Afflux at bridges and culverts can be a significant source of flood risk by ... in a high flood risk urban area, where the costs of river survey and modelling .... which has previously been investigated by Katz and James (1997) and HEC (1995).
RECENT ADVANCES IN MODELLING FLOOD WATER LEVELS AT BRIDGES AND CULVERTS ROBERT LAMB, PETER MANTZ, SERTER ATABAY, JEREMY BENN JBA Consulting ANDREW PEPPER ATPEC Key Words: Afflux, bridges, culverts
Abstract: Afflux at bridges and culverts can be a significant source of flood risk by causing elevated flood water levels. A wide range of methods are currently used to model afflux, but a review of current practice found that these are not always well understood and can be applied inappropriately. Some of the underlying assumptions and calibration data are not the most relevant for typical situations in the British Isles. This paper presents a summary of recent research to develop more consistent afflux methods and software for use in Flood Risk Management and related activities. INTRODUCTION What is afflux? Afflux is an increase in water level that can occur upstream of a structure, such as a bridge or culvert, that creates an obstruction in the flow. The afflux is illustrated in Figure 1 for a bridge structure located in a watercourse. The dashed line represents the normal water surface for the undisturbed watercourse. The solid line represents the water surface when the structure is present. Afflux is shown as the maximum increase of water level above normal depth in the undisturbed stream. Note that the afflux differs from the headloss across the structure, as the latter varies depending on the upstream and downstream locations of measurement.
Figure 1. Side elevation at a bridge contraction
3a.1.1
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. To maintain a steady flow, this local loss of energy is compensated by an increase in potential energy immediately upstream of the structure. A backwater is thus created which begins at the afflux location. Why is afflux important? Elevated water levels upstream of bridges and culverts are a potential source of flood risk. In general, the afflux increases with increasing flow rates and with an increasing degree of obstruction, which may be related to the size and form of the structure or to transient debris blockage. Whilst bridges and culverts can be located anywhere, they tend to be concentrated in urban areas, and so the consequences of even quite small increases in level above a threshold may be severe in terms of property flooding or disruption of infrastructure. The effects of bridges and culverts on flood water levels need to be understood for design, planning, hydraulic modelling (including models used for flood mapping), risk analysis, maintenance and incident management. The hydraulics of bridges and culverts are complex, and not all applications justify a costly, detailed analysis. But what methods should be used for analysis or modelling? SCOPING STUDY Consultation with the Flood Risk Management professions In 2001 the Defra/EA Flood and Coastal Erosion Risk Management joint research programme commissioned a scoping study to review the requirements for analysis and modelling of afflux in the UK, identify relevant theoretical approaches and data, and recommend research and development to improve the capability for dealing with afflux within Flood Risk Management (FRM). The scoping study produced a final technical report (Benn et al., 2004), research plan, interim best practice guidance and seven detailed expert papers. These documents are available electronically via the Environment Agency’s online publications catalogue. The scoping study included a consultation with 22 professionals involved with FRM or related activities and for whom the analysis of bridges and culverts in flood conditions would be a concern. The consultation revealed the lack of a common understanding of the appropriate methods for analysis and modelling. The scoping study identified at least 10 different methods or formulae for analysis of afflux at bridges and culverts. 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 (D’Aubuisson, 1840, Nagler, 1917, Yarnell,1934), embankment bridges (Kindsvater et al., 1953, Bradley, 1978) and arched bridges (Biery and Delleur, 1962, Brown, 1989). There are several methods published in classical hydraulic textbooks for calculating the afflux at culverts of simple geometry. 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. They have therefore become incorporated into recent computer codes which model both the open channel and structure hydraulics. Requirements for afflux analysis The choice of analysis method should be influenced by the impact of the study and should in turn drive the investment made in collecting data (in particular river survey), the time allocated, and the experience of the analyst. It is useful to think of two types of application. The first is a ‘high impact’, application, for example an important bridge or culvert in a high flood risk urban area, where the costs of river survey and modelling are justified by the value gained from a detailed analysis. The second, ‘low impact’ application would not
3a.1.2
justify as much data and analysis, but require a simpler, and much quicker, approach to analyse the structure; an example might be a pipe culvert for a farm access. One of the objectives of the research reported in this paper was therefore been to provide methods for both the ‘high impact’ and ‘low impact’ applications within a consistent theoretical framework. VISION FOR THE ‘AFFLUX ESTIMATION SYSTEM’ (AES) To support analysis of bridges and culverts in flood conditions, the research and development has been encapsulated within the ‘Afflux Estimation System’ (AES). The AES is a collection of related project outputs, consisting of -
a simple ‘Afflux Advisor’ providing quick, approximate results in an accessible spreadsheet form for situations where only a single channel cross section is available and the bridge or culvert is described in summary form
-
the ‘Afflux Estimator’, a more detailed backwater model for flow through a structure, implemented within a steady-state hydraulic river model
-
research reports and technical guidance to assist users of the above software.
