35
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Comparison between the experimental values and the Afflux Advisor values
Comparison of Water Surface Elevations
0.30
100
Road Level
0.25
Soffit level
80
Water Surface Elevation (m)
Computed Afflux using Afflux Advisor (mm)
90
70
60
50
40
Skew Angle = 0
30
0.20
0.15
Skew Angle = 0
0.10
Skew Angle = 30
Skew Angle = 30
Skew Angle = 45
Springer level
20
0.05
Skew Angle = 45
10
0
0
10
20
30
40
50
60
70
80
90
100
0.00
0.00
0.05
0.10
Rating Curve for Arch bridge (nmc = 0.010, nfp = 0.009, Skew angle = 0)
AA uncertainty
River Rating
Road Level
0.30
Soffit Level
0.20
0.10
0.00
0.000
0.050
0.100
0.150
0.200
Afflux Advisor
AA uncertainty
0.40
River Rating
Road Level
0.30
Soffit level
0.20
0.10
Springer level
Springer level
0.250
Discharge (m3/s)
0.00
0.000
0.050
0.100
0.150
0.200
3
Discharge (m /s)
Rating Curve for Arch bridge (nmc = 0.010, nfp = 0.009, Skew angle = 45)
0.60
Measured
Water Surface Elevation (m)
0.50
Afflux Advisor
AA uncertainty
0.40
River Rating
Road Level
0.30
Soffit level
0.20
0.10
0.00
0.000
0.30
Measured
0.50
Afflux Advisor
Water Surface Elevation (m)
Water Surface Elevation (m)
0.25
Rating Curve for Arch bridge (nmc = 0.010, nfp = 0.009, Skew angle = 30)
Measured
0.40
0.20
0.60
0.60
0.50
0.15
Measured Water Surface Elevation (m)
Measured Afflux (mm)
Springer level
0.050
0.100
0.150
0.200
0.250
Discharge (m3/s)
main channel friction, nmc = 0.010, floodplain friction, nfp = 0.009
Figure 3-9: Afflux and Rating comparisons for the Arch bridge type with skew
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
36
0.250
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
3.3.4
How were bridge flows tested with USGS field data?
Table 3-3 summarises the data used for the preparation of the algorithms used by the HRC (2004)
method for sub-soffit flows and for a Froude number less than 0.1 (see Section 2.2.4). The
algorithms were derived from HEC-RAS models of the field data. The model results were first
published by the US Hydrologic Engineering Center (HEC, 1995). The data were modelled again for
this study (results labelled JBA (2005) in Table 3-3). The mean computed afflux from the two sets of
models was used to derive the AA algorithms using the HRC dimensionless variables.
Table 3-3: Comparison of measured and AA afflux estimates for the USGS data
USGS ID and river
name
Flow
3 -1
(m s )
Bridge
Span
(m)
Floodplain
width
(m)
Opening Flow
Ratio depth
(m)
Modelled afflux
Afflux from
observed
(m)
WS – mean
modelled
eb`= g_^=
Mean
(m)
ENVVRF EOMMRF=
Afflux
Advisor
estimate
(m)
591 Bogue Chitto
708
230
1360
0.27
5.69
MKQT= MKPV= 0.43
0.32
0.43
591 Bogue Chitto
892
230
1360
0.26
5.95
MKRP= MKRR= 0.54
0.53
0.49
596 Okatoma Cr.
456
65
560
0.14
5.60
MKTV= MKUU= 0.84
0.76
0.68
603 Cypress Creek
42.5
40
240
0.40
2.38
MKNV= MKNT= 0.18
0.31
0.24
604 Flagon Bayou
134
70
480
0.21
4.94
MKMV= MKMN= 0.05
0.12
0.22
606 Tenmile Creek
181
160
640
0.42
4.51
MKNU= MKNU= 0.18
0.18
0.23
607 Buckhorn Cr.
118
80
280
0.26
2.91
MKPS= MKOP= 0.30
0.33
0.23
608 Pea Creek
50.4
78
340
0.41
2.19
MKOT= MKOS= 0.27
0.39
0.19
609 Poley Creek
53.8
62
400
0.25
2.16
MKOQ= MKPO= 0.28
0.33
0.25
609 Poley Creek
130
62
400
0.23
2.59
MKQR= MKPV= 0.42
0.50
0.40
610 Yellow River
56.6
78
400
0.29
1.93
MKNS= MKNQ= 0.15
0.16
0.12
600 Alexander Cr.
156
75
300
0.41
3.85
MKMR= MKMM=
N/A
0.30
N/A
600 Alexander Cr.
269
75
300
0.36
4.47
MKMU= MKMR=
N/A
0.27
N/A
Although these data sets exhibited non-uniform flows and scour, they were the only available field
data for use with AA. (Note that the Alexander Creek data could not be modelled using HEC-RAS
due to the flow being very non-uniform). The AA rating curves used the USGS recommended
friction values and the approach cross section upstream of the bridge. The energy slope was
visually calibrated with the available rating data and represented the average friction slope; it was
verified against the HEC-RAS models. In summary, AA assumed that the flows were uniform as
represented by the above conditions. Figure 3-10 illustrates a typical cross section and calibrated
river rating for the Bogue Chitto data. The bridge rating curve is also shown in Figure 3-10, and the
low weir flow due to the very wide floodplain is demonstrated.
Figure 3-11 summarises the comparison of AA afflux with measured afflux for these 11 data sets. A
reasonable correspondence was obtained for this varied field data, and the standard error for the
difference between measured and AA estimates was about 12% of the measured data. Since the
standard error approximately represents a 67% confidence level, the AA uncertainty for low Froude
number flows (< 0.1) was set at 12%. This value was comparable with the super-soffit bridge error
of about 14%.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
37
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Figure 3-10: Cross section plot, calibrated rating curve and Afflux Advisor bridge rating for the
Bogue Chitto
Afflux predicted by Afflux Advisor (m)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Measured afflux (m)
Figure 3-11: Comparison of ‘measured’ and Afflux Advisor afflux estimates for the USGS data
(see Table 3-3)
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
38
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
3.4
How was the Culvert Application tested?
