depth. Ice acceleration produces an ice momentum that must be overcome to arrest
ice motion at a location downstream where thickening takes place. During shoving
and thickening of accumulating ice, water depth and velocity, ice thickness, and ice
velocity are all interrelated and vary with distance and time. It is this unsteady
nature of shoving and thickening that this study addresses.
Spatial extent
The horizontal and vertical extent of a jam are also used to classify jam type. In
plan, jams are either partial or complete, according to their extent across a river. A
partial jam means that a portion of the river width remains as an intact ice sheet, or
one channel around an island jams while the other remains clear. In vertical sec-
tion, jams are classified as floating or grounded. Grounding, when ice extends to
the channel bed, takes place quite often near the riverbanks, at shallow areas such
as bars or crossings, and near the toe region of a thick jam. Grounded jams usually
result from very unsteady water and ice flows. They severely limit water flow, greatly
increasing water levels. Water may flow as seepage through grounded accumula-
tions or even over the top of a jam. Little is known about the mechanism of ground-
ing or the permeability of grounded jams. Floating jams are more common and
easier to analyze, though they may become partially grounded when river flow
recedes. Most analyses to date assume floating jams, whose flotation follows
hydrostatic pressure law.
State of evolution
The final classification category is that describing the state of jam evolution:
steady-state, evolving in time, or evolving up-channel. An evolving jam continues
to be subject to unsteady flow rates, ice discharges, or changes in other ice variables
(such as strength). A breakup jam, already formed and undergoing shoving and
thickening, will continue evolving with nonuniform thickness, depth, and water
velocities. A freezeup jam may experience fairly steady flow rates, but frazil ice
production and transport may cause it to shove and thicken with time. Figure 12
shows ice jam evolution with time. As the jam thickens and progresses upstream,
water levels rise and velocities decrease. Whatever the final water surface level and
jam thickness profile might look like, the ice thickness and velocity are not steady
as the jam develops.
If conditions do become steady, uniform, and stable, a jam may have an equilib-
rium section. Strictly speaking, an equilibrium section is uniform only in a reach-
averaged sense. Figure 12d shows that the thickness and depth are nearly constant
in the longitudinal direction. Moreover, the bed slope, water-surface slope, and
energy slope are equivalent in the equilibrium section. These conditions of unifor-
mity were assumed by ice researchers when formulating the first analyses of forces
exerted on a stationary jam (e.g., Pariset and Hauser 1961, Uzuner and Kennedy
1976).
Analysis of stationary jams
A major advance in addressing the effects of ice jams on water levels, and in
estimating jam thicknesses, was the realization that a floating jam could be likened
to a granular material contained between two parallel walls. The behavior of a
granular material is influenced by the forces exerted upon it and its material prop-
erties. As the length of a jam increases, these forces increase, as do stresses within
the jam.
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