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EAH 225: HYDRAULICSSediment Transport in Rivers
ZORKEFLEE ABU HASAN
REDAC
CONTENTS • INTRODUCTION TO SEDIMENT TRANSPORT
• RIVER MORPHOLOGY AND QUALITATIVE
ANALYSIS
• SEDIMENT PROPERTIES
• INCIPIENT MOTION
• MODE OF TRANSPORT
• FLOW RESISTANCE
• BED LOAD
• TOTAL BED MATERIAL LOAD
• STABLE CHANNEL DESIGN
• REFERENCES
• ASSIGNMENTS
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EAH 225: HYDRAULICSSediment Transport in Rivers
ZORKEFLEE ABU HASANZORKEFLEE ABU HASAN
REDAC
INTRODUCTIONINTRODUCTION
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INTRODUCTIONINTRODUCTION
Fluvial sediment transport is the study of the interaction between channelized, unidirectional flows of relatively clear water and natural, generally non-cohesive, sediment.Sediment transport is an important in engineering b h l l k “hbecause it helps answer questions like “how can we keep sediment out of these turbines?”
INTRODUCTIONAN ALLUVIAL RIVER GENERALLY IS CONTINUALLY CHANGING ITS POSITION AND SHAPE AS A CONSEQUENCE OF HYDRAULIC FORCES ACTING ON ITS BED AND BANKS.THESE CHANGES MAY BE SLOW OR RAPID AND MAY RESULT FROM NATURAL AND MAY RESULT FROM NATURAL ENVIRONMENTAL CHANGES OR FROM CHANGES CUSED BY MAN’S ACTIVITIES
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INTRODUCTIONWHEN A RIVER CHANNEL IS MODIFIED LOCALLY, THE CHANGE FREQUENTLY CAUSES CHANGES IN CHANNEL CHARACTERISTICS BOTH UP AND DOWNSTREAMEXAMPLES OF HUMAN ACTIVITIES ARE CONSTRUCTION OF DAM AND RIVER STRAIGHTENINGSTRAIGHTENINGNATURAL CAUSES ARE EARTHQUAKES AND HEAVY RAINFALL
River System
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Figure 3.3 Typical Meandering River
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River Corridor
NATURAL RIVERSNATURAL RIVERS
Sungai Kampar @ Kg Jahang,
Gopeng
Sungai Ulu Paip, Kulim
Sungai Sedim, Kulim
Sungai Kulim, Kedah
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Nuki River (Kitakyushu City, Fukuoka Prefecture)
Example of River Rehabilitation in JapanExample of River Rehabilitation in Japan
Before construction( October 1991 )
23 months after construction (July 1995)Sediment was deposited on which vegetation grew,
Creating a natural water space. Immediately after construction
(August 1993)
Low Flow(22 Mei 2003)
Man made river at Kampus Kejuruteraan USMMan made river at Kampus Kejuruteraan USM
High Flow(19 Mei 2003)
(a) Completed works30 January 2003
(b) 4 months after construction
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River Equilibrium
SEDIMENT SEDIMENT TRANSPORT TRANSPORT CONCEPTCONCEPT
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MODE OF SEDIMENT TRANSPORT
WASH LOAD
BED
SUSPENDED LOAD
TOTAL LOAD
BED MATERIAL
BED MATERIAL
LOAD
TOTAL BED MATERIAL LOAD
Shields DiagramShields Diagram((Featherstone & Nalluri 1993Featherstone & Nalluri 1993))
No Sediment Transport
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Bed Form in Natural WaterwaysBed Form in Natural Waterways
RIVER WORKS RIVER WORKS DESIGNDESIGN
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21
321 SRV =
Manning’s n for River Design
SRnV
1.216/1
50dn= Uniform Sediment
(Cu = d60 / d10 ≤ 3)1.21
266/1
90dn= Non -Uniform Sediment
(Cu = d60 / d10 > 3)
Suggested Manning ‘s nSuggested Manning ‘s n
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River Reconstruction After 19River Reconstruction After 19thth
November 1997 Flood (Sungai Pari)November 1997 Flood (Sungai Pari)
Critical Shear StressCritical Shear Stress((Van Rijn, 1984Van Rijn, 1984))
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Critical Velocities, (m/s) for various conduit materials
Sediment Transport Sediment Transport EquationsEquations
Type of Equation Equation Data Rangeyp q q g
Bed Material Load
Shields 1.56 < d50(mm) < 2.47
Meyer-Peter-Muller 3.17 < d50(mm) < 28.6
Einstein – Brown ψ < 10
Einstein 0.785 < d50(mm) < 28.6
Graf 0 09 < d (mm) < 2 78
Total Bed Material Load
Graf 0.09 < d50(mm) < 2.78
Engelund & Hansen 0.19 < d50(mm) < 0.93
Yang0.137 < d50(mm) < 1.71yo(m) < 1.0 m
Ackers & White 0.04 < d50(mm) < 4.94
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River sediment River sediment River sediment River sediment data data
measurementmeasurementmeasurementmeasurement
Data MeasurementData Measurement(a)(a) Flow Discharge:Flow Discharge:
Current Meter Swoffer 2100 for wading Current Meter Model Neyrflux Type 80 for deep flow
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Data MeasurementData Measurement(b) Bed Material:
Van Veen Bed Material Sampler
Data MeasurementData Measurement(c) Bed load sampler:.
Low Flow High FlowHelley-Smith Bed Load Sampler
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Data MeasurementData Measurement(d) Suspended Load :
DH48 -Low Flow DH59 – High Flow
Data MeasurementData Measurement(d) Channel Slope:
(f) Water Temperature:
Survey Equipment
Thermometer
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Sediment Data MeasurementSediment Data Measurement
Data MeasurementSample Sediment Data
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Particle Size Distribution of River Bed Material
Stesen SP7 Sg. Pari
100 00Peratus Telus (%)
30 00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
d90
d65
d35
d50
d60
0.00
10.00
20.00
30.00
0.01 0.10 1.00 10.00 100.00
Sampel 1 Sampel 2 Sampel 3 PurataSaiz Partikel (mm)
d10
RELATIONSHIPS RELATIONSHIPS RELATIONSHIPS RELATIONSHIPS BETWEEN FLOW BETWEEN FLOW AND SEDIMENT AND SEDIMENT
LOADLOAD
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DATA ANALYSIS(a)(a) Relationship between flow discharge and total Relationship between flow discharge and total
sediment load discharge. sediment load discharge.
(b)(b) R l ti hi b t fl di h d t t l b dR l ti hi b t fl di h d t t l b d(b)(b) Relationship between flow discharge dan total bed Relationship between flow discharge dan total bed material load.material load.
(c)(c) Relationship between flow discharge and bed load Relationship between flow discharge and bed load discharge. discharge.
(d)(d) Relationship between flow parameter and transport Relationship between flow parameter and transport parameterparameterparameter.parameter.
(e)(e) Sediment Rating Curve for sediment size distribution.Sediment Rating Curve for sediment size distribution.
(f)(f) Assessment of common sediment transport Assessment of common sediment transport equations.equations.
