Porosity (p)

40

30

20

Angle of Internal Friction, φ ()

Figure 11. Relationship between angle of internal friction, φ, and passive pressure

coefficient, Kp.

jams, Beltaos (1999) used Kp = 12. Healy et al. (1997)

variables. In some cases, density (D) of frazil de-

evaluated the non-equilibrium breakup jam that

posits or accumulations has been reported. Den-

occurred in 1986 on the Thames River (New

sity and porosity are related as follows:

Brunswick) using the Canadian model ICEJAM

(Flato and Gerard 1986). They found that jam thick-

D

p = 1-

ness and stage were relatively insensitive to

ρi .

(26)

changes in Kp as it was varied from 8 to 12. Tuthill

and Mamone (1998) used a value of Kp = 5.83, cor-

Reported values of porosity discussed below are

responding to φ = 45, when modeling freezeup

summarized in Table 4 and Figure 12.

jams on the middle Mississippi River.

Freezeup ice jams and frazil deposits

Porosity (p)

Petryk (1995) reports that ICESIM uses a value

The porosity of an ice accumulation is used in

of 0.73 in modeling porosity of ice jams formed

estimating the volume of ice contributing to the

from undercover deposition of frazil. This value

ice accumulation and in determining such vari-

was in the range of 0.65 to 0.85 that Beltaos (1995)

ables as its coefficient of internal strength. Poros-

calculated from data reported in Kivisild (1959).

ity is described by

Beltaos and Dean (1981) made bulk measurements

in a thick (16-m) frazil deposit and found porosi-

Vv

V

p=

= 1- i

ties of 0.541 and 0.33 for the bottom and top of the

(25)

Vt

deposit, respectively. They also reported densities

of 400 to 600 kg/m3, with lower densities near the

where Vv is the volume of voids, both above and

bottom of the deposit and higher densities just

beneath the water surface, Vi is the volume of the

below the surface of the ice cover. Majewski and

ice, and Vt is the total volume of the jam. As Beltaos

Grzes (1986) measured density along a 42-km-long

(1995) noted, the porosity of an ice jam can be much

freezeup jam on the Vistula River (Poland) be-

tween W/ c/ wek and P/ ck and found a wide

larger than the porosity of the floes comprising

lo la

lo

the jam. Few field measurements of porosity ex-

range of density in deposits and a narrow range

ist; most reported values are either assumed or

of density in shoved areas. They reported that

back-calculated from measurements of other ice

density of hanging dams ranged from 100 to 700

16