ANALYSIS OF EXPERIMENTAL AND FIELD DATA Data sources Table 1 summarises the most significant data sets for bridge afflux. Much of the early twentieth century data is inaccessible and often specific to certain types of bridge found in the USA, but not common in the British Isles. Table 1. Sources of data for afflux Source
Date
Details
Available?
Rehbock Nagler
1922 1917
No
Yarnell Kindsvater, Carter and Tracy Biery and Delleur Matthai
1934 1953
Bradley USGS
1978 1978, 1979 1988 1988 1993 2001
Over 2000 laboratory experiments 256 laboratory experiments on 34 different bridge models 2600 laboratory experiments with pier bridges Laboratory data from the Georgia Institute of Technology Laboratory study on arched bridges Verified the Kindsvater et al. (1953) method with data from 30 field sites Laboratory experiments, Colorado State University Hydrologic Investigations Atlases. Observed water surfaces for 35 flood events, 22 field sites. Laboratory study, arched bridges, 203 tests Field data from bridges in the UK, 66 data sets. Field observations from Canns Mill bridge, Devon University of Birmingham laboratory tests in compound channels, 145 measurements, bridges normal to flow direction. Extension of University of Birmingham lab tests in compound channels, 225 measurements, skewed bridges.
HR Wallingford HR Wallingford Hamill Atabay and Knight
Seckin, Knight, Atabay and Seckin
1962 1967
2004
3a.1.3
Yes, paper maps Yes, (partial records) Yes
It was hoped for this study to recover useful data from the original field measurements used in the HR Wallingford (Brown, 1989) work on arch bridges. However, inspection of the archives revealed almost no directly useful field data. The main limitation of the field measurements is that they gave only estimates of headloss. Additionally, there was scant information to determine the exact locations of the measurements or the flow conditions. The bridges were not originally instrumented for the study of afflux and so these limitations are not surprising. After careful review, it was concluded that the most relevant measurements for this study would be contained within two data sets, the USGS (1978) field surveys and the recent University of Birmingham (UB) laboratory measurements of Atabay and Knight (2002) and Seckin at al. (2004). Both data sets provide high quality, detailed measurements of water surface elevations for some distance upstream and downstream of a bridge. The USGS (1978) data is for wide (~100 to ~1000 m), rough, vegetated floodplains with low bed slopes. Although rather extreme for the British Isles, the data are very detailed and remain overall the best quality field measurements available. The UB data have the possible limitation of being made in a laboratory flume. However, they also provide the detailed information needed for a rigorous analysis of afflux. A total of 145 afflux measurements were made for arch bridge types of single and multiple openings, and beam bridges with or without piers. An important feature is that the tests were made for a compound channel and for bridges at various skew angles. The USGS and UB data therefore provide a basis for analysis over a range of scales from ~1 m to ~1000 m, and a range of roughness, expressed in terms of Manning’s n. Clearly there is a gap in the data for a scale of ~10 m to ~100 m, which is unfortunately the scale most relevant for typical applications in practice. Only one detailed set of measurements exists for afflux analysis at this scale, which is the data of Hammill (1999) at Canns Mill in Devon. Recovery of afflux data For practical purposes, afflux is not directly measurable in the field because it is the inferred difference between water levels with and without an obstruction. To recover estimates of the afflux and associated hydraulic variables from field data it is therefore necessary to model the reach in the absence of the obstruction. For the USGS (1978) measurements, the authors therefore set up models using HEC-RAS for 11 flood events at 10 bridges. This was a reanalysis of the data, required to extract relevant variables, which has previously been investigated by Katz and James (1997) and HEC (1995). For calibration, the HEC-RAS models included the bridge structures, however the reaches measured by the USGS were long enough to allow for confidence in the hydraulic modelling, regardless of the presence of the bridges. For the UB data, the laboratory measurements provided accurate estimates of the afflux and associated flow conditions. Dynamic similarity analysis A preliminary analysis of the data was made using the dynamic similarity method of Raju et al, (1983), also applied by Brown (1988). A simplified version of this method involved expressing bridge afflux (dh) in dimensionless terms as follows: dh/Y3 = f(F3, J3) where Y3 is the normal flow depth at section 3 (see Figure 1) in the absence of the structure, F3 is the Froude number of the flow in the absence of the structure, and J3 is a blockage ratio to the flow caused by the structure, i.e, the ratio between the area of flow blocked by the bridge and the total flow area in the undisturbed channel. Figure 2 illustrates the available data plotted on the dimensionless scales used here, and shows the fitted functional relationship for selected values of the blockage ratio J3. It can be seen that although the available data do not include physical scales intermediate between the small laboratory flume and the very large USGS floodplains, a range of hydraulic conditions (defined in terms of the Froude number and