(g)(g) River ModellingRiver Modelling
Relationship between flow discharge dan total sediment load Relationship between flow discharge dan total sediment load (T(Tjj))
DATA ANALYSISDATA ANALYSIS
100
10
0.1
1
0.1 1 10 100Q (m 3 /s)Sungai Pari @ Manjoi
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Flow Parameter (Flow Parameter (ψψ) and Transport Parameter () and Transport Parameter (φφ))
DATA ANALYSISDATA ANALYSIS
1000
0.1
1
10
100
Para
met
er A
liran
, ψ
φ=0.5(ψ)-2.52
φ=10.39(ψ)-2.52
0.001
0.01
0.001 0.01 0.1 1 10 100Parameter Pengangkutan, φ
Sg Pari @ Tmn Merdeka Sg Pari @ Manjoi Sg Pari @ BuntongSg Kinta Sg Raia @ Kg Tanjung Sg Raia @ Bt GajahSg Kampar @ KM 34 Sg Kerayong Sg KulimSg Langat @ Kajang Sg Langat @ Dengkil Sg Lui @ Kg LuiSg Semenyih @ Kg Sg Rinching Persamaan Graf (1968) Persamaan Modified Graf (4.4)
Sediment Rating Curve
DATA ANALYSISDATA ANALYSIS
4.00
5.00
6.00
g/s)
Sungai Pari @ Manjoi
0.00
1.00
2.00
3.00
9.00 14.00 19.00 24.00 29.00 34.00 39.00 44.00 49.00 54.00Q (m3/s)
T i (k
g
> 10.00 mm 5.30 mm - 10.0 mm 4.00 mm - 5.30 mm 3.35 mm - 4.00 mm2.00 mm - 3.35 mm 1.18 mm - 2.00 mm 0.71 mm - 1.18 mm 0.60 mm - 0.71 mm0.43 mm -0.60 mm 0.30 mm - 0.43 mm 0.15 mm - 0.30 mm 0.08 mm - 0.15 mm< 0.08 mm
0 60
0.700.80
Sungai Pari @ Buntong
0.000.100.20
0.300.400.500.60
9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00Q (m3/s)
T i (k
g/s)
> 10.00 mm 5.30 mm - 10.0 mm 4.00 mm - 5.30 mm 3.35 mm - 4.00 mm2.00 mm - 3.35 mm 1.18 mm - 2.00 mm 0.71 mm - 1.18 mm 0.60 mm - 0.71 mm0.43 mm -0.60 mm 0.30 mm - 0.43 mm 0.15 mm - 0.30 mm 0.08 mm - 0.15 mm< 0.08 mm
g @ g
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RIVER RIVER MODELLINGMODELLINGMODELLINGMODELLING
EXAMPLEEXAMPLE
FLUVIALFLUVIAL--1212
FLOW CHARTFLUVIAL-12
mula
data input
t = t + Δt
penghalaan air
tempohmasa telah diliputi?tidak
ya
tamatpenghalaan endapan
penyesuaian geometri saluran
tamat
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STUDY REACHSungai Pari
RIVER MODELLING
g
STUDY REACHSungai Pari
Permodelan SungaiPermodelan Sungai
Taman Merdeka, Ch. 2475 ( 21 Oktober 2002)Alor Limpah Batu, Ch. 1220 ( 25 Julai 2001)
Ch. 3020 ( 21 Oktober 2002) Jambatan Manjoi, Ch. 3380 ( 21 Oktober 2002)
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Permodelan SungaiPermodelan Sungai
Tokong Buddha, Ch. 4160 ( 21 Oktober 2002)Ch. 3600 ( 21 Oktober 2002)
Jambatan Silibin, Ch. 4540 ( 21 Oktober 2002) Kuala Sungai Pari ( 22 July 2001 )
WATER LEVELWATER LEVELParas AirParas Air
Permodelan SungaiPermodelan Sungai
Perbezaan Paras Air Sungai Pari
37 00
38.00
39.00
m
Paras Air Cerapan Sungai PariParas Air Cerapan
WATER LEVELWATER LEVEL
34.00
35.00
36.00
37.00
2000 2500 3000 3500 4000 4500 5000Keratan Rentas, m
Para
s,
P. Air 7/10/2002 (35.00 Cumecs) P. Air 8/10/2002 (34.70 Cumecs)P. Air 9/10/2002 (47.80 Cumecs) P. Air 10/10/2002 (14.15 Cumecs)P. Air 21/10/2002 (7.05 Cumecs)
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RIVER MODELLINGRIVER MODELLING
HYDROGRAPHHYDROGRAPH
Puncak Hidrograf Tahun 2000 Sungai Par i
60
80
100
120
ir, m
3 /s
Profil Aliran Berhayun Sungai Pari
39.0
40.0
0
20
40
60
2390 2400 2410 2420 2430 2440 2450M as a, jam
Kada
rali
OSCILATING FLOW OSCILATING FLOW
33.0
34.0
35.0
36.0
37.0
38.0
0 50 100 150 200 250 300 350 400 450 500Masa, jam
Para
s Ai
r, m
RIVER MODELLINGRIVER MODELLINGSEDIMENT RATING CURVESEDIMENT RATING CURVE
0 10
0.15
0.20
0.25
apan
, Qs
(m3 /s
)
Taburan Purata Saiz Endapan Bahan
Dasar Untuk Sungai Pari
80 00
90.00
100.00
d50 = 1.80 mm
0.00
0.05
0.10
0.00 10.00 20.00 30.00 40.00 50.00Masa (jam)
Out
put E
nda
0.00
10.00
20.00
30.0040.00
50.00
60.0070.00
80.00
0.01 0.10 1.00 10.00 100.00
Saiz Partikel, mm
Pera
tus
Telu
s, %
Cerapan Dasar Hil ir Cerapan Dasar Hulu
d50 = 2.50 mm
BED BED MATERIALMATERIAL RIVER BANK MATERIALRIVER BANK MATERIAL
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RIVER MODELLINGRIVER MODELLING
Flood Hydrograph
35.5036.0036.5037.0037.5038.00
Par
as, m
Profil Paras Air Sungai Pari Bagi Kadaralir Q=15 m3/s
Flood Hydrograph Year 200034.50
35.00
2000 2500 3000 3500 4000 4500 5000Keratan Rentas, m
Paras air simulasi (FL-12) Paras air cerapan
37 50
38.00
38.50
mSimulation Simulation FluvialFluvial--1212
Profil Paras Air Sungai Pari Bagi Kadaralir Q=48 m3/s
35.50
36.00
36.50
37.00
37.50
2000 2500 3000 3500 4000 4500 5000Keratan Rentas, m
Para
s, m
Paras air simulasi (FL-12) Paras air cerapan
River modellingRiver modellingPerbandingan Penyelakuan Perbandingan Penyelakuan
FLUVIALFLUVIAL--12 dan FLUVIAL12 dan FLUVIAL--14 14
Bagi Sungai PariBagi Sungai Pari
Hidrograf Tahun 2000
38.00
40.00
42.00
, m Bagi Sungai Pari Bagi Sungai Pari
Perbandingan Penyelakuan Paras Dasar dan Air Sungai Pari
( Waktu Puncak )
32.00
34.00
36.00
1000 1500 2000 2500 3000 3500 4000 4500 5000
Keratan Rentas, m
Para
s,
P Dasar Sim ulas i FL14 P. Dasar Sim ulas i FL12P Air Sim ulas i FL14 P. Air Sim ulas i FL12P. Dasar Mula
40 00
42.00
Perbandingan Penyelakuan Paras Dasar dan Air Sungai Pari
( Akhir Penyelakuan )
32.00
34.00
36.00
38.00
40.00
1000 1500 2000 2500 3000 3500 4000 4500 5000Keratan Rentas (m)
Para
s (m
)
P. Air FL-14 P. Air FL-12 P. Dasar FL-14P. Dasar FL-12 P. Air Pada Puncak
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River modellingRiver modelling
1 50
2.00
Hidrograf Puncak Tahun 2000Perbandingan Penyelakuan Perbandingan Penyelakuan
FLUVIALFLUVIAL--12 dan FLUVIAL12 dan FLUVIAL--14 14
Bagi Sungai PariBagi Sungai Pari
0.00
0.50
1.00
1.50
1000 1500 2000 2500 3000 3500 4000 4500 5000
Keratan Rentas, m
Hal
aju,
m/s
Halaju pd 2399 hr Halaju pd 2407 hr Halaju pd 2442 hr
1.00
Perbandingan Penyelakuan Halaju FLUVIAL-12
Bagi Sungai Pari Bagi Sungai Pari
0.00
0.20
0.40
0.60
0.80
