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07 March 2007### Modeling River Ice and River Ice Jams with HEC-RAS

Dr. Steven F. Daly

USACE ERDC/CRREL

Hanover, NH 03755

Overview of Lecture

- River Ice Hydraulics
- Modifications to Manning’s equation
- Available flow area
- Composite roughness
- Hydraulic radius
- standard step backwater procedure with ice
- Entering Ice Data in HEC-RAS
- Wide river ice jams – Theory
- Simulating Ice jam with RAS

Manning’s Equation

Manning equation for steady flow,

expressed for the flow velocity or the total discharge, Q

d

B

Manning’s Equation with IceRiver 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.

d

B

Manning’s Equation with Ice: Area and Hydraulic RadiusAdjust the terms of the Manning’s equation to account for the presence of ice

Recall that for open water R ~ d

Ice region

Bed region

Max velocity

Velocity Profile

under steady flow conditions

If 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;

Composite Roughness valueni

nb

Sabaneev Formula

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

Type of Ice Condition Manning’s n value

Sheet ice Smooth 0.008 to 0.012

Rippled ice 0.01 to 0.03

Fragmented single layer 0.015 to 0.025

Frazil ice New 1 to 3 ft thick 0.01 to 0.03

3 to 5 ft thick 0.03 to 0.06

Aged 0.01 to 0.02

Thickness Manning’s n value

ft Loose frazil Frozen frazil Sheet ice

0.3 - - 0.015

1.0 0.01 0.013 0.04

1.7 0.01 0.02 0.05

2.3 0.02 0.03 0.06

3.3 0.03 0.04 0.08

5.0 0.03 0.06 0.09

6.5 0.04 0.07 0.09

10.0 0.05 0.08 0.10

16.5 0.06 0.09

The suggested range of Manning’s n values for ice jamsManning’s Equation with Ice for Rectangular Channels

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

Energy Losses with Ice

The energy head loss can be expressed as the product of the mean

friction slope, , and the distance between cross sections, L

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 Ice

K can be expanded as

There are several means of estimating the mean friction slope. The

Simplest is probably the mean of the upstream and downstream slope

Or other combination method

Entering ice data

- All ice data is entered using the geometry data window.
- The most basic way to enter the ice data is cross section by cross section using the cross section editor

Enter the ice cover thickness

Enter the Manning’s n values

Ice jam data will be

covered in the next

section

Ice cover data

- Using this window the ice cover properties can be entered for each cross section
- However this has been found to be a long and tedious process
- So a short cut table has been developed
- Return to the main geometry editor

Ice cover table

- This table allows a fast way to enter the ice cover thickness and roughness at all the cross sections at once.
- As long as the “ice jam channel” is set to “no” or (n) for all cross sections the program will calculate the flow properties using the ice properties that are entered.

Ice thickness in LOB, channel and ROB

Manning’s n value

in LOB,

channel and ROB

As long as all sections are “n” the ice cover properties entered

will be used.

Ice data

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

Shear Resistance at Banks

Internal Shear Strength

(Plan View)

Wind stress

Shear From

Water Flow

(Profile)

Downstream Component

of Jam Weight

Forces on an Ice JamTransition

Uniform

Equilibrium Section

Transition

Uniform

Solid Ice

Cover

Maximum depth

given by equilibrium section

Ice Jam SectionsIce Jam Force Balance For Wide River Jam

Longitudinal Force

Gravity component, Sw = water surface slope

Fluid shear stress

Bank Shear Stress

Vertical StressGranular ice mass floating at hydrostatic equilibrium

z

Average vertical stress

Longitudinal stress

Transverse stress

Bank shear

Estimating the ice jam thickness based on the complete ice jam force balance equation

Starting with the ice jam force balance equation:

