If the upstream Froude number

zero for breakup jams to 20 lb/ft2 for

freezeup jams)

τ = shear force on underside of accumu-

lation, approximated by ρ*g *(*y*i/2)*S*,

is less than or equal to the right-hand side of eq

where *y*i = under-ice depth.

1, a solution by juxtaposition is assumed possible.

The accumulation's leading edge thickness *h*,

which satisfies eq 1, is then found by trial and

The water velocity beneath an ice cover may

error.

be high enough to erode ice pieces and thin the

The second method, derived by Ashton (1974),

accumulation in a manner analogous to sediment

is based on the particle Froude number *F*p:

transport. The user inputs a threshold velocity

(VEROS), above which erosion or thinning of the

2 1 -

ice cover takes place. The "thinned" ice cover

≤

thickness is estimated by the following form of the

ρ

2

.

(3)

5 - 3 1 -

ρ

*V*

1

*H *- (H - *S*i h)

Again, ICETHK checks to determine whether a

(5)

*V*c

solution is possible, i.e., left-hand side less than

or equal to right-hand side for *h/y *= 1/3, then

solves for *h*, the leading edge thickness.

where *h*t = thickness of "thinned" ice cover

Thickening due to shoving is calculated by eq

4. The underlying theory was developed through

by user) (VEROS)

the work of many, including Kennedy (1958),

Pariset and Hausser (1961), Michel (1965), Pariset

et al. (1966), Uzuner and Kennedy (1976), and

0.916.

Beltaos (1978).

As stated earlier, the equations describing thick-

Typical values for VEROS range from 3 to 5 ft/s

ness by shoving apply only to the equilibrium

for freezeup-type jams and 4 to 8 ft/s for break-

reach of the jam (see Fig. 1). Assumptions include

up. If the HEC-2 calculated water-current velocity

uniform flow, constant ice thickness, and the trans-

is greater than VEROS, eq 5 will reduce the ice

fer of all downstream forces on the ice accumula-

thickness, but not to a value less than the thick-

tion to the banks. It should be restated that diffi-

ness of the initial (pre-jam) ice cover (ITHICK).

culties arise when using ICETHK to model the

head and toe of the jam, where conditions of var-

ied flow and changing ice thickness exist.

Of the four roughness options available in

Under steady-state conditions, the uniform

ICETHK, two involve direct assignment of Man-

section of an ice accumulation, compressed by

ning's *n *values and two involve calculation of

shoving, can be described as

roughness. Ice roughness can be calculated as a func-

tion of ice thickness or as a function of ice piece size.

ρ

1 i *gh*2 - ( gρi SB - 2 *C*i ) h - τ*B *= 0

Existing field data show that thick jams are typ-

(4)

ρ

ically made up of larger ice pieces and are hydrau-

lically rougher than thin jams. Relationships in the

ICETHK model, based on Nezhikovskiy's (1964)

where *h *= thickness of the ice accumulation

= coefficient related to the internal

data, relate Manning's *n *values for the ice cover

to the ice accumulation thickness. The relation-

strength of the accumulation, ranging

ships take the form of a similar equation by Beltaos

from 0.8 to 1.3

ρ, ρi = densities of ice and water

(1983). Nezhikovskiy's data were measured in

wide canals 6.6 to 9.8 ft deep for ice floes, dense

slush, and loose slush. For breakup situations with

ice accumulations greater than 1.5 ft thick,

3