Fluvial Geomorphology.pdf

7/26/2019 Fluvial Geomorphology.pdf

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A STUDY OF FLUVIAL GEOMORPHOLOGY

ASPECTS OF HYDRAULIC DESIGN

A STUDY OF FLUVIAL GEOMORPHOLOGY

ASPECTS OF HYDRAULIC DESIGN

A. David Parr, Ph.D.and John Shelley

CEAE DepartmentUniversity of Kansas

(Funded by KDOT)

A. David Parr, Ph.D.and John Shelley

CEAE DepartmentUniversity of Kansas

(Funded by KDOT)


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Jim Richardson

Brad Rognlie

Mike Orth

KDOT Bridge Section

Jim RichardsonJim Richardson

Brad RognlieBrad Rognlie

Mike OrthMike Orth

KDOT Bridge SectionKDOT Bridge Section

AcknowledgmentsAcknowledgments


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Stable Channel DesignStable Channel DesignStable Channel DesignKDOT is sometimes required to realign

short reaches of alluvial channels to

facilitate highway improvements or toprovide protection for highway structuresor roadway embankments.

The new stream reaches should be dynamicallystable and should have geomorphic properties thatare characteristic of natural streams in similar

settings.

They should also be hydraulically and ecologicallycompatible with the contiguous upstream anddownstream stream reaches.

KDOT is sometimes required to realignKDOT is sometimes required to realignshort reaches of alluvial channels toshort reaches of alluvial channels to

facilitate highway improvements or tofacilitate highway improvements or toprovide protection for highway structuresprovide protection for highway structuresor roadway embankments.or roadway embankments.

The new stream reaches should be dynamicallyThe new stream reaches should be dynamicallystable and should have geomorphic properties thatstable and should have geomorphic properties thatare characteristic of natural streams in similarare characteristic of natural streams in similarsettings.settings.

They should also be hydraulically and ecologicallyThey should also be hydraulically and ecologicallycompatible with the contiguous upstream andcompatible with the contiguous upstream anddownstream stream reaches.downstream stream reaches.


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Stream Modification - Road ProjectStream ModificationStream Modification -- Road ProjectRoad Project

Old RoadOld Road

Old StreamOld Stream

New StreamNew Stream

New RoadNew Road

(b)(b)

(a)(a)


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Protection - Meanders on the Kansas RiverProtection - Meanders on the Kansas River

(a)

(b)


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Bank-full Discharge ConditionsBankBank--full Discharge Conditionsfull Discharge Conditions

Copeland* states Bank-full discharge is

the maximum discharge that a steam can

convey without overflowing into the

floodplain. The water surface elevation

for this condition is called the bank-fullstage.

Bank-full discharge is also referred to asthe channel-forming discharge.

Copeland* statesCopeland* states BankBank--full discharge isfull discharge is

the maximum discharge that a steam canthe maximum discharge that a steam can

convey without overflowing into theconvey without overflowing into the

floodplainfloodplain.. The water surface elevationThe water surface elevation

for this condition is called the bankfor this condition is called the bank--fullfullstage.stage.

BankBank--full discharge is also referred to asfull discharge is also referred to asthethe channelchannel--forming dischargeforming discharge..

*http://chl.erdc.usace.army.mil/library/publications/chetn/pdf/chetn-viii-5.pdf*http://chl.erdc.usace.army.mil/library/publications/chetn/pdf/chetn-viii-5.pdf


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Upstream Supply ReachUpstream Supply ReachUpstream Supply Reach

Project SiteProject Site

Flow

Riffle on Stable Upstream

Supply ReachRiffle on Stable Upstream

Supply Reach

Supply ReachCross SectionSupply ReachCross Section

Sinuosity = Lstream/Lvalley


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Bankfull Conditions for Supply

Reach Cross Section(1.2 to 2 year recurrence interval)

Bankfull Conditions for SupplyBankfull Conditions for Supply

Reach Cross SectionReach Cross Section((1.2 to 2 year recurrence interval)

Wbf

Abf

dmax

Wbf

= bankfull width

Abf= bankfull area

dbf= Abf/Wbf= bankfull depth

Bankfull

Stage


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Determination of Bank-full Stage(http://www.stockton.edu/~epsteinc/rosgen~1.htm)

Determination of Bank-full Stage(http://www.stockton.edu/~epsteinc/rosgen~1.htm)

Involves assessing the elevation wherethe channel, under bank-full dischargeconditions, ends and the floodplain begins.The indicators used to assess thiselevation are as follows:

Top of the point bar

A change in vegetation

Slope change in channel cross section

Top of the undercut slopeChange in particle size (where soils end andsediments begin),

Drift lines and water marks

Involves assessing the elevation wherethe channel, under bank-full dischargeconditions, ends and the floodplain begins.The indicators used to assess thiselevation are as follows:

Top of the point bar

A change in vegetation

Slope change in channel cross section

Top of the undercut slopeChange in particle size (where soils end andsediments begin),

Drift lines and water marks


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University of Kansas StudiesUniversity of Kansas StudiesUniversity of Kansas Studies

Guidelines for Stream Realignment Design KAMMethod

McEnroe, Young and ShelleyReport No. K-TRAN KU-08-2

Stream Realignment Design using a ReferenceReach ARR Method

McEnroe, Young and ShelleyReport No. K-TRAN KU-09-4

A Study of Fluvial Geomorphology Aspects ofHydraulic Design (HEC-RAS applications)

Parr and Shelley

Report No. K-TRAN: KU-08-5

Guidelines for Stream Realignment DesignGuidelines for Stream Realignment Design KAMKAMMethodMethod

McEnroe, Young and ShelleyMcEnroe, Young and ShelleyReport No. KReport No. K--TRAN KUTRAN KU--0808--22

Stream Realignment Design using a ReferenceStream Realignment Design using a ReferenceReachReach ARR MethodARR Method

McEnroe, Young and ShelleyMcEnroe, Young and ShelleyReport No. KReport No. K--TRAN KUTRAN KU--0909--44

A Study of Fluvial Geomorphology Aspects of

Hydraulic Design (HEC-RAS applications)Parr and ShelleyParr and Shelley

Report No. KReport No. K--TRAN: KUTRAN: KU--0808--55

This StudyThis Study


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KAM and ARR MethodsKAM and ARR MethodsKAM and ARR Methods

Consider alluvial (noncohesive) and threshold(cohesive) channels.

StrengthsInclude planform design for stream meanders and

pool spacingDesigns pool depth

Uses a simple version of the Meyer-Peter Mueller

sediment transport equation for analytical methodsARR incorporates features of both analytical andreference reach methods

Consider alluvial (noncohesive) and thresholdConsider alluvial (noncohesive) and threshold(cohesive) channels.(cohesive) channels.

StrengthsStrengths

Include planform design for stream meanders andInclude planform design for stream meanders and

pool spacingpool spacingDesigns pool depthDesigns pool depth

Uses a simple version of the MeyerUses a simple version of the Meyer--Peter MuellerPeter Mueller

sediment transport equation for analytical methodssediment transport equation for analytical methodsARR incorporates features of both analytical andARR incorporates features of both analytical andreference reach methodsreference reach methods


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KAM and ARR Methods (Cont.)KAM and ARR Methods (Cont.)KAM and ARR Methods (Cont.)

Limitations

Plane bed (no bedforms)

Wide channels (Large width to depthratios)

No consideration of grain sizedistribution other than d50Does not allow for separation of bedand bank hydraulic roughness

LimitationsLimitations

Plane bed (no bedforms)Plane bed (no bedforms)

Wide channels (Large width to depthWide channels (Large width to depthratios)ratios)

No consideration of grain sizeNo consideration of grain sizedistribution other than ddistribution other than d5050Does not allow for separation of bedDoes not allow for separation of bedand bank hydraulic roughnessand bank hydraulic roughness


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Study ObjectivesStudy ObjectivesStudy ObjectivesDevelop procedures to use HEC-RAS 4.0 in the

design of stable channel reaches for alluvial

streams using the Analytical Approach.

