topic 4: applied hydraulics table of contents

Unit CIV2262: Waterway Engineering Topic 4: Applied Hydraulics

4.1

TOPIC 4: APPLIED HYDRAULICS

TABLE OF CONTENTS

1. PREVIEW .....................................................................................................................2 1.1. Introduction ........................................................................................................ 2 1.2. Objectives ........................................................................................................... 2 1.3. Readings ............................................................................................................. 2

2. HYDRAULIC STRUCTURES – FLOW CONTROLS................................................3 2.1 Long-Throated Flumes ........................................................................................ 3 2.2 Broad-Crested Weirs ......................................................................................... 11 2.3 Sharp-Crested Weirs.......................................................................................... 12

3. HYDRAULIC STRUCTURES – OVERFLOW SPILLWAYS .................................23 3.1 Spillway Crests.................................................................................................. 25 3.2 Spillway Chutes................................................................................................. 26 3.3 Energy Dissipaters and Stilling Basins ............................................................. 26 3.4 Design Procedure .............................................................................................. 29

4. INTRODUCTION TO RIVER BEHAVIOUR AND PROCESSES ..........................32 4.1. Introduction ...................................................................................................... 32 4.2. Overview of River Morphology ....................................................................... 32 4.3. Hydraulic Resistance of Alluvial Channels...................................................... 42 4.4. Sediment Transport in Rivers........................................................................... 42

5. THE THRESHOLD OF MOTION..............................................................................44 5.1 Introduction ....................................................................................................... 44 5.2. Flow over a Sediment Bed ............................................................................... 44 5.3. The Threshold of Motion ................................................................................. 46 5.4. The Competent Velocity Approach.................................................................. 49

6. SCOUR AND SCOUR PROTECTION AT BRIDGE SITES ....................................51 6.1. Introduction ...................................................................................................... 51 6.2. Constriction Scour ............................................................................................ 51 6.3. Local Scour Around Bridge Piers..................................................................... 54 6.4. Local Scour around Embankments................................................................... 56 6.5. Scour Protection ............................................................................................... 59

7. BANK AND BED PROTECTION .............................................................................62 7.1. Introduction ...................................................................................................... 62 7.2. Processes of Bank Failure ................................................................................ 62 7.3. Bed Scour ......................................................................................................... 66 7.4. River Training .................................................................................................. 66 7.5. Bank Protection ................................................................................................ 70 7.6. Bed Protection .................................................................................................. 75

Department of Civil Engineering, Monash University

Edition Date: (9-2003)

MONASHU N I V E R S I T Y


4.2

1. PREVIEW 1.1. Introduction This topic is on application of the theories that you have learned so far, for solving some of the key problems in waterway engineering. The first two sections are on basic hydraulic structures. Flumes, broad-crested and sharp crested weirs used for control and measurements of flow in open channels are explained in Section 2. The consequent section is on overflow spillways that are mainly used for evacuation of floods. River engineering is introduced in Section 4. The consequent section is about the threshold of motion that is the key theory for understanding the sediment transport in rivers. Section 6 is on scour and associated problems. It particularly deals with scour protection at bridge sites. The last section is on bank and bed protection. 1.2. Objectives The aim of the topic is to learn how to manage natural and man made waterways. After completing this topic you should be able to:

Design a long throated flume;

Design a broad crested weir;

Design a sharp crested weir;

Design an overflow spillway;

Understand the main concepts of river morphology;

Understand the main concepts of sediment transport in rivers;

Be able to assess sediment transport in rivers;

Understand scour and associated problems;

Be able to assess scour around bridge piers, and design the protection;

Be able to conceptually design bank and bed protection structures 1.3. Readings The bibliography is suggested at the end of each section. However, the general text books on open channel hydraulics are also recommended (listed in the Introduction into Topic 2).





Department of Ci

vil Engineering, Monash University



4.3

2. HYDRAULIC STRUCTURES – FLOW CONTROLS A channel control is defined as any channel feature (natural or man-made) that fixes a relationship between depth and flow rate in its neighbourhood. If this relationship is known, an engineer can do the following: (1) assesses the function of the control (e.g. the ability of a spillway to evacuate floods); (2) assesses how the control influences the longitudinal profile in the channel (e.g. calculate depth and velocity in the neighbourhood of the control); (3) measure flow rate in the channel (e.g. the depth of water is measured, and the relationship used to calculate the flow rate). 2.1 Long-Throated Flumes Because critical flow represents a unique relationship between depth and flow rate, devices which induce critical flow are often used to measure flow in open channels. Most of these devices, however, require calibration in the laboratory because the flow characteristics are not in accordance with the usual theoretical assumptions. Chief among these is the assumption that the pressure distribution is hydrostatic. In many devices, the strongly curved stream lines negate this assumption, resulting in the necessity for empirical coefficients. The long-throated flume (Figure 4.1) is one device for which the flow rate can be predicted theoretically without the need for such coefficients. The major property of a long-throated flume is that it is designed to create a constriction in the flow area sufficient to produce critical flow over the full range of expected flow rates. In addition, the head loss across the structure should not be excessive and afflux should be kept to a minimum. The most commonly used flume is the Parshall-Flume.

Figure 4.1 Parshall-Flume for Flow Measurements

The primary advantages of these devices are listed in the following:


4.4

• Provided that critical flow occurs in the throat, a rating table can be calculated with an error of less than 2 % in the listed discharge. This can be done for any combination of a prismatic throat and an arbitrarily-shaped approach channel.

• The throat, perpendicular to the direction of flow, can be shaped in such a way that the complete range of discharges can be measured accurately, without creating an excessive backwater effect.

• The head loss across the structure required to obtain undrowned flow conditions is minimal, and can be estimated with sufficient accuracy for any of the structures placed in any arbitrary channel.

• Because of their gradually converging transitions, these structures have few problems with floating debris.

• Field and laboratory observations indicate that the structures can be designed to pass sediment transported by channels with subcritical flow. It should be noted, however, that excessively high sediment loads or significant reductions in the velocity of the approach flow may create sedimentation problems.

• Provided that its throat is horizontal in the direction of flow, a rating table based upon post-construction dimensions can be produced, even if errors were made in construction to the designed dimensions.

• Under similar hydraulic and other boundary conditions, these structures are usually found to be the most economical for the accurate measurement of flow.

With regard to the hydraulic characteristics of the flume itself, five components may be recognised as follows (as illustrated in Figure 4.2):

Figure 4.2: Schematic of Long-Throated Flume





4.5

1. The approach channel, where the flow should be stable so that the water level and the energy level can be accurately determined (measured using a level meter).

2. A converging transition region into the throat, which is designed to provide a smooth acceleration of the flow with no discontinuities or flow separation. The transition may be rounded or consist of plane surfaces.

3. The throat, where the flow is accelerated to the critical condition. The throat must be horizontal in the flow direction, but can, in principle, be of any shape transverse to the flow. The invert of the throat may be higher than the invert of the upstream and downstream channels.

4. A diverging transition to reduce the flow velocity to an acceptable level and to recover head. If there is ample available head, an abrupt transition may be used.

5. The tailwater channel in which a known hydraulic control is exercised by the downstream conditions and the hydraulic properties of the channel. The flow in the throat MUST not be under influence of the tailwater.

The general profile of flow through a long-throated flume is shown schematically in Figure 4.3. The figure also shows the nomenclature for the theoretical analysis of the flume. In particular, we note that the energy level, H, and the stage height, h, are referenced to the invert level in the throat. As noted in 3. above, this is not necessarily the same as the channel invert level.

Figure 4.3: Flow Profile through a Long-Throated Flume

The control section is the approximate location of critical flow within the throat of the flume. It is not necessary to know precisely where this occurs because the developed head-flow rate relationship is expressed in terms of the head upstream. With reference to Figure 4.3, application of the energy equation yields:

H y vgcc

1

2

2= + (4.1)

where subscript c refers to critical conditions. To proceed further, the shape of the control section must be known. For a rectangular cross-section, the properties of critical flow are such that:





4.6

y vgcc

2y q

gc+ = =2 2

332

32

(4.2)

where q is the flow rate per unit width within the control section [m2/s]. Substitution of Equation 4.2 into 4.1 and expanding yields:

H qg1

33 23

2=

(4.3)

from which:

q g H=

23

23 1

32 (4.4)

In terms of the width of the control section, b, Equation 4.4 is written as:

23

132

32 bHg

=Q (4.5)

where Q is the total flow rate [m3/s]. The development of Equation 4.5 has assumed ideal flow conditions – in particular, that there is no energy loss between the location of the upstream head, H1, and the critical control. This is taken into account by introducing a discharge coefficient, Cd, such that:

23

132

32 Hbgd

CQ = (4.6)

Cd may be determined by an analysis of the boundary layer between the upstream head measurement point and the control section, but the complex procedure is rarely justified. However, at the design stage, it is normally sufficient to assume a value for the discharge coefficient of Cd=0.95.

H h1 1= +vg

h QgA

12

1

2

122 2

= + (4.7)

where A1 is the cross-sectional area at the upstream location. Equation 4.7 demonstrates that Equation 4.6 is difficult to use in practice because the head term, H1, contains the unknown flow rate, Q, in addition to the measured head, h1. An iteration method can be followed, using the following steps (although tedious, this method will lead to high accuracy):

1. Assume, as a first approximation, that h1= H1 and compute the discharge.

2. Use this approximate discharge to determine the velocity head and then use these data to calculate an improved value of the total head at the gauging section.

3. Compute a more refined discharge value using this total head value.





4.7

4. Repeat steps (2) and (3) until the difference between successive discharge values is an order of magnitude less than the required tolerance.

A much more convenient approach is developed by defining a velocity coefficient, Cv, from the equation:

23

132

32 bhgCv

CQ d= (4.8)

(the energy level, H1 is approximated with the water depth, h1) Further analysis shows that Cv is a function of the discharge coefficient, Cd, flow cross-section area of the channel upstream from the through, A=A1, and flow cross-section area in the thought, b×h. This relationship is presented in Figure 4.4 for rectangular channel.

Figure 4.4: Cv Relationship for Rectangular Cross-Sections

The rating equations for non-rectangular cross-sections are easily determined once the relationship between the critical depth, yc, and the upstream energy level, H1 is known. For example, application of the specific energy principles to the triangular cross-section yields:





4.8

y Hc =45 1 (4.9)

Substitution of Equation 4.9 into Equation 4.5 and subsequent manipulation yields:

Q C Cd v= g h1625

25 2 1

52tanθ (4.10)

where θ is the vertex angle of the control section. Design of a Long Throated Flume: Several criteria must be satisfied:

1. The flow in the throat MUST not be drowned (under influence of the tailwater). 2. The flume should have minimal influence on the change of water depths

upstream or downstream from the structure. 3. Some of the criteria for the flume design are presented in Figure 4.5.

h3

∆z

hch1

bT

>3/2(T-b) >3hc >3(T-b) >8 ∆z >10 ∆z

Plan view

T

Longitudinal section∆z>h -h -1/2(h -h )3 c 1 c

Figure 4.5: Sizing a Measuring Flume The design a long throated flume is explained in the example below. Example 4.1 The flow in a rectangular 4 m wide channel varies within the range 5 - 20 m3/s. The slope of the channel is 1 %, Manning coefficient is n=0.014286 m-1/3 s. The flow in the channel is uniform. Design a long throated flume for flow measurements in the channel. Solution: Step 1: The depth of tailwater should be equal to the uniform depth in the channel. The Manning Equation:

21

321 SAR

nQ = ( )

( )4014286.0 ×=Q 2

1

3/23

3/53 01.0

24

hh×+

×

For Qmax=20 m3/s ⇒ h3 = 2.2 m





4.9

Step 2: The throat width will be determined so that the depth upstream from the throat is not disturbed.

For Qmax=20 m3/s h1=h3 = 2.2 m

=

×

+= 22

2

1

max

11 gTh

Q

hH 2.463 m =×

×+81.9242.2

20

2.

