flood loading methodology for bridges

A FLOOD LOADING METHODOLOGY FOR BRIDGES

Nick Wellwood, B.Eng.(Honsl), A.M.A.S.C.E., M.I.E.(Aust.), R.P.E.Q., Project Engineer, Sinclair Knight and Partners

and

John Fenwick, B.E., D.Phil.(Oxon), M.I.E.(Aust.), R.P.E.Q., Bridge Engineer, Department of Transport, Queensland (Chairman - Bridge Loading Subcommittee (AUSTROADS))

SUMMARY

A revised Australian Bridge Design Code is due for publication in 1990, and will include limit states design philosophy. The bridge designer will be required to investigate a range of flood events, and the accurate prediction of flood loads requires realistic values of drag coefficients and design velocities. The paper reviews research into hydrodynamic bridge loads and examines current and proposed flood loads specified in Australian bridge design codes. New model testing equipment for hydrodynamic load detennination at the University of Queensland is described as well as proposed bridge model geometrics being investigated. Formulae are presented to calculate maximum flood velocities based on previous work by Vanoni for steady uniform flow conditions. Guidance is given in the fonn of a flood loading methodology to enable the designer to calculate the critical design flood forces for a range of flood events.

PROCEEDINGS 15th ARRB CONFERENCE, PART 3 315

I 316

Nick Wellwood graduated as Queensland Government Scholarship Holder from the Queensland University of Technology in 1985 with a First Class Honours Degree in Civil Engineering. He commenced work as a design engineer in the Hydraulics Section of Bridge Branch within the Main Roads Department, Queensland. While in Bridge Branch, Nick was involved with numerous hydraulic and hydrological analyses for bridge and culvert schemes, flood plain management and physical hydraulic modelling as well as research into the flood loads on bridges. Since Bridge Branch Nick has been involved in civil construction and design in both the public and private sectors. He is presently a Project Manager - Civil Works with Sinclair Knight and Partners in Brisbane which involves a wide variety of urban and commercial developments including large tourist projects in Queensland.

John Fenwick graduated in 1965 and worked for the Co-ordinator General's Department for two years. After three years study at Oxford and a year at the Road Research Laboratory on steel box girder research, he joined the Queensland Main Roads Department. He has been involved in the design of most of the major road bridges since then, and was appointed Bridge Engineer in 1988. He has been involved with ARRB research committees since 1973, and has supervised a series of research projects on concrete technology, bridge components and bridge loadings. He is Convenor of the Austroads Bridge Loading Committee, and was Federal President of the Concrete Institute of Australia from 1987 to 1989. He was recently appointed to a position coordinating the introduction of QUality Management into the Department.

PROCEEDINGS 15th ARRB CONFERENCE, PART 3

INTRODUCTION

1. A revised AUSTROADS Bridge Des i gn Code is due for publication in 1990 and includes a modified approach to calculating design flood loads for two reason s :

(i) Rece nt research has shown that hydrodynamic drag forces may be larger than previously as s umed and this may be critical for longer span bridges.

(ii) Limit States Design requires that the risk of failure under varying load types should be approximately constant. Bridges designed to be above a 50 year average return interval (ARI) flood. but which may be submerged in a larger flood. up to 2000 years ARI. must be checked for submerged hydrodynamic loads.

2. For longer span brid~s on high piers. where the superstructure is submersible the lateral flood forces on a pier can be quite large (in the order of 2000 kN or more). In such cases. it is e s sential for safe and economical design that flood depth. velocity. drag factors and variation of velocity with depth and across the stream are known with reasonable accuracy.

3. This paper describes a methodology for calculating flood velocity parameters and describes research aimed at accurately determining critical drag factors for typical bridge profiles at the point of submergence.

THEORY OF HYDRODYNAMIC LOADING

4. Hydrodynamic loads result from the direct action of water on a structure causing a combination of boundary layer pressure drag (form drag) and viscous drag. Boundary layer pressure drag occurs from streamline convergence and subsequent pressures. while viscous drag is due to tangential shearing flow on the structure surfaces. For bridge s tructural elements their hydrodynamic bluffness cause predominantly pres sure drag.