Provide examples for streams with

Sand beds

Gravel/cobble beds.

Compare HEC-RAS methods with McEnroesKAM and ARR Methods.

Develop procedures to use HECDevelop procedures to use HEC--RAS 4.0 in theRAS 4.0 in thedesign of stable channel reaches for alluvialdesign of stable channel reaches for alluvial

streams using thestreams using theAnalytical ApproachAnalytical Approach..

Provide examples for streams withProvide examples for streams with

Sand bedsSand beds

Gravel/cobble beds.Gravel/cobble beds.

Compare HECCompare HEC--RAS methods with McEnroeRAS methods with McEnroessKAM and ARR Methods.KAM and ARR Methods.


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Stable Channel Design in HEC-RASStable Channel Design in HECStable Channel Design in HEC--RASRAS

Uses Steady Flow modeling to determine parameters

needed for the sediment transport modeling components.

Velocity

DepthArea

Only Mannings n-values can be used in the HEC-RAS

steady flow model for resistance.

Uses Hydraulic Design Functions to perform uniform flow

and sediment transport capacity calculations. Brownlie,

Strickler, Limerinos and Manning equations can be usedto account for channel resistance. Brownlie and

Limerinos resistance equations account for bed form

resistance as well as resistance due to grains.

UsesUses Steady FlowSteady Flow modeling to determine parametersmodeling to determine parameters

needed for the sediment transport modeling components.needed for the sediment transport modeling components.

VelocityVelocity

DepthDepthAreaArea

Only ManningOnly Mannings ns n--values can be used in the HECvalues can be used in the HEC--RASRAS

steady flow model for resistance.steady flow model for resistance.

UsesUses Hydraulic Design FunctionsHydraulic Design Functions to perform uniform flowto perform uniform flow

and sediment transport capacity calculations. Brownlie,and sediment transport capacity calculations. Brownlie,

Strickler, Limerinos and Manning equations can be usedStrickler, Limerinos and Manning equations can be usedto account for channel resistance. Brownlie andto account for channel resistance. Brownlie and

Limerinos resistance equations account for bed formLimerinos resistance equations account for bed form

resistance as well as resistance due to grains.resistance as well as resistance due to grains.


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HEC-RAS Hydraulic Design

Functions used in Analytical Design

HECHEC--RAS Hydraulic DesignRAS Hydraulic Design

Functions used in Analytical DesignFunctions used in Analytical Design

Stable Channel Design

Uniform Flow

Sediment Transport Capacity

Stable Channel DesignStable Channel Design

Uniform FlowUniform Flow

Sediment Transport CapacitySediment Transport Capacity

Sand BedsSand Beds

Gravel/Cobble BedsGravel/Cobble Beds


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Resistance Formulas Used

in

Hydraulic Design Functions

Resistance Formulas UsedResistance Formulas Used

inin

Hydraulic Design FunctionsHydraulic Design Functions


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HEC-RAS Resistance Formulas

for Alluvial Channels

HECHEC--RAS Resistance FormulasRAS Resistance Formulas

for Alluvial Channelsfor Alluvial Channels

Equation Applicability Strengths Limitations

Manning All natural and artificialstreams.

Easy to use and to understand.

Required for HEC-RAS hydraulic

modeling.

Requires a high level of

engineering judgment to

choose an appropriate

value from a table or from a

book of reference streams.

Stricker Cobble bed streamsdominated by grain sizefriction.

Quantified the hydraulics lossesdue to grain size friction based on

measurable parameters.

Does not include losses dueto bed forms. May be

unrealistically low.

Limerinos Stream beds withsediment sizes from

coarse sand to cobble

under an upper flowregime.

Includes losses due to both grain

roughness and bedforms. Based

on measurable parameters.

Not applicable to other

sediment sizes or to the

lower regime flow.

Brownlie Sand bed streams ofeither an upper or a

lower regime.

Includes losses due to both grain

roughness and bedforms. Based

on measurable parameters. Can be

used for either the upper or the

lower flow regime. Correlates with

the Brownlie sediemnt transport

function.

Not applicable to other

sediment sizes.


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Mannings EquationManningMannings Equations Equation

V= Mean Velocity in ft/sec,

1.49 = coefficient for English Units (1.0 for Metric),n = Mannings n value,

R = Hydraulic radius, ft. = Area/Wetted Perimeter,

S = Slope of the Energy Grade Line.

(Bed slope for uniform flow)

V= Mean Velocity in ft/sec,V= Mean Velocity in ft/sec,

1.49 = coefficient for English Units (1.0 for Metric),1.49 = coefficient for English Units (1.0 for Metric), n = Manningn = Mannings n value,s n value,

R = Hydraulic radius, ft. = Area/Wetted Perimeter,R = Hydraulic radius, ft. = Area/Wetted Perimeter,

S = Slope of the Energy Grade Line.S = Slope of the Energy Grade Line.

(Bed slope for uniform flow)(Bed slope for uniform flow)

2 /3 1/ 21.49n R S

V=


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Strickler EquationStrickler EquationStrickler Equation

1/ 6

s

s

Rn k

k

=

50

90

, ,

.

0.0342

0.0342

s

s

where k Nikuradse equivalet sand roughness ft or m d

for natural channels and d for riprap lined channels

R Strickler function for natrual channelsk

for velocity and stone size calculations in riprap chann

= =

= =

=

0.038

els

for discharge calculations in riprap channels

R hydraulic radius

==


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Limerinos EquationLimerinos EquationLimerinos Equation

d84

= the particle size, ft, for which 84% of thesediment mixture is finer. Data ranged from0.00328 to 0.820 ft (1.5 to 250 mm). BIG STUFF

n = Mannings n value. Data ranged from 0.02 to

0.10.

R = Hydraulic radius, ft. Data ranged from 1 to 6ft (0.35 to 1.83 m).

dd8484 = the particle size, ft, for which 84% of the= the particle size, ft, for which 84% of the

sediment mixture is finer. Data ranged fromsediment mixture is finer. Data ranged from0.00328 to 0.820 ft (1.5 to 250 mm).0.00328 to 0.820 ft (1.5 to 250 mm). BIG STUFFBIG STUFF

n = Manningn = Mannings n value. Data ranged from 0.02 tos n value. Data ranged from 0.02 to

0.10.0.10.

R = Hydraulic radius, ft. Data ranged from 1 to 6R = Hydraulic radius, ft. Data ranged from 1 to 6ft (0.35 to 1.83 m).ft (0.35 to 1.83 m).

1/ 6

10

84

0.0926

1.16 2.0 log

Rn

Rd

=

+


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Brownlie Resistance Equations

Sand Only

Brownlie Resistance EquationsBrownlie Resistance Equations

Sand OnlySand Only

d50 = the particle size, ft, for which 50% of thesediment mixture is finer by weight,

s = the geometric standard deviation of the

sediment mixture.

dd5050 = the particle size, ft, for which 50% of the= the particle size, ft, for which 50% of thesediment mixture is finer by weight,sediment mixture is finer by weight,

ss = the geometric standard deviation of the= the geometric standard deviation of the

sediment mixture.sediment mixture.

( )

( )

0.1374

0.1670.1112 0.160550

50

0.0.6620.1670.0395 0.1282

50

50

1.6940 0.034

1.0213 0.034

Lower Regime

Rn S dd

Upper Regime

Rn S d

d

=

=


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Brownlie Resistance Equations

(Cont.)

Brownlie Resistance EquationsBrownlie Resistance Equations

(Cont.)(Cont.)'

' '

'

'1/ 3

50

0.8 1.25

0.006

1.74

( 1)

( 2.65 )

g g

g g g

g g

g

g

s

s

Lower Regime F F

Transition F F F

Upper Regime S or F F

FS

VF grain Froude number

s gdwhere

s sediment specific gravity for sand

=

= =

=


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HEC-RAS

Sediment Transport

Equations

HECHEC--RASRAS

Sediment TransportSediment Transport

EquationsEquations


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Sand Beds - Brownlie SedimentTransport Equation

Sand BedsSand Beds -- Brownlie SedimentBrownlie Sediment

Transport EquationTransport Equation

Used in the Stable Channel Hydraulic Design

Function for sand bed channels only. Themethod is called the Copeland Method.