2

The following relationship applies:

2/3463.232

××× b81.93295.0 ×=Q

23

132

32 Hbgd

CQ =

The throat width is: b = 3.2 m Step 3: The relationship between the depth upstream from the throat, h1, and the flow rate, Q, will be determined (using iterations) from:

2/3

1193.5

.93295.0

HQ

Q

×=

×= 2/312.3

3281 H×××

2

11 0.01053

+

hQ

2

111 2.281.92

1=

××

+= hh

QhH

1st

Iteration 2nd

Iteration 3rd

Iteration 4th

Iteration 5th

Iteration 6th

Iteration 7th

Iteration h1 [m] Q (h1) H1 Q H1 Q H1 Q H1 Q H1 Q H1 Q [m3/s] 0.8 3.70 0.87 4.18 0.89 4.32 0.89 4.37 0.89 4.38 0.90 4.38 0.90 4.38 0.9 4.42 0.98 4.99 1.00 5.16 1.00 5.21 1.01 5.23 1.01 5.23 1.01 5.23 1 5.17 1.09 5.85 1.11 6.04 1.12 6.10 1.12 6.12 1.12 6.13 1.12 6.13

1.1 5.97 1.19 6.75 1.22 6.97 1.23 7.04 1.23 7.06 1.23 7.07 1.23 7.07 1.2 6.80 1.30 7.69 1.33 7.94 1.34 8.02 1.34 8.05 1.34 8.05 1.34 8.06 1.3 7.67 1.41 8.67 1.44 8.95 1.45 9.04 1.45 9.07 1.46 9.08 1.46 9.08 1.4 8.57 1.52 9.69 1.55 10.01 1.56 10.11 1.57 10.14 1.57 10.15 1.57 10.15 1.5 9.50 1.63 10.74 1.66 11.10 1.67 11.21 1.68 11.24 1.68 11.25 1.68 11.26 1.6 10.47 1.74 11.84 1.77 12.23 1.79 12.35 1.79 12.39 1.79 12.40 1.79 12.40 1.7 11.47 1.84 12.96 1.89 13.39 1.90 13.52 1.90 13.57 1.90 13.58 1.90 13.58 1.8 12.49 1.95 14.12 2.00 14.59 2.01 14.73 2.01 14.78 2.01 14.79 2.02 14.80 1.9 13.55 2.06 15.32 2.11 15.82 2.12 15.98 2.13 16.03 2.13 16.04 2.13 16.05 2 14.63 2.17 16.54 2.22 17.09 2.23 17.26 2.24 17.31 2.24 17.33 2.24 17.33

2.1 15.74 2.28 17.80 2.33 18.39 2.34 18.57 2.35 18.62 2.35 18.64 2.35 18.65 2.2 16.88 2.39 19.09 2.44 19.71 2.46 19.91 2.46 19.97 2.46 19.99 2.46 20.00





4.10

0

5

10

15

20

25

0.5 1 1.5 2

Depth, h1 [m]

Flow

, Q [m

3/s]

2.5

Step 4: To assure that the tailwater would not drown the throat, the downstream end should be lowered for ∆z. The criteria is:

( ) ( ) cc hzh −∆−≥ 3hh −121

For Qmax=20 m3/s h1=h3 = 2.2 m, and the critical depth is: m59.12.381.9

202

2

=×

hc 3=

( ) m305.059.1 =−

mz 31.0=∆

z 2.22159.12.2 −−≥∆

Step 5: Sizing the sections of the flume. The lengths of the sections are calculated according to the criteria presented in Fig 4.5. The final design is presented below.

2.2m

0.31m

0.31m

1.59m2.2m20m3/s

3.2m4m

1.5m 4.8m 3.1m 2.5m

Plan view

4m

Longitudinal section





4.11

2.2 Broad-Crested Weirs A broad-crested weir is constructed as a step in channel bed on which critical flow is formed. Figure 4.6 presents a broad–crested weir placed in a small river. The weir is totally submerged, as showed in the schematic presentation in Figure 4.7.

Weir length

Figure 4.6: Broad – Crested Weir in a Small River.

Figure 4.7: Flow over a Broad – Crested Weir.

The crest length must be larger than the water depth on the weir to accommodate the following: (1) parallel streamlines to the crest, (2) the pressure distribution on the crest is hydrostatic, and (3) the critical flow depth is formed on the crest. The criteria for the crest length is:

1.5 to 3 (4.11) >−WHL

1

where L is the crest length [m], H1 is the specific energy upstream from the weir [m], and W is the height of the weir [m].





4.12

Using the approach used in the above section (derivation of Equation 4.4), we can conclude that, if there are no energy losses, the specific discharge (flow per unit width) over a broad crested weir, q, [m2/s] is:

( ) 2/313

2 WHg −×32q = (4.12)

However, the experimental measurements indicate that there are some energy losses. They can be taken into account if a discharge coefficient, Cd [-], is introduced:

( ) 2/313

2 WHg −×32Cq d= (4.13)

Cd is a function of the weir geometry and size, as well as of the upstream energy level. For the first approximation for Cd is:

Cd = 0.95 if 15.0 . (4.14) 6.01 <−

<W

WH

2.3 Sharp-Crested Weirs It is a device that usually consists of a vertical plate mounted at right angles to the flow and having a sharp-edged crest as in Figures 4.8, and 4.9. Sharp-crested weirs are often used to measure flow in open channels. Among their advantages, are that they are easy to install, accurate, and relatively inexpensive. They do, however, have a major disadvantage in flows containing substantial amounts of sediment, in that they trap sediment and other solids behind them. For this reason, sharp-crested weirs are most commonly used in relatively clean water.

Figure 4.8: Flow over V-notch Sharp-Crested Weir

2.3.1 Rectangular Sharp-Crested Weir This weir present in Figure 4.9 is called “rectangular sharp-crested weir”. Figure 4.10 presents schematic of the flow over the weir, including also the necessary nomenclature for the analysis. It is noted first that the pressure distribution at the weir crest is non-hydrostatic. This situation arises because the pressure at both Points A and B is atmospheric by definition, and there are significant vertical components in the velocity as the flow contracts to pass over the weir crest.





4.13

Figure 4.9: Rectangular Sharp-Crested weir

vg02

2

Figure 4.10: Schematic of Flow over Rectangular Sharp-Crested Weir From Figure 4.10, it is noted that (as expected) the total energy line (TEL) is situated an

elevation above the free surface, where v0 is the approach velocity [m/s]. In many

cases, the magnitude of the approach velocity head may be considered to be negligible. Two further assumptions are utilised for simplicity:

1. The flow does not contract as it passes over the weir – i.e. the elevation of A is the same as that of the upstream water surface.

2. The pressure is atmospheric across the whole section AB.

3. The approach velocity head may be considered to be negligible.





4.14

With reference to Figure 4.10, these assumptions lead to an expression that the total energy in front of the weir (= depth y, as sketched in Fig. 4.10) is converted to the

kinetic energy ( ). Therefore the velocity at C is: g

v2

2

(4.15) v gy= 2 The flow rate per unit width through an elemental strip of height dy at C, is then given by: (4.16) dq gydy= 2 The integral of Equation 4.16 may then be expressed as:

(4.17) q gydyh

= ∫ 20

where h is the water depth above the weir. Equation 4.17 is simply integrated and a contraction coefficient, Cc, introduced to allow for flow contraction over the crest, to yield:

(4.18) q C ghc=23

23

2

If the magnitude of the approach velocity head cannot be ignored, the integral form of Equation 4.16 is expressed as:

q gydyv g

h v g=

+

∫ 202

02

2

2 (4.19)

Evaluation of Equation 4.19 yields:

3

(4.20) q g vg

h vg

= + −

23

22 2

02 2

02

32

Manipulation and introduction of the contraction coefficient leads finally to the result:

q C gh vc= +

23

2 13

2 0

ghvgh

−

2 2

23

202

32

(4.21)

The equation is made more compact by introducing a discharge coefficient, Cd (to take care of the influence of the approaching velocity), leading to:

q C ghd=23

23

2 (4.22)

in which:





Department of Ci

Figure 4.12: V-notch Weir




4.15

C C vd c= +

1 02

ghvgh

−

2 2

32

02

32

(4.23)

It is evident from the form of Equation 4.23 that, if the velocity head is negligible compared with h, Cd = Cc and Equation 4.22 is then identical to Equation 4.18. Early work by Rehbock (Henderson, 1966) indicated that the value of Cd is given by:

CdhW

= +0 611 0 08. . (4.24)

There are a lot of different formulae that have been developed for Cd (usually valid for different ranges of h/W). The total flow rate over the weir is then given by the product of Equation 4.22 and the transverse crest length, b. To use this equation the weir should be ‘fully contracted’. This means that the sides and bottom of the channel are sufficiently distant from the weir crest and have no effect on the contraction of the nappe. To achieve the full contraction the weir has to have the dimensions that will satisfy the criteria given in Figure 4.11.

Definition of fully contracted rectangular sharp-crested weir:

B ≥ 4h b ≤ 2h W ≥ 3h 0.07 ≤ h ≤ 0.61 m b ≥ 0.31 m W ≥ 0.31 m

Figure 4.11: Criteria for Fully Contracted Rectangular Sharp-Crested Weirs. 2.3.2 V-Notch Sharp-Crested Weir

The triangular sharp-crested weir (Fig. 4.12) is analysed under the same assumptions as the rectangular weir. The structure is shown schematically in Figure 4.13, as well as explanation of all variables that will be used below. The following analysis is again simplified by the assumption that the approach velocity head is negligible.


4.16

Figure 4.13: Schematic of Flow over V-notch Sharp-Crested Weir

It needs to be recognised, however, that the concept of “flow rate per unit width” can not be used because the width varies over the height of the weir. Accordingly, the elemental flow rate through the element of width b is given by:

(4.25) dQ b gydy= 2

Integration of Equation 4.25 requires the expression of the weir width, b, as a function of the energy, y. From Figure 4.13, and using similar triangles:

yH −=2

tan2b θθ (4.26) ( ) ( )yh −≈2

tan2

Substitution of Equation 4.26 into Equation 4.25, integration between the limits of y = 0 and y = h, and inclusion of the discharge coefficient yields:

Q Cd= (4.27) g h815

22

52tanθ

The value of Cd is dependent on the ratio of , but, more particularly, on the vertex

angle, θ. For the commonly used value for θ of 900, a value for Cd of 0.58 is commonly assumed. This type of weir is called Thompson’s weir. For other situations, values for Cd may be obtained from standard texts on open channel flow such as Henderson (1966) and French (1985).

hW

As in the case of the rectangular weir the most accurate flow measurements are achieved if the weir if fully contracted. The criteria for the fully contracted V-noch weir are presented in Figure 4.14.





Departme

nt of Civil Engineering, Monash University



4.17

Definition of fully contracted V-notch

sharp-crested weir: T ≤ 5h W ≥ 2.5 h 0.05 ≤ h ≤ 0.38 m T ≥ 0.93 m W ≥ 0.46 m

Figure 4.14: Criteria for Fully Contracted V-notch Sharp-Crested Weirs.

The analytical techniques discussed above can be applied to any weir crest shape. Example 4.2 Derive the following equation for the trapezoidal sharp-crested weir.

Solution

dQ gyb dy= 2 1

∴ = ∫Q gyb dyh

2 10

We need to express b1 as a function of y

When

y h,

y b b h= = +0 221, tan θ

When b b= = 1

∴ = +b b1 2

∴ =∫Q g

h

−h y2

22

tan tanθ θ

+ −b h y ydy2 2

22

20

tan tanθ θ


4.18

Expand

Q g by hh

= +∫2 2

21

21

2

0

tan y y dy− 2

23

2 tanθ θ

Integrate

Q g by h y= +

223

22

23

32

32tan y

h

−

225 2

52

0

. tanθ θ

= +

223

43 2

32g bh tan −

45 2

52

52h htan

θ θ

= +

223

32g bh

8

15 25

2htanθ

= +

45 2

32 b htan

θ23

2gh

Add discharge coefficient to include effects of pressure distribution and drawdown

232 gCQ d

= 23

2tan

54 hhb

+θ

Example 4.3 An effluent weir plate contains 25 V-notches with (25 V-notch shape weirs are placed in a row).

θ = 900

a) Calculate the discharge if the head over the notches is 200 mm. Assume Cd = 0.60.

b) If the accuracy in measuring the head is estimated as ± 15 mm, calculate the corresponding percentage accuracy in the discharge assessment.

Solution

a.) =8

15θ

Q C ghd 22

52 tan

θ = 900 ∴ =tanθ2

1

h = 200mm = 0.2m Cd=0.60

Qnotch = ×

815

0 60. g× × ×2 0 2 15

2. =0.253m3/sec

sec/m634.0 3=25253.0 ×=∴ totalQ

b.)

dhh

= =15200

7 5%.





4.19

=8

15θ

Q C g hd 22

52tan

∴ =dQ Cd8

152 g h dh

252

32tan .

θ

/sm 0.00475 3=015.02.025181.926.0

158 2

3×××××××=dQ

%75.0634.0

00475.0==

QdQ

2.3.3 Sutro Weir The Sutro weir, shown schematically in Figure 4.15, sometimes called the linear proportional weir, is designed such that the head over the weir is linearly proportional to the flow rate. Such a relationship is especially beneficial when the velocity must be maintained constant, regardless of flow rate. It is, thus, a useful devise to utilise as a control in water and west water treatment plants.

Figure 4.15: Schematic of Flow Over Sutro Weir

Now, flow through the elemental strip of width x is given by:

dQ gyxdy= 2 (4.28)

Adopting the same principles as previously:

Q gyxdyh

= ∫ 20

(4.29)





4.20

The solution to Equation 4.29 requires an expression for x as a function of y – i.e. a characterisation of the shape of the weir section. The shape of the curved section of the weir is most easily obtained by a process of reverse deduction. It is shown in the following that a linear relationship between flow rate and head is obtained if the weir is shaped such that:

( ) Constant== ky−hx (4.30)

Substitution of Equation 4.30 into Equation 4.29 yields:

h

= ∫0

(4.31) Q gky

h ydy

−

2

12

We now make the substitution that : zh y

h=

−

y h= − hz , dy hdz= − , (4.32) y

h yz

z−=

−1

Furthermore, when y = 0, z = 1; y = h, z = 0. Substitution of these into Equation 4.31 yields:

( )kz

zh dz

−−∫

1

1

0

Q g= 2 (4.33)

or, because h is constant for a given flow rate,

= (4.34) Q gkhz

zdz

−∫2

1

0

1

The integral function in Equation 4.34 may be found by trigonometric substitution or from integral tables and has the value of . π

2 Thus:

Q gk h= 22π

(4.35)

The required linear relationship between Q and h is proven!

Introducing a discharge coefficient and noting that the numerical value of is 1.57,

Equation 4.35 is expressed as:

π2

Q C gkhd= 157 2. (4.36)

In designing and using a Sutro weir, the following practical aspects are important:





4.21

• The curved profile cannot be taken right to the weir crest as this would require an infinite width. It is usual to cut off the ends of the weir with a rectangular height – dimension a in Figure 4.15 – of about 2 cm.

