Indian Roads CongressSpecial Pubilcafion 13

GUIDELINES FORTHE DESIGN OFSMALL BRIDGESAND CULVERTS

Pub~shedby the Indian Roads congress

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PREFACE

The Paperentitled “Guidelines for the Design ofSmall BridgesandCulvert?’ by Shri GoverdhanLal whoretiredasAdditionalDirector Generalto theGovernmentof India (Roads),was published asPaper No. 167 in\rolume XVIII-Part 2 of the Journal of the IndianRoads Congress. One of the main objectives of theAuthor in preparingthis Paperwas to help theHighwayEngineers in the country to do the planning anddesign of culverts and small bridges for road projectscorrectly and expeditiously. The object of the Authorseems to have greatlybeenachievedastherehasbeencontinuousdemandfor this Paper and every HighwayEngineer has been wantiqg to possess it as abook ofreference. The Indian Roads Congress is, therefore,indebted to the Author for his labourand ingenuityinmaking the abovementionedcontributionwhich has notonly helpedthe membersof the profession, but hasalsoassisted in accelerating theprogress of road develop-ment in the country.

While the Paperin its original form hasstill greatvalue,the IndianRoadsCongressfelt that if it is revisedin the light of the~revisedIRC Bridge Codesand theexperiencesgainedsince its firstpublication, it will makethe Paperalmostan uptodatetext-book or manual forthe designof culvertsand small bridges;Shri GoverdhanLal, the Author of the Paper has kindly permitted theIndianRoadsCongressto revisethis Paperand bring itout asa SpecialPublitation of the Congress.The Indian

Roads Congress express their high appreciation andthanks to Shri Goverdhan Lal for this kind permission.They also expresstheir thanks to the Director General(Road Development) for kindly getting the manuscriptof this SpecialPublication examinedin the RoadsWingand for the useful suggestionsoffered. We arc sure thatthis new publication “Guidelines for the Designof SmallBridges and Culvert?’ would prove as a useful book ofreference to the Highway Engineersandalsoa guide tothe engineeringstudents.

iv

CONTENTS

Page

Introduction . ix

ARTICLE I Site Inspection ...

2 The EssentialDesign Data .•. 5

3 Empirical Formulae for Peak Run-off

from Catchment 11

4 Rational Formulae for Peak Run-off

from Catchment 175 Estimating Flood Discharge from the

Conveyance Factor andSlope of theStream 31

6 EstimatingFlood Discharge from Flood

Marks on an Existing Structure7 Fixing Design Discharge ... 41

8 Alluvial Streams—Lacey’sEquations ... 45

9 Linear Waterwayof Bridges ~,. 51

10 The Normal Scour Depth of AlluvialStreams 55

11 The Normal Scour Depth of Quasi-Alluvial Streams 59

12 The Effect of Contractionon the NormalScour Depth .., 67

13 Maximum ScourDepth ~.. 71

14 Depth of Bridge Foundations(LI,) ~., 79

15 Length of Clear Span and NumberofSpans 83

ARTICLE 16 StructuralDetailsof Minor Bridges andCulverts 87

17 Elements of the Hydraulics of Flowthrough Bridges 95

18 Afflux 10519 Worked out Examples on Discharge

Passed by Existing Bridges from FloodMarks 113

20 Overtopping of the Banks 12121 Feasibility of Pipe and Box Culverts

Flowing Full 12522 Hydraulics of the Pipe and Box Culverts

Flowing Full 131

APPENDIXHighest Intensity of Rainfall in mm 143

PLATES

1 Chart for Time of Concentration 161

2 Run-off Chart for Small Catchments 162

3 Velocity Curves 163

4 Abutment and Wing Wall Sections forCulverts 164

5 Details of SegmentalMasonry Arch Bridgeswithout Footpath Spans6ME 9M, and 12 M 165

6 Reinforcement Details of R.C.C. Slabsfor Culverts 166

7 R.C.C. Slab Bridges without Footpaths,Simply Supported Clear Spans3,4,5,6and8 M for Square Crossings 167

8 R.C.C, SlabBridges with Footpaths Simplysupported Clear Spans4, 6 and 8 Metresfor Squre Crossings ... 168

vi

9 General Arrangementof R.C~C.Skew SlabBridgewithout FootpathsSimply SupportedClearRight Spans5, 6 and 8 M . 169

10 ReinforcementDetailsof R.CC. Skew SlabBridge without FootpathsSimply SupportedClearRight Spans5, 6and 8 M ... 170

11 R.C.C. Box Cell Bridge without Footpaths3 Cells Eachof 3M ClearSpan ... 171

i2 R.C.C. Pipe Culvert with Single Pipe of1 Metre Dia. and ConcreteCradle Beddingfor Heightsof Fill from 4.0 M to 8MM ... 172

13 R.C.C. Pipe Culvert with Single Pipe of1 Metre Dia. and FirsV Class Bedding forHeights of Fill varying from 0.6 M to4MM ... 173

14 R.C.C. PipeCulverts with 2 Pipesof 1 MetreDia,~and ConcreteCradleBeddingfor Heightsof Fill from 4.0 M to 8.0 M ... 174

15 R.C.C.Pipe Culvert with 2 Pipesof 1 MetreDia. and First ClassBedding for Heights of 175Fill varyingfrom 0.6 M to 4 M

16 Circularand RectangularPipesFlowing Full 176

SYNOPSIS

Thediscussionbeginsby stressing the importanceof collecting sufficientdata before designingis started. Methods for calculatingflood dischargesfromthe catchmentareaandrainfall, from the conveyancefactor and slopeof thechannel,andfrom flood markson existing structureshave been outlined andsuggestionsmadefor fixing the designdischarge(Articles 3—7j.

After giving anoutline of the “Lacey’s Theory of Flow in IncohetentAlluvium” the procedurefor designingthe linear waterway and estimatingthe normaldepthof scourfor alluvial streams has been included. This isfoih’wed by a discussionon the normalscourdepth of quasi-alluvial streamsand the effect of contractionon thescour depth. Rules for calculating thentaviintim depthof scouranddesigningthedepth of foundations have been

1WI ItlL’Ll Their application hasbeenillustrated with workedout examples.

Nateson fixing the length andnumberof spansand on some importantst rtmctam aI detailsof minor bridgesconic next

The hydraulicsof flow throughbridgesand its applications to thecal-culationof dischargesthroughexisting bridgesas well as of afliux throughproposettbridgeshave beendealt with in somedetail, rxamplcshavebeen~yorl’et out in illustration.

Brief noteson how to (teal with overflowshave been added, The dis-cussionconcludeswith Ar~ides on the feasibility of pipe and box culvertsandthe h>draulicsof designingthem.

SmxteenPlateshave been addedat the endto facilitate routine compti-tat ion.

IPITROOUCTtON

Road project estimatesprepared for the Five-Year Planaresometimesbasedon insufficientdataandthis causesdelay in sanc-tioning them. While speedin executionof the Plan is essential,thequalityof work hasto be maintained.

Thedesigning of a culvert or a small bridge is ~ota smallmatterto be despisedby engineers. It must be rememberedthat thenumberof culvertsand small bridgesin anyroad project is so largethat, together,theyaccountfor a considerableportion of the totalexpenditure.

The object of this SpecialPublicationis to draw attention tosome aspectsof designingculvertsand small bridgesfor roadprojects.What is said here might appear simple and commonplace but cx-periencehasshownthat serious mistakes are made in thesesimplemattersand that leads to waste through unsafeanduneconomicaldesigns.

Observations in this Special Publication apply only to smallbridgesandculverts. Largerstructuresrequire moredetaileddesignprocedure.

Site Inspection

1

Site Inspection

ARTICLE 1

SITE INSPECTION

1.1. Selectionof Site. Wherethere is any choice, select asite

(i) which is situatedon astraight reachof the stream, suffi-ciently belowbends

(ii) which is so far away from the confluence of largetributa-ries asto be beyondtheir disturbinginfluence

(iii) which haswell-defined banks

(iv) which makesapproachroadsfeasibleon the straight;and

(v) which offers asquarecrossingas far as possible.

In siting small bridgesandculverts,due considerationshould be

given to the geometricsof the approach alignment and the latter

should essentiallygovernthe selectionof site unless there are anyspecial problemsof bridge design.

1.2. Existing Drainage Structures. If, by chance,there is an

existing roador railway bridge or culvert over the same streamandnot very far away fromthe selectedsite, the best meansof ascertain-ing the maximum dischargeis to calculateit from data collected bypersonalinspectionof the existing structure. Intelligent inspectionand local enquiry will provide veryuseful information, namely,marksindicating the maximum flood level, the affiux, the tendencyto scour,the probablemaximum discharge,the likelihood of collection ofbrushwood duringfloods, and manyother particulars. It should be

seenwhetherthe existingstructureis too largeor toosmall or whetherit hasother defects. All theseshould be carefully recorded.

1.3. Inspectionshouldalso include taking notes on channelconditionsfrom which the silt factor and the co~etTIcientof rugositycan be estimated.

lhe tssential Design Data 5

2

The EssentialDesign Data

ARTICLE 2

THE ESSENTIAL DESIGN DATA

2.1. In additionto the information obtained by personalinspectionof an existing structure, the designdatadescribedin theñllowing paragraphshave to becollected. What is specified hereissufficientonly for small bridges and culverts. For larger structures,detailedinstructionscontainedin the IndianRoads CongressStandardSpecifications & Codeof Practice fin RoadBridges—-SectionI, Clauses100-102,should be followed.

2.2. Catchment Area. When the catchment,as seenfrom the“topo” sheet, is less thanabout 1.25 sq.km. in area, atraverseshouldbe made along thewatershed with a chain and compass. Largercatchmentscanbe readfrom the 1 cm = 500 m topo maps of theSurvey of India by marking the watershed in penciland readingthe included areaby placing over a pieceof transparent squarepaper.

2.3. Cross-sections.As a rule, for a sizable stream, threecross-sectionsshouldbe taken,namely,one at the selected site, oneupstreamandanotherdownstreamof the site, all to the horizontalscale of notlessthan 1 cm to 10 metres or 1/1000 and with anexaggeratedvertical scaleof not less than 1 cm to 1 metreor 1/100.Approximatedistances,upstreamand downstreamof the selectedsiteof crossing at which cross-sectionsshould be taken are asunder.

TABLE

Catchinent area Distance (u/s & c/s of the crossing) atwhich cnns-sections should be taken

1. 2.5 sq. km. 150 in

2. From 2.5 to 10 sq. km. 301’ m

3. Over tO sq. km. 4’t) nt to totJiJ in

8 The Essential Design Data

The cross-sectionat the proposed site of the crossingshouldshow levels at closeintervals and indicate outcrops of rocks, pools,etc. Often an existing roador a cart-trackcrossesthe streamat thesite selectedfor the bridge. In sucha case,the cross-section shouldnot be takenalong the centreline of the road or the track as thatwillnot representthe naturalshapeandsize of the channel. Instead,thecross-sectionshouldhe takena short distance upstream or down-streamof the selectedsite.

2.4. In the caseof very smallstreams(calchmentsof 40 hectaresor less),onecross-sectionmay do hut it shouldhe carefully plottedsoas to representtruly the normal size and shape of the channelon astraight reach.

2.5. The Maximum H.F.L. The maximum high flood levelshould be ascertainedby intelligent local observation, supplementedby local enquiry, andmarkedon the cross-sections.

2.6. LongitudinalSection, ‘[he longitudinal section shouldextendupstreamand downstreamof the proposed site for the dis-tancesindicatedin Table I anti shouldshow levels of the bed, the lowwater surfaceand ihe li.FJ...

2.7. Velocily Observation. Attempts should he made toobservethe velocity during an actual flood and,ii that flood is smallerthan the maximum flood, the observed velocity shot.ild be suitablyincreased.The velocity thus obtainedis a good check on the accuracyof’ tltat calcuiatedtheoretically.

2.8. Trial Pit Sections. Where the rockor some firm undis-turbed soil stratum is not likely to be far below the alluvial bed ofhe sttcam, a~trial pit should be dug down to such rock or firm soil.

But if there is no rock or undisturbedfirm soil for a great depthbelow the stream bed level, then the trial pit may he taken downroughly two timesthe maximum depthof the (existing or anticipated)scour line. The location of each trial pit should be shown in thecross-sectionof the proposedsite. The trial pit section should beplotted to show the kind of soils passedthrough.

2.9. For very small eulverts,one trial pit will do. The resultscanbe insertedon the cross-section.

The Essential Design Data 9

2.10. In Conclusion. No satisfactory designing can be doneunlessthe minimum essentialdesign data listed above are collectedandrecorded.

These data canbe collectedwith very little effort. Failure tocollect thesecanonly result in designs being based on guessworkand such designsare likely to be either unnecessarilycostly or toresult in the failure of the structure when built.

Empirical Formulae for Peak 11Run-ofi from Catchment3~

EmpiricalFormulae forPeak Run-offfrom Catchment

ARTICLE 3

EMPIRICAL FORMULAE FOR PEAK RUN-OFF FROM CATCIIMENT

3.!. Although recordsof rainfall exist to some extent, actualrecordsof floc1ds are seldomavailable in suchsufficiency as to enablethe engineer accuratelyto infer the worst flood conditionsfor whichprovision shouldbe madein designinga bridge. Therefore,recoursehas to be taken to theoretical computations.

In this Article someof the most popularempirical formtdaearementioned.

3.2. Dickens’ Formula

Qr=CMt

where, Q=the peak run-off in en,m./secand M is thecatchmentarea in sq. km.

C=1l—14 where the annualrainfall is 60-120 cm;14—19 ia MadhyaPradesh;22 in WesternGhats.

13. Ryve’sFormula

Q=CMI

This formulawasdevisedfor Madras,

Q=run-off in cu. rn/sec. and M is the catchment areain

sq. km.C=6.8 for areaswIthin 25 km of the coast

8.5 between25 and 16C km of the coast10,0 for limited areasnearthe hills.

3.4. Inglis’ Formula

125 AtViflhI’~

14 Empirical Formulaefor Peak Run-off from Catchment

v~here Q ‘zr. max imuni flood dischargein eu.ni. see.

it! ,:tlte areaof the catchmentin sq. Km.

‘1’ he firm ula ssas desised for Bombay Presidcncs

— fl empimic’~il formuhic invols e only one factor, ii:’

the area ot’ the catehntent arid all the so mansother factors thatahleL t tl’tc ruri’olf haveto he takencare of in selectingan appropriatevalue of the co-efficient. This is extreme simplification of theproh1cm and cannot be espectedto ~ield accurateresults,

to

S

rio

a

2

0

36. A correct s, altie of C can ortl\ he derived in a civenregion Porn an extensi~e analytical stud of the measured flooddi seharges rim—i—ifs catchment areas of streamsin the region, Anysalueof C” n ill he “a lid only for the region for ~sfitch it has beendeterminedin this ‘zs ay. Eachbasin hasits own singularitiesaffectingrti n’otf, Sinec actual flood recordsare seldomavai able, the formulaeleave much to the judgment of the engineer. Marty othersimilarempit icil fbi’inulae are in use bttt none of them enc6bipasscsallpossibleconditionsof terrain and climate,

3 1, ft assist routinc computations,frigs, I and 2 havebeen,

I udcil in v~fitch curves havebeen plot ted to representthe eqnation

e

~QE4 M IN HECT&RES -~

Fig,.

Empirical Formulaefor PeakRun-off from Catchment 15

I OM~. 1 wo curves, one f~reach of the common valuesof n,

/:,, and ~, havebeendra~~ii.

.-~~— — —1 1

—

.~,..

~—- —“

c~-

RL~-OFF

rcb4t~.1rr ~— Q ~ :~_ * —

*~-.

9~=

—-.—----

~ON~4— /

- - - -_—

C. W

180

1160

“~ 140In

I 20

e 80

I,~60

In

020

0

J—--—~-~----~*-

1~ -

5 ~5 20 25 30 35 40 4 ~ 60AREAM IN SQ. KM. ~

Fig. 2

Rational Formulae for Peak 17Run-ofi from Catchment4

RationalFormulae forPeak Run-offfrom Catchment

ARTICLE 4

RATIONAL FORMULAE FOR PEAK RUN-OFFFROM CATCHMENT

4.1. in recentyears,hydrologicalstudieshavebeenmadeandtheories set forth which comprehendthe effectof the characteristicsof the catchment on run-off. Attempts also have been madetoestablish relationships between rainfall and run-off undervariouscircumstances. Some elementaryaccountof the rationale of thesetheoriesis given in the following paragraphs.

4.2. Main Factors. The size of the flood dependson thefollowing major factors

Rainfall

(1) Intensity(2) Distribution in time and space(3) Duration

Nature of the catchment

(4) Area(5) Shape(6) Slope(7) Permeabilityof the soil andvegetablecover(8) Initial stateof wetness

4.3. Relation between the Intensity and Duration of a Storm.Suppose in an individual storm, Fcm of rain falls in Thours, thenover the whole interval of time T, the main intensity I will be

- cm perhour. Now, within the duration T,. imagine a smaller

time interval t (Fig. 3). Sincethe intensity is. not uniform through-out, the mean intensity reckoned over the time interval t (placedsuitablywithin T) will be higherthan the meanintensity I taken overthe whole period.

20 Rational Formulae for Peak Run-off from Catchment

0I-U)

I’0

I-U,zLUI-z

Fig. 3

We also know that the mean intensity of a storm of shorter

durationcan be higher than that of a prolongedone.In other words, the intensity of a storm is someinverse func-

tion of its duration, It has been reasonablywell establishedthati T+cI — t+c

where C is a constant.

Analysisof rainfall statisticshasshownthat for all but extremecases,c= 1 [9*,when time is measuredin hours andprecipitationincm.

Thus,

I — T+l

fT+li

Also, ‘~r ~

-TDURATION OF STORM

~~1

*Relers to the number of the book in the Bibliography given at the endof the Publication,

Rational Formulae for Peak Run-off from Catchmerit

Thus,if we know the total precipitationF and duration 7” of,a storm,we can estimatethe intensity correspondingto t, which is a timeinterval within the durationof the storm.

4.4. For an appreciationof the physical significanceof thisrelationship,let us considersometypical cases.

First takean intensebut briefstorm which drops(say) 5cm ofrain in 20 minutes. The averageintensitycomesto 15 cm per hour.For a shortinterval t of, say,6 minutes, within the durationof thestormthe intensitycanbeas high as

FIT+l \ 5 1 0.33+1 \0.1+1 )r~zr18.2cm perhour.

Stormsof very short duration and6-minute intensitieswithin them(and, in general, all such high but momentaryintensitiesof rainfall)havelittle significancein connectionwith thedesignof culvertsexceptin built-upareaswhere the concentrationtime can be very short (seepara4.6)dueto the rapidity of flow from pavementsandroofs.

Next consider a region wherestorms areof mediumsize andduration. Suppose 15 cm of rain falls in 3 hours. The averageintensityworksout to 5 cm per hour. But in a time interval of onehour within thestorm the intensitycan be asmuchas

151 3+1 \1+1 )=locmperhour.

For the purposeof designingwaterwayof bridge such a stormis said to be equivalentof a“one hour rainfall of 10 cm”.

Lastly, considera very wet rogion of prolongedstorms, wherea stormdrops, say, 18 cm of rain in 6 hours. In a time interval ofone hourwithin the storm the intensitycan b~as high as:

~ ~ )=io.scmperhour.

Thus sucha storm is equivalentof a “onehour storm of 10.5 cm”.

4.5. “One-hour Rainfall” for a Region for Designing Water-way, of Bridges. Supposewe decidethat a bridge should be designedfor the peak run-off resulting from the severeststorm (in the region)

22 Rational Formulae for Peak Run-off from Catchment

that occurs once in 50 years or any other specified period. Let thetotal precipitationof that storm be F cm and duration 7” hours.Considera time intervalof onehour somewherewithin the duration

‘of the storm. Theprecipitationin that hour could be as high as

F/T-fl\ /-~ ~-~-~)or ~ F I + cm

Hencethe designof the bridgewill be basedon a “one-hour rainfallof say J~cm “, where

10= ~ (1 + -~) ..

SupposeFig. 3 representsthe severeststorm experienced in aregion. If t representsonehour, then the shadedarea ABCD willrepresent!~.

It is convenientand common that the storm potential of aregion for a givenperiodof yearsshouldbecharacterisedby specifyingthe “one hour rainfall” 1, of the region for the purposeof designingthe waterwaysof bridgesin that region.

1~hasto be determinedfrom the F and T of the severeststorm.That stormmay not necessarily be the most prolongedstorm. Thecorrectprocedure for finding J~) is to takea numberof really heavyand prolonged stormsand work out 1~from the F and T of eachofthem. The maximum of the valuesof I~thus found should beacceptedas “the one hour rainfall” of the region for designingbridges.

The l~of a regiondoes not have to be found for eachdesignproblem. It is a characteristicof the whole region andappliesto apretty vast areasubject to the same weather conditions. 1~of aregion shouldbe found oncefor all and shouldbeknown to the localengineers.

The Meteorological Department of the Governmentof India,havesupplied the heaviestrainfall in mm/hourexperiencedby variousplacesin india. This chartis enclosedas Appendix “A” and thevaluesindicatedtherein, may be adopted for I~,in absenceof othersuitable data.

RatknalFormulaefor Peak Run-off from Catchment 23

We start with I~and thenmodify it to suit the concentrationtime (seenext para)of the catchmentareain eachspecific case. Thiswill now beexplained.

4.6. Time of Concentration (re). Thetime takenby the run-offfrom the farthest point on the peripheryof the catchment(called thecritical point) to reachthe siteof the culvert is calledthe “concentra-tion time”.

In consideringthe intensity of precipitationit was saidthat theshorter the duration consideredthe higher the intensity will be.Thus safetywould seemto lie in designingfor a high intensity corres-pondingto a verysmall interval of time. But this interval shouldnot be shorter than the concentrationtime of the catchment underconsideration, as otherwise the flow from distant partsof the catch-ment will not be able to reach the bridge in time to make itscontribution in raising the peak discharge. Therefore, whenwe areexamining a particular catchment,we needonly considerthe intensitycorrespondingto the duration equal to the concentration period(ta)

of’ the catchment.

4.7. Estimating the ConcentrationTime of aCatchment(tn)

The concentrationtime dependson (I) the distancefrom the criticalpoint to the culvert; and (2) theaveragevelocity of flow, The latteris governedby the slope and the roughnessof the drainagechannelandthedepthof flow. Complicated formulae exist for deriving thetime of concentration fromthe characteristicsof the catchment. Forour purposes, however,the following simplerelationship[“J will do.

* O.9~5t~= ( 0.87 ~—k-) ‘“(4.7)

where t~=the concentrationtime in hours.

L=the distance from the critical’point to the culvert inkm.

H=the fall in level from the critical point to the culvertin metres.

L andH can be found from the surveyplansof the catchmentareaand t,~calculated fromEquation(4.7).

Plate I contains graphsfrom which t~can bedirectly readforknown valuesof L and 11.

24 Rational Formulae for Peak Run-off from Catchment

4.8. The Critical or DesignIntensity. The critical intensity fora catchment is that maximum intensity which can occur in a timeinterval equal to the concentrationtime t~of the catchment duringthe severest storm(in the region) of a given frequency. Call it !~.

