1.00

0.80

0.60

0.40

0.20

0.00

0.0

0.2

0.4

0.6

0.8

1.0

Downstream Moment, M

(M ft-lb)

y

cylindrical-pier ICS arrested the initial runs but released

design downstream force acts halfway up the pier, and

the resulting ice jams at about 50% of the design dis-

the design transverse moment is half of the design down-

charge. However, this scenario should not occur at the

stream moment.

prototype ICS. The piers will form a small pool that

These design loads may occur simultaneously on a

will preferentially freeze early and solidly. With this

pier because they often derive from the same event.

ice upstream, the ICS will arrest an ice run and hold a

For this reason, although we did not record transverse

jam well beyond the design discharge. Any later ice

forces, *F*y, we may estimate the design value as

runs will impact and add to the jam rather than inter-

acting directly with the piers.

verse and downstream moments act at the same height

on the pier (4.4 ft above the bed) for the design event.

We may compare these results with the downstream

The model data can provide design ice loads for

loads used to design the original weir-with-piers ICS.

downstream and transverse overturning moments and

Recall that its function was different. During breakup,

forces. The peak downstream moments measured during

floes arriving from upstream would collect in the pool

each test were cast in a statistical framework for the

upstream of the ICS, causing the overlying ice sheet to

purpose of determining these design loads. We recom-

ride up the piers, essentially to their tops. The design

value of the downstream ice load was assumed to result

level of 99.9% and describe design loads here based on

from the crushing failure of a 1-ft-thick sheet across

that probability. This corresponds to an average return

the 3-ft width of the pier at a pressure of 262 psi, result-

ing in *F*x = 0.11 106 lb (U.S. Army 1986b). Although

interval of 1000 years, assuming one ice-breakup event

per year. Design loads based on higher or lower proba-

this is lower than *F*x determined here, it acted much

bilities can be determined using the same procedure.

higher on the pier so that the design overturning moment

The results on Figure 11 directly yield *M*d = 2.0 106

was similar, *M*d = 1.5 106 ft-lb. Rather than experi-

ft-lb as the design value for downstream overturning

encing ice-crushing failure, however, the piers in the

moment. We may use this value to estimate the other

present ICS are subjected to direct ice-floe impacts and

design loads. Because *L*p tends to increase slightly for

unsteady ice-jam formation and collapse events.

increasing *M*y, we may obtain a conservative estimate

It is also interesting to compare the recommended

of design value of the downstream force, *F*x = *M*d/*L*p,

design loads with those resulting from application of

by using the average value of *L*p = 4.4 ft. This yields

the AASHTO (1998) design standards for bridge piers.

These standards rely heavily on the work of Montgom-

force. Similarly, because *M*x/*M*y tends to decrease

ery et al. (1984), which also formed the basis for design

for increasing *M*y, we may obtain a conservative esti-

standards in Canada (CSA 1988).

mate of design value of the transverse moment,

The AASHTO standards differentiate among crush-

ing (across the full width of a pier), bending, and im-

= 0.45. This yields *M*x = 0.90 106 ft-lb as the design

pact ice-failure modes. They note that impact failure,

value for transverse moment. Roughly speaking, the

where a small floe comes to rest before it has crushed

TO CONTENTS