• The value of the discharge coefficient, Cd, is dependent on the bottom width and on the value of a. It typically has a value of 0.61.

• To allow sufficient nappe aeration, preventing submergence, the tail water elevation should be at least 5 cm below the weir crest.

If these conditions are met, the weir will give a response that is very close to linear. However, if high accuracy as a flow meter is desired, it is recommended that the weir is calibrated. Example 4.4 It is desired to maintain a constant velocity of 0.3 m/sec in a constant-velocity sedimentation rectangular channel of width 2 m. Flow rates of 0.15 to 0.6 m3/sec are to be accommodated. Design a suitable Sutro weir.

Solution

Q C gkhd= 157 2. - maintains a constant velocity regardless of flow rate.

V = 0.3 m/sec Channel width = 2m Depths of water in the channel:

3.0215.0sec/m15.0 3=Q = 0.25m ×

=⇒ h

3.026.0

×=⇒ hsec/m6.0 3=Q = 1m

Set weir crest at bed level

∴ =0 6 ×157 0 61 2. . . gkh k = 01415. ∴Weir shape is formed by condition that xz

12 01415= . ,

where z is elevation above the bed z=h-y and x is opening width at elevation z (see Figure 4.15)





4.22

The shape of the weir is: 2

11415.0

zx =

Elevation, z (m) Opening Width, x (m)

1.0 0.142 0.9 0.149 0.8 0.158 0.7 0.169 0.6 0.183 0.5 0.200 0.4 0.224 0.3 0.258 0.2 0.316 0.1 0.447 0.05 0.663 0.02 1.001

Half Profile of Proportional Weir

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6

Transverse Distance from Centre Line (m)

Ver

tical

Hei

ght a

bove

Cre

st (m

)

Activity 4.1 (30 minutes)

Find about other systems used for flow measurements in open channels





Department of Ci




4.23

3. HYDRAULIC STRUCTURES – OVERFLOW SPILLWAYS A dam is a large structure built a cross a valley to help store water in the upstream reservoir. The water level in the reservoir should not overtop the dam itself (if it happens that may cause a dam failure). Therefore, the dams are equipped with spillways (Figure 4.16) and culverts to discharge a Probable Maximum Flood (e.g. a 100 year event for small concrete dams or 1000 year event for large earthfill dams). A spillway is designed to discharge flood water under controlled conditions. It usually consists of 3 sections, as marked in the sketch of a typical spillway in Fig. 4.16: (1) a crest, (2) a chute and (3) an energy dissipater. The photos of tow spillways are presented in Fig. 4.17. The most common type of the crest, the ogee weir, is presented in Figure 4.18. Two different chutes are shown in Figure 4.19, and two types of energy dissipaters in Figure. 4.20. Note that both the chute to the right in Fig. 4.19, and the energy dissipater to the right in Fig. 4.20 have been damaged due to cavitation.

Figure 4.16: Sketch of a typical spillway with an Ogee crest.

Figure 4.17: Two different spillways.


Departme

nt of Civil Engineering, Monash University



4.24

Figure 4.18: Ogee crests.

Damaged by cavitation

4.19: Chutes

Damaged by cavitation

4.20: Energy dissipaters


(4.39)

4.25

3.1 Spillway Crests The crest is typically designed to maximise the discharge over the spillway. It can be any type of weir that we have already studied (broad-crested or sharp crested). However the most common one in the practice is the OGEE weir which is presented in Figure 4.18. Ogee crest weir The crest is shaped so as to confirm to the lower surface of the nappe from a sharp crested weir (Figures 4.10 and 4.16). In this way, the pressure on the crest will be atmospheric (provided that the crest surface is smooth). If the pressure is above atmospheric, the discharge will be reduced, while if it is below atmospheric, cavitation may occur and damage the surface (as in the chute in Fig. 4.19 to the right). Discharge over an ogee weir can be calculated from Equation 4.22. Because the height of weir (W) is much higher than the height of the water on the crest (h), the discharge coefficient can be calculated from Equation 4.24 and h/W ≈ 0. Finally, the specific discharge of the overflow is:

2/3804 shh

2/3148.2 dhq =

.1q =

Figure 4.21: The ogee crest and the

equivalent sharp-crested weir.

(4.37)

However, experiments show that the rise of the lower nappe from the sharp-crested weir is 0.11×hsh (as in Figure 4.21). Using this, Equation 4.37 becomes:

(4.38)

where hd, is called the design head (Fig. 4.21). If the spillway that operates under lower heads (h < hd), the hydrostatic pressure on the crest will be positive (above atmospheric), and therefore the discharge coefficient will be lower. If more water is flowing (h > hd), the pressure will be negative (below atmospheric) and higher discharge coefficients will apply. Experiments show that the design head can be safely exceeded by at least 50%, with 10% increase in the discharge coefficient, provided that the local pressure does not fall below the cavitation level. The standard ogee crest is based upon experimental observations. It has to be smooth and continuous (no variations of the crest curvature). The most used profile is called the Creager profile and is given by the following mathematical expression (Chanson, 1999):

8.0

8.1

47.0dhxy =

where x is and y are presented in Figure 4.21. Ideally the crest profile should start tangentially to upstream apron with a smooth and continuous variations of the radius of curvature (Henderson, 1966).





4.26

3.2 Spillway Chutes Once the water passes the crest it travels along the chute, also called the spillway face, which is constructed as surface at angle θ to the horizontal plane. A typical chute is presented in Figure 4.22. The cute is designed as a tangent to the crest line (in this case the Ogee Creager crest). Because, the water accelerates and air enters, the equations used for non-uniform flow can not be easily used (in some cases, S2 profile could be used once the flow becomes fully turbulent, but taking into account the aeration). To calculate the velocity at the base of the chute, we start from the theoretical velocity that could be developed (no friction and no air entrainment), vt:

v (4.40)

−=

22 hZgt

where Z and h are presented in Figure 4.22.

Figure 4.22: Sketch of a Chute

For steep chutes (typically 0.8H : 1V to 0.6H:1V), the velocity at the foot of the spillway could be much smaller than vt. Physical models are sometimes required to determine the true velocity. 3.3 Energy Dissipaters and Stilling Basins They are built at the end of chutes to dissipate the excess in kinetic energy before water re-enters the streams. This can be done in a number of ways. Only a few basic and standard structures will are presented (as illustrated in Figure 4.23):

(1) A standard stilling basin downstream of a steep spillway in which a hydraulic jump is created – Fig 4.23 (a) and Fig 4.20 to the right.

(2) Bucket-Type energy dissipater (Plunge Pool) – Fig 4.23 (b). (3) Ski-Jump (Flip-Bucket) dissipater - Fig. 4.23 (c) and Fig 4.20 to the left.

However, energy can be dissipated even along a chute. For example, along a stepped chute (steps along the chute length).





4.27

Figure 4.23: Standard types of energy dissipaters

Stilling Basins Most energy is dissipated in a hydraulic jump that is formed in the stilling basin. Its formation may also be assisted by chute blocks and baffle blocks (Fig. 4.23 (a)). If the stilling basin is of rectangular cross-section, and the water depth at the point of the water entry into the stilling basin is y1 (Figure 4.23 (a) to the right), the water downstream from the jump will be y2 (see Section 7 on Hydraulic Jump in Topic 2 and Equation 2.65):

= 12 yy (4.41)

−+ 181

21 2

1Fr

where . The Bernoulli Equation can be used to calculate the head loss, ∆H, in the jump.

11 / gyvFr =

The length of the jump (‘the roller length’), Lr, may be estimated as (Chanson, 1999):

162 1 << Fr1220

tanh 11 −

=

FryLr (4.42)

This is valid only for rectangular horizontal channels (of width B) where y1/B < 0.1. Stilling basins should be designed to accommodate the hydraulic jump: the water depth in the basin should be > y2, and the length of the basin > Lr. They have to maximise energy dissipation at minimal costs. Several standardised stilling basins where developed in the mid of 20th century. The most commonly used ones are (Figure 4.24): (1) The USBR (the US Bureau of Reclamation) Type II basin – for large structures and





4.28

Fr>4.5, (2) The USBR Type III basin and the SAF basin – for small structures and Fr > 4.5, and (3) The USBR Type IV basin for oscillating jump flow conditions.

Figure 4.24: Standardised stilling basins as recommended by US Bureau of Reclamation

(USBR) (Henderson, 1966) – note that Imperial units are used.





4.29

These basins have been tested extensively over more than 50 years, and therefore can be used without any further model studies. The recommendations for their design is summarised in Table 4.1.

Table 4.1: Standard types of stilling basins presented in Fig 4.24 - for explanation of

some variables see Figure 4.16 (Chanson, 1999) Name Application Flow Conditions Tailwater depth, y3

Basin length, L USBR Type II Large structures Fr > 4.5

q = 46.5 m2/s H1 < 61 m

y3 = 1.05 y2 L=4.4 y2

USBR Type III Small structures Fr > 4.5 q = 18.6 m2/s V < 15 to 18.3 m/s

y3 = 1.0 y2 L=2.8 y2

USBR Type IV Oscillating jump 2.5< Fr <4.5 y3 = 1.1 y2 L=6 y2

SAF Small structures 1.7 < Fr < 17

y3 = 1.0 y2 L=4.5 y2 Fr-0.76

3.4 Design Procedure An overflow with a stilling basin at the toe is usually designed in the following steps (Figure 4.16):

(1) Select the crest elevation (i.e. the weir hight, W);

(2) Choose the crest width B;

(3) Determine the design discharge Qd from risk analysis and flood routing (as in Topic on Hydrology);

(4) Calculate the upstream head above the crest, h = H1-W, for the designed flow Qd (e.g. for Ogee crest use Equation 4.38);

(5) Choose the chute toe elevation that is also the level of the stilling basin bed called apron elevation, za. It can differ from the natural bed level (i.e. tailwater bed);

(6) For Qd calculate the flow depth and velocity at the end of the chute, y1 and v=vt, using Equation 4.40.

(7) Calculate the downstream depth (the conjugate depth, y2) for the hydraulic jump in the stilling basin using Equation 4.41. Calculate the Jump Height Rating Level (JHRL). For a stilling basin with horizontal bed, it is:

JHRL = za + y2

(8) Calculate the roller length, Lr, using Equation 4.42. The stilling basin must be longer than this.

(9) Compare the JHRL with the Tail-Water Rating Level (TWRL), which is the level of the natural stream downstream from the spillway. If TWRL and JHRL are not the same, some alterations to the design have to be made: either the crest elevation,





4.30

the crest width, or the elevation of the stilling basin bed must be changed. Alter one or a few of them and do the calculations again.

Activity 4.2 (30 minutes) Read about a major dam disaster.

Example 4.5

An overflow spillway is to be designed with an uncontrolled ogee crest followed by a smooth chute and a hydraulic jump dissipator. The width of the crest, chute and dissipation basin will be 120 m. The crest level will be at 336 m R.L. and the design head above crest level will be 3.2 m. The chute slope will be set at 48o.The elevation of the chute toe will be set at 318 m R.L.. The chute will be followed (without transition section) by a horizontal channel (no steps) which ends with a broad-crested weir, designed to record flow rates as well as to raise the tailwater level.

(a) Calculate the maximum discharge capacity of the spillway.

(b) Calculate the flow velocity at the toe of the chute.

(c) Compute the jump height rating level (JHRL) at design flow conditions (for a hydraulic jump dissipator).

(d) Determine the height of the broad-crested weir necessary at the downstream end of the dissipation basin to raise artificially the tailwater level to match the JHRL for the design flow rate.

(e) If a standard stilling basin (e.g. USBR, SAF) is to be designed, what standard stilling basin design would you select: USBR Type II, USBR Type III, USBR Type IV, SAF?

(d) Sketch the spillway.