Shallow culverts were tested using the CIRIA worked example for a box culvert in free flow (CIRIA,
1997). Deep culverts were tested using the DEFRA/EA Benchmarking example for a deep culvert
(Crowder et al., 2004). Since these examples did not have measured field data, they were modelled
using HEC-RAS and the computed ratings were compared with AA.
3.4.1
How were shallow culverts tested with the CIRIA example?
The CIRIA example for shallow culverts (CIRIA, 1997) used a small stream with a relatively large
culvert (Figure 3-12, top). The example gave data for stream bed slope and design flows, and the
remaining data were synthesised to provide a rating curve as illustrated in Figure 3-12. Although
the manual provided design data for box culverts only, the examples were extended to pipe, flat
based arch (equal springer and invert elevations) and twin box culvert types for the full testing of
AA. Since the CIRIA method involved manual calculation, testing of AA culvert ratings were made
by comparison with ratings derived using HEC-RAS. (Note that for simplicity, the AA twin barrel
type was tested against HEC-RAS for a single barrel type of similar span to the combined barrel
widths.)
Figure 3-12 illustrates the rating comparisons for the four culvert types. In general, the under road
flows for AA are slightly less than the ratings for HEC-RAS. However, the HEC-RAS ratings lie
within the upper limits of AA uncertainty. For the over road flows, it is apparent that AA reaches
95% submergence at lower flows than HEC-RAS. The submergence criteria used are the same for
both codes. However, the errors are maximum at over road flows, since both weir flow and full
culvert flow are being computed with iteration to give the same upstream water levels. Further
comments are made towards this difference in the light of deep culvert testing below.
3.4.2
How were deep culverts tested with the Defra/EA Benchmark example
The Defra/EA example for deep culverts (Crowder et al., 2004) used a deep stream with a relatively
small culvert (Figure 3-13, top). The example gave data for stream cross section, bed slope and
friction; it was designed for use with unsteady flows. It is adopted herein for steady flows, and the
cross section and rating curve are illustrated in Figure 3-13. The example was extended to pipe,
flat based arch (equal springer and invert elevations) and twin box culvert types for the full testing of
AA. The testing of AA culvert ratings were made by comparison with ratings derived using HECRAS. (Note that for simplicity, the AA twin barrel type was tested against HEC-RAS for a single
barrel type of similar span to the combined barrel widths.)
Figure 3-13 illustrates the rating comparisons for the four culvert types. In general, the under road
flows for AA are both higher and lower than the ratings for HEC-RAS. However, the HEC-RAS
ratings mainly lie within the limits of AA uncertainty. For the over road flows, the HEC-RAS ratings
are systematically lower than the AA ratings. The curvature of the over road ratings are however
similar. If uncertainty were included in the HEC-RAS estimates, then the estimates would overlap.
Since both shallow and deep culverts represent extreme examples and have shown small opposite
differences in AA to over road flows computed using HEC-RAS, the AA estimates were considered
satisfactory.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
39
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Cross Section Plot
30.50
Rating curve
31.50
Elevation: mAD
Elevation: mAD
30.50
29.50
28.50
Soffit
29.50
Road
Springer
27.50
28.50
26.50
27.50
25.50
26.50
Offset: m
24.50
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Rating curve for a shallow pipe culvert
30.5
Discharge: m3/s
25.50
0.00
5.00
10.00
15.00
20.00
25.00
30.00
Rating curve for a shallow box culvert
30.5
Elevation: mAD
Elevation: mAD
30.0
30.0
Culvert
29.5
HEC-RAS
29.0
28.5
Culvert
29.5
River
28.5
Road
River
HEC-RAS
29.0
Road
Soffit
Soffit
28.0
28.0
27.5
27.5
27.0
27.0
26.5
26.5
26.0
26.0
Discharge: m3/s
Discharge: m3/s
25.5
25.5
0
5
10
15
20
25
30
0
Rating curve for a shallow arch culvert
30.5
5
10
15
20
25
30
Rating curve for a shallow twin box culvert
30.5
Elevation: mAD
Elevation: mAD
30.0
30.0
Culvert
29.5
HEC-RAS
29.0
28.5
Culvert
29.5
River
29.0
28.5
Road
River
HEC-RAS
Road
Soffit
Soffit
28.0
28.0
27.5
27.5
27.0
27.0
26.5
26.5
26.0
26.0
Discharge: m3/s
25.5
0
5
10
15
20
25
30
Discharge: m3/s
25.5
0
5
10
15
20
25
30
Figure 3-12: Comparison of AA and HEC-RAS ratings for shallow culverts. (The blue line is the undisturbed
river rating, brown line is the culvert rating and black line is the HEC-RAS culvert rating).
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
40
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Rating curve
30.00
Elevation: mAD
Cross Section Plot
30.00
25.00
Elevation: mAD
25.00
20.00
20.00
15.00
15.00
Road
10.00
10.00
5.00
Discharge: m3/s
5.00
0.00
-1.0
-0.8
-0.6
-0.4
-0.2
Offset: m
Soffit
0.0
0.2
0.4
0.6
0.8
Elevation: mAD
30.00
50.00
60.00
Elevation: mAD
20
River
HEC-RAS
15
15
40.00
Culvert
River
HEC-RAS
20.00
Rating curve for a deep box culvert
25
Culvert
20
10.00
1.0
Rating curve for a deep pipe culvert
25
0.00
0.00
Road
Road
10
10
5
5
Sof fit
Soffit
Discharge: m3/s
Discharge: m3/s
0
0
0
10
20
30
40
50
Rating curve for a deep arch culvert
25
Elevation: mAD
0
60
15
30
40
Elevation: mAD
50
River
HEC-RAS
15
Road
10
60
Culvert
20
River
HEC-RAS
20
Rating curve for a deep twin box culvert
25
Culvert
20
10
Road
10
5
5
Soffit
Soffit
Discharge: m3/s
Discharge: m3/s
0
0
0
10
20
30
40
50
60
0
10
20
30
40
50
60
Figure 3-13: Comparison of AA and HEC-RAS ratings for deep culverts. (The blue line is the undisturbed river
rating, brown line is the culvert rating and black line is the HEC-RAS culvert rating).
