I.2 Hydraulic Design of Culvens 651

The inrerception efficiency is ihen

E = RfEO + R/J - Eo) = [1 x ;().35 + 0.20(1 - 0.35)] = D.48The interception capacity isQ = EQ == U:48 x 10 = 4.8 ft3/s, and Qb = 10 - 4.8 = 5.2 ft3!s. A bermcould be placed downstream of the .grate inlet for total interception of flow in the ditch.

16.2 Hl7DRAlilLlCDESIGN OF CULVERTSCulverts are hydraulically short closed -conduits thatconvey streamflow through a road embank-ment or some other type of flow obstruclion. The flow in culverts may be full flow over allitsIength or partly full, resulting in pressurized flow and/or open-channel flow, Thecharacteristics offlow in culverts are very.complicated because the flow is controlled by many variables, includinginlet geometry, slope, size, flow rate, roughness, and approach and tailwater conditions,-Culverts have nurnerous cross-sectional shapes, including circular, box {rectangular}, elliptical,

pipe arch, and arch.Shape seection is typically based upon cost of construction, Iimitation onupstream water. surface elevation, roadway embankment height, and hydraulic performance.Culverts are also rnade of numerous materials, depending upon structuralstrength, hydraulicroughness, durability, and corrosion and abrasion resistance. Concrete, corrugated aluminum, andcorrugated steel are the three most coromon.

Various types of inlets are also used for-culverts, including both prefabricated and constructed-in-place inlets. Some of the commonly used inlets are illustrated in Figure 16.2.1. Inlet .design isimponant because the hydraulic capacity of a culvert may be improved by the appropriate inletselection. Natural channels are usualIy rnuch wider than the culvert barrel, so that the inlet is a flowcontraction and can be the primary flow control.

\ \ \ \

Precast end sectior./ .

Fi,!wr\j".2.J FOUJ ~i"ndrd mlet Iype~ (schernatic) t lrorn Normann el al. (i98S)).

~,.~--------~-~~"---'-----------------------------------

6'52 Chapter 16 Stormwater Control: Street and Highway Drainage and Culverts .

16.2.1.1 Types of Control

There are two basic typesof flowcontrol in culverts: inlet control and outletcontrol. Cuvens withiret control have high-velocity shallow flow lhal is supercritical, as shown in figure HJ.2.2. Thecontrol section is al the upstream end (inlet) of thecuvert banel.Culverts with outlet "Control haveIower velocity, deeper flow that is -subcritical as shown in Figure 16.2.3. The control section is althe downstrearn end (outlet) of thecuvert barrel, 'fai~water depths are-either critical depth or higher.

Figurei6.2.2 illustrates four different examples of inlet "Control that depend on fue submergenceof the inlet and outlet ends of the culvert. In Figure 1-6.22a, neither end of the culvert is "Sub-merged. Flow passes through critical depth just downsoeam of fue culvert entrance with super-critical flow in tne culvert barrel, Partly full flow occurs throughout the length of the -cuven.approaching normal-depth at fue outet.

In Figure 16.2.2b, theoutlet is submerged and the inJet is unsubmerged. 'fhe flow just down-stream -of the inlet is supereritical and a hydraulic jump occurs in the cuivert barrel. In }"igure16.2.2{:,the inlet is submerged and the outlet is unsubmerged. 'Supercritical flow occurs through-out the length of the culvert barrel, with critical depth ..occurring just downstream of the ~1;llvertentrance. Fow approaches normal depth at the ownstream-end, This flow condition is typial o-design conditions. Figure 16.2.2d shows an unusual-condition in whch submergenoe -oecurs alboth ends of the culvert with a hydraulic jump occurring in the culvert barrel. Note the medianinlet, which provides ventilation of fue culvert barre!.

