River Ice HydraulicsRiver Ice Hydraulics

Introductory lectures in

River Ice EngineeringIntroductory lectures in

River Ice Engineering

Effects of Ice on the FlowEffects of Ice on the Flow

1.1. River ice floats with about 90% of its River ice floats with about 90% of its thickness submergedthickness submerged• this reduces the active flow areathis reduces the active flow area

2.2. River ice resists the flow of waterRiver ice resists the flow of water• wetted perimeter is approximately doubledwetted perimeter is approximately doubled

For an ice cover with underside roughness equal to the For an ice cover with underside roughness equal to the bed roughness, the water level will be about 30% higher bed roughness, the water level will be about 30% higher than for the same discharge under open water conditions.than for the same discharge under open water conditions.

150.8

150.9

151.0

151.1

151.2

151.3

151.4

151.5

151.6

Jan-1 Jan-8 Jan-15 Jan-22 Jan-29

Wa

ter

Le

vel

(m)

water level increase due to freeze-up at the gauge site was approximately 0.5 m

Jan. 16, freeze-up front passed through the gauge site

Mackenzie River at Fort Providence, 1994Mackenzie River at Fort Providence, 1994

(Hicks et al, 1995, data source, Water Survey of Canada)(Hicks et al, 1995, data source, Water Survey of Canada)

Effects of the Flow on the IceEffects of the Flow on the Ice

1.1. under turning pansunder turning pans

2.2. consolidation or shoving (ice jams)consolidation or shoving (ice jams)

THICKER ICE COVERSTHICKER ICE COVERS

UNSTEADY FLOWUNSTEADY FLOW

Complications to consider…Complications to consider…

photo source: R. Gerard

Open water rating curves are not applicable under ice affected Open water rating curves are not applicable under ice affected conditions…conditions…

Mackenzie River (Hicks et al., 1993)

open water conditions

ice affected conditions

~1.5m

Liard River above Fort Simpson (source WSC)Liard River above Fort Simpson (source WSC)

(Hicks et al., 2000)

(Hicks et al., 2000)

Roughness of the underside of the ice cover is difficult to measure Roughness of the underside of the ice cover is difficult to measure directly, or to deduce indirectly from velocity profiles…directly, or to deduce indirectly from velocity profiles…

These ripples formed due to warm water flowing under the ice cover.

This ice floe has been turned over, to view the ripples on the underside.

photo by F. Hicks

Frazil slush may be obstructing the waterway…Frazil slush may be obstructing the waterway…

February 16, 1978February 16, 1978 February 23, 1978February 23, 1978

fromResistance coefficients from velocity profiles in ice-covered shallow streams”by Calkins, Deck and Martinson, CJCE, Vol. 9, Number 2, 1982

Ottauquechee RiverOttauquechee RiverOttauquechee RiverOttauquechee River

Peace River at Peace River, March 9, 1999Peace River at Peace River, March 9, 1999

300

305

310

315

0 50 100 150 200 250 300 350 400 450

Station (m)

Ele

vati

on (

m)

Bed

Water level

Bottom of ice

Bottom of slush ice

Preliminary WSC data

(Hicks et al., 2000)

There may only be a partial ice cover…There may only be a partial ice cover…

photo by S. Beltaos

Hydraulics of Ice Covered ChannelsHydraulics of Ice Covered Channels

(Ashton, 1986)(Ashton, 1986)

ICE

BED

Longitudinal Velocity ProfileLongitudinal Velocity Profile

Composite Roughness ApproachComposite Roughness Approach

The channel cross section is divided into two The channel cross section is divided into two sub-sections, one affected only by the ice, and sub-sections, one affected only by the ice, and

one affected only by the bed.one affected only by the bed.

ice affected area

bed affected area

(Ashton, 1986)

General practice is to assume the line of zero shear, General practice is to assume the line of zero shear, which divides the two subsections is coincident with which divides the two subsections is coincident with

the isoline of maximum velocity.the isoline of maximum velocity.

This is actually true only ifThis is actually true only if n nii == n nbb

ice affected area

bed affected area

(Ashton, 1986)

nnbb is for the rougher of two boundaries is for the rougher of two boundaries

(Ashton, 1986)(Ashton, 1986)

Common practice is to use Sabaneev’s equation to Common practice is to use Sabaneev’s equation to determine a composite roughness.determine a composite roughness.

valid for valid for nnbb 0.04 and depth > 2m with an accuracy of 1% or better0.04 and depth > 2m with an accuracy of 1% or better

Ice Jam RoughnessIce Jam Roughness

ice roughness on the underside of ice jams can be as high as ni = 0.05 to 0.09--- the use of Sabaneev’s equation here will be inaccurate…

(adapted from Ashton, 1986)(adapted from Ashton, 1986)

(adapted from Beltaos, 1995)(adapted from Beltaos, 1995)

Ice Jam HydraulicsIce Jam Hydraulics

there is currently no “model” for jam toe configuration

If the jam is sufficiently long, and the channel geometry is not If the jam is sufficiently long, and the channel geometry is not highly variable, an ‘equilibrium section’ may form. highly variable, an ‘equilibrium section’ may form.

