Design of Weirs and Spillways

Design of weirs and spillways

19

19.1 INTRODUCTION 19.1.1 Definitions: dams and weirs Dams and weirs are hydraulic structures built across a stream to facilitate the storage of water. A dam is defined as a large structure built across a valley to store water in the upstream reservoir. All flows up to the probable maximum flood must be confined to the designed spillway. The upstream water level should not overtop the dam wall. Dam overtopping may indeed lead to dam erosion and possibly destruction. A conventional weir is a structure designed to rise the upstream water level: e.g. for feeding a diversion channel. Small flow rates are confined to a spillway channel. Larger flows are allowed to pass over the top of the full length of the weir. At the downstream end of the weir, the kinetic energy of the flow is dissipated in a dissipator structure (Figs 19.1a and 19.2a and Plate 30). Another type of weirs is the minimum energy loss (MEL) weir (Figs 19.1b and 19.2b). MEL weirs are designed to minimize the total head loss of the overflow and hence to induce (ideally) zero afflux. MEL weirs are used in flat areas and near estuaries (see Appendix A4.2). Practically, the differences between a small dam and a conventional weir are small, and the terms 'weir' or 'small dam' are often interchanged.

19.1.2 Overflow spillway During large rainfall events, a large amount of water flows into the reservoir, and the reservoir level may rise above the dam crest. A spillway is a structure designed to 'spill' flood waters under controlled (i.e. safe) conditions. Flood waters can be discharged beneath the dam (e.g. culvert and bottom outlet), through the dam (e.g. rockfill dam) or above the dam (i.e. overflow spillway). Most small dams are equipped with an overflow structure (called spillway) (e.g. Fig. 19.3). An overflow spillway includes typically three sections: a crest, a chute and an energy dissipator at the downstream end. The crest is designed to maximize the discharge capacity of the spillway. The chute is designed to pass (i.e. to carry) the flood waters above (or away from) the dam, and the energy dissipator is designed to dissipate (i.e. 'break down') the kinetic energy of the flow at the downstream end of the chute (Figs 19.1a and 19.2). A related type of spillway is the drop structure. As its hydraulic characteristics differ significantly from that of standard overflow weirs, it will be presented in another chapter.

Notes 1. Other types of spillways include the Moming-Glory spillway (or bellmouth spillway) (see Plate 31, the Chaffey dam). It is a vertical discharge shaft, more particularly the circular hole form of a drop inlet spillway, leading to a conduit undemeath the dam (or abutment). The shape of the intake is similar to a Moming-Glory flower ft is sometimes called a Tulip intake. The Moming-Glory spillway is not recommended for discharges usually greater than 80 m^/s.

392

Design of weirs and spillways

2. Examples of energy dissipators include stilling basin, dissipation basin, flip bucket followed by downstream pool and plunge pool (Fig. 19.3). 3. At an MEL weir, the amount of energy dissipation is always small (if the weir is properly designed) and no stilling basin is usually required. The weir spillway is curved in plan, to concentrate the energy dissipation near the channel centreline and to avoid bank erosion (Fig. 19.2b and Appendix A4.2). 4. MEL weirs may be combined with culvert design, especially near the coastline to prevent salt intrusion into freshwater waterways without upstream flooding effect. An example is the MEL weir built as the inlet of the Redcliffe MEL structure (Appendix A4.3).

Crest

Chute <

Bank top /

(b)

Section AA

Fig. 19.1 Sketch of weirs: (a) conventional weir and (b) MEL weir.

Energy dissipator

•

19.1 Introduction

19.1.3 Discussion Although a spillway is designed for specific conditions (i.e. design conditions: 2des ^ndi/^es)? i^ must operate safely and efficiently for a range offlowconditions. Design engineers typically select the optimum spillway shape for the designflowconditions. They must then verify the safe operation of the spillway for a range of operatingflowconditions (e.g. from O.lgdes to gdes) and for the emergency situations (i.e. Q > gdes)In the following sections, we present first the crest calculations, then the chute calculations followed by the energy dissipator calculations. Later the complete design procedure is described.

ftp-'Jl";

^^41..