1,

::2J1 ./ Water surface ;:s--~sz~--HW _~./ ~-.~~ ..~-2--~-~_L~_~_~__~_~__~_~__~-==1 (b) ~

Water surface/

(e)

Median drain

~""" .J

fij?UJT )( .:.: 'l ypc. t'l 11lt'1nllitr,': lO' Outlet ,\: miel unsuhmerped: lb) Ourlet subrnerped. inkllJi~uhme'I~'("~: ., ,11\1

l(>.2 Hydraulic Design of Culverts 653

fi{!m-e H.2.3 illustrates Iive flow -conditions for oudet control, 'Subcritical flow occurs for thepartly fuil flow conditions. Figur-e 16.2.3a is the classic condition with both the iniet and the out-etsubmerged, with pressurizedflow throughout the culvert. in Figure Ui.2.3b, the outlet '-S sub-rnerged and the inlet is unsubmerged. In Figure 16.2.3c, the entrance is submerged enough that fullflow OCCill"S throughout the culvert length but t.~ exit is unsubmerged, Figure 1~.2.3d is a typical-condition in which the entrante is submerged by the headwater and {he outlet end ows freely witha low tailwater, The cuvert barrel flows partly full part of the length with subcritical flow and-passes through critical just upstream of the outet, Figure 16.2.3e is another typical condition inwhich neiilienhe inlet nor the outiet is submerged, The flow is subcrtical and partly full through-'Out the length of the-culvert barreJ.

16.2.1.2 Iniet-Control Design Equations

Aculvert under inlet-control conditions performs as an orfice when the inlet is submerged and asa weir when it is unsubrnerged. The (submerged orfice dischatge equation is computed using

Water

'1 SUrface7_~~ ~ 'S7 H W.S.HW _ ~,,--~-=71~=d:a.1 - J

(a)

vi , ~=>sHW r-- -~!

Hj

L'p W.S.

(b)

W.s.

J,c)

W.s.----4

~e)

FiJ>un 1{).2.~ 1YfJ('~ o outlet control rfrorn Norrnann el .al. (1985)).

654 Chaptei JStom1wate Control: Street and Highway Drainage and Culverts

fHW-' f Q -1:v --!=Cl~ +Y+ZL D J LAD .. J .

(}6.2.J )

where HW is the headwaterdepth above the inlet control section invert (ft), D isthe interior heigh: .of the culveri barre] :(fl) .Q is thedischarge (ft3s), A is the-full cross-sectional 'area of the culven.barre] in U12), SOis the culven barrel slope duft), e and Y are ronstants from Table 16.2.1, and Zis the slope correction factor where 2;: -(L5So ingeneral and Z = +'O.7So{or mitered inlets.

The tunsubmerged weir discharge e.quarion is (FOrnl J):

fHWl f H l r Q .":IM f /l ~. - ;: _e 1+1;"1-'-' -J + Z for l-!!j'- - J~ 3.5L D J L [J J LApo.s 1ADo.5 J. where H, is the specific head al critical dep\h {He = de + V:/~) (!(l), de is tbe critical deptb {tl),Ve is the critical velocity (ft/s), and K and M are -constants in Table 16.2.1. A simpler -equation touse for tbe unsubmerged conditionis (Form 2):

(16.2.2)

[HW] r Q "'1

M.r -Q ]._.;: KI~o~' +2 for .I~o" $3.5

. Dl AD . J l AD ..J

Form 2is easier 10 appy and is fue only documemed form f'Or someof the design inlet 'Controlnomographs inNormann el al. (}9~5). . '.

Equations 00.2.1) 10 06.2.3) are irnplemensed by assuming aculven diameter D and using iton the right-hand sirle of these equations and solving or 1HWID]. The headwater deptb is thenobtained by rnultiplying DiHW/D3. Typical inlet-control nomographs are presemed in Figures16.2.4 and 16.2.'5.

Table J6.2.J Constanis for lnlet Control Design Equations

06.2.3)

Chart"No.

Shapeand

Material

Unsubmerged Submerged

NomographScale lnlet f;d{!e Descnpiion

EquationForro" K M e y

0:0098 2.0 0.0398 0.67.0078 2.0 J)292 :74:0045 2.0 .0317 .69

.,0078 2.0 .0379 .69.0210 1.33 .0463 .75.0340 DO -,0353 .54:OOr8 2.50 .0300 .74,0018 2.50 .0243 .83

:026 LO .0385 .si----,.61 0.7~ .0400 .80.-06J D.75 .0423 .82

.5 J{) M7 .0309 .80

.486 . .0249 .83

.51~ .M .0375 -o./ ,

.49:" .6t. .0314 .8248 .' 'tot."i .0252 .8t~-

lb.2 Hyraulic Design of Culvens 6'55

Tabll' 16.2.1 Consrams JO! lnlet C-ontrol Design Equatons j.continued)