Sinceeachcatchmenthasits own t~,it will haveits own I~.

if we put t=~t,~in the basicequation (Equation4.3~)and writeI~-for the resultingintensity, we get

F ( T+ 1

1c

Combining this with Equation(4.5), we getf2

Ic~fO

4.9. Calculation of Run-off

A precipitation of f~cm perhour over an areaof A hectares,will give rise to a run-off

Q=O.028A I~cu. m./sec.

To accountfor lossesdue to absorption,etc., introducea co-efficientP. Then

Q==O.028PA I~ ...(4.9)

where Q=max.run-off in cu. m./sec.

A=areaof catclimentin hectares.

I~=criticalintensityof rainfall in cm per hour.P=percentageco-efficient of run-off for the catchment

characteristics.

Theprincipal factorsgoverningP are (i) porosity of the soil,(ii) area,shapeand size of the catchment, (iii) vegetation cover,(iv) surfacestorage,viz,, existence of lakes andmarshes,(v) initialstateof wetnessof the soil. Catchmentsvary so much with regardto thesecharacteristicsthat it is evidently impossibleto do morethangeneraliseon the valuesof P. Judgmentand experiencemust be

used in fixing P. Also seeTable2 for guidance.

Rational Formulaefor Peak Run-off from Catchment 25

TABLE 2

MAXIMUM VALUE OF PIN THEFORMULA Q~’.’O.O28PAIc

Steep,barerock, Also city pavements ... 0.90

Rock, steepbutwooded ... 0.80

Plateaus,lightly covered ... 0.70

Clayey soils, sti~andbare ... 0.60

-do- lightly covered . ~. 0.50

Loam, lightly cultivated or covered ... 0.40

-do- largely cultivated ... 0.30

Sandy soil, light growth ... 0.20-do- covered,heavybrush ... 0.10

4.10. Relation between intensity and Spread of Storm. Wehaveso far deliberatelyeschewedany mention of the spreadof thestorm. Rainfall recording stations are points in the space andthereforethe intensitiesrecordedthereare point int~nsities.Imaginean arearound a recordingstation. The intensity will be highestatthe centreandwill gradually diminish as we go fartheraway fromthe centre,till at the fringes of theareacoveredby the storm, inten-sity will be zero. The larger the areaconsideredthe smaller will be’the meanintensity. It is thereforelogical to say that the meanin-tensity is someinversefunctionof the sizeof the area.

If I is the maximum point intensity at the centreof the storm,then the meanintensity reckonedover an area “a” is somefraction“f” of I. The fractionf dependson the area“a” and the relationis representedby the curve in Fig. 4 whichhasbeenconstructedfromstatisticalanalysis[i].

In hydrologicaltheories it is assumedthat the spreadof thestorm is equal to the area of the catchment. Therefore in Fig. 4the areais takento be the sameas the areaof the catchment. Theeffect of this assumptioncan lead to errors which, on analysis,havebeenfound to be limited to about 12 percent[9.

26 Rational Formulae for Peak Run-off from Catchment

1~0

0’9

08

50’1’

0~~

0’S0 ~00O0 20000 3QOoO 40000

Catchmentareain hectaresFig. 4

4.11. The Final Run-off Formula. Introducingthe factorf inthe Equation4.9 we get,

Q=0.028P.fA.I~ ...(4.l1~)

Also, combiningwith Equation(4.8k)

Q=0.028 P.fA.!0 ~ )

=0.028A.!0. ( ~ )

=AI0A ...(4.llb)

0.056.JPwhereA=

RationalFormulaefor PeakRun-off from Catchment 21

In the lastequation,!~measuresthe role playedby the ‘cloudsof the regionand A that of the catchment in producing the peakrun-off.

It shouldbe clearfrom the foregoingparasthat thecomponentsof A are functionsof A, L and [I of the catchment.

4.12. Resume of the Steps for Calculating the Run-off

Step1. Note down A in hectares,L in km, and H in metresfrom the surveymapsof the area.

Step2, Estimatethe I~for the region preferably fromrainfall

records: failing that from local knowledge. I~=4—. (i+ —~-),

whereF is cm of rain droppedby the severeststormin T hours.

Step3. SeePlate I andreadvaluesof t~,F, and f for knownvaluesof L, II and A.

0.056fPThen calculateA= ~

Step4. CalculateQ=A.10.A.

4.13. Example. Calculate the peak run-off tbr designinga5ridgeacrossa stream,given

Catchment L=5 km; H=30 metresA=l0 sq. km.=1000 hectares.Loamy soil largelycultivated.

Rainfall : The severeststorm that is known to haveoccurredin 20 yearsdropped15 cm of rain in 2,5 hours.

Solution. I~=—~-~-(~ )10.5cm/hour

From PlateI,

t~=1.7hours; f=0.97; P=0.30

A— 0.056x0.97x0.30 —1,7+1 0.006

Q=l000x 10.5xO.006=63.6cu. m./sec.

28 RationalFormulaefor PeakRun-off from Catchment

4.14. Run-off Curves for Small Catchment Areas (Plate 2).Supposewe know the catchmentareasA in hectaresand theaverage

slope S of the main drainagechannel. If we assume that the lengthof the catchmentis 3 times its width, then both I, and H (as definedin para4.7) can be expressed in terms of A and S and then t~calculated from Equation(4.7).

Also for small areas,f-may be takenequal to one. Then ~idepara 4.11,

Q=P.I0A(_~~_)

For 10= 1 cm, this becomes,

...(4.14)

Hence Q can he calculated for various valuesof P. A and S.This hasbeendoneand curvesplotted in Plate 2.

4.15. Plate 2 can be usedfor small culvertswith basins upto1 500 hectaresor 15 sq. km. The valuesof run-off read from Plate 2are for “one hour rainfall”, J~,of one cm. These valueshaveto bemu~ipliedby the 1~of the region. An examplewill illustrate the useof this Plate.

4.16. Example. The basinof a streamis loamy soil, largelycultivated,and the areaof the catchmentis 10 sq. km. The averageslopeof tht~streamis 10 per cent. Calculate the run-off. (!~,the onehour rainfall of the region, is 2.5 cm).

Use Plate2. For largely cultivated loamy soil, P=030 videthe Table insetin Plate2.

Enter the diagram at A=l0 sq. km.= 1000 hectares; moveverlically up to intersectthe slope line of 10 per cent. Then, movehorizontally to intersectthe 00 line; join the intersection with P=0.3and extendto the run-off (q) scaleand read

q=lO.2 cu. m./sec.

Multiply with !~

Q=10.2x2.5=25.5 cu. m.Jsec.

Rational Formulae for Peak Run-off from Catchment 29

4.17. In Conclusion. The .useof empirical formulaeshould beavoided. They are primitive andare safe only in the handsof theexpert. The average designer who cannot rely so much on hisintuition and judgmentshouldgo by the rationalprocedureoutlinedabove.

The data requiredfor the rational treatment, viz., A, L and Hcanbe easily read from the survey plans. As regards!~it should herealizedthat this does not have to be calculatedfor each designproblem. This is the storm characteristicof the whole region, withpretty vast area,andshould he known to the localengineers.

Complicated formulae, of which thereis quite an abundance,havebeenpurposelyavoided in this Article. Indeed, for a tersetreatment, the factors involved are so manyandtheir interplaysocomplicatedthat recourseneedbe takento suchtreatmentonly whenvery important structures are involved and accuratedatacanbecollected. Forsmall bridges,the simpleformulae given hereshoulddo.

EstimatingFlood Discharge 31from the Conveyance Factor

and Slope of the Stream5

Estimating FloodDischarge fromthe ConveyanceFactor and Slopeof the Stream

ARTICLE 5

ESTIMATING FLOOD DISCHARGE FROM THECONVEYANCE FACTOR AND SLOPE OF THE

STREAM

5.1. In a stream with rigid boundaries(bed and banks)theshapeand the size of the cross-sectionis significantly the sameduringa flood as after its subsidence. If we carefully plot the H.F.L. andmeasurethe bedslope it is simpleto calculatethe discharge.

52. But a stream flowing in alluvium, will havea larger crosssectionalareawhen in flood than that which may be surveyed andplotted after the flood hassubsided, During the flood the velocityis high and thereforean alluvial stream scoursits bed; but whenthe flood subsides, the w achydiminishes and the bed progressivelysilts up again. From this it follows that, beforewe startestimatingthe flood conveying capacity of the streamfrom the plotted cross-section, we should ascertain the depth of scour and plot on thecross-section the average scoured bed line that is likely to prevailduring the high flood.

5.3. The best thing to do is to inspect the scourholes in thevicinity of the site; look at the size andthe degreeof incoherenceofthegrains of the bed material; havean idea of the probablevelocityof flow during the flood; study the trial boresection;and then judgewhat should be takenasthe probableaveragescouredbed line.

5.4. Calculationof Velocity. Plot the probablescouredbed line.Measurethe cross-sectionalareaA in sq.m. and the wetted perimeter

P in in. Then, calculate the hydraulicmeandepthR= m.

Next, measure the bed slopeS from the plotted longitudinalsection of the stream, Velocity can thenbe easily calculatedfromone of the many formulae, To mentionone, viz., Manning’s formula:

(5.4a)

34 Estimating Flood Discharge

where,

V== the velocity in m persec.considereduniform throughoutthecross-section;

R==thehydraulicmeandepth;

S==the energy slopewhich may be taken equal to the bedslope,measuredovera reasonablylong reach;

n=therugosily co-efficient.

For valuesof n, seeTable3 below. Judgmentandexperienceare necessaryin selectinga proper valueof n for a given stream.

TABLE 3

Rugosity Co-efficient

Valueof “n in the formula V=11

Surface Perfect Good Fair Bad

Naturalstreams

(1) Clean,straight bank, fullstage,norifts or deeppools 0.025

(2) Same as (I), but someweedsandstones ... 0.030

(3) Winding,some poolsandshoals,clean -.. 0.035

(4) Same as (3), lowerstages, more ineffectiveslopeandsections ... 0.040

(5) Sameas(3), some weedsandstones ... 0.033

(6) Same as (4), stony sec-tions

(7) Sluggish river reaches,ratherwçedy or with verydeeppools

(8) Very weedy reaches

00275 0.030 0.033

0.033

0.040

0.035 0.040

0.045 0.050

0.045 0.050 0.055

0.045

0.040 0.045

0.055 0.060

~O.035

0.050

0,060

0.100

0.050

0.0150.0700.125

0.080

0.150

EstimatingFlood Discharge 35

5.5. Calculation of Discharge

Q = ~d. V.

~ ... (5.5)

(5.6)

where A =

fl

Now A is a function of the size, shape and roughness of thestream and is called its conveyance factor. Thus the dischargecarrying capacity of a stream dependson its conveyancefactor andslope.

5.6. When the cross-section is not plotted to the naturalscale (the same horizontally and vertically), the wettedperimetercannot be scaled off directly from the section and has to becalculated.

__~~il~lililiIilil~I~Iili I i11cm: tOM

FIG. 5

i)ivide up the wetted line into a convenientnumberof parts,A!?, BC, CD, etc. (Fig. 5). Consider one such part, say, PQ.Let PR and QR be its horizontaland vertical projections. Then,

PQ—v(PR2+QR2.) Now, PR canbe measuredon the horizontalscaleof the given cross-sectionandQR on the vertical. PQ canthenhe calculated. Similarly eachof theotherpartsis calculated. Theirsum gives the wettedperimeter.

5.7. If the shape of the cross-sectionis irregular~ashappenswhen a stream rises above its banks and shallowoverflows are

lCrn:irYi

TN

~1 I

¶Cm2 ~m

36 Estimating Flood Discharge

created (Fig. 6), it is necessaryto subdividethe channelinto two orthree sub-sections. Then R and n are found for eachsub-section,andtheir velocities anddischargescomputedseparately.

Where further elaboration is justified, correctionsfor velocitydistribution, change of slope, etc., may be applied. Books onHydraulicsgive standardmethodsfor this.

5.8. Velocity Curves. To save time in computation, curveshavebeenplottedin Plate3. Given R, S, and n, velocity can beread from this Plate.

5.9. BetterMeasurethanCalculate Velocity.. It is preferableactually to observe the velocity during a high flood. Whenit isnot possible to wait for the occurrenceof a high flood, the velocitymay he observedin a moderateflood and used as a check on thetheoretical calculations of velocity, in making velocity obser-vations, the selectedreachshouldbe straight,uniform and reasonablylong.

5,10. The flood discharge shouldbe calculatedat each of thethree cross-sections,which, asalreadyexplainedin para2.3, shouldbe plotted for all except very smallstructures. If the differencein thethreedischargesthus calculated is more than 10 per cent,the discre-pancyhas to be investigated.

Fig. 6

Estimat~ngFlood Discharge 37from Flood Marks on anExisting Structure

6

Estimating FloodDischarge fromFlood Marks onan ExistingStructure

ARTICLE 6

ESTIMATING FLOOD DISCHARGE FROMFLOOD MARKS ON AN EXISTING

STRUCTURE

6. I. Having collectedthe necessaryinformationfrom inspectionas mentionedin para 1.2, the dischargepassedby an existingstructurecanbe calculatedby applying an appropriateformula. In Article 17,some formulaefor calculatingdischarges fromflood markson existingbridges are discussed. Worked out examples have beenincludedin Article 19.

6.2. Distinct water markson bridge piersandother structurescan be easily foundimmediately following the flood. Sometimesthesemarks can beidentified yearsafterwardsbut it is advisableto surveythem assoonafterthe flood as possible. Turbulence, standingwaveand splashingmay have causeda spread in theflood marks but thebelt of this spread is mostlynarrow and a reasonably correctprofileof the surfaceline canbe tracedon the sides of piers and faces ofabutnients.

Fixing Design Discharge 41

7

Fixing DesignDischarge

ARTICLE 1

FIXING DESIGN DISCHARGE

7.1. The Recommended Rule. Flood discharges can beestimatedin threedifferent ways asexplainedin Articles 4 to 6. Thevalues obtained should becompared. The highestof these valuesshouldbe adoptedas the designdischarge Q, provided it does notexceed the nexthighest dischargeby more than 50 per cent. If itdoes,restrict it to that limit.

7.2. Sound Economy. The designeris not expectedto aim atdesigninga structureof such copiousdimensionsthat it shouldpass aflood of any possiblemagnitude that canoccur duringthe lifetime ofthe structure. Soundeconomyrequiresthat the structure should beable to pass easily floodsof a specified frequency(sayonge in 20years forsmall bridgesand 100 yearsfor big ones) and that extra-ordinary and rarerfloods shouldpass without doing excessivedamageto the structureor the road.

7.3. The necessity for this elaborateprocedurefor fixing Q,arisesfor sizeablestructures. As regardssmall culverts, Q may betaken as the dischargedeterminedfrom the run-off formulae.

Alluvial Streams-Lacey’S 45Equation’s8

Alluvial Streams-Lacey’sEquations

ARTICLE 8

ALLUVIAL STREAMS—LACEY’S EQUATIONS

8.1. The sectionof a stream,having rigid boundaries,is thesame during the flood and after its subsidence. But this is not so inthe case of streams flowing within, partially or wholly, erodibleboundaries. in the latter case, a probableflood sectionhasto beevolved from theoretical premises for the purposesof designingabridge ; it is seldom possible actually to measurethe cross-sectionduring the high flood.

8.2. Wholly ErodibleSection. Lacey’sTheory. Streamsflow-ing in alluvium arewide and shallow andmeandera greatdeal. Thesurface width and the normal scoureddepth of such streamshavetobe calculated theoretically from concepts which are not whollyrational. The theory that has gained wide popularity in India is“Lacey’s Theory of Flow in Incoherent Alluvium”. The salientpoints of that Theory, relevant to the presentsubject,are outlinedhere.

8.3. A stream,whosebed and banks are composedof loosegranular material, that hasbeendepositedby the streamandcan bepickedup and transportedagainby the currentduring flood, is saidto flow throughincoherentalluvium andmay be briefly referredto asan alluvial stream. Sucha streamtendsto scouror silt up till it hasacquiredsuchacross-sectionand(moreparticularly) sucha slopethatthe resultingvelocity is “non-silting and non-scouring”. When thishappensthe streambecomesstable andtendsto maintainthe acquir-ed shapeand sizeof its cross-sectionand the acquired slope. It isthensaid “to havecometo regime” and canbe regardedasstable.

8.4. Lacey’s Equations. When an alluvial stream carrying aknown dischargeQ cu. m. per sechas cometo regime, it has a regimewettedperimeterP metre, a regimeslope S, and a regime hydraulicmean, depthR metre. In consequence,it will have a fixed area ofcross-sectionA sq.m. anda fixed velocity V metrepersec.

48 Alluvial Streams—Lacey’sEquations

(a) RegimeCross-section

P~4.8Q~

R= 0.473.Q~f?t

s=~~03.~5hQ*

(b) Regime Velocity and Slope

V=O.44Q* x f~t

2.3 . Q~

ni size ofgrain in mm

f (silt factor)

SiltVery fine 00.081 00.500Fine 00.120 00.600Medium 00.233 00.850Standard 00.323 1.000

SandMediumCoarse

00.50500.725

1.2501.500

For theseregimecharacteristicsof an alluvial channel, Laceysuggests[18] the following relationships. It shouldbe noted that theonly independententitiesinvolved in them areQ and f. The “f” iscalled silt factor and its valuedependson thesize andloosenessofthe grains of the alluvium. Its value is given by theformulaf=l.76~/m, where ‘m’ is the mean diameterof the particlesinmillimetre. Table4 gives valuesof “f” for different bed materials.

- . ,(8.4a)

.(8.48)

“18.4r)

.(8.4e)

TABLE 4

SILT FACTOR ‘f’ IN LACEY’S EQUATIONS [18]

Alluvial Streams—Lacey’sEquations 49

8.5. The RegimeWidth and Depth. Provided a stream is trulyalluvial, it is destinedto cometo regime accordingto Lacey. it willthen be stable and have a. section and slope conforming to hisequations. For wide alluvial streamsthe stablewidth W canbe takenequalto the wettedperimeterP of Equation (8.4a).

That is

W=4.8xQ~

Also the normal depth of scourD on a straight and unobstructedpart of a wide streammay be takenas equalto the hydraulicmeanradius R in Equation(8.48). Hence

D 0.473 . Q~f~5

8.6. Curvesfor D. In Fig. 7 and8 curves havebeen plotted

50 tOO t30 200 260 300 alO 400 4~O ~OQ

D,SCHARGZ 4 IN CUJ4 P~R53c

Fig. 7

50 Alluvial Streams—Lacey’s Equations

IdlwfrS

r

-oC

‘40

I

Fig. S

from Equation(8~5h). Knowing Q andf for an altuvial stream,the

regime depth D canbe directly read off thesecurves.

btscsnoiq ~i ~jM Ptt SEC—a—

Linear Waterwayof Bridges 51

9

Linear Waterwayof Bridges

ARTiCLE 9

LINEAR WATERWAY OF BRIDGES

9.1. The General Rule for Alluvial Streams. The linearwaterwayof a bridgeacrossa wholly alluvial streamshouldnormallybe keptequal to the width required foE stability, viz., that givenbyEquation(8.5a).

9.2. UnstableMeanderingStreams. A large alluvial stream,meandering overa wide belt, may have several active channelsseperatedby land or shallow sectionsof nearly stagnantwater. Itsactual(aggregate)width may be much in excessof the regime widthrequired for stability, in bridgingsuch a stream it is necessarytoprovide training works to contractthe stream. Thecost of the latter,both initial and recurring, hasto be taken into accountin fixing thelinear waterway.

9.3. In the ultimateanalysis it may be found, in somesuchcases,that it is cheaperto adopta linear waterway for the bridgesomewhatin excessof the regime width given by Equation(8.5G).But, as far as possible,this shouldbe avoided. When the adoptedlinearwaterwayexceedsthe regime width it doesnot follow that thedepth will become lessthan the regime depthD given by Equation(8.58). Hencesuch an increase in the length of the bridgedoes notleadto any countervailingsaving in the depthof foundations. Onthe contrary,an excessivelinear waterwaycan be detrimental in sofar as it increasesthe action againstthe training works.

9.4. Contraction to be Avoided. The linear waterwayof thebridge acrossan alluvial streamshould not be less than the regimewidth of the stream. Any design, that envisagescontractionof thestreambeyondthe regimewidth, necessarilyhasto provide for muchdeeper foundation. Much of the saving in cost expected fromdecreasingthe length of the bridgemay be eatenup by the concomi-tant increasein the depth of the substructure and the size oftraining works. Hence, except where the sectionof the stream is

54 Linear Waterway of Bridges

rigid, it is generally troublesomeandalso futile from economycon-siderationto attemptcontractingthe waterway.

9.5. StreamsnotWholly Alluvial. When the banksof a streamare high, well defined,andrigid (rocky or of someothernaturalhardsoil that cannotbe affectedby the prevailing current)but the bedisalluvial, the linear waterway of the bridge should ‘be made equalto the actual surfacewidth of the stream,measured from edgetoedgeof water alongthe H.F.L., on the plottedcross-section.

Such streamsare later referredto as quasi-alluvial.

9.6. Streams withRigid Boundaries. In wholly rigid streamsthe rule of para9.5 applies,but some reductionin the linear water-way may,across some streams withmoderate velocities,be possibleand may be resortedto, if in the final analysisit leadsto tangiblesaving in the cost ofthebridge.

9.7. As regardsstreamswhich overflow their banksand createvery wide surfacewidths with shallow side sections, judgment hasto be used in fixing thelinear waterwayof the bridge. The bridgeshouldspanthe activechannelanddetrimental afflux avoided. Seealso Article 20.

The Normal Scour Depth of 55Alluvial Streams10

The NormalScour Depth ofAlluvial Streams

ARTICLE 10

THE NORMAL SCOUR DEPTH OF ALLUVIAL STREAMS

10.1. What Is the Significanceof the NormalScour Depth? Ifa constantdischarge were passedthrough astraight stablereachofan alluvial streamfor an indefinite time, the boundaryof its cross-sectionshould ultimately becomeelliptical.

Thiswill happenwhen regimeconditionscometo exist. Thedepth in the middle of the streamwould thenbe thenormal scourdepth.

In nature, however,the flood discharge in a stream does nothave indefinite duration. For this reason the shapeof the flood sec-tion of anynatural stream wouldbe governedby the magnitudeanddurationof the flood discharge carriedby it. Someobservershavefound that curves representingthe. natural stream sectionsduringsustainedfloods havesharpercurvaturein the middle thanthat of anellipse. In consequence,it is believed that L’acey’s normaldepthis anunder-estimatewhenapplied to naturalstreamssubject to sustainedfloods. We will, however,applyLacey’sEquations,pending furtherresearch.

10,2. As discussedlater in Article 14, thedepthof foundationsis fixed in relation to the maximum depth of scout,which in Wrn isinferred from the normaldepthof scour. The normaldepthof scourfor alluvial streamsis given by Equation (

8.5b) so long as the bridgedoes not contract the stream beyondthe regimewidth W given byEquation(8.5,,).

10.3. If the linear waterway of the bridge is, for some specialreason,kept lessthanthe regimewidth of the-stream,thenthe normalscourdepthunder the bridge wilr begreaterthanthe regimedepthofthe stream(Fig. 9).

wD==D[T] ,(1O.3)

The Normal ScourlDepth of Alluvial Streams

W=the regime width of the stream

L=the designedwaterway.When the bridge is assumedto causecontraction,L is lessthan W

D=thenormalscourdepth whenL=W

D’=the normal scourdepthunder the bridge with L less

than W.

