coupled model of jam evolution is needed to accurately predict jam thickness.
5. The shape of an inflow water hydrograph and its peak flow are important in
estimating jam thickness because they determine whether jams fail and reform pro-
gressively or completely. Fast-rising hydrographs with attendant rising water lev-
els result in larger gradient terms across a computational reach. The gradient terms
(including ice momentum) result in greater predicted jam thickness. They are not
present in equilibrium thickness formulations, which thereby underpredict thick-
ness and water levels. The time that a flow remains at its peak value is also impor-
tant. Instantaneous peaks are attenuated as they travel downstream, resulting in
lower local discharges and lower stresses on the underside of the jam, leading to
thinner jams.
RECOMMENDATIONS FOR FUTURE RESEARCH
The flume experiments and numerical model bring to light several areas where
deficiencies in knowledge and formulation persist.
Several parameters are necessary to characterize the properties of ice accumu-
lated in a jam. Among the properties are angle of internal resistance φ, coefficient of
ments of φ have been obtained for particulate materials, with an estimate given as
the dry angle of repose of the material. No known experiments have been con-
ducted, however, to determine suitable values of λ or k0 for ice. Further laboratory
experiments to define them are necessary.
The full effects of ice momentum have not yet been fully identified because of
the influence of ice velocity on the parameters mentioned above. Of particular
importance is the temporal variation of these parameters as an ice jam fails and
mobilizes, during which the forces on a jam continually change. The value of Kp is
related to φ and has been shown to be adequately described by Mohr-Coulomb
theory for a stationary jam. The Rankine states of active and passive pressure
described using Mohr-Coulomb theory are intended as point values at the instant
of particulate material failure. Questions surround the value of the passive pres-
sure coefficient once a jam fails or is moving downstream. A similar argument goes
for the value of coefficient of friction of the ice along the shear boundary at the
banks λ. Certainly, if this coefficient is developed in a way similar to that for the
simple static coefficient of friction, there must be changes that occur as the material
comes into motion. It is likely that the coefficient would reduce once a jam moves,
thereby resulting in a lower resistance to downstream movement. Thicker jams
would result when the moving ice is finally arrested because bank friction is
reduced.
Several modifications to the model are possible to make the simulations more
realistic. The modifications include the ability to use actual cross-section geometry,
and changes in roughness coefficients, channel width, and ice parameters with dis-
tance. Extending the model to two-dimensional coordinates would not only
increase the computational time, but would also introduce difficulties in defining
the failure mechanism. The model developed in this study assumes that ice param-
eters are satisfactorily given as bulk properties. A more suitable advance might be
the adaptation of the model to simulate branched systems, where jam formation in
one channel would affect water and ice movement in another.
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