in assessing the shield design. A large amount of
January, or 26 March, at about 2.5 m (8.2 ft) deep.
information can be displayed in a format that is
If the water flow stopped at this time, our model
easily interpreted.
showed it to be safe from freezing. We then
Our previous modeling runs and the earlier
stopped the water at the end of February and ran
work done by Gunderson suggest that a wide
the model for 70 days or into the first of May. In
horizontal layer of insulation is effective at slow-
this scenario the pipe got very cold but did re-
ing frost penetration. We modeled this on the
main (barely) above freezing.
Second Avenue pipe configuration by using a 6-
From the above numerical simulations, we felt
cm (2.4-in.)-thick layer of insulation in a total
that a 1.2-m (4-ft)-wide shield with either 10.1- or
width of 2 m (6.5 ft). The numerical simulations
15.2-cm (4- or 6-in.)-thick insulation, depending
predicted that this would prevent the 0C iso-
upon how deep the pipe was buried, would be
therm from contacting the pipe. The problem,
adequate.
however, is that this width of insulation is usu-
ally impractical to excavate for in a normal utility
line installation. That is why it is often preferable
LABOSSIERE STREET
to use the inverted U configuration shown in Fig-
ure 5.
Initial design
After modeling several different combinations
When the initial excavation began on Second
of insulation thickness and shield width, using
Avenue it was discovered that the existing pipe
the inverted U, we found that a 10.2-cm (4-in.)-
leading into the avenue was tightly surrounded
thick shield with a total minimum width of 101.6
by ledge. It would have been very difficult and
cm (40 in.) would prevent the freezing front from
expensive to excavate around it while still main-
touching the pipe.
taining water service to the dwellings on the line.
We then modeled the pipe as being 1.37 m (4.5
We decided to move to our second-choice street--
ft) deep and found that there was not a practical
Labossiere. The water line in this street was a
insulation thickness that could prevent the freez-
dead-end line about 123 m (405 ft) long, and
ing front from touching the pipe. The next ap-
records showed that the existing pipe was buried
proach we took was to see if water flowing in the
from 1.2 to 1.4 m (4 to 4.5 ft) deep. We dug three
pipe would supply enough heat to prevent freez-
test pits along the length of the pipe, and these
ing. We used a 15.2-cm (6-in.)-thick shield, 1.22-m
pits indicated that the closest ledge was about
(4-ft)-wide, and ran the model with a pipe bound-
1.37 to 1.52 m (4.5 to 5 ft) below the surface. Since
ary temperature to simulate water flowing in it.
this was essentially the same situation we had
We then stopped the flow to see if the 0C iso-
thought we had at Second Avenue, we felt that
therm would progress to the pipe. In our model
the design could remain the same.
this is a two-step procedure.
The first step of the numerical simulation is
Final design
performed with a specified pipe boundary tem-
It was quickly discovered during the initial
perature derived from the known water tempera-
excavation for the new pipeline that ledge was in
tures. This simulates the actual temperatures at
fact present up to the surface for nearly the entire
any time we might need. These are then used as
length of the pipeline. In an incredible stroke of
starting temperatures in the second step, for a
bad luck, the only three places that showed ledge
numerical simulation without the specified pipe
down to 1.4 to 1.5 m (4.5 to 5 ft) were the three
boundary temperatures. As noted earlier, this is
spots where we had dug our test pits. Conse-
equivalent to a situation where no water is flow-
quently, we found ourselves in a situation where
ing in the pipe. We then run the model for any
the pipeline was being installed and our design
length of time needed to determine if the 0C
was suspect. Again, this is because ledge has a
isotherm progresses to the pipe.
much higher thermal conductivity and contains
The protection of the water pipe in the above
less moisture than soil. These two conditions al-
situation is dependent upon the initial tempera-
low the freezing front to advance faster and deeper
ture of the water, the time of year the water stops
through ledge than through relatively moist soil.
flowing, and how long it remains off. In our simu-
A series of numerical simulations were made
lations, we showed the time of maximum frost
that modeled ledge to the surface with a pipeline
penetration to be approximately 85 days after 1
buried 1.5 m (5 ft) deep. This depth was close to
6
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