Unsubmerged Submerged

ShapeChart" and Nomograph iEquationNo. Material Scale lnlet Edgefrescription Form" K M e y12 Rectangular '45' non offset wingwallflares 2 .497 .667 .0339 ..805

box " nlA' non offset wingwall flares .493 .667 .0361 .8Q6..314"xhamfers 3 18:4' non offset wngwall flares .495 .667 .03'86 .71

3()Cskewed barrel

13 Rectangular 4Y wingwall flares - offset 2 .495 .667 .{)302 .835.box :2 33.7< wingwall flares - offset .493 "'67 .00'52 .881Top bevels 3 nl:4< wingwall flares - offset .497 .667 .0227 $87

16-19 CM boxes 1 90< headwall .00"83 2.0 .0379 .092 Thick wall projecting .0]45 1.75 .0419 ,643 Thin wall projecting J)340 1.5 .0496 :57

29 Horizontal J Square edge with headwall .0100 2.0 .0398 .67ellipse 2 Groove end with headwall .0018 2.5 .0292 .74'Concrete 3 Groove end projecting .0045 2.0 .0317 .69

30 Vertical Square edge with headwall .0100 2.0 ".0398 :67-ellipse 'l Groove end with headwall .0018 .2.5 .0292 .744-corrcrete 3 Groove end projecting .0095 2.0 :03]7 .69

34 Pipe arch 1 90c headwall .0083 2.0 .0379 .6918" comer 2 Mitered to slope .0300 1.0 .04.63 .75radius.cM 3 Projecting .0340 1.5 .0496 .57

35 Pipe arch 1 Projecting .0296 1.5 .0487 .55l~" comer 2 No. bevels .0087 2.0 .0361 .66radius CM 3 33.7< bevels .0030 2.0 .0264 .75

36 Pipe arch Projecting ;0296 1.5 .0487 .553]"-comer No. bevels .0087 2.0 .0361 .66radiusCM 33.7< bevels .0030 2.0 .0264 .75

40-42 Arch CM 1 9D' headwall .0083 2.0 .0379 .692 Mitered to slope .0300 1.0 .0463 .753 Thin wall projecting .0340 1.5 .0496 :57

55 Circular Smooth tapered inlet throat 2 .534 .555 .0196 J!9" Rough tapered inlet throat .519 .64 :02139 .90"-

56 .Ellipcal Tapered inlet-beveled edges 2 .536 .622 .{)3b8 ..83.lnlet face " Tapered inlet-square edges :5035 .719 ,0478 .'00..

3 '[ apered iniet-thin edge projecting .547 ..s0 .0598 .7'5

S Rectangular Tapered inlet tbroat 2 .475 .667 .0179 .97"SF Rectangular Side tapered-c-less 'favorable edges 2 .56 .M7 .fi466 .85

-concrete ~ Side tap.ered-more favorable edges .56 .M7 .397~ .87..'~9 Rectangular Slope tapered=-tess favorable edges '1 :SO .667 .0466 .65

65tr Chapter J{ StormwaterComrol: Street and HighwayDrainape and Culvens

;j.f'.:,.t~,r.

~:~f 10~~:~. Exompie --1.5- -." .~ .e '" '" ,,' .- - 'o f. __ ," ~~ S4. f- .'~I _"/,} 1{)0 ~_ID~ 48.r _ - r ""_ _/ 801 ~o L" ' ' ""0;1- HW Entrance -:; ., 't15 42 ' o '1-, ~ I '.'{)f 1.0,le '1 'SO}- D seae type - tQ; 4'Q,l . 1{)t 1Gmoveend with ti: 933,}-1_ ~oJ,'. heedwell l l' ---+: ---;:jt"-

"" - (3) 'Groove end ):t lO!