Solution: (a) Discharge, Q

hd=3.2 m 5.12.3148.2120 ××2/3148.2 =×== dhBBqQ Q=1475.5 m3/s

(b) Velocity at the toe

−=

22 hZgvt




Z = zc - za = 336 - 318 = 18 m


4.31

h = hd =3.2 m

−×

22.31881.9= 2tv =17.94 m/s

(c) Hydraulic jump:

=×

=94.17120

5.1475

t×=1 vB

Qy 0.685 m

917.6685.081

94.17=

×.911 ==

gyvFr t

[ ]1917.681 2 −×+21685.0181

21 2

112 =

−+= Fryy = 6.372 m

JHRL = za + y2 = 318 + 6.372 = 324.4 m

(d) Broad-crested weir: Critical depth is formed at the weir and the energy level at the weir must be equal to the available energy level after the jump.

m56.6372.6

2

=

gvyE

1201475

81.921372.6

22

22

××+=+=

m49.2gqyc 120

33

2

==81.9

5.14752

2

=×

Ec myc 73.323

==

Wb = 6.56 – 3.73 = 2.83 m

(e) The USBR Type III or SAF

(d)





4.32

4. INTRODUCTION TO RIVER BEHAVIOUR AND PROCESSES 4.1. Introduction Rivers have been a major component of human activity since man first appeared on earth. Transport, water supply and waste disposal are but three of the many uses of rivers. Although there are many benefits to be obtained from rivers, they have also been the source of much human misery and tragedy. Floods and other river disasters are perhaps even increasing in frequency in many parts of the world as river training schemes and land use changes are implemented. Engineers and scientists have studied rivers for centuries, fascinated by the self-formed geometric shapes and the response of the rivers to changes in nature and human interference. Indeed, although few other subjects have been studied as extensively as rivers, some major aspects of the hydraulics, sedimentation and fluvial processes have become clear only very recently, while the explanations for others remain elusive. As engineers we are involved in water supply, channel design, flood control, river regulation, navigation improvement and many other aspects which involve the imposition of controls on natural river behaviour. It has become clear in recent times that rivers cannot be mastered by force, but instead can be utilised for the good of humankind only by understanding. Such understanding has become critically important in recent years as environmental issues and concerns have become more prominent. These notes are intended as an introduction to those components of river behaviour and processes which are of most importance to our understanding of the response of rivers to natural and artificial changes. River morphological issues are discussed first, including alluvial bed forms. This is followed by a discussion of various aspects of sediment movement and sorting. 4.2. Overview of River Morphology River morphology is concerned with the structure and form of rivers, including channel configuration and geometry (plan-form and cross-sectional shape respectively), bed form and profile characteristics. Channel morphology changes with time and is affected by water discharge, sediment discharge, sediment characteristics such as particle size and specific gravity, the composition of bed and bank materials and many other factors. Time scales for changes in river morphology may be classified as short term - measured in days; medium term - measured in tens or, perhaps, hundreds of years; and long term - measured in thousands or millions of years. The engineer is normally interested in short and medium term changes and responses. Different rivers and different reaches of the same river have different alignments, channel cross-section shape, bed and bank material, slope and valley characteristics. Lane (1) has identified the principle channel forming parameters as being flow discharge, valley slope, sediment discharge, and particle size. He expressed this in the





4.33

form of a stable channel balance, illustrated in Figure 4.25, and expressed by the following relationship: QSd ∝ QS (4.43) where QS is the sediment discharge, d is the mean sediment size, Q is the water discharge, and S is the valley slope.

Figure 4.25: Stable Channel Balance (1)

Anding (2) stated that stream discharge is the most obvious factor in determining stream form, pointing out that it is not just the magnitude of the discharge that is important, but also the integrated effect of its constant fluctuation. It is now generally accepted that the bankfull discharge is the channel-forming discharge for downstream changes in channel geometry. This simplified approach recognises that lower discharges, which move less sediment, contribute less to the channel formation, while rises in discharge above the bankfull stage are largely absorbed by the broad flood plain, thereby having less effect on the channel shape. Channel Configuration The alignment of a river is generally characterised as one or more of three basic types as follows: • Straight Channels: Straight channels occur rarely in nature. When they do occur,

they are usually relatively short reaches of river and are transitory in nature because even minor irregularities in channel shape or alignment or a temporary obstruction can create a local disturbance which will set up a transverse flow leading to meandering.





4.34

• Meandering Channels: Meandering channels comprise, in plan, a series of bends of alternate curvature connected by straight crossing reaches. Slopes are usually relatively flat. Meandering channels are statically unstable, although they may develop a dynamic or quasi-stability whereby the meander bandwidth and wavelength do not vary despite overall movement of the meander pattern. Erosion normally occurs in the downstream reaches of concave bends. Deep pools generally occur at the outside of the bends and velocities are high along the outer concave bank. Depths at the point of inflexion between two bends of alternate curvature are generally shallow compared with depths in bends. Meandering channels may be further characterised as those with “surface” bends and those with “entrenched” bends. Channels with free surface bends generally flow in alluvial valleys and change their course on the flood plain with time. Streams with entrenched bends, however, are cut into resistant parent material and generally maintain a stable course.

• Braided Channels: Braided channels comprise a number of separate channels

which divide and rejoin. The stream is normally wide and the banks are poorly defined and unstable. At low flows, there are typically two or more main channels which cross each other, subsidiary channels, sand bars and islands. At high flows most bars are inundated. Braided rivers generally have relatively steep slopes and carry a large sediment load.

Typical channel configurations of the three types are illustrated in Figure 4.26 (3).

Figure 4.26: Typical Channel Configurations (3)





4.35

The study of braiding and meandering has been one which has intrigued geologists, geographers, and engineers for many years. One particular issue has been why some streams braid and others meander, or why some sections of a particular stream may be braided while other sections are meandering. Various stability criteria have been developed to explain the occurrence of channel type, notably by Parker (4), Engelund and Fredsoe (5), and Bettess and White (6). Bettess and White explained the different behaviour in terms of the relationship between the valley slope and the various possible equilibrium slopes for the channel. In this context, if the stream remains in a single channel, the equilibrium slope of the channel, SR1, will be that corresponding to the full discharge. The equilibrium slope of each channel of a two-channel braided system, SR2, will be that corresponding to one-half of the discharge. The corresponding slope of a three-channel braided system, SR3, will, similarly, be that corresponding to one-third of the discharge. For a given value of valley slope, SV, a channel will adopt one of the following patterns as a result of its equilibrium adjustment (the types of channel and the corresponding slope criteria are illustrated schematically in Figure 4.27):

Figure 4.27: Relationship Between Valley Slope, SV, and Equilibrium Water Surface

Slope: (a) SV = SR1; (b) SR2 > SV >SR1; (c) SV = SR2; (d) SV = SR3

• Straight channel: Where SV is equal to the one-channel equilibrium slope, SR1, the stable channel is straight.

• Meandering Channel: Where SV exceeds SR1 but is less than SR2, the equilibrium pattern will be a single channel form with a stable slope of SR1. This is achieved in a valley with a slope of SV by adjustment of channel length through the adoption of a meandering alignment with a sinuosity of SV/SR1.

• Braided Channel: Where SV is greater than SR2, the equilibrium condition may be accommodated by adjustment either of slope through meandering or discharge





4.36

through braiding. For example, in the case where SV is equal to SR2, two possible equilibrium conditions theoretically exist; a straight two-channel braided system or a single meandering channel with a sinuosity of SV/SR1. In practice, however, braiding only becomes a stable form for values of SV greater than SR3 because of inherent instability in two channel systems (6).

• Unstable Channel: Where SV is less than SR1, no channel adjustment mechanism exists to create an equilibrium condition. In the long term, equilibrium is possible by adjustment of valley slope instead, by such processes as upstream degradation and downstream aggradation.

Design of Stable Artificial Meanders The concepts developed above naturally lead to the question of whether or not it is possible to predict the stable condition for an existing meandering channel or to develop a stable form for a proposed river training scheme or diversion. Such models have recently been developed (7), based on extremal hypotheses of minimum stream power developed by Chang (8,9). These hypotheses provide two relationships as follows: • Minimum stream power per unit channel length: “For an alluvial channel, the

necessary and sufficient condition of equilibrium occurs when the stream power per unit channel length, QγS, is a minimum subject to given constraints. Hence an alluvial channel with water discharge Q and sediment load QS as independent variables tends to establish its width, depth, and slope such that QγS is a minimum. Since Q is a given parameter, minimum QγS also means minimum channel slope, S.”

• Minimum stream power for a channel reach: “The equilibrium geometry of an

alluvial channel reach of equal discharge is so adjusted that the power expenditure is a minimum subject to the given constraints. Minimum power expenditure for the channel reach is equivalent to equal power expenditure per unit channel length or uniform energy gradient along the channel”

These hypotheses, combined with independent models for continuity, sediment transport rate, flow resistance, bank slope, transverse bed slope, and plan form geometry permit closure of the equation set, providing in principle a full solution for both the cross-sectional shape as it varies around the meander, and for the plan form shape. The independent variables which determine the geometry are those shown in Figure 4.25; ie the discharge, sediment discharge, sediment size, and valley slope. Although the model is still some way from routine design application, first results from the model are yielding good agreement with observed equilibrium geometry. Bed Forms The phenomenon of bed forms has fascinated engineers and scientists because of its association with so many aspects of river sedimentation and river morphology. For example, because the bed forms are flow-induced and directly affect the flow resistance,





4.37

computation of the river stage and flow velocity relies on the determination of bed form roughness. Many terms are used to describe bed forms. The following descriptions are based on those of (10) and the primary ones are illustrated in Figure 4.28.

Figure 4.28: Idealised Bed Forms in Alluvial Channels (10) • Bars: These are bed forms having lengths of the same order as the channel width, or

greater, and having heights comparable to the mean depth of the generating flow. Among the different types of bars are: Point Bars which are deposits of sediment occurring on the inside of channel bends; Alternating or Alternate Bars which tend to be distributed periodically along a channel with bars near alternate channel banks. Their lateral extent is significantly less than the channel width and they move slowly downstream.

• Ripples: These are small bed forms, typically with a height of about 30mm and a

wave length of about 300mm. In longitudinal section, ripples vary in shape from the classical saw-tooth shape of a long gentle upstream slope and a downstream slope approximately equal to the natural angle of repose of the sediment to symmetrical, nearly sinusoidal shapes.

• Dunes: These are bed forms which are larger than ripples but smaller than bars.

Their longitudinal shape is out of phase with the water surface, as shown in Figure 4.28(c). Dunes generally occur at higher sediment transport rates and velocities than





4.38

do ripples. Often ripples may occur, superimposed on dunes. The longitudinal profiles of dunes are approximately triangular, with fairly gentle upstream slopes and downstream slopes which are approximately at the natural angle of repose of the sediment. The large lee eddies occurring in dune troughs often cause surface boils of intense turbulence.

• Transition: This bed configuration comprises an heterogeneous array of bed forms,

primarily low amplitude ripples or dunes and flat areas as shown in Figure 4.28(d). The transition stage occurs at a higher flow intensity than does dunes.

• Antidunes: These are bed forms which exist in phase with water surface waves. The

free surface waves have a larger amplitude than the sand waves and grow with increasing velocity and Froude number, eventually becoming unstable and breaking in the upstream direction. In longitudinal section, antidune profiles vary with flow and sediment properties from approximately triangular to sinusoidal, the latter occurring at higher Froude numbers.

• Chutes and Pools: This bed configuration occurs at relatively large slopes and

sediment discharges. It comprises large elongated mounds of sediment forming chutes within which the flow is supercritical and connected by pools within which the flow may be supercritical or subcritical. They are depicted in Figure 4.28(h).

The formation of the above bed form characteristics may be divided into categories of lower flow regime, transition zone, and upper flow regime in order of increasing velocity as follows: (1) Lower flow regime

Ripples Dunes with ripples superimposed Dunes

(2) Transition

Bed roughness varies from dunes to plane bed or standing waves (3) Upper flow regime

Plane bed Antidunes Chutes and pools

Table 4.2, taken from (10) summarises some of the important characteristics of each of the three flow regimes. In seeking a better understanding of the interaction between the flow and the bed material and the interdependence of the bed form, roughness, and sediment transport rate, extensive theoretical and empirical studies have been directed at the prediction of bed forms. The physical processes have long been recognised as being extremely complex and theoretical approaches have necessarily been considerably simplified. Despite a number of important contributions to the prediction of bed form occurrence





4.39

and characteristic features, a universally acceptable analytical solution is still lacking and the cause of bed forms remains largely unexplained.

Table 4.2: Classification of Bed Forms and their Characteristics (10)

Flow Regime

Bed Form

Bed

Material Concn. (ppm)

Mode of Sediment Transport

Type of

Roughness

Phase Relation

Between Bed and Water

Surface

Lower Regime

Ripples Ripples on

dunes Dunes

10-200 100-1,200

200-3,000

Discrete

steps

Form roughness

predominates

Out of phase

Transition Zone

Washed out dunes

1,000-3,000 - Variable -

Upper

Regime

Plane beds Antidunes

Chutes and pools

2,000-6,000 Above 2,000 Above 2,000

Continuous

Grain roughness

predominates

In phase

Bed Form Dimensions Bed form dimensions are clearly of importance in determining the hydraulic roughness of the bed. Indeed, many flow resistance formulae are based on bed form dimensions. Large bed forms, such as dunes and antidunes, may have wave heights which are of the same order of magnitude as the flow depths. Accordingly, their dimensions affect navigation and the prediction of scour depths at bridge piers and abutments. It is usual to add one half of the bed form height to the computed scour depth when determining minimum bed elevations. A number of methods for determining the magnitude of dunes has been presented in the literature. Van Rijn’s method (11) is reasonably accurate and is described in the following as an example of the methods available. Van Rijn used dimensional analysis to produce the functional relationship

∆D

dD

d T*=

f 1 , , (4.44)

where ∆ is the bed form height, d is the median sediment size, D is the depth of flow, d* is the dimensionless particle diameter, defined by Equation 4.45 below, T is the transport stage parameter, defined by Equation 4.46 below.





4.40

( )

d d (4.45) gS

2=

−

ρ ρρν

1/3

*

where ρS is the mass density of sediment, ρ is the mass density of the fluid, ν is the kinematic viscosity, g is the acceleration due to gravity

T = (4.46) 0'τ ττ− C

C

( ) ( )

where τC is the critical bed shear stress from Shields curve, τ0

’ is the bed shear stress related to grain roughness, computed from

τ ρ0' =

g18log

2

3/

U12R db 90

(4.47)

where Rb is the hydraulic mean radius of the alluvial bed. Comparable to Equation 4.44, a functional relationship for the bed form steepness has been developed of the form

∆λ=

f 2

dD

d T*, , (4.48)

where λ is the wavelength of the bed form. Extensive flume and field data were utilised to determine the form of the functional relationships 4.44 and 4.48 and regression equations were developed as follows:

( )( )e T-0.5T− −1 25∆D

dD

=

0110 3

..