5. The total hydrodynamic drag force F't acti-ng on the bridge structure can be resolved into a time-mean component F and a superimposed fluctuating component f't' due to vortex shedding in the boundary layer. as shown in equation 1.

F' t F + f't •.•....•.•.••..•.•.•.•••.•.••••..•.•..••••..•...•••.••••.. 1

6 . Calculating the mean component is satisfactory for structures such as bridges with a high natural frequency and high damping. The mean drag force due to hydrodynamic loading is expressed as:

P Cd V2 dhdx ••.•.•....••••.••. • ••••.••••••. 2 2


Equation 2 is usually simplified to:

FD .s!d V2 A ••••...•.•••.•••.•..•..•..•..•.•••..•••.•.•.••••••.•.. 3 2

where; A Reference Area

V Mean Design Velocity over Reference Area

Cd Coefficient of drag

The estimation of the hydraulic components of equation 3 are examined later in greater detail.

HYDRODYNAMIC LOADS SPECIFIED IN CURRENT NAASRA BRIDGE DESIGN SPECIFICATION

7. The current NAASRA Bridge Design Specification (1976) is in a Working Stress format and provides guidance for the calculation of hydrodynamic loads for bridge piers. debris load and 10 g impact only. The stream flow pressure from bridge piers is given as:

p =

where;

l{V2 D •••••••••••••••••••••••••••••••••••••••••••••••••••••••• 4

Average Stream Velocity (m/s)

K 0.70 for square ends (Cd = 1.4)

0.26 for angle ends (Cd 0.52)

The angle of attack of flow is limited to 5 degrees.

8. 0.52. there

Debris loads are also calculated using equation 4 with a K value of A minimum depth of 1.2 m of debris is specified for bridges where is a likelihood of debris collection. Log impact loads are not

applied concurrently with debris mat loading.

9. For the condition of partial or full submergence of bridge superstructures. which is common place in Queensland. there is no guidance for the selection of drag coefficients and it has been common place to utilize the drag coefficient of square ended piers for this hydrodynamic condition. Following recent research in this area. which is discussed in detail in Section 7. this practice of using Cd = 1.4 for superstructure submergence could lead to under estimation of hydrodynamic loads. This underestimation has been reduced to some degree by the use of 3 m high debris mats on bridge superstructures in some states. This problem has been addressed in the new limit states bridge code.

HYDRODYNAMIC LOADS SPECIFIED IN DRAFT LIMIT STATE AUSTROADS BRIDGE DESIGN CODE

10. Under the limit states format of the new AUSTROADS Bridge Design Code a serviceability limit state and an ultimate limit state for hydrodynamic loadings must be checked. These limit states correspond to the average recurrence intervals (ARl) of flood events stated below:

318 PROCEEDINGS 15th ARRB CONFERENCE, PART 3

Serviceability Limit State 20 year ARI Ultimate Limit State 2000 year ARI

11. The expression given for the calculation of hydrodynamic loads is similar to equation 4. however. a drag coefficient Cd is used instead of the factor K. This is shown below:

F* = 0.5 Cd CV)2A .••••.•••.....••.•......••.....•••....•.••.••........ 5

12. The draft code breaks the hydrodynamic loads into substructure and superstructure water flow loads. For bridge substructures. drag and now lift coefficients for piers are provided. The drag coefficients given are the same as stated in the current NAASRA Code. and are dependent on upstream and downstream pier nose shape.

13. Superstructure partial or full submergence is now covered by the use of an all encompassing drag coefficient of 2.2 to cover all flow cases. It is however. stated that reference should be made to more accurate estimates of drag coefficients as they become available. The drag coefficient of 2.2 is appreciably larger than the values of 1.4 used previously to cater for the superstructure submergence flow case.

14. For debris loads. a drag coefficient of 1.04 is utilized as stated in the current bridge code. The depth of debris specified is equivalent to the superstructure depth. including any substantial railing or traffic barrier. plus a minimum of 1.2 m. The maximum depth is to be taken as 3.0 m unless local experience indicates otherwise. The debris mat length can be taken as the entire length of the superstructure. For debris on piers a maximum length of 20 m is applicable or half the sum of the adjacent spans. Guidance on log impact loading is also provided and as previously it is not to be applied concurrently with debris loads.