3a.1.4
blockage) are represented. Figure 3 shows the close correspondence between afflux estimated from the above analysis and measured in the laboratory flume for the UB data.
Dimensionless afflux (as a factor of unobstructed flow depth)
1.2
1.0
UB laboratory data J3 = 0.9
USGS field data J3 = blockage ratio
0.8
J3 = 0.7
0.6 J3 = 0.5
0.4 J3 = 0.3
0.2 J3 = 0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Froude number for unobstructed flow
Figure 2. Summary of afflux data plotted on dimensionless scales
Predicted afflux (mm)
100
80
60
40
20
0 0
20
40 60 80 Measured afflux (mm)
100
Figure 3. Comparison of afflux estimates for the University of Birmingham laboratory data
3a.1.5
The similarity analysis provides a robust estimate of afflux at some location upstream of a ‘simple’ bridge located in a uniform channel. However, a more detailed hydraulic model of the water surface profile should allow for the channel to be non-uniform, and consider the location of the afflux and the downstream transition to unobstructed flows. The UB and USGS afflux data were therefore also used to study the transition lengths, defined as the distance between the afflux and the upstream bridge face (contraction length), and between the downstream bridge face and the location at which unobstructed flow recommences (expansion length). Typically, these lengths are estimated as a function of the amount of obstruction across the channel at the structure, following analysis by HEC (1995). The similarity analysis was also found to apply for the transition lengths, expressed as a dimensionless variable. A robust, unbiased relationship was found that fits both the UB laboratory data and the USGS field data, and which suggests greater variability than previously assumed. Further research needs This research has made best use of available data, and shown that a range of flow conditions can be represented. However, it remains the case that there are almost no suitable, detailed field measurements of bridges in the UK. It is to be hoped that with the development of modern sensor technology such as water level transducers, Doppler velocity meters and GSM telemetry, cost effective measurements can be made that will improve our understanding of bridge and culvert hydraulics for practical analysis. A related issue for FRM is the impact of blockage at structures. Blockage was an important element of the original scoping study of Benn et al. (2004), but a combination of budget constraints and scarcity of data meant that it was not pursued further. With the development of risk-based flood management methods over recent years, it seems that further attention should be given to characterising blockage frequency, and how it is represented in afflux calculations. AFFLUX ADVISOR SPREADSHEET METHOD The Afflux Advisor allows a user to enter survey data for a single cross section, together with summary bridge data, and automatically calculates the afflux for a range of flow depths. The results can be viewed as a rating curve (based on the assumption of normal depth) for the unobstructed section, a rating curve upstream of the structure and an estimate of the afflux, with uncertainty, at a flow specified by the user. The Afflux Advisor computes up to nine flow modes through a bridge as water levels increase. Note that Afflux Advisor includes sluice and orifice flow when the water level reaches the bridge soffit, and then modular and drowned weir flows (concurrent with pressure flow through the submerged opening) once water levels rise above the deck. All these flow modes are computed and automatically incorporated within the rating curve as required. For culverts, the Afflux Advisor also calculates the upstream rating curve using the methods set out in CIRIA (1997), assuming a culvert placed within a uniform channel, as specified by the user. The Afflux Advisor assumes a subcritical, normal flow in a natural channel of uniform cross section. The bridge and culvert types used in Afflux Advisor have been chosen to represent those commonly found in the UK. AFFLUX ESTIMATOR MODEL To provide detailed analysis of the water surface profile through a structure, and to relax some of the assumptions within the Afflux Advisor, a bridge backwater model, referred to as the ‘Afflux Estimator’, was developed. The backwater model uses the standard step method (Sturm, 2001, HEC, 2004) based on the principle of conservation of energy to model the water profile. Conveyance in the channel is calculated using Manning’s equation with roughness defined in three panels (main channel, plus left and right overbank panels).