(4.49)

and

( )( )− −1 25e T-0.5T∆λ=

0 0150 3

..d

D (4.50)

These equation, together with an error range of a factor of 2 and with the data superimposed, are shown in Figure 4.29 within the range of application of 0<T<25. T=0 represents the threshold of bed load movement and T=25 represents the upper limit for dune formation. It should be noted that d* does not appear in Equations 4.49 and 4.50, implying that temperature is not a significant determinant in the dune dimensions. From Equations 4.49 and 4.50, an expression for the dune wavelength may be derived in the form





4.41

(4.51) λ = 7 3. D Kennedy (12) developed an equation for the wavelength of antidunes as follows:

(4.52) λ π= 2 U2g

2

Equation 4.52 compares reasonably well with observed wavelengths. At incipient breaking, the antidune steepness (ratio of wave height to wave length) was found by Kennedy to be about 0.14.

Figure 4.29: Bed Form Height and Steepness (11)





4.42

4.3. Hydraulic Resistance of Alluvial Channels An important aspect of river sedimentation is the determination of the flow induced resistance associated with the bed forms. Alluvial bed roughness has been the subject of extensive investigation with a number of resistance relationships developed. These relationships follow two basic approaches - those that divide total resistance into grain resistance and form resistance and those that do not. Detailed consideration of this topic is beyond the scope of this lecture. 4.4. Sediment Transport in Rivers Assessment of the sediment load carried by rivers is often of great importance, both in understanding the behaviour of the river and in effectively utilising the river for the benefit of society. As pointed out earlier in this lecture, the sediment load is a key determinant of the stable form of the river. In utilising a river for social needs, the sediment load clearly affects such issues as water abstraction for irrigation and the design life of reservoirs. The sediment carried by rivers is commonly classified as bed load and suspended load. Bed load is defined as that part of the load moving on, or near, the bed by rolling, saltation, or sliding. Suspended load moves, by definition, in suspension. In addition to bed load and suspended load, reference is made to the wash load, which refers to the finest portion of sediment, generally silt and clay, that is washed through the channel. An alluvial stream bed is formed during the fluvial process of sorting, through which clay and silt are removed as wash load. The discharge of wash load depends primarily on the rate of supply and is generally not correlated with the flow characteristics. Bed load and suspended load, on the other hand, are usually correlated with water discharge. There are many sediment transport formulae to be found in the literature. In the main, these formulae have been developed for non-cohesive sediment in steady uniform flow and are not, therefor, applicable to cohesive sediment which normally constitutes the wash load. The processes of sediment transport are extremely complex and, for this reason, the prediction of sediment transport rates cannot be accomplished purely by theoretical means. Sediment transport formulae are classified according to their application as bed load formulae, suspended load formulae, and total load formulae. There are an abundance of formulae of each type to be found in the literature. It is beyond the scope of this lecture to consider these formulae in detail. However, a comprehensive review has recently been published (13) and is recommended for further reading.





4.43

References (1) Lane, E.W.(1955): The importance of Fluvial Geomorphology in Hydraulic

Engineering, Proc. ASCE, vol. 81, Paper 745, pp1-17.

(2) Anding, M.G.(1970): Hydraulic Characteristics of Mississippi River Channels, Interim Report FY 1970, Potomology Research Report 10, U.S. Army Engineer District, Vicksburg, Miss.

(3) Peterson, Margaret S. (1986): River Engineering, Prentice-Hall, New Jersey

(4) Parker, G.(1976): On the Cause and Characteristic Scales of Meandering and Braiding in Rivers, Journal of Fluid Mechanics, vol. 73 (3), pp457-480

(5) Engelund, F. and Fredsoe, J.(1982): Hydraulic Theory of Alluvial Rivers, Advances in Hydroscience,13, pp187-215

(6) Bettess, R. and White, W.R.(1983): Meandering and Braiding of Alluvial Channels, Proc. Instn. Civ. Engrs., Part 2, vol. 75, pp 525-538

(7) Keller, R.J. & White L.J. (1993): Prediction of the Stable Form of Meandering Channels, Proceedings of the 25th Congress of the International Association for Hydraulic Research, Tokyo, Japan, September., Vol. II, pp. 600-607.

(8) Chang, H.H.(1979): Geometry of Rivers in Regime, Journal of Hydraulics Division, ASCE, vol. 105, No. HY6, pp 691-706

(9) Chang, H.H.(1982): Mathematical Model for Erodible Channels, Journal of Hydraulics Division, ASCE, vol. 108, No. HY5, pp 678-689

(10) Simons, D.B., Richardson, E.V., and Nordin, C.F.(1965): Sedimentary Structures Generated by Flow in Alluvial Channels, Am. Assoc. Petrol. Geologists, Special Publ. No. 12 - (Quoted in Chang, H.H.(1988): Fluvial Processes in River Engineering, John Wiley and Sons, New York)

(11) van Rijn, L.C.(1984): Sediment Transport, Part III: Bed Forms and Alluvial Roughness, J. Hydraulic Engineering, ASCE, vol 110(HY12), pp 1733-1754, December

(12) Kennedy, J.F.(1963): The Mechanics of Dunes and Antidunes in Erodible Bed Channels, Journal of Fluid Mechanics, vol. 16(4), pp 521-544, August

(13) Fisher, K.R.(1995): Manual of Sediment Transport in Rivers, Report SR 359, HR Wallingford, May





4.44

5. THE THRESHOLD OF MOTION 5.1 Introduction When the flow of a fluid over a surface comprising loose grains is gradually increased, a condition is reached where the grains start to move because of the forces exerted by the fluid flow. A knowledge of the hydraulic conditions corresponding to this condition of incipient motion is of considerable practical importance. Apart from being the limit indicating the onset of sediment motion, the critical condition influences the design of erodable channels carrying clear water. Clearly there is a need for a thorough understanding of the hydraulic conditions which initiate motion on a sediment bed of known characteristics. A completely theoretical solution for the incipient motion condition is not available and we must turn to solutions based on experimental data. Two basic approaches have been utilised in the analysis of experimental data. The first is based on the premise that there is a particular velocity - sometimes called the competent velocity - which causes motion. Indeed, this approach was used by Brahms in 1753, who put forward the equation:

61

kWVcr = (4.53)

where Vcr is the competent velocity k is an empirical constant W is the weight of the grain As will be shown subsequently, this approach is insufficient to characterise the inception of motion. The second approach depends on the hypothesis that there is a certain force, applied by the fluid, which leads to the movement of the particles. Depending upon whether the lift force or drag force on the particle is considered important, this approach may again be subdivided into the so-called lift approach and the so-called critical shear stress approach. The critical shear stress approach has proved to be the most practical and is emphasised in this lecture. In this lecture, a physical description of flow over a sediment bed is first presented and the conditions at the threshold of bed motion are described. Subsequently, this condition is analysed from the point of view of critical shear stress and utilising experimental data. Finally, the incompleteness of the competent velocity approach is discussed. 5.2. Flow over a Sediment Bed A grain on the bed surface is subject to fluid forces and a force due to its own weight. These forces give rise, further, to shear stresses between the grains in motion and those forming the stationary boundary, with the fluid between them taking part in this shearing. All forces may be resolved into normal and tangential components. The





4.45

forward motion of the particle is maintained by the tangential component. Where the fluid flows over a horizontal bed, the tangential component is transmitted entirely by the fluid. At the other extreme, the tangential component may be due entirely to the particle’s own weight as when granular material is sliding down a steep slope. In general, however, the direction of forward motion of the particle is contributed to by both the fluid forces and the particle weight. Generally, near the bed there is a mean velocity profile upon which turbulent velocity fluctuations are superimposed. If the flow is laminar near the boundary or if the viscous sublayer thickness is sufficient to cover the sediment particles completely, individual grains will not shed eddies and the drag will be due to viscous shear alone. Accordingly, surface roughness will not influence the drag force and the surface is said to be hydraulically smooth. As the velocity increases, the viscous sublayer reduces in thickness and some of the grains will poke through into the main boundary layer. Each of these more exposed grains sheds eddies and a wake is formed downstream. The size of the wake depends upon the size and shape of the particle and on the point of separation of the boundary layer formed on the particle. In turn, the point of separation is a function of the shape of the particle and of the local Reynolds number. Under these conditions, the total drag force is now the resultant of surface drag (viscous skin friction) and form drag due to pressure differences between the upstream and downstream sides of the particle. The point of application of the resultant drag force depends on the magnitudes of lift and drag components which, in turn, are functions of the shape and location of the particle and of the local Reynolds number. Figure 4.30 shows these various concepts in diagrammatic form.

Figure 4.30: Schematic of an Exposed Grain, Subject to Fluid Forces

The picture is further complicated by the fact that, in turbulent flow, both lift and drag are fluctuating quantities in magnitude, point of application, and direction. Indeed, not even the laminar sublayer can be looked upon as steady two-dimensional laminar flow.





4.46

Studies of this region (1, 2, 3) reveal a complex flow structure which, although dominated by viscosity, comprises large three-dimensional high and low speed velocity streaks. Thus, except for fully laminar flow conditions, a sediment bed is subject to randomly varying velocities and shear stresses. Considering the fluctuating forces in terms of time averages, they may be classified as applied forces, comprising fluid forces and the weight component, and resisting forces, comprising the normal component of weight and any constraining forces due to neighbouring particles. The particle becomes unstable when the moment of the applied forces about a point of contact is greater than that of the resisting forces about the same point. The threshold of motion for a given particle can be thought of as the condition where the two opposing moments are equal. As soon as some particles are in motion, the picture is further complicated by impact forces between moving and stationary grains. The evident complexity of the physics of flow over a sediment bed is the reason why purely theoretical approaches to the prediction of the inception condition do not work. 5.3. The Threshold of Motion The term threshold implies a limiting condition marking the boundary between one state of affairs and another. Like many threshold conditions, the threshold of sediment motion cannot be defined with absolute precision. As the velocity of flow over an initially stationary bed of sediment is steadily increased, there is no point at which sediment movement suddenly becomes general. First, there is a condition in which a grain is detached from the bed every few seconds, the reason for which could be ascribed to the unstable initial position of that particular grain. As the velocity is increased, more and more particles are detached from the bed until eventually the movement of grains becomes general over the whole bed. This description of events appears to imply a certain subjectivity in experimentally determining the threshold condition. However, the difficulty of detecting this condition is more apparent than real. If a number of observers are asked to watch the progressive increase in velocity over an initially stationary sediment bed and to nominate the point at which bed movement has become generally established, their decisions are remarkably consistent, leading to values of the threshold velocity which vary by only a few percent. For this reason, in the following discussion, the threshold condition can be regarded as a sound and well-founded concept. Many attempts have been made to express analytically the resultant force acting upon a typical sediment particle at the moment of its entrainment by the flow. However, as implied in Section 2, application of this rational approach to a complete sediment bed would be very complex statistically. The classical work on the inception of sediment motion is that of Shields (4), who avoided the rational approach by making certain gross assumptions and confirming and supplementing the analysis experimentally. His experimental parameters were arranged according to a dimensional analysis. In contrast, in the following treatment a semi-rational approach is adopted to develop the Shields criterion.





4.47

The stability of a non-cohesive particle on the bed of a channel depends on the forces acting on it, i.e. the submerged weight, drag forces and lift forces. With reference to Figure 4.31, the condition for equilibrium can be expressed by the relation: GaFb = (4.54) in which F is the resultant of the drag and lift forces.

Figure 4.31: Forces Acting on a Bed Particle

Equation 4.54 may be expressed as:

( )gad s ρρbdUC bFππρ =22

421

−3

6 (4.55)

where CF combines the lift and drag coefficients and d is equivalent particle diameter.

Noting that Ub is proportional to the shear velocity, , where τ0 is the bed

shear stress, Equation 4.55 may be expressed in the form ρ

τ 0* =u

( )

(4.56) ϕρρ

ρ=

− gdu

s

2*

( )

in which ϕ depends on the particle shape and the velocity profile. The term on the left-hand side of Equation 4.56 is called the Shields parameter and is normally written in either of the two forms:

(4.57a) gds

uFs

s 1

2*

−=





4.48

( )dsF

ss 1

0

−=γ

τ (4.57b)

where is the sediment specific gravity ρρ s

ss =

Shields demonstrated experimentally that the particle Reynolds number, , is

sufficient to characterise the flow pattern near the particle and, thus, that: υ

du**Re =

( )*RefFs = (4.58) The experimentally determined function is shown in Figure 4.32. Since Shield’s original work in 1936, the line signifying the threshold of motion has been corroborated by many experimental studies and is now widely accepted. A further point of interest in Figure 4.32 is the annotation of the various modes of transport and bed formations which are determined by position on the ~ - Re~ plane.

Figure 4.32: Shields Entrainment Function

The particle diameter, d, appears in both the ordinate and the abscissa of Figure 4.32. For non-uniform sediments, the characteristic particle size should be taken as the d75 size of the mixture. The reason for this lies in the phenomenon of armouring, whereby the fine particles in the bed are preferentially removed. At the point of general inception of motion of the whole bed, the surface layer will have already lost significant fine material and it may be assumed that the d50 size of this layer is approximately equivalent to the d75 size of the parent mixture.