LIMIT STATE IMPLICATIONS FOR ESTIMATING BRIDGE FLOOD LOADS

15. Before limit state methodology. conventional design procedures have been based on the selection of a peak discharge for a predetermined return period depending on the road and bridge immunity. This peak discharge often corresponds to a 50 or 100 year. average recurrence interval CARI) flood event. typical of immunities of highway road links. The hydrodynamic loads associated with this design return period are incorporated into a working stress design methodo10 gy. but can often underestimate the magnitude of hydrodynamic loading by analysing only one load case.

16. With the advent of limit state loadings the magnitude and probability of occurrence are to be defined and to a greater accuracy. As already highlighted serviceability and ultimate limit state loads are required to be calculated under the provision of the draft bridge code. To this end it is necessary to determine the critical serviceability hydrodynamic load up to the 20 year ARI flood event. It will be shown that the 20 year hydronamic load may not provide the critical serviceability limit state and a lower return period flood event may be critical. Similarly it is necessary to calculate other hydrodynamic loads of lower recurrence interval events than the 2000 year ARI hydrodynamic load in order to determine the critical ultimate limit state for a brid ge.


17. The calculation of flood events greater than the 100 year ARI flood is inherently more time consuming and of a lower accuracy than lower return interval floods. Most hydrological methods of flood estimation utilize the ARI of rainfall events as a basis for analys is. Rainfall estimations for events less than an equal to the 100 year ARI event are easily calculated using Australian Rainfall and Runoff (ARR) (1987) Volume 2. For flood events greater than the 100 year ARI event it is necessary to interpolate between the Probable Maximum Precipitation (PMP) and the 100 year ARI event critical to the catchment under consideration. This process is documented in ARR (1987) but requires the use of empirical equations for the determination of the PMP and empirical interpolation methods. Currently these calculations are seldom if ever performed by engineers for the calculation of hydrodynamic bridge loadings.

REVIEW OF HYDRODYNAMIC RESEARCH

18. In Australia. the estimation of flood forces on bridge piers has generally been based on research work by Apelt and Isaacs (1968) and provides good design estimations of drag and lift coefficients for a number of pier types and flow angles. This research of bridge pier hydrodynamic loads has been confirmed by experimental work by Sethuraman and Vasudevan (1971). This information is contained in the draft AUSTROADS Bridge Design Code. Further experimental work is required for different pier geometries and pile group combinations. however. large increases in drag and lift coefficient for piers are not anticipated. Indeed. if all bridges could be constructed at levels pr-eventing superstructure submergence for all probable flood events the problems of hydrodynamic load estimation would be greatly simplified. However. due to economic. climatic and terrain constraint s. "non-submersible" bridge superstructures are relatively rare in Queensland.

19. There has been little conclusive research carried out on hydrodynamic loads for the partial or full submergence of bridge superstructures. The research which has been carried out shows inconsistencies and a wide spread of drag coefficients for bridge superstructures ranging from 1.6 to 3.0. A summary of research findings and analysis of other authors is provided below.

20. Tainsh (1965)

Tainsh performed a number of model flow tests on bridge girder geometries as shown in Figure 1.

6-6

6-0

1-8

Fig. 1 - Bridge Geometry - Tainsh (1965)


21. This geometry is similar to current prestressed concrete (P. S. c. ) girders used extensively in medium span (20 to 40 m) bridges. The research work measured hydrodynamic loads for single girders and multiple girders with and without a deck. The original experimental work developed effective prototype loads and was later converted into drag coefficients for multiple girder bridges.

22. For a single girder, Tainsh stated that a maximum drag coefficient of 2.7 was measured at overtopping while a steady state drag coefficient of 2.2 was measured for deep submergence, equivalent to a superstructure submergence of 12 feet (prototype). For multiple girders with no deck, the maximum drag loads showed a close correlation to those for the single girder. For the case of a deck with multiple girders an increase of drag force of 15% was measured over the case with no deck. However the same drop in drag force following overtopping was recorded in all cases. A plot of Tainsh measurements of this variation in drag coefficient (following conversion by Denson (1982) for the case of multiple girders with no deck is given in Figure 2, where h = depth of submergence and W = deck width. .

