Ind ian Journal of Engineering & Materi als Sciences Vol. 10, December 2003, pp. 458-464

Bridge afflux in compound channels

Galip Seykin, Mehmet. Ard lC,; llOglu, Mustafa Mamak* & Serter Atabay

C ivi l Engineering Department, C ukurova Uni vers ity, 0 1330 Adana, Turkey

Received 23 April 2003; accepled 18 Augusl 2003

T he resul ts o f mode l testing of arch and straight deck bridge constrictions are presented. All tests were carried out in a compound flume that consists of a main channel and two symmetric fl oodplains set at a fi xed bed slope. A simple generali zed afflu x equation is al so proposed. The equati on which describes the model characteri zes the affl ux as a function of Froude nu mber. and blockage ratio in terms of the downstream condit ions.

Bridges cause signi ficant constriction of floodplains duri ng fl ood events because of their structural design. Thus, they cause increasing upstream flow depth and resulting structural damage to themselves and nature. Hence, one of the most importan t tasks of a ri ver engineer is to predict the afflu x due to bridge structures. Although many investigations of hydrauli c behaviour of well-designed straight deck bridges are avaliabl e l

-4, there is a li tt le in fo rmation for arch

bridges5 -~ .

As shown in Fig. I , the increase (dh) in water surface from the normal stage to the afflux stage at section 1 is known as the affl ux of the constriction 10. 11. The flow through bridge constriction is class ified as low flow if it doesn' t come in to contact wi th the lower chord of the bridge I2,13. When the water surface through the bridge is completely subcritical and profi le passes above critical depth, type A low flow occurs. For either subcritical or supercritical profiles, type B flow can exist when the profi le passes through critical depth I2, 13.

Bridge afflux analysis is generally based on the application of either the momentum or the energy principle. When the energy conservation principle is applied to sections I and 3 (Fig. I ) for a rectangular channel, afflux value (dh =hl-113) is obtained as follows :

.. . (1)

where dh is the afflux, VI and V 1 are cross-section mean velocities at sections 1 and 3, respectively, g is

*For correspondence (E-mai l: mmamak@cukurova.edu .tr)

Aclual water surface

"

2 Nonnal water surface

Cri:ical depth

d~--- +1- I __ I I I I I , ____ _

m I " 0% ~#/##//#/#/#~

Fig. I- Defi nition sketch of fl ow profi les th rough a bridge constriction

grav itational acceleration, and I1E is total energy losses.

Energy losses, through a bridge constnctlOn, include friction, form losses, and eddy losses due to expansion and contractions. In addition, in the case of flood fl ows, there wi ll be additional losses caused by turbulence and acceleration 14.

Most of the well-known bridge affl ux formulae avaliable was developed based on the energy princi pIe 12.15,16.

Alternatively, if the momentum conservation principle is applied to sections 1 and 3, afflux value is then obtained as follows6

:

." (2)

where Fr3 is Froude number at section 3 which refers to normal depth, J) is blockage ratio at section 1 (area of bridge below water leveVtotal flow area), and h3 is normal depth of flow at section 3 (=l1n). Here, it should be pointed out that section 3 is located sufficiently downstream from the structure so that the

SECKIN el al.: BRIDGE AFFLUX IN COMPOUND CHANNELS 459

flow is not affected by the bridge (i .e., the flow has fully expanded, and becomes uniform)12.13.17.

For a simple channel of prismatic section where the flow velocity distribution is well-represented by the mean velocity, the Froude number Fr is defined by

.. . (3)

For a compound channel, the Froude number Fr is defined as follows:

.. . (4)

in which a is the kinetic energy flux correction factor which is constant with depth.

Blalock and Sturm18.19 showed that both Egs (3) and (4) produced poor results, and have found that the value of a is not a constant value. Blalock and Sturm18.19 also proved that the value of a varies as a function of flow depth in compound channels.

While many methodsl8.25 are available for predicting critical depth in a compound channel, Lee et at. 25 noted that the Chaudhry and Bhallamudi22 and Blalock and Sturm l8 approaches have been the most widely used, and the latter is implemented numerically in ' computer programs such as HEC­RAS 13. Sturm and Sadiq24 and Lee et al.25 pointed out that there is very little difference between the two approaches. In current study, Blalock and Srurm l8

formulae was used for computing the values of Froude number, and given by,

.... (5 )

in which an is the nth subsection property defined by Blalock and Sturml8 as,

.. . (Sa)

... (5b)

... (5c)

where Ai is the cross-sectional area and Ti is the top width of flow .