1000 1500 2000 2500 3000 3500 4000 4500 5000Keratan Rentas, m
Hal
aju,
m/s
Halaju pd 2407 hr (Puncak) Halaju pd 2399 hr (Initial)Halaju pd 2444 hr (Akhir)Perbandingan Penyelakuan Halaju FLUVIAL-14
River modellingRiver modelling
38.00
39.00
40.00
41.00
aras
, m
Perbandingan Penyelakuan Perbandingan Penyelakuan
FLUVIALFLUVIAL--12 dan FLUVIAL12 dan FLUVIAL--14 14
Bagi Sungai PariBagi Sungai Pari
Perbandingan Keratan Rentas Ch. 2475, Taman Merdeka
Hidrograf Tahun 2000 ( Waktu Puncak )
36.00
37.00
0.00 10.00 20.00 30.00 40.00 50.00Jarak Dari Tebing Kiri, m
Pa
P. Dasar Awal P. Air AwalP. Dasar Simulasi FL-12 P. Air Simulasi FL-12P. Dasar Simulasi FL-14 P. Air Simulasi FL-14
39 00
40.00
41.00
Bagi Sungai Pari Bagi Sungai Pari
Perbandingan Keratan Rentas Ch. 3020
Hidrograf Tahun 2000 ( Waktu Puncak )
35.00
36.00
37.00
38.00
39.00
0.00 10.00 20.00 30.00 40.00 50.00Jarak Dari Tebing Kiri, m
Par
as, m
P. Dasar Awal P. Air AwalP. Dasar Simulasi FL-12 P. Air Simulasi FL-12P. Dasar Simulasi FL-14 P. Air Simulasi FL-14
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River modellingRiver modelling
36 00
37.00
38.00
39.00
40.00
ras,
m
Perbandingan Penyelakuan Perbandingan Penyelakuan
FLUVIALFLUVIAL--12 dan FLUVIAL12 dan FLUVIAL--14 14
Bagi Sungai PariBagi Sungai Pari
Perbandingan Keratan Rentas Ch. 3380, Jambatan Manjoi
Hidrograf Tahun 2000 ( Waktu Puncak )
34.00
35.00
36.00
0.00 10.00 20.00 30.00 40.00 50.00Jarak Dari Tebing Kiri, m
Pa
P. Dasar Awal P. Air AwalP. Dasar Simulasi FL-12 P. Air Simulasi FL-12P. Dasar Simulasi FL-14 P. Air Simulasi FL-14
38 00
39.00
40.00
m
Bagi Sungai Pari Bagi Sungai Pari
Perbandingan Keratan Rentas Ch. 3600
Hidrograf Tahun 2000 ( Waktu Puncak )
34.00
35.00
36.00
37.00
38.00
0.00 10.00 20.00 30.00 40.00 50.00Jarak Dari Tebing Kiri, m
Para
s, m
P. Dasar Awal P. Air AwalP. Dasar Simulasi FL-12 P. Air Simulasi FL-12P. Dasar Simulasi FL-14 P. Air Simulasi FL-14
USM_USM_REDAC_2003REDAC_2003
1
RIVER MORPHOLOGY ANDRIVER MORPHOLOGY AND QUALITATIVE ANALYSIS
1
ObjectivesStudents be able to
• understand basic concept of river morphology
• Predict qualitative response of river system
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Streamflow and Fluvial Processes (river morphology)
• Streams are powerful i ierosive agents moving
material from their bed and banks
• Streams also deposit vastamounts of sediment onthe terrestrial landscapethe terrestrial landscapeand within lakes andocean basins.
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The Long Profile of Streams
• At their headwaters: the grade is usually steep
• As streams get closer to sea level, the angle of the grade becomes more gently sloping.
• Near the mouth of the stream, the grade becomes almost flat.
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3
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Cross‐sections
• Stream channel near the h d theadwaters.
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Cross‐sections
• Stream channel near th iddl f t i lthe middle of a typical stream profile
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Cross‐sections
• Stream channel near the th f tmouth of a stream
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Historical problems
• Many channels are already clogged (due to erosion from previous generations)erosion from previous generations).
• Erosion control programs have reduced sediment loads to channels.
• Channels have been straightened.
• Riparian areas have been cleared.
• Roads and bridges constrain channels.
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Current problems
• Our channels are finding a new equilibrium.
• Some will get worse before they get better.
• Many are not stable.
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Reasons for instability
• Peak flows too high (urbanization)g ( )
• Sediment load too high (watershed sources)
• Removal of riparian vegetation
• Change of grade
S i h i f h l• Straightening of channels
• Widening of channels
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More reasons for channel instability
• Lack of flood plain
• Restriction of flow (bridge or culvert)
• Channelization
• Deposition in channel ‐ formation of point bars and islandsbars and islands
• Trash or debris
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STABILITY OF RIVER CHANNEL?
RIVER WILL BE IN THE STATE OF INEQUILBRIUM IFRIVER WILL BE IN THE STATE OF INEQUILBRIUM IF
THERE ARE CHANGES IN THE RIVER AND/OR ITS
SURROUNDINGS
THE RESULT: SCOUR AND DEPOSITION WHICH CHANGES THE CHARACTERISTIC OF THE RIVER.
EFFECT: LOSS OR GAIN OF LAND DUE TO NEWLY
FORMED MEANDERS, DAMAGE TO HYDRAULICS
STRUCTURES DUE TO SCOUR OR/AND DEPOSITION
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9
Effects of instability
• Head cutting
• Bank sloughing
• Meandering
• Formation of point bars and islands
• Braiding of stream• Braiding of stream
• Erosion of banks
• Loss of aquatic habitat17 of 53
EFFECTS OF SCOUR & DEPOSITION
EXAMPLES
• LOCALISED DAMAGE OF BANK PROTECTION
STRUCTURES
• SCOUR AT THE BRIDGE PIERS
• DEPOSITION AT THE CULVERTSDEPOSITION AT THE CULVERTS
• SCOUR UNDER THE HYDRAULICS STRUCTURES
• …...
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Head Cutting
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Grade change down stream and steep channel grade cause upstream migration of head cut.
Bars, Islands, and other obstructions
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Obstruction of the channel causes erosion of the banks.
11
Definition of Stable Channel
• A stable channel carries all the water andsediment it receives without changingshape or pattern.
• This means:there should be neither erosion nordeposition.