3-0

2,5

0·5

V/.rgii' 0·225 e ----0·301 Q _ •• -0· 376. -_.-0·4510-· .. -0·526 Q ---0·600 ~ _ ... . -

0·1 0'2 0·3 0·4

RE LATIVE SUBMERGENCE. hI ....

Fig_ 2 - Drag Coefficients - Multiple Girders Tainsh and Denson (1982)


23. Denson (1982)

In 1982. Denson performed a series of studies on bridge superstructures to model all possible water forces and moments. As well as determining drag coefficients. Denson also derived lift coefficients and rolling moments about the longitidinal axis of the bridge.

24. Of most interest is Denson's study of AASHTO Type III PSC girders incorporated into a two lane bridge. Denson reported that a maximum drag coefficient of 2.5 was measured and unlike the research of Tainsh there was no noticeable reduction of drag coefficient with depth of submer~nce except for one flow condition. This is shown in Fi gure 3.

322

"tJ U

...: z IJ.J U

2·5

2·0

1· 5

LL 1·0 LL IJ.J o U

l!)

« a: Cl

0·5

0·0

V/vgh 0·15 CI---0·20 ()---0·25 e-'--0·30 Q-•. -

0·35 e--'--

e /

o Multiple Data Points

0·1 02 0·3 0·4

RELATIVE SUBMERGENCE, hI.,..

Fig. 3 - Drag Coefficeints - AASHTO Type III Denson (1982)


25. The maximum value of lift coefficient was 6.0 for all models tested and decreased with increasing velocity and inundation depth. Denson also based his model Froude number on bridge width and not flow depth and hence, the Froude number was not constant as depth increased.

26. Roberts (1983)

Roberts, undertook model studies of one-lane timber bridges typical of those used in Queensland. Measured drag coefficients were found to range from 3.1 to 3.3 for all overtopping and flow velocities. On testing of the bridge model with voids blocked off the drag coefficient reduced to around 3.0 and this was recommended for design use. The drag coefficients determined from this research are considerably higher than other experimental values and may not have a high accuracy due to the lack of variation of drag coefficient with inundation depth and flow velocity.

27. Naudascher and Medlarz (1983)

Naudaschan and Medlarz studied partial submergence on bridge superstructures as shown in Figure 4.

Fig. 4 - Superstructure Partial Submergence Naudascher and Medlarz (1983)

No tests were undertaken for overtopping of the bridge model. For the case of partial submergence a maximum drag coefficient of 2.1 was recorded and this tended to decrease with ~he depth of partial submergence; consistent with later research by Ape1t. This decrease of drag coefficient. with depth is an interesting phenomena and further research is required into its cause.

28. Apelt (1986)

The latest published research into hydrodynamic loads on submerged bridges was carried out by Apelt at the University of Queensland. For this preliminary research a bridge model geometry as shown in figure 5 was tested.


1000

500t-_L~~~~==~==~~~~ 1300

1250

8500 PIER

1000 <P

5000

10000

Fig. 5 - Bridge Geometry - Apelt (1986)

29. The published drag coefficients were based on the total force on the complete bridge structure tested. and gave a maximum drag coefficient of 2.2. As already discussed there is a drop in drag coefficient during increased partial submergence and then a subsequent increase in drag coefficient near the point of overtopping. This is shown in Figure 6.


3

W 2 LJ Z UJ 19 0:: UJ L co => V'l

UJ > ~ ~ UJ 0::

o

•

• •

., CURRENT TESTS

:' MINNS

+, NAUDASCHt R & MEDLARZ

[TOP OF DECK

----- -

2 3 DRAG COEFFICIENT, CD

Fig. 6 - Drag Coefficient Apelt (1986)

30. On examination of the raw test data. its also apparent that the measured drag coefficient continues to increase after overtopping and during deeper superstructure submergence. As stated by Apelt the present tests were undertaken at low Froude numbers. based on flow depth. of approximately 0.1. In prototype streams in Queensland Froude numbers in excess of 0.4 would be common place.

31. Apelt also undertook drag force experiments for various types of debris mat. A large variation of drag coefficients was measured depending on the internal geometry and porosity of the mat tested. It is reasonable to suggest that analysis of actual debris mats is required to accurately predict the composition and flow characteristics of the prototype.