Fig. 19.2 Examples of spillway operation: (a) Diversion weir at Dalby QLD, Australia on 8 November 1997. Ogee crest followed by smooth chute and energy dissipator (note fishway next to right bank), (b) Overflow above an MEL weir: Chinchilla weir at low overflow on 8 November 1997. Design flow conditions: 850 m^/s, weir height: 14 m and reservoir capacity: 9.78 x lO^m^.

393

394

Design of weirs and spillways

Fig. 19.3 Examples of spillway design: (a) Overflow spillway with downstream stilling basin (Salado 10 Auxiliary spillway) (courtesy of USDA natural resources conservation service), (b) Overflow spillway with downstream flip bucket (Reece dam TAS, 1986) (courtesy of Hydro-Electric Commission Tasmania). Design spillway capacity: 4740 m^/s, overflow event: 365m^/s. (c) Stepped spillway chute (Loyalty Road, Australia 1996) (courtesy of Mr Patrick James). Design spillway capacity: 1040m^/s, step height: 0.9 m, chute slope: 51° and chute width: 30 m.

19.2 Crest design Total head line (THL)

1

(a)

*-crest

Fig. 19.4 Flow pattern above a broad-crested weir: (a) broad-crested weir flow and (b) undular weir flow.

19.2 CREST DESIGN 19.2.1 Introduction The crest of an overflow spillway is usually designed to maximize the discharge capacity of the structure: i.e. to pass safely the design discharge at the lowest cost. In open channels and for a given specific energy, maximum flow rate is achieved for critical flow conditions^ (Belanger, 1828). For an idealfluidoverflowing a weir (rectangular cross-section) and assuming hydrostatic pressure distribution, the maximum discharge per unit width may be deduced from the continuity and Bernoulli equations:

r(2 f q = ^g\-(H, - Az)J

Ideal fluid flow

(19.1)

where g is the gravity acceleration, Hi is the upstream total head and Az is the weir height (e.g. Fig. 19.4). In practice the observed discharge differs from equation (19.1) because the pressure distribution on the crest may not be hydrostatic. Furthermore, the weir geometry, roughness and inflow conditions affect the discharge characteristics (e.g. Miller, 1994). The real flow rate is expressed as: 3/2

3(^i-Az)

(19.2)

where Co is the discharge coefficient. ^Flow conditions for which the specific energy (of the meanflow)is minimum are called criticalflowconditions.

395

396

Design of weirs and spillways

The most common types of overflow weirs are the broad-crested weir, the sharp-crested weir and the ogee-crest weir. Their respective discharge characteristics are described below.

Notes 1. Jean-Baptiste Belanger (1789-1874) was a French professor at the Ecole Nationale Superieure des Fonts et Chaussees (Faris). In his book (Belanger, 1828), he first presented the basics of hydraulic jump calculations, backwater calculations and discharge characteristics of weirs. 2. CD is a dimensionless coefficient. Typically C^ = 1 for a broad-crested weir. When CQ > 1, the discharge capacity of a weir is greater than that of a broad-crested weir for identical upstream head above crest (Hi — Az).

19.2.2 Broad-crested weir A broad-crested weir is a flat-crested structure with a crest length large compared to the flow thickness (Fig. 19.4). The ratio of crest length to upstream head over crest must be typically greater than 1.5-3 (e.g. Chow, 1973; Henderson, 1966): ^''''' > 1.5-3 H^- Lz

(19.3)

When the crest is 'broad' enough for the flow streamlines to be parallel to the crest, the pressure distribution above the crest is hydrostatic and the critical flow depth is observed on the weir crest. Broad-crested weirs are sometimes used as critical depth meters (i.e. to measure stream discharges). The hydraulic characteristics of broad-crested weirs were studied during the 19th and 20th centuries. Hager and Schwalt (1994) recently presented an authoritative work on the topic. The discharge above the weir equals: 2 12 q= - J - g{H^ - Az)^

Ideal fluid flow calculations

(19.1a)

where Hi is the upstream total head and Az is the weir height above channel bed (Fig. 19.4). Equation (19.1a) may be rewritten conveniently as: q = 1.704(i/i - Azf^

Ideal fluid flow calculations

(19.1b)

Notes 1. In a horizontal rectangular channel and assuming hydrostatic pressure distribution, the critical flow depth equals: 2 d^ = —E

Horizontal rectangular channel

where E is the specific energy. The critical depth and discharge per unit width are related by: Rectangular channel g q — ^ gdc

Rectangular channel

19.2 Crest design 2. At the crest of a broad-crested weir, the continuity and BemoulU equations yield: ^

2 '

Note that equation (19.1) derives from the continuity and Bernoulli equations, hence from the above equation.