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
41
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
This page left intentionally blank.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
42
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
4
WORKED EXAMPLES
This section provides worked examples for each of the River, Bridge and Culvert applications.
When the AA runfile (named Afflux Advisor.xls) is activated, the code is loaded with the River Main
data and Bridge and Culvert examples for use in the following exercises. The user may edit any of
this data, and the following examples describe:
•
•
•
Changing the River application from the River Main to the River Dane;
Changing the Bridge application for bridge dimensions and types whilst observing the
physical limits for computation;
Changing the Culvert application for culvert dimensions and types whilst observing the
physical limits for computation.
The intention of this section is that a user may proceed directly from the ‘Introduction’ of this
manual to using Afflux Advisor. All help information is given as comments at the relevant data cells
in the applications, and this manual is included on the main Excel menu for immediate reference.
4.1
Worked example for the River Application
4.1.1
The River Application worksheet
Afflux Advisor opens at the River Application. Data for the River Main (CESM, 2004) has been
entered, and the river cross section plot and rating curve appear as in Figure 4-1. There are five
user entry panels (marked 1 through 5) which are superimposed on Figure 4-1 in red. The data
required for each are as follows:
1. The offset-elevation pairs which describe the channel cross section. These may be entered
manually, or pasted from any other Windows application. (Note that specific positions for the
bridge and culvert cross sections are given in the comments section of the Elevation worksheet
cell. These positions may be relaxed if the total reduction in floodplain width caused by the two
bridge or culvert approach embankments is small. For such a case, only a cross section near
the upstream and downstream limits of the structure need be used for the bridge and culvert
respectively.)
2. The left and right overbank offsets (Left OB and Right OB), which represent the lateral extent of
the main channel. These are entered from an Excel combination box control which lists the
cross section offsets. Both the left and right OB data must be entered before the positions are
plotted on the cross section plot as red points.
3. The Manning’s roughness rating coefficients for the left OB, main channel and right OB, and the
average channel bedslope (or friction slope if the flow is not normal). A table of roughness
values is available by activating the Roughness Rating command button, if no data are
available. Data may be entered manually with any number of decimal places, or changed using
the spin buttons provided.
4. Measured flow-elevation data which may be used to visually calibrate the rating curve that has
been derived from the roughness rating data. These flow-elevation data may be entered
manually, or pasted from any other Windows application.
5. Command controls that:
•
•
•
•
Clear a structure sketch that is superimposed on the cross-section plot when the afflux
code is run. (This is for use when entering new river data),
Access river data that is stored on a separate worksheet (Figure 4-2). The latter contains
data for the River Main and River Dane at present, but may be supplemented with user
data,
Access the Bridge Application,
Access the Culvert Application.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
43
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Afflux Advisor - River Application
Offset Elevation
Overbank Offset
0
5.01
Left OB 13.50
5.3
1.41
Right OB 27.60
13.5
0.92
14.4
0 Roughness Rating
26.6
0 Channel
0.028
27.6
0.97
Left OB
0.046
35.7
1.38 Right OB
0.046
40.8
5.04 Bedslope
0.0019
2
3
1
Data Rating
Flow
Elevation
0
0
8.1
0.6
19.9
1.05
41.4
1.47
57.9
1.8
Elevation: mAD
Cross Section Plot
6.00
5.00
4.00
3.00
2.00
1.00
Offset: m
0.00
0.0
6.00
5.0
10.0
15.0
20.0
Elevation: MAD
25.0
30.0
35.0
40.0
45.0
Rating curve
5.00
4
4.00
3.00
2.00
Select
Clear Structure
River Data
Bridge
Culvert
1.00
3
Discharge: m /s
0.00
0.00
5
28
46
50.00
46
100.00
150.00
200.00
250.00
300.00
350.00
400.00
450.00
500.00
19
Figure 4-1: River application worksheet
Afflux Advisor - River Dane
Afflux Advisor - River Main
Offset
Elevation Overbank Offset
-145
17.5 Left OverBank
12
-145
17 Right OverBank
38
4.5
16.19
12
16.19 Roughness Rating
15
15.28 Channel
0.036
16
14.25
Left OB
0.083
17
13.51 Right OB
0.083
18
13.45 Bedslope
0.0005
19
12.47
24
12.04
Data Rating
28
12.29 Flow
Elevation
30
13.44
0
12.04
32
14.76
20.2
14.19
34
15.1
107.64
16.66
38
16.76
45.5
16.76
388
16.4
388
17.5
Offset
0
5.3
13.5
14.4
26.6
27.6
35.7
40.8
Elevation
5.01
1.41
0.92
0
0
0.97
1.38
5.04
River
Overbank Offset
Left OB
Right OB
13.5
27.6
Roughness Rating
Channel
Left OB
Right OB
Bedslope
Data Rating
Flow
0
8.1
19.9
41.4
57.9
0.028
0.046
0.046
0.0019
Elevation
0
0.6
1.05
1.47
1.8
Figure 4-2: River Data worksheet
4.1.2
Changing the River Application from the River Main to the River Dane
For this example, the rivers are changed using the River Dane data located in the River Data
worksheet (Figure 4-2). The following steps may be used:
1. If a structure sketch has been drawn on the cross section plot from a previous example, clear
this sketch first by activating the Clear Structure command button.
2. Copy the 30 lines of offset-elevation pairs from the River Data worksheet, and paste into the
river application. (Use the right mouse button for copying and pasting.)
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
44
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
3. Copy the 13 lines of flow-elevation pairs from the River Data worksheet, and paste into the river
application.
4. Enter the left and right overbank offsets using the combination boxes. It is only when the right
overbank offset is entered that the offsets are plotted.
5. Enter the roughness coefficients and bedslope manually, and allow the code to run to
completion before each entry. This may take several seconds since the code is writing data to
other worksheets for manual checking.
6. The spin buttons may now be used to calibrate the rating curve to the data rating points, so
that the two match up visually. If there are no data rating points, then the rating curve cannot
be calibrated in this way, but Afflux Advisor will still run.