3a.1.6
Conveyance through the structure is calculated using a composite roughness that takes account of the structural surface friction. Beam or arch bridges of up to 20 openings can be simulated. For arches, the conveyance calculation takes account of the changes in wetted perimeter and flow area above the springer level. The Afflux Estimator model computes orifice and weir flows as necessary if water levels exceed the soffit. Extrapolation of the cross section is carried out automatically if water levels rise above the limits of the survey data. Using the UB and USGS data, energy loss coefficients were calibrated for the backwater model transition reaches and related to the floodplain and bridge scales. Hence the Afflux Estimator automatically provides suitable values for the transition lengths and energy loss coefficients, which do not need to be supplied by the user. The Afflux Estimator model has been tested against the UB and USGS data, and also compared with outputs from HEC-RAS at every stage in development, with satisfactory results. Figure 4 shows the results obtained after applying the Afflux Estimator model to the UB flume experiments. These results indicate an overall unbiased fit to the data. The results shown here include cases where critical flow is experienced locally through the bridge, as well as those where subcritical conditions apply throughout. Further tests are underway with reference to the USGS field scale data, with good results.
0.08
Measured afflux (m)
0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Modelled afflux (m)
Figure 4. Comparison of Afflux Estimator (modelled) and measured UB flume data
DELIVERY OF THE AES SOFTWARE The methods for computing afflux (and hence water levels or rating curves) described here will be delivered to users in the form of two software applications. The simpler Afflux Advisor is a spreadsheet application that runs within Microsoft Excel. The more sophisticated Afflux Estimator method is to be delivered to users as a component within the new Conveyance Estimation System (CES) ‘stand alone’ river modelling utility, developed as an output of related R&D funded by Defra and the Environment Agency (HR Wallingford, 2004.). JBA Consulting and Wallingford Software have been working together to embed the Afflux Estimator within CES, to provide a
3a.1.7
unified model incorporating the contemporary methods for water level calculation provided by CES and AES. New source code developed within the project will also enable future implementation of the research in other 1D river models. Detailed descriptions of the theory, analysis and software developed in this study will be available within the project record. CONCLUDING REMARKS This paper is a brief overview of R&D carried out over the past three years. The research has distilled the many theoretical and empirical approaches currently used to define a single, consistent, empirical basis for analysis. This makes use of recent measurements for compound channels and spans a wide range of physical scales and hydraulic conditions. In contrast to the current situation, users will not be faced with a wide range of methods and coefficients to apply. The Afflux Advisor spreadsheet will be available for quick calculations with limited data. The Afflux Estimator model will provide greater flexibility and accuracy where there is more information to describe the river channel and structure. There is no need for users to choose between different calculation methods as the appropriate algorithms are applied automatically. ACKNOWLDEGMENTS This work was funded by the Defra/EA science projects W5A-061 and SC030218. The authors would like to thank Mervyn Bramley, OBE, for initiating and guiding the project. The support of the Scottish Executive is also acknowledged. We are grateful to Donald Knight, Les Hammil, Nigel Wright, Paul Samuels and John Riddell who have provided expert technical review of the research and to Galip Sekin for laboratory data. REFERENCES D’Aubuisson, J.F. (1840) Traite d’Hydraulique. 