This relationshipis explainedin Article 12.

_________* STREAM WIDTH W

58

where,

-1

——— ——~----*—

~ E OF ABU1~

Fig. 9. This figure representsa hypotheticalcondition, i.e;,uniform scour, D is thenormal scourdepthcorres-ponding to streamwidth Wand .D’ normalscourdepthcorrespondingto reducedwaterwayunderthebridge.

The Normal Scour Depth of 59Quasi-Alluvial Streams11

The NormalScour Depth ofQuasi-AlluvialStreams

ARTICLE 11

THE NORMAL SCOUR DEPTH OF QUASi-ALLUVIAL STREAMS

11.1. Quasi-alluvIalStreams. Some streamsare not whollyalluvial. A stream may flow between banks which are rigid ‘inso far as they successfully resist erosion, but its bed may hecomposedof loose granular material which the current can pickup andtransport. Such a stream may be called quasi-alluvial todistinguish it, on the one hand, from a stream with wholly rigidboundariesand,on the other, from a wholly alluvial stream. Sincesuch a stream is not free to erode its banks and flatten out theboundariesof its cross-sectionas a wholly alluvial streamdoes, itdoesnot acquire the regime cross-sectionwhich Lacey’s Equationsprescribe.

ii .2. It is not essentialthat the banksshouldbe of rock to beinerodible. Natural mixtures of sand and clay may, under theinfluenceof elements,producematerial hard enough to defy erosionby the prevailingvelocity in the stream.

Whenwe comeacrossa streamsection, the natural width ofwhich is nowherenearthat prescribedby Lacey’sTheory,we shouldexpect to find that the banks,even thoughnot rocky are not friableenoughto be treated as incoherentalluvium for the applicationofLacey’sTheory. Suchcaseshave, therefore,got to be discriminatedfrom the wholly alluvial streams and treated on a differentfooting.

11.3. In any suchcasethe width Wof the section,being fixedbetweenthe rigid banks,can be measured. But the normal scourdepth 1) corresponding to the designdischargeQ hasto be estimatedtheoreticallyas it cannotbe measuredduring the currencyof a highflood. -

11.4. When the Stream Width is Large Compared to Depth.In Article 5, for calcul~itingthedischargeof thestreamfrom its plottedcross-section,we drew the probable scoured bed line (para5.3).

62 The Normal ScourDepth of Quasi-Alluvial Streams

When the stream scours downto that line it shouldbe capableofpassing the dischargecalculated there, say q Cu. m./sec. But theJisehargeadopted for design, Q, may be anythingupto 50 per centmorethan q (see para7.1). Therefore, the scourbedline will haveto be lowered further. Supposethe normal scour depth forQ is 1)andthat for q is d, then,

D=dx (_Q~1s ...(l1.4)\ qj

Since d is known, D can be calculated. This relationshipdependsort the assumptionthat the width of the streamis largeascomparedwith its depth, and therefore, the wetted perimeter isa~roximatelyequal to thewidth and is not materially affected byvariations~in depth. It also assumes that the slope remainsunalterd.

Q=areax velocity

=(RP) ~

=K. R51~

whereK is a constant.

Hence,R variesas Q ~. Since in such streamsR is very

3/ -

nearlyequalto the depth, therefore,D varies as Q ~. Hence the

Equation(11.4).

From the above relationshipit follows that if Q is 150 per centof q, D will be equalto 127 percent of d.

11.5. Alternatively, the normal depth of scour of wide streamsmay be calculatedas under. If the width of the stream is largeascomparedwith its depth,we maywrite W for P and D for R.

Q=areax velocity

=(P.R))< V=(W.D). V.

i.e., D=

The Normal Scour Depth of Quasi-Alluvial Streams 63

Now ~Vis the known fixed width of the stream. if thevelocityV hasactuallybeenobserved(para5.9), then D can be calculatedfrom the aboveequation.

11.6. Suppose the velocityhas not been actually measuredduring a flood, but the slope S isknown.

Q=areax velocity

S~

=(RxP)x

WxS~x ...(1l.6)

Knowing Q, W andS, wecancalculateD from this equation.

For quickness,velocity curves inPlate 3 canbe used. Assumea valueof R and fix a suitable value of the rugosity co-efficientn appropriatefor the stream. Correspondingto these valuesand theknown slope, readthe velocity from Plate3. Now calculate thedischarge(=Vx Rx W). If thisequalsthe design dischargeQ, theassumedvalueof R is correct. Otherwise assume another valueofR and repeat. Whenthe correctvalueof R hasbeen found, takeDequal to R. (Seethe workedout Examplein para 18.8).

11.7. Another Formula. The procedure described above canbe applied if we know eithertheslopeof the stream or the actualobserved velocity. If we do not know eitherof these, we can applythe following procedurefor approximatecalculation of the normalscour depth.

Supposethe wetted perimeterof the streamis F and its hydrau-lic meandepthR. If Q is its discharge,then,

Q=areax velocity

=(P.R) (C. R1 S~) .. .(i)

Now if this stream, carrying the discharge Q, had been whollyalluvial, with a wettedperimeterP~andhydraulicmean depth R

1 forregime conditions,then,

Q=(P1. R~)(C.R~.S4) .(ii)

64 The Normal ScourDepth of Quasi-AlluvialStreams

Also for a wholly alluvial streamLacey’sTheorywould give:

Pi=4.8. . - ~

and R1= 0.473 ...(iv)

f~Equatingvalues of Q in (i) and (ii), andrearrangingwe get:

$1R( P1 ~R1~P ) .. V

Now substitutingvaluesof Pi and R1 from equations (iii) and(iv) in (v), we get

R---- 1.2l.Q°~°5 .,(vi)

— fo.~ x ~

If the width Wof thestreamis large comparedwith its depthD, thenwe can write W for P andD for R in equation(vi). This willgive

D— l.2l.Q0~°5 ...(Il.7)— fo.~8x W~

Thus,if the design dischargeQ, the natural width W, and the siltfactorfare known, the normalscour depthD can be calculated fromEquation(11.7).

The abovereasoningassumesthat the slopeat the section inthe actualcaseunderconsiderationis the same as the slopeof thehypothetical(Lacey’s) regimesection, carrying the same discharge.This is not improbable wherethe streamis old and its bed materialis really incoherentalluvium. But if thereis any doubt abeut this,the actualslopemustbe measuredandthe procedure given in para11.6 applied.

11.8. When the Stream is not Very Wide. If the width of thestreamis not very large as compared with its depth, then themethodsgivenabovewill not give accurateenough results. In sucha casedraw the probable scoured bed line on the plotted cross-section,measurethe areaand the wetted perimeterand calculate R.

The Normal ScourDepthof Quasi-Alluvial Streams 65

Correspondingto thisvalue of R and the known valuesof S and n,read velocity from Plate 3. If the productof this velocity and theareaequalsthe design discharge,the assumed scouredbed line iscorrect, Otherwise, assume another line and repeat. ThenmeasureD.

11.9. Effect ~f Contraction on Normal Scour Depth. If, forsome specialreason,the linear waterway L of a bridge acrossaquasi-alluvial streamis kept less than the naturalunobstructedwidthW of the stream(Fig. 9), then thenormal scour depth under thebridge I)’ will be greaterthan the depthD ascertained abovefor theunobstructedstream. The following relationshipwill apply

D’ ~ (—~!~Y~ ...(ll.9)

For proofseeArticle 12.

The Effect of Contraction on 67the Normal Scour Depth12

The Effect ofContraction onthe NormalScour Depth

ARTICLE 12

THE EFFECT OF CONTRACTION ON THE NORMALSCOUR DEPTH

12.1. In Fig. 10, Wis tI-te width, D the normal scour depth,and is the velocity of the streamin an unobstructed reach upstreamof the bridge.

x_

—

S ~

Fig. 10

If XX is the normal scourbed line and further scouring hasceased,thenaccordingto Kennedy’sSilt Theory

u=m .(i)

Since the vent-areaof the bridge is smallerthan that of the stream,therefore,whenthe waterarrivesat the bridgethe initial velocity V

a4

________ I-_—

——

70 The Effect of Contractionon the Normal ScourDepth

throughthe bridge will be greaterthanu. At thatstage,

w

The initial high velocity V underthe bridge is momentary. It startsfurther scouringand,in the process,itself beginsto decrease (becausefurther scouringmeansmoreareaof flow through the bridge) tiltequilibrium is reached. If in that state of equilibrium, the depthunderthe bridge is D and the final reduced velocity v, then byKennedy again,

(ii)

Fromequations(1) and(ii)

V ID’\0.64

Now, sincethe dischargeat all sections is the same,therefore,

u. W. D=v. L. D’

where L is the linearwaterwaythrough the bridge,

(W.D\

i.e., v= ~ L . D’ ) xu ..(iv)

Substitutingfor v, from (iv) in (iii), we get

D’=D ( 1+’ )O.61 ...(12.1)

Knowing D, W and L we can calculate the increaseddepth ofscourD’ underthe bridge from the aboveequation.

12.2. In this discussionit is tacitly assumedthat scourdevelopsuniformly and the bed line is lowered acrossthe whole sectionof thebridgein a smooth curve. Whenthat happensthe depth D’ will bethe normal scourdepth. In natUral streams, however,scour is notuniform. At some points thereis deeperscour than that at others.An expressionfor the deepestscourin such cases wilt be developedlater(see para13.5).

Maximum Scour Depth 71

13

Maximum ScourDepth

ARTICLE 13

MAXIMUM SCOUR DEPTH

13.1. In consideringbed scour,we areconcernedwith alluvialand quasi-alluvialstreamsonly and not with streamswhich haverigid beds.

13.2. In naturalstreams,the scouring action of the currentisnot uniform all alongthe bed width. It is not so even in straightreaches. Particularlyat the bendsas also roundobstructionsto theflow, e.g.,the piersof the bridge, thereis deeperscourthan normal.In the following paragraphs,rules for calculatingthe maximumscourdeptharegiven. It will be seen that the maximum scour depthistakenas a multiple of the normal scour depth according to the cir-cumstancesof the case.

13.3. In order to estimate the maximum scour depth, it isnecessaryfirst to calculatethe normal scour depth. The latterhasalreadybeendiscussedin detail, To summarisewhat has been saidearlier, the normal scour depth will be calculatedas under

(i) Alluvial Streams. Provided the linear waterway of thebridge is not less than the regimewidth of the stream, thenormal scourdepth D is the regime depth as calculatedfrom Equation(8.5k).

(ii) Streamswith Rigid Banks but Erodible Bed. Providedthe linear waterway of the bridge is not less than thenatural unobstructedsurface width of the stream,thenormal scour depth D is calculated as explained inArticle 11.

(iii) Modification of Normal Scour Depth. When the bridgecausescontraction, i.e., L is less than W, both for alluvialand quasi-alluvial streams, the modified normal scourdepthD’ is given by

D’=D ( W )O.61

74 Maximum Scour Depth

where, L— linear waterway of the bridge.

Wr.zz..regime width in the case of alluvial streams and un-obstructed natural width in the case of quasi—al iuv~taistreams.

I 3.4. Rulesfor Finding Maximum ScourDepth. The rules forcalculating the maximum scour depth from the normal scour depthare

Rule 1 For average conditions on a straight reach of thestream and when the bridge is a single span structure, i.e., it has nopiers obstructing the flow, the maximum scour depth should be takenas 1,27 times the normal scour depth, modified for the effect of con-traction where necessary.

Rule 2 : For bad sites on curves or where diagonal currentsexIst or the bridge is a multi-span structure, the maximum scourdepth should be taken as 2 times the normal scour depth, modifiedfor the effect of contraction when necessary.

Rule 3 For bridges causing contraction, the maximum scourdepth obtained by Rule I or 2, should be compared with that givenby the following equation and the greater of the two valuesadopted

U’ 1.56

D.~=Dwhere D~,is the maximum scour depth, and

0, L, W have the same significance as above. Anexplananon of thislast Rule will now follow.

115. Explanationof the Formula

Hf 1,56

DrnD ( ~_)

We have to revert to the discussion in Article 12. There we assumedthat scouring under the bridge was uniform and worked out an ex-pression for the normal scour depth under the bridge, in naturalstreams scouring is not uniform and deeper scour develops at somepoints than at others (Fig. II). To work out what the maximumscour will be under such conditions we assume that, as scour deve-

Maximum Scour Depth 75

lops, the velocity through deepened parts, P and Q in Fig. 11, doesnot decrease. More water can rush into portions of deeper scourfrom the sides and the initial velocity through the bridge, viz., V ismaintained in those portions.

———----—-— STREAM WIDTH W

F-

--V

.(i)

When the maximum scour depth D,~has developed there will be equi-lihrium between V and D~4.

Flence, by Kennedy,tn(D,,,)°’” .,.(ii)

Also, as in Article 11u = m(D)°’M . . .(iii)

From(ii) and (iii)

V D °‘°~

- ...(iv)

Substituting for V from (i) in (iv) and rearranging

Dm~I) (W)1.56 ..,(13.5)

12 It is easy to prove that, where Rule I applies, themaximum scour depth given by it governs so long as the linearwaterway of the bridge L is not less than 65 per cent of Hf. Beyondthat limit, the maximum scour depth given by Equation (13.5) isgreater.

Fig. It

wI ~-

76 Maximum ScourDepth

But where Rule 2 applies,the maximum scourdepth, given byit, will governwhere L is anything down to 47 per cent of W, Sincecontractionsbelow this limit are not resortedto in practice, checkingby Rule3 becomesneedless.

Examplesat the endof this Article will makethis clear.

13.7. The finally adoptedvalue of Dm must not be less thanthe depth (below H.F.L.) of thedeepestscourhole that maybe foundby inspectionto exist at or nearthesite of the bridge.

The following examples will illustrate the application oftherules in para13.4 above,

13.8. Example 1. A bridge is proposedacross an alluvialstream(f= 1.2) carryinga dischargeof 600 Cu. m./sec. Calculate thedepth of maximumscour whenthe bridgeconsistsof:

(a) 3 spansof 15, 25 and 15 m;

(b) 5 spansof 15 m each;

(c) 4 spansof 30 m each.

Regime surfacewidth of the stream

W=4.8 Q~=4.8x600~=1l7.5m

Regimedepth

~==o473—~-_=O.473x6OO~=3.76m(1.2)~

Case(a). Rule 2 applies, since the bridge has piers:

Dm2 x D’2 >( D(W/L)°~’

/ 117.5 \O.61=2x3.76(~ 55 / =11.9m

For check,calculateD,~by Equation(13.5)

1175 ~Drn=D(W/L)1~=3.76( 55 ) =12.3m

Maximum ScourDepth 77

Adopt 12.3 m say 12.5 m

[Note—In this case Equation (13.5) governs because thecontractionexceeds47 per cent. Comparepara 13.6].

Case(b). Rule 2 applies

D,,~=2D’=2fl(WfL)°’6’

/ 117.5 \O.~I=2x3.76x~~ )75 =9.9 in

Checkby Equation (13.5).

D,~=D(WfL)l.56=3.76(117.5 )~‘~7.6

Adopt 9,9 in say 10.0 mCase (c). Rule 2 applies

Drn2Dr2X3.767.52 in

Equation (13.5) will not apply asL=W

Adopt 7.52 m say 7.5 in

13.9. Example 2. A stream with rocky banks has a width of90 m. Its bed is alluvial (.1= 1.2) anddischarge600 cu. m./sec.Calculatethe maximum scourdepthundera bridge(a) a singlearchspanof 60 m, (b) threespansof total linear waterway60 m.

By Equation(11.7):

D=1.2lQ°~3/(f°~xW0~o)

1.21 x600°’68= l.2°33x90°~

4,35 m

Case(a). By Rule I

D,~’=I .5D’ = 1 .5D(W/L)°~’/ 90 \0.61

=l.5x4.35x~—)60 =8.36 in

Check by Equation(13.5),

D7~=D(WL)1~6=4.35(...~-)82

78 Maximum Scour Depth

Adopt 8.25 m

[Note : When contractionis 67 per cent,Rule I and Equation(13.5) give nearly equalvaluesof D,~].

Case(h). By Rule 2

Dff~=2 D~=2~<D x (~4;7L)O’6l

/ 90 \061=2 :~4.35>~ —)60 =11.15 in

Check by Equation(13.5),

90 ‘~

D(W/L)1.56=4.35( ~ ) =8.2 in

Adopt 11.15 m

[Note : In this example,the datado not mention the velocityor the slopeof the stream, yet Equation(11.7) enablesus to find the normal depth D of the unobstructedstream].

Depth of Bridge Foundations 79

(Df)

14

Depth of BridgeFoundations (Df)

ARTICLE 14

DEPTH OF BRIDGE FOUNDATIONS (Di)

14.1. The following rules should be kept in view while fixingthe depth of bridge foundations

Rule (1) Erodihle Beds. The foundations shall be takendown to a depth below the maximum high floodlevel one-third greater than the calculated depth ofmaximum scour subject to a minimum depth belowthe scour line of two metresfin arched bridges, and1.2 metres J’or other bridges.

Rule (2) Hard’Bcds. When a substantial stratum of solidrock or other material not erodible at the calculatedmaximum velocity is encountered at a level higherthan or a little below that given by Rule (I) above,the foundations shall be securely anchored into thatmaterial. (This means about 0.3 metre or so intorock and about 0.6 metre or so into other hardmaterial).

Rule (3)~All Beds. The pressure on the foundation materialmust be well within the bearing capacity of thematerial.

These rules enable us to fix the level of the foundations ofabutments and piers.

14.2. The rules mentioned in the last para apply when no bedfloor is provided under the structure and the stream is free to scouras it may. The structure is then said to have deep foundations.It is sound to design deep foundations as far as circumstancespermit.

14.3. In the case of small culverts, however, bed floors may beprovided. In this connection the following is considered soundpractice for culverts on erodible soil .

82 Depth of Bridge Foundations

Keep the top of the floor about 0.3 metre below the bed level.Take the foundations of the abutment 1.25 metres below thetop of the floor. Provide an upstream curtain wall I to 1.5metres deep and a downstream curtain wall 1.5 to 2.5 metresdeep from the top of the floor. The precise depth of curtainwalls, within the stated limits, will depend on the velocityof flow through the structure and erodibility of the bedmaterial.

This rule may he followed when it is intended to avoid calcula-tion of maximum scour depths for want of sufficient site data,

Length of Clear Span and 83Number of Spans15

Length of ClearSpan andNumber of Spans

ARTICLE 15,

LENGTH OF CLEAR SPAN AND NUMBER OF SPANS

15.1. As a rule, the numberof spansshouldbe as small aspossible, since piers obstruct flow. Particularly in mountainousregions,where torrential velocities prevail, it is betterto spanfrombankto bankusingno piers if possible.

15.2. Considering only the variable items, the cost of super-structure increasesand that of the substructuredecreaseswith anincrease in the span length. The most economical span length isthat,which satistlesthe equation.

Cost of variable parts in the 5 Cost of thesuperstructure j — substructure

15.3. Wherethe bridge is big, and difficult conditions areanticipated in the sinking of foundations,accurate and detailedexamination of the economic aspect is essentialand any deviationfrom the ideal casehas to be justified strongly.

15.4, Length of Span. In small structures,where openfoun-dationscanbe laid andsolid abutmentsandpiers raised on them, ithasbeenanalysedthat the following approximaterelationshipsgiveeconomicaldesigns.

For masonryarchedbridgesSr~2H. ...(15.4a)

For R.C.C. slab bridges:S=1.5H ...(15.4b)

where S=clearspanlength in metres.

11= total height of abutmentor pier from the bottom of itsfoundationto its top in meters. For archedbridgesitis measuredfrom foundationto the intrados of thekey stone.

86 Length of Clear Span and Number of Spans

15.5. We have earlier found the depth of foundations, D~. Weshould now fix the vertical clearance, which, added to D,, will give.11. The following minimum vertical clearance shall be provided:

Discharge in m3/sec Minimum verticalclearance in mm

uptoo.3 1500.3 to 3.0 . 4503to30 60030 to 300 900300 to 30.00 1200Above 3000 1500

In designing culverts for roads across flat regions where streams arewide and shallow (mostly undefined dips in the~ ground . surface), andin consequence the natural velocities of flow are very low, theprovision of clearance ‘serves no purpose. Indeed it is proper todesign such culverts on the assumption that the water at the inlet endwill pond up and submerge the inlet to a predetermined extent. Thiswill be discussed later in detail (Articles 21 and 22).

15.6. The Number of Spans. If the required linear waterwayL is less than the economical spin length it has to be provided, as itis, in one single span.

15.7. When i~is more than the economical spark length, 51 thenuniber of spans required (N) is tentatively found from the followingrelation:

L = NS.

15.8. Since N must be a whole number (preferably odd), 5’ hasto be modified suitably. In doing so it is permissible to adoptvarying span lengths in one structure to keep as close as possible tothe requirements of economy and to cause the least obstruction to thcflow.

15.9. To facilitate inspection and carrying out ot’ repairs, theminimum vent—dimension of culverts should normally he 750 mm.The vent size of irrigation culverts may be decided considering theactual requirements and site conditions.

Structural Details of Minor 87Bridges and Culverts16

Structural Detailsof Minor Bridgesand Culverts

ARTICLE 16

STRUCTURAL DETAILS OF MINOR BRIDGES ANDCULVERTS

16.1. Abutment andPier Sections

The abutments and pier sections should be so designed as towithstand safely the worst combinationof loads and forces as specifiedin the IRC Code of Practice for Road Bridges. Bridges and Culvertson National Highways should he designed for one lane of Class 70Ror two lanes of Class ‘A’ loading, whichever produces more severestresses in the various members under construction.

For eulverts with small spans designed for IRC Class 70Rloading or 2 lanes of IRC Class ‘A’ loading, the abutment sectionsmay be adopted from Plate 4. In case of bridges, detailed designshave to be carried out to arrive at the safe sections.

The base widths of the abutment and the pier depend on thehearing capacity of the soil. The pressure at the toe of the abutmentshould he worked out to ensure that the soil is not oversiressed.

In scourable beds, the length of the pier should be kept mini-mum and preferably made circular in the case of skew bridges.

16.2. Wing Walls and Return Walls

Long and hefty wing walls should be avoided. Where thefoundations of the wing walls can be stepped up, having regard to thesoil profile, this should he done for the sake of economy. Quite oftenshort return walls meet the requirements of the ease and should beadopted. Plate 4 gives the sections of wing walls and return wallsfor various spans and heights.

16.3. UnreinforcedMasonryArches

The type of superstructure depends on the availability of thematerials of construction and their cost. An evaluation of the rela-

go StructuralDetailsof Minor Bridgesand Culverts

tive economicsof R.C.C. slabs and masonry arches shouldbe madeand the latter adoptedwherefound moreeconomical.

The masonryarchesmay be eitherof cement concreteblocks1:3:6 or dressedstones or bricks in1:3 cementmortar. The crushingstrengthof concrete,stone or brickunits shallnot be less than 106 kgpersq.m. Wherestonemasonryis adoptedfor the arch ring, it shallbe eithercoursedrubblemasonryor ashlar masonry. Plate5 showsthe detailsof arch ring of segmental masonry archbridges withoutfootpathsfor spans6 m, 9 m and 12 m.