Brown6-8 developed HR Arch Bridge Method based on laboratory experiments conducted at HR Wallingford 17 using Eg . (2) to obtain aftlux at arch bridge sites. All the experiments at HR Wallingford were carried out in rectangular flume. HR Method was then verified using the field data collected at arch bridge sites by Regional Water Authorities in UK. All the archived data and records of this major field and laboratory study were re-analyzed at the University of Birmingham26.27

. Brown7 and Knight and Samuels27

concluded that where the floodplain was poorly defined, some errors occurred at high overbank flows.

Brown6-8 and Hamill & Mclnally9 pointed out that there were not enough reliable field data avaliable for arch bridges. Thus, laboratory experiments retain these popularity to analyze aftlux effects through bridge waterways. Nevertheless, most of the laboratory experiments up till recently were carried out to investigate aftlux effects in channels with fairly smooth surfaces and having no floodplains 5

.8.28 . In the

current study, all the experiments were performed in a compound channel with different roughness patterns29.

Brown7 pointed out that present day formulae l2 on bridge hydraulics are appropriate to apply to modern designs of bridges, but are inapplicabie to ancient arch structures.

Because of reasons mentioned above, this study is focused on investigation of the hydraulic performance of both single opening and multiple opening arch and straight deck bridge models, which operated under low flow conditions in a compound channel. An attempt is also made to develop a simple aftlux formulae that is applicable to both arch and straight deck bridges.

Experimental Procedure The majority of the tests reported here were

performed in a compound channel that consists of a main channel and two symmetric floodplains (Fig. 2) with an 18 m test length at the Hydraulic Laboratory of Birmingham University . The floodplains sides of the flume were constructed of glass materials . The channel bottom was also made of smooth PVC

460 INDIAN J. ENG. MATER. SCI. , DECEMBER 2003

170mm

Fig. 2-Cross-section of compound channel flume at Hydraulic Laboratory of Birmingham Uni versity

materials. The slope of the tlume was fixed at 2.024 x 10-3. Four bridge models, namely single opening semi-circular arch bridge model (ASOSC), multiple opening semi-circular arch bridge model (AMOSC), single opening elliptic arch bridge model (ASOE), and single opening straight deck bridge model with and without piers (DECK) (Fig. 3a-i), were tested with both smooth and roughened surfaces. The tlume has a recirculation system. Discharges were measured

a) Single opening semi-circular arch bridge model (a=19.9 cm, b=19.9 cm)

c) Multiple opening semi-circular arch bridge model (a=9.5 cm, b=9.5 cm)

L4tU}-J! ". ~-«~'"V~~'" 1 em

e) Single opening straight deck bridge model with piers (Bridge span width = O.398m)

g) Single opening straight deck bridge model with piers (Bridge span width = O.498m)

b) Single opening elliptical arch bridge ' model (a= 19.9 cm, b=12 cm)

d) Single opening straight deck bridge model without piers (Bridge span width= O.398m)

f) Single opening straight deck bridge model without piers (Bridge span width = 0.498m)

b) Single openl1ng straight deck bridge model without piers (IBridge span width = O.598m)

i) Single opening straight deck bridge model with piers (Bridge span width = O.598m)

Fig. 3-Different types of bridge models used in this study

SECKIN el {II. : BRIDGE AFFLUX IN COMPOUND CHANNELS 461

by an electro-magnetic flow meter, a venturi meter and a dall tube respectively . For the preliminary experiments, at the downstream end of the flume three adjustable tailgates were used to achieve uniform flow conditions when no bridge model existed on the flume. These control gates were adjusted to obtain several Ml and M2 profiles until the water surface slope was equal to the bed slope. Under this condition the ave rage flow depth , known as the normal depth, the average flow velocity was constant for all cross­sections.

Velocity measurements

For each test case, longitudinal direction velocity measurements were all made at the same depth , which was at 0.4 H (where H is the total depth of flow) from the bed of main flume , using a Novar Nixon miniature propeller cunent meter with a propeller diameter of 12 mm. Velocity measurements were made by taking five readings at ten second intervals for each 2 cm lateral distance for each test case (Fig. 4).

The section mean velocity (it) obtained by integration of the individual local velocity readings (u) was compared with the section mean velocity (U) obtained from the venturi meter, electro-magnetic flow meter, and dall tube. The mean error between it and U was 1.21 % with a standard deviation of 1.56%.

Roughness conditions The United States Geological Survey30 reported

that floodplain Manning n roughness coefficient may increase up to 1.6 for the dense vegetation that is present in many rivers. Chow lO also pointed out that there may al so be some perturbations such as roots, bushes, large logs and other drift on the main channel bottom; trees continually falling into channel because of bank caving. In the laboratory experiments, up till

Distance, (m)

Fig. 4--Comparison of the lateral veloc ity distribution for the rigid symmetric compound chann::1 for the smooth case.

recently, roughness material used has not reflected these dense vegetation yielding resistances appreciably greater than those of the laboratory inbanks and overbanks.