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Transport capacity may be too high or too low
• Too high transport capacity–Channel too steep
–No flood plain
– Lack of riparian vegetation
• Too low transport capacity– Too much sediment load (from watershed)
–Obstructions in channel
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12
Channel must carry all the sediment and water completely through the
reach.
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Which channel is more efficient?
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“C” Channel “E” ChannelStraight Channel
13
The “C” Channel is most efficient
• “C” channel carries water and sediment most ffi i tlefficiently.
• Straight channel has no flood plain.– Deposition occurs under low flow.
– Erosion occurs under high flow.
• “E” channel has too tight curves• E channel has too tight curves.
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Sinuosity reduces grade.
100’
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Medium grade Steep grade Low grade
90’
14
Stream Bank Stabilization ‐ Armoring
• Armoring a stream bank is expensive.
• Armoring one place causes another to blow out.
• Armoring gives poor aesthetics.
• Armoring gives poor aquaticArmoring gives poor aquatic (and terrestrial) habitat.
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Stream Bank Stabilization ‐Bio‐Engineering
• protecting banks with vegetation– preferred if it will work
– may not stand the highest flows
– may be self‐healing
• may incorporate some structural support
• Less expensive than all structures
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Stream Restoration
• Re‐establish meander pattern
• Re‐establish profile
• Re‐establish riffle and pool structure
• Slope back high banks
• Establish bank egetation
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• Establish bank vegetation
• Establish riparian vegetation
How much is worth doing?
• Before investing large budget, determineif the stream is stable.– If not stable, will it recover by itself? or
– Is restoration needed?
• Riparian area value may be its own
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justification.
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QUALITATIVE RESPONSE OF RIVER SYSTEM
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Qualitative Response of River System
• Nearly all channels are formed, maintained, d lt d b t d di t thand altered by water and sediment they carry
• Channels are in equilibrium when hydraulics and sediment variables are in balance
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Qualitative Response of River System
• Many rivers have achieved a state of approximate equilibrium throughout long reaches.
• Regardless of the degree of channel stability, man’s local activities may produce changes in river characteristics both locally and throughout an entire reach.
• All too frequently the net result of riverAll too frequently the net result of river improvement is a greater departure from equilibrium than that which originally prevail.
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An extreme example of habitat simplification. On theleft is the original urban stream in an Eastern Europeancity. Note the good riparian vegetation, and the variedwater velocities in the channel. On the right is thechannel after it has been ‘channelised’ for flood control.Note the simplification of the stream with uniform flow,and a single reed species at the water’s edge.
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Qualitative Response of River System
• Good engineering design must invariably seek to h th t l t d f th tenhance the natural tendency of the stream
towards poised condition.
• Predicting the response to channel development is a very complex task.
• There are a large number of variables involved inThere are a large number of variables involved in the analysis.
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Qualitative Response of River System
• Studies to investigate channel response to t l d i d h b L (1955)natural and imposed changes by Lane (1955),
Leopold and Maddock (1953), Schumm (1971), Santos and Simon (1972), Simon, Li and Associates (1982) support the following general relationship
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Qualitative Response of River System
Depth of flow (y)Depth of flow (y) αα Water discharge (Q)Water discharge (Q)
Channel width (W)Channel width (W) αα Water discharge (Q) and Water discharge (Q) and Sediment Discharge (Qs)Sediment Discharge (Qs)
Channel shape, Channel shape, expressed as W/yexpressed as W/y
αα Sediment Discharge (Qs)Sediment Discharge (Qs)
Channel slope (S)Channel slope (S) 1/1/αα Water discharge (Q)Water discharge (Q)
Si it ( )Si it ( ) V ll lV ll lSinuosity (s)Sinuosity (s)[sinuosity: stream channel [sinuosity: stream channel length divided by length of length divided by length of meander belt axis or by meander belt axis or by valley length]valley length]
αα Valley slopeValley slope
1/1/αα Sediment Discharge (Qs)Sediment Discharge (Qs)
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Qualitative Response of River System
Transport of bed Transport of bed material (Qs)material (Qs)
αα Stream Power (Stream Power (ττoV)V)
αα Concentration of fine materialConcentration of fine materialαα Concentration of fine material Concentration of fine material (C(Cf))
1/α1/α Bed material diameter (dBed material diameter (d5050))
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Adopted from Simon and Senturk (1992)
Application of Qualitative Analysis
• Geomorphic principles are useful for qualitative analysis of river response withoutqualitative analysis of river response without describing transient behaviour
• A well known geomorphic relationship proposed by Lane (1955), depicting concept of equilibrium
Q d QSQsd50 α QS• This principle as illustrated as a relationship of balance
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Application of QualitativeApplication of Qualitative Analysis
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Dam Construction
aggradation degradation
Aggradation (deposition) upstream of dam will reduce Qs downstream Assuming fallreduce Qs downstream. Assuming fall diameter and water discharge remain constant, slope must decrease downstream of dam
24
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Lowering of main river bedFrom QsdFrom Qsd5050 αα QSQS, , it it can be seen that the can be seen that the increase in slope Sincrease in slope Sincrease in slope S increase in slope S must be balance by must be balance by increase in sediment increase in sediment transport Qs. Thus transport Qs. Thus under the new under the new imposed condition, imposed condition, local gradient of the local gradient of the
48 of 53
tributary stream tributary stream significantly significantly increased increased →→headcuttingheadcutting..
25
Channel Straightening
49 of 53
Channel Straightening
• The initial shortening of channel increase its l d th t l it hi h islope and thus stream velocity, which increase the stream’s capacity to transport sediment
• Sedimentation occurs at the downstream end due to reduction of velocity
50 of 53
26
Channel Widening
51 of 53
Channel Widening
• The enlarged cross‐section at the upstream d f th id d h d b tend of the widened reached causes an abrupt
decrease in stream velocity → induces sedimentation in the reach with greatest deposition occuring near the upstream end.
• Gradually, the stream develops a narrow, y, p ,meandering channel through the deposits
52 of 53
27
Channel Widening
• The enlarged cross‐section produces drawdown ff t hi h b i t th t d f theffect which begins at the upstream end of the widened reach and extend upstream.
• Resulting increased velocities cause erosion of the upsteam natural channel, and the erosion progresses upstreamp g p
53 of 53
01‐Mar‐09
1
APPLICATION OF QUALITATIVE ANALYSIS
Extracted from:SEDIMENT TRANSPORT TECHNOLOGY, WATER AND SEDIMENT DYNAMICDaryl B.Simons and Fuat Senturk
1
SEDIMENT PROPERTIESSEDIMENT PROPERTIES
DIFFERENCES BETWEEN RIGID BOUNDARY DIFFERENCES BETWEEN RIGID BOUNDARY AND LOOSE BOUNDARIES FLOWAND LOOSE BOUNDARIES FLOW
RIGID BOUNDARY CHANNELRIGID BOUNDARY CHANNELNo movement at the boundaries of flow.No movement at the boundaries of flow.
LOOSE BOUNDARY CHANNELLOOSE BOUNDARY CHANNELThe sediment grains moves after a The sediment grains moves after a Threshold Condition [Incipient Motion].Threshold Condition [Incipient Motion].The sediment movement is influenced by The sediment movement is influenced by the hydraulic and sediment characteristics. the hydraulic and sediment characteristics.