The sectionsof abutments andpiers for masonryarch bridgeswill haveto be designedtaking into account the vertical reaction,horizontal reactionandthe momentat springing dueto deadloadand live load. Table 5 gives the details of horizontal reaction,vertical reactionand moment at springingfor arch bridgesof spans

6 m, 9 m and 12 m consideredin Plate 5 and Table6 gives the in-fluenceline ordinates for horizontal reaction, vertical reactionandmomentat springing for a unit load placedon the archring.

TABLE 5 VERTICAL REACT1ON, HORIZONTAL REACTION AND MOMENT

AT SUPPORT DUE TO DEAD LOAD, DUE TO ARCH RING

MASONRY, FiLL MATERIAL AND ROAD CRUST FOR ONEMETRE OF ARCH MEASURED ALONG THE TRANSVERSE

DIRECTION (i.e., PERPENDICULAR TO THE DIRECTION

OF TRAFFIC). RIGHT BRIDGES

Horizontal Vertical Moment atreaction reaction springing(Tonnes) (Tonnes) (TonneMetres)

SI. Span (metres)No. (Effective)

1. 6 9.35 10.92 (+) 0.30

2. 9 17.40 21.00 (+) 0,47

3. 12 27.00 33.60 (+) 0.62

Notes: I. Unit weight of arch ring masonry, fill material and the road crustis assumedas 2,24 tonnesper cubic metre;

2. Positive sign for moment indicatestension on the inside of archring.

StructuralDetails of Minor Bridges and Culverts 91

TABLE 6 INFLUENCE LINE ORDINATES FOR HoRIzoNTAL REACTION

(H), VERTICAL REAcTIoN AT SUPItORT (VA) AND (VB) AND

MOMENT AT SPRINGING (MA) AND (MB) FOR UNIT

LOAD, SAY 1 TONNE LOCATED ALONG THE ARCH

AXIS AT AN ANGLE 0 DEGREES FROM THERAD!US OC. RISE OF ARCH IS ONE

QUARTER OF SPAN

MA MBSI. 0 HNo. degree in tonncs

(a) Effective Span 6 m

1, 0 0.93 0.500 0.500 (—)0.2213 (—)0.22132. 5 0.91 0.577 0.423 (—)0.1388 (—)O.27753. 15 0.75 0.725 0.275 (+)0.0713 (—)0.30754. 25 0.52 0.849 0.152 (+)0.2513 (—)0.25885. 35 0.25 0.940 0.061 (+)0.3413 (—)0.13886. 45 0.05 0.989 0,012 (+)0.2438 (—)0.03387. 53°8 0 1.000 0 0 0

(b)Effectlve Span 9 m

1. 0 0.93 0.500 0.500 (-.)0.3318 (-.)0.33182. 5 0.91 0.577 0.423 (—)0.2081 (—)0:41633. 15 0.75 0.725 0.275 (+)0.1069 (—10.46124. 25 0.52 0.849 0.152 (+)O.3769 (—)0,3881S. 35 0.25 0.940 0.061 (+)0.5l 19 (—;0.20816. 45 0.05 0.989 0.012 (+)0.3656 (—)0.05067. 53°8’ 0 1.000 0 0 0

UN~TLOAD(t T0NNE) C * CROW~4

VA V8

in tonnes in tonnes

92 Structural Details of Minor Bridges and Culverts

(c) Effective Sian 12 m

1. 0 093 0.500 0.500 (—)0.4425 (—)0.44252. 5 0.91 0.577 0.423 (—)O.2775 (—)0.55503. 15 0,75 0.725 0.275 (+)0.1425 (—)O.61504. 25 0.52 0,849 0.152 (+)0.5025 (—}0.51755. 35 0.25 0.940 0.061 (+)0.6825 (—)O27756. 45 005 0.989 0.012 (+)O.4875 (—)006767. 53°8 0 1.000 0 0. 0

Note: Positive sign for moment indicates tension on the inside ofarch ring

16.4. R.C.C. Slabs

In case a R.C.C. slab has to be used for culverts, its dimén-sions and reinforcementdetails shouldconform to those given inPlate 6. For R.C.C. slab bridges at square crossings, the dimensionsand reinforcement details should conform to Plate 7, if withoutfootpaths and to Plate 8, if with footpaths. For R.C.C. slab bridgesat skew crossings, the dimensions and details of reinforcement aregiven in Plates 9 and 10 for slabs without footpaths. The dimen-sions and details of reinforcement of R.C.C. box cell bridges of3 m span for different heights without footpaths are given inPlate Il.

The above drawings are for structures designed for one laneof IRC Class 70 R or two lanesof IRC Class A loading, whicheveris severer.

16.5. Width of Roadway

The length of a culvert (along the direction of flow) should besuch that the distance between the outer faces of the parapets wilequal the full designed width of the formation of the road. Anyproposed widening of the road formation in the near future shouldalso be taken into account in fixing the width of the culvert.

In small bridges, the length (parallel to the flow of the stream)should be sufficient to give a minimum clear roadway of 4.5 metresfor a single lane bridàe and 7.5 metres for a two lane bridge betweenthe inner faces of the kerbs or wheel guards. Extra provision shouldbe made for footpaths, etc., if any are required.

StructuralDetails of Minor Bridges and Culverts 93

16,6. R.C.C. Pipe Culverts

For small size structures, R.C.C. pipe culverts with single ordoublepipes,dependingupon thedischargemay be used as faraspossible,as they arelikely to prove comparativelycheaper thanslabculverts. Thedetailsof pipe culvertsof 1 metredia., with single ordouble pipeshavingcementconcreteor granular materials in bed,may betaken from Plates12 to 15, for IRC Class 70R or 2 lanes ofClassA loading.

Elements of the Hydraulics 95of Flow through Bridges17

Elements of theHydraulics ofFlow throughBridges

ARTICLE 17

ELEMENTS OF THE HYDRAULiCS OF FLOWTHROUGH BRIDGES

17.1. The formulae for discharges passing over broad crestedweirs and drowned orifices have been developed ab Initlo in thisSection. These formulae are very useful for computing flooddischarges from the flood marks left on the piers and abutments ofexisting bridges and calculating afflux in designing new bridges. It isnecessary to be familiar with the rationale of these formulae to beable to apply them intelligently.

17.2. Broad Crested Weir Formula applied to Bridge

In Fig. 12, XX is theenergy line.

At Section 1, the total energy,

Openings

Fig. 12

water surface profile, and ZZ the total

(i)

98 Elements of the Hydraulics of Flow Through Bridges

At Section 2, let the velocity head AB be afraction n ofH, i.e.,

AB=f. =~n.H ... (ii)

Ignoring the loss of headdue to entry and friction, and equat-ing total energiesat Sections1 and2:

H==AC=AB+BC=nH 4-BC

Hence,the depthBC=(l—n) H ... (iii)

Theareaof flow at Section2,

a~=BCxlinear waterway==(l—n)HXL.

Velocity at 2, from (ii),

v=(2gn

Therefore,the dischargethroughthe bridge

Q=a.v.

=(l —n) H,L. >< (2gn

To account for losses in friction, a co-efficient C.~,may beintroduced. Thus,

Q==C~(1—n) H.L. (2gn

==C~T~TL. Hit (~~:a/2) ... (iv)

The depth BC adjustsitself so that thedischargepassingthroughit is maximum. In that condition,

dQ ~dn —

i.e., ~.n1 —~/2n~=0, i.e., n=~.

Puttingn=~in (iv)

Q=l.706 Cw, LH~(l7.2~)

Elementsof the Hydraulics of Flow Through Bridges 99

Combiningwith (I),

Q=1.706 C~.L(Du+~ ... (17.2k)

SinceAB is ~ H, thereforeBC is ~ H, or 66.7percentof if.

On exit from the bridge, some of the velocity head isreconvertedinto potential head dueto the expansionof the sectionand the water surface is raised, so that Dd is somewhatgreaterthan BC, i.e., greater than 66.7percent of H. In fact, obser~a-tions have proved that, in the limiting condition, Dd can be 80percent of D~. Hence, thefollowing rule

“So long as the affiux (D~—Dd) is not less than ~ D~,theWeir Formula applies, i.e., Q dependson D~andis independentof D~”.

The fact that the downstreamdepth Dd has no effect on thedischargeQ, nor on the upstreamdepthDM whenthe affiux is not lessthan ~ D~,is dueto the formation of the “StandingWave”.

The co-efficient C,, may betakenasunder:

(1) Narrow bridgeopening with orwithout floors 0.94

(2) Wide bridge openingwith floors 0.96

(3) Wide bridge opening with nobedfloors. ... 0.98

17.3. The Orifice Formula

—zsuDr*.c~

Fig. 13

100 Elementsof the Hydraulics of Flow Through Bridges

When the downstream depthD~is morethan 80 percent ofthe upstream depth D~,the Weir formula does not hold good,i.e., the performanceof the bridge opening is no longer unaffectedby ~

in Fig. 13, XX is the water surface line and ZZ the totalenergy line.

Apply Bernouli’s Equation to points 1 and 2, ignoring the lossof head(h) due toentry and friction.

D~+$—=D’+ +g

or L_= D~_D’+~!!_~2g 2g

r=4./2g(Dd —D’+—~2g

Put D~—D’==h’

Then, V\/2~~(h’+

The discharge throughthe Section 2,

Q=a . v.

=L.D’.\/2g (h’+~—)

Now the fractional differencebetweenD’ and D,~is small. PutD(~for D’ in (i).

Q=L.D1i.v’2g(h’+4~) ,,.(ii)

In the field it is easierto work in termsofh=D~—D~~,insteadof h’. But h is less thanh’, as on emergencefrom the bridge thewater surface rises, due to recovery of some velocity energy as

potential head. Suppose~__ representsthe velocity energy that is

converted into potential head.

Elementsof the Hydraulics of flow Through Bridges 101

Then = h +

Substituting in (ii)

Q==L.D4s/2~(h+e4I

Now introduce a co—efficient C , to account for losses of headthrough the bridge. We get

L

~.L.Ddv::rl

For values of e and C~,see Figures 141 and I 5~[19

a COEFFiCIENT “e “—

ctL __

—or—AW

—FOR—

(173)

— TUE ORiFiCE FORMULA

O~5 0~6 O~7 08 09 1.0

Fig. 14

102 Elements of the Hydraulics of Flow Through Bridges

— COEFFICIENT C0——FOR—

—THE ORIFICE FORMULA—

0~~Sa L ___

—orA W

Sum of bddqe spansW Unobsirucied width of streom.0’ ~.TQQ ot How under M hTnjqgA ;UnobslructRd Arto of (tow ci t~

$Prc.Orfl -

Fig. 15

toints

17.4. in Conclusion, Let us get clear on sonic important

1) In all these form u]ae D1~ is not affected in an~’ way bythe existence of the bridge It depends only on. theconveyance factor and slope of tail race. (,~has,therefore, got to be actually measured or calculatedfrom area-slope data of the channel as explainedalready in Article II.

(2) The Weir Formula applies only when a standing wave.is formed, i.e., when the affiux (h=~D~—D4)is not less

‘1~00

096

1II Ill Il

1 I I Il

06 0-7 0-8 0.9 1-0

than ~ D~.

Elements of the Hydraulics of Flow Through Bridges 103

(3) The Orifice Formula with the suggested values of Cand e should be applied when the afflux is less than

IDa.

17.5. Examples have been worked out in Articles 18 and 19 toshow how these formulae can be used to calculate afflux and dischargeunder bridges.

Affiux 105

18

Afflux

ARTICLE 18

AFFLUX

18.1. The afflux at a bridge is the headingup of the watersurface caused by it. It is measuredby the differencein levelsofthe water surfacesupstreamand downstreamof the bridge(Fig. 16),

PLANFig. 16

18.2. Whenthe waterway area of the openingsof a bridgeisless than the unobstructednaturalwaterwayareaof the stream,i.e.,

PIER

— — -~. ~ ffu~

SEC’rlO~4

w

I

//717///

108 Afflux

when the bridgecontractsthe stream,afflux occurs. Contraction ofthe stream is normally not done; but under some circumstances it is

takenrecourseto, if it leadsto ponderableeconomy. Also, in thecaseof somealluvial streamsin plains the natural stream width may

be much inexcessof that requiredfor regime. When spanningsucha stream,it has to be contractedto, moreor less,the width requiredfor stability by providing training works.

18.3. Estimating afflux is necessaryto see its effect onthe~clearance’ underthe bridge;on the regimeof the channelupstreamof the bridge; andon the designof training works.

18.4. For calculatiugafflux we mustknow (1) thedischargeQ.(2) the unobstructedwidth of the streamW, (3) the inner waterwayof the bridge L, and (4) the averagedepth downstreamof the bridgeDd.

18.5. The downstreamdepth D,~is not affectedby the bridge;it is controlled by the conveyance factor and slopeof the channelbelow the bridge. Alsothe depth, that prevailsat the bridgesitebeforethe constructionof the bridge,can be assumedto continuetoprevail just downstreamof the bridge after its construction. ThusD,~is the depth that prevailsat the bridge sitebeforeits construction.To estimate afflux we must know D~. In actual problems,Dr1 jSeithergiven or can be calculatedfrom the datasupplied.

18.6. Example. A bridge, havinga linear waterwayof 25 m,spans achannel 33 m wide carrying a dischargeof 70 cu. m./sec.Estimatethe afilux when thedownstreamdepthis 1 metre.

Dd=~1m; W=30 m; L=25 m

Dischargethroughthe bridgeby the Orifice Formula,

Q=C~~,/2~.L.Dd ~J(h+[~u2)

~= ~= 0.757

Afflux 109

Correspondingto this, C0=0.867, e=O.85,g=9.~mfsec~

70=0.867x4.43x25x1 f~~i.85u2‘V 2g

h+ 0.0944u2 053 .. (i)

Also, just upstream of the bridge

Q==Wx(Dd+h)Xu

70=33(l±h)u70

or h= ~——l

Substitutingfor h from (ii) in (i) and rearranging

u -0.0617 U3 1.386 .~. u—3.68 rn/sec

Substitutingfor u in (i)

h ____

33 X 1.680.263m

Alternatively

Assumethat h is more than ~

and apply the Weir Formula

Q= 1.706x C,1,.LH~/2

70=l.706x0.92x25x111J

2H=1.47m

Now, H=Du+4_ =.D,4 (approx.)

D,~=1.47 m approx.

Now, Q~=WxD~xu,i.e., 70=33x1.47u

U2

u==1.44; —=0.1055m2g

U2

i.e., I.47=D~+0.l0S5

D~=J,3645m

110 Afflux

h =D~—D~1=1.3645—1.0=0.3645

Adopt h=0.365 m.

Sinceh is actually more than ~ thereforethe valueof affluxairived at by the Weir Formulais to be adopted.

18,7. Example. The unobstructedcross-sectionalareaof flowof a streamis 265 sq. ni. and the width of ~ow is 90 m. A bridgeof4 spansof 18 m clear is proposedacrossit. Calculatethe afflux whenthe dischargeis 650 cu. m./sec,

W=90 m; L=72 m; Dd= -=2.944m

The depth beforethe construction of the bridgeis the depthdown-streamof the bridgeafter its construction.HenceDd=2.

944 m.

~= ~=0.8. ThereforeC0=0.877 ande=0.77.

By the Orifice Formulathe dischargethroughthe bridge

650=0.877 4.43x 72 x2.94x

2g

650=825 h+0.0877t~

i.e. h...{0.0877u2=0.62 (I)

Now, the dischargejust upstreamof the bridge

650 =90 (2.944+h)~

65

or h=~——2.944

Puttingfor h from (ii) in (i) and rearranging

u—0.0246u3+2.02

u=2.34 rn/sec

Putting for u in(ii)

h=0.137 m

Affi u X 111

18.8. Example. A bridgeof 5 spansof 36 m each is proposedacross a stream, whose unobstructed width is 250 in, slope 1/2000 anddischarge 1800 cu,ni/sec. Calculate the afflux (n=003).

We have first to find D~.

- 11 ~- 18007,- ‘ - W 250

Knowing n o=003; Sr— 1(2000, read velocity for various valuesof R from Plate 3 and select that pair whose product is 7.2, Thuswe get

R 3.9

1.85

i’~tkej)~::::rR- —3,9 in

Now, W—-250 m; L— 180 m; Thr=3.9 m

L I ~ 0.72,therefore C0 - rO,87; e ‘0.90

By the Orifice Formula, the discharge through the bridge.

i800=0.87>~4,43 180x 3.9 fk~i.9u2

2g

Q :~QOcum/s~c;s ‘¼oooFIG- l~

Le, ii —L 0.097 742_.. 0.442 (i)

112 Afflux

The discharge just upstream of the bridge

1800=250(3,9+h)u

7.2

i.e., — —3.9

Put for h from (ii) in (i) and rearrange

u—O.0224u’== 1.66

u=L8 ni/sec.

Put this value of u in (ii), we get:

h~O.442—O.3.14=O.128m.

Worked out Exampleson 113Discharge Passed by Existing

Bridges from Flood Marks —19

Worked outExamples onDischargePassed byExisting Bridgesfrom FloodMarks

ARTICLE 19

WORKED OUT EXAMPLES ON DISCHARGE PASSED BYEXISTING BRIDGES FROM FLOOD MARKS

19.1. Calculating Discharge by the Weir Formulae

Example. The unobstructedwidth of astream is 70 m. Thelinear waterwayof a bridge acrossit is 47 m. In a flood, the averagedepth of flow downstreamof the bridgewas 3.4 mandthe affiux was0.95 m. Calculatethe discharge.

______ —-.—1—-uDsj:4.35m

Fig. 18

h 0.95 —0 03D~ 3.4 .3

Since h is more than0.25 Dd, therefore the Weir Formula willapply.

W= 70 m; L=47 in; h=0.95 m

Let the velocity of approachbe u rn/sec. The dischargeat asectionjust upstreamof the bridge (Fig. 18)

Q=u x 4.35 x70=304.5u

The dischargethroughthe bridgeby the Weir Formula

2/Q=l.706x0.98x47 (4.35+— 19.6 2

.(ii)

116 Discharge Passed By existing Bridges

Equatingvaluesof Q from (i) and(ii)

8

304.5u=78.5( 4.35+_~f~_)~

Rearrangingu’ —0.0206u~=l.76

or u=2.64 rn/sec.

Puttingthe valueof u in (i) or (ii) we get Q.Q=304.5x2.64

=804 cu. m./sec.

Try the Orifice Formula

L47W 70 —0.6

C0=0.865; e=0.95

Dischargethroughthe bridgeby the OrificeFormula

Q=0.85>< 4.43><~7~><~ f0.95±1.95 u2

19.6=602 ~/0.95-f-0.lu2 ...(f)

Dischargejustupstreamof the bridge

Q=70x4.35xu

=304.5u

Equating values of Q in (1) and(ii)

602 \/(0.95+0.1u2)=304.5u

Simplifying andsquaring

~ 0.95

U— 0.155 :. u=2.48 rn/secSubstitutingfor u in (i) or (ii) we get Q.

Q=304.5x2.48=756cu. m./sec.

This result is aboutthe same as givenby the first method. Infact, theOrifice Formula,with therecommendedvaluesof C

0 and

Discharge Passed by Existing Bridges 117

e gives nearly correct results even where the conditions are appro-priate for the Weir Formula. But the converse is not true.

19.2. Calculating Discharge by the Orifice Formula

Example. The unobstructed width of a stream is 130 m andthe linear waterway of a bridge across it 105 m. During a flood theaverage depth of flow downstream of the bridge was 2.6 m and theafflux 0.10 m. Calculate the discharge.

I’V= 130 in; L=103 m; h=0.1 in; Let the velocity

be u. The dischargeat a section just upstream of

Q=ux2.7x130=351u

a L 105Contraction=—~-=—y = -~-~~—=O.8O

Corresponding to this, C0=0.875 and e=0.72. The discharge

under the bridge, by the Orifice Formula,

Q=0.875x4.43x2.6x105 0.1±1.72i~ )

=1060 V0.l+0.0877u2) ...(ii)

Equating values of Q in (i) and (ii)

351 u=1060 yOTW+0.0877~s2

Squaring and rearranging

U2— 0.10.0213

flG-’%9Given

of approachthe bridge

u=2.17 rn/sec.

118 Discharge Passed by existing Bridges

Subsitute for 14 ~fl (i) or (ii) to get Q.Q=351 x2.17=760 Cu. m./sec.

193. The Border-line Cases. An example will now follow toillustrate what results are obtained by applying ihe Weir Formula andOrifice Formula to caseswhich are on the border line, i.e., ‘where theafflux is just ~ D~.

19.4. Example. A stream, whose unobstructedwidth is 230 mis spanned by a bridge whose linear waterway is 200 m. During aflood the average downstream depthwas 2.5 m and the afflux was0.065 m, Calculate the discharge.

h 0.065D4 ‘ 2.6 0.25

Since Ii is nearly 1 Dr, thereforeboth the Weir Formula andOrifice Formula should apply.

By the Weir Formula

If the velocity of approach is u, the discharge just upstream ofihe b~idge.

Q=230 x 2.665 >< u=614u

The discharge through the bridge

Q=1.706x0.98x200 ( 2.665+~-~) i

.(i)

Dus2.G65m

— ~*O.o65vn

6rri

Fig. 20

(ii)

Discharge Passed by existing Bridges 119

Equatingvaluesof Q from (1) and(ii)

614u=334 (2.665+0.051

Rearranging

u~—0.0374u~=1.78 :. u=3.2rn/sec.

Put for u in (1)

Q=6l4x3.2=1935cu. m./sec.

By the Orifice Formula

a L 200 8A 230 —0. ~

C, =0.906 e=0.44

If u is the velocity of approach,the discharge just upstream of thebridge

Q=230x2,665u=614u

The dischargeunderthe bridge by the Orifice Formula

Q=0.906>< 4.43x 200 x 2.6 (0.065+0.0735u2)~

=2090 (0.065+0.735 U2)~ ...(ii)

Equatingvaluesof Q from (1) and (ii)

614 u=2090 (0.065+0.0735U2)~

0.0855 u2=0.065+0.0735u2

Squaring,andrearranging

0.0650.0120=-5.42

=u2.33rn/sec.

Substitutingfor u in (i) or (ii) we get QQ=614x233=1430cu. m./sec.

Overtopping of the Banks 121

20

Overtopping ofthe Banks

ARTICLE 20

OVERTOPPING OF THE BANKS

20.1. In plainswhere the ground slopes are gentle andthenaturalvelocitiesof flow in streams are low, the flood water mayspill overoneor both the banksof thestreamat places.

20.2. Height of Approach Roads.Considerthe casewhere thebulk of the dischargeis carriedby the main channelanda small frac-tion of it flows over the bankssomewhereupstreamof the bridge. Ifthe overflow strikeshigh ground at a short distance from the banks,it canbe forced back into the streamand made to passthrough thebridge. Thiscanbe doneby building the approachroadsof the bridgesolid andhigh so that they intercept the overflow. In this arrange-ment, the linear waterwayof the bridge mustbe ampleto handle thewhole dischargewithout detrimentalafflux. Also, the top level of theapproachroadsmustbehigh enoughnotto beovertopped.If the velo-city of the streamis Vm/sec.,the water surfacelevel, where it strikes

the roadembankment,will be ,n higher than the H.F.L, in the

streamat the point, wherethe overflow starts. This arrangementis,therefore,normally feasiblewherethe stream velocity is not immo-deratelyhigh.