4.1.3
The interpretation of uncertainty
The River rating curve is shown as a solid blue line, with adjacent dashed blue lines that represent
the uncertainty of the result. The computation of these lines was derived from the Roughness
Coefficients table (Table A-1), which can be accessed from Afflux Advisor by activating the
Roughness Rating command button (Figure 4-1). The table gives a minimum and maximum
roughness coefficient (Manning’s n), which may be called the roughness error. This error is the
major factor in rating curve uncertainty and is discussed in Section 2.1.3 of this report.
The averaged minimum n values for natural streams and floodplains have a roughness error of
about 27% of the mean value. The averaged maximum n values for natural streams and floodplains
have a roughness error of about 37% of the mean value. AA uses this error to compute the
uncertain flow discharge limits, and then linearly interpolates the mean rating curve to compute the
water level uncertainty limits. Since the upper and lower error limits are dissimilar, the uncertainty
curves are asymmetric about the mean rating curve.
In summary, a simple interpretation for river rating uncertainty is that the major roughness error
produces a discharge that averages about ±30% from its mean value.
4.2
Worked examples for the Bridge Application
All of the following bridge and culvert examples are for use with the River Main, so having
completed the above worked example, it will be a repeated exercise to change back to the River
Main.
4.2.1
The Bridge Application worksheet
The Bridge application (Figure 4-3) may be accessed from the River or Culvert Applications, using
the command buttons provided. There are four user entry panels on the worksheet (marked 1 to 4)
which are superimposed on Figure 4-3. The actions required for each are as follows:
1. The option (or radio) button is used to select any one of four bridge types;
2. The data required for bridge computation are accessed using the Data entry command button,
which accesses a Data entry worksheet for the selected bridge type (Figure 4-4). If the bridge
is skewed or eccentric (off centre) to the flow, then these variables may be set using the spin
buttons illustrated. The detail of skew and eccentricity are given in the comment to these
worksheet cells. (Note that the bridge rating curve must be recomputed when these variables
are changed.) Finally, the Bridge rating curve for any type is computed by activating the
Compute Rating command button.
3. When bridge afflux has been computed, the Interpolator may be used to find afflux and water
level for any particular discharge. The required discharge is manually entered in the Discharge
cell, and the Interpolator command button is activated to compute the afflux and water level
statistics.
4. The two command buttons are used for accessing the River or Culvert Applications.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
45
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Figure 4-3: The Bridge Application worksheet
4.2.2
The Data entry worksheet
There are five data requirements for the Arch and Arches bridge types (Figure 4-4), four for the
beam bridge since there is no springer level, and five for the piered beam bridge since an additional
total pier width dimension is required. All data entries are detailed in the associated comment cells,
and those for the Arch type follow as an example:
1. Abutment type is illustrated at the bottom of Figure 4-4, and is for use with the USBPR (1978)
afflux calculation.
2. Springer elevation is usually the same on both sides of the arch. If it is not, then an average
value must be used.
3. Soffit elevation is the highest point of the arch. If however the underside of the opening is
beamed or obstructed in any way, then the soffit elevation is measured to the lowest point of
the obstruction.
4. Road elevation is the average across the river cross section. If the road has a large curvature,
then Afflux Estimator must be used for the computation.
5. The bridge span is the width between abutments below the springer level.
4.2.3
Computing afflux for an Arch bridge
The main purpose for these bridge worked examples is to illustrate the physical limits for bridge
computations. The user may begin by selecting an Arch bridge type, setting the skew to zero and
the eccentricity to within ± 0.8 (since these computations begin for eccentricity greater than 0.8 or
less than -0.8). The Arch data entry page is then accessed using the Data Entry command button.
Afflux Advisor begins with the Arch data entry page as illustrated in Figure 4-4. If the data differs,
then change the data to that shown in Figure 4-4. Note that if any data entry is omitted, AA will give
an appropriate warning when the computation is run. An example warning is ‘Please enter a Road
elevation value’.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
46
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Bridge Data Entry
Arch section
Soffit
elevation
Span
Springer
elevation
Road
elevation
Datum
Abutment type 1
Springer elevation
Soffit elevation
Road elevation
Span
1.00
0.50
1.00
1.50
1.50
Bridge
Abutment Type -showing plan view of bridge (road and embankment)
1
2
3
Road
90 degree
wingwall
Road
Road
Flow
30 degree
wingwall
Flow
Spillthrough
or semicircular
Flow
Figure 4-4: Bridge data entry for the Arch type
Furthermore, warnings are given if the soffit elevation is lower than the springer elevation, if the
road elevation is lower than the soffit elevation, and if the road elevation is higher than the highest
river cross section elevation.
After completing the above data entry, the user may return to the Bridge Application by activating
the Bridge command button (Figure 4-4). The Bridge rating curve is then computed by activating
the Compute Rating command button (Figure 4-3). If the River Application is accessed then the
river cross section chart now includes a sketch of the bridge modelled (Figure 4-5). An immediate
physical picture of the bridge and river is thus displayed. Note that for this sketch, the bridge is
centred in the main channel and the arches and piered beam bridge types are displayed as
composite bridges for simplicity.
There are minimum and maximum limitations for the span width used in bridge computations.
These are demonstrated as follows:
• If the span is changed from 1.5m to 1.4m (Figure 4-4) and AA is run, then the warning ‘The span
is too narrow for the USBPR method’ appears. This warning is activated if the bridge opening
ratio is less than 0.1; it may be encountered for either the USBPR (1978) or HRC (2004) method.
The bridge opening ratio is described in the Technical Background section of this report, and
the warning represents the physical limitation of either method.
• If the span is now changed from 1.4m to 12.7m and AA is run, then the warning ‘Please enter a
Span within the river width’ appears. This warning is activated if the span width is larger than
the river width at the springer elevation (Figure 4-5). If the span is now changed to 12.6m, the
code runs.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
47
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Maximum span
Figure 4-5: Bridge sketch on the River cross section plot
4.2.4
Interpolator
Continuing with the above worked example for the Arch bridge, the span may be changed back to
3 -1
1.5m and the Bridge command button activated. A discharge value of 100m s is then entered in
the Interpolator Discharge cell, and the Interpolator command button is activated. The afflux is
computed as 0.74m within an uncertainty bound of 0.58m to 0.89m. These values may be roughly
checked on the bridge rating curve at the Interpolator vertical bar, and represent the difference
between the undisturbed river (from the River application) and the bridge (with river) rating curves
for that discharge. Since the bridge uncertainty limits are sometimes asymmetrical about the mean
value, an average uncertainty is also calculated as ±0.15m.