32. At present there is a wide range of estimated drag coefficients for bridge superstructures and values of Cd over 2.0 are common. The adoption-~f a drag coefficient of 2.2 by the draft AUSTROADS Bridge Design Code appears to be a reasonable value at the present time. This value, however, requires further investigation and clarification in order to accurately define the drag coefficients on prototype superstructures undergoing partial or full submergence.

33. The use of drag coefficients higher than 2.2 would lead to increased substructure costs. Lower d.rag factors would save in substructure costs but would have to be supported by detailed model testing of the actual superstructure ~ometry.

CURRENT HYDRODYNAMIC RESEARCH AT THE UNIVERSITY OF QUEENSLAND

34. Drag and lift coefficients are dependant on a number of parameters including the geometric bluffness of the bridge, stream bed proximity and the Reynolds number and Froude number of the incident flow. Further research is presently being undertaken at the University of Queensland to clarify the inconsistencies between previous research studies into the hydrodynamic loads on bridge superstructures as well as examining and achieving quantifiable results in the following areas:

(a) The effect of Froude Number and stream bed proximity on the coefficient of drag of bridge superstructures.

(b) The effect of flood forces on bridge superstructures under oblique flow conditions.

(c) The magnitude of dynamic vertical flood force components on bridge superstructures at submergence.

(d) The effect of superelevation of the bridge superstructure on flood force drag and lift coefficients.

35. To provide a more accurate assessment of model loads and subsequent drag and lift coefficients a new testing rig was designed and commissioned at the University. The model testing rig designed by Wellwood and Fenwick and reviewed by Apelt is shown below in Figure 7.

36. The aluminium framed testing rig was designed to translate vertical and horizontal water loads to 5 cantilever beam load cells. The cantilever beam load cells have a linear range to 150 N and can read accurately to + 0.1 N. The load cells can be incorporated into a PC Data Logger to enable easier reduction of raw data and the calculation of actual drag and lift loads. Following recent calibration and shakedown testing at the University of Queensland minor modifications were made to reduce vertical redundancies and prevent lateral instability.

37. Bridge models are attached via two aluminium blades with spacing equal to the width of the testing flume. The models to be tested were constructed from perspex and at scale of 1:100. The models incorporated separate superstructure and substructures to enable interchanging and testing of the effect of different pier flow interactions. Three major superstructure model types will be tested, consisting of: (a) Prestressed concrete deck units.-

(b) Type IV Prestressed concrete girders.


, ~

I

"~" I

i I' fn'

~ ii i I t 'f' I r ; ,q I ~

I I

; ~ I

~~

it r .~ 5+· I-

if ~ I

I

I I

iJJ ~~ I Ii I, ;J1 I--c:,,~~-::._: :--

I :-. ~ ! .. :-"~~ ~ =

1 rr-i

~ r

I Ii ~ : ~~

I ! ~

~ i ~

J.

! e 5

~ ~ : I f

1 , , , ,

I ~ -,

!.. ~ i ~ , ~

, , ~ 1

1 1

I t J . . I

I f

! r I < ~ .I . ;;

i. . , .-..... -." ..

I

Fi g. 7 - Kodel Test ing Rig


~I

I ,: : ,;

, '

I . ~

I , !

I , I I " '- II: ,. : , !IIIII

~

327

(c) Steel girders with a composite deck.

38. The model substructure~ construct~d consist of a headstock on piles. twin circular columns and a blade pier. Further calibration of the model rig and load cells will be undertaken before detailed experimental runs are performed. The testing flume at the University of Queensland has been recently modified to achieve Froude numbers to 0.5, giving a good hydraulic range for the measurement of drag and lift coefficients.

