83, and 85 combine to give the force due to normal pressure for a general channel

shape, i.e.

η(x)

[

]

[

]

(87)

0

0

For a rectangular channel, *b *is constant in the vertical and equal to the top width *B*.

Therefore

η(x)

′ = *K gB *1 - *p *

p (

) ∫

(88)

0

0

2

η

(89)

.

2

The time integral of this net normal force in the *x*-direction is

(

)

2

∫

(90)

2

1

1

1

1

where

η2

(1 - *p*).

(91)

2

It should be recognized that, by setting the value of *k*1 = *K*p in eq 85, the jam is

considered to be at its strength limit. A jam at rest could probably experience *k*1

values ranging from *K*a, the active pressure coefficient, to *K*p, the passive pressure

coefficient. For a cover in motion, *k*1 most likely depends on ice velocity. More

research is needed to determine the proper values of *k*1 to be used in different states

of ice motion.

An important further force is a shear stress τxy, produced by ice grinding against

the banks or channel sides. It relates directly to the normal stress in the *x*-direction

at failure, i.e.

τxy = σxk0λ = σv k0λ*K*p

(92)

where *k*0 is the coefficient of lateral thrust (percentage of normal stress acting in the

coefficient of ice on ice at the banks. Bank shear stress acts equally at either bank

(for one-dimensional formulations, at least) and may vary between section *x*1 and

η2

(93)

2

The time integral of this force is

40