3 -1
The computed water level at 100 m s is also directly verified as 3.04m from the bridge rating curve.
However, the river uncertainty from the River Application is added to the bridge uncertainty for
estimating the maximum and minimum possible water levels of the river with bridge rating curves.
Again, an average uncertainty for water elevation is calculated as 0.53m. This may be compared
3 -1
with the river uncertainty alone of about 0.38m (at 100 m s ) from the River Application.
As detailed in the ‘Technical Background’ section, the afflux uncertainty limits for sub-soffit flows
are taken as the USBPR (1978) and HRC (2004) ratings (except for low Froude number and highly
skewed flows). These errors are in the order of a few percent but may become larger. For supersoffit flows, the weir iterated flows are the addition of the weir error (6% of the discharge due to the
weir flow coefficient) and the bridge friction error (8% of the discharge for the uncertainty in bridge
friction). In summary, sub-soffit flows have variable uncertainty of a few percent, and super-soffit
flows have discharge errors of 14%.
There is now sufficient information to compute afflux for the arches, beam and piered beam bridge
type examples in AA. It is left to the user to determine that the minimum and maximum spans for
the given examples are:
• 2.4m and 32.1m for the arches type, afflux at Q = 100m s is 1.87m and 0.01m respectively;
3 -1
• 3.0m and 39.2m for the beam type, afflux at Q = 100m s
3 -1
is 2.63 m and 0.00m respectively
• 4.0m and 39.2m for the piered beam type with a total pier width of 1m, afflux at Q = 100m s
2.63m and 0.00m respectively.
3 -1
is
Similarly, the skew and eccentricity variables may be verified towards increasing afflux when skew
increases and eccentricity more than 0.8 or less than -0.8.
Note that afflux must be recomputed once these variables are changed.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
48
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
4.3
Worked examples for the Culvert Application
All of the following culvert examples are for use with the River Main, so it is necessary to change
the River application to the River Main if another river is modelled.
4.3.1
The Culvert application worksheet
The Culvert application (Figure 4-6) may be accessed from the River or Bridge applications, using
the command buttons provided. There are four user entry panels on the worksheet (marked 1 to 4)
which are superimposed on Figure 4-6. The actions required for each are as follows:
1. The option (or radio) button is used to select any one of four culvert types;
2. The data required for culvert computation are accessed using the Data entry command button,
which accesses a Date entry worksheet for the selected culvert type (Figure 4-7). For
simplicity, there are no skew or eccentricity controls for the culvert. The culvert rating curve for
any type is computed by activating the Compute Rating command button.
3. When culvert afflux has been computed, the Interpolator may be used to find afflux and water
level for any particular discharge in the same way as for bridges. The required discharge is
manually entered in the Discharge cell, and the Interpolator command button is activated to
compute the afflux and water level statistics.
4. The two command buttons are used for accessing the River or Bridge Applications.
Afflux Advisor - Culvert Application
Culvert Type
Pipe
Box
Arch
Multiple Barrels
Section
Free flow
1
Variables
Data entry
Culvert
Span
0.50
Rise
Road
Embankment
Span
Span
Span
Rise
Rise
Rise
2
Soffit
Soffit
elevation
elevation
elevation
Compute Rating
Springer
elevation
Road
elevation
Soffit
Invert
Flow
Datum
Interpolator
Full flow
Discharge 30.00
Afflux
Culvert
Maximum 2.46
2.29
Mean
Minimum 2.11
Uncertainty 0.18
Water surface elevations
Maximum 4.10
3.73
Mean
Minimum 3.29
Uncertainty 0.40
Elevation: mAD
9.00
3
4
Select
River
Bridge
Embankment
Road
Culvert
7.00
Interpolator
6.00
5.00
River
4.00
3.00
2.00
1.00
Co
Rating
8.00
Flow
Soffit
Co
Invert
Road
Soffit
Springer
Discharge: m3/s
0.00
0.00
100.00
200.00
300.00
400.00
500.00
Figure 4-6: The Culvert Application worksheet
4.3.2
The Data entry worksheet
The Culvert data entry is more complex than that of the bridge, mainly because of the addition of
four more entries for the culvert inlet type. There are 10 data requirements for the Pipe and Box
culvert types (Figure 4-7), 11 for the Arch type since there is an additional springer level, and 13 for
the multiple barrel type since the number of barrels and culvert type are also required.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
49
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Culvert Data Entry
Pipe section
Span
Rise
Soffit
elevation
Road
elevation
Datum
1
Brick, cement mortar, good condition
Rise
4.00 Length
100.00
Inlet shape Rectangular
Culvert n =
Inlet material Concrete
Inlet Ki =
Inlet type A
Inlet sketch
Inlet edge type Square
Coefficients
Outlet Invert elevation
0.00
Road elevation
4.50
Culvert
Barrel roughness
Span
4.00
2
3
Inlet Type - showing plan view of culvert, road and embankment
A
B
C
Edge
Flow
Road
Headwall
Road
Headwall & Wingwalls
Road
Projecting
11
0.0150
0.500
D
Road
Mitred to slope
Figure 4-7: Culvert data entry for the Pipe type
The required entries fall into three groups, namely barrel data (group 1), inlet data (group 2) and
elevation data (group 3). The groups are annotated on Figure 4-7 in red. Several data entries are
detailed where necessary in the associated comment cells, and those for the Pipe type groups
follow as an example:
1. These are the barrel roughness, span, rise and length. Throughout the code, both the span and
rise are restricted to a minimum of 0.45 m, in accord with CIRIA (1997). For a Pipe culvert type,
the rise is computationally set to the span and the rise entry need not be made. The barrel
roughness description is entered using a combination box, and the Manning’s friction
coefficient is automatically computed and displayed as ‘Culvert n’. The user may wish to
access the Culvert Roughness table (Table A-2, Appendix A) by activating the command button
adjacent to the Barrel roughness entry, and check the friction value. Alternatively, the user may
change the Barrel roughness, and check for changes in ‘Culvert n’.