20.3. Subsidiaryor Relief Culverts. Sometimes,however,theoverflow spreadsfar andaway from the banks~~Thisis often the casein alluvial plains, where the ground level falls continuouslyawayfrom the banksof the stream, In such cases,it is impossibleto forcethe overflow backinto the main stream. The correct thing to do isto passthe overflow through relief culverts at suitable points in theroad embankment. These culverts have to be carefully designed.They shouldnot be too small to cause detrimental pondingup ofthe overflow, resulting in damageto the road or some property. Nor,should they be so big as to attractthe main current.

20.4. PermanentDips and BreachingSections in ApproachRoads. It is sometimesfeasible as well as economicalto provide

124 Overtopping ot the Banks

permanentdips (or alternalivel~ hi eaching sections) in the bridgeapproachesto take excessiveoverflowsin emergencies. The dips orbreachingsections haveto he sited anddesignedso that the velocityof flow throughthem doesnot become erosive,cutting deep channelsand ultimately leadingto the shifting of the main current.

205. Retrogressionof Levels. Supposewater overflows alowhanksomewhereupstream of thc bridgeand after passingthrough arelief culvert, rejoins the mainstreamsomewherelower down. Whenthe flood in the main channel subsides,the ponded up water at theinlet of the subsidiaryculvert getsa free overfall. Under suchcondi-tions deeperosioncantakeplace. A deepchannelis formed, beginn-ing at the,outfall in the main stream and retrogressing towardstheculvert. This endangersthe culvert. To provide against this, pro-tectionhas to hedesigneddownstreamof the culvertso asto dissipatethe energyof the falling water on thesamelines asis doneon irriga-tion “falls”. That is, a suitable cistern and baffle wall should beaddedfor dissipatingthe energy and the issuing current shouldbestilled througha properly designedexpandingflume.

Feasibility of Pipe and Box 125Culverts Flowing Full21

Feasibility ofPipe and BoxCulverts FlowingFull

ARTICLE 2!

FEASIBILITY OF PIPE AND BOX CULVERTS FLOWING FULL

211. Many a plain is one vast flat without any deepanddefineddrainagechannelsin it. Whenthe rain falls, the surfacewatermoves in some direction in a wide sheetof nominal depth. So longas this movementof water is unobstructed,no damagemay occur topropertyor crops. But when a road embankmentis thrown acrossthe country interceptingthe natural flow, water pondsup on onesideof it. Reliefhas then to be afforded from possible damage fromthis pondingup by taking the wateracross the road throughcause-waysor culverts.

21.2. In such contourlessregions the road runs acrosswidebut shallow dips and therefore the most straightforward way ofhandlingthe surfaceflow is to providesuitabledips (i.e., causeways)in the longitudinal profile of the roadand let water passover them.

21.3. Theremay, however,be caseswhere the abovesolutionis not the best. Someof its limitations may be cited. Too manycausewaysor dips detractfrom the usefulnessof the road. Also, theflow of water overnumeroussections of the road, makes its propermaintenanceproblematicandexpensive. Again, considerthe caseofa wet cultivated or waterloggedcountry (and flat plains are not in-frequently swampyand waterlogged) where the embankmenthasnecessarilygot to be takenhigh abovethe ground. Frequentdippingdown from high roadlevels to the ground produces a very undesir-able road profile. And, evencementconcreteslabs,in dpsacrossawaterloggedcountry,do not rest evenlyon the mudunderneaththem.Thus, it will appearthat constructingculvertsin such circumstancesshouldbe a betterarrangementthan providing dips or small cause-ways.

21.4. After we havedecidedthat aculvert hasto be construct-ed on a road lying acrosssomesuchcountry, we proceed to calcu-late the dischargeby usingoneof the run-off formulae, having due

128 Feasibility of Pipe and Box Culverts Flowing Full

regardto the natureof the terrain and the intensity of rainfall asalreadyexplainedin Article 4.

But the natural velocity of flow cannot beestimatedbecausei~i)thereis no definedcross-sectionof the channelfrom which we maytakethe areaof cross-sectionandwettedperimeter;and (ii) there isno measurableslopein the drainage Line. Even where we wouldcalculateor directly observethe velocity, it may beso small that wecould not aim at passingwaterthroughthe culvert at thatvelocity, be-

causethe areaof waterwayrequiredfor the culvert [A= ~. ] will

be prohibitively large. En suchcases,the designhas to be basedonan increasedvelocity of flow through the culvert and to createthatvelocity the designmust provide for heading up at the inlet end ofthe culvert. Economyin design being the primaryconsideration,thecorrectpractice,indeed,is to designa pipe or a box culvert on theassumptionthat water at the inlet end may head up to a predeter-mined safe level abovethe top of the inlet opening. This surfacelevel of the headedup water at the upstreamend has to be so fixedthat the road bank shouldnot be overtopped, nor any property inthe flood plain damaged.

Next, the level of the downstreamwater surface should benoted down. This will dependon the sizeand the slopeof the lead-ing out channeland is, normally,the surfacelevel of the natural tin-obstructedflow at the site, that prevailsbeforethe roadembankmentis constructed.

After this we cancalculatethe requiredareaof cross-sectionofthe barrelof theculvert by applying the principlesof Hydraulicsdis-cussedin Article 22.

21.5. The procedureset out aboveis rational and considerableresearchhasbeencarriedout on the flow of water through pipeandbox culverts,flowing full.

21.6. In the past,use wasextensivelymade of empirical for-mulaewhich gave the ventwayarearequiredfor aculvert ,to drain agiven catchmentarea, Dun’s Drainage Table is one of that classandis purely empirical. This Tableis still widely used, as it saves

.4-..

Feasibility of Pipe and Box Culverts Flowing Full 129

the troubleof hydraulic calculations. But it is unfortunate that re-courseis often takenrather indiscriminatelyto suchshort cuts, evenwhereothermoreaccurateand rational procedureis possibleandwarrantedby the expenseinvolved. Dun’s Table,or others in thatclass,should NOT be used until suitable correction factors havebeencarefully evolvedfrom extensiveobservations(in eachparticularregion with its own singularitiesof terrain and climate) of the ade-quacyor otherwiseof the existing culverts vis-a-vis their catchmentareas.

21.7. Considerationsof economyrequire that small culverts,in contrastwith relatively largerstructuresacross detlned channels,neednotbe designednormally to function with adequateclearancefor passingfloating matter. The depth of a culvert should be smallandit doesnot matterif the opening stops appreciably below theformation level of the road. Indeed,it is correct to leave it in thatposition and let it function evenwith its inlet submerged.This makesit possibleto design low abutmentssupportingan archor a slab, oralternatively,to useroundpipesor squarebox barrels.

21.8. Nor should high headwalls be provided for retainingdeep over-fills; instead,the lengthof the culvertsshouldbe increasedsuitablyso that the roadembankment,with its naturalside slopes,isaccommodatedwithout high retainingheadwalls.

21.9. Wheremasonryabutmentssupportingarchesor slabsaredesignedfor culvertsfunctioning under“head”, bed pavementsmustbe provided. And, in all cases, including pipe and box culverts,adequateprovisionmust bemadeat theexit againsterosionby design-ing curtainwalls. Where the exit is a free overfall, a suitable cisternan3baffle wajI must be added for the dissipation of energyandstilling of the ensuingcurrent.

Hydraulics of the Pipe and 131Box Culverts Flowing Full22

Hydraulics of thePipe and BoxCulverts FlowingFull

- --.-~.-. ___

ART1CLE 22

HYDRAULICS OF THE PIPE AND BOX CULVERTSFLOWING FULL

22.1. The PermissibleHeading up at the Inlet. It has beenexplainedalreadythat where a defined channel does not existandthe naturalvelocity of flow is very low, it is economical to design aculvert as consistingof a pipe or a number of pipesof circular orrectangularsection functioning with the inlet submerged.As the floodwater startsheadingup at the inlet, the velocity through the barrelgoes on increasing. This continuestill the dischargepassing throughtheculvert equalsthe dischargecoming towards the culvert. Whenthis stateof equilibrium is reachedtheupstreamwater level does notrise any higher.

For a given design dischargethe extent of upstream headingup dependson the ventwayof the culvert. The latter has to be sochosenthat the headingup should not go higher than a predeter-mined safe level, the criterion for safety being that the roadembankmentshouldnot be overtopped, nor any property dama-ged by submergence. The fixing of this level is the first step in thedesign.

22.2. SurfaceLevel of the Tail Race. It is essentialthat theH.F.L. in the outfall channelnearthe exit of the culvertshouldbeknown. This may be takenas the H.F.L. prevailing at the proposedsiteof the culvert before theconstructionof the road embankmentwith someallowancefor the concentrationof flow causedby the cons-truction of the culvert.

22.3.The Operating Head when the Culverts Flow Full. In thisconnectionthe casesthat haveto be considered are illustrated inFig. 21. in each case the inlet is submergedand the culvertis flowing full. In case(a), the tail race water surfaceis below thecrown of the exit and in case(b) it is abovethat. The operatingheadin eachcaseis marked“H”. Thus we seethat “When the

134 Hydraulics of the Pipe and Box Culverts Flowing Full

(a)

-,. i,.~

I ~1The OperatingHead ‘H’ whenthe Culvert FlowsFull

Fig. 21

culvert flows full, the operatinghead,H, is the height of the upstreamwater level measuredfrom the surfacelevel in the tail race or fromthe crOwn of the exit of the culvert whicheveris higher”.

22.4. The Velocity Generatedby ~‘H”. The operatinghead“H”is utilised in (1) supplyingthe energyrequiredto generatethe velocityof flow throughthe culvert, (ii) forcing water through the inlet ofthe culvert, and (iii) overcomingthe frictional resistanceoffered bythe inside wettedsurfaceof theculvert.

If the velocity through the pipeis v, the headexpendedin

generatingit is -f As regards the head expendedat the entry,

it is customary to express it as a fraction K0 of the velocity

head j— Similarly, the headrequiredfor overcomingthe friction

of the pipe is expressedas a fraction K, of -j._, From this it

follows thatvs . ..(22.4)H=[l +K~+K,]*2g

Hydraulics of the Pipe and Box Culverts Flowing Full 135

From this equationwe cancalculatethe velocity v, which a givenhead H will generate in a pipe flowing full, if we know K0 andK,.

22.5. Values of K0 and K,. K0 principally dependson theshapeof the inlet. The following valuesare commonlyused:

K~=O.08for bevelledorbell-mouthedentry

...(22.5~)=0.505for sharpedged

entry J

As regardsK, it is a functionof the Length L. of the culvert, itshydraulic meanradiusR, and the co-efficient of rugosity n of itssurface.

The following relationshipexists betweenK, andn

14.85n2 LK,= . . ..(22.5~)

For cementconcretecircular pipesor cementplasteredmasonryculverts of rectangularsection, with the co-efficient of rugosityn=0.015,the aboveequationreducesto:

0,00334LK,—

The graphsin Fig. 22 are based on Equation 22.5~. For aculvert of known sectionalareaandlength, K, can be directly readfrom thesegraphs.

22.6. Values of K~and K, modified through research.Considerableresearchhasrecently beencarriedout on the head lostin flow throughpipes. The resultshaveunmistakably demonstratedthe following

The entry lossco-efficient, K0, dependsnot only on the shape

of the entry but also on the sizeof entryand the roughness of itswettedsurface. In general,K0 increaseswith an increasein the sizeof the inlet.

136 Hydraulics of the Pipe and Box Culverts Flowing Full

Fig. 22

Hydraulics of the Pipe and Box Culverts Flowing Full 137

Also Kj, the friction loss co-efficient, is not independentof Ke.Attemptsto make the entry efficient repercuss adversely on thefrictional resistanceto flow offered by the wetted surfaceof thebarrel. In otherwords, if the entry conditions improve (i.e., if K~decreases),the friction of the barrel increases(i.e., Kf increases).Thisphenomenoncan be explainedby, thinking of the velocity distributioninside the pipe. When the entry is square and sharp edged, highvelocity lines are concentratednearerthe axis of the barrel; while thehell-mouthedentry gives uniform distribution of velocity over thewhole section of the barrel, From this it follows that the averagevelocity being the samein both cases, the velocity near the wettedsurfaceof the pipewill be lower for squareentry thanfor bell-mouthedentry. Hence the frictional resistanceinside the culvert is smallerwhen the entry is squarethan whenit is bell-mouthed. Streamliningthe entry is, therefore,not an unmixedadvantage.

Consequently,it has beensuggestedthat the values of K~andK1 should be as given in Table 5.

TABLE 5

Valuesof K~and K, Ii

“~

Ci~u/ar

Squareentry

pipe’s

Bevelledentry

dii!! ar duhTrts

Squareentry

Bevelledentry

K~= 1107 RO.~. 0.1

000394L,’RL~0.00394L/Rll

0.572 R°3 0.05

000335LR12~ O.00335L/’k”2~

22~7. Design Calculations

We havesaid that

H= [ l+K~4K,

138 Hydraulics of the Pipe and Box Culverts Flowing Full

/ H \~~ v=4.43 I\ l+K,-47?7)

Hence,

~—A 443 ( H ...(22.7)~ ‘ k 1+K0+K, )

Supposewe know the operatingheadH and the length of thebarrelL, andassumethat the diameterof a round pipe or the sideof a squarebox culvert is D.

FromD calculatethe cross-sectionalareaA and the hydraulicmeanradiusR of the culvert.

Now from R andL compute K4 and K,, using appropriatefunctions from Table 5. Then, calculate Q from Equation(22.7). if this equalsthe designdischarge,the assumedsize of theculvert is correct. If not, assumeafreshvalueof D and repeat.

22.8. DesignChart (Plate 13)

Equation(22.7) may be written as

(22.8~~

where A= A ... (22.8~)(1+K0±K,)~

It is obvious that all componentsof A in Equation(22’Sb) are

functionsof the cross-section,length, roughness,and the shape ofthe inlet of the pipe. Therefore, A representsthe conveyingcapacityof the pipe and may be called the ‘Conveyance Factor’. Thedischarge,thendependson the conveyancefactor of the pipe andtheoperating head. In Plate 16, curves have beenconstructedfromequation(22.84 from which Q can be directly readfor any knownvaluesof A and H.

Also, in the samePlate,Tablesareincludedfrom which A canbe taken for anyknown valuesof (I) length, (2) diameterin caseofcircular pipes or sidesin caseof rectangularpipes,and(3) conditionsof entry, viz., sharp-edgedor round. The materialassumedis cement

Hydraulicsof the Pipe and Box Culverts Flowing Full 139

concreteand valuesof .K0 andK, usedin the computationarebasedon functionsin Table 7.

The use of Plate 16 rendersthe designprocedureverysimpleandquick. Exampleswill now follow to illustrate.

22.9. Example. Data : (1) Circular cement concrete pipeflowing full with bevelledentry.

(2) Operatinghead=l m

(3) Length of the pipe=25m

(4) Diameter=l m

Find thedischarge.

See, in Plate 16, the Table for circular pipes with roundedentry.

For L=25 m and D=l m, the conveyancefactor

A=0.6l 8

Now refer to the curvesin the samePlate. For ?~=0.6l8and11=1 m.

Q==2.72cu. m./sec.

22.10.Example. Designa culvert consistingof cementconcretecircular pipes with bevelled entry and flowing full, given : (seeFig. 23).

Discharge = 10 cu.m./sec.

R.L. of ground in metres = 100.00

H.F.L. of tail race in metres = 100.80

Permissibleheadingup at inlet R.L. = 101.80

Length of culvert = 20 m

Since we shall try pipes of diametersexceeding0.8 m, theculvertwill function as sketched

140 Hydraulics of the Pipe and Box Culverts Flowing Full

Assumedvalueof D=(l) 1 m; (2) 1.5 m;

CorrespondingH=l.8—D

Dischargeper pipefrom Plate 16, QNumberof pipesrequiredlO/Q =(l) 3.93; (2) 2.85

say4 say3

iot~8O

I,D

~oo.oe

Fig. 23

=(l) 0.8 m; (2)0.3 m;

=(l) 2.54 cu.m./sec,;(2) 3.5 cu.m./sec.

Hence4 pipesof 1 metrediameterwill suit.

Bibliography

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142 Bibliography

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(15) StandardSpecifications and Code of Practice for RoadBridges—Section1—GeneralFeaturesof Design(in MetricUnits) (Fourth Revision),IRC: 5-1970.

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(17) StandardSpecifIcations and Code of Practicefor RoadBridges—SectionIll—Cement Concrete (Plain and Rein-forced)(FirstRevision),IRC: 21-1966.

(18) RegimeFlow in IncoherentAlluviurn—G. Lacey, CentralBoardof Irrigation PaperNo. 20.

(19) The Hydraulics of Culverts by F. T. Mavis, The Penn-sylvaniaState College EngineeringExperimentalResearchStationSeriesBulletin No. 56.

Appendix

Appendix

143

Appendix

HEAVIEST RAINFALL ir~ONE HOUR (mm)

(All hoursin !.S.T.)

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec.

mm 3.6 2.5 2.0Date 6 27 20T,ime 12-13 8-9 19-20Year 1953 1956 1954

3. Allgarh (1950)

mm 8.1 0 5.1Date 24 — 14Time 16-17 — 20-21

4. Allahabad (1948-1966)

mm 16.5 13.2 29.5Date’ 28 3 21Time 20’21 23-24 20-21Year 1958 1956 1950

5. Amlni DevI (1964-66)

mm 5.7 7.5 0Date 25 12 —

Time 16-17 14-15Year 1966 1965 —

6. Am~ltsat (1951-66)

mm 14.5. 10.7 9.9Date 13 23 15

Year

7. Anantapur (1965.66)

mm 1.7 0Date 30 —

Time 21-22 —

Year 1966 —

19.0 16.0 60.2 54.528 29 .30 28

21-22 4-5 11-12 2-31962 1959 195! 1962

5.8 12.2 37.3 30.920 29 1 10

16-17 12-13 5-6 0-11966 1965 1966 1966

6.9 15.0 28.0 51.318 11 27 24

54.9 51.3 33.0 7.927 2 23 30

23-24 16-17 11-12 3-41964 1956 1966 1956

74.8 64.5 25.5 9.7 6.316 10 22 1 31

13-14. 5-6 18-19 13-14 8-91961 1956 1959 1956 1953

52.7 40.0 24,4 24.06 7 12 71-2 5-6 6-7 0-1

1964 1966 1966 1966

50,026301914.15 1-2

3-411-121961, 196419621966

1. Agartata (1953-1966)mm 14.0 32.0 32,6 39.6 65.5 60.0Date 10 21 30 29 19 15Time 14-15 12-13 23.24 7-8 17-18 13-14Year 1957 1958 1959 1962 1960 1961

2. Ahmedabad (1951-1966)

66.0 61.329 2712-13 13-141964 1965

59.7 61.03 9

19-20 22-231956 1954

50.8 —

5 *

12-13 —

17.5 11.8 42.55 13 17

17-18 17-18 19-201963 1963 1960

2.8 5.6 24.41 30 23

23-24 17-18 0.1

80.0 25.9 20.0 1.32 1 25 29

0-1 15-16 8-9 20-211958 1955 1963 1960

27.4 2.3 0I It *

14-1522-23 —

0,52422-23

49.5131-2

1965

74.4 32.5 9.5 12.52 4 5 12

Time 12-13 21-22 22-23 18-19 15-16 1-2 5-6

1961 1954 1952 1960 1966 1960 1956

0 9.1 35.3 44.0—‘ 20 1 7— 22-23 16-17 1-2—‘ 1965 1966 1966

2-3 23-24 20-21

1955 1959 1963

34,7 18.4 21.82 17 9

23-24 7-8 19-201966 1966 1965

14.9 38.2 22.425 29 1916-Il 22-23 5-6

1966 1966 1966

146

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec.

8. Asansol (1953-66)

mm 13.7 13,4 16.0 39.4 64.5 60.5 60.0 86,0 72.4 47.8 13.2 6.6Date 21 19 11 25 14 28 9 20 26 20 7 28Time 17-18 17-18 16-17 16-17 12-13 14-15 17-18 20-21 14-15 16-17 13-14 6-7Year 1953 1965 1956 1963 1956 1965 1964 1960 1956 1958 1955 1954

9. Auranqabad (Chikalthana)(1952-1966)mm 16.7 5.5 16.3 6.2 27.5 60.5 44.2 33.5 37.1Date 7 5 20 11 20 15 30 21 20Time 18-19 13-14 17-18 18-19 16-17 22-23 19-20 2-3 22-23Year 1965 1961 1954 1964 1961 1955 1954 1965 1952

10. Bagdogra (1962-1965)

mm 0 4.6 20.7 20.0 37.1 70.2 60.0 32.5 42,0Date — 7 20 29 8 13 29 15 14Time — 6-7 7-8 14-15 4-5 0-1 15-16 15-16 2-3Year — 1965 1964 1963 1963 1963 1964 1963 1964

ii. Bagra

mmDateTimeYear

Tawa (1952-66)12,8 9.4 18.8 11.2 44.5 59.711 14 2 4 30 263-4 7-8 16-17 15-16 3-4 18-191966 1955 1957 1960 1959 1955

12. Bangalore Aerodrome (1954-66)

mm 18.5 13.7 18.0 29.3 55.0 32.8 31.7Date 31 2 24 5 5 6 2Time 22-23 1-2 21-2215-16 16-17 17-18 17-18Year 1959 1959 1954 1965 1963 1960 1965

13. Bangalore Central Observatory (1950-66)

mm 7.8 20.0 12.5 35.7 44.8 61.0 59.2Date 31 1 7 3 13 1 11

21-22 22-23 22-23 0-1 21-22 22-23 17-18

1959 1959 1957 1961 1961 1952 1952

14. Barakachar (1952-55)

mm 4.6 3.6 3.6 19.8 3.1 32.0 50.8Date 21 22 23 4 12 19 22Time 1-2 4-5 16-17 23-24 17-18 19-20 19-20Year 1953 1952 1955 1952 1955 1953 1954

15. Barahkshetra (1952-66)mm 15.2. 15.4 32.3 32.9 54.9 88.5 68.0Date 11 8 24 13 IS 30 27Time 19-20 5-6 16~170-1 22-23 23.24 21-22Year 1957 1961 1953 1965 1958 1966 1964

23.0 21.0 20.24 25 2

14-15 18-19 8-91959 1958 1966

17.7 11.7 0.35 4 8

23-24 3-4 18-191962 1963 1963

50.8 2~.4 39.02! 1 816

14-15 22-23 21-2223-24

1952 1950 19651956

38.5 63.2 63,018 6 15

12-13 23-24 17-181960 1964 1961

30.0 12.0 8,92 25 8

10-11 22-23 11-121961 1963 1956

53.9 22.9 17.23 7 8

16-17 16-17 22-231956 1957 1965

Time

Year

50.0 57.930 13

22-23 21-221964 1955

50,8 48.0

10 8

0-1 22-23

1965 1964

32.3 53.324 2619-20 0-i1955 1954

78.0 61.517 26

13-14 11-121961 1963

18.5 025 —

20-21 —

1955 —

0.530

3.41954

83.8 10.0 7,82 2 3

17-18 8-9 0-11953 1963 1966

147

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dcc.

