2.0

1.5

1.0

0.5

0.0

.01

.1

1

5 1 0 2 03 0

50

7 08 0 9 0 9 5

99

99.9 99.99

Percent

7.0

tively be long in duration. Thus, we selected

the largest downstream moment, impact or sus-

6.0

tained, measured on any of the five instrument-

ed piers as the peak downstream moment for each

5.0

test, *M*d.

Table 2 shows the resulting values of *M*d.

4.0

Interestingly, these peak moments are not cor-

related with ice thickness, ice strength, or pier

3.0

gap (Fig. 10). We also saw no dependence on

pier location. This allows us to treat the *M*d

2.0

values as a single population and thereby

develop a statistical basis for design loads. Fig-

1.0

ure 11 shows the resulting probability distribu-

0.0

0.0

0.2

0.4

0.6

0.8

1.0

scale. A straight line fits the data reasonably

Downstream Overturning Moment, M (M ft-lb)

well, implying a normal distribution.

y

We also compiled for each test the peak Figure 13. Effective moment arm, *L *, versus downstream

downstream force, *F*x, peak transverse over- moment, *M*y, at the time of the peak downstream force, *F*x,

turning moment, *M*x, and the downstream over- during each test.

turning moments at the times of those peaks,

able assumption for cylindrical piers during breakup.

Figure 13 shows that *L*p tends to increase slightly for

strength, or pier gap.

increasing *M*y, indicating that rising ice-contact height

From the ratio *M*y/*F*x,

and increasing downstream force both contribute to

we may compute the

large downstream overturning moments. Similarly, Fig-

effective moment arm,

ure 14 shows that the ratio *M*x/*M*y tends to decrease for

increasing *M*y, although the correlation is not strong.

sured downstream

In only one case (test 3) did the ICS not arrest the

force to the down-

initial breakup ice run. This test began with no ice in

stream overturning

the main channel upstream of the ICS. The test out-

moment (Fig. 12).

come agrees with observations at the Hardwick sloped-

This calculation as-

block ICS: after release of an initial jam, a subsequent

sumes that vertical ice ice force, *F *, to downstream

ice run consisting of 1-ft-thick floes (or less) will not

forces contribute neg- overturning moment, *M*y,

jam across the 14-ft gaps at the ICS. We repeated this

ligibly to *M*y, a reason- measured on six-axis load cell.

test with thicker ice (tests 9 and 10) and found that the

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