2
DIFFERENCES BETWEEN RIGID BOUNDARY DIFFERENCES BETWEEN RIGID BOUNDARY AND LOOSE BOUNDARIES FLOWAND LOOSE BOUNDARIES FLOW
RIGID BOUNDARY CHANNELRIGID BOUNDARY CHANNELChannel boundary does not changeChannel boundary does not changeWetted perimeter is impermeableWetted perimeter is impermeable
LOOSE BOUNDARY CHANNELLOOSE BOUNDARY CHANNELChannel eometry changes Channel eometry changes Wetted perimeter is not impermeable. Wetted perimeter is not impermeable. Hence, the flow does not stop at the flow Hence, the flow does not stop at the flow boundaryboundary
Channel boundary Flow in loose boundary channel
goes beyond the boundary. Flow in loose boundary channel
goes beyond the boundary.
3
CHANNEL GEOMETRY CHANGES
4
Channel xChannel x--section chanes with channel section chanes with channel dischargesdischarges
P e r b a n d i n g a n B e n t u k K e r a t a nA n d a i a n P a r a s T i d a k B e r u b a h d i T i t i k 3 . 9
mm
0 . 3 0
0 . 4 0
0 . 5 0
0 . 6 0
0 . 7 0
as D
asar
[m]
Y q 1 . 5 9 Y q 0 . 6 0
Y q 0 . 5 1 Y q 0 . 3 0
0 . 0 0
0 . 1 0
0 . 2 0
0 2 4 6
L e b a r [ m ]
Ara
Sediment PropertiesSediment PropertiesTermsTerms Sign / Sign /
SymbolSymbolDesctiptionsDesctiptions UnitUnit
aa DensityDensity ρρ Mass per unit volumeMass per unit volume Kg/mKg/m33
bb Specific Specific weightweight
γγ = = ρgρg
Weight per unit volume. Where g is Weight per unit volume. Where g is the gravitional accelarationthe gravitional accelaration
Kg/mKg/m33,,N/mN/m33
cc Specific Specific gravitygravity
γγss//γγ Ratio of specific weight of a given Ratio of specific weight of a given material (material (γγss) to the specific weight of ) to the specific weight of
t (t ( ) t 4) t 4ooC A ifiC A ifiwater (water (γγ) at 4) at 4ooC. Average specific C. Average specific weight of sediment is 2.65weight of sediment is 2.65
dd Fall velocityFall velocity ωω The average terminal fall velocity of a The average terminal fall velocity of a particle falling alone in quiescent, particle falling alone in quiescent, distilled water of infinite extent.distilled water of infinite extent.
m/sec , cm/sm/sec , cm/s
ee Kinematic Kinematic ViscosityViscosity
υυ The ratio of dynamic of dynamic The ratio of dynamic of dynamic viscosity to mass densityviscosity to mass density
mm22/s/s
5
Water PropertiesWater Properties
Yang (1996)
19-Feb-09
1
Incipient motionIncipient motionConsider a plain stationary bed consisting of loosecohesionless (mobile) solid particles of uniform sizeflowing over it.As soon as liquid starts flowing, hydrodynamicforces are exerted upon the solid particles of thebed at the wetted perimeter of the conveyancesystem.A further increase in the flow in flow intensity causesan increase in the magnitude of these forces.For a particular stationary bed, a condition isFor a particular stationary bed, a condition iseventually reach at which particles in the movablebed are unable to resist the hydrodynamic forcesand, thus, get first dislodge and eventually stars tomove.
Graf (1984)
τo = ρgRSShear stress
τo < τc
CHANNEL BED
τc
Critical Shear stress
19-Feb-09
2
τo < τc
CHANNEL BED
Critical condition, or initial scour, or Critical condition, or initial scour, or incipient motion [threshold condition]incipient motion [threshold condition]
τo ≅τc
CHANNEL BED
19-Feb-09
3
Incipient motionIncipient motion
IncipientIncipient motionmotion cancan bebe determineddetermined bybyusingusing criticalcritical velocityvelocity andand Shield’sShield’sDiagramDiagram
Critical Velocity / Permissible VelocityCritical Velocity / Permissible Velocity
Defined as the maximum mean velocity of a channel that will not cause erosion of thechannel that will not cause erosion of the channel boundary [Chang, 1988]Hjulstrom and ASCE Studies: Hjulstorm prepare the curves based on the data of several investigators. ACSE Task Committee presented a graphical relationship showing the criticala graphical relationship showing the critical water velocities fro quartz sediment as a function of mean grain size.
19-Feb-09
4
Critical Velocity / Permissible VelocityCritical Velocity / Permissible Velocity
Critical Velocity / Permissible VelocityCritical Velocity / Permissible Velocity
19-Feb-09
5
Critical Velocity / Permissible VelocityCritical Velocity / Permissible Velocity
Critical Velocity / Permissible VelocityCritical Velocity / Permissible Velocity
Frontier and Scobey’s Study (1926): They d t i fi ld fmade an extensive field survey of
maximum permissible value of mean velocities in canal.The permissible velocities for canals of different materials are as summerizeddifferent materials are as summerized
19-Feb-09
6
ShieldsShields DiagramDiagramShields introduce the concept of the dimensionless entrainment function
as function of shear Reynold number υ/dU=R
[nalluri, pg353]
Reynold number υ/dU** =eR
19-Feb-09
7
ShieldsShields DiagramDiagramImportant factors areshear stress τ, sediment dU( / ) /τ ρ 1 2shear stress τ, sedimentdiameter d, kinematicviscosity ν, density ρ, andaccelaration due togravity g. These factorsare group into twodimensionless functions:
ddUc f( / ) *τ ρ
ν ν=
τρ ρ
τγ ρ ρ
c
s f
c
s fd g d( ) [( / ) ]−=
− 1
dimensionless functions:
ρs and ρf sediment density and fluid density, γ specificweight of water, U* shear velocity [√(τo/ρ)] , and τccritical shear stress.
ShieldsShields DiagramDiagramWhen flow is fully turbulent around the bed material (Re* > 400 and d > ≈ 4 mm ) the ( e )Shield criterion can be written as
19-Feb-09
8
ShieldsShields DiagramDiagramRelationship between these parameters is derived from researches by Shields and other yresearchers:
Example of Application : determine armour size to p ppprotect river bank and bed erosion
Shields DiagramShields DiagramThe Shields diagram contains the critical value for τ*c as an implicit th t t b bt i d di tl T
2/1
110 ⎥⎤
⎢⎡
⎟⎟⎞
⎜⎜⎛
− gdd sγthat cannot be obtained directly. To overcome this difficulty, the ASCE Sediment Manual (1975) utilize a third dimensionless parameterWhich appears as a family of parallel lines in the diagram From the value of the third parameter the
11.0 ⎥⎦
⎢⎣
⎟⎟⎠
⎜⎜⎝
− gdv γ
Chang [pg83]:
diagram. From the value of the third parameter, the value of critical Shields stress is obtained at the intersection with the Shields curve which can be calculated.
19-Feb-09
9
Shields DiagramShields Diagram
Shields DiagramShields Diagram
19-Feb-09
10
Computation Computation ExampleExample
A wide channel having a slope of 0.001 d fl i t 0 3 d th E i thand flowing at 0.3 m depth. Examine the
stability of the bed material if the mean diameter is 1.0 mm.