2nd Ed., Pitois, Levrant et Cie, Paris. Atabay, S. and Knight, D.W. (2002) Bridge Afflux Experiments in Compound Channels, R&D Project Record W5A-061/PR6 (Afflux at bridges and culverts – Review of current knowledge and practice, Annex 6), The Environment Agency, Bristol, UK. Benn J.R., Mantz P., Lamb R., Riddell J., Nalluri C. (2004) Afflux at bridges and culverts – Review of current knowledge and practice. Environment Agency R&D Technical Report W5A-061/TR1 (ISBN 1 8443 2291 2), 135 pp. Biery, P.F. and Delleur, J.W. (1962) Hydraulics of single span arch bridge constrictions, Proceedings of the ASCE, Journal of Hydraulics Division, 88(HY2). Bradley, J. (1978) Hydraulics of Bridge Waterways, 2nd Edition, US Dept. of Transportation, FHWA, US. (Published electronically in 1978.) Brown, P.M. (1988) Afflux at arch bridges, Report SR182, Hydraulics Research Ltd., Wallingford, UK. CIRIA (1997) Culvert design guide, Report 168, London, UK. FHWA (2001) Hydraulic design of highway culverts, US Department of Transportation, Federal Highway Administration, Washington D.C. Hamill, L. (1999) Bridge Hydraulics, E. & F.N. Spon, London.
3a.1.8
HEC (1995) A comparison of one-dimensional bridge hydraulic routines from HEC-RAS, HEC-2 and WSPRO, US Army Corps of Engineers, Davis, CA, US. HEC (2004) River Analysis System, Version 3.1.2, US Army Corps of Engineers, Davis, CA, US. HR Wallingford (2004) Reducing Uncertainty in River Flood Conveyance, Phase 2, Conveyance Manual, Environment Agency R&D Technical Report W5A-057/PR/1. Kaatz, K.J. and James, W.P. (1997) Analysis of alternatives for computing backwater at bridges’, American Society of Civil Engineers, Journal of Hydraulic Engineering, 123(9), September, 784-792. Kindsvater, C.E., Carter, R.W. and Tracy, H.J. (1953) Computation of Peak Discharge at Contractions, USGS Circular 284, Washington, DC. Liu, H.K., Bradley, J.N. and Plate E.J. (1957) Backwater effects of piers and abutments, Civil Engineering, Report No. CER57HKL10, Colorado State University, US. Matthai, H.F. (1967) Measurement of peak discharge at width contractions by indirect methods. Techniques of water resource investigations of the USGS, Chapter A4, Book 3, Application of hydraulics, US Govt Printing Press, Washington DC. Nagler, E.A. (1917) Obstruction of bridge piers to the flow of water, Transactions of the ASCE, 82, 334395. Rehbock, T. (1921) Bruckenstau und Walzenbildung. Der Bauingenier, Berling, 2, 13. Seckin, G., Knight, D.W., Atabay, S. and Seckin N. (2004) Bridge afflux experiments in compound channels, Unpublished Technical paper presented for JBA Consulting Engineers & Scientists and the Environment Agency. Sturm, T. (2001) Open channel hydraulics, McGraw Hill, Boston. USBPR (1978) Hydraulics of Bridge Waterways, US Dept. of Transportation, FHWA, Hydraulic Design Series No.1, published electronically in 1978. USGS (1978) Hydrologic Investigation Atlases HA591 – HA611, Department of the Interior, Denver, CO, US. WSPRO (1986) Bridge waterways analysis: Research report, by Shearman, J.O. and Kirby, W.H., Schneider, V.R. and Flippo, H.N., Report No. FHWA/RD-86/108, NTIS, VA, US. Yarnell, D.L. (1934) Bridge piers as channel obstructions, Technical Bulletin 442, US Dept of Agriculture, Washington DC.
3a.1.9