4.49

The curve in Figure 4.32 shows the classic pattern of variation of a dimensionless coefficient with Reynolds number (cf. friction factor - Reynolds number curves for pipe flow, and drag coefficient - Reynolds number curves for submerged bodies). There is a laminar flow region in which the coefficient varies inversely as Re*, a transition region, and a region of fully developed turbulence in which the coefficient is substantially constant. The initiation of motion is involved in many geomorphic and hydraulic problems such as clear-water scour, stable channel design, and rip-rap design, each of which is considered in later lectures. These problems can be properly handled only when the concept of the threshold of motion is clearly understood. Many experimental studies on the inception of motion have been carried out since the original work of Shields and, although there are some minor differences in detail, the general trend of Shields’ results has not been questioned. The least data are available at the fine material end of the Shields’ curve. In 1973, Mantz (5) reported some results from experiments with small flakes. His experiments covered flakes with a range of fall diameters from 22 to 80µm and face diameters of up to double this size. The plot of his experimental data at the inception of motion has a much flatter slope than the line of Shields. The lower entrainment values of flakes are explained by the fact that the flakes are separated by a fluid film and, hence, are able to slide more easily because only fluid friction has to be overcome. 5.4. The Competent Velocity Approach Some authors prefer to express the inception of sediment motion in terms of the average velocity because it is a more familiar parameter to practising hydraulic engineers than is the shear velocity. The main drawback in using the flow velocity as the threshold parameter is that the boundary shear stress for the same mean velocity of flow decreases with increasing depth of flow. Other authors have used a critical bed velocity in place of a critical mean flow velocity. Here, however, the difficulty is the definition of the relationship between the mean velocity and the bed velocity. A recent example of this approach is that of Yang (6) who used the conventional drag and lift concepts combined with the logarithmic velocity distribution and arrived at an expression for the ratio of critical velocity, Vcr, to fall velocity, w, of the form

66.006.0

5.2*

+−

υdulog

=w

Vcr (4.59)

for 0 < Re* < 70. For value of Re* > 70, Yang assumed that Vcr/w is no longer a function of Re* and the formula reduces to:

(4.60) 05.2=w

Vcr





4.50

Equation 4.59 implicitly includes the flow depth through the presence of the bed shear velocity, u*. However, Equation 4.60 is subject to doubt when applied to conditions other than those used for derivation of the constants, because it does not allow for the variation of bed shear stress with depth. References 1. Kline, S.J., Reynolds, W.C., Straub, F.A., Runstadler, P.W. (1967): The Structure of

Turbulent Boundary Layers, Journal of Fluid Mechanics. Vol. 30, Pt. 4. 2. Corino, E.R., Brodkey, R.S. (1969): A Visual Investigation of the Wall Region in

Turbulent Flow, Journal of Fluid Mechanics, Vol. 37, pp. 1-30. 3. Grass, A.J. (1971): Structural of Features of Turbulent Flow over Smooth and

Rough Boundaries, Journal of Fluid Mechanics, Vol. 50, pp. 233-255. 4. Shields, A. (1936): Anwendung der Aehnlichkeits - Mechanik und der

Turbulenszforsehung auf die Geschiebebewegung, Preussische Versuchsanstalt ifir Wasserbau und Sch~ffl,au, Berlin.

5. Mantz, P.A. (1973): Cohesionless Fine-graded Flaked Sediment Transport by

Water, Nature, PhysicalScience, Vol. 246, pp. 14-16. 6. Yang, C.T. (1973): Incipient Motion and Sediment Transport, Proceedings, Journal

of the Hydraulics Division, American Society of Civil Engineers, Vol. 99, HY10, pp. 1679-1704.

Bibliography 1. Raudkivi, A.J. (1976): Loose Boundary Hydraulics, 2nd. Ed., Pergamon Press,

Oxford. 2. Henderson, F.M. (1966): Open Channel Flow, Macmillan, New York. 3. Yalin, M.S. (1977): Mechanics of Sediment Transport, 2nd Ed., Pergamon Press,

Oxford. 4. Simons, D.B., Senturk, F. (1977): Sediment Transport Technology, Water

Resources Publicatins, Fort Collins, USA.





4.51

6. SCOUR AND SCOUR PROTECTION AT BRIDGE SITES 6.1. Introduction Scour at bridge sites is a major cause of bridge failure. Bridge piers are normally supported by friction piles. If the scour depth is great enough to uncover the supporting piles, friction between the piles and the surrounding soil is reduced and settlement and/or failure may follow.

There are four interrelated factors which may cause a change in the bed elevation under a bridge. These are:

• Constriction Scour

• Local Scour

• River Morphology

• Degradation and Aggradation

Detailed consideration of the last two of these is beyond the scope of these notes. River morphology is a very broad subject in itself and has been subject to a large range of investigations. In certain situations where the river is well confined, it may not be a major factor. In other cases, however, such as the construction of a bridge across a wide channel bend or braided river, river morphology may be the most important consideration in bridge pier design, and informed engineering judgement becomes particularly important.

Degradation or aggradation of the river bed is usually a very slow process. Assessment of its significance during the design life of a bridge may rest on progressive changes in measurements of bed elevations during previous years. Often consideration of the stability of a long reach of the river is necessary to assess its effect.

In this lecture the phenomena of constriction scour and local scour are considered. Included in the latter is local scour around bridge piers and around embankments. The lecture concludes with some notes on scour protection.

6.2. Constriction Scour In many cases of bridge design, a constriction of the waterway occurs at the bridge site. Some common causes of constriction are the bridge piers, approaches and abutments, debris jammed against the bridge deck and the siting of the bridge at a naturally narrow section of the river. Where such a constriction occurs, the bed elevation is likely to be lower than that in the unconstricted reach because of the increased scour associated with the concentrated flow. Especially in terms of flood, the difference in bed elevation can be substantial.

Two types of constriction scour can be identified: clear-water scour in which there is no contribution from the bed upstream to the sediment in transport; and live-bed scour which occurs when threshold conditions are exceeded and the bed is generally in motion. The analysis of live-bed scour requires an expression for the sediment discharge rate. Clear-





4.52

water scour is simpler to analyse because at equilibrium there is no bed load sediment transport. Indeed, within the constriction the bed shear stress is that associated with the threshold of sediment motion. It has been determined that for a particular constriction geometry and bed material, the maximum depth of clear-water scour is greater than that for live-bed scour by about 10% (1). Since in practical cases scour cannot be predicted to better than this accuracy, it is sufficient to confine design attention to the clear-water case.

In its simplest form the problem reduces to that of determining the scour in a constriction sufficiently long for uniform flow to be established. Although this does not reproduce precisely the conditions at bridge sites under flood conditions, limited corroborative field data have been obtained and this approach is recommended in the absence of more precise procedures.

The basic problem analysed is that of uniform flow in a long contraction. Within the contraction the bed will scour until the bed shear stress reaches the critical value for the material. The bed shear stress can be expressed independently in terms of Shields entrainment function and from the Manning equation. Equating the two expressions yields an equation from which the depth in the contraction can be calculated.

Figure 4.33: Definition Sketch for Flow in a Long Contraction

With reference to Figure 4.33, Manning's equation may be applied to the contracted region to give

V2

QA

R Sn2

22/3

21/2

2

= = (4.61)

where V is the velocity, Q is the discharge, A is the flow cross-sectional area, R is the hydraulic mean radius, S is the energy slope, and n is the Manning's roughness coefficient.





4.53

From Equation 4.61 the bed shear stress, τ2 (= γR2S2), be expressed in the form

(4.62) τγ

2 = Q n A R

222

22

21/3

( )τ γ 1= −F S dS S

( )

From the definition of Shields entrainment function, the bed shear stress may also be expressed in the form

(4.63) 2

where Fs is Shields entrainment function, which at equilibrium has the threshold value given by a plot of Shields entrainment function against particle Reynolds number, Ss is the specific gravity of the bed material relative to that of water and, d is the characteristic size of the bed material, here taken as the d75 size.

Equating the right-hand sides of Equations 4.62 and 4.63 yields

A R (4.64) Q n

F S d

222

S S 75

=−1

n d2 751/6= 0 038.

22

21/3

Equation 4.64 is the general expression describing flow within the constriction where the flow depth, y2, is included in the cross-sectional area and in the hydraulic mean radius.

For bed particles of sufficient size that at the critical bed shear stress the flow is fully rough turbulent, Fs has the constant value of 0.056 and n2 is given by

(4.65)

It is noted further that, for most sediments, a value of Ss of 2.65 is appropriate.

By substituting Equation 4.65 and the appropriate values of Fs and Ss into Equation 4.64 and assuming further that the flow cross-section is rectangular so that A2 = B2y2 and

an expression for y2 is obtained in the form RB y

B y22 2

2 2

=+ 2

y

B y27

2 2+ 210 Q

B d-6

6

27

752

= ×382. (4.66)

Further simplification is possible if it can be assumed that the constricted reach is hydraulically wide (ie B2 > 5y2). This permits the substitution of R2 = y2 in Equation 4.64 leading to the explicit equation for y2 of

y2 =Q

B d

6

26

752

0168

1/7

. (4.67)





4.54

For those bed materials for which the flow is not fully rough turbulent at the threshold bed shear stress, Fs does not in general take the value of 0.056 and Equation 4.65 is inapplicable. For such transition flow cases a rather complex procedure is necessary to determine Fs and n2. The procedure has been presented elsewhere (2,3) and is beyond the scope of these notes.

The theory presented here has been tested extensively against laboratory data (2,3,4) but only isolated field data are available. These data indicate that the theory embodied in Equations 4.66 and 4.67 underpredicts the true depth in the constriction by about 20%. Accordingly, in using Equations 4.66 and 4.67 in design, a multiplying factor of 1.2 should be applied to the value of y2. It should be noted, though, that in the absence of corroborative field data, the equations should be used with some caution.

6.3. Local Scour Around Bridge Piers In alluvial channels, the scour around bridge piers is initiated by interference mechanisms between the pier and the approach flow. The erodible bed deforms until it reaches an equilibrium scour configuration for which the rate of sediment supplied to the scour area is balanced by the rate of transport out of the area.

Figure 4.34: Horseshoe Vortex System around Circular Pier.

The dominant feature of the flow near a pier is the large-scale eddy structure, or vortex system, which develops about the pier. Figure 4.34 is a schematic showing the interaction mechanism between a circular pier and the approach flow. Because of the vertical velocity gradient in the approach boundary layer, a gradient in stagnation pressure occurs along the nose of the pier. This initiates a vertical downward motion of water down the nose of the pier and leads to the transverse vorticity at the bed. The transverse vortex wraps itself around the pier, giving the characteristic horseshoe shape. The action of this vortex is to erode bed material away from the base region of the pier. If the rate of sediment transport away from the local region is greater than the transport rate into the region a scour hole will develop. As the depth of scour is increased, the strength of the vortex is reduced, reducing the transport rate from the hole. Ultimately, a state of equilibrium is established.





4.55

Although the vortex system is known to be the cause of local scour, the present state of the art is not sufficiently advanced to permit the calculation of the strength of the vortex and to relate the velocity field with subsequent scour. For this reason, the formulae developed for

espite the large number, the equations contain only a limited number of variables. Some of these equations are discussed in the following paragraphs. For a more

predicting local scour around bridge piers are based on experimental data, most of which have been obtained in the laboratory. These formulae utilise average velocity and local flow depth.

Many different equations for predicting local scour around bridge piers have been proposed. D

comprehensive discussion, the reader is referred to Reference (5).

Laursen (6) developed an equation for the scour depth at a rectangular pier of the form

D D D

S S= +55115

1 1..

(4.b D

0 0

where b is the width o

D

0

−

11 7.

68)

f pier normal to the flow Do is the depth of flow upstream of the pier, and Ds is the depth of scour below mean bed elevation

ed a sediment of mean diameter

it does not include the effect of approach velocity.

The experiments on which this equation is based utilisbetween 0.46 and 2.2mm.

The scour depth Ds is implicit in Equation 4.68. However, a more serious problem with the equation is the fact that

Shen et al (7) developed an equation for rectangular piers of the form

( )b

Fb

S0

0=

3 4 2 3. / D

where Fo = Vo/(g Do)½ is the F based on the mean upstream velocity, Vo,

D 1/3

(4.69)

roude number and depth Do. A similar equation developed by the Colorado State University for the US Federal Highway Administration (8) and based on the same data has the form

( )DD

bD

FS0=

2 2

0 650 43.

..

An advantage of Equatio ment of the constant 2.2 by 2.0 provides

0 0

(4.70)

n 4.70 is that the replace excellent agreement with available data for circular piers.

rmal to the flow. A number of studies have shown that the strength of turbulent motion as well as the scour depth can be

Where the pier alignment is not parallel with the flow direction, the scour hole will be deeper due to the effective increase in the pier width no

reduced by streamlining the pier shape. However, the designer cannot always take advantage of this fact because streamlined piers can collect debris more readily than non-





4.56

streamlined shapes. In such a case, the debris itself will contribute to the eventual scour depth.

The equations reviewed herein apply only to non-cohesive bed materials. Local scour around piers in cohesive beds shows a different pattern with the scour hole extending far downstream of the pier instead of being concentrated at the nose of the pier. The scour

lash floods. Furthermore, when general sediment motion occurs and bed forms travel along the river bed, the maximum scour

h cross-sections other than circular or rectangular, it is advisable to carry out a model investigation to obtain more accurate

Scour around Embankments ocal scour occurs around embankments, spur dikes and abutments because of the

obstruction to flow caused by such structures. Figure 4.35 shows, schematically, the vortex bankment. Figure 4.36 shows a

equilibrium when the rates of sediment inflow and outflow are in balance. However, the depth of the scour hole rarely remains constant because of the

depth in cohesive soils is heavily dependent upon the characteristics of the bed material and much research remains to be done in this area.