2. There are the four inlet type variables which are entered by combination boxes. The
combination box listings have been restricted to entries which are allowable from an inlet
coefficients table (Table 4-1). The latter may be accessed by activating the ‘Coefficients’
command button. The inlet variables of shape and material are self explanatory. The ‘inlet
type’ variable is illustrated in two dimensions at the bottom of Figure 4-7, and in three
dimensions (Figure 4-8) by activating the ‘Inlet sketch’ command button. The ‘Inlet edge type’
is also illustrated in Figure 4-8.
When the four inlet type variables are changed, an inlet loss coefficient (Ki) is automatically
entered in the ‘Inlet Ki’ cell and the remaining inlet parameters are automatically defined upon
activation of the ‘Coefficients’ command button. If any of the inlet parameters are not listed in
the coefficients table, the inlet parameters default to the first listing in the “Inlet structure design
coefficients” table (Table 4.1).
Invert elevations are at the bottom of the culvert and are illustrated in the Culvert Application
worksheet. The outlet invert elevation is at the exit of the culvert. The road elevation is also
illustrated in the Culvert application worksheet, and is assumed to be horizontal for simplicity.
Finally, the Culvert command button will return the user to the Culvert Application worksheet
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
50
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Table 4-1: Inlet structure design coefficients (from CIRIA, 1997)
Inlet shape
↓
Material
Circular
Concrete
Corrugated
metal
AA
Inlet
type
A
A
C
A
D
C
Inlet
edge
type
Square
Pipe
socket
Square
None
B
Rectangular
A
Concrete
C
A
Pipe
Arch
Corrugated
metal
Arch
Corrugated
metal
Corrugated
metal
Square
A
A
C
B
A
C
A
D
A
D
C
Pipe
socket
Bevels
Square
None
Square
None
Bevel
None
Square
None
`fof^=fåäÉí=EÉÇÖÉF=íóéÉ=
ÇÉëÅêáéíáçåë=
Design coefficients
K
M
c
Y
Ki
0.0098
0.0078
0.0045
0.0340
0.0018
0.0018
2.000
2.000
2.000
1.500
2.500
2.500
0.0398
0.0292
0.0317
0.0553
0.0300
0.0243
0.67
0.74
0.69
0.54
0.74
0.83
0.50
0.30
0.30
0.50
0.70
0.90
0.0260
1.000
0.0385
0.81
0.30
0.0610
0.750
0.0400
0.8
0.50
0.0610
0.750
0.0423
0.82
0.70
eÉ~Çï~ää=EOMãã=ÅÜ~ãÑÉêëF=
0.5150
0.667
0.0375
0.79
0.50
eÉ~Çï~ää=EQRø=ÄÉîÉäëF=
eÉ~Çï~ää=
qÜáÅâ=ï~ää=éêçàÉÅíáåÖ=
qÜáå=ï~ää=éêçàÉÅíáåÖ=
eÉ~Çï~ää=
mêçàÉÅíáåÖ=
eÉ~Çï~ää=EPPKTø=ÄÉîÉäëF=
jáíêÉÇ=íç=ëäçéÉ=
eÉ~Çï~ää=
jáíêÉÇ=íç=ëäçéÉ=
qÜáå=ï~ää=éêçàÉÅíáåÖ=
0.4950
0.0083
0.0145
0.0340
0.0085
0.0320
0.0030
0.0300
0.0083
0.0300
0.0340
0.667
2.000
1.750
1.500
2.000
1.500
2.000
1.000
2.000
2.000
1.500
0.0314
0.0379
0.0419
0.0496
0.0430
0.0491
0.0264
0..0463
0.0379
0.0463
0.0496
0.82
0.69
0.64
0.57
0.61
0.54
0.75
0.75
0.69
0.75
0.57
0.50
0.50
0.60
0.60
0.50
0.90
0.27
0.70
0.50
0.70
0.60
eÉ~Çï~fä=
eÉ~Çï~ää==
mêçàÉÅíáåÖ=
eÉ~Çï~ää=
jáíêÉÇ=íç=ëäçéÉ=
mêçàÉÅíáåÖ=
eÉ~Çï~fä=~åÇ=ïáåÖï~ääë=~í=
PMøJTRø=íç=Ä~êêÉä=~ñáë=
eÉ~Çï~ää=çê=ÜÉ~Çï~ää=~åÇ=
ïáåÖï~ääë=~í=NRø=íç=Ä~êêÉä=
eÉ~Çï~ää=~åÇ=ïáåÖï~ääë=~í=
Mø=íç=Ä~êêÉä=~ñáë=
Figure 4-8: Inlet and edge types for culverts (after CIRIA, 1997)
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
51
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Each Afflux Advisor inlet type code (A to D) listed in Table 4-1 corresponds to one of four inlet type
sketches, shown in Figure 4-8. These codes have been associated with the design coefficients
table, for use in Afflux Advisor, by interpretation of the CIRIA inlet type descriptions. For further
details of inlet types and other configurations see Normann (1985). The coefficients K, c, M and Y
are used in Analysis Module 3 of CIRIA (1997) for calculating headwater depth under inlet control.
Note that the coefficient M in Table 4-1 is not the same variable as the structure opening ratio, used
elsewhere in this report. (Coefficients for two types of pipe arch were averaged to one type for
simplicity.)
4.3.3
Computing afflux for the Pipe, Box and Arch culvert types
Once data entry has been completed for a culvert type, the Culvert command button is activated on
the Data entry worksheet (Figure 4-7) and the user returns to the Bridge Application (Figure 4-6).
The Compute Rating command button is then activated and the culvert rating curve is updated.
Interpolation is identical to the bridge method, however the associated uncertainty calculation
differs slightly for the under road culvert flows. The major error for the latter is friction, and the
Culvert friction table (Table A-2) gives about 8% errors in the discharge. The over road flow errors
are however the same as for bridge super-soffit flows, being about 14% of the computed
discharge.