Computation ExampleComputation Example
19-Feb-09
1
Mode of TransportMode of TransportWhen the flow characteristics (velocity, average shear stress etc.) in an alluvial channel exceed )the threshold condition for the bed material the particles moves in different modes along the flow direction. Some particle roll or slide along the bed inermittently and some others saltate (hopping and bouncing along the bed). Fi ti l ( ith l f ll l iti )Finer particles (with low fall velocities) are entrained in suspension by the fluid turbulence and transported along the channel in suspension.
[nalluri, pg357]
transport determinantstransport determinants
particle sizeparticle shapeparticle specific gravityvelocitysediment dischargeg
19-Feb-09
2
Mode of Sediment TransportMode of Sediment Transport
There are two common classifications of th l d i th t [ h 131]the load in the stream [chang, pg 131] First: divide the load into bed load and suspended loadSecond: separates the load into bed material load and wash loadmaterial load and wash load
bedloadbedload
“sediment that moves by sliding, rolling, or saltating (bouncing) on or very near the bed.”
Leopold et al (1992) – Fluvial Processes in GeomorphologyLeopold et al (1992) – Fluvial Processes in Geomorphology
19-Feb-09
3
types of suspended loadtypes of suspended loadsuspended load –
wash load “sediment load of a stream whichwash load – sediment load of a stream which is composed of particles sizes smaller than those found in appreciable quantities in the shifting portions of the stream bed” – TOO SMALL TO DEPOSITsuspended load – “particles which are moved b d d d i th t l b tby and suspended in the water column, but can settle in locations where the travel velocity is low or settling depth is small.” CAN DEPOSIT UNDER SOME CONDITIONS.
Garde and Raju (2000) – Mechanics of Sediment Transport and Alluvial Stream Problems.Garde and Raju (2000) – Mechanics of Sediment Transport and Alluvial Stream Problems.
washloadwashload
generated from caving of streambanks of a tributary and washes through a reach withouttributary and washes through a reach without appreciable deposition.simplification - these particles pass through the river system relatively unrelated to the hydraulic condition in a given reach – the wash load is independent of the discharge; i t d d d i / il bilit finstead, depends on erosion/availability of fine materials from upstream.Einstein recommended that washload include the particle size for which 10 % of the bed material is finer. (Einstein H.A. 1950)
19-Feb-09
4
Federal Interagency Stream Restoration Working Group (FISRWG). (1998).
(ASCE, 1997)
19-Feb-09
5
Mode of Sediment TransportMode of Sediment Transport
WASH LOAD
BED LOAD
SUSPENDED LOAD
TOTAL LOAD
BED MATERIAL
BED LOAD
TOTAL BED MATERIAL LOAD
(Nalluri & Featherstone, 2001)
19-Feb-09
6
Classification of alluvial channels. Schumm’s classification system relates channel stability to kind of sediment load and channel type.[Figure 7.10, (FISRWG,1998).
1
SEDIMENT TRANSPORTSEDIMENT TRANSPORT
FLOW RESISTANCEFLOW RESISTANCE
11
RESISTANCE OF FLOW IN RESISTANCE OF FLOW IN ALLUVIAL CHANNELALLUVIAL CHANNEL
Resistance of an alluvial channel varies considerably with flow velocitiesconsiderably with flow velocitiesThe bed forms are flow induced and directly affect the roughness or flow resistanceVariation of bed form roughness has i t t ff t th t di h
22
important effects on the stage-discharge relationship during the passage of flood in the short term.
2
RESISTANCE OF FLOW IN RESISTANCE OF FLOW IN ALLUVIAL CHANNELALLUVIAL CHANNEL
Stage-discharge predictor is a flow-resistance relationship used to determineresistance relationship used to determine the depth or hydraulic radius of flow for a given discharge, channel shape, channel slope, bed material properties, and temperatureThe relationship between mean velocity (V) the depth (y ) or hydraulic radius (R)
33
(V), the depth (yo) or hydraulic radius (R), slope (S) and sediment size (d), can be divided into 2 categories
a) Total Resistance approachb) Grain and form resistance approach
RESISTANCE OF FLOW IN RESISTANCE OF FLOW IN ALLUVIAL CHANNELALLUVIAL CHANNEL
Total Resistance approachLacey Equation (Lacey, 1930)One of the earliest resistance relationship for alluvial channel flow based on the regime canal data from India
44
India.
V = 10.8 R2/3 So1/3 (SI unit)
3
RESISTANCE OF FLOW IN RESISTANCE OF FLOW IN ALLUVIAL CHANNELALLUVIAL CHANNEL
Total Resistance approachJ E ti (S i 1974)2) Japanese Equation (Sugio, 1974)The equation developed using data from Japan.
V = K R0.54 So0.27 (SI unit)
K values for different bed form are
55
K values for different bed form areK = 6.51 for rippleK = 9.64 for dunesK = 11.28 for transition regime
66Bed forms of sand bed channels (Simons and Richardson, 1966) [source Yang, 1996)
4
RESISTANCE OF FLOW IN RESISTANCE OF FLOW IN ALLUVIAL CHANNELALLUVIAL CHANNEL
Total Resistance approachG d R R j (1966)3) Garde – Ranga Raju (1966)Garde and Ranga Raju analysed data from flume, canals and natural streams.A graphical relationship between parameter
77
K1 V/√(ΔgR) versus K2(R/d)1/3S/ΔK1 and K2 are functions of sediment size
Total Resistance approach
3) Garde – Ranga Raju (1966)j ( )
KK11 V/V/√√((ΔΔgRgR) versus K) versus K22(R/d)(R/d)1/31/3S/S/Δ Δ [Fig 14.2, Featherstone and [Fig 14.2, Featherstone and NalluriNalluri, 1995], 1995]
88
[Fig 14.3, Featherstone and Nalluri, [Fig 14.3, Featherstone and Nalluri, 1995]1995]
5
RESISTANCE OF FLOW IN RESISTANCE OF FLOW IN ALLUVIAL CHANNELALLUVIAL CHANNEL
Grain and form resistance approachThi ti i t d th t fThis equation introduces the concept of splitting the overall resistance into grain resistance and form resistanceGrain resistance: resistence contributed by the surface drag (tangential force)
99
Form resistance: cause by pressure different between the front and back surfaces of the bed form
(Chang, 1988)