Discussion (A) Undular weir flow For low discharges (i.e. {dx — Az)/Az 0.05

-^crest

di - A z > 0.06 m Ai:^ 0.15m

0.95^

o . i 5 < ^ ^ i : i ^ < 0.6 Az Notes: ^Re-analysis of experimental data presented by Ackers et al. (1978); r. curvature radius of upstream comer.

I^^(THL)

Upper nappe

d^ Az

Detail of the lower nappe

Lower nappe

-<

•=

0.25(Hi - Az) Fig. 19.5 Sharp-crested weir.

(Tables 19.2 and 19.3). In practice, the following expression is recommended: C = 0.611+0.08 " ^ ^ " ^ Az

(19.5)

Notes 1. Sharp-crested weirs are very accurate discharge meters. They are commonly used for small flow rates. 2. For a vertical sharp-crested weir, the lower nappe is deflected upwards immediately downstream of the sharp edge. The maximum elevation of the lower nappe location occurs at about 0.1 l(//i — Az) above the crest level in the vertical direction and at about 0.25(//i - Az)fi*omthe crest in the horizontal direction (e.g. Miller, 1994).

19.2 Crest design 399 Table 19.2 Discharge coefficient for sharp-crested weirs (full-width weir in rectangular channel) Reference (1) vonMises (1917)

Henderson (1966)

Discharge coefficient C (2) TT

^1

77 + 2

Remarks (4)

-Az Az

1

-Az < 5 Az

0.611+0.08^^^^ ^z

0

.

1.135

di

-Az = 10 Az

1.06 1 +

Bos (1976)

Range (3)

Az Jj-Az

0.602 + 0.075

^1

20 < ^

Ideal calculations of lucaifluid iiuiu flow 1 orifice flow Experimental work by Rehbock (1929)

-Az Az

di - Az> 0.03 m Az

Based on experiments performed at Georgia Institute of Technology

Az Az> 0.40 m Chanson (1999)

1.0607

Az = 0

Idealflowat overfall

Table 19.3 Discharge correlations for sharp-crested weirs (full width in rectangular channel) Reference (1) Ackers era/. (1978)

Herschy(1995)

Discharge per unit width q (mVs) (2)

Comments (3)

/ ^ _ Az^ /— ,/o 0.564 1 + 0.150-i\4g{d, - Az + 0.0001)^^ ^ )

Range of applications ^i - Az > 0.02m Az>0.15 {di - Az)/Az < 2.2 Approximate correlation (±3%): (^1 - Az)/Az < 0.5

1.85(^1 -

^zf

3. At very low flow rates, {dx — Az)/Az is very small and equation (19.4) tends to: q ~ 1.803(^1 - A z ) 3/2

Very small discharge

4. Nappe aeration is extremely important. If the nappe is not properly ventilated, the discharge characteristics of the weir are substantially affected, and the weir might not operate safely. Sometimes, the crest can be contracted at the sidewalls to facilitate nappe ventilation (e.g. Henderson, 1966; pp. 177-178).

19.2.4 Ogee-crest weir The basic shape of an ogee crest is that of the lower nappe trajectory of a sharp-crested weir flow for the designflowconditions (discharge g^es and upstream headi/^es) (Figs 19.2a and 19.5-19.8).

400

Design of weirs and spillways

Detail of the crest -•X

Fig. 19.6 Sketch of a nappe-shaped ogee crest.

Fig. 19.7 Spillway chute of Hinze dam (Gold Coast QLD, 1976). Dam height: 44 m and design spillway capacity: 1700 m^/s. (a) Ogee-crest chute in September 1997 (view from downstream, on right bank).

19.2 Crest design

Fig. 19.7 (b) Concrete veins at downstream end of chute, directing tiie supercritical cfiute flow into the energy dissipator (looking upstream on September 2002). (c) Spillway in operation in the early 1990s for Q ~ 300-400 m^/s (courtesy of Gold Coast City Council). View from the left bank, with turning veins in foreground (underwater). Flow from right to left.