Based on dimensional analysis and regressionof a very large body of field and laboratorysediment transport data for sand beds.

Only applied to the movable bed does notconsider sediment transport from the mainchannel banks.

Used in the Stable Channel Hydraulic DesignUsed in the Stable Channel Hydraulic Design

Function forFunction for sand bed channels onlysand bed channels only. The. Themethod is called the Copeland Method.method is called the Copeland Method.

Based on dimensional analysis and regressionBased on dimensional analysis and regressionof a very large body of field and laboratoryof a very large body of field and laboratorysediment transport data for sand beds.sediment transport data for sand beds.

Only applied to the movable bedOnly applied to the movable bed does notdoes notconsider sediment transport from the mainconsider sediment transport from the mainchannel banks.channel banks.


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Brownlie Sediment Transport Equation

(Sand Bed Natural Channels)

Brownlie Sediment Transport EquationBrownlie Sediment Transport Equation(Sand Bed Natural Channels)(Sand Bed Natural Channels)

( ) 0.33011.978 0.6601

509022( ) /g goC F F S r d

=

( )

*

50

50

0.5293 0.14

/ /

4.596o

g s

go

where C bed material concentration in ppm by weight

r representative grain roughness height

d geometric mean grain size of bed material

S slope of energy grade line

F V gd grain Froude number

F S

==

=

=

= =

=

( )( )

*

05 0.1606

7.7

0.6

3

50

0.22 0.06(10)

/

/

o

g

Y

g

g s

g

critical grain Froude number

Y critical shear stress

geometric standard deviation of bed material

Y R

R gd grain Reynolds number

=

= + =

=

=

= =


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Gravel/Cobble Beds Sediment Transport

Potential Functions

Gravel/Cobble BedsGravel/Cobble Beds Sediment TransportSediment Transport

Potential FunctionsPotential Functions

Ackers-White

Engelund-Hansen

Laursen-Copeland

Meyer-Peter Muller

Toffaleti

Yang

AckersAckers--WhiteWhite

EngelundEngelund--HansenHansen

LaursenLaursen--CopelandCopeland

MeyerMeyer--Peter MullerPeter Muller

ToffaletiToffaleti

YangYang


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Ranges for Sediment Transport FunctionsRanges for Sediment Transport FunctionsRanges for Sediment Transport Functions

dran

ge,mm

dran

ge,mm

Mean

d,mm

Mean

d,mm

Veloc

ity,fps

Veloc

ity,fps

Depth

,ft

Depth

,ft

Energ

yGrad

Energ

yGrad

Width

ft

Width

ft

Temp

,oF

Temp

,oF

Spec

Gravity

Spec

Gravity


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Sand Beds

HEC-RAS Stable ChannelDesign

Sand BedsSand Beds

HECHEC--RAS Stable ChannelRAS Stable ChannelDesignDesign


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HR Stable Channel DesignHR Stable Channel DesignHR Stable Channel Design

Copeland Method using Brownlie Resistance

and Sediment Transport Eqs.

Sand Bed Channels Only.Resistance Due to Sidewall Roughness, Grains

of the Bed Material and Bed Forms.

Sediment Transport from Bed Only.

Sidewall Roughness Method Applied.

Does not specify channel plan form geometry or

profile features. (See McEnroe KAM and ARR

methods.)

Copeland Method using Brownlie ResistanceCopeland Method using Brownlie Resistance

and Sediment Transport Eqs.and Sediment Transport Eqs.

Sand Bed Channels Only.Sand Bed Channels Only.Resistance Due to Sidewall Roughness, GrainsResistance Due to Sidewall Roughness, Grains

of the Bed Material and Bed Forms.of the Bed Material and Bed Forms.

Sediment Transport from Bed Only.Sediment Transport from Bed Only.

Sidewall Roughness Method Applied.Sidewall Roughness Method Applied.

Does not specify channel plan form geometry orDoes not specify channel plan form geometry or

profile features. (See McEnroe KAM and ARRprofile features. (See McEnroe KAM and ARR

methods.)methods.)


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HR Stable Channel Design

Requirements

HR Stable Channel DesignHR Stable Channel Design

RequirementsRequirements

Upstream Supply Channel: (Trapezoidal channel

geometry required.) Bottom width, depth,channel slope, side slopes, discharge,

Mannings n for sidewalls, sediment gradation or

sediment conc.Design Channel: Mannings n for sidewalls, side

slopes, sediment gradation ,and either the

bottom width, depth, or channel slope.Both: Need d16, d50 and d84

Upstream Supply Channel:Upstream Supply Channel: (Trapezoidal channel(Trapezoidal channel

geometry required.) Bottom width, depth,geometry required.) Bottom width, depth,channel slope, side slopes, discharge,channel slope, side slopes, discharge,

ManningMannings n for sidewalls, sediment gradation ors n for sidewalls, sediment gradation or

sediment conc.sediment conc.Design Channel:Design Channel: ManningMannings n for sidewalls, sides n for sidewalls, side

slopes, sediment gradation ,and either theslopes, sediment gradation ,and either the

bottom width, depth, or channel slope.bottom width, depth, or channel slope. Both:Both: Need dNeed d1616, d, d5050 and dand d8484


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Procedure for Stable Channel Design of

Sand Bed Channels

Procedure for Stable Channel Design ofProcedure for Stable Channel Design of

Sand Bed ChannelsSand Bed Channels Establish the bank-full properties of an upstream

reference reach riffle cross section. Discharge, cross

section geometry via station-elevation data, stage, bedmaterial (d16, d50 and d84), longitudinal energy grade line

slope.

Open the Uniform Flow function with the Manning for the

bank resistance and Brownlie for the movable bed

resistance. Input the slope and discharge. By iteration,

determine the bank n-values needed to obtain the

desired bank-full water surface elevation (stage) for thegiven bank-full discharge and slope.

Establish the bankEstablish the bank--full properties of an upstreamfull properties of an upstream

reference reach riffle cross section. Discharge, crossreference reach riffle cross section. Discharge, cross

section geometry via stationsection geometry via station--elevation data, stage, bedelevation data, stage, bedmaterialmaterial ((dd1616, d, d5050 and dand d8484)), longitudinal energy grade line, longitudinal energy grade line

slope.slope.

Open the Uniform Flow function with the Manning for theOpen the Uniform Flow function with the Manning for the

bank resistance and Brownlie for the movable bedbank resistance and Brownlie for the movable bed

resistance. Input the slope and discharge. By iteration,resistance. Input the slope and discharge. By iteration,

determine the bank ndetermine the bank n--values needed to obtain thevalues needed to obtain the

desired bankdesired bank--full water surface elevation (stage) for thefull water surface elevation (stage) for thegiven bankgiven bank--full discharge and slope.full discharge and slope.


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Sand Bed Channels (Cont.)


Sand Bed Channels (Cont.)Sand Bed Channels (Cont.)

Using the bank n-values from the previous step,change the resistance formula for the bed to

Manning then by iteration determine theappropriate n-value for the bed to obtain thedesired bankfull stage.

Create an upstream supply reach that has threeof the natural channels using the bank and bedn-values determined above for the bankfullchannel.

Run the HEC-RAS model.

Using the bank nUsing the bank n--values from the previous step,values from the previous step,change the resistance formula for the bed tochange the resistance formula for the bed to

Manning then by iteration determine theManning then by iteration determine theappropriate nappropriate n--value for the bed to obtain thevalue for the bed to obtain thedesired bankfull stage.desired bankfull stage.

Create an upstream supply reach that has threeCreate an upstream supply reach that has threeof the natural channels using the bank and bedof the natural channels using the bank and bednn--values determined above for the bankfullvalues determined above for the bankfullchannel.channel.

Run the HECRun the HEC--RAS model.RAS model.