1'0,000 f8.000i-

f

6,000:1

5,{).OOf4'000, f3;OOOt

2,OOO}

r1,OOOt

800,} t' } S"'OOOr j jtl ''SOO~ 2.t .r--- --+!. 400,

o.~O.:

b58 Chapter Hl Stormwarer-C oneol: Streei and -Highway Drainape and Culveras

and in 't1.'S. custornary uniis is

H6.2.4b)

or in Sl units is

(~6.2:4c)

where X, is the -entrance Iosscoefficient, n is Mannings roughness coefficient, R is the hydraulicradius of the full-culven barrel in fttrn), Vis the velocity in flls-{mls), and L is the culven lengihin ft (m). 'OtherIosses such as bend Iosses Hb' junction losses H; .and-grate )OS5eS H can also beadded ro equation 06.2.4). Table 16.2.t lists common values of Manning's n values forculvens.:rabie ]fl.2.3 Iisrs entrarrce loss coefficients fOJ outlet control, full or pan full flow,

1ablf )6.~.:2 Manning n Values for-Culverts+

Type of Conduit Wall Description Manning n

-Conorete pipe Smooth walls 0:01-0-0:0]3

-Concrete boxes Smooth walls 0.012-0.015

Corrugated metal pipes and boxes, 22/3" by ]/2" corrugations O.O2~-O:O27annular or helical pipe (Manning 6" by l"corrugations 0.022-0.025n vares with barre I size) 5" by l " corrugations 0.025-0.026

3" by l " corrogations 0;027-0.0286" by 2" structural 0.033-0.035

plate corrugations~ 9" by 2 )/2" structural 0.033-0.037

plate corrugations

Corrugated metal pipes, helical 2 2/3" by 1I2"

l2 Hytirauhc Design of Culverts 659

Table 16.2.3 Entrance LossCoefficients for Dullet -Control, Full or Partly Full 11, = K, ,1212g]vcontinved;

Type ofStrucrure and Design of Entrance Coefficient K,

Pipe or pipe-arch, corrugated metalProjecting from fill (no headwall)Mitered to conform lo fill slope, paved or unpaved slopeHeadwall or headwall and wingwalls square-edge

"End section conorming to fill slopeBeveled edges, 33.7c or 45c bevelsSide-or slope-tapered inlet

Box, reinforced concreteWingwalls parallel (extensin of sides)

Square-edged al crownWingwalls al 10 lo 25 or 3Do to 75 lo barrel

Square-edged al crownHeadwall parallel 10 embankment {no wingwalls)

Square-edged on 3 edgesRounded on 3 edges lo radius of 1/12 barre]

dimension, or beveled edges on 3 sidesWingwalls al 30 to 7'5" lo barrel

Crown edge rounded lo radius of 1/l2 barre]dimensin, or beveJed 10p edge

Side- or slope-tapered inlet

0.9'.7

:50:"5'0.20.2

0.7

0.5

.0:5

0.2

{).2

0.2

"Note: "End section conforming to fill slope," made of either metal or 'Concrete, are the secrions -cornmonly avail-able from manufacturers, From Iimited hydraulic tests, they are equivalent in operation to a headwall in both inletand outlet control. Some end sections, incorporating a closed taper in their design, have superior hydraulic perform-ance. These latter sections can be designed using the information given for the beveled inlet.

Source: Normann et al. (985),

Figure 16.2.6 illustrates the energy and hydraulic grade lines for full flow in a culvert. Equatingthe total energy at section 1 (upstream) and section 2 (downstream) gives

V2 V2HWo ~ -"- = TW ~....!L + H f + H, ~ HZg 2g 11{:.2.3)

where HWo is the headwater depth above the outlet invert and 7W is the tailwater depth above theoutlet invert. Neglecting the approach velocity head and the downstrearn velocity head {fi!,ure16.2,6), equation 06.2.5) reduces lo

HWo = 7W + Hj + H. + Ho 06.2.6)

For full flow TW::: D; however, for partly full flow, the headloss should be computed from a back-water analysis. An ernpirical equation fOI the head Ioss H for this condition is

'"bO 'Chapter .{ .SeormwaterC ontrol: SHeet and H.~hway Drainage and Culvens

I V'I u H,

_-E:J~_.2",,,.--g ----- * i: --:-t =-tI \ '-- ------------ 1 I" I \ -- + r V'

I- - - - - - - - - - - E.G.L." Hf H -!!...