1010Bed forms of sand bed channels (Simons and Richardson, 1966) [source Yang, 1996)
6
Grain and form resistance approachThe divided resistence approach can be expressed in terms of the energy gradient asas
S = S’ + S”or for hydraulic radius
R = R’ + R”Th th d f t
1111
There are many methods for stage-dischare prediction. Only Einstein and Barbarossa (1952) is explained
Grain and form resistance approachEinstein and Barbarossa’s Method (1952)Under fully rough condition, R’ is obtained ffrom
V = average flow velocity
1212
U*’ = √(gR’So ) [U*’ = Shear velocity related to grain size]
7
Grain and form resistance approachEinstein and Barbarossa’s Method (1952)For cases where grain roughness does not produce fully rough condition, R’ is computed from Manning equationcomputed from Manning equation
The form roughness is assumed to be related to
1313
the sediment transport rate along the channel bed because flow resisance due to bed forms is a function of flow to which the sediment rate may be related
Cont…
Einstein and Barbarossa’s Method (1952)…contA functional relationship suggested for the lower flow regimeg
1414
The functional relationship between V/U*” was determined from field data as shown in next slide
8
Einstein and Barbarossa’s Method (1952)Einstein and Barbarossa’s Method (1952)
1515
Yang, 1996)
Sample CalculationSample Calculation
16160.56 m
9
Sample CalculationSample Calculation
1717
Sample CalculationSample Calculation
1818
10
Sample Calculation Sample Calculation [E[E--B: Yang, pg 73]B: Yang, pg 73]
1919
Sample Calculation Sample Calculation [E[E--B: Yang, pg 73]B: Yang, pg 73]
2020
11
Sample Calculation Sample Calculation [E[E--B: Yang, pg 73]B: Yang, pg 73]
2121
2222
12
2323
2424
13
2525
2626
1
SEDIMENT TRANSPORTSEDIMENT TRANSPORTSEDIMENT TRANSPORTSEDIMENT TRANSPORTBED LOADBED LOAD
ZORKEFLEE ABU HASANZORKEFLEE ABU HASAN
11
Mode of Sediment TransportMode of Sediment Transport
WASH LOAD
BED LOAD
SUSPENDED LOAD
TOTAL LOAD
BED MATERIAL
BED LOAD
TOTAL BED MATERIAL LOAD
2
SEDIMENT TRANSPORTSEDIMENT TRANSPORTBEDLOADBEDLOAD
Several empirical equations from laboratory have been proposed with basic assumptionshave been proposed with basic assumptions that the sediment is homogenous and non cohesive.The results differ appreciably and it is dangerous to transfer the information to outside the limit of the experiment
33
outside the limit of the experiment.The following are the most commonly used equations
SEDIMENT TRANSPORTSEDIMENT TRANSPORTBEDLOADBEDLOAD
a1. Shields Equation (1936):q = bed load per unit widthqb = bed load per unit widthq = unit discharge in channelΔ = (γs/γ) – 1τo = ρgRSoτc = from Shields Diagram
44
[ranges 0.06 < Δ < 3.2; 1.56mm < d50 < 2.47 mm]
3
SEDIMENT TRANSPORT BEDLOADSEDIMENT TRANSPORT BEDLOAD
a2.Shields EquationCritical Shear Stress [Van Rijn 1984]
Category Dgr τc/(ρgΔd50) Category
1 Dgr <4 0.24xDgr-1.0 1
2 4< Dgr <10 0.14xDgr-0.64 2
3/1
250
1
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−
=ν
γγ gs
dDgr
55
3 10< Dgr <20 0.04xDgr-0.1 3
4 20< Dgr <150 0.013xDgr0.29 4
5 Dgr >150 0.059 5
SEDIMENT TRANSPORTSEDIMENT TRANSPORTBEDLOADBEDLOAD
b.b. MeyerMeyer--PeterPeter--Muller Equation (1948) [MPM]:Muller Equation (1948) [MPM]:
66
4
SEDIMENT TRANSPORTSEDIMENT TRANSPORTBEDLOADBEDLOAD
c. Einstein’s Equation/Approach:Einstein introduce probability concepts of sediment ste t oduce p obab ty co cepts o sed e tmovement and developed an emphirical relationship
φ = f(ψ)The relationship is expressed in the plot of φ versus ψfunctions Einstein defined the transport function as
⎤⎡
77
( ) ⎥⎦
⎤⎢⎣
⎡−
=Φ 3ss
bw
dγγgγ
γq
qbw = bed load discharge by weight per unit channel width
Relationship between Relationship between φφ versusversus ψψ for Einstein bed load for Einstein bed load functions functions
88
[Yang, [Yang, 1996]1996]
5
SEDIMENT TRANSPORTSEDIMENT TRANSPORTBEDLOADBEDLOAD
d. Einstein - Brown Equation;B (1950) d l d b d l d t tBrown (1950) developed a bed-load transport function based on Einstein’s (1942) equation:
3140 ⎟⎠⎞
⎜⎝⎛Ψ
=Φ
99
For ψ < 10, The relationship is expressed in the plot of φ versus functions
Relationship between Relationship between φφ = f(1/= f(1/ψψ) for ) for EinsteinEinstein--Brown equationBrown equation
1010Yang, 1996Yang, 1996
6
DISCREPANCY RATIODISCREPANCY RATIO
Discrepancy Ratio is one of the methods to l t th it bl di t t tselect the suitable sediment transport
equation for a particular river reach.DISCREPANCY RATIO (DR) is the ratio between computed sediment load against measured load. Acceptable range is:measured load. Acceptable range is:
½ ≤ DR ≤ 2
1111
Sample ComputationSample ComputationFlow Discharge, Q = 0.6 m3/sFlow velocity, V = 0.42 m/sy,Surface width, B = 5.70 mFlow Area, A = 1.43 m2
Hydraulic radius, R = 0.24 m2
Bed Gradient, So = 0.001
1212
Water Temperature, T = 25 oCBed load, Qb = 9.48 x 10-6 m3/sSuspended load, Qs = 9.60 x 10-6 m3/sMean diameter, d50 = 1.1 mm
7
Sample ComputationSample ComputationAssumptions
Sediment specific gravity γs = 2 65Sediment specific gravity, γs = 2.65
Water specific gravity, γ = 1.0Water Density ρ = 1000 kg/m3
Gravity g = 9.81 m/s2
Kinematic viscosity ν = 1 x 10-6 m2/s
1313
Kinematic viscosity ν 1 x 10 m /s
DISCREPANCY RATIO (DR)½ ≤ DR ≤ 2
Transport Parameter,
Sample Sample Computation: Computation: EinsteinEinstein--Brown EquationBrown Equation
3140 ⎟⎠⎞
⎜⎝⎛Ψ
=Φ
Flow Parameter,
⎠⎝ Ψ
Volumetric concentration, Cv = Qb/Q
1414
8
Sample Computation: Sample Computation: EinsteinEinstein--Brown EquationBrown Equation
1515
Sample Computation: Sample Computation: Shield EquationShield Equation
1616
9
Sample Computation: Sample Computation: Shield EquationShield Equation
1717
Sample Computation: Sample Computation: Meyer Meyer -- Peter Peter -- MullerMuller
1818
1
EAH 225: HYDRAULICS EAH 225: HYDRAULICS (2008/09)(2008/09)(2008/09)(2008/09)
SEDIMENT TRANSPORTSEDIMENT TRANSPORTTOTAL BED MATERIAL LOADTOTAL BED MATERIAL LOAD
11
ZORKEFLEE ABU HASANZORKEFLEE ABU HASAN