The equilibrium section is significant, since it is currently The equilibrium section is significant, since it is currently believed that it produces the maximum depth within the ice believed that it produces the maximum depth within the ice

jam profile.jam profile.

(adapted from Ashton, 1986)(adapted from Ashton, 1986)

A non-dimensional depth versus discharge relationship for equilibrium A non-dimensional depth versus discharge relationship for equilibrium conditions was developed by Beltaos (1983):conditions was developed by Beltaos (1983):

o

ioo f

fff 3/13/1 11.011

75.563.0

andand represent the non-represent the non-dimensional depth and dimensional depth and

discharge, respectively, and discharge, respectively, and are defined as :are defined as :

BS

h

3/12

BS

gSq

BB = accumulation width = accumulation widthSS = stream slope= stream slopeqq = discharge per unit width= discharge per unit widthhh = flow depth from the water surface to the bed ( depth of flow = flow depth from the water surface to the bed ( depth of flow

below the ice cover plus the submerged ice thickness). below the ice cover plus the submerged ice thickness).

is a jam strength parameter, typically ranging from 0.9 to 1.3is a jam strength parameter, typically ranging from 0.9 to 1.3

K.D. White, CRREL Report 99-11K.D. White, CRREL Report 99-11

ffoo is the composite friction factor for the flow under an ice jam: is the composite friction factor for the flow under an ice jam:

ffii and and ffbb denote the friction factors denote the friction factors

for the ice and bed influenced for the ice and bed influenced portions of flow, respectively.portions of flow, respectively.

ff f

oi b

2

Arguing the insensitivity of his relationship to variations in friction Arguing the insensitivity of his relationship to variations in friction factor (due to the small exponent), Beltaos introduced the following factor (due to the small exponent), Beltaos introduced the following

non-dimensional graph fornon-dimensional graph for versus versus

Cohesion is assumed to be negligible (a conservative assumption).Cohesion is assumed to be negligible (a conservative assumption).

known only as a range

Scatter in the diagram is due to variation in friction factor.

All points are based on actual field data.

(adapted from Ashton, 1986)

(Beltaos, 1995)

…due to variation in friction factor

Example calculation of water depth associated with Example calculation of water depth associated with equilibrium jam conditions:equilibrium jam conditions:

First, determine First, determine ,, the non-dimensional discharge, using:the non-dimensional discharge, using:

800)0002.0)(50(

)0002.0)(81.9(1

3/12

3/12

BS

gSq

GIVEN:GIVEN:BB = accumulation width = 50 m = accumulation width = 50 mSS = stream slope = 0.0002= stream slope = 0.0002qq = discharge per unit width = 1 m= discharge per unit width = 1 m33/s/m/s/m

FIND:FIND:hh = flow depth from the water surface to the bed. = flow depth from the water surface to the bed.

(Beltaos, 1995)

250

From the graph, From the graph, , the non-dimensional depth equals 250:, the non-dimensional depth equals 250:

Now, we can determine the flow depth, Now, we can determine the flow depth, hh, using:, using:

m5.2)0002.0)(50)(250(or BShBS

h

The maximum flow depth, associated with the The maximum flow depth, associated with the equilibrium section of the ice jam, would be 2.5 m.equilibrium section of the ice jam, would be 2.5 m.

Note also though, the scatter in the observed data indicated that Note also though, the scatter in the observed data indicated that could range from about 230 to 280, so could range from about 230 to 280, so h h could be anywhere could be anywhere

from 2.3 to 2.8 m. (The variation is due to the fact that from 2.3 to 2.8 m. (The variation is due to the fact that roughness is not accounted for in this calculation.)roughness is not accounted for in this calculation.)

Ice Jam ModellingIce Jam ModellingThis is the preferred approach for most applications…This is the preferred approach for most applications…

(adapted from Ashton, 1986)(adapted from Ashton, 1986)

Ice Jam ModelsIce Jam Models

1.1. RIVJAMRIVJAM• S. Beltaos, National Water Research InstituteS. Beltaos, National Water Research Institute

2.2. ICEJAMICEJAM• Flato and Gerard, University of AlbertaFlato and Gerard, University of Alberta

3.3. HEC-RAS (U.S. Army Corps of Engineers)HEC-RAS (U.S. Army Corps of Engineers)• Daly, Cold Regions Research and Engineering Daly, Cold Regions Research and Engineering

Laboratory (based on ICEJAM model)Laboratory (based on ICEJAM model)http://www.hec.usace.army.mil/software/software_distrib/hec-ras/hecrasprogram.htmlhttp://www.hec.usace.army.mil/software/software_distrib/hec-ras/hecrasprogram.html

To learn about ice jam modelling with RIVJAM and ICEJAM see the paper by To learn about ice jam modelling with RIVJAM and ICEJAM see the paper by Healy and Hicks Healy and Hicks in the ASCE Journal of Cold Regions Engineering in the ASCE Journal of Cold Regions Engineering

(1999, Vol. 13, No. 4, pp. 180-198)(1999, Vol. 13, No. 4, pp. 180-198)..