Transition

Transition

Uniform

Transition

Uniform

"Equilibrium"

Section

Ice Accumulation

Maximum Depth Given

by Equilibrium Section

Solid Ice

Cover

Flow

ρ

0 = *g*ρi 1 - i η2 - ( gρiSf - 2*C*i )η - τ*B *(17)

determine when the assumption of steady state

ρ

will be violated to a sufficient degree that unsteady

where is the coefficient of internal strength of

methods should be utilized. Preliminary results

the ice cover, sometimes called the friction coeffi-

indicate that the steady-state assumption is accept-

cient, and *C*i is the cohesion. Cohesion is often

able in many cases.

neglected for breakup ice jams, but can be impor-

A number of expressions are available for cal-

tant for freezeup jams. The shear stress on the

culating the equilibrium ice jam thickness in

underside of the jam, τ, can be expressed as

breakup ice jams, that is, the uniform thickness

section of an ice jam that has formed through

τ = ρ*gR*iSf .

(18)

shoving of the ice (Pariset et al. 1966; Uzuner and

Kennedy 1974; Beltaos 1978, 1995). The expression

For negligible cohesion (*C*i = 0), eq 17 yields the

selected for use in HEC-RAS is based on

following expression for the equilibrium ice jam

the ice-jam force balance equation in which the

thickness:

stresses within the jam are balanced against the

external stresses on the jam (USACE 1997, Daly

4(1*-s*i )Ri

1 + 1 +

η=

et al. 1998):

2(1 - *s*i )

(19)

( ) + 2τ b η = ρ *gS *η + τ

where *s*i is specific gravity of ice (ρi/ρ). The water

(16)

i

f

surface elevation in the equilibrium section of a

breakup ice jam, *h*, is calculated by

where σx is the stress in the streamwise direction

(20)

channel, *B*), η is the thickness of the ice accumula-

In summary, application of equilibrium ice

banks, and τ is the shear stress on the underside

thickness models (e.g., eq 19) will require some

of the jam. This force balance, expressed by Ashton

knowledge or estimation of the following ice prop-

erties: *C*i, , ρ, ρi, *n*b, *n*i, *n*c, *L*, and *H*, of which two,

(1986) in the form below, was used by Tuthill et al.

ρ and ρi, are well known.

(1998) in the ICETHK option of HEC-2:

7