TOTAL BED MATERIAL LOADTOTAL BED MATERIAL LOAD
Based on the mode of transport, total load i th f b d l d d d dis the sum of bed-load and suspended load.The following approaches describe some of the available direct methods of estimating total bed material load
22
estimating total bed material load
2
SEDIMENT TRANSPORTSEDIMENT TRANSPORTTOTAL BED MATERIAL LOADTOTAL BED MATERIAL LOAD
a.a. Graf’s EquationGraf’s Equations d1γ
⎟⎟⎞
⎜⎜⎛
( ) 52.239.10 −Ψ=Φ o
50s
RS
d1γγ
⎟⎟⎠
⎜⎜⎝
−=Ψ
vVRCΦ
33Range: 10-2 < φ <103
350
s
v
d1γγ
g ⎟⎟⎠
⎞⎜⎜⎝
⎛−
=Φ
SEDIMENT TRANSPORTSEDIMENT TRANSPORTTOTAL BED MATERIAL LOADTOTAL BED MATERIAL LOAD
b.b. Ackers Ackers -- White EquationWhite Equation n10.1
gr dR11.3A
⎥⎥⎤
⎢⎢⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−
( )/m1v
50s
JC1K
d1γγg
V+=
⎟⎟⎠
⎞⎜⎜⎝
⎛−
2n/s
50g
8λ
dK
⎟⎠⎞
⎜⎝⎛
⎥⎦⎢⎣⎟⎠
⎜⎝
=
/m12n/
s
n1gr λAR ⎥
⎤⎢⎡
⎟⎞
⎜⎛
⎟⎟⎞
⎜⎜⎛⎟⎟⎞
⎜⎜⎛
−
44
50
C8BRd
J
⎥⎥⎥⎥⎥
⎦⎢⎢⎢⎢⎢
⎣
⎟⎠
⎜⎝⎟⎟
⎠⎜⎜⎝⎟⎟⎠
⎜⎜⎝=
2VgRSo8λs =
3
SEDIMENT TRANSPORTSEDIMENT TRANSPORTTOTAL BED MATERIAL LOADTOTAL BED MATERIAL LOAD
b.b. Ackers Ackers -- White EquationWhite Equation (…cont)(…cont)3/1
s 1γγg
dD ⎥⎥⎤
⎢⎢⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−
=
ν = kinematic velocity
Coefficient Fine Transitional Coarse
Dgr <1.0 1.0 < Dgr ≤ 60 Dgr > 60
n 1 0 n = 1 00 0 56 log D 0 00
250gr dD
⎥⎥⎥
⎦⎢⎢⎢
⎣
=ν
55Range: 0.04 <d (mm) < 4.0 ; Fr ≤ 0.8
n 1.0 n = 1.00 – 0.56 log Dgr 0.00
Agr − Agr = 0.14 + 0.23/ √( Dgr ) 0.17
m − m = 1.34 + 9.66/ Dgr 1.50
C log C = 2.86 log Dgr - (log Dgr)2 -3.53 0.025
Source: Pg.155, Yang, 1996
SEDIMENT TRANSPORTSEDIMENT TRANSPORTTOTAL BED MATERIAL LOADTOTAL BED MATERIAL LOAD
c.c. Yang’s EquationYang’s Equation
S
S
WW *50
TUlog0.457
νdlog0.2865.435logC −−=
⎞⎛⎞⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟⎟
⎠
⎞⎜⎜⎝
⎛−−+
SSS
S
WWWW oc*50 SVVSlogUlog0.314
νdlog0.4091.799
0.660.06
νdUlog
2.5V50*
c +−⎟
⎠⎞
⎜⎝⎛
=SW
70νdU
1.2 50* <<for
V dUf
66
05.2Vc =SW ν
dU70 50*≤for
where ( ) ( )
γγ
ppmCppmCs
Tv =
4
77
Sample ComputationSample Computation
88
5
Sample ComputationSample Computation
99
ANSWERANSWERYANG EQUATIONYANG EQUATION
1010
6
ANSWERANSWERYANG EQUATIONYANG EQUATION
0.660 06dUlog
2.5V50*
c +−⎟
⎞⎜⎛
=SW 0.06
νlog ⎟
⎠⎜⎝
1111
1212
7
ANSWERANSWERYANG EQUATIONYANG EQUATION
1313
ANSWERANSWERACKERSACKERS--WHITE EQUATIONWHITE EQUATION
1414
8
ANSWERANSWERACKERSACKERS--WHITE EQUATIONWHITE EQUATION
1515
ANSWERANSWERACKERSACKERS--WHITE EQUATIONWHITE EQUATION
1616
9
ANSWERANSWERACKERSACKERS--WHITE EQUATIONWHITE EQUATION
1717
ANSWERANSWERGRAF EQUATIONGRAF EQUATION
1818
1
STABLE CHANNELSTABLE CHANNELSTABLE CHANNEL STABLE CHANNEL DESIGNDESIGN
ZORKEFLEE ABU HASANZORKEFLEE ABU HASAN
11
Application of Beginning of Motion Application of Beginning of Motion to Practical Problemsto Practical Problems
The initiation of motion is involved in many The initiation of motion is involved in many hydrauics problem such as local scour slopehydrauics problem such as local scour slopehydrauics problem such as local scour, slope hydrauics problem such as local scour, slope stability, stable channel design, etc.stability, stable channel design, etc.The design of stable channels is very important.The design of stable channels is very important.Incipient motion criteria presented earlier Incipient motion criteria presented earlier (Incipient Motion) apply to the channel bottom. (Incipient Motion) apply to the channel bottom. Certain modifications of incipient motion criteriaCertain modifications of incipient motion criteriaCertain modifications of incipient motion criteria Certain modifications of incipient motion criteria are needed before they can be applied to stable are needed before they can be applied to stable channel design.channel design.
22
2
Stability of a particle on a sloping surface
Source: Chang,
33
1988
Stability of a particle on a sloping surfaceStability of a particle on a sloping surface
For particle on a side slope, there is a gravitional forcegravitional force component acting parallel to the slope which tends to roll the particle down.Forces acting on a Lane (1953) developed
t bl h l d iForces acting on a particle at point A;FD → tractive forceW → submerged weight
44
stable channel design curve for trapezoids with different typical slope.[Fig 2.14, Yang (1996)]
3
Stability of a particle on a sloping surfaceStability of a particle on a sloping surface
Source: Yang, 1996
55
Stability of a particle on a sloping surfaceStability of a particle on a sloping surface
Figure 2.14 (Yang, 1996) are based on maximum allowable tractive forceFig 2.14a: for the channel sidesFig 2.14b: for the channel bottomFig 2.14 indicates that h t tshear stress at:
channel bottom = γd50Schannel slope = 0.75 γd50S
66Source: Yang, 1996
4
Stability of a particle on a sloping surfaceStability of a particle on a sloping surface
The shear stress on channel side at incipient motion
2/1
2
2
sw tanθtan1tancosθWτ ⎟⎟⎠
⎞⎜⎜⎝
⎛−=
φφ
incipient motion
φtanWτ sb =At channel bottom, θ = 0,
Ratio of limiting forces acting on the channel side and channel bottom
77
φφ 2
22/1
2
2
b
w
sinθsin1
tanθtan1cos θ
ττK −=⎟⎟
⎠
⎞⎜⎜⎝
⎛−==
Stability of a particle on a sloping surfaceStability of a particle on a sloping surface
Value of τb can be obtained from Shield Diagram or US Bureau
f R l tiof Reclamationφ - Angle of repose as Fig 2.13, Yang (1996)Value K can be estimated from Fig 5.7, Chang (1988)
88
Chang (1988)
Source: Yang, 1996
5
Stability of a particle on a sloping surfaceStability of a particle on a sloping surface
99
Source: Chang, 1988
Sample ComputationSample Computation
1010
6
1111
1212
7
1313
1414
8
1515
REFERENCES
1. CIVIL ENGINEERING HYDRAULICS, C. NALLURI AND R.E. FEATHERSTONE
2. SEDIMENT TRANSPORT TECHNOLOGY, WATER AND SEDIMENT
DYNAMICS, DARYL B. SIMONS AND FUAT SENTURK
3. FLUVIAL PROCESSES IN RIVER ENGINEERING, HOWARD H. CHANG
4. SEDIMENT TRANSPORT, THEORY AND PRACTICE, CHIH TED YANG
5. KAJIAN PENGUMPULAN DATA DAN ANALISIS ENDAPAN SUNGAI,
LAPORAN AKHIR, REDAC