Nappe-shaped overflow weir The characteristics of a nappe-shaped overflow can be deduced from the equivalent 'sharpcrested weir' design. For the design head i/des? equation (19.4) leads to: ^des

2 ^ I I ^des ^z 3^^^!^ Qgg

(19.6)

where Az is the crest elevation (Fig. 19.6). For a high weir (i.e. (//des ~" Az)/Az 3.0

1.7 1.77 1.92 2.07 2.10 2.14 2.16 2.18 2.19

1.0 1.04 1.13 1.21 1.23 1.257 1.268 1.28 1.28

Comments (4)

(3)

Reference: US Bureau of Reclamation (1987). Notes: Qes = ^des/(^des - ^?'^\ (CD)des = q^J{Ji{2l3f'\H^,,

Broad-crested weir

Large weir height -

^zf'\

For vertical-shaped ogee crest, typical values of the discharge coefficient are reported in Table 19.4 and Fig. 19.9a. In Table 19.4, the broad-crested weir case corresponds to Az/(//des ~ ^ ) — 0 and it is found (CD)des = 1 (equation (19.1)). For a high weir (i.e. LZI{H^Q^ - AZ) > 3), the discharge coefficient Qes tends to 2.19m^^^/s. Such a value differs slightly from equation (19.7) but it is more reliable because it is based upon experimental results. For a given crest profile, the overflow conditions may differ from the design flow conditions. The discharge versus upstream head relationship then becomes: q = C{H^ - ^zf'^

{Non - design flow conditions: q -h q^^^

(19.9)

in which the discharge coefficient C differs from the design discharge coefficient QesGenerally, the relative discharge coefficient C/Qes is a function of the relative total head {Hx — ^y(H^Qs — Az) and of the ogee-crest shape (e.g. Fig. 19.9b).

Discussion For Hi = //des the pressure on the crest invert is atmospheric (because the shape of the invert is based on the lower nappe trajectory of the sharp-crested weir overflow). When the upstream head Hi is larger than the design head H^Q^, the pressures on the crest are less than atmospheric and the discharge coefficient C (equation (19.9)) is larger than the design discharge coefficient Qes (typically 2.19 m^^^/s). For Hi < //des> the pressures on the crest are larger than atmospheric and the discharge coefficient is smaller. At the limit, the discharge coefficient tends to the value of 1.704m^^^/s corresponding to the broad-crested weir case (equation (19.1b)) (Table 19.5).

Standard crest stiapes With nappe-shaped overflow weirs, the pressure on the crest invert should be atmospheric at design head. In practice, small deviations occur because of bottom fiiction and developing boundary layer. Design engineers must select the shape of the ogee crest such that sub-atmospheric pressures are avoided on the crest invert: i.e. to prevent separation and cavitation-related problems. Several ogee-crest profiles were developed (Table 19.6). The most usual profiles are the WES profile and the Creager profile. The Creager design is a mathematical extension of the original data of Bazin in 1886-1888 (Creager, 1917). The WTESstandard ogee shape is based upon detailed observations of the lower nappe of sharp-crested weir flows (Scimemi, 1930) (Figs 19.5 and 19.8).

403

404

Design of weirs and spillways 2.21

2.1 Qes 1.92

r ^ (N.

Wdes

A ^\3/2 ^^y

^desl"des

T^HL

1.77

^ F

V V //

//

/\

// //

17

1.62

0.5

C

1.0

1.5 2.0 Az/(Hdes-Az)

2.5

3.0

1.1 Dessign flow CO nditions 1.0C/Cdes 0.9

0.8-

0 1.04 1.02

1

0.4

'*

0.6

0.8 1.0 1.2 (Hl-Az)/(Hdes-Az)

1.4

1.6

3H:3V

2H:3V^^^-*^.N ^

1H:3V"^-x-

'inclined 'ertical

0.2

^

>

\

•

1H •

1.0

^

•

•.

^

.

.

0H:3V

0.98

0.5

1.0

1.5

Az/(Hdes-Az) Fig. 19.9 Discharge coefficient of a USBR-profile ogee crest (data: US Bureau of Reclamation, 1987).

19.2 Crest design Table 19.5 Pressures on an ogee crest invert for design and non-design flow conditions Upstream head (1)

Pressure on crest (2)

Discharge coefficient (3)

H\ > //des H\ < //des H\