, \ / -__ ---------"- .1- 1 2& I~I '--./ V'-'-_ ----\.1. i l' I

I HWo T - --~- ---'1 r-~'-- ~2~g~__ .....:..H:.::,'G=-.::::L~. ~~_==~ '1.2.! I -;.:-r111', I -- j 7W, I 1

1' j I

I .1 j

Section

:ros}

96~

I::~66 ~

'60~

54 t48.'

l.2 Hydraulic Design ofCuivens 66]

II

eL" I:Io.

~II

1

HW

for outlet-ctown not-.submerged, compute HW bymethods described in the oe'sign prdCedure

D= 48

FiI!Urt' ]6.2.7 Head fOI concrete pipe culverr- flowingfull, /j = 0.0]2 (frorn Norrnann el al. (i9BS)).

d, + D 4.2+ S.O .--- = = 4.64 ~l.

2 2Slfr 4 17, = TW 01 Id, -, Djr. whichever i~iarger. For thisproblern h; = 4.64 ti ISlCr ~ l.\f Tahle 16.2.310 obiain the entrance lo~~coefficient. For the square-edped enuance. K, =.oS

~!fT l' Determine headlos ses throuph thr culven barrel: use equation 116.:.4).:

't { 29n: L \. \1:J - A -. --.-. ,-

\ R1" , 2~,H=

JO f/~. R = Aip = ~()/I(, - f' - e ~ I = l.3D fl. For

M2 ChapierI b SIOfm\~'-aH:TC(mHOl: S!rITI and Hi.ghway Drainape

,IIII/

]{.2 Hydrauic Design of Cuvens b63

----

"outlel :o.;Q/Ap; Ap:O area of flow prism based onbarrel geometryand depthequal to norme1depth

n~un ]{.2.Hl Details o rulvert Jm Exarnple l6.2.1.

,1~ TW> D.d:o D

j

~I-+-d, Normal Oepth Id )

i - - - - ~ - - - - - - - - -:-::-::-:::-=-::--L-l.J;z_+ ~ --------," -- .Steep slope d"" d" ,

D> TW> de' d:o TWdepth

.,.---------,,~~ 11\'

"oulle::O "O/Al'; A" :o ares 01flow prism baseoonbarrel geometry and d

(b)

Figure ]6.2.9 Outlet velocity fOI la) inlet and lb) outlet control-rfrom Norrnann et al. (985)).

Maximum Roadwayshoulder) elevation '13.5 (ft)ELlu : , "0.0 1ft) /

---",.--'-_~"=--F -!"!?..:~::::=-.---- - _.t: - ! -;\-- - ~ --.,/11"'. 'Si' ,-----'-- ~\7 ~,.

EL, = 100 (ft) -"---- --- -==~ ,...--'-1

EL 95.0 (ft)

HW r{)"1"- ='-'CI--. ,1+ y+ ZD 'LADo.-_

64Ch&Jler lb Stormwaser Controi: Street and Highway Drainage and Culvens~ .

Tben EL'; = 95 - 341 ~4.64 = 103 h. Also the approach velocity head {","2/2&) and the-dcwnstream

r>. velocity head can be vonsidered in the calculation o ELhO by adding VJf2gand 'Subtracting V;J'2gfrorn the right-hand sitie -o-the aoove equation for ELho'

Now consider inletcontrol and -determine headwater elevation, EL.,.

'Step 9 Thedesign headwater elevation is nowcomputed as ELh' = JfVIl + EL, so HW must be com-puted usingequation (]th ni mldw~: cre ,1 ovenopped 111tI (m), and HVt', ]; lffi

EXAMPLE 16.2.2

i.2 Hydraulic Oesign of -Cuivens 66~

~HW, --------t--_---h,

e,

1

]j

",1 J

2."90' 0.~5 0.90j

oootk, ~

0.70l0.60\

0.50 '--_--''-- __ '-- __ -'--_.L:-J0.6 0.7 0.8 0.9 '.0

h,lHW,

(cr5ubmergence factor

1.0 2.0HW, (ft)

3.0 4.0

(b) Dischar{le coetlicient for H": IL, s 0.15

Fgure 16.2.11 Discharge coeffrcienrs for roadway overiopping (frorn Normann et al. 11985)).

upstrearn depth measured from the roadway crest to the water surface upstream of the weirdrawdown in ft (m).