SIMPLIFIED KETROD OF VELOCITY ESTIMATION FOR BRIDGE LOADINGS

39. As discussed further research to improve the estimation of drag and lift coefficients is currently being undertaken. To reliably determine the new limit state hydrodynamic loads on bridge superstructures there is also a need to more accurately define the design velocities at critical levels. At present the unrestricted surface velocity is commonly based on the average unrestricted velocity of t 'he stream divided by a constant factor. In Queensland a constant of 0.7 is generally utilised to determine the surface velocity as shown in equation 6:

V surface v average/D. 7 • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •• 6

40. This method would appear to provide an acceptable estimate of surface velocity for use in typical Queensland streams where Manning n = 0.05 and the average hydraulic radius Rh = 4.0. However. for streams of different hydraulic profiles this method can provide an underestimation or a conservative estimate of surface velocity. There is also a need to determine the ve10'city of flow at any depth. This is required for cases of superstructure submergence in order to determine the velocity at the bridge deck level. '

41. Such a velocity methodology has been developed based on earlier work by Vanoni (1941). The velocity distribution formulae derived by Vanoni for open channels is based on Prandt1' s Universal Logarithmic Velocity Distribution law:

U

where; U To

5.75

stream velocity bed shear stress

To 10g10 ro ..•...••..•..••.•.. 7

f' ro-r

f' density

42. This formulae can be re-expressed for open channels as:

where: v* k

328

Y1 Y

U - Umax 2.3 1 10g10 Y .••..•....•.......•....... 8

V* k

shear velocity Von Karman Constant flow depth in channel

y

distance from bed to point under consideration


The shear velocity v* can be expressed as follows:

........... . .................... 9

where: Rh S g

Hydraulic Radius Flow Energy Slope Acceleration due to gravity

For an infinitely wide channel:

•••••••••.••.•.•••.••••.•••••.• 10

Integrating equation 8 over the depth yields:

1 y1 U V + J gRhS (1 + 2.3 log10 -- • • . •. 11

k Y

where: V average unrestricted velocity

Equation 11 may be redefined using Manning's equation as:

n V Rh -2/3 •••.••••••••••••••.•••••••• 12

where: n Manning's roughness coefficient

Substitute into equation 11 yields:

,J gRh nV Rh -2/3

U V + k

Using k = 0.3 for turbulent Flood waters

Ch R 1/6 _h __ equation 13 becomes: n

10.4 23.9 U V [ 1 + +

Ch Ch

43. At the stream surface where y1 becomes:

U max V

=

[ 1 +

V

10.4n

R 1/6 h

y1 [ 1 + 2.3 log10 _ .... 13

Y

and the Chezy coefficient

y1 Log10 -- ............. 14

y

y the maximum surface velocity

•••.•••••.•..••.••••.•...•• 15

where Y' is a stream flow parameter varying with Manning n and hydraulic radius. A graph of ~ (the ratio of the surface velocity to the average velocity) is shown in Figure 8.


~> II 1-5

o !:i

Manning

n= 0·08

a: 1 ~ 0-74-------------------------~~~----------------

~ 1·4 -' UJ >

1·2

o

- ___ ~n=0 ·04

~---___ ..!!.n=o-03

5 10 15 HYDRAULIC RADIUS, RH (m)-

Fig. 8 - Velocity Ratio v Hydraulic Radius

44. Generally the ratio f will vary from 1.2 to 1. 7 depending on flow characteristics. Using the previous surface velocity methodology. equation 15. yields ~ 1.43. To determine the velocity at any level in the mainstream. for a particular flood surface level and discharge. equation 14 can be used.

45. It should be noted that this velocity methodology is applicable to streams where the average mainstream depth approaches the section hydraulic radius and where steady uniform flow conditions exist. For more complex flow phenomena it is recommended that a finite element


analysis of the flow be carried out in order to determine velocity isochrones and hence surface velocities. This highlighted methodology does not cater for the fact that in natural streams the maximum velocity lies at a small depth from the flood surface. hence precluding that the velocity distribution is strictly logarithmic. However. the methodology does provide a good design estimation of velocity at varying depths based on the stream flow characteristics. Due to the design use of bridge velocity estimations. more complicated methodologies such as finite element analysis are not utilized due to their inherent calculation time and the uncertainties when dealing with natural stream bed profiles.

A PROPOSED FLOOD LOADING METHODOLOGY

46. Due to the variability ' associated with flood immunities. stream hydraulics and the geometry of bridges it is impossible to generalise what will be the critical loading case for both serviceability and ultimate limit states. It is therefore necessary that a rational approach to flood loadings be developed to accommodate all possible bridge flood load scenarios.

47. A multiple load case approach is required consisting of four principal load case categories:

(a) Superstucture non-submergence. (b) Partial superstructure submergence. (c) Overtopping of superstructure. (d) Deep submergence.