16. Barhi (1953-55)

mm 13.5 7.5 3.7 8.8 22.0 56.0 39.0 41.9 49.2 31.5 10.8 8.7Date 21 10 29 22 30 26 23 9 14 23 4 2

30Time 5-6 8-9 17-18 21-22 15-16 21-22 13-1421-22 17-1822-23 17-18 23-24

2 1-22Year 1955 1964 1965 1964 1964 1965 1964 1953 1964 1963 1963 1966

17. Barmul (1952-58)

mm 3.1 24.1 11.9 24.9 34,5 53.3 66.5 45.7 74.9 26.9 6.3 3.8Date 21 24 15 2 24 21 19 26 25 15 10 29Time 23-24 20-21 19-20 18-19 14-15 19-20 18-19 18-1920-21 14-15 20-21 21-22Year 1953 1958 1956 1952 1956 1952 1953 I953 1956 1953 1953 1954

18. Baroda (1948-66)

mm 4.6 4.6 6.6 2.5 37.6 71.4 52.8 66.5 44.7 42.4 12.7 2.0Date 6 4 16 13 28 22 26 5 9 10 25 5Time 17-18 10-11 18-19 15-16 23-24 4-5 7-8 0-1 19-2010-11 11-12 1-2Year 1953 196! 1962 1962 1956 1966 1957 1956 1960 1956 1963 1962

19. Barrackpore (1957.65)

mm 22-i 14.7 34.3 31.5 54.5 43.0 48.5 58.2 56.5 54.0 20.5 0Date Il 26 1 27 31 1 30 6 10 16 11 —

Time 0-1 8-9 20-21 20-21 20-21 15-16 18-19 2-3 12-13 16-17 23-24—

Year 1957 1957 1960 1958 1959 1962 1964 1957 1961 1959 1958 —

20. Bhlmkund (1957-66)

mm 5.6 16.0 30.0 41.7 28.0 50.0 62.0 52.0 60.0 30.0 7.3 1.0Date 26 7 9 2 27 23 27 8 11 14 3 8,2,1Time 8-9 10-li 12-13 15-16 18-19 18-19 15-16 9-10 2-3 15-16 13-1423-24

3-43-4

Year 1962 1961 1962 1965 1959 1961 1959 t963 1963 1966 1963 1962,63,66

21. Bhopal (Bairagarh)(1953-66)

mm 15.5 6.5 26.9 9.3 61.0 59.9 70.0 71.5 61.2 24.9 11.2 5.8Date 11 5 24 12 30 26 1 7 25 2 15 8Time 17-18 19-20 16-17 15-16 17-1820-21 9-10 16-17 22-2321-22 2-3 3-4,

14-15Year 1966 1962 1957 1962 1956 1957 1964 1963 1961 1955 1966 1956

22. Bhubaneshwar (1964-1966)

mm 13.7 19.3 11.0 20.0 25.0 46.0 30.0 45.5 43.0 30.0 16.8 5.8Date 3 17 29 27 16 23 10 13 23 8 22 17Time 13-14 16-17 14-15 19-20 18-19 14-15 19-2017-18 18-19 17-18 11-12 5-&Year 1966 1966 1965 1964 1964 1966 1964 1966 1964 1966 1966 1965

148

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec.

23. Bhuj (1964-1966)

mm 1.7 0 5.5 0.6 0Date 21 — 31 11 —

Time 4-5 — 17-18 6-7 —

Year 1964 — 1965 1965 —

24. Bishungarh (1953-66)mm 19.6 8.0 14.2 18.5 40.0 36-0Date 9 10 5 24 11 13Time 15-16 8-9 23-24 14-IS 13-14 15-16Year 1957 1964 1957 1962 1963 1963

25. Bokaro (195 1-66)

mm 23.6 15.8 23.9 32.5 36.6 32.7Date 9 7 9 19 15 13Time 17-18 18-19 17-18 17-18 14-15 19-20Year 1957- 1961 1957 1951 1958 1966

26. Bombay (Colaba) (1948-66)

mm 5.5 15.0 2.8 7.3 27,0 62.5Date 26 5 26 28 16 27Time 4-5 5-6 6-7 2-3 5-6 1-2Year 1962 1961 1951 1959 1960 1958

27. Bombay(SantaCruz) (1952-66)mm 6.3 11.6 0 1.0 17.8Date 24 5 — 26 16Time 1-8 10-11 — 3-4 5-6Year 1965 1961 — 1954 1956

28. Calcutta(Alipore) (1948-66)

68.1 53.3 128.5 43.2 31.7 35.014 5 22 11 22 57-8 6-7 14-15 7-8 3-4 4-51949 1957 1949 1948 1948 1962

16.1 48.8 46.0 17.5 7.5 022 19 26 6 6 —

16-1721-22 15-16 16-17 17-18 —

1966 1966 1965 1966 1966 —

-0

59.5 43.0 39.05 8 270-1 22-23 22-231961 1963 1963

59.0 13.2 6.322 2 280-1 5-6 4-5

1959 1956 1954

48.0 48.5 57.9 44.811 1 6 418-19 13-14 21-22 17-181951 1953 1953 1959

5.6 6.911 29

1-2 17-181953 1954

83.3 91.419 17

5-6 6-71953 1952

mmDateTime

Year

55.9 57.0 44.2 10.0 16.46 9 8 10 5

11-1223-24 2-3 17-18 5-61954 1962 1960 1964 1962

14.2 33.2 24.412,22 23 13- 3-4, 18-1920-213-41957, 1958 1948196!

43.9 54.925 20

19-20 18-19

1952 1954

51.0 61.512 29-10 6-7

1959 1965

59.0 48.313 273-4 9-10

1966 1963

41.79

11-12

1948

24.9 4.61 28

19-20 20-21

1950 1954

29. Chambal (1963-66)mm 1,0 0.2 1.5Date 14 12 30Time 16-17 23-24 14-15Year 1963 1966 1963

30. Ctiandwa (1953-66)

mm 13.5 10.8 12.2Date 21 7 3

Time 19-20 16-17 22-23

Year 1959 1961 1958

1.8 21.5 83.5 40.8 58.9 44.0 4.0 11.6 0.129- 26 20 6 26 5 16 21 2619~2020-21 19-20 15-16 14-15 14-15 18-19 14-15 3-41963 1964 1965 1964 1965 1963 1963 1963 1963

6.2 21.3 55.3 46.0 37.1 29.0 38.1 5.8 20.51 10, 10 23 15 12 20 2 8

95-6 13-14 18-19 15-16 19-20 7-8 17-18 3-4 3-4

7-81965 1956 1960 1960 1953 1959 1958 1956 1967

1963

149

Jan. Feb. Mar. Apr. May Jun. July Aug. Sept. Oct. Nov. Dec.

31. Cherrapunjj (1940-61)

mm 9.2 25.4 51.8 87.4 101.4 108,7 127,0Date 22 10 30 29 4 17 IITime 12-13 4-5 2-3 8-9 8-9 6-7 0-1Year 1959 1950 1951 1948 1956 1949 1952

32. Colmbatore (1963-66)

mm 7.8 0 2.4 36.6 80.0 11.5 33.5Date 14 * 25 18 24 26 28Time 20-21 * 15-16 15-16 22-23 14-15 0-IYear 1966 — 1963 1965 1965 1963 1964

76.2 106.7 44.2 16.8 18.34 15 4 18 6

19-20 0-1 11-12 23-24 21-221957 1951 1951 1950 1954

19.6 42.8 31.8 22.8 55.030 24 16 23 7

14-15 17-18 17-18 19-20 23-241963 1966 1964 1965 1963

33. Dadeldhura (1959-66)

mm 8.5 8.0 9.0 26,6Date 20 24 20 13Time 4-5 23-24 0-1 16-17Year 1965 1962 1965 1963

19.6 26.7 36.117 8 8

17-18 5-6 13-141964 1961 1961

25.3 22.2 13.0 11.5 5.46 2 13 7 13

19-20 12-13 23-2415-16 21-221962 1965 1961 1963 1963

35. Dhanwar (1957)

mm 19.3 2.5 7,9 0Date 15 22 22 —

Time 14-15 15-16 21-22 —

36. Dholpur (1962-66)

mm 3.9 2.2 5.8 3.7Date 15 12 4 6Time 0-1 11-12 19-20, 14-13

22-23Year 1963 1965 1962 1963

54.3 43.0 30.5 4.8 7611 6 13 9 28

821-22 11-12 11-12 0-1 6-7

11-121958 1958 1952 1953 1954

1955

56.5 50.0 60.0 36.8 20,314 9,3 30 6 52-3 1-2 0-i 0-1 23-24

1-21965 1958 1961 1956 1965

1960

34. Dhanbad (1952-1961)

mm 23.1 13.7 12.9 14,5Date 21 7 27 26Time 16-1720-21 14-15 3-4

Year 1953 1961 1955 1958

73.7

3

1-2

1953

34.0 58.0

24 25

14-15 14-15

1954 1958

0 19.6— 26— 10-11

10.0 40.012 169-10 4-5

1966 1966

17.8 10.9 43.9 5.3 0 020 7 15 12 — —

19-20 1-2 17-18 15-16 — —

46.6 33.5 34.4 24.525 21 19 1817-18 13-14 16-17 0-1

1966 1966 1964 1965

0 4.1— 29* 5-6

— 1966

37. Dlbrugarh (Mobanbari) (1953-66)

mm 9.4 25.6 26.0 36.0 50.0 92.5Date 21 13 22 15 25 25Time 23-24 6-7 21-22 3-4 0-1 23-24

Year 1961 1960 1964 1961 1960 1965

9.33014-15

1959

150

Jan. Feb. Mar. Apr. May J~n.July Aug. Sept. Oct. Nov. Dec.

38. Dum Dum (1948-66~mm 13.5 30.2 28.2 66.0 50.0 63.0 68.1 56.9 64.9 40.1 13.2 6.1Date 30 6 7 20 8 2 9 6 7 8 26 28

29Time 7-8 2-3 18.19 16-17 14-15 17-18 13-14 11-12 2-3 13-14 7-8 21-22

16-17Year 1959 1948 1949 1962 1963 1953 1953 1955 1960 1949 1951 1954

39. Oumri (1954-66)

mm 9,7 7.6 10.2 24.5 48.8 42.7 40,1 59.2 53.5 66.0 9.4 6.8Date 29 27 26 22 31 6 15,25 25 26 22 25 2Time 18-19 19-20 14-15 15-16 18-19 14-15 17-18 1-2 21-22 0-I 4-5 11-12

14-15Year 1959 1958 1955 1964 1954 1958 1955 1956 1960 1959 1966 1966

40. Durgapur (1957-66)mm 8.5 16.4 10.0 12.0 52.5 58.0 52.0 90.0 64.0 41.2 4.9 1.0Date 22 5 20 2! 12 8 28 21 18 21 3 1Time 1-2 21-22 19’20 18-19 23-24 16-17 15-16 6-7 17-18 15-16 18-19 23-24Year 1959 [961 1965 1962 1964 1969 1959 1964 1959 1964 1963 1966

41. Gangtok (1956-66)mm 26.7 16.2 40.6 53.5 60,8 81.2 33.9 41.7 35.7 37.5 12.6 5.0Date 5 24 22 22 16 9 10 30 22 14 17 14Time (6-17 18-19 15-16 16-17 14-15 16-17 19-20 21-22 0-1 22-23 15-16 14-15Year 1958 1963 1957 1963 1959 1966 1958 1958 196S 1966 1961 1961

42, Gannavararn (1963-66)mm 1.3 0 10.0 19.0 26.0 39~030.8 51.4 61.4 38.6 19.8 2.3Date 3 — 26 2 21 21 23 2~ 7 24 4 31Time 6-7 — 12-13 20-21 1-2 21-22 18-19 15.16 6,7 3-4 13-14 15-16

13-14Year 1966 — 1963 1965 1965 1964 1963 1966 1964 1963 1966 1964

43. Gauhati (1955-66)mm 5.5 8.2 20,0 33.0 32.0 67.0 60.5 51.5 60.1 21.7 11.7 6.1Date 30 23 30 30 9 19 9 28 26 8 30 15Time 22-23 23-24 2-3 1-2 19-20 22-23 17-18 19-20 4-5 19-20.15-16 17-18Year 1959 1964 1965 1961 1966 1958 1955 1960 1961 1959 1955 1956

44. Gaya (1948-66) (Except 61)

mm 14.5 7.1 28.2 15.7 41.0 49,2 40,6 69.9 58.1 38,6 12.7 5.1Date 9 24 5 29 28 27 3 1 15 11 27 29Time 23-24 21-22 18-19 2-3 16-17 19-20 22-23 14-15 16-17 21-22 4.5 18-19Year 1957 1954 1957 1962 1963 1965 1953 1957 1962 1956 1948 1956

45. Gorkha (1956-61-64-66)mm 11.7 7.0 5.6 29.3 27.9 43.9 62.0 43.2 49.4 25.9 49.3 7.1Date 9 13 30 13 31 16 6 30 12 6 4 11Time 22-23 13-14 9-10 17-18 23-24 0-1 9-10 22-23 3-4 5-6 19-20 18-19Year 1957 1966 1958 1965 1957 1965 1965 1957 1966 1966 1965 1956

151

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Drc.

46. Gwalior (1963-66)mm 3.5 4.0 1.3 1.5 1.8 25.0 29.5 62.5 48.5 0.3 3.0 9.5i)ate 14 12 29 1 27 26 16 6 19 17 17 29Time 20-21 20-2! 20-21 22-23 23-24 13-14 13-14 14-15 18-19 20-21 2-3 8-9Year 1963 1966 1965 1965 1964 1966 1963 1966 1964 1965 1963 1966

47. Hazaribagh (1952-66)

mm 15.7 21.8 15.5 20.3 29.3 67.6 49.5 78.0 56.6 33.0 9.3 7.4Date 16 13 5 15 7 12 21 10 2 5 16 29Time 16-17 15-16 16-17 14-15 0-1 14-15 8-9 16-17 18-19 16-17 17-18 19-20Year 1953 1958 1957 1952 1961 1953 1959 1966 1963 1953 1966 1956

48. Hlrakud (1952-66)mm 8.9 33.0 24.9 11.5 20.0 82.3 64.0 68.0 55.0 40.6Date 16 27 3 8 13 20 2 14 27 25Time 3-4 2-3 22-23 4-5 21-22 19-20 23-24 16-17 4-5 3-4Year 1957 1964 1958 1961 1963 1957 1953 1961 1964 [957

49. Hyderabad (Begumpet) (1948.66)mm 3.6 20.8 38.3 40.0 30.2 42.9 43.7 101.6 32.1 47.0Date 23 20 11 29 13 9 24 1 18 27Time 0-1 14-15 13-14 18-1923-24 0-1 23-24 0-i 19-20 13-14Year 1953 1950 1957 1958 1965 1952 1953 1954 1960 1961

40.0 30.0 33.5 18.86 25 18,1 18

15-16 13-14 14-IS 19-2016-17

1963 1963 1964 19631966

52. Jabalpur(1952.66)mm 25.9 12.7 26.7 10.0 50.0 77.3Date 24 27 26 30 4 22Time 16-17 16-17 13-14 19-20 17-18 20-21Year 1955 1958 1957 1963 1966 1965

53. Jagda~pur(1953-66)

mm 12.8 15.3 23.9 50.0 39.4 66.0Date 12 20 23 26 13 27Time 4-5 20-21 16-17 16-17 20-21 19-20Year 1966 1962 1965 1964 1956 1959

73.7 67.5 52.8 28.0 21.6 21.320 27 16 9 I I0-1 8-9 4-5 21-22 4-5 12-13

1952 1963 1954 1959 1956 1966

73.1 52.6 48.0 50,3 15.6 33.729 I 30 2 4 2

14-15 14-15 11-12 19-20 1~-1913-141954 1954 1955 1954 1961 1962

50. Imphal (1956-66)8.6 16.1 11.1 17.8 41.0 48.1

Date 12 26 3 24 9 16Time 10-Il 3-4 18-19 11-12 14~l518-19Year 1957 1964 1961 1966 1963 1958

51. Indore (1963-66)

fl_nfl 7.3 18.3 5.5 1.3 2.7 59.5Date 11 26 26 30 30 26Time 15-16 21-22 17-18 21-22 17-18 16-17

Year 1966 1963 1964 1963 1964 1964

5.5 3.05 1

14-15 18-191961 1966

32.8 24.05 2

20-21 21-221948 1966

15.3 9,613 1516-17 6-71961 1965

18.4 5.213 1215-16 13-14

1966 1965

25,3 44.0 26.7 23.69 11 14 17

11-12 18-19 3-4 22-231958 1959 1966 1956

152

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec.

54. Jaipur(1950-59)

55. Jalpur (Sanganer A.erodrome) (1959-66)

56. Jamshedpur (1948-66)

57. Jamui(1955-65)

58. Jawai Dam (1962-66)

inmDateTimeYear

2.02

10-I 11965

1.1 6.012 30

17-18 11-121965 1963

59. Jharsuguda(1954-66)

60. Jodhpur (1948-65)

nm 13.2 4.1 17.0 5.4 17.8 27.9 60.0 52.0 50.8 25.7 7.5 2.!Date 18 20 3 9 30 27 7 18 24 2 28 29Time 16-17 23-24 23-24 22-23 3-4 17-18 16-17 4-5 13-14 22-23 11-12 20-21Year 1948 1948 1962 1961 1951 1951 1964 1964 1954 1956 1958 1960

6!. Tonk Dim Site (1952-53)

0

mm1)ateTimeYear

12.2 9.7 16.527 20 5

18-19 5-6 5-61956 1954 1957

5.1 12.210 21

3-4 16-171958 1950

37.1 57.1 45.515 2 111-2 14-15 4-51951 1956 1955

inmDateTimeYear

6.5 24.5 5.31 12 30

10-tI 14-15 20-211961 1965 1966

9.1 24.824 27

13-14 19-201963 1964

48.0 49.0 54.018 7 155-6 18.19 13-141966 1962 1959

mmDateTimeYear

53.6 54.6 7.9 1.327 3 28 2!

21-22 7-8 14-15 16-171954 1956 1958 1958

23.8 22.5 12.6 2.36 7 5 292-3 13-14 17-1821-221961 1961 1959 1960

53.2 34.3 17.8 11.97 22 25 308’9 22-23 23-24 20-21

1964 1959 1948 1956

14.0 29.3 19.327 7’ 24

21-2221-22 18-191949 1961 1951

22.6 54.4 85.924 20 10

18-1915-16 0-i1962 1949 1949

53.5 61.717 2916-17 21-221964 1953

mm 12.9 5.1 18.5 26.4 26.7Date 9 7 30 22 31Time 5-6 10-Il 14-15 13-14 14-15Year 1957 1961 1965 1964 1959

56.9 44.0 59.5 50.025 19 13 255-6 0-1 23-24 14-151957 1962 1964 1957

39.9 10.0 4.74 28 12

13-14 11-12 11-121957 1965 1961

12.2 7.9 0.417 25 2617-18 7-8 3-41963 1963 1963

5,5 21.2 22.3 98.0 59,8 40.522 13 28 19 20 19

17-18 3-4 15-16 22-23 17-18 16-171963 1964 1963 1962 1965 1964

i_nil)DateTimeYear

15.5 19.6 14.516 24 291-2 9-10 19-201957 1958 1965

14.5 31.211 13

18-19 16-171966 1956

50.0 63.0 71.1 53.522 3 25 6

15-1621-22 13-14 13-141958 1954 1957 1958

77.03

22-231954

5.3 11.02 117-8 14-15

1956 1961

mm 5.8 4.6 7.1 2.1 0 24.9 37.1 46.0 19.1 29.5 01)ate 20 5 15 15 — 29 3 24 4 15 —

‘rime 3-4 22-23 18-19 8-9 — 18-19 21-22 18-19 19-20 19-20, —

Year 1953 1953 19521953 — 1952 1952 1952 1952 1952 —

153

Jan. Feb. Mar. Apr. May June July Aug. Sept.Oct. Nov. Dec.

62. Kathmandu (1952-66)mm 5.6 16.0 11,2 23.5 24.4 44.0 41.7 33.2 35.3 27.4 5.1 3.5Date 28,9 11 22 25 9 19 19 12 15 1 2 18Time 22-23 16.17 4-5 16-17 23-24 1-2 19-20 22-23 14-15 ~-3 22-23 6.7

23-24Year 1956,57 1956 1956 1962 19561965 1952 1961 1963 1961 1952 1961

63. Khalarl (1963-1966)mm 0 6.0 10.0 19.2 22.5 30.0 37.5 63.2 21.8 30.5 6.5 7.5Date — 10 31 1 23 13 23 13 9 20 25 1Time — 9-10 18-19 14-1514-15 13-14 23-24 16-17 0-I 23-24 3-4 19-20Year — 1964 1965 1965 1965 1963 1965 1966 1964 196419~61966

64. Khijrawan (1958-1961)mm 12.0 11.4 17.5 5.7 14.0 29.8 36.5 28.0 40.0 66.0 8.6 8.7Date 7 24 20 24 13 1 23 23 5 23 12Time 8-9 15-16 5-6 0-1 18-19 17-18 15-16 10-11 11-12 15-16 13-14 2-3Year 1960 1958 1960 1961 1958 1958 1964) 1961 1958 1960 1958 1961

65. Kodalkanal (1948-1966)mm 35.6 20.0 38.1 68.6 83.3 24.9 40.6 30.0 40.0 65.5 30.8 25.1Date 16 24 20 20 6 5 22 24 4 9 7 18,4Time 19-20 2-3 21-2218-19 16-17 17-1812.13 15-16 19-20 18-19 0-1 15-16

28-19Year 1948 1962 1962 1957 2964 1953 1964 1964 1964 1953 1959 1957

196!

66. Konar (1960-1964)mm 5.6 17.4 5.8 24.0 32.5 58,7 41.4 50.0 41.0 27.1 2.5 8.0Date 16 7 5 18 25 20 19 31 30 2 3 8Time 3-4 18-19 21-2213-14 12-13 16-17 13-1410-11 21-22 20-21 14-15 11-12Year 1963 1961 2962 1962 1961 1964 1964 1963 1963 1962 1963 2962

67. Luchipur (1963-1966)

mm 10.0 5,5 19.8 55.0 36.5 62.5 29.0 45.5Date 3 20 20 25 26 29 9 14Time 23-24 18.19 19.20 20-21 22-2322-23 16-1715-16Year 1966 1965 1965 1964 2963 1965 1964 1965

68. Lucknow (Amausi) (1953-1966)mm 12.9 8.6 14.5 10.2 40.0 50.0 70.063.7Date 16 1 21 24 21 22 9 2Time 1-2 1-2 17-18 16-17 1-2 13-14 3-4 13-14

Year 1953 1961 1960 2963 1964 1964 1960 1955

69. Madras (Meenambakkam) (1948-1966)mm 24.5 8.4 13.2 35.3 52.6 49.9 36.4 62.2Date 10 3 24 II 19 22 14 28Time 7-8 0-I 20-21 14-I5 3-4 3-4 23-24 2-3Year 1963 1959 1963 1951 1952 1961 2966 1950

36.5 30.0 11.0 3.87 21 4 1

13-2421-2218-1922-231964 1963 1963 1966

59.3 39.0 8.0 9.514 2 1 17

6-7 19-20 21.22 23-2423-24

1958 1958 1963 1961

52.6 49.0 61.0 43.71~ 9 4 I4-5 0-1 2-3 16-17

1956 1963 1957 1952

154

Jan. Feb Mar. Apr. May. Jun. J-.1• Aug Sept Oct. Nov. Dec.