4. Add the culveri flow and roadway ovenopping flow for the conesponding headwater ele-vations 10 obtain the overall culvert performance curve. Figure 16.2.] 2 shows a culvert per-formance curve with roadway ovenopping, showing the outlet-comro ponion and the iniet-control.ponion.

Tuncok and Mays (1999) provide a brief review of various cornputer modes for culverts includingHYDRA]}\' rwww.fhwa.dot.pov) by the Federal Highway Adrninistration and CAP (hup:llwa\eJ.usg5;:!,DV~oflware/) by the l.'.S.-Geolofita1 Survey.

The objecuve i~10 develop ihe performance curve fOI an existing -fl by 7-ft and 200-I long concretebox culven on ,: perr ent ~lope that was designed 401 ~ '50-year flood of 600 ft:/s al a design headwa-ter r-levanon 01 ] j 4 I1 Ireter 10 Figure i6.2.l2 for funher details), The roadway is a 4{) fl wide fraveJroad that can he appioximaied as a broad-crested weir with cemerline elevation of la 6 ft. The culven .inlet invert {'lf~'':Jn' :~ -]0(1 t: Therailwater depth-discharpe fe!aliomhip is:

.Q dl'/~, 4Q(1 110(1 800 1000 ]200

Tv"11 :1- : :J 4 ,1 " ,:; Illl)dlfif'(~norn ?'Pln,C1:ld. r : :, ,] Y~:')L

60(; (,haple1 J b Stormwater eornrol: Sueet ano Hi;ghway Drainage andCulvens

Roadway rstroutder)

// >Crown e1evation 116 ft

i f ;;;;;z:zru$ZZOnc:* r -~ .~-,-' ~=~~v.=-- < __ ~::.~4,~:_~ ..:..~- -~ - - - : - .

- , \ 57 ~'-- \~ t

1,--------- = ~'EL, : -oo.oon t --L

H: 90:0 ~ft)

El-he: 1 i 4:0 -(ft)

fl, I l' I I We1r-performaoce ~--}--_I---r---r--r- 1 I ! -t-rt --1 1 j II I ,:, --r- I I I I I \~J -- ::::[--l-'9~~~i~g--J---L--t 1 I I

j :1 \ i I I i 1 I " 1 1

, ! ! 1 .Cuvert , I i I1 Il I I ! I 1i 1 performance ! II 11 II 1 I

1I il

i

I III I I

II I I I I1- l' I I

\! /1I I Ii I iI ! ! I

~

I I ! ! I;

I i11 , i \

V , ~i i I,

o' I Ii ! i, s ;;::1 I I

, . I .:.c'~

I 11:' , , I1 i GOl

1,

!-c ; -.o . , i! :p. , - , , i 1 ,

iv-"",ltm

110

~ ~ : ,:; ; - - - - --

Cd == 2.7{) '@. Jfv.', = :S7Q _.r L( H1l7 )1.5. = r- -,l.nr

.cd = 2.9T@ JlV.', = l.9k = 1

Probierns M7

The performance .curve -cornputations are given in Table 16.2.5. The resulting performance curve isshown in Figure ltl.2.l2b.

Table J6.2.4 Oischarge-beadwater Compurations for-Cuven Flow-e-Example 16.2_2

FlowHeadwater Calculations

Control'fota] P.er HeadFlow 'Barre] lnlet Control Outet Control .Elevation

,Q("() .Q/N HW/D HW E-L,u TW d, d, ~ D ho K H EL/,o2400 400 US 8.] ].08.] 2.6 4.6 5.8 5.8 0.5 1.95 97.8 108.1600 eoo ] ~'5 lL6 111.6 3.1 6.1 6.6 6.6 0:5 4.4 W1.0 111.6700 700 1.95 13.7 113.7 3.5 6.8 6.9 6.9 0:5 6.0 1"02.9 :li 3.7800 800 235 1'0.5 116.5 3..8 >7 7.0 7.0 0:5 7.9 104.9 H6_S850 85{) 2:55 17.9 117.9 3.9 >7 7.0 7.0 0.5 9.0 106.0 117.91000 1000 3.21 22.5 ~22.5 4.1 >7 7J) 7.0 0.5 1.26 109.6 H~2.5

Table J6.2.~ Performance Curve Computations=-Example 16.2.2

a.Culvert 110w EL"