To these load case categories a design upper bound and lower bound return period is applied equivalent to the 2000 year and 20 year ARI flood events respectively. From the four load case categories the critical serviceability and ultimate limit state hydrodynamic loads are defined.

48. Due to changes in ' drag coefficient at overtopping of the bridge superstructure. the peak hydrodynamic load may occur at the point of overtopping rather than at deeper submergence corresponding to the 2000 year ARI flood event. Indeed for extremely low level brid ges the peak hydrodynamic load may occur at the overtopping immunity of say 10 year ARI. This complicated situation necessitates that all load cases be examined. The critical limit state load would be defined as the critical hydrodynamic load of an ARI equal to or less than that of the limit state being analysed. This is shown diagramatically in Figure 9.


-.oJ UJ

> UJ -.oJ

Cl o o -.oJ u...

20

// ,/' I

~TOP OF I r-~--SUPERSTRUCTUREI--

I BOTTOM OF I

--- SUPERSTRUCTURE 1-

A.R.I. (years)

I I I I I I

2 00

Fig. 9 - Hydrodynamic Load Variability

49. For each bridge geometry and location in the horizontal and vertical plane a graph of hydrodynamic load v flood ARI can be formed as shown in Figure 10.


Bridge Deck at

.~scenario

/ :

o <t o -.J

LJ

:L <t Z

100 year Flood Immuni ty

g Immunity of g; Superstructure >- Soffit :r:

I

20 2000

A.R.I. (y.ears)

Fig. 10 - Hydrodynamic Load v Flood ARI

---...- Scenario 2

50. For the case of superstructure non submergence the critical hydrodynamic loading on the bridge would usually consist of stream flow on piers and possible debris mats. This load case is shown in Figure 11.


Cd = Cd for debris mat

FLOOD EVENT - T1

Fig. 11 - Superstructure Non-Submergence

51. If the 2000 year ARI flood event is less than the superstructure level then no superstructure submergence calculations are reqUired.

52. For each loading case involving partial or total superstructure submergence. a methodical multi-parameter analysis of the hydrodynamic load can be undertaken as highlighted below for transverse loads:

(a) Establish design water depth (y) and flood recurrence interval (T) associated with the flood event.

(b) Determine critical design velocity at reference level (y1) on the brid~ superstructure using equation 14.

334

v v [1 + 10.4 Ch

+

or the restricted velocity

23.9 Ch

10g10 y1] .•••.•....•...... 14

Y

V Q •••••••••••••••••••••••••••••••••••••••••••••••••• 16

~ where Ab bridge waterway area

Q total discharge through bridge


(c) Determine effective wetted depth (DS) for superstructure (including traffic barrier) or pos s ible debri s mat (Dm).

(d) Determi ne drag coefficient for debri s mat. value of 1.04 is utilised.

Presently a constant

(e) Determine drag coefficient for bridge s uperstructure. Presently a constant value of 2.2 is specified. however. Cd will be eventually found as a function of:

bridge geometry stream bed proximity flow Froude Number Fr v

JWf (f) Determine hydrodynamic transverse load for stream flow or debris mat using equation 17.

H Cd 2

v2 D ••.••.••....•.•••••••••••••••.•..••••.•.••••• 17

where D submerged depth of debris mat or superstructure

53. The critical hydrodynamic load for each loading case of stream flow. debris and log impact can be determined. This is shown in Figure 12 for two loading cases.

Check both (i ) Cd-Mat (i i) Cd - Superstructure Geometry (+ log Impact)

- Fr = V2

.f9Y2

FLOOD EVENT - T2

Cd - Deep Submergen ce

FLOOD EVENT - T3

Fig. 12 - Superstructure Submergence


HYDRODYNAMIC IMPLICATIONS FOR BRIDGE DESIGN

54. As discussed. with the introduction of the new AUSTROADS Bridge Design Code. drag factors for bridge superstructures will be significantly increased to Cd = 2.2. established from research. Coupled with the limit states format of the code. hydrodynamic loads will be more critical for bridges undergoing superstructure submergence.