The methods proposed determine the mean scour depth that will occur during an extended flood. This scour level may not be reached during f

depth will be larger than the mean depth. It is recommended (9) that one-half of the height of the dunes be added to the mean scour depth.

It is important to realise that the various equations yield, at best, only rough estimates of the scour depths to be expected. Especially for piers wit

information. The same is true for the pattern of local scour around composite piers such as rows of piles.

6.4. Local L

pattern associated with flow around the end of an emtypical resultant scour pattern.

The scour hole develops as overbank flow re-enters the main channel setting up large vortices. The scour reaches an

passage of dunes and other bed forms. The time required for movement of a large dune past the embankment is normally much larger than the time required for the development of local scour. Thus, even with steady state conditions, the depth of scour will fluctuate with time when there are dunes travelling on the channel bed. The larger the dunes, the more variable will be the depth of the scour hole. When the crest of the dune reaches the local scour area, the transport rate will increase, the scour hole will tend to fill, and the scour depth will temporarily decrease. When a trough approaches, there will be less sediment supply and the scour depth will increase to try to re-establish equilibrium in sediment transport rates. The equilibrium scour depth is defined as the mean depth between the oscillations. Typically, maximum scour hole depths may be 30% greater than equilibrium scour depths. For engineering applications, the maximum scour depth may be considered to be the equilibrium scour depth plus one-half of the bed-form height.





4.57

Figure 4.35: Schematic Representation of Vortex Formation at an Embankment

Figure 4.36: Typical Scour at an Embankment and Adjacent Pier

Detailed studies of abutment scour have been carried out, in the main, in laboratories. Field studies are handicapped by the difficulties of making measurements during floods. In one set of field studies (10) the equilibrium local scour depth was measured and found to follow the equation:

(4.71) ( )DD

c aD

FS

0 00=

0 400 33

..

where DS is the equilibrium scour depth measured from the mean bed level; a is the embankment length normal to the river bank;





4.58

Do is the approach depth; and Fo is the Froude number of the approach flow.

The constant c has the value of 1.1 for scour development at a spill slope. If the embankment terminates at a vertical wall and has a vertical wall on the upstream side, c takes the value of 2.15.

Using field data collected at rock dikes on the Mississippi River (8) the following equation for embankment scour was developed :

(4.72) ( )DD

FS

00= 4 0 33.

The data used to establish this equation were scattered, primarily because equilibrium depths were not measured. Dunes as large as 6-9m high move down the Mississippi at various river stages and the associated time for dune movement is very large in comparison to the time required to form local scour holes.

It is recommended that Equation 4.71 be used for embankments where 0 < a/Do < 25, and Equation 4.72 be used where a/do > 25. The equations are shown graphically in Figure 4.37.

Figure 4.37: Recommended Prediction Equations for Embankment Scour (8)

In applying Equation 4.71 the embankment length, a, is measured from the high water line at the valley bank perpendicular to the end of the embankment at the bridge.

If the embankment is angled downstream, the depth of scour is reduced because of the streamlining effect. On the other hand, embankments that are angled upstream have deeper scour holes. Figure 4.38 shows graphically the correction factor to be applied for inclination (11).





4.59

Figure 4.38: Correction Factor for Embankment Scour for Angle of Inclination (11)

6.5. Scour Protection In general, three basic methods may be used to protect structures from damage due to local scour. The first is to prevent damaging vortices from developing and the second is to provide protection at some level at or below the stream bed to arrest development of the scour hole. The third is to place the foundations of structures at such a depth that the deepest scour hole will not threaten the stability of the structure. The last method is often very expensive, and risk is involved because of the uncertainty associated with estimating the additive effects of scour due to constriction and local effects.

Vortex reduction : Streamlining the piers can reduce scour depth by 10 to 20 percent. Another method of reducing the vortex strength at the pier is to construct barriers upstream of bridge piers, as for instance with a cluster of piles. While the piles will be subjected to scour, such action will not damage the bridge. Debris can collect on the upstream piles, which tends to increase the vortex strength. This keeps the noses of the bridge piers relatively free of debris. The pile-up of water at the upstream piles reduces the dynamic pile-up of water at the bridge piers and reduces the vortex strength at the piers.

Spur dikes can be placed at the ends of approach embankments to reduce local scour.

Bed protection: Riprap piled up around the base of the pier is a common method of controlling scour. It should be expected that the region of the bed beyond the riprap will scour, and as the scour hole is formed the riprap will slide down into the scourhole eventually armouring the side and bed of the scour hole adjacent to the pier. An estimate of the depth of scour is needed to determine the quantity of riprap required for effective protection. Because of armouring, the effective depth of scour may be less than that calculated from the procedures discussed herein. There are few studies to establish dependable guidelines, but 50 to 60 percent reduction in DS may be used to estimate the final scour depth. By frequent inspection it can be determined whether the size and quantity of riprap used initially is adequate. If additional amounts of riprap are necessary,





4.60

placement from the water surface is possible in times of low flow with consideration given to the falling path of rocks in a flowing stream.

A structural concrete shelf placed at about 0.5 DS, where DS is calculated from one of the Equations 4.68 to 4.70, extending laterally from the pier and completely surrounding the pier may be effective in limiting the scour depth. The lateral extent of the shelf may be about 0.3 DS cotφ, where φ is the angle of repose of the bed material. While this method may be effective for DS < 6m, it may become impractical for larger values of DS.

Protective mattresses made from rock and wire have been suggested in the past, and have been used in some circumstances. While they may have merit where adequate size riprap may be scarce, anchoring and stabilisation of the mattresses to conform with scour holes may be difficult. Use of mattresses in conjunction with riprap may be quite effective if the mattress performs essentially as a flexible filter blanket which deforms as the scour hole develops. References (1) Chabert, J. and Engeldinger, P.(1965): Etude des affouillements autour des ponts,

Laboratoire National d'Hydraulique, Chatou (s et O), France.

(2) Keller, R.J.(1977): General scour in a Long Contraction, MWD Central Laboratories Report No 3-77/1.

(3) Keller, R.J.(1983): General Scour in a Long Contraction, Proceedings, XXth Congress of IAHR, Moscow, USSR, Vol II, pp280-289.

(4). Keller, R.J. and James, B.(1986): Analytical and Experimental Investigation of General Scour at Bridge Sites, Proceedings, Fifth Congress of the APD of IAHR, Seoul, Korea, Vol II, pp313-331.

(5) Shen, H.W.(1971): Scour Near Piers, in Shen, H.W. (ed) River Mechanics, H.W. Shen, Colorado, USA, Chapter 23.

(6) Laursen, E.M.(1962): Scour at Bridge Crossings, Transactions, ASCE, Vol 127 (1), pp 166-180.

(7) Shen, H.W., Schneider, V.R. and Karakis, S.(1969): Local Scour around Bridge Piers, Journal of the Hydraulics Division, ASCE, Vol 95, No HY 11, pp1919-1940.

(8) Colorado State University (1975): Highways in the River Environment : Hydraulic and Environmental Design Considerations, prepared for the Federal Highway Administration, US Department of Transportation.

(9) Neill, C.R. (ed) (1973): Guide to Bridge Hydraulics, University of Toronto Press, Ontario.





4.61

(10) Liu, H.K., Chang, F.M. and Skinner, M.M.(1961): Effect of Bridge Construction of Scour and Backwater, Department of Civil Engineering, Colorado State University, Report No CER60-HKL22.

(11) Ahmad, M.(1953): Experiments on Design and Behaviour of Spur Dikes, Proceedings of the IAHR, ASCE Joint Meeting, University of Minnesota.

Bibliography (1) Raudkivi, A.J.(1976): Loose Boundary Hydraulics, 2nd Ed, Pergamon Press,

Oxford.

(2) Henderson, F.M.(1966): Open Channel Flow, Macmillan, New York.

(3) Yalin, M.S. (1977): Mechanics of Sediment Transport, 2nd Ed, Pergamon Press, Oxford.

(4) Simons, D.B. and Senturk, F. (1977): Sediment Transport Technology, Water Resources Publications, Fort Collins, USA.

(5) Shen, H.W. (Ed) (1971): River Mechanics, H.W. Shen, Fort Colorado, Chapter 23





4.62

7. BANK AND BED PROTECTION 7.1. Introduction The need to protect the banks and beds of rivers against erosion is often determined by the need to develop and utilise the land on each side of the watercourse. There are many traditional methods of protection which have developed more in the nature of an art than a science. More recently the development of new materials and an improved understanding of the mechanics of erosion processes have led to the development and utilisation of more effective protective measures. Engineering effectiveness is not the only criterion, however. Regardless of the form of construction and of the materials used, the bank protection forms a part of the natural environment, and the effectiveness of the design must be judged on environmental as well as engineering grounds. Bank erosion frequently occurs as a result of man’s activities in such areas as river engineering works, adjacent land use changes, and wave action from boat traffic. It is important to realise also, however, that bank erosion can occur in channels which are in equilibrium. Local erosion and deposition can occur especially in channel bends, even though, in the longer term, the average shape and dimensions of the channel may be unaltered. Erosion and deposition resulting from river engineering works or adjacent land use changes occurs as the river seeks a new regime or equilibrium state. The speed at which the river responds to changes in, for example, discharge or sediment load depends on the degree of change and the natural stable conditions of the river. As has been discussed in an earlier lecture, mathematical models are now becoming available which can predict the changes in river plan form and cross-section consequent to such changes. The purpose of the present notes is not to provide a definitive treatise on the subject - such would not be possible within the terms of reference of this course. The aim is, however, to discuss the processes of bank failure and bed scour and to discuss some of the engineering remedial measures which can be adopted. The use of vegetation is specifically excluded as this is covered in another lecture. 7.2. Processes of Bank Failure Surface erosion on banks occurs when the erosive forces exceed the resistive forces. In turn, the erosion of surface material often results in mass failure by destabilising a significant section of the bank. Figure 4.39 shows some of the hydraulic processes which can cause bank or bed erosion. These processes include:

• Surface runoff of rain water causing gulleying or sheet erosion





4.63

• Seepage flows, which may be either steady (due to ground water discharge) or unsteady (due to fluctuations of water level in the channel) causing bank surface failure due to uplift forces

• Current attack causing surface erosion, especially at the toe of a bank

• Wave attack around the waterline due to wind waves and/or boat waves

Figure 4.39: Channel Cross-section Illustrating Surface Erosion Processes (1) Several different types of mass failure can occur in banks. These include sliding along a deep failure surface, shallow slips and block failures. These failure types are illustrated in Figure 4.40.

Figure 4.40: Channel Cross-section with Processes Responsible for Mass Failure (1)





4.64

Although banks may fail at almost any time - particularly in the presence of active surface erosion or toe scour - by far the greatest number of river bank failures occur during heavy rain or high river stages and shortly thereafter. Figure 4.41 shows examples of the different failure types, for each of which, the conditions under which they may occur are summarised. Further detail on the geotechnical aspects of bank failure are provided in (1).

Figure 4.41: Types of Mass Failure of Banks (1)





4.65

Figure 4.41: Types of Mass Failure of Banks (1) - continued As a result of mass failure, large volumes of material are deposited on the lower part of the bank. Individual particles may be entrained by the river or, especially if cohesive or bound by a vegetative root mat, they may remain intact. As long as the material remains





4.66

at the foot of the failure, the bank will be protected from further collapse. However, following removal of the material by the flow, the bank can again reach a critical condition and the failure process is repeated. Alternatively, the debris may remain to form a cohesive layer on which vegetation may become established. In this case the flow regime of the river will be affected, triggering erosion elsewhere and leaving the former failure area in relative stability. 7.3. Bed Scour Bed scour may be local, such as around bridge piers or other in-river hydraulic structures, or it may be wide-spread and progressive, often migrating upstream. Local bed scour is considered in another lecture in this course. Progressive bed scour is often associated with natural or artificial changes in a localised part of the river bed and is associated with the river’s attempt to reach a new state of equilibrium in the light of the change. Such scour is frequently associated with downstream artificial changes such as swamp drainage, and with artificial and natural cutoffs of meander loops. 7.4. River Training River training covers all of the engineering works in a river to regulate the river flow and sediment transport for the purposes of flood control, navigation, irrigation, and channel stabilisation. Rivers are often trained because of urbanisation; indeed land reclamation from flood plains has resulted in the channelisation of many rivers throughout the world. Two principles are of great importance in river training. Firstly, the training works must be designed to withstand the design flow. Secondly, the consequent impacts on the river should be understood and evaluated. These mean that the training works must be strong enough to withstand the design velocity and must also extend beyond the potential scour in order to safeguard against undermining. The need for understanding of the impacts on the river suggest that channel responses are the criteria for determining the adequacy of a design scheme. It must be clearly understood that river training measures in one part of a river may cause severe instability in another part. Modifications in design are often necessary in arriving at the final plan. In the design of river training works, the most challenging component is frequently the prediction of the consequent river channel response. This often requires the use of detailed physical and/or mathematical modelling. Some of the more common types of structure used to train rivers are shown in Figure 4.42 and include:

• Impermeable groynes (also known as groins, spurs, or spur dikes). These are transverse structures extending out from a bank, and can be used to protect the bank itself or to re-align or deflect the flow.





4.67

• Permeable groynes (also known as jetties or retards). These are similar to impermeable groynes but allow some flow to pass through the structure.

• Guide banks (also known as guide bunds). These can often comprise sections of longitudinal bank with curved upstream and downstream sections to collect and channel flow through, for example, the main spans of a bridge.