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Sand Bed Channels (Cont.)


Sand Bed Channels (Cont.)Sand Bed Channels (Cont.)

Determine an equivalent trapezoidal channelthat has the same conveyance as the natural

supply reach. Open the Stable Channel Designfunction.

Input the side slopes, base width, bank n-values

and the energy grade line slope of theequivalent upstream supply channel.

Input the side slopes and bank n-values for thedesign channel.

Run the Stable Channel Design model.

Determine an equivalent trapezoidal channelDetermine an equivalent trapezoidal channelthat has the same conveyance as the naturalthat has the same conveyance as the natural

supply reach. Open the Stable Channel Designsupply reach. Open the Stable Channel Designfunction.function.

Input the side slopes, base width, bank nInput the side slopes, base width, bank n--valuesvalues

and the energy grade line slope of theand the energy grade line slope of theequivalent upstream supply channel.equivalent upstream supply channel.

Input the side slopes and bank nInput the side slopes and bank n--values for thevalues for thedesign channel.design channel.

Run the Stable Channel Design model.Run the Stable Channel Design model.

S d B d E l


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Sand Bed ExampleSand Bed ExampleSand Bed Example

49.021.6

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80

Station (ft)

Ele

vation

(ft)

Sta-Elev Bankfull Elevation Movable Bed

49.021.6

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80

Station (ft)

Elev

ation

(ft)


2828 4444

Bank-full Conditions

d16, d50, d84 = 1.33, 2 and 3 mm, respectively

Q = 325 cfsStage = 7 ft

Slope = 0.00157

BankBank--full Conditionsfull Conditions

dd1616, d, d5050, d, d8484 = 1.33, 2 and 3 mm, respectively= 1.33, 2 and 3 mm, respectively

Q = 325 cfsQ = 325 cfs Stage = 7 ftStage = 7 ft

Slope = 0.00157Slope = 0.00157

U if Fl ith Fi l M i lU if Fl ith Fi l M iU if Fl ith Fi l M i ll


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Uniform Flow with Final Mannings n values(Initially Brownlie for movable bed, unknown for banks)

Uniform Flow with Final ManningUniform Flow with Final Mannings n valuess n values(Initially Brownlie for movable bed, unknown for banks)(Initially Brownlie for movable bed, unknown for banks)

N t l S l R hN t l S l R hN t l S l R h


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Natural Supply ReachNatural Supply ReachNatural Supply Reach

E i l t T id l Ch lE i l t T id l Ch lE i l t T id l Ch l


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Equivalent Trapezoidal ChannelEquivalent Trapezoidal ChannelEquivalent Trapezoidal Channel

Abnk Pbnkh

0

5

10

15

20

0 10 20 30 40 50 60 70 80

Station(ft)

E

levation

(ft)

StaElevPoints Bankfull WaterSurface

EquivalentChannel MovableBed

0

5

10

15

20

0 10 20 30 40 50 60 70 80

Station(ft)

Ele

vation

(ft)

StaElevPoints Bankfull WaterSurface

EquivalentChannel MovableBed

Equivalent

Trapezoidal ChannelEquivalent

Trapezoidal Channel

T id l Ch l S l R hT id l Ch l S l R hTrape oidal Channel S ppl Reach


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Trapezoidal Channel Supply ReachTrapezoidal Channel Supply ReachTrapezoidal Channel Supply Reach

St bl Ch l D i F tiStable Channel Design F nctionStable Channel Design Function


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Stable Channel Design FunctionStable Channel Design FunctionStable Channel Design Function

ComputeComputeCompute


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ComputeComputeCompute

Select Design Channel for b = 20 ftSelect Design Channel for b = 20 ftSelect Design Channel for b = 20 ft


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Select Design Channel for b = 20 ftSelect Design Channel for b = 20 ftSelect Design Channel for b = 20 ft

20 FT20 FT

Stability Curve Width vs SlopeStability Curve Width vs SlopeStability Curve Width vs Slope


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Stability Curve, Width vs. SlopeStability Curve, Width vs. SlopeStability Curve, Width vs. Slope

181.42 ppm181.42 ppm


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Gravel/Cobble Beds

HEC-RAS Sediment

Transport Capacity

Function

Gravel/Cobble BedsGravel/Cobble Beds

HECHEC--RAS SedimentRAS Sediment

Transport CapacityTransport Capacity

FunctionFunction


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HR Sediment Transport Capacity (STC)HR Sediment Transport Capacity (STC)HR Sediment Transport Capacity (STC)Grain size classes are input as grain size

and percent finer.

Computes STC for each size class, gsi

Total STC is computed by the equationgs,total = pigsiwhere pi = fraction of size class i in the bed.

Can compute the total STC for all sixSediment Transport Potential functions.

Grain size classes are input as grain sizeGrain size classes are input as grain sizeand percent finer.and percent finer.

Computes STC for each size class, gComputes STC for each size class, gsisi

Total STC is computed by the equationTotal STC is computed by the equationggs,totals,total == ppiiggsisiwhere pwhere pii = fraction of size class i in the bed.= fraction of size class i in the bed.

Can compute the total STC for all sixCan compute the total STC for all sixSediment Transport Potential functions.Sediment Transport Potential functions.


46/84

4646

Gravel/Cobble ExampleGravel/Cobble ExampleGravel/Cobble Example

The stream has the following bank-full

conditions

Water surface elevation = 11.7 feetDischarge = 3,100 cfs

Slope = 0.0015.

The stream has the following bank-full

conditions

Water surface elevation = 11.7 feetDischarge = 3,100 cfs

Slope = 0.0015.

12027.78

0

10

20

30

0 20 40 60 80 100 120 140 160

Station (ft)

E

levation(ft)


12027.78

0

10

20

30

0 20 40 60 80 100 120 140 160

Station (ft)

Elevation(ft)


5252 9696


47/84

4747

Pebble Count for Gravel/Cobble StreamPebble Count for Gravel/Cobble StreamPebble Count for Gravel/Cobble StreamINCHES PARTICLE MILLIMETER SIZE CLASS COUNT % CUM % Dtop(mm)

Silt/Clay < 0.062 S/C 12 12 12

Very Fine .062 - .125 S 7 7 19 0.125

Fine .125 - .25 A 2 2 21 0.25

Medium .25 - .50 N 2 2 23 0.5

Coarse .50 - 1.0 D 4 4 27 1

.04 - .08 Very Coarse 1.0 - 2 S 3 3 30 2.00

.08 - .16 Very Fine 2 - 4 12 12 42 4.00

.16 - .24 Fine 4 - 5.7 G 2 2 44 5.7

.24 - .31 Fine 5.7 - 8 R 3 3 47 8.00

.31 - .47 Medium 8 - 11.3 A 1 1 48 11.3

.47 - .63 Medium 11.3 - 16 V 0 0 48 16.00

.63 - .94 Coarse 16 - 22.6 E 2 2 50 22.6

.94 - 1.26 Coarse 22.6 - 32 L 5 5 55 32.00

1.26 - 1.9 Very Coarse 32 - 45 S 7 7 62 45.00

1.9 - 2.5 Very Coarse 45 - 64 6 6 68 64.00

2.5 - 3.8 Small 64 - 90 C - 6 6 74 90.00

3.8 - 5.0 Small 90 - 128 O L 6 6 80 128

5.0 - 7.6 Large 128 - 180 B E 6 6 86 180

7.6 - 10 Large 180 - 256 B S 5 5 91 256

10 - 15 Small 256 - 362 B D 1 1 92 362

15 - 20 Small 362 - 512 O E 1 1 93 512

20 - 40 Medium 512 - 1024 U R 0 0 93 1024

40 - 160 Lrg to Very Lrg 1024 - 2048 L S 0 0 93 2048

BEDROCK BDRK 7 7 100

NOTENOTE


48/84

4848

Log-probability plot of Bed MaterialLogLog--probability plot of Bed Materialprobability plot of Bed Material

Sand Gravel Cobble

Make New HEC-RAS Model with oneMake New HECMake New HEC--RAS Model with oneRAS Model with one


49/84

4949

cross section and no dischargecross section and no dischargecross section and no discharge

Uniform Flow Bed uses Limerinos banksUniform FlowUniform Flow Bed uses Limerinos banksBed uses Limerinos banks


50/84

5050

Uniform Flow Bed uses Limerinos, banks

use Manning (T&E gives nbank = 0.077)

Uniform FlowUniform Flow Bed uses Limerinos, banksBed uses Limerinos, banks

use Manning (T&E gives nuse Manning (T&E gives nbankbank = 0.077)= 0.077)

Uniform Flow Bed uses Mannings BanksUniform FlowUniform Flow Bed uses Mannings BanksBed uses Mannings, Banks


51/84

5151

Uniform Flow Bed uses Mannings, Banks

use n = 0.077 (T&E gives nbed = 0.0363)

Uniform FlowUniform Flow Bed uses Mannings, BanksBed uses Mannings, Banks

use n = 0.077 (T&E gives nuse n = 0.077 (T&E gives nbedbed = 0.0363)= 0.0363)

Create and Run Natural Supply ReachCreate and Run Natural Supply ReachCreate and Run Natural Supply Reach


52/84

5252

pp ypp ypp y

Sediment Transport Capacity FunctionSediment Transport Capacity FunctionSediment Transport Capacity Function


53/84

5353

Sediment Transport Capacity FunctionInput Grain Sizes (Fake size for banks)

Sediment Transport Capacity FunctionSediment Transport Capacity FunctionInput Grain Sizes (Fake size for banks)Input Grain Sizes (Fake size for banks)

Diam, mm % Finer Diam, mm % Finer Diam, mm % Finer

2000 19 0.125 19 2000 19

2000 21 0.25 21 2000 21

2000 23 0.5 23 2000 23

2000 27 1 27 2000 27

2000 30 2 30 2000 30

2000 42 4 42 2000 42

2000 44 5.7 44 2000 44

2000 47 8 47 2000 47

2000 48 11.3 48 2000 48

2000 48 16 48 2000 48

2000 50 22.6 50 2000 502000 55 32 55 2000 55

2000 62 45 62 2000 62

2000 68 64 68 2000 68

2000 74 90 74 2000 74

2000 80 128 80 2000 80

2000 86 180 86 2000 86

2000 91 256 91 2000 91

2000 92 362 92 2000 92

2000 93 512 93 2000 93

2000 93 1024 93 2000 93

2000 93 2048 93 2000 93

ROBLOB Main

Compute Sediment Rating Curve PlotCompute Sediment Rating Curve PlotCompute Sediment Rating Curve Plot


54/84

5454

Compute, Sediment Rating Curve Plot,

Generate Report

Compute, Sediment Rating Curve Plot,Compute, Sediment Rating Curve Plot,

Generate ReportGenerate Report


55/84

Meyer-Peter Mueller Function ResultsMeyerMeyer--Peter Mueller Function ResultsPeter Mueller Function Results


56/84

5656

1010

77

Design 1 (b = 35 ft m = 3:1 hor: vert)Design 1 (b = 35 ft m = 3:1 hor: vert)Design 1 (b = 35 ft m = 3:1 hor: vert)


57/84

5757

Design 1 (b = 35 ft, m = 3:1 hor: vert)Design 1 (b = 35 ft, m = 3:1 hor: vert)Design 1 (b = 35 ft, m = 3:1 hor: vert)

Assume slope

Create 3 cross section model with

trapezoidal xsecs with same ns and Q assupply reach

Run steady flow model

Run Sediment Transport Capacity function

See if STC equals 1083 tons/day if not back

to the top with a new slope

Assume slopeAssume slope

Create 3 cross section model withCreate 3 cross section model with

trapezoidal xsecs with same ntrapezoidal xsecs with same ns and Q ass and Q assupply reachsupply reach

Run steady flow modelRun steady flow model

Run Sediment Transport Capacity functionRun Sediment Transport Capacity function

See if STC equals 1083 tons/daySee if STC equals 1083 tons/day if not backif not back

to the top with a new slopeto the top with a new slope

Design 1 (b = 35 ft, m = 3:1 hor: vert)Design 1 (b = 35 ft, m = 3:1 hor: vert)Design 1 (b = 35 ft, m = 3:1 hor: vert)


58/84

5858

S = 0.003 S = 0.0017

b = 35 Natural Design b = 35 Natural Design

Function Function

A-W 836000 410900... NA A-W 836000 113600... NAE-H 8217 26640 0.31 E-H 8217 9883 0.83

Laur 645200 212400... NA Laur 645200 750300 0.86

MPM 1083 2427 0.45 MPM 1083 1151 0.94

Toff 680.4 627 1.09 Toff 680.4 586.7 1.16

Yang 27290 88360 0.31 Yang 27290 32300 0.84

S = 0.0016 S = 0.00162


Function Function

A-W 836000 992100 0.84 A-W 836000 102100... NA

E-H 8217 8908 0.92 E-H 8217 9105 0.90

Laur 645200 673200 0.96 Laur 645200 688800 0.94

MPM 1083 1063 1.02 MPM 1083 1081 1.00

Toff 680.4 582.9 1.17 Toff 680.4 583.7 1.17

Yang 27290 29000 0.94 Yang 27290 29670 0.92

Nat/Des

Nat/Destons/day

Nat/Des

tons/day

tons/day

Nat/Destons/day

S = 0.003 S = 0.0017


Function Function

A-W 836000 410900... NA A-W 836000 113600... NA

E-H 8217 26640 0.31 E-H 8217 9883 0.83

Laur 645200 212400... NA Laur 645200 750300 0.86

MPM 1083 2427 0.45 MPM 1083 1151 0.94

Toff 680.4 627 1.09 Toff 680.4 586.7 1.16

Yang 27290 88360 0.31 Yang 27290 32300 0.84

S = 0.0016 S = 0.00162


Function Function

A-W 836000 992100 0.84 A-W 836000 102100... NAE-H 8217 8908 0.92 E-H 8217 9105 0.90

Laur 645200 673200 0.96 Laur 645200 688800 0.94

MPM 1083 1063 1.02 MPM 1083 1081 1.00

Toff 680.4 582.9 1.17 Toff 680.4 583.7 1.17

Yang 27290 29000 0.94 Yang 27290 29670 0.92

Nat/Des

Nat/Destons/day

Nat/Des

tons/day

tons/day

Nat/Destons/day

T & E gives S = 0.00162T & E gives S = 0.00162

Final DesignFinal DesignFinal Design


59/84

5959

Design 2 - Select slope and sideDesign 2Design 2 -- Select slope and sideSelect slope and side


60/84

6060

g

slopes, find bslopes, find bslopes, find b

b = 15

bnk ht = 15.62 S = 0.0018 m = 2.5 Function All Grains

RS 0 RS 100 RS 200 A-W 192600...

Station Elevation Station Elevation Station Elevation E-H 12280-46.550 15.620 -46.550 15.800 -46.550 15.980 Laur 901500

-7.500 0.000 -7.500 0.180 -7.500 0.360 MPM 1091

7.500 0.000 7.500 0.180 7.500 0.360 Toff 438.7

46.550 15.620 46.550 15.800 46.550 15.980 Yang 37320

STC in Tons/Dayb = 15

bnk ht = 15.62 S = 0.0018 m = 2.5 Function All Grains

RS 0 RS 100 RS 200 A-W 192600...

Station Elevation Station Elevation Station Elevation E-H 12280-46.550 15.620 -46.550 15.800 -46.550 15.980 Laur 901500

-7.500 0.000 -7.500 0.180 -7.500 0.360 MPM 1091

7.500 0.000 7.500 0.180 7.500 0.360 Toff 438.7

46.550 15.620 46.550 15.800 46.550 15.980 Yang 37320

STC in Tons/Day

S = 0.0018, m = 2.5:1 hor: vertS = 0.0018, m = 2.5:1 hor: vertS = 0.0018, m = 2.5:1 hor: vert

S = 0.0018, m = 2.5:1 hor: vertS = 0.0018, m = 2.5:1 hor: vertS = 0.0018, m = 2.5:1 hor: vert


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6161

S 0.0018, m 2.5:1 hor: vertS 0.0018, m 2.5:1 hor: vertS 0 00 8, 5 o e t

Design Channel, b = 15', hor:vert = 2.5:1, S = 0.0018

0

4

8

12

16

-60 -40 -20 0 20 40 60

Station (ft)

Elevation

(ft)

Design Channel Bankfull Elevation Movable Bed

Design Channel, b = 15', hor:vert = 2.5:1, S = 0.0018

0

4

8

12

16

-60 -40 -20 0 20 40 60

Station (ft)

Elevation

(ft)


b = 15 ft, bank ht = 15.62 ftb = 15 ft, bank ht = 15.62 ft

Design 3 - S = 0.0013, m = 2.5:1 hor: vertDesign 3Design 3 -- S = 0.0013, m = 2.5:1 hor: vertS = 0.0013, m = 2.5:1 hor: vert


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6262

g ,gg ,

0

5

10

-60 -40 -20 0 20 40 60

Station (ft)

Elevation

(ft)


0

5

10

-60 -40 -20 0 20 40 60

Station (ft)Elevation

(ft)


b = 76 ft, bank ht = 8.73 ftb = 76 ft, bank ht = 8.73 ft

4 b = 76.0 1082bnk ht = 8.73 S = 0.0013 m = 2.5 Tons/day

RS 0 RS 100 RS 200 Function All Grains

Station Elevation Station Elevation Station Elevation A-W 388200

-59.825 8.730 -59.825 8.860 -59.825 8.990 E-H 4981

-38 0.000 -38 0.130 -38 0.260 Laur 545400

38 0.000 38 0.130 38 0.260 MPM 108259.825 8.730 59.825 8.860 59.825 8.990 Toff 1078

Yang 19240

Final Design 2MPM Gs (Tons/day) =4 b = 76.0 1082

bnk ht = 8.73 S = 0.0013 m = 2.5 Tons/day

RS 0 RS 100 RS 200 Function All Grains

Station Elevation Station Elevation Station Elevation A-W 388200

-59.825 8.730 -59.825 8.860 -59.825 8.990 E-H 4981

-38 0.000 -38 0.130 -38 0.260 Laur 545400

38 0.000 38 0.130 38 0.260 MPM 1082

59.825 8.730 59.825 8.860 59.825 8.990 Toff 1078

Yang 19240

Final Design 2MPM Gs (Tons/day) = Final Design 3

Sidewall Correction MethodSidewall Correction MethodSidewall Correction Method


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6363

bd

yd

md

1

md

1 1

md

1

md

nwnw

nb

Wd

} 4 /32 /3 1/ 2 2

2 4 /3

3/ 4 3/ 43/ 42 4 /3 2 2

2 4 /3 2 3/ 2

1 1'

1 1 1

square

co

AMetric version of Manning s Equation V R S V S

n n P

Einstein assumed V and S are constant in bank area and sidewall area

V A V A A V

S n P S n P n P S

= =

= = =

( ) ( ) ( )

3/ 2 3/ 2 3/ 2

3/ 2 3/ 2 3/ 2 3/ 2 3/ 2 3/ 2

2 /3 3/ 2 3/ 23/ 2 3/ 2

3/ 2 3/ 2

1

nstant

Constantw b

w b

w b

w bw b w b w w b b

w w b bw w b b w b

P PPn n n

A A A

P PPA A A n n n n P n P n P

n P n Pn n P n P also A A and A A

P n P n P

= = =

= + = + = +

= + = =

64748

Aw/2Aw/2 AbAbAw/2Aw/2

Sidewall ExampleSidewall ExampleSidewall Example

S 0 0002


64/84

6464

50

5

n = 0.025

n = 0.045n = 0.045

12

12

S = 0.0002

nw = 0.040 nw = 0.040nb = 0.025

( ) ( )

2 2

2 2 2

2 /3 2 /3

3/ 2 3/ 2 3/ 2 3/ 2

50 ; 2 5 10 22.4 72.4

(5)(10)50*5 250 ; 2 50 300

2

1 1(0.040) 22.4 (0.025) 50

72.4

0.0300

1.49 (300

0.0300

b w b w

rect tria rect tria

w w b b

P ft P ft P P P ft

A ft A ft A A A ft

n n P n PP

n

Q

= = + = = + =

= = = = = + =

= + = +

=

=

( ) ( )

5/33

2/3

3/ 2 3/ 22 2

3/ 2 3/ 2

2 2

)0.0002 543 /

(72.4)(0.040) (0.025)22.4 50

300 143 300 157(0.030) 72.4 (0.030) 72.4

50 250

w b

w b

ft s

A ft and A ft

Geometric values A ft and A ft

=

= = = =

= =

ARR Analytical MethodARR Analytical MethodARR Analytical Method


65/84

6565

( )

( )( )

5/3

2/3

3/ 250

3/2

50

50

50

1.49. 4 2

8 0.047 . 4 6

0.047 1. 4 8

0.047 1

, , , , 2.65, , .

dd d

d d

s

m sm

m d d m

d d s

d d d m d s m m

AManning for Design Channel Q S ARR Eq

n P

bMPM B yS d ARR Eq

y S G dB B b b ARR Eq

y S G d

Given Q m n S S G d b and y

=

=

= =

= =

. 4 2 4 8

, .

d dUse iteration to solve Eqs and for b and y by iteration

Subscripts d and m denote design channel and match reach channels respectively

bd

yd

md

1

md

1 1

md

1

md

nwnw

nb

Wd

nd = Manningscomposite n

ARR vs HEC-RASComposite n 0 061 from HEC RAS Supply Reach

ARR vs HECARR vs HEC--RASRASComposite nComposite n 0 061 from HEC0 061 from HEC RAS Supply ReachRAS Supply Reach


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6666

Composite n 0.061 from HEC-RAS Supply ReachComposite nComposite n 0.061 from HEC0.061 from HEC--RAS Supply ReachRAS Supply ReachARR solution for Design 1 ( HR solution bd= 35 ft) dm(mm)

md = 3 Sd = 0.001622 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

10.96 42.9 829.9 112.2 108.6 3100 0.000

ARR solution for Design 2 ( HR solution bd= 15 ft) dm(mm)

md = 2.5 Sd = 0.0018 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

13.38 22.8 752.1 94.8 89.7 3100 0.000

ARR solution for Design 3 ( HR solution bd = 76 ft) dm (mm)

md = 2.5 Sd = 0.0013 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

11.91 58.8 1055.6 123.0 118.4 3897.35 797.350


md = 3 Sd = 0.001622 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

10.96 42.9 829.9 112.2 108.6 3100 0.000


md = 2.5 Sd = 0.0018 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

13.38 22.8 752.1 94.8 89.7 3100 0.000

ARR solution for Design 3 ( HR solution bd = 76 ft) dm (mm)

md = 2.5 Sd = 0.0013 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

11.91 58.8 1055.6 123.0 118.4 3897.35 797.350


md = 3 Sd = 0.001622 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

10.96 42.9 829.9 112.2 108.6 3100 0.000


md = 2.5 Sd = 0.0018 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

13.38 22.8 752.1 94.8 89.7 3100 0.000

ARR solution for Design 3 ( HR solution bd = 76 ft) dm(mm)

md = 2.5 Sd = 0.0013 nd = 0.061 22.6yd bd Ad Pd Wb Qb Q

11.91 58.8 1055.6 123.0 118.4 3897.35 797.350


md = 3 Sd = 0.001622 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

10.96 42.9 829.9 112.2 108.6 3100 0.000


md = 2.5 Sd = 0.0018 nd = 0.061 22.6

yd bd Ad Pd Wb Qb Q

13.38 22.8 752.1 94.8 89.7 3100 0.000

ARR solution for Design 3 ( HR solution bd = 76 ft) dm(mm)

md = 2.5 Sd = 0.0013 nd = 0.061 22.6yd bd Ad Pd Wb Qb Q

11.91 58.8 1055.6 123.0 118.4 3897.35 797.350

bHR = 35 ft

bARR= 42.9 ftbHR/bARR= 0.82

bHR = 35 ft


bHR = 15 ft


bHR = 15 ft


ARR did not converge

bHR = 76 ft


ARR did not convergebHR = 76 ft


ARR vs HEC-RASComposite n values from HR Design Reaches

ARR vs HECARR vs HEC--RASRASComposite n values from HR Design ReachesComposite n values from HR Design Reaches


67/84

6767

Composite n values from HR Design ReachesComposite n values from HR Design ReachesComposite n values from HR Design Reaches(b) ARR solution for Design 1 ( HR solution b

d

= 35 ft)

md = 3 Sd = 0.00162 nd = 0.066 dm (mm)= 22.6

yd bd Ad Pd Wb Qb Q

12.35 33.2 867.7 111.3 107.3 3100 0.000

(c) ARR solution for Design 2 ( HR solution bd= 15 ft)

md = 2.5 Sd = 0.0018 nd = 0.072 dm (mm)= 22.6

yd bd Ad Pd Wb Qb Q

15.19 17.8 847.3 99.6 93.8 3100 0.000

(d) ARR solution for Design 3 ( HR solution bd= 76 ft)

md = 2.5 Sd = 0.0013 nd = 0.054 dm (mm)= 22.6

yd bd Ad Pd Wb Qb Q

11.91 58.8 1055.6 123.0 118.4 4402.562 1302.562

(b) ARR solution for Design 1 ( HR solution bd= 35 ft)md = 3 Sd = 0.00162 nd = 0.066 dm (mm)= 22.6

yd bd Ad Pd Wb Qb Q

12.35 33.2 867.7 111.3 107.3 3100 0.000

(c) ARR solution for Design 2 ( HR solution bd= 15 ft)

md = 2.5 Sd = 0.0018 nd = 0.072 dm (mm)= 22.6

yd bd Ad Pd Wb Qb Q

15.19 17.8 847.3 99.6 93.8 3100 0.000

(d) ARR solution for Design 3 ( HR solution bd= 76 ft)

md = 2.5 Sd = 0.0013 nd = 0.054 dm (mm)= 22.6

yd bd Ad Pd Wb Qb Q

11.91 58.8 1055.6 123.0 118.4 4402.562 1302.562

n = 0.066

bHR = 35 ft

bARR= 33.2 ft

bHR/bARR= 1.05

n = 0.066

bHR = 35 ft

bARR= 33.2 ft

bHR/bARR= 1.05

n = 0.072

bHR = 15 ft


n = 0.072

bHR = 15 ft



n = 0.054bHR = 76 ft



n = 0.054bHR = 76 ft


ARRs Simplified MPM EquationARRARRs Simplified MPM Equations Simplified MPM Equation

RR simplified MPM equation


68/84

6868

( ) 3/ 2

3/ 2

'

'

( )

8( ) 0.047

b s m

b

b

b

b

eyer Peter Mueller MPM

bB RKR R S d

nRKR Nikuradse roughness ratio

n

n Manning coefficient for grain size

n total Manning coefficient

=

= =

=

=

}

( )}

50

3/ 21

3/ 28 ( ) 0.047

dy

b s m

RR simplified MPM equation

bB RKR R S d

=

64748


69/84

Analysis of Bed Grain SizeAnalysis of Bed Grain SizeAnalysis of Bed Grain Size


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7070

DistributionDistributionDistribution

Sieve AnalysisVisual-Accumulation Tube

Pebble Count

Sieve AnalysisSieve AnalysisVisualVisual--Accumulation TubeAccumulation Tube

Pebble CountPebble Count

Log-normal DistributionLogLog--normal Distributionnormal Distribution


71/84

7171

84.1

log 15.9

50

loglog

log84.1 84

15.9 16

log

log log1 1(log ) exp

22

10 10

(log ) (log ) (log ) /100

d

dd

d

d

g

d

Probability Density Function PDF

d df d

Cumulative Distribution Function CDF

d d

d d

F d f d d d P

Standa

=

= = =

= =

84.1

log 15.9

84.1 84.1log 84.1 15.9

15.9 15.9

log84.1 84

15.9 16

1 1(log log ) log log

2 2

10 10d

d

d

d

g

rdDeviation

d dd d

d d

Geometric standard deveiation

d d

d d

= = =

= = =

Standardized Random VariableMean = 0, standard deviation =1

Standardized Random VariableStandardized Random VariableMean = 0, standard deviation =1Mean = 0, standard deviation =1


72/84

7272

Mean 0, standard deviation 1Mean 0, standard deviation 1,

2

50

log

log log 1( ) exp

22

( ) ( ) ( ) 1 ( )

d

z

d d zz PDF f z

CDF F z f z dz where F z F z

= =

= =

F(z) for Standard Normal Random Variable zF(z) for Standard Normal Random Variable z

z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.53590.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7703 0.7734 0.7764 0.7793 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8906 0.8925 0.8943 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7703 0.7734 0.7764 0.7793 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.81330.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8906 0.8925 0.8943 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

Example - Sand Bed MaterialExampleExample -- Sand Bed MaterialSand Bed Material


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Log-Probability Plot of Sand Bed DataLogLog--Probability Plot of Sand Bed DataProbability Plot of Sand Bed Data


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7474

d(mm)

Cumulative Distribution Function Expressed as a probability (%)

d84=0.363 mm

d50=0.232 mm

d16=0.158 mm

( ) ( )log 50

84.1log

15.9

0.181

0.386 log 0.386 0.181 log 0.232 .565

65

0.363log log 0.181

0.158

10 1.52

10 10 10 0.272d

d

g

d

d

d

d mm

+ +

= = =

= =

= = = =

Log Probability Plot using NORMSINVLog Probability Plot using NORMSINVLog Probability Plot using NORMSINV


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Function in EXCELFunction in EXCELFunction in EXCEL

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

-4 -3 -2 -1 0 1 2 3

log10

(d)

d15.9

NORMSINV(P/100)

d50 d84.1

log(d84)log(d84))

log(d50)log(d50))

log(d16)log(d16))

NORMSINV and NORMSDIST

EXCEL Functions

NORMSINV and NORMSDISTNORMSINV and NORMSDIST

EXCEL FunctionsEXCEL Functions


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7676

d50= 0.48 mm log10(d50)= -0.3188

g= 1.28 mm log10(g)= 0.1072

P (% finer) F(z) z=NORMSINV(F) di (mm) F(z)=NORMSDIST(z)

1 2 3 4 5 6

20 0.2 -0.8416 d20= 0.390 0.2

40 0.4 -0.2533 d40= 0.451 0.4

60 0.6 0.2533 d60= 0.511 0.6

80 0.8 0.8416 d80= 0.591 0.8

99.99 0.9999 3.7190 d99.99= 1.202 0.9999

50 0.5 0.0000 d50= 0.480 0.5

di (mm) z F(z)=NORMSDIST(z) P (% finer)

1 2 3 4

0.41 -0.6385 0.2616 26.2

0.63 1.1016 0.8647 86.5

50

50

( ) ( )

( ) ( )

( )

10 i g

ii

g

log d z log

i

log d log d z

log

d

+

=

=

50( ) ( )

( )i

i

g

log d log d z

log

=

d50= 0.48 mm log10(d50)= -0.3188

g= 1.28 mm log10(g)= 0.1072

P (% finer) F(z) z=NORMSINV(F) di (mm) F(z)=NORMSDIST(z)

1 2 3 4 5 6

20 0.2 -0.8416 d20= 0.390 0.2

40 0.4 -0.2533 d40= 0.451 0.4

60 0.6 0.2533 d60= 0.511 0.6

80 0.8 0.8416 d80= 0.591 0.8

99.99 0.9999 3.7190 d99.99= 1.202 0.999950 0.5 0.0000 d50= 0.480 0.5

di (mm) z F(z)=NORMSDIST(z) P (% finer)

1 2 3 4

0.41 -0.6385 0.2616 26.2

0.63 1.1016 0.8647 86.5

50

50

( ) ( )

( ) ( )

( )

10 i g

ii

g

log d z log

i

log d log d z

log

d

+

=

=

50( ) ( )( )

ii

g

log d log d zlog

=

Geometric Standard DeviationGeometric Standard DeviationGeometric Standard Deviation


77/84

7777

( ) ( )

( ) ( ) ( ) ( )( )

( ) ( )

( )

84 50 50 16

84 50 50 16 84 50 16 50

84 16 84 16 84 16

84 16

84 50 84 50

2log log log log log

2log log / log / log /

12log log / log log / log /2

/

log log log /

log

top top

d d d d

d d d d d d d d

d d d d d d

d d

Alternative Method in HEC RAS Manuald d d d

= +

= + =

= = =

=

= =

( )

( )

50 16 50 16

84 50

50 16

log log /

0.5 0.5

bot bot

ave top bot

d d d d

d d

d d

= =

= = + = +

Geometric Standard Deviation when

P for smallest sample d is greater than 0.16

Geometric Standard Deviation whenGeometric Standard Deviation when

PP for smallest sample d is greater than 0.16for smallest sample d is greater than 0.16


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Pifor smallest sample d is greater than 0.16PP

iifor smallest sample d is greater than 0.16for smallest sample d is greater than 0.16

( )

( )

1

1 1

1

1

84

84 1

(1 )84 84

1

(1 )

84

(1 )log log log

loglog loglog log

(1 ) (1 )

P

zP P

P

z

P

z d d

d

d d d d

z z d

dd

=

= = =

=

Let Pi = the lowest percent finer from the pebble

count analysis and let zi = the standardized

normal variable that gives F(z) = Pi/100.

Let Pi = the lowest percent finer from the pebble

count analysis and let zi = the standardized

normal variable that gives F(z) = Pi/100.

Example for Smallest d > d16Example for Smallest d > dExample for Smallest d > d1616


79/84

7979

( )

1

84 32

1

11 1

(1 )(1 0.469 ) 1.469

84

8450 84

8450

8 2

32 ( ) 0.32 ( ) 1 ( ) 1 0.32 0.68

0.469 0.469

5.7 5.72.04

2 2

log log log 2.04 log2.04

2.

z

P

Given d mm and d mm

P F z F z F z

z z

d

d

dd d

dd

= =

= = = = =

= =

= = = =

= =

= 5.7 2.7904 2.04

mm = =

Pebble Count for Gravel/Cobble StreamPebble Count for Gravel/Cobble StreamPebble Count for Gravel/Cobble Stream


80/84

8080

Sand Gravel Cobble

Theoretical Justification for Pebble

Count

Theoretical Justification for PebbleTheoretical Justification for Pebble

CountCount


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8181

0

, , ,

/ ; ; ( )

(1 )

/

(1 )

L

pores total pores pores pores

s

i

i i s

i s i i ii

s total s s total s total total

i

porosity V V A nA V A x dx

A n A area of A occupied by soil

A area of A occupied by particles of a specified size range

f A A

W V V V p

W V V n V

p

= = =

= =

=

=

= = = =

( ) [ ]( )

[ ]( )

0 0 0 0

0 0

(1 )

(1 ) (1 ) (1 ) (1 )

(1 ) (1 )(1 )

(1 ) (1 ) (1 )

L L L L

i i i s i

total

L L

i i

i

i

i i

A dx A dx f A dx p n A dx

n V n AL n AL n AL

f n A dx f n Adxf n AL

p n AL n AL n AL

p f

= = = =

= = =

=

L

SOIL PARTICLES

PORES

A

Actual Pebble Count Shielding, settling, etc.Actual Pebble Count Shielding, settling, etc.

Mixed Sand and Gravel BedsWatershed Institute, Inc. Pebble Count Data

Mixed Sand and Gravel BedsMixed Sand and Gravel BedsWatershed Institute, Inc. Pebble Count DataWatershed Institute, Inc. Pebble Count Data


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MT043442RR01

D16 D50 D84

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

normsinv(P/100)

log10(D)

Pebble Count Data D16 D50 D84 Extrapolated

D (mm)

D16 0.0763

D50 0.344

D84 14.8

d (mm)

d16 0.0763

d50 0.344

d84 14.8

d16 d50 d84MT043442RR01

D16 D50 D84

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

normsinv(P/100)

log10(D)


D (mm)

D16 0.0763D50 0.344

D84 14.8

d (mm)

d16 0.0763d50 0.344

d84 14.8

d16 d50 d84

SN321115RR

D16 D50 D84

-3

-2

-1

0

1

2

3

-1.5 -1 -0.5 0 0.5 1 1.5 2

normsinv(P/100)

log10(D)


D (mm)

D16 0.00224

D50 0.500D84 20.6

d (mm)

d16 0.00224

d50 0.5d84 20.6

d16 d50 d84SN321115RR

D16 D50 D84

-3

-2

-1

0

1

2

3

-1.5 -1 -0.5 0 0.5 1 1.5 2

normsinv(P/100)

log10(D)


D (mm)

D16 0.00224

D50 0.500

D84 20.6

d (mm)

d16 0.00224

d50 0.5

d84 20.6

d16 d50 d84

Mixed Sand and Gravel Beds (cont.)Mixed Sand and Gravel Beds (cont.)Mixed Sand and Gravel Beds (cont.)Two Bed Materials

60

Two Bed Materials


83/84

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0

10

20

30

40

50

60

-1.5 -1 -0.5 0 0.5 1 1.5 2

log D

Wfiner(gm)

Gravel Sand

Sand Gravel

D50 0.4 10

g 1.5 2

W (gm) 40 50

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

log10(d)

0

10

20

30

40

50

60

-1.5 -1 -0.5 0 0.5 1 1.5 2

log D

Wfiner(gm)

Gravel Sand

Sand Gravel

D50 0.4 10

g 1.5 2

W (gm) 40 50

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

log10(d)

Two Bed Materials

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-10 -5 0 5 10norminv(P/100)

logD

Sand Gravel

Sand Gravel

D50 0.4 10

g 1.5 2

W (gm) 40 50

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

log10

(d)

NORMINV(P/100)

Two Bed Materials

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-10 -5 0 5 10norminv(P/100)

logD

Sand Gravel

Sand Gravel

D50 0.4 10

g 1.5 2

W (gm) 40 50

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

log10

(d)

NORMINV(P/100)

Mixed Sand and Gravel Beds (cont.)Mixed Sand and Gravel Beds (cont.)Mixed Sand and Gravel Beds (cont.)Combined

100

Combined

100


84/84

8484

0

10

20

30

40

50

60

70

80

90

-1.5 -1 -0.5 0 0.5 1 1.5 2

log D

WFiner(gm)

Sand GravelD50 0.4 10

g 1.5 2

W (gm) 40 50

log10(d)

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

0

10

20

30

40

50

60

70

80

90

-1.5 -1 -0.5 0 0.5 1 1.5 2

log D

WFiner(gm)

Sand Gravel

D50 0.4 10

g 1.5 2

W (gm) 40 50

log10(d)

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

Combined

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-8 -6 -4 -2 0 2 4

norminv(P/100)

lo

g

D

log D50 D50(mm)

0.537 3.44

Sand Gravel

D50 0.4 10

g 1.5 2

W (gm) 40 50

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

log

10

(d)

log10(d50) d50 (mm)

0.537 3.44

Combined

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-8 -6 -4 -2 0 2 4

norminv(P/100)

log

D

log D50 D50(mm)

0.537 3.44

Sand Gravel

D50 0.4 10

g 1.5 2

W (gm) 40 50

Sand Gravel

d50 0.4 10

g 1.5 2

W (gm) 40 50

log10

(d)

log10(d50) d50 (mm)

0.537 3.44

Documents

Fluvial Geomorphology.pdf