70. Madras (Nungambakkam) (1957-66)mm 26.2 13.5 10.0 33.9as 41.2 38.1 31.1 44.7 74.5 47.7 304Date 10 3 25 23 6 22 12 15 30 7 fi 7.TIme 74 10-11 13-14 10-11 2-3 34 22-23 34 0-I 2-3 21-fl 10-IlYear 1963 1959 1963 1963 195$ 1961 1961 1966 1960 1959 $961 190

71. Mahabalesluw (1941-1966)mm 5.1 0.5 19.3 34.8 30.2 50.1 45.238.5 41.2 45.2 29.0 16.8Date 2221 616262310 9 1 120 5Time 10-21 14-15 17-18 17-18 14-1323-2422-23 16-1710-11 15-1621-fl 9-10Year 1941 1941 1948 1959 1956 1951 1965 1963 1951 1951 1951 1962

72. NaIthon(1957-1966)mm 6.0 7A20S35.026.031.054.038.452.025.07.0 2.8Date 3192325113030 810203,4 2TIme 22-23 27-18 14-1519-20 15-16. 9-10 20-21 34 16-Il 13-14 18-19 11-12

19-20Year 1966 1965 1965 1964 1958 1963 1965 1963 1966 1951 1963 1966

73. NasgaSs (1953-1966)mm 5.6 0 31.5 24.9 71.1 58.0 43.5 47.0 29.5 56.0 38.5433Date 7 — 27 29 21 26 10 15 27 17 22 10Time 2-3 — 23-24 19-20 0-1 56 4-S 1243 2-3 34 18-19 14-15Year 1954 — 1963 1956 1965 1961 1964 1962 1955 1963 1958 1965

74. Nmaga.(1964-1966)mm 1.9 040.5 060.35I,839.325.732A39A42.0$.0Date 4 1 I — 3 6 820279 13 11Time 5-6 2-3 12-13 — 10-lI 20-21 2-3 14-IS 20-21 56 34 10-lIYear 1965 1966 1964 — 1966 1964 1964 1965 1965 1964 3966 1965

75. Nawsyaram(1960-1966)mm 10.0 12.6 45.2 42.0 86.4127.0118.5 103.0100.0 32.0 27.0 2.5Date 4 22 1 29 19 Ii 7 2 13 20 5 12TIme 8-9 21-fl 21-fl 22.13 34 22-23 20-21 0-1 20-21 4-514-15 15-16Year 1966 1964 1961 1962 1950 1966 1964 1964 1960 19641963 1966

76. NinIesy(1963-1966)mm 143 13.5 7.7 643 34.3 42.0 542 22.2 70.0 64.1 38.5 31.7Date 9 10 13 24 4 3 24 .10 26 23 19 3TIme 9-10 15-16 15-16 1-2 21-22 23-24 9-10 19-20 13-14 1-2 15-1620-21Year 1963 1963 1963 1963 1963 1964 1963 1965 19651965 1963 1965

77. Mukhlm (1956-1966)

mm 4.0 5.7 8.5 14.7 22.6 26.2 36.7 57.3 43.3 22.6 9.7 6.6Date 4111914 21 301420~15 7 431lime 22-23 23-24 1415-1622-23 22-23 34 3415-1617-181142 4-5Year 1959 1959 1966 1963 2956 1964 19651965 1960 1961 1959 1960

155

Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sept. Oct. Nov. Dec.

78. Nagpur (1948-1966)

79. Nandurbar (1952-1966)

80. New Delhimm 28.7Date 15Time 18-29Year 1953

81. NorthmmDatelimeYear

(1948-1966)16.6 19.1

5 123-24 18.191962 1952

82. Okha (1963-1966)mm 4.7 0Date 2 —

Time 3-4 —

Year 1965 —

83. Okhaldunga (1952-2966)mm 7.1 18.0 15.7 25.0Date 10 22 24 13Time 0.1 14-15 16-17 22-23Year 1957 1954 1953 2963

84. Palganj (Giridih) (1953-57)mm 9.9 5.3 9.1 7.1Date 21 2 27 10Time 7-8 13-14 13-14 14-15Year 1955 1956 1955 1955

85. Panaji (1965-66)mm 0.2 0.9Date 4 1Time 5-6 1-2Year 1965 1966

24.5 34.0 72.5 36.0 32.4 50.0 20.0 5.716 24 2 29 18 9 3 4

16-17 6-7 22-23 14-15 17-1822-23 2-3 22-231965 1957 1963 1958 1964 1959 1959 1962

71.1 55.0 50.8 65.0 36.8 19.6 23.89 21 24 28 10 3 17

3-4 7-8 3-4 3-4 2-3 0-1 1-21959 1959 1964 1960 1965 1963 1965

43.4 47.6 51.8 49,4 9.0 30.0 14.6 3.620 27 10 19 21 3 12 16

23-24 22-23 17-18 15-16 0-1 16-17 16-17 11-122954 1961 2956 1963 1961 1964 1961 1955

51.3 40.1 43.4 55.9 55,9 24.1 2.8 23.628 13 14 27 6 9 7 2911-12 6-7 13-14 15-16 22-23 21-22 12-13 16-171956 1956 1956 1957 1954 1954 1955 1954

mmDate

29.06

9.421

28.529

19.825

37.820

78,027

65.427

51.827

53.64

31.522

12.25

21.84

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mmDateTimeYear

6.9 0 8.8 33.024 — 28 29

15-16 — 15-16 16-171963 — 1963 1958

5.1 13.5 35.5 73.0 49.5 79.3 26.4 8.4 8.62 30 25 22 7 7 9 20 29

8-9 15-16 18-19 16-17 10-I I 8-9 2-3 13-14 18-191952 1950 1966 1965 1960 1948 2956 1957 1963

Lakhimpur (1957-1966)9.6 10.0 21.3 22.9 51,5

20 16 28 16 84.5 11-12 6-7 13-14 3.4

1961 1960 1964 1964 1958

0 0 0 53.0 76.1— — — 22 19— — — 0-1 22.23— — — 1966 1966

24.0 6.2 5.3 7.4 0.527 6 15 25 2915-16 7-8 18-19 5-6 23-241964 1966 1963 1963 1964

0 28.2 42.8 20.4 30.7 11.6 54.0 18,0 20.4 18.6— 16 3 16 19 31 ‘ 22 2 14 11— 23-24 I0’Il 16-17 22-23 17-18 3-4 18-19 4-5 10-lI— 1965 1966 1966 1965 1966 1965 1966 1966 1965

86, Panambur (Manalore Project) (1965-66)mm 4.0 0 0 11.0 29.2 37.3 31.4Date 14 — — 20 30 27 29Time 2-3 — — 1-2 0-1 0-1 18-19Year 1966 — — 1966 1965 1966 2965

26,01922-221965

21.5 33.2 22.5 17.53 15 6 11

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95. Putkl (1960-66)mm 9,0 9.5 24.0 32.0 30.0 46.0 34.0 45.2 49.0 30.0 10.1Date 3 10 29 25 7 30 16 3 2 3 4Time 29-20 12-1318-19 17-18 17-18 23-24 16-17 0-1 15-16 15-1618-19Year 1966 1964 1965 1964 1964 1963 1960 1953 1963 1963 1963

96. Ralpur (1962.66)mm 3.2 7.8 18.6 9.2 15.7 51.4 40.0 48.9 49.0 21,7 11.9 18.4Date 6 28 31 17 19 18 11 23 20 19 23 1Time 10-11 7-8 3-4 21-2217-18 15-16 15-16 20-22 15-16 16-17 15-1614-15Year 1965 1963 1965 1962 1962 1966 1965 1965 1965 2964 1966 1966

97. Ramgarh (1953-66)

mm 19.8 16.1 16.6 15.6 26.5 43.6 45.0 42.8 55.6 36.5 5.2 11,0Date 31 3 32- 25 27 7 27 3 23 21 . 10 8Time 15-16. 6-7 17-18 16-17 17-18 6-7 22-23 18-19 1,7-18 10-iT 21-22 8-9Year 1953 ‘1956 1959 1964 1959 1961 1957 1963 1965 1964 1953 1962

98. SagarIsland (1948-66)

mm 20.3 34,5 24.5 48.8 51.4 .,~.992.7 94.0 88.3 57.4 27.2 29.2Date 17 6 24 7 2 10 18 15 21 30 18 29Time 5-6 9-10 0-I 22-23 22-2310-11 14-15 4-5 11-22 10-11 8-9 7-8Year 1953 1948 1965 1949 1962 1950 2957 1963 1964 1962 1950 1954

99. ShIllong (1957-66)mm 9,1 8.4 36.0 43.2 31.2 30.4 57.5 22,5 6.5 5.3Date JO 12 29 30 18 27 2 22 6 9Time 9-10 21-2215-16 13-14 2-3 21-22 18-19 23-24 11.12 15-16Year 1957 1960 1964 1958 1960 1961 1958 2965 1961 1957

100. Slndri (2963-66)

mm 1.7 5.4 18.5 20.0 13.3 6.3Date 3 20 29 8 4 1Time 21-21 16-17 19-20 1-2 17.18 21-22Year 1966 1965 1965 1963 1963 1966

10.2 13.526,3 25

16-17 18-1922-231965 19541958

102. Srlnagar (1953-1966)

mm — —. 7.4Date — — IiTime — — 15-i6Year — — 1954

0

28.0 36.020 ‘~‘

15-k 13-i41964 1956

23.5 29.025 - 21

18-19 12-131964 1964

101. Sonepur (1952-66)mm 10.0 13.2 11.5Date 27 4 10Time 16-17 9~105-6

Year 1966 1956 1962

77.5 36.5 500 31.530 - 9 24 15

23-24 19-20 i4-1~17-181963 2964 1963 1963

38.0 76.0 78.2 61,019 19 11 16

18-19 6-7 21-2218-19

1966 19-65 1953 1952

8.8 17.3 22.0 10.021 31 10 18

16-17 9-10 5-6 1’Z~~l81963 1966 1960 1965

34.51717-18

1958

2.9 9.022 15-6 28-19

1966 1966

10.0 10.73 30

4.5 1-21964 1966

10.2 7.8 4.13 6 27

0-1 20.21 12-13i9~ ‘459 1953

158

Jan. Feb. Mar. Apr. May Jun. July Aug. Sept. Oct. Nov. Dec.

ShantiNiketan (1960-66)5.3 17.5 23.2 20.0 46,5 42.04 6 29 26 11 231~2 23-24 21-22 19-20 15.16 2-31966 1961 1965 1964 1962 1962

103.mmDateTimeYear

104.mmDateTime

Year,

Taplejung (19541956)7.4 11.0 18.!Ii 16 8

19-20 1.2 20-21

1957 1960 1963

38.0 88.0 4.0 1,77 21 21 1

16-17 17-1822-23 23-241964 1964 1966 i~cb

41.5 49,028 29

15-16 9-101961 1960

32.9 31,021 47-8 16-17

1962 1958

16.7 37.0 49.825 13 5

15-16 16-17 17.18

1965 1959 1965

28.051-2

1959

59.2 5.5 722 4~t 14

14.15 4-5 19-2015-16

1956 1963 19631965

23.7 40.6 35.66 19 24

16-17 16-17 0-11963 1956 1960

10.4 28.77 29

9-tO tO-If1957 1956

25.1 53,328 29

10-11 3-41958 5957

33.0 10.4 6.6 12.017 9 21 272-3 5-6 2-3 11-121962 1956 1957 1962

105. Tehri (1956-1966)mm 9.9 11.1 14.2Date 9 4 19Time 12-13 14-15 20-21Year 1957 1965 1965

106. Tezpur (1957-1964)

mm 10.0 7.6 19.1Date 23 20 30Time 14-15 2~-22 16-17Year 1959 1957 1959

107. Thikri (1952-1966)mm 10.9 0.8 3.01)ateTimeYear

108.mmDateTime

Year

52,0 63,0 50.0 48.520 26 10 305-6 23-24. 0-1 6-71963 1963 1963 1961

32.8 10.6 4.015 9 77-8 3-4 7-81963 1959 1964

7.7 30.0 55.9 39.3 61.0 61.0 35.6 8.0 30,027 5 10 17 17 23 25 13 1 1 28 3

20-21 6-7 19-20 18-19 16.17 20.21 19-20 15-16 14-15 19-2020-21 0-I1955 1961 1960 1959 1960 1956 1960 1953 1954 1955 1958 1962

Tiliava Dam SIte (1956-1966)

9.3 9.9 8.0 16.8 21.6 50.0 33.0 8O.0 40.0 35.6 12.8 2.829 7 6 24 14 26 15 11 14~24 1 16 29

22-23 15-1621.22 12-1313-14 21-22 15-16 16-17 17-1822-2315-16 19-204-5 20-21

1959 1961 1960 1962 1956 1965 1962 1966 1964 1959 1966 19561965

109. Tiruchlrappalli (1954-1966)mm 29.7 4.7 27.4 41.6 41.! 30.0 46.3 55.5 68.7 77.7 31.2 20.2Date 8 3 22 23 4 10 8 6 27 26 1 7Time 17-18 14-15 1-2 19-20 20-21 18-1920-21 21-2221-2220-21 17-18 14-ISYear 1963 1962 1962 1959 1954 1966 1965 1958 1962 1955 1961 1962

110. Trivandrum (1952-66)mm 53.0 59,5 96.3 71.0 51.8 50.5 25.0 16.9 40.0 68.0 45.2 69.8Date 30 23 24 9 17 7 3 26 25 18 14 3Time 0-1 17-18 6.7 20-21 14-15 4-5 3-4 2-3 3-4 2-3 14-15 15-16Year 1962 1962 1954 1962 1957 1953 1964 1962 1966 1964 1953 1965

159

Jan. Feb. Mar. Apr. May Jun. July Aug. Sept. Oct. Nov. Dec

ill. Vengurla (1952-66)mm 2.9 0 0.3 9,9 57.! 66.0 42,2 52.3 61.0 40.5 40.1 43.5Date 4 — 15 18 20 12 IS 7 2 3 5 2Time 4-5 * 2-3 18.19 4-5 25-16 18-29 23-24 6-7 2-3 19-2020.21Year 1965 — 1954 1952 1955 1960 1953 1958 1966 1964 1962 1962

112. Veravil (1952-66)mm 10.2 5.9 0 0.3 1.8 50.3 121.5 64.4 48,0 55.0 3.2 8.0Date 31 4 — 14 11 18 2 26 12 13 25 4Time 19-20 13-14 — 7-8 10-Il 18-19 11-12 4-5 14-15 19-20 8-9 12~13Year 1961 1961 — 1956 1966 1962 1960 1961 1958 1959 1963 1962

113. Vleakhapatnam (1951-66)

mm 40.0 40.6 16.0 45.5 27.4 63.0 48.5 56,7 52.0 47.0 45.2 30,0Date 3 7 30 18 7 16 20 24 19 18 21 7Time 4-5 9-10 15-16 22-23 6-7 5-6 20-21 4-5 2-3 14-15 19-20 21-22Year 1966 1961 1957 2963 1955 1960 1951 1965 1959 1961 1966 1960

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THE SIZE 05 lCW.~WI4ERE I.lEC~,6SAR~.q.4. THE SEcTIoNs AR.SAPPLlCAaLt F0~CULVERTS DESIOP4ED;ORRC_CLASS 70R OR Z L&H2S OF CLASS A LOt~Dtl4G, WHIC3~EVE~ISSEVERER, WITHOUT PROVISION OF APPROACH SLAaS.

5 T~i~!CT\OlISSNAL 1. _~jti CE~461.11 Co~ç~j~3.6 ~ RIO 3’.

ASOI4RVIN C EHAORTP.g I:~3oE CouRSe7D RUB ~LE NAS~~(~1IND SO Rh 1.4 CEMENT MOR~TP.?~.3-THE FOU$TION~ôi~cgeT2SHALL BE IN CEP~ENTCOMCRE’T~ 1:3:6.

—o ~

H t ~Io6 fl,iCkrIess~ weOrIn~ coat

0 L.

SPAN UPTO ~ME~TRES 3 METRES 4 METREIO 5 I.~ETp~E~ 6 M~TRIS

50 2,-DO 2-30 300 3.50 4-00

— .— — — .—~pie0aoi3o3a0-43o~9

-50 2.00 25~T7o5-50 4-00 -50 t.00j11013-0, 3-50

— ~_-±-.-_.

4.00 2.00 350 3-00 3.50 3Q~ 5-00 2-50 3-00

40~90~4~39440O29O34O39Q44O7SO3Oo04S00~00)SO4O045

3-30 I..00

ba 0-450-57 C~700~I20.95 07 0-44 0-59 0-71 0-840-95 I-09 0-48 0-50~0-T3 0-50 0-93 -10 0-52 0-75 0-87 100 I- IS 0.55 0-750-U 00 I~l3

1-13 130

193210

1-45 I-eS

~245

1-63

aes~eo

200 1-15

I952~3

.33 ~.5Q .5$ 55

3°2432’I263

203 I’ll

191

I~4~.52

~j~32t

-6’?

92

I-5’7 2-0~~-37 135 ‘72 -90 2-26

7t.G4~a-IT2~35t~2Z.7OI2eaa.Ia~23512-53

-35 55 I-IS ‘90

2.10

V08

Z~

F 82

WINO WALL 5kC’T ION ~T 1UOH E~D

NOTES:-1. ABl,1TM51.~T AND WING 1.~ALL SECTIONS ARE APPLlCABt~_~Q~A

CFOR ALL ~l’~M5)

ABUTMENT AND WING WALL SECTIONS FOR CULVERTS

TABLE

EFFECTIVE SPAH(L) METRES 6 9 12

-r-

CLEAR 5P0H(S~ (METRtS~ 5-572 8-512 11-368

RISE (n.) (MILLIMETRES) 1500 2,250 3000

RADIUS OF CENTRE LINE (~)(MILLIMETREs) 3750 5625 7500

‘760CLISI-IIO)4 460V6 CROWN (C)(MILLIMETRES) 610 760

ARCH II4ICRNESS(.T)(MILLIMSTRES)

(UNIFoRl~SECT1ON FROM SPRINGING TO CROWN)

535 1,10 790

05 P51-I OF I1ALINCI-j FILLING 3,1 PIER 5 ASUTMEN’To~A! (MIL~IME’rREs)

101 5 I 4-30 159 S

300c/c

CROSS SECTION AT ThE CRQY~NOF A.P,c!j~ALE~

GENEP~LNOTES -

1 SP�CIflCAT IONS P C STANDARD SPECIFICATIONS AIC COOS OF PRACTICE FOR ROAD BRIDGES SEC’tIONS t,KAMDE

2 DESION LIVE LOAD IS-C CLASS A LOADING TWO LANES OR CL*3~7o.R’ LOADI1.l~ONE LANE

3 MATERIAL THE MASOHR’A OF THE ARCH RING MAY CONSIST OF EITHER cONcRE’r49LoCI~(CC.I:36)00 ORE0500 5T’OIIES CO 55101.15 1.1(73) CEMENT MORTAR. THE CRUSHING STRENGTH o~CONCRETE • STONE OR 501CR UNITS SHALL 1.~TBE LS~5 ‘SHAM 05 I4G/CI.~’,WI4ER~STONI

MASONRY IS ADOPTED 10R THE ARCH RING, IT SMALL SE EITHER COURSED 20851-f.

?MSOHRV OR &SHLAR MASONRY,

4 DES~NSTRESSESP~2MIS4IbI.ECOMPQESSIVR STRESS SPECIFIED ~ IRC BRIDGE CODE SECTiON ~ (i~i)

5 RAILINGS As PER DETAILS APPROVEO,

NOT£ S

I THIS DRAWING 5 APPLICABLE TO 551005$ LOCATED IN 1.401.4- SE1SMIC ZONES. ONLY.

2 THE RATIO OF RISE TO SPAN 06 hIkE CENTRAL LINE OF ARCH RING SHALL BE ~

3 SPECIFICATION FOR ROAD CRUST OVER THE ARCH BRIDGES MAY BE SAME AS THAT ADOPTEDFOR THE ADJACENT STRETCHES 06 ROAD-

4. THE DIMENSIONS AND THE OIA1.AETRES OF REINFORCEMENT BARS ARE INDICATED IN MILLIMETRESEi’.CEPT WHERE S1-~WI4 OTHERWISE.

5 FIGURED 0IP~5MSIOI’35 SHALL BE TAMEN INSTEAD OF SCALED OIM~ENSI0HS.

165

PLATE 5

DETAILS OF SEGMENTAL MASONRY ARCHBR1T~GES-WITHOUT FOOTPATHS SPAN

6 M, 9 M, & 12 M

~oo ~5

SECTIONAL ELEVATION

12,000

166 ~bb0’ - I P1101927MM, 094

75,.-.,, 101C4( ESPOEU’ IC CONCRETE 1~~”~~ -

I ,~_- TYPE ‘C’ 6300 - -~ /1~’’° ~ .- ___________—~ ~.. -~ ___________ ________

- ~—- -~--~~ ~- ~-

- L ~ ~,, ‘o’ oo o ~M5(R27 ~ ,yooC.C08I479EOT ~.0F 160~R

’

10,00 70

,

MIDDLE 105119 1441 RO&QCA3’97,

!