55. The flood loading methodology as highlighted in section 9.0 provides a rational approach for the calculation of new hydrodynamic loads. Using the drag coefficients specified in the draft AUSTROADS Code a graphical representation of the interaction of velocity and drag coefficient can be constructed for deck unit and girder bridges. A summary of effective depths are tabulated below:

TABLE 1 EFFECTIVE DEPTHS

Geomerty Type

Effective Depth D

3 m Debris Mat 2.5 m Debris Mat 2.0 m Debris Mat Type IV Girders Type III Girders 18 m Span Deck Units 15 m Span Deck Units 12 m Span Deck Units

3.0 m 2.5 m 2.0 m

2.15 m 1.88 m 1.08 m 0.95 m 0.90 m

56. This graphical interaction of transverse flood load is shown in Figure 13 for deck unit bridges and Figure 14 for girder bridges.


-E -.. z :.::

::c Cl < 0 ....J

Cl 0 0 ....J LL

W Vl 0:: w > Vl z < 0:: I-

25

20

15

10

5

DECK UNIT BRIDGES

Hydrodynami c Transverse Load acting on Deck Units

Debris 3 Mat

o ~--~----~----~----.-----r---~----~----~ o 0-5 '-0 1-5 2-0 2-5

DESIGN VELOCITYVo (m/s)

3-0 3-5 4-0

Fig. 13 - Transverse Flood Load - Deck Unit Bridges


E --:z :.::::

::J:

Cl « 0 --' Cl 0 0 --' u..

UJ Vl c:: UJ > Vl :z « g

338

GIRDER BRIDGES

25 Debris 3m Mat

Hydrodynamic Transverse Loading acting on Girders Debris

2·5m Mat

20 / / o.b';,

2m Mat

. / 15 /' .1 /1 .j 10 II

Design Min. Transverse Load B

II /1/1 / /

5 11//" /

1//./ /' /f~/~//

{j,~ // Z// Z· ..,,/

O~---,----~----'-----~----r----'----~--~ o 0·5 1·0 1·5 2·0 2·5

DESIGN VELOCITY ---<Vo (m/s)

3·0 3·5

Fig. 14 - Transverse Flood Load - Girder Bridges

400


57. This illustrates that stream flow directly on the superstructure using a Cd of 2.2 for girder bridges exceeds the load exerted by a 3 m debris mat. For deck unit bridges the 3 m and 2.5 m debris mat predominates. However. for developed catchments where debris mats may be of a minimum depth of 102m. stream flow forces on the deck units controls. There is also a minimum load of 7.3 kN/m illustrated; applied as a base limit. This base limit load is not specified in the bridge specification but is based on differing experiences of State bridge authorities. Under the new limit state implications such a base limit will have less impact on designs. Presently the base limit applies to design velocities of less than 2.0 m/s for girders and 1.75m/s for deck units.

CONCLUSION

58. A review of research on hydrodynamic drag forces on bridge superstructures indicates a "safe" design value for Cd of 2.2 should be used for typical multibeam concrete bridge structures. and that further research is needed to confirm accurate values for a range of typical bridge cross sections.

59. For larger spans. flood loads may dominate substructure design if flood velocities are medium to high (>2m/s). Safe and economical design requires calculation of realistic velocity profiles with depth and at critical positions across the stream. Methods for estimating velocity distributions have been described.

60. As design restraints vary with the probability of occurrence of the flood load. a range of flood events must be checked to ensure that critical conditions have been considered. In general. the critical flood forces occur at or just after overtopping. As the flood depth over the bridge increases. the hydrodynamic forces may decrease as the effective drag coefficient tends to decrease. If the velocity increases significantly with increasing level. larger floods may become critical.

61. In mature stream bed conditions it is usually fairly easy to place bridge superstrucutres above even the rarer floods. and thus minimise forces on piers. However. in more juvenile stream profiles economical bridge design will often place the superstructure at a level where submergence may be very common (ARI < 10 years) or quite rare (ARI 50 to 2000 years). In these cases the designer must consider the various flood conditions specified in the code to determine those critical for design.

ACKNOWLEDGMENTS

62. The authors wish to thank the Commissioner of Main Roads. Queensland for permission to publish this paper and the assistance of Professor C.J. Apelt from the University of Queensland during the design of model testing equipment at the University.

REFERENCES

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flood loading methodology for bridges

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