As an exercise, the afflux may be computed for each of the Pipe, Box and Arch (flat based) culvert
types using the data entry loaded with AA (If these entries have been changed, please return them
to the original values shown in Figure 4-7). The following results should be obtained:
• Pipe: 2.47m ±0.18m afflux and 3.93m ±0.42m water level at Q = 30m s ,
3 -1
• Box: 2.08m ±0.18m afflux and 3.54m ±0.41m water level at Q = 30m s ,
3
-1
• Arch: 2.52m ±0.22m afflux and 3.99m ±0.45m water level at Q = 30m s , using a flat based
arch (with equal springer and invert elevations).
3
-1
Note that the associated uncertainties imply that a pipe afflux, for example, should be rounded as
3 -1
2.5m ±0.2m and the water level as 3.9m ±0.4m for Q = 30m s . The results are physically
meaningful, since the 4m x 4m box has a larger cross section area than the 4m diameter pipe, and
thus a lower friction loss. The Arch type is intermediate in cross section area.
4.3.4
Computing afflux for the Multiple barrel culvert type
The only additional entries for the Multiple barrel Data entry worksheet are the number of barrels
and culvert type (pipe, box or arch). If the number of barrels is set to unity, then the same results
will be computed as for the exercise immediately above. That is, the data entry applies to a single
barrel of a multiple barrel culvert, and the inlets for each barrel are the same. The user may run
each culvert type with a single barrel to confirm the above results.
The number of barrels used is restricted by the span of each barrel and the width of the main
channel. If the product of the span and number of barrels is greater than the main channel width,
then a warning is given. For example, the number of barrels may be set to four in the AA example,
and activation of the Culvert command button gives the warning ‘Total span must be within the
main channel width’.
It is expected that a multiple barrel of equal total area to a single barrel will give a higher afflux (for
equal rises). However, this is not always the case. A culvert may be under inlet or outlet control
(whichever demands the greatest energy). If the culvert is under inlet control, then a multiple barrel
culvert of equal total area to a single barrel culvert will give the same afflux. (A technical user may
find whether the culvert is in inlet or outlet control from the ‘FFCulvert’ spreadsheet data of this
application.)
As a final example, if the number of barrels is set to 2 for a 4m by 4m box culvert, the computed
3 -1
afflux is 0.74m ±0.12m and the water level is 2.21m ±0.35m for Q = 30m s . This afflux is
approximately half that of the single box culvert.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
52
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
This page is intentionally left blank.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
53
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
REFERENCES
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
54
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
This page is intentionally left blank.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
55
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
References
Ackers, P., White, W.R., Perkins, J.A. and Harrison, A.J.M. (1978) tÉáêë= ~åÇ= cäìãÉë= Ñçê= Ñäçï=
ãÉ~ëìêÉãÉåí, John Wiley and Sons, Chichester, UK.
Atabay, S. and Knight, D.W. (2002) Bridge Afflux Experiments in Compound Channels, oCa=mêçàÉÅí=
oÉÅçêÇ=tR^JMSNLmoS E^ÑÑäìñ=~í=ÄêáÇÖÉë=~åÇ=ÅìäîÉêíë=Ó=oÉîáÉï=çÑ=ÅìêêÉåí=âåçïäÉÇÖÉ=~åÇ=éê~ÅíáÅÉI=
^ååÉñ=SF, The Environment Agency, Bristol, UK.
Biery, P.F. and Delleur, J.W. (1962) Hydraulics of single span arch bridge constrictions, mêçÅÉÉÇáåÖë=
çÑ=íÜÉ=^p`bI=gçìêå~ä=çÑ=eóÇê~ìäáÅë=aáîáëáçå, 88(HY2).
nd
Bradley, J. (1978) eóÇê~ìäáÅë=çÑ=_êáÇÖÉ=t~íÉêï~óë, 2 Edition, US Dept. of Transportation, FHWA,
US. (Published electronically in 1978.)
Brown, P.M. (1988) Afflux at arch bridges, oÉéçêí= poNUO, Hydraulics Research Ltd., Wallingford,
UK.
CES (2004) `çåîÉó~åÅÉ=bëíáã~íáçå=póëíÉãI=sÉêëáçå=NKMKNKN, Wallingford Software Ltd., Wallingford,
UK.
CESM (2004) `çåîÉó~åÅÉ=rëÉê=j~åì~ä, Draft Edition, 2 April, HR Wallingford Ltd., Wallingford, UK.
(Now available as Environment Agency R&D Technical Report W5A-057/TR6).
CIRIA (1997) `ìäîÉêí=ÇÉëáÖå=ÖìáÇÉ, Report 168, London, UK.
Crowder, R.A., Pepper, A.T., Whitlow, C., Sleigh, A., Wright, N. and Tomlin, C., (2004)
Benchmarking Hydraulic River Modelling Software Packages, oCa=qÉÅÜåáÅ~ä=oÉéçêí=tRJNMRLqoM,=
The Environment Agency, Bristol, UK.
Danish Hydraulic Institute (2000) jfhb=NNI=^=jçÇÉääáåÖ=póëíÉã=Ñçê=oáîÉêë=~åÇ=`Ü~ååÉäë, Horsholm,
Denmark.
FHWA (2001) eóÇê~ìäáÅ= ÇÉëáÖå= çÑ= ÜáÖÜï~ó= ÅìäîÉêíë, US Department of Transportation, Federal
Highway Administration, Washington D.C.
Hamill, L. (1999) _êáÇÖÉ=eóÇê~ìäáÅë, E. & F.N. Spon, London.
HEC (1995) ^=Åçãé~êáëçå=çÑ=çåÉJÇáãÉåëáçå~ä=ÄêáÇÖÉ=ÜóÇê~ìäáÅ=êçìíáåÉë=Ñêçã=eb`Jo^pI=eb`JO=~åÇ=
tpmol, US Army Corps of Engineers, Davis, CA, US.
HEC-RAS (2004) oáîÉê=^å~äóëáë=póëíÉãI=sÉêëáçå=PKNKO, US Army Corps of Engineers, Davis, CA, US.
JBA (2004) Afflux at bridges and culverts – Review of current knowledge and practice, oCa=
qÉÅÜåáÅ~ä=oÉéçêí=tR^JMSNLqoN, The Environment Agency, Bristol, UK.
JBA (2005) Hydraulic Performance of River Bridges and Other Structures at High Flows, Phase 2:
Unpublished Progress Notes, Environment Agency R&D Project W5-110.