AT MID SPA~I AT SUP000T

C~O5SSEC’!ION

GENERAL NOTES 1—

1,0931611 SPiCIFlC3.1I0HSCI.RCSS.~do.-d0p,91~,~CoAs of proàcofo.’R.o.I Bodies S,ofo”,s I U$-O~

-4,

2.95SIGN LIVE lOAD’ Two I~nps IRC&f~4A,5C2nl~ doss 705 (‘Trock

11d WT~.oIed)~ -3PE~0PCtMEAT- ~teDIroon~004~

4~3~3Mn,n~.,, olco, ~

5.~.(A!i!~0-To.’~~po-o.-ooyso~foIoI, A’7’PI 05

~1~_~_~2O, Eo,r~~

TYPE’O’ 5A55

- . -.--9----~

STEEL IN LONGITUDINALEARS

I o..~SlICE IEMOALTIC C0110MTE

I,,,,, L*~00SO0 lOOT V.L080 91114

11209114 I11011EGMS’TEO SILT

CAPSTO BE P0114505200

WVTOVI. STEEL WI VOLUME, DISTRIbUTEDA9uALI’l AT TOP 1120 DOTIOPA Ill 5070

DTRICT’ON5

r\or’llSlAov IJX 1 ‘. •. 4

C’ EARS11T —

-i

~1~

‘5

‘C94

TRANSVEESS 01W

31

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17

_4)_—

~— 02

1190 c ~ I 55~0F~

2.7 510 2-I 220~‘6 50 SC- O~-ZIP’ OS ZOO TUAo -o ISO 60 -79 ~

,J~c~f~o~c ~L~i~of~-~r~ ~4~~C 14-6 310 IS ISO 80]~’~~~-.25090140132 b ~ 453038644’ IC

0-3 420 20150 50 3-1Th~~35~0940IC lb ,~oJ~o]5E~3~7~-o6-0 1402 6-9 425 ~

_______ 51501. IN LO1140ITIJIDIHALDIRFI‘S0,PO ‘a’ EARS TYPEb~ SASS

44

8

16-6110 90040

UsCL‘C03

79’ 48

21816! 13 300 40 2-52 013 3-381

o I~SilS ~l 4’

0140 ,~F4,-’

S

I,

301 88

0

36 ISO II~1334

5~]0~]4

123 45

GTE, QUAH’Tfl.~F14$ REIN-FORCE MENTPER SPARIN TONHES(scLusNE OF

$7, FORLAPS AND

WATAIS ES

12- 030,34 SI

L

TOTAL~U3,64TITY

OF -CONC RETEPER SPAN

INCUBIC METRES,

168-68

4,

--‘I—---’

300 30 4S0!Q’2$~5-347l 213 - 68

~30~3-43 $-mjs331~~4:

36 ¶50 4 11 314IZ’ZI3~’I10 10 300 7

10 300 6

lb 25 1_I 1-83170 2131006-8 10 300 9

7510

- I ~ 00 Ej ~ p

94Cj0 On

S 7S’2-38~773

265 - 69

II.~9 it-iso] it- 76

PLATE 6

REINFORCEMENT DETAILS OF R.C.C.SLAB FOR CULVERTS

16 125 ?‘? IA 2203p5413 10 300 ¶2

‘89

C—

LO,o<.0

310- 28lb 12,5 47 Il1’S0~

0-55,2,

II 33 51 1100 30 ~iiksi-oi 0 -silO IS

0-127] 34 99

CONTROU~D CONCRETE_M ZOO

~T T~1 1—

17~ I:

13 lOS 55 11,5,4

0-645

3-66

11-39 2-I2’~I4S52

2 233flM-N.Iz-034j412$I

IC

I- III5,59

11-89 2-321 161 -91

9’

I’ 662

300 19 IT 19 p2-127 230 41

‘7’49

F

‘C

40

2-506

I3~20

94

23 11-0913-127 27892

—

1~

3- 402

204I

I

P

4~J~’8O

1 ‘~ ~

L~

~ 2—~

— ~~ ~d4

£~~

STEEL 34 TRANSVERSE DIRECTIONBAcks TYPE (1’ BARS

-5

I..- y -1F

F

3

-r2

4194494

0

2

S

1.’,

S‘C

1~0SC

07

4,

2

TOTAL 9138111-IYOF MS.SINFORCE —

MEN’S PEP,!PAH IN TOIl”FlEE (INCLU’

53148 OFS’/.FOE LAPS 3,14]209th ttre 3

TOTALQUANTITY

OF CONCRETEPER SPAN

INCUBICMETRES

U!

15

20

3 0

5O4~0

i03~

300 2 1

30026

300 3 6

4030046345

58

6040068445

~O lb 180

180 IS, 180

215 1215060

475 18 150

395 20150

660 9~0U90’71.9, flS6~ I90[66 4791-5211649

660 33~’CIA’ I 33 0-41 60-3] 13, ~93 96 I 91- 2-33~ss4’o.iiIA-Il 2314361130 80~245.Z.83

80 OM34~4093745 -97

616O80~S48 ~ ~5,001410-4,635-31 5°,900 390~85j~~)’..I04

S280~4CT so~j~&

10 360 33

1531 10 360 33

26810 30040

09-4 ‘0 300 40

~1P 300131 10 30040

91-34~O4O67S3s5739’7

1550061907

0-35 0-39 2-467

0-550-03-037

3-550-1854 87

O4D’035,,,~

5-75 8053-597

62-9381 ‘ 41

121 ‘49

166 -29

~ii~ES2,69 8830786

¶6

IS

16

IS76

~5 02

100 ‘71~Q0

150 24

ISO 30ISO 39

1615044

lIES

II 95 72-233

2,511-954143

11-842 I??

11-95412-23

11-554 203

085’0235n,I0

I220Is90

5589

11806

294-4

66-99770

10

IS

8

ID

~

300

300

300

300

300

300

30023

5

7

9

it

5

9

I~e9ilUT6O~3 O’S,GZ

11-89 121213 84-89 I ‘ 054

II-~I2~tt7jIO9.I4 .2.5811$’ 01271145.524! 2- 000

II.8’I2I0~I8I905j Z-556I891i~~-41]J3-’7O

3

9I2~j~45Bi

2-884 54

6-11

II ‘ 589-OS

27~5O

3930

FI-

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MAXIMUM REACTIONS IN TONNES

DETAILS AT RSCALE ITO

Cot)’4ERAL NOTES, -

DES ~N~ If C~TIO6liLR�.SISSDA11Q~ 88.~,L2,E.— 55E 5030 54019 9,342”

~tS!G~i_LINt ~ 1~ 4183013,2! *6 CL*2S A ~ 0441 1.44,0 44*4547,5— i~viJs4~r.p0SW4’4L~CO~y58C’.T

Cob C PET C C044’C0TTf.72*~L~2!!o CUBL7TUEA4G’Fl’

— -

PERNlSSI5),’4S’L~t5 ~

REINFORCE5’T’4NT 51419 51156 0A9~ C~4JCQ6’01b3T0 3432/I’46905Ap5J,

TESTED 514156

1414414480 ALESS COVEIS 1410 50 ELIs4!~PCE-Nl-Sl544*61040.1,’1 �46451 W44�00E 300W1jp741ERWISE

CA M~ER. 542’-11AAJiSi~!i!~5~L5 ~ 85 P10OVlO4O

0 ¶140 wEP.OI400 COAT

~

168

Al 0110 SPAN

SEC’T)0E4.

PLATE 8

SCOLI I 20

DETAILS AT~-ET1 w605 462 m661 462 lSBT

L— SEC’IION A~1CC.

804t4454 00,585 5*444 750..’o’. 4141 - 3011 01 o’brlb

I” ~Sl0 S~*~~C1~C(J) \ i*6oosobt5 0 *1’.1l00OI~0ILl,~

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_____ °~ t__’± I ________

TyPtotbQI’l’itfr_1113010 01,,’ LIP)

— ~ ~-~- ~ —— ——‘--4LSECTIONO~ ~OOTPA’Tt4Al P~t~ LSEC’TION Al ~B _____________

0~50 50041111. T44C ,R&oh

01.,,Inr 00 Pb.o& 8c411&’4-4”0400 1.4044 ~ LONGITUDIN.A,L SECjj,QJj

5(ALC I SO _________

SCNEDUL� OF R�INFQBE.r~.t~I (~s~SPAN) ~

~IL---0’- - -— - -__ -___

0*40 Cl*~15L0, 0411 STEEL *4 I.OIIOITUDIIIA,l, DIR5CTION $155L Ill

1R404535555 0IP4CTI0I-4

~ ~ ~ ~. Ii El PANSIO14 J057IT blob L51455)pj4P P5004 D71~,,

lb 040. 0~ 2, ‘~,~P3I0~Dk3~44b**J*0 ~ ~ oIl 91,o~~44o* I ~ DOS b4Eoo~oOl~) ~. --soso 05 IGRI 1,. 34415 SOALL 01 00 *144 lPS’4400(tbT’OPE

P 8-mi “ “~° - ‘ EAlSI r~.~”3’44 SAW, 0~LlRI ~‘ I~°’~ 0P0443F0l44�004 Iooo,,.Sps,, —‘.‘*‘1 ~ P37~ - VI I ~+~--~‘~ 0 rOl VI 400’. 00W~1~00~L.’.4P~ 07!7I,~P’.’. ‘.0 VI [VI j)

00~NC~~ 5p0~9! 74400SC 806’ Pt

33 50 ~5l4 514 40915 *4J4505’ 30 50 ‘Ti ~ 4404145420 344 ~J~j

000~ 44$ ~$3N ~

4 ~o72th~~&05 0 3 44 5 ~ r’ _______ S SPEEDS Ss OAfS ‘l S

L:~~~ ~ ~ : ::~ç__ ____ - ~1ITIIII”Iii_1rIi - ~1

04,4.1 5’155t54tD54O1TI~SIVU63410~~ STEEL 1428155 DI C’ N ~ 57552 31 55555 215541435 J~T5,5I,Ib4I,5345l1Ubl345b.5I95CT~I

- ‘ ~ -r ~o~’o— II ~ ~i IT a I c..._____~ -,~ ~ L i~ 7’T°rh, ~ l7-~--’2 —

~ ~TJJo~5~It m~::4:~i~~4 t.Q IS 4410 4-$- 8E54~ 5 33 4~2 31.2 3*3~4098j 8 300 50 511 ~ 200 I~~SI’,1A $ ~ ~ l.215-4S*0Jl04’%J44 ‘00 ~~~00$40 525

435-5-

R.C.C. SLAB BRIDGES WITH FOOTPA1’HSSIMPLY SUPPORTED CLEAR SPANS

4, 6 & 8 METRES FOR SQUARECROSSINGS

4444

Sn

0

I,x‘14‘a

-J4

ii - 318

~0l WALL~ --50200 5b1i’T51ESI CAP ¶010 ,~ “—150.1 510 rT~0rPT’RCAP ~VO59aUS$40 %P~Q14 WITh -_. _~_,CL1A0 OP&H ~RUlS1D 5040010 W5TN~ 0.110144440414 STOI4ES ~ 0’O*R 610. 10445045 O~:~~_ ~5l500uI$0UM *T04�8

~CT%Oi~LM ‘sb’

169

PLATE 9

- Em,o.4os0u.JOINT5141118 35.,oV 144404(T’ool Cog. $HAAJTI’E404401 011000)

17,,.,.’ !*PA$0SO0N 304143 WOASINC COAT’

~O~c,!,~HT NO’S SEiOWN

SECTION AT 5AA’_____ ______________

z

‘4

a40-l

~ETN~Q~JJ

1044

4l

4-

I

1459 P1

~8~3’70

IA

80001 05 6*5W——’

PLAN OF BOTTOM REINFORCEMENT-

12,

OF TOP R~fc~RC�MEN-r

p4

STIRP.IJP’S NOT SHOWN

COMPOSI100

TIP! ~ —‘--__~

‘SIP! )2~ ““

SECTION Al

-kNC~OR ~AR1 435 30854551 POST

-~ —$I’T8144440L5 30114414!

I --- TVP!

4,, -

-H

1130�

DETAIL AT SSCALE 55

poso CAP

r~P~12,

SECTION ~‘CC’ SECTION AT ‘EE’

GENERAL ARRANGEMENT OF R.C.C.SKEW SLAB BRIDGE—WITHOUTFOOTPATHS—SIMPLY SUPPORTEDCLEAR RIG~HTSPANS 5,6 & 8 MkIR~~fINPO~CEMENTNOT SHOWN 5I4OWIP(~~ RitPWORC~M~N’TAND ~ RftNFOWfl’*N’T Al BOTTOM MOE ShOWN

170 SCHEDuLE OF PEINFORCE.MENT (PER sPAN) PLATE 10

T2S~12 70 3760 ‘IS 157] 470

CLSARSPAN’5001’I SFFECTIVE 5PAN~5~7M OVERALL LENGTH OF $1.48. ~.74Si

P ~ p - ~ ~1” T’IP4p~ T’1PE p4 f’~’~~�~ 1,PE~~ ‘J 1’9PE 12s ~‘r’~P~ ~ ~ ~ ,‘~‘J

744 ~~~~“-‘j ~ ,j! VT~j~J1~~I j1ji”’Ti’~L! j ~ ~jj~!~ ~a ~ p ~ ~ ~-—-~“~ -—--~--~-- ~hHJ~~ ~ ~~

54~o,o20No,, IT’S, 155 5 42 4 TeA, 30,2,80 6226 63895 20~300,, 8,16 40 I25308&54 9909 03008924 5695 013

00007634I9011 0]38013212 4O~ 54 2964 2852—- L - - . ‘ ‘114~o0’~~’ ~-‘ ‘‘-1 ~‘0_~+’~ ‘ I — ______ —

SEE 24 ‘1 ~‘‘‘3 4501, 4501 5 20 50)4, o’ 145~ COO 345 20 7516886 10 ~ 20 23343610 0 1 55 I2 300 5055 II IO9,,95 II 30419115 IC 99 ACI 4 35Q6742,,J~42I4I3O O,~,~O222244 90 59 I 341$ 25.04

JpQ~3:~ ~ ~ __ ______________________ ______ ::t~1~ 0104

NOTESI ALl, DIMENSIONS ASS 110 IDOl’S 100581 14.00455 SHOAN OTWESIAISE -

3 TES 11446455505 05 SAPS AS APPEARING IN 15-45 SC,~E0ULE 505 300271.15 PCJ5~’0t!, ~41 551’4.A,41I444, S’TttL

3 FUI,, SCALE ELEVATIONS EQS THE ~Et9 SpELL 5,5557 541 1 N~OIjT CS & 54,400� PI,SS’CEEED 51.000,10“I-S 50401 5’ ‘ACNSIC,’A’S 40 4515 SoS! 53407 (1,5655405 305T5’,5514 DIFOSOSLOI 5-ASS 450114504 11.1� SARR

5.6l’ol EOACT’LY ‘TO 3655� SHAPES -4,iF FLLI, 1.5005,144 5655’ 905 NOT AVJIt,Ae,L5 201,15 51555 TO PIE 05051055’, 151.210 jC)INIS ASP, P0E’IISSISLI

5 TkE’~ ACE OF TbSP, SAA~5ESTRENGTH AS ‘75-45 5~*S5JOINE5, 4115’ AD-P WEL1, STAGGESED.144� ARRA4GE?AE.N’5OP bOWlS 05 LAPPINO OF 40655 S40A1.L 40� t’-ECICED 5o 1930 ENGINEES’ IN-Cl445,55 WELL IN ACSISWCE

5 5U~P0S1 CHAIRs OS 2554441,4 59 PSOVIS’SD AT SUIIEOLE IN’755IJ#L2.S 304050355 405165 81,06% 05 4155140100 NOT LESS ‘74464 ‘45 0451,45 CQ’-SCSElE Ss55~LDSE USED 13

5351.425 7545 SEGUISITS (‘LtoP CovEs 402 11915 EEIISEORCLS,5E40’T.

1 ‘7445 V,L91H CE REARIonG 53ISLL 51 IlOon’,-,, HOWEVER,, 14.11 W1D’T54 MA~ 65 SUIT9EL-1 MODIFIED TO SUIT95-153 IO4DIVIOLIAL CASE AT 1445 DISCEETIOM OF 5645 !N3lI0�f’R,.IN- CHAPS,!, IN SUCH AN 5VLNI 1441SCHEDULE OP REINCORCE4-4.9MT I TO SE 5UI1’ASL’1 M001FIEO

8 THIS DRAWING IS APPLICASLE FOR 5445W 52136$ WIllS 41434� 05 54430W I5~1060 FO~4N’~INTER-MEDIATE AIO3LE OS 5495W SE’PW!EN THOSE OIVE4A TN THE -0!INCORCEM~E44T1’ASLE, SPACIIoIGOF5885 CAN SE LINEAR L’S INTERPOLATED-

9,04415 ORAWIND IS APPLICABLE FOR. BRIDGES WIThA CLEAR ROADWA9 WIDTH 05 7 5M!TRESOHL’l

0 508 SA’IEW ANGLIS L!RS ~ 45 164! uSUAL 4.’,955409 OF (SUCULATINO MOMENT FOP ASIOSbI 55100� OF SPAN CENTRE TO 059-4155 05 SuPPORTS MEASURED PARALLEL ‘SQ CENTRELINE OF 50809981 AND PROVIDIN3 MAIN lt’SPORCEMEP4’S IN A DlREc’T’TOM PAR)oLI.EI. TO TRASFIC,.WITh 1590+55585! RIIIIFORC�WENT P44,556.6.04. OCT ASUTE’NP,H MA’l 51 ADOPTED-

II TAISE 5400W 33.65 5530359 851 DESIO9-SISD ITS 80(05066305 044144 1545 INFLUENCE SSJRFAC� CO~SOURSP98561+119 IN 114! !004’i 5’1 5635404 84-49 454EP,GENRODER. F1.ô~,ISHR,D 8’~CS CA~LOHDON)

RAI,NOIES-

DESIGN LNc. LOAD

CONCRE T~

PERMISSIBLE STSESSESRE NFORCEIs’s�l’ST

COVER

C AM ~ER

,

DRAINAGE

‘*�A~1NCCOATQ.AILIN3 S

I ‘1 C 5lklaDACQ SPkIFIC,ATIc5’,SAJID CODE OFS’30.~lIC5 505 5062’T 5543045 55(71001St 9)35

l#IQ L~stS OF ISO (4403 5 ~ 09-15 1,8145 CS

1,4655 ‘TO -R (T~ACIoPDOS WHEELRD)554-4ICLE

CID”4C11E1E TO 0111CC 25~DA’YTS WORIcS CUSS9144403114200 44.~jC’n”T 005 530#’VI CIJ40!S,~ 6l4.i~JCl”~AND fo’ 350 449]C~00, 43’, 04

054140 STEEL SASS C00+SORMIHG 10 IS-4’35/Ip66 GRADE I TF$’TW STEEL-T-IINIMUI’\ CoEAR. cOV6~RTO MILD STEEL~5INCOPC30tA8.NT SHALL SE 25,’n”SECEPT WHERE SHOWN OTHERWISE -

CAI54P’�S IN ‘74545 TRANSVERSE DIRECTION SHALLGE PSOVED IN THE WEARING COST,SS4SLL CONFORM TO CAUSE II7OF I,Q,C,ERt~E

CODE SECTION I’ShALL BE AS PER DETAILS APPROVEO’

SHALL BE AS PER DETAILS APPRO460-

Il. ‘1144 lOP OS PI~CAP SAD SSUIO’4E3-I’T CAP 51451.3. 81 FINISAAED54140019 954 RUSSIsS, WIllS CARSORUNDuM $10418’. 54410104 SLAb S444LL 5$ (45’S 55505 4956.500440 S$4IJTTIQI$4C,.OIL ON lOP SI CAPS (‘ospIcAl-’ Fu.AAO 85 MSHUISCTU510

S’S ~I5 0580 356449880 54510514 14445 ‘044$ 201*00 530.015 SHALL 90 PLACED Il-I POSOTI0I’~ SUTTIOAO

1441 9001 WALL 04060 P,SUTMRWIS AND SUTTI4.G TWO 31511464.

SAC! 05 111! 50540 05 044! SPAN 05060. PIERS P5105 10

1446 (OI’OCSITIPOC* OF ‘0445 AOJACO’l’ol’ SPANS 1441 SIALDOSOCOMPOUND SMALL SI POURED IN 1446 301141 SrTwEEN1441 90699 .0141041 ‘TOP OF 1040 FILLER AFTER CLEANING‘TIlE 203141 34 1141 440411 OF 0014P515SED AIR,

REINFORCEMENT DETAILS OF R.C.C: SKEWSLAB BRIDGE WITHOUT FOOTPATHS

SIMPLY SUPPORTEDCLEAR RIGHT SPANS 516 & 8 M

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PLATE 12

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173

PLATE 13

1, LONGITUDINAL SLOPE OF PIPE SI~ULDE.EMINIMUM OF I IN 4000ALL DIMENSIONS I/-I MIL(MEIR.&S

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175

I-—-’PLATE 15

NOTESI. ~T PEspsou L~ ~j,

MhN1~R~IINIO~O.2, ALL DIP~Et454oHs IN MILLPMR.TRES EXCEPT

WHERE OTHER.WISE ME04TIO NED

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VARYING FROM 0.6 M-4.0 M

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T h~°° —1

I oEo I 2. 3M

STONE / BRICK

176CIRCULAR CULVERTS CONVEYANCE FACToR )~IN THE FORMULA Q~~’2gH

Length ‘M’—÷

4. Diameter ‘M’5 10 15 20 25 30 35 40 45 50 55 60

EntryRoundEdged

EntrySharpEdged

0.75

1.0

1.5

2.0

0.75

1.0

1.5

2.0

0.394 0.373 0.355 0.339 0.325 0,313 0.302 0,292 0.283 0.225 0.267 0.26

0.714 0.686 0,66 0.638 0.618 0.597 0.582 0.565 0.55 0.535 0,522 0.512

1.637 1.60 1.56 1.52 1.485 1,45 1.42 1,395 1.365 1.34 1.315 1,295

2.93 2.88 2.83 2.77 2.72 2.68 2.64 2.59 - 2.56 2.52 2.48 2.45

0•‘p

0

0.381 0.333 0.319 0.308 0.297 0.288 0,279 0.271 0.263 0.257 0.251 0.245

0.611 0.585 0.572 0.56 0.545 0.532 0,526 0.507 0.497 0.487 0,48 0,47

1.34 1.315 1.295 1.275 1.255 1.235 1.215 1.195 1.175 1.165 1.145 1.135

2.33 2.3 2.27 2.24 2.22 2.19 2,17 2.142 2.12 2,1 2.08 2,06

PLATE 16

¶5

4)4

RECTANGULAR CULVERTS CONVEYANCE FACTOR )~IN THE FORMULA Q

Length ‘M’—>

4. Ventway ‘M’

0 75 >~ 0.75

40

30

z.o

1~5

1.1.0.7

i~p0.6(4,

5 10 15 20 25 30 35 40 45 50 55 60 Z

Ml 0.4-0.516 0.488 0.466 0.445 0.427 0.412 0.397 0.384 0.373 0362 0.352 0.393 >

0,693 0.66 0.632 ~ 0.607 0.584 0.562 0.545 0.528 0513 0.497 0.485 0.473 00.935 0,90 0.867 3.837 0.81 0.788 0.765 0.745 0.727 0.71 0.693 0.677 ~ 0-3

1.175 1.135 1.1 1.068 1.037 1.01 0.985 0.96 0.937 0.917 0,898 0.88

1.47 1,43 1.385 1,35 1.315 1.285 1.252 1.225 1.2 1.175 1.15 1.13

1.78 1.73 1.68 1.64 1.6 1.568 1.532 1.5 1.47 1.44 1.415 1.39 O•22.14 2.08 2.03 1.99 1.95 1.91 1.87 1.835 1.8 1,765 1.74 1.71

1.0

1.25

1.25

1.5

1.5

~< 0.75

>11

xl

x 1.25

x 1.25

> 1.5

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7~7~4~_777~

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(FOR~SEE ThE 0%~p05~TFTA~Af

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1.0

1.25

1.25

1.5

1.5

>( 0,75

x 0.75

xl

>~1

x 1.25

x 1.25

>( 1.5

0.46

0.615

0.442

0.593

0.425

0.572

0.41

0.553

0.396

0.~35

0.383

0,52

0.371

0.505

0.361

0.492

0.35

0.48

0,343

0.468

0.334

0.457

0.326

0.447

0,824 0.797 0.775 0.755 0.735 0.717 0.7 0.685 0.67 0.655 0.642 0.632

1.03 1.005 0.98 0.955 0.933 0.914 0.895 0.877 0.86 0,844 0.828 0.815

1.285 1.255 1.225 1.2 1.175 1.15 1.13 1.11 1.09 1.07 1.05 1.035

1,545 1.51 1.48 1.45 1.425 1.4 1.37 1.35 1.33 1.31 1.29 1.27

1.85 1.81 1.78 1.75 1.72 1.69 1.665 1.64 1.615 1.59 1.57 1.55

0

0•75 1-0 1•5 V0 3~0 4-0

D%ScHARG~ IN