February and decreased to 1.7 m (5.6 ft), a small
against. In our future comparisons we will be
improvement.
using the actual surface temperature as our top
As mentioned earlier, we model ledge as a con-
boundary condition to see if we can more closely
tinuous mass of solid rock where actual ledge
model the maximum frost penetration depth. The
might not be so. During the construction of the
results of these runs will help tell us if the ledge
pipeline it was evident that portions of the ledge
thermal conductivity needs to be adjusted and
were fractured, with seams of water within some
what effect inaccuracies in the material thermal
of the fractures. These areas would greatly influ-
conductivities have upon our model results.
ence the thermal conductivity of the area and
would slow frost penetration compared to solid
rock. The above analysis suggests that we have a
LITERATURE CITED
higher numerical ledge thermal conductivity
than is appropriate.
Coutermarsh, B.A. and G.E. Phetteplace (1991a)
Analysis of frost shields using the finite element
method. In Proceedings of the Seventh International
Conference, Numerical Methods in Thermal Problems
PRELIMINARY CONCLUSIONS
(R.W. Lewis, J.H. Chin and G.M. Homsy, Ed.),
AND RECOMMENDATIONS
Vol. VII, Part 1, p. 122.
The winter of 199495 was too warm to pro-
Coutermarsh, B.A. and G.E. Phetteplace (1991b)
vide us with a good test of the shielding concept.
Numerical analysis of frost shields. Cold Regions
We still do not know what the water tempera-
6th International Specialty Conference (D.S. Sodhi,
tures will be at the test site during a very cold
Ed.), American Society of Civil Engineers, p. 178.
year or what effect they will have upon the shield's
Gunderson, P. (1975) Frostproofing of pipes. U.S.
performance.
Army Cold Regions Research and Engineering
It appeared that the shield was providing some
Laboratory, Draft Translation 497.
protection to the water line, as the temperature of
Gunderson, P. (1989) Distribution network for
the water increased as it flowed up the hill. It is
district heat, electricity, water and sewage. Nor-
difficult to draw any firm conclusions, however,
wegian Building Research Institute, Oslo, Project
since the ground at the pipe depth remained
Report 46 (in Norwegian).
above freezing throughout the winter.
Lunardini, V.J. (1981) Heat Transfer in Cold Cli-
Another area of concern is the performance
mates. New York: Van Nostrand Reinhold Com-
of the service lines to the residences. These
pany.
small-diameter lines are relatively shallow and
Phukan, A. (1985) Frozen Ground Engineering.
uninsulated and would seem to be susceptible
Englewood Cliffs, New Jersey: Prentice Hall,
to freezing.
Inc.
The numerical model appears to be function-
Segerlind, L. (1984) Applied Finite Element Analy-
ing well where we have accurate input to check it
sis. 2nd edition. New York: John Wiley and Sons.
15
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