Kaatz, K.J. and James, W.P. (1997) Analysis of alternatives for computing backwater at bridges’,
American Society of Civil Engineers, gçìêå~ä=çÑ=eóÇê~ìäáÅ=båÖáåÉÉêáåÖ, 123(9), September, 784-792.
Kindsvater, C.E., Carter, R.W. and Tracy, H.J. (1953) Computation of Peak Discharge at
Contractions, rpdp=`áêÅìä~ê=OUQ, Washington, DC.
Liu, H.K., Bradley, J.N. and Plate E.J. (1957) Backwater effects of piers and abutments, `áîáä=
båÖáåÉÉêáåÖI=oÉéçêí=kçK=`boRTehiNM, Colorado State University, US.
Montes, S. (1998) eóÇê~ìäáÅë=çÑ=çéÉå=ÅÜ~ååÉä=Ñäçï, ASCE, US.
Nagler, E.A. (1917) Obstruction of bridge piers to the flow of water, qê~åë~Åíáçåë=çÑ=íÜÉ=^p`b, 82,
334-395.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
56
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Seckin, G., Knight, D.W., Atabay, S. and Seckin N. (2004) _êáÇÖÉ=~ÑÑäìñ=ÉñéÉêáãÉåíë=áå=ÅçãéçìåÇ=
ÅÜ~ååÉäë, Unpublished Technical paper presented for JBA Consulting Engineers & Scientists and
the Environment Agency.
Sturm, T. (2001) léÉå=ÅÜ~ååÉä=ÜóÇê~ìäáÅë, McGraw Hill, Boston.
USBPR (1978) Hydraulics of Bridge Waterways, US Dept. of Transportation, FHWA, eóÇê~ìäáÅ=
aÉëáÖå=pÉêáÉë=kçKN, published electronically in 1978.
USGS (1978) eóÇêçäçÖáÅ=fåîÉëíáÖ~íáçå=^íä~ëÉë=e^RVN=Ó=e^SNN, Department of the Interior, Denver,
CO, US.
WSPRO (1986) _êáÇÖÉ= ï~íÉêï~óë= ~å~äóëáëW= oÉëÉ~êÅÜ= êÉéçêí, by Shearman, J.O. and Kirby, W.H.,
Schneider, V.R. and Flippo, H.N., oÉéçêí=kçK=cet^LoaJUSLNMU, NTIS, VA, US.
Yarnell, D.L. (1934) Bridge piers as channel obstructions, qÉÅÜåáÅ~ä= _ìääÉíáå= QQO, US Dept of
Agriculture, Washington DC.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
57
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Appendix A:
Roughness coefficients
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
58
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
This page is intentionally left blank.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
59
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Table A-1: Roughness coefficients for natural channels (after CIRIA, 1997)
Type of Channel and Description
Manning's n value
Minimum Normal Maximum
Natural Streams (top width at flood stage < 30m)
Clean, straight stream
- full stage, no rifts or deep pools,
- as above, but more stones and weeds.
Clean, winding stream
- some pools and shoals,
- as above, but some weeds and stones,
- as above, lower stages, more ineffective slopes sections,
- as above but more stones.
Sluggish reaches, weedy deep pools.
Very weedy reaches, deep pools, or floodways with heavy stands
of timber and underbrush.
Mountainous streams, no vegetation in channel, banks usually
steep, trees and brush along banks submerged at high water
levels
- gravel bed with cobbles and few boulders,
- cobble bed with large boulders.
0.025
0.030
0.030
0.035
0.033
0.040
0.033
0.035
0.040
0.045
0.050
0.040
0.045
0.048
0.050
0.070
0.045
0.050
0.055
0.060
0.080
0.070
0.100
0.150
0.030
0.040
0.040
0.050
0.050
0.070
0.025
0.030
0.030
0.035
0.035
0.050
0.020
0.025
0.030
0.030
0.035
0.040
0.040
0.045
0.050
0.035
0.035
0.040
0.045
0.070
0.050
0.050
0.060
0.070
0.100
0.070
0.060
0.080
0.110
0.160
Flood Plains (examples only)
Pasture, no brush
- short grass,
- high grass.
Cultivated areas
- no crop,
- mature row crops,
- mature field crops.
Brush
- scattered brush, heavy weeds,
- light brush and trees, in winter,
- light brush and trees, in summer,
- medium to dense brush, in winter,
- medium to dense brush, in summer.
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
60
Environment Agency R&D Project: W5-110
Afflux at Bridges and Culverts
Afflux Advisor – Interim Report and User Guide
Table A-2: Roughness coefficients for culvert barrels (from CIRIA, 1997)
Barrel, wall and joint description
Concrete pipe
- good joints, smooth walls
- good joints, rough walls
- poor joints, rough walls
Concrete box
- good joints, smooth walls
- good joints, rough walls
- poor joints, rough walls
Metal pipe
- 68mm x 13mm corrugations
- 100mm x 20mm corrugations
- 127mm x 25mm corrugations
- 153mm x 50mm corrugations
- 200mm x 55mm corrugations
- spiral rib metal pipe, good joints
Concrete
- trowel finish
- float finish
- unfinished
Brick
- glazed, good condition
- cement mortar, good condition
- poor condition
Manning's n value
Minimum
Normal
Maximum
0.011
0.014
0.016
0.012
0.015
0.0165
0.013
0.016
0.017
0.012
0.014
0.016
0.0135
0.015
0.017
0.015
0.016
0.018
0.022
0.022
0.025
0.033
0.033
0.012
0.0245
0.0235
0.0255
0.034
0.035
0.0125
0.027
0.025
0.026
0.035
0.037
0.013
0.011
0.013
0.014
0.0125
0.0145
0.017
0.014
0.016
0.020
0.011
0.012
0.022
0.014
0.015
0.026
0.017
0.018
0.030
JBA Consulting
www.jbaconsulting.co.uk
N:\2003\Projects\2003s0319 - Environment Agency - Headquarters - Afflux Stage 2\FINAL DELIVERABLES\web\Afflux Advisor Technical
Report\W5A(03)01 - Afflux Advisor - User Manual - Final 003.pam.doc: 01/08/2007
61
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement