Engineer Research and Development Center US Army Corps of Engineers Modeling River Ice and River Ice...

Engineer Research and Development Center

US Army Corpsof Engineers

Modeling River Ice and River Ice Modeling River Ice and River Ice Jams with HEC-RASJams with HEC-RAS

Dr. Steven F. DalyDr. Steven F. Daly

USACE ERDC/CRRELUSACE ERDC/CRRELHanover, NH 03755Hanover, NH 03755

07 March 200707 March 2007



Overview of LectureOverview of Lecture• River Ice HydraulicsRiver Ice Hydraulics

- Modifications to Manning’s equationModifications to Manning’s equation Available flow areaAvailable flow area Composite roughness Composite roughness Hydraulic radiusHydraulic radius

- standard step backwater procedure with standard step backwater procedure with iceice

• Entering Ice Data in HEC-RASEntering Ice Data in HEC-RAS• Wide river ice jams – TheoryWide river ice jams – Theory• Simulating Ice jam with RASSimulating Ice jam with RAS



Manning’s EquationManning’s Equation

2 3 1 20

2 3 1 20

1

1

U R Sn

Q AR Sn

Manning equation for steady flow, expressed for the flow velocity or the total discharge, Q



River ice covers always float at hydrostatic equilibrium.Or more exactly Non-hydrostatic pressure will always be temporary and relatively short lived and for practical applications can be ignored.

'

'

submerged depth at hydrostatic equilibrium

water surface z d

B

d

Manning’s Equation with IceManning’s Equation with Ice



Adjust the terms of the Manning’s equation to account for the presence of ice

'i oA A B

2 2 2i

w

AFlowArea Bd dR

WettedPerimeter P B d

Recall that for open water R ~ d

B

d

Manning’s Equation with Ice: Area and Hydraulic RadiusManning’s Equation with Ice: Area and Hydraulic Radius



Velocity Profile under steady flow conditionsIf we assume that the average flow velocity in the ice region and the bed region are equal;And we assume Manning’s equation applies to each;And we assume the energy grade line is the same in both;

Ice region

Bed region

Max velocity

ni

n

b

23 3 3

2 2

2i b

c

n nn

Sabaneev Formula

Composite Roughness valueComposite Roughness value



Type of Ice Condition Manning’s n value

Sheet ice Smooth 0.008 to 0.012Rippled ice 0.01 to 0.03Fragmented single layer 0.015 to 0.025Frazil ice New 1 to 3 ft thick 0.01 to 0.033 to 5 ft thick 0.03 to 0.06Aged 0.01 to 0.02

Suggested Range of Manning’s n Values for Ice Covered RiversSuggested Range of Manning’s n Values for Ice Covered RiversThe suggested range of Manning’s n values for a single layer of iceThe suggested range of Manning’s n values for a single layer of ice



Thickness Manning’s n valueft Loose frazil Frozen frazil Sheet ice0.3 - - 0.0151.0 0.01 0.013 0.041.7 0.01 0.02 0.052.3 0.02 0.03 0.063.3 0.03 0.04 0.085.0 0.03 0.06 0.096.5 0.04 0.07 0.0910.0 0.05 0.08 0.1016.5 0.06 0.09

The suggested range of Manning’s n values for ice jamsThe suggested range of Manning’s n values for ice jams



2 13 2

1.486ii o

c

Q A R Sn

23 1

21.486

2 2i

oc

BdQ Bd S

n B d

35

12

'1.32

1.486i

c

o

QnH

BS

At least 32% increase in total depth due to ice cover at uniform flow

Manning’s Equation with Ice for Rectangular ChannelsManning’s Equation with Ice for Rectangular Channels



d1

d2

Z1

Z2

1

2

1 2

V

g

2

2

2 2

V

g

2 22 1

2 2 2 2 1 1 1 1

' '

2 2 e

V VZ d Z d h

g g

Standard Step Backwater MethodStandard Step Backwater Method



e fh LS

2

2f

QS

K

The energy head loss can be expressed as the product of the mean friction slope, , and the distance between cross sections, LfS

The friction slope is found from Manning’s equation. Often it is Re-written in the following form, using the conveyance, K

Energy Losses with IceEnergy Losses with Ice



231.486

iic

K A Rn

Energy Losses with Ice

Or other combination method

1 2f f fS S S

K can be expanded as

There are several means of estimating the mean friction slope. TheSimplest is probably the mean of the upstream and downstream slope



Entering Ice Data in HEC-RASEntering Ice Data in HEC-RAS



Entering ice dataEntering ice data

• All ice data is entered using the All ice data is entered using the geometry data window. geometry data window.

• The most basic way to enter the The most basic way to enter the ice data is cross section by ice data is cross section by cross section using the cross cross section using the cross section editorsection editor



Pull down menus

River schematic

Cross sectioneditor

Short cutButtons



Add ice cover



Enter the ice cover thicknessEnter the Manning’s n values

Ice jam data will be covered in the next

section



Ice cover dataIce cover data

• Using this window the ice cover Using this window the ice cover properties can be entered for each properties can be entered for each cross sectioncross section

• However this has been found to be However this has been found to be a long and tedious processa long and tedious process

• So a short cut table has been So a short cut table has been developeddeveloped

• Return to the main geometry editorReturn to the main geometry editor



Enter ice cover data



Ice cover tableIce cover table

• This table allows a fast way to enter This table allows a fast way to enter the ice cover thickness and the ice cover thickness and roughness at all the cross sections roughness at all the cross sections at once.at once.

• As long as the “ice jam channel” is As long as the “ice jam channel” is set to “set to “nono” or (” or (nn) for all cross ) for all cross sections the program will calculate sections the program will calculate the flow properties using the ice the flow properties using the ice properties that are entered.properties that are entered.



As long as all sections are “n” the ice cover properties enteredwill be used.

Ice thickness in LOB,

channel and ROB

Manning’s n valuein LOB,

channel and ROB



Ice dataIce data

• Once the ice data has been Once the ice data has been entered the geometry file can be entered the geometry file can be resaved with a new name to resaved with a new name to separate the open water from the separate the open water from the ice covered geometry data. ice covered geometry data. This This can be done by selecting can be done by selecting Save Save Geometry Data AS Geometry Data AS from the from the “Geometric Data” window“Geometric Data” window under under the “file” menuthe “file” menu



(Plan View)(Plan View)(Plan View)(Plan View)

Shear Resistance at BanksShear Resistance at BanksShear Resistance at BanksShear Resistance at Banks

Internal Shear Strength

(Profile)(Profile)(Profile)(Profile)

Wind stressWind stressWind stressWind stress

Shear FromShear From Water FlowWater FlowShear FromShear From Water FlowWater Flow

Downstream ComponentDownstream Component of Jam Weightof Jam Weight

Downstream ComponentDownstream Component of Jam Weightof Jam Weight

Forces on an Ice JamForces on an Ice Jam



TransitionTransitionTransitionTransition

TransitionTransitionTransitionTransition

UniformUniformUniformUniform

UniformUniformUniformUniform

Maximum depthMaximum depthgiven by equilibrium sectiongiven by equilibrium sectionMaximum depthMaximum depthgiven by equilibrium sectiongiven by equilibrium section

Solid Ice Solid Ice CoverCoverSolid Ice Solid Ice CoverCover

Equilibrium SectionEquilibrium SectionEquilibrium SectionEquilibrium Section

Ice Jam SectionsIce Jam Sections



Ice Jam Force Balance For Wide Ice Jam Force Balance For Wide River JamRiver Jam

'

2'

x

g w

x bw i

f tB

gS t

d t tgS t

dx B

Longitudinal Force

Gravity component, Sw = water surface slope

Fluid shear stressBank Shear Stress



1 1

1

'.5 ' 1 1z

x p z p

y x p

b o y o p

g e t t

K K t

k k K t

k k k K t

z Vertical StressGranular ice mass

floating at hydrostatic equilibrium

Average vertical stress

Longitudinal stress

Transverse stress

Bank shear



Estimating the ice jam thickness Estimating the ice jam thickness based on the complete ice jam based on the complete ice jam

force balance equationforce balance equation

11'

2o

wp

k kdtgS t F

dx K t B

Starting with the ice jam force balance equation:



Ice Jam Force BalanceIce Jam Force BalanceSolution ProcedureSolution Procedure

2

ds us

ds us

us ds

dt t tF F

dx Lt t FL

F FF



Modeling ice jamsModeling ice jams

• HEC-RAS simulates river ice HEC-RAS simulates river ice jams by adjusting the jam jams by adjusting the jam thickness until the ice jam force thickness until the ice jam force balance equation and the balance equation and the standard step backwater standard step backwater equation are satisfied.equation are satisfied.



Ice Jam Force Balance Solution Ice Jam Force Balance Solution ProcedureProcedure

• Ice Jam Force Balance is solved from upstream to Ice Jam Force Balance is solved from upstream to downstreamdownstream

• Assume an jam thickness at the next downstream sectionAssume an jam thickness at the next downstream section

• Iterate until a solution is found. (25 Iterations max.) Iterate until a solution is found. (25 Iterations max.) Relaxation procedure used.Relaxation procedure used.

• Ice cannot completely block cross section at assure this Ice cannot completely block cross section at assure this a maximum flow velocity allowed under ice (5 fps default)a maximum flow velocity allowed under ice (5 fps default)

• Minimum ice jam thickness based on the thickness set by Minimum ice jam thickness based on the thickness set by the userthe user



Global Solution ProcedureGlobal Solution Procedure

• Initial Backwater calculations downstream to upstream Initial Backwater calculations downstream to upstream using entered ice thicknessusing entered ice thickness

• Ice Jam Force Balance solved upstream to downstream Ice Jam Force Balance solved upstream to downstream using flow values determined from backwater analysisusing flow values determined from backwater analysis

• Backwater and Ice Jam Force Balance are alternated until a Backwater and Ice Jam Force Balance are alternated until a solution is achievedsolution is achieved

• The ice jam thickness is allowed to change only 25% of The ice jam thickness is allowed to change only 25% of calculated required change in each iteration. (Global calculated required change in each iteration. (Global relaxation)relaxation)



Global Solution ConvergenceGlobal Solution Convergence

• Water surface elevation at any cross section changes less than 0.06 ft, or a user supplied tolerance, and the ice jam thickness at any section changes less than 0.1 ft, or a user supplied tolerance, between successive solutions of the ice jam force balance equation.

• A total of 50 iterations (or a user defined maximum number) are allowed for convergence.



Modeling Wide River Ice JamModeling Wide River Ice Jam

• User specifies (globally or at each section)User specifies (globally or at each section)

• Extent of the jamExtent of the jam

• Limit jam to channel or include overbanksLimit jam to channel or include overbanks

• Material properties of the jamMaterial properties of the jam Internal friction angle (45º)Internal friction angle (45º) Jam Porosity (0.4)Jam Porosity (0.4) K1 (.33)K1 (.33) Maximum flow value under the jam (5 fps)Maximum flow value under the jam (5 fps) Manning’s n or let RAS estimateManning’s n or let RAS estimate



Selecting the ice jam locationSelecting the ice jam location

• The user must select where an ice jam will The user must select where an ice jam will be located. HEC-RAS cannot determine on be located. HEC-RAS cannot determine on its own where a jam will be.its own where a jam will be.

• The The ice cover editorice cover editor available from the available from the cross section data window, or the cross section data window, or the ice cover ice cover tabletable, available from the geometry data , available from the geometry data window can be used to locate the jam.window can be used to locate the jam.




• The user must also determine if The user must also determine if the jam will be confined to the the jam will be confined to the channel or be allowed to extend channel or be allowed to extend into the over banks.into the over banks.




Confining the jam to the channel is Confining the jam to the channel is appropriate where appropriate where

• the water levels do not reach the overbankthe water levels do not reach the overbank

• The river ice is confined to the channel by The river ice is confined to the channel by treestrees

• The overbank areas are very broad and an The overbank areas are very broad and an ice jam could not form in these areasice jam could not form in these areas



Confined to Channel

ROB

Ice jam confined to channelIce jam confined to channel

LOB




• If the jam is allowed to enter the If the jam is allowed to enter the overbank area, then the flow overbank area, then the flow properties of the overbank and properties of the overbank and the channel are combined to the channel are combined to determine the average flow determine the average flow properties acting on the jam. properties acting on the jam.



Ice jam in channel and over Ice jam in channel and over banksbanks

LOB ROB



Select ice jam option by setting where the ice jam will be located

Channel Channel plus over banks

By selecting Channel or Over banksThese boxes will become available



The ice jam option can also be set in the ice cover table. This is done bychanging the no’s, n, to yes’s, y, in the appropriate column. The user must select if the ice jam is confined to the channel or will include both the channel and the over banks.

Change each cross section individually. The values cannot be set toy or n all at once, as the numeric values can.

Channel Channel plus over banks



Selecting ice jam locationSelecting ice jam location

• Remember: there must be section with Remember: there must be section with fixed ice thickness at the upstream and fixed ice thickness at the upstream and downstream end of the jam. downstream end of the jam.

• Therefore, every cross section can not be Therefore, every cross section can not be set to yes. There must be at least one set to yes. There must be at least one section with no at the upstream and section with no at the upstream and downstream ends of the jam.downstream ends of the jam.



Ice Jam ParametersIce Jam Parameters

= angle of internal friction= angle of internal friction ’’ = density of ice= density of ice

• e e = porosity of jam= porosity of jam

• kk11 = ratio of lateral to = ratio of lateral to

longitudinal pressurelongitudinal pressure



’ = density of ice

= angle of internal friction

e = porosity of jam

k1 = ratio of lateral to longitudinal pressure

The user can enter the values on the ice cover editor for each cross section individually. Note that defaultvalues of the parameters have already been entered.



Ice jam parametersIce jam parameters

• The user can also set the ice jam The user can also set the ice jam parameters globally using the parameters globally using the ice cover table. Note that default ice cover table. Note that default values of the parameters have values of the parameters have already been entered.already been entered.



k1 = ratio of lateral to longitudinal pressure

e = porosity of jam

= angle of internal friction

’ = density of ice

The numeric values can be set globally,

like the icethickness and

roughness values



Manning’s roughness of jamManning’s roughness of jam

• The user can either fix the The user can either fix the Manning’s n value for the jam or Manning’s n value for the jam or let HEC-RAS estimate the value let HEC-RAS estimate the value based on Nezhikovsky’s formulabased on Nezhikovsky’s formula



0.23 0.40

0.23 0.77

0.0690

0.0593

i i

i i

n H t

n H t

t >1.5 ft

t <1.5 ft

Estimation of Manning’s n for Estimation of Manning’s n for Ice JamIce Jam

using Nezhikovsky’s formulausing Nezhikovsky’s formula



By un-checking this box, the user allows RAS to estimate the Jam roughness

If the box below is checked, these values are

considered fixed, and will be used



By changing this column from yes to no, the user will allowHEC-RAS to estimate the Manning’s n value of the jam.



Maximum under ice velocityMaximum under ice velocity

• Note that there is one parameter Note that there is one parameter that we have not discussed. This that we have not discussed. This is the maximum under ice is the maximum under ice velocity. Where did this come velocity. Where did this come from?from?




• Recall from the early lecture that Recall from the early lecture that the stresses in the cover were the stresses in the cover were developed assuming that the ice developed assuming that the ice cover is floating at hydrostatic cover is floating at hydrostatic equilibrium.equilibrium.

Assume zero stress at bottom of jam




• As a result, the stress analysis is not valid As a result, the stress analysis is not valid when the ice cover contacts the bed of the when the ice cover contacts the bed of the channel.channel.

• Therefore the calculations must assure that Therefore the calculations must assure that the ice cover does not contact the bed.the ice cover does not contact the bed.

• When the ice cover contacts the bed, the When the ice cover contacts the bed, the under ice area approaches zero. under ice area approaches zero.




• Recall by continuity Recall by continuity Q=VA orQ=VA or

V=Q/A=Q/(dB)V=Q/A=Q/(dB)• Therefore, by setting a maximum under ice Therefore, by setting a maximum under ice

velocity, we are assuring that the area velocity, we are assuring that the area under the ice cover does not become too under the ice cover does not become too small.small.

• The value can be increased by the user if The value can be increased by the user if necessary. The result will be that the ice necessary. The result will be that the ice jam will become thicker and the area jam will become thicker and the area beneath the jam less.beneath the jam less.



The user can enter the values on the ice cover editor for each cross section individually. Note that a default

value has already been entered.

Maximum under ice velocity



The numeric values can be set globally,

like the icethickness and

roughness values

Set the maximum under ice velocity globally



0 1000 2000 3000 4000 5000 6000 700080

100

120

140

160

180

200

MVD_Ice Plan: Dam Removed - Modified

Main Channel Distance (f t)

Ele

va

tion

(ft)

Legend

WS 2Yr

Ground

Ice Cover

RIVER-1 Reach-1



Running the ice jam simulationRunning the ice jam simulation

• Once a geometry file has been Once a geometry file has been created with the ice jam option created with the ice jam option selected, RAS will do an ice jam selected, RAS will do an ice jam simulation.simulation.

• Select the steady flow analysis Select the steady flow analysis button from the main interfacebutton from the main interface



Use file menu to name and save plan

Push compute button to perform analysis



Indicates progress of calculation and if finished normally

Indicates Number of iterations of the ice jam force balance



Viewing ResultsViewing Results

• We can view results using the We can view results using the profile plot, the cross section profile plot, the cross section plot, the x-y-z perspective plot, plot, the x-y-z perspective plot, and the rating curve. and the rating curve.



Profile plot



X-y-z perspective plot



Profile Output Table

Ice Cover Table



Modeling Ice JamsModeling Ice Jams• Jam LocationJam Location

• Volume of Ice in JamVolume of Ice in Jam- RAS will calculate volume but will not limit jam length RAS will calculate volume but will not limit jam length

based on volume.based on volume.

- Volume = (Reach length x width x thickness ) x % of ice Volume = (Reach length x width x thickness ) x % of ice that reaches jam locationthat reaches jam location

• Make sure thickness is not limited by max velocityMake sure thickness is not limited by max velocity

• If channel is dry – there will be problems modeling If channel is dry – there will be problems modeling iceice

• Appropriate Flows – Not high flows (2-10 year Appropriate Flows – Not high flows (2-10 year range)range)

• BridgesBridges

Engineer Research and Development Center US Army Corps of Engineers Modeling River Ice and River Ice...

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