For reasons explained above, many scenarios were produced, and roughened surfaces were then created by means of various arrangements of aluminium mesh on both floodplain s and main channel smooth surfaces together. At the end of these anangements, roughness coefficient was varied between 0 .01 and 0.136 for overbanks, while it ranged from 0.01 to 0.039 for main channel. For representing vegetation , the same roughness elements made of aluminium mesh, were also used by Sellin el al. 31, but these had different dimensions in length, width and height.

Manning roughness coefficients were directly computed using the velocity measurements for main channel and floodplain flow proportions for each case.

Model tests As shown 111 Figs 3a-i, nine models were used in

the testing program under different boundary roughness conditions. Fifty tests for elliptic and single and multiple semi-circular arch bridge model s, and ninety-five tests for straight deck bridge models with and without piers were run for a range of discharges from 0.015 m3 Is to 0.055 m3/s. For all tests, each bridge model was placed 8 m downstream from the beginning of the test section. The width of each bridge model was limited to 10 cm with vertical wall abutments.

Water surface profile measurements were made along the centre line of the flume at each location as seen in Fig. 5 for each particular discharge. In this figure, Q, Yn, I1mc, and I1fp demonstrate the discharge, normal depth of flow, main channel Manning

370

350

3)0

. )10 E '§'290 = .~ 270 ;; ;:; 250

Oii 230

21 0

190

170

---tr- Q-27I1s., h3-<l .1J41m, nmc-o.O) 1, nfp-O.OH I ~<F24 v, h]-o . I224 m. ,m,"'.U". "0-0 051 -0- 0-21 VI, h3-o.i 103 m, nmc-o.027, nfp-o.047

-'.~.'"\ ~Q-18 lis. h3-o.098 1 m, nmc-o.02~ . nfp"(I.041

, -If- Q-1S Vs. h)oo() .OS94 m. nmc-o.02!li. nrp-o.f)40 j

'"'" .::: -0-- ....,...

~

-

~

g ~ ~ ~ ~ ~ ~ B W ~ ~ ~ ~ M M ~

Distance (m)

Fig. 5-Measured water surface profiles along the flume

462 INDI AN J. ENG. MATER. SCI.. DECEMBER 2003

roughness coefficient, and floodplain Manning roughness coefficient, respectively . Normal water surface measurements were made at the same locations (without of bridge models) on the flume for all cases. In the experiments, type A low flow was observed for 100 ex perimental runs , whereas type B low fl ow occurred in 45 runs. Types of flow for each test case were also verified using the HEC-RAS package program I] . The experimental results are given in detai l by Seckin29

.

Results and Discussion Eq. (2) demonstrates that dh depends on the

downstream Froude number (Fr3), the upstream blockage rati o (11 ), and drag coefficient (CD).

Brown6 showed that downstream blockage ratio (h) may be used instead of i l rearranging Eq . (2) . Knight and Samuels27 also indicated that Eq. (2) may be developed further using i 3 in place of i i, in order to es timate the afflux in terms of the downstream condition:, . In current study, these parameters were experimentally obtained. The values of Froude number were computed using Blalock and Sturm formulae l8

. Froude number (Fr3) varied between 0.24 and 1.1, the downstream blockage ratio (h) ranged between 0.25 and 0.63. Non-dimensionalized afflux (dhlh3) values ranged from 0.02 to 0.9 for all test cases. All the experimental work was carried out under low flow conditions.

All measured afflux/normal depth va lues (dhlh3)

versus Froude number times blockage ratio (Fr x h)

I .:> DECK 0.9

0.8 0

0 0.7

0 0

0.6

.E 0

:2 0.5 0 '0

0.4

0 0.3

0.2 0

0.1

0

0 0.1 0.2 0.3 0.4 0.5 0.6 Fr3*J3

Fig. 6--Plot of dhlh ) versus Fr3* h for straight deck bridge models

are shown in Figs 6-9 . Results of square analysis app lied to each bridge model , namely si ngle opening semi-circul ar arch bridge model (ASOSC), multiple opening semi-circular arch bridge model (AMOSC), single opening elliptic arch bridge model (ASOE), and straight deck bridge models with or without piers (DEC K) are also given in Table 1. Least square analys is results show that second order polynomial functions are well correlated with the experi mental data for each type of bridge model. Experimental results obtained from different types of bridge models including arch and rectangular openings show simi lar trends with minor differences as can be seen in Figs 6-9 . This shows that there is little difference between the behaviour of single rectangular and arched openings. Thi s confirms the earlier findings of Biery and Delleur5 and Hamill and Mclnally9.