• Longitudinal dykes (also known as training walls or bulkheads). These are artificial banks approximately parallel to the main channel but constructed at a distance out from the existing banks.

• Flood embankments (also known as bunds or levees). These are raised embankments constructed along the banks or set back from them to contain certain design flood discharges.

Figure 4.42: Typical Layout of Training Works for Channelisation

Impermeable groynes have a stronger effect on the flow but can be subject to deep scour around the tip. They can also cause severe erosion elsewhere if they are not well planned. They are usually rock-filled or masonry structures. Rock-filled groynes are constructed with well-graded stones so that large voids are eliminated. Such groynes





4.68

need to be extended sufficiently deeply into the erodible bed because of the severe potential scour near the toe, around which large stones are usually dumped. Permeable groynes allow some continued flow parallel to the bank but by reducing velocities they are intended to prevent scour and promote sediment deposition. Experience has shown that permeable dykes are more effective than impermeable dykes as a bank protection, especially in silt and sand rivers. Since the flow is not severely disturbed by permeable dykes, intensive eddies and severe scour holes do not normally occur. However, there are few generalised guidelines available on what degree of permeability is appropriate in particular cases. Typical permeable dykes made from timber piles are depicted in Figure 4.43.

Figure 4.43: Timber Pile Dike (8)





4.69

It is not normally recommended to construct a single isolated groyne because it is likely to cause erosion downstream and may initiate development of a meander. Groynes are normally installed in groups or “fields”. The projected length LP of a groyne (measured normal to the flow) should not exceed about 20 to 25% of the total width of the channel. Within a group of groynes, the lengths should be varied to produce a smoothly curved boundary to the main flow. The required spacing between groynes is determined by the length of bank that each groyne is able to protect. The recommended spacing is typically in the range 2LP to 4LP with the upper limit appropriate when there are four or more groynes in a group.

Figure 4.44: Plan Shapes of Groynes





4.70

Various plan shapes of groynes in common usage are depicted in Figure 4.44. There is no general agreement on the most appropriate angle between the groyne and the bank line. Groynes angled upstream are sometimes termed “attracting” groynes because the flow tends to be attracted towards that bank. Conversely, groynes angled downstream tend to deflect the flow towards the opposite bank and are termed “repelling” groynes. A repelling groyne requires more extensive armour protection than an attracting groyne and can also cause more scour on the section of river bank immediately upstream. However, the respective benefits of these alternatives are not clear cut and it is normally recommended that groynes should be set perpendicular to the bank line as this gives the most economical solution. 7.5. Bank Protection Different types of bank protection are in use, including riprap, rock trench, gabions and rock mattresses, soil cement, and concrete blocks. In general, the top elevation of bank protection should stay above the design high water level. Within curved reaches, the superelevation of the water surface should also be considered. A freeboard is usually incorporated for water waves, also serving as a safety margin for such factors as erratic hydrologic phenomena, changes in flood plain vegetation, unforeseen riprap settlement, channel bed aggradation, and accumulation of trash and debris. A detailed survey of recommended practice is given by Hemphill and Bramley (1). They group the various alternatives into three categories as follows:

• Natural bed protection, using grass, grass reinforced with geotextiles or geomembranes, reeds, willows, timberwork, brushwood etc.

• Vertical bank protection, using sheet piling, gabions, concrete or masonry walls, precast units, reinforced earth structures etc.

• Revetments, consisting of a sloping earth bank protected by a cladding which can be of rock riprap, concrete, geotextile, or asphalt.

The choice of protection system is determined by such factors as:

• Severity of current or wave attack

• Location (urban, suburban, or rural)

• Appearance (ranging from hard vertical wall to soft sloping vegetated bank)

• Environmental aspects (habitats for flora and fauna)

• Type of bank material (which affects required permeability and flexibility of protection)

• Hydraulic roughness (which should be compatible with the existing channel)

• Cost

• Construction constraints (such as ability to work in the dry)

• Maintenance requirements





4.71

The suitability of protection systems is detailed in (1). In particular, it should be noted that bank protection against boat traffic induced waves is a most important issue. Methods of estimating the height and frequency of both wind and boat waves are given in (1). Revetments are widely used for bank protection and comprise an external armour layer and an under-layer between the armour and the subsoil formation that is being protected. This is illustrated in Figure 4.45. Both components of a revetment are very important and must be considered in conjunction.

Figure 4.45: Components of a Typical Revetment (1)

The armour layer provides protection against the direct actions of waves and currents. Two key properties are its permeability and its flexibility. High permeability reduces the hydrodynamic forces on the armour material and facilitates ground-water drainage through the revetment. However, it also exposes the under-layer and the subsoil to larger fluctuating forces. Flexibility enables the armour layer to accommodate minor deformations due to settlement, loss or migration of underlying material, and thus maintain the composite integrity of the revetment. The under-layer includes all material between the armour layer and the subsoil formation. It may be granular material, geotextile, or a combination of the two. The component materials are generally selected to perform one or more of the following functions:

• Filtration (restrain movement of the subsoil due to water movement into or out of the subsoil)

• Drainage (provide a drainage path for the under-layer and the topsoil)

• Erosion protection (prevent erosion of the subsoil by flow over its surface parallel to the slope of the revetment)

• Regulation (even out the formation surface and provide an even foundation for the revetment)

• Separation (prevent mixing of particles between the armour layer and the subsoil)





4.72

Other less-common purposes of the under-layer can include the provision of secondary protection in case of the loss of the armour layer, and the dissipation of the energy of internal flow in the under-layer caused by wave or current action. Types of armour layer found in practice include the following: • Stone - riprap or rock armour,

- hand-pitched stone, - random or dressed masonry, - gabion or wire mesh mattresses

• Concrete - plain precast blocks

- open-jointed or grouted interlocking blocks - cable-tied or geotextile-bonded blocks - cast in-situ slabs and monolithic structures - concrete-filled fabric bags

• Geotextiles - grassed composites - mats, fabrics, and meshes

- three-dimensional retaining mats and grids - two-dimensional fabrics

• Asphalt - open stone asphalt-filled geotextile mat

- open or dense stone asphalt Rock riprap is one of the most widely used revetment materials because of its availability and effectiveness. It is capable of providing protection even with minor undermining of the toe because the loose stones will settle into the scour hole and thus extend the protection. The stability of rock riprap under current and wave attack depends on the major factors of stone weight, stone shape, gradation, and layer thickness and has been the subject of much research. Stones used for riprap should be hard, durable, and angular in shape. Slab-like stones should be avoided because they are susceptible to hydrodynamic forces. Well-graded material should be used so that the interstices formed by large stones are filled by smaller ones in an interlocking fashion. Most specified gradings fall within the following upper and lower size limits:

WW

to 5100

50

= 2

WW

to 3.385

50

= 17.

(4.73)

WW

to 0.415

50

= 01.





4.73

WW

to 1285

15

= 4

In these equalities, W85, for example, is the weight of stone which is greater than that of 85% of the mixture by weight. Stability formulae are often expressed in terms of a mean nominal stone size Dn50 defined by

(4.74) DW

gn5050

S

=

ρ

13

where ρS is the density of the stone and g is the acceleration due to gravity. Many procedures have been developed for determining the size of riprap necessary for a particular situation. Many of these are based on a tractive force analysis. One widely used in the US and in Australia is based on the so-called Factor of Safety Method documented in (2). Recent research at HR Wallingford (3) has quantified the effect of turbulence on the stability of stone to current attack. The recommended design equation is as follows:

n50 (4.75) D CvgS

b=−

ρρ ρ

2

2 where ρ is the density of water, and the coefficient C is related to the turbulence intensity Ti by the equation C = 12.3Ti - 0.20, for Ti ≥ 5% (4.76) The velocity, vb in Equation 4.75 is the mean value at a height above the toe of the bank equal to 10% of the water depth. In the absence of field or model data, vb can be estimated using the recommendations of Neill (4): For a straight channel, parallel flow: v = 2V/3 (4.77) For impinging flow, bend, or groyne v = 4V/3 (4.78) where V is the cross-section area averaged velocity. The turbulence intensity, defined as the root-mean-square fluctuation/mean velocity) is also measured at a height above the toe of the bank equal to 10% of the water depth. Typical values of turbulence intensity are as follows:





4.74

Straight section of river channel: Ti = 6-7% Downstream of gates or of a relatively weak hydraulic jump: Ti = 20-25% Equations 4.75 and 4.76 are valid for riprap on a flat bed or on banks with slopes up to 1V:2H. Several different types of formulae have been developed for the stability of riprap subject to wave attack. For random wind-generated waves with a significant wave height HS and a zero crossing period TZ the formula recommended is (1):

( )ρ ρS n50/ D−

=1 α

S S OZH H L

0 440 5

. tan/

.

(4.79)

where α is the angle of the bank to the horizontal, and LOZ is the deep water wave length given by

(4.80) LT

2OZZ2

=gπ

The recommended formulae for boat generated waves are as follows (1): (a) Transverse stern wave (primary wave)

( )ρ ρS / 1α

n50

i

DH cot

.− =

0 671/3 (4.81)

( ) (b) Secondary bow and stern waves

( ) ( )βn50 cos. .= 05 0 5ρ ρS

i

DH

/ −1 (4.82)

where Hi is the crest to trough height of the highest wave, and β is the angle of incidence of the secondary waves to the bank (usually 55o for a boat moving parallel to the bank). If wind generated waves have wave heights exceeding about 1m, it is recommended to use a more comprehensive design formula such as that due to van der Meer (5). A filter layer is often needed beneath the riprap cover to prevent the water from removing bank material through the voids. The filter layer may be either a granular filter blanket or plastic filter cloth. The former provides a transition between the rock layer and the bank material, with sizes of gravel ranging from about 5mm to about





4.75

75mm. The need for this transition depends on the size and gradation of the rock layer in relation to the bank material. A filter is not required if the stones are sufficiently small. One suggested set of criteria for gradation is as follows (8):

d of filterd of base

5 15

85

⟨ ⟨d of filterd of base

4015

15

⟨

and

d of filterd of base

4050

50

⟨

where “filter” refers to the overlying material, and “base” refers to the underlying material. These criteria are applicable to any two adjacent layers among the riprap, filter blanket, and base material. In the case of very large stones in the riprap layer, multiple filter layers with gradual size variations are required. Recently, geotextile fabrics have become widely used as filter layers. They possess the advantages of cost, in-plane tensile strength, and limited thickness. Care must be exercised during placement of stones directly on the cloth to avoid damage. The sides and toe of the filter fabric should be sealed or trenched to contain the base material. Geotextile fabrics are easy to damage and difficult to repair and careful design and installation are required to accommodate settlement or uneven formation of the base material. 7.6. Bed Protection Bed protection is often assured by the use of grade control structures whose purpose is to maintain a slope which is flatter than the terrain. The excess energy in the flow is then absorbed in a controlled manner through energy dissipation on the downstream side of the structure. Rock chutes are often used to stabilise an erosion head in a stream bed. The crest of a structure or a chute usually extends across the channel, and the side walls should extend into the bank and have adequate bank protection to prevent flanking at high flows. Each structure should also have adequate upstream and downstream protection. Dumped rock may be placed on the downstream side to the anticipated scour depth. A typical drop structure, recommended by the US Corp of Engineers (6), is shown in Figure 4.46, incorporating a downstream apron and end sill. The length of the basin and the end sill height are determined from the relationships shown in the figure. While a grade control structure stabilises the upstream channel bed, it usually induces downstream changes. These changes are either related to the gradation change in the reach or to local scour or to both. Gradation change is associated with any imbalance in sediment transport in the river reach and ceases when a dynamic equilibrium is





4.76

established. When major gradation is expected, a series of small grade control structures may be used to limit the extent of change at each structure. Local scour is related to the flow pattern as affected by the structure, occurring when excess energy and high velocity are dissipated in the turbulent eddies. An important component of the design of a grade control structure is the provision of protection for downstream local scour.

Figure 4.46: Typical Grade Control Structure (8)

The use of rock structures for energy dissipation is often preferred because of environmental and aesthetic benefits and because construction is non-labour intensive, quick, and does not often require expensive diversion of flows. These structures are particularly suitable for use in small to medium sized streams where the height of each individual structure can be kept relatively low. Guidelines for the design of these structures have been presented by Craigie (7). References (1.) Hemphill, R.W. and Bramley, M.E.(1989): Protection of River and Canal Banks,

CIRIA and Butterworths, London (ISBN 0-408-03945-0) (2.) Simons, D.B. and Senturk, F.(1977): Sediment Transport Technology, Water

Resources Publications, Fort Collins, Colorado








4.77

(3) Escarameia, M. and May, R.W.P.(1992): Channel Protection: Turbulence

Downstream of Structures, HR Wallingford, Report SR 313 (4) Neill, C.R.(1973): Guide to Bridge Hydraulics, Road and Transport Association of

Canada, University of Toronto Press (5) van der Meer, J.W.(1988): Deterministic and Probabilistic Design of Breakwater

Armour Layers, Proc. ASCE, vol 114, WW1, pp 66-80 (6) Corps of Engineers (1970): Hydraulic Design of Flood Channels, EM 1110-2-1601,

Department of the Army, Office of the Chief of Engineers, July (7) Craigie, N.(1989): Interim Standards for Stream Restoration Works in the DVA

District, Dandenong Valley Authority, Melbourne, Australia (8) Chang, H.H.(1988): Fluvial Processes in River Engineering, John Wiley and Sons,

New York

topic 4: applied hydraulics table of contents

Documents