Modeling ice jams

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

Ice Jam Force Balance Solution Procedure

- Ice Jam Force Balance is solved from upstream to downstream
- Assume an jam thickness at the next downstream section
- Iterate until a solution is found. (25 Iterations max.) Relaxation procedure used.
- Ice cannot completely block cross section at assure this a maximum flow velocity allowed under ice (5 fps default)
- Minimum ice jam thickness based on the thickness set by the user

Global Solution Procedure

- Initial Backwater calculations downstream to upstream using entered ice thickness
- Ice Jam Force Balance solved upstream to downstream using flow values determined from backwater analysis
- Backwater and Ice Jam Force Balance are alternated until a solution is achieved
- The ice jam thickness is allowed to change only 25% of calculated required change in each iteration. (Global relaxation)

Global 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 Jam

- User specifies (globally or at each section)
- Extent of the jam
- Limit jam to channel or include overbanks
- Material properties of the jam
- Internal friction angle (45º)
- Jam Porosity (0.4)
- K1 (.33)
- Maximum flow value under the jam (5 fps)
- Manning’s n or let RAS estimate

Selecting the ice jam location

- The user must select where an ice jam will be located. HEC-RAS cannot determine on its own where a jam will be.
- The ice cover editor available from the cross section data window, or the ice cover table, available from the geometry data window can be used to locate the jam.

Selecting the ice jam location

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

Selecting the ice jam location

Confining the jam to the channel is appropriate where

- the water levels do not reach the overbank
- The river ice is confined to the channel by trees
- The overbank areas are very broad and an ice jam could not form in these areas

Selecting the ice jam location

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

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

By selecting Channel or Over banks

These boxes will become available

Channel plus over banks

Channel

The ice jam option can also be set in the ice cover table. This is done by

changing 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 to

y or n all at once, as the numeric values can.

Channel

Channel plus over banks

Selecting ice jam location

- Remember: there must be section with fixed ice thickness at the upstream and downstream end of the jam.
- Therefore, every cross section can not be set to yes. There must be at least one section with no at the upstream and downstream ends of the jam.

Ice Jam Parameters

- = angle of internal friction
- ’ = density of ice
- e = porosity of jam
- k1 = ratio of lateral to longitudinal 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 default

values of the parameters have already been entered.

Ice jam parameters

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

The numeric values

can be set globally,

like the ice

thickness and

roughness values

k1 = ratio of lateral to longitudinal pressure

e = porosity of jam

= angle of internal friction

’ = density of ice

Manning’s roughness of jam

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

If the box below is

checked, these values are

considered fixed, and will be used

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

Jam roughness

By changing this column from yes to no, the user will allow

HEC-RAS to estimate the Manning’s n value of the jam.

Maximum under ice velocity

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

Maximum under ice velocity

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

Assume zero stress

at bottom of jam

Maximum under ice velocity

- As a result, the stress analysis is not valid when the ice cover contacts the bed of the channel.
- Therefore the calculations must assure that the ice cover does not contact the bed.
- When the ice cover contacts the bed, the under ice area approaches zero.

Maximum under ice velocity

- Recall by continuity

Q=VA or

V=Q/A=Q/(dB)

- Therefore, by setting a maximum under ice velocity, we are assuring that the area under the ice cover does not become too small.
- The value can be increased by the user if necessary. The result will be that the ice jam will become thicker and the area beneath the jam less.

Maximum under ice velocity

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.

The numeric values

can be set globally,

like the ice

thickness and

roughness values

Set the maximum under ice velocity globally

Running the ice jam simulation

- Once a geometry file has been created with the ice jam option selected, RAS will do an ice jam simulation.
- Select the steady flow analysis button 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 Results

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

Modeling Ice Jams

- Jam Location
- Volume of Ice in Jam
- RAS will calculate volume but will not limit jam length based on volume.
- Volume = (Reach length x width x thickness ) x % of ice that reaches jam location
- Make sure thickness is not limited by max velocity
- If channel is dry – there will be problems modeling ice
- Appropriate Flows – Not high flows (2-10 year range)
- Bridges

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