As shown in Tabl e 1, although each second order polynomial functio n for each type of bridge models is reasonable for each set of data, a general formulae is proposed to obtain a general equation to give afflux magnitudes for all types of the bridge models used in current study . A meaningful regression is determined as fo llows, and shown in Fig. 10:

dh -=5.6638 (Ffj*J3)2 - 1.4445 (Ffj *JJ + 0.1352 I~

... (6)

0 ASOSC I 0.9

.1 0.8

0.7

0.6 ..,

.c 0 :c 0.5 '0 0

0.4

0.3

0.2 O¢<?>

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6

Fr3*J3

Fig. 7-Plot of dIJ1h3 versus Fr3* h for single opening semi ­circul ar arch bridge model

SECKIN et af.: BRIDGE AFFLUX IN COMPOUND CHANNELS 463

OAMOSC 0.9

0.8

0.7

0.6

E :2 0.5 '0

0.4

0.3 o

0.2

0.1

0

0 0.1 0.2 0.3 0.4 0.5

Fig. 8-P10I of dhlh3 versus Fr3* h for multiple opening semi­ci rcular arch bridge model

Fig. 9-Plot of dh/h3 versus Fr)* h for single opening elliptic arch bridge model

Determination coefficient (R2) is equal to 0.9796 with a standard deviation of 2.16%. The upper and lower bands in Fig. 10 are 90% confidence level of the relationship established. Using Eq. (6), the prediction interval for afflux in terms of flow depth, wi th 90% confidence limits, was found to vary in the range of +0.061 to +7.02% on the upper interval and in the range of - 6.43 to - 0.05% on the lower interval, from low to hi gh values of Froude number and blockage ratio.

Eq. (6) needs to be refined with more experimental data together field data.

0.9

0.8

0.7

0.6 ...

..c: :c 0.5 '0

0.4

0.3

0.2

0.1

0

0

o DECK

o ASOSC

o AMOSC

6 ASOE

- Eq. (6)

0.1 0.2 0.4 0.5 0.6

Fig. IO-Plot of dhlh 3 versus Fr)* h for all types of bridge models used in current study

Table I- Least square analysis results applied to each type of bridge model used in current study

Type of Detemlination Experimental dhlh) versus Fr* h

bridge cefficient (R2) relationships

ASOSC 0.9779 dhlh ) = 6.4754 (Fr3* hi - 1.9463 (Fr3* h) +0.2045

AMOSC 0.9938 dhlh3 = 9.0323 (Fr3* h)2 - 3.6389 (Fr3*hl + 0.4606

ASOE 0.9821 dill/I ) = 8.2 197 (Fr3*h)2 -2.92 I (Fr3*h) + 0.3294

DECK 0.9807 dhlh3 = 4.5229 (Fr3* h)2 - 0.8333 (Fr)*h) + 0.069

Although many popular methods which are able to give highly accurate results I for afflux are avaliable, the proposed equation (Eq. 6) allows rapid computation of afflux at arch and straight deck bridge sites.

The data presented herein was obtained under the following conditions: 0.4x105 < Re < 1.1 x105

; 0.24 <Fr< 1.1 ; 0.22<V< 0.65 ; 15<Q<55 .

Conclusions An empirical equation based on laboratory

experiments is establi shed to give afflux at arch and straight deck bridge sites for low flow conditions in compound channels. The equation can predict afflux value with the known values of downstream Froude number, normal depth, and downstream blockage ratio (h) of flow with a determination coeffic ient of 97.96%. This model can be used in the design stage

464 INDI AN J . ENG. MATER. SC I. , DECEMBER 2003

where very accurate results are not required. Proposed model is limited to type A and type B low flow only in a compound flume with vertical wall abutments.

Acknowledgement The au thors would like to gratefully thank Prof. D

W Knight for providing the experimental facilities at Birmingham Uni versity Hydraulic Laboratory.

Nomenclature A = the cross-sec tional area o f fl ow CD = drag cocffi c ient dh = afflu x F, = Froude number g = gravitatio nal acce lerat io n h = normal depth of fl ow J = bloc kage rati o (area of bridge be low water level/to ta l

flow area) K; = the conveya nce of the ith subsec tion II rp = fl oodplain Manning roughness coeffi c ient li me = mai n channe l Manning roughness coefficient P, = the we tted perimeter for the ith subsection Q = discharge Re = Rey nolds nu mber R; = the hydrauli c rad ius of the cross-secti on T = the top width of water surface u = ind iv idua l loca l ve loc ity reading U = cross-sec ti on mean velocity

U = the sec ti on mean veloc ity

I';E = LOt::!1 energy losses C( = kine tic energy flu x correct ion facLO r

Gn = the 11th subsection property

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