Insulation to prevent ground freezing

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Insulation to prevent ground freezing

ISSN

?

,

INSULATION IU

MAY

I

NATIONAL RESEARCH COUNCIL

L

62535

Division of Building Research National Research Council of Canada

INSULATION 'ID

PREVENT

by

D . G . Stephenson

The ground can b e kept unfrozen a l l w i n t e r if it is covered at the

end o f t h e summer with a t h i c k layer of straw (or o t h e r i n s u l a t i o n ) ,

This note

I t assumes t h a t t h e straw-covered a r e a is l a r g e enough t h a t edge e f f e c t s can b e n e g l e c t e d . This means t h a t t h e cover must extend about 10 ft

beyond t h e perimeter o f t h e area that must be p m t e c t e d .

'Ihe o t h e r assumptions are:

1) A t the time when the straw i s applied the temperature of the ground i s To a-t: a l l depths and t h a t the temperature of t h e air is also

To at that time.

2) The ground is homogeneous w i t h a thermal c o n d u c t i v i t y R

and d i f f u s i v i t y

a

soil '

3) The straw cover has a known c o n d u c t i v i t y ,

K

n e g l i g i b l e h e a t storage capacity. s trawl

4) The straw

remains

t h e 3 2 O ~ isothen p e n e t r a t e s i n t o t h e s t r a w .

The variation in air temperature w i t h time can be represented as t h e sum of a series o f ramp functions w i t h d i f f e r e n t slopes and d i f f e r e n t s t a r t i n g times and w i t h t h e same _{temperature darum. For example,} a _ramp

w i t h a slope of - 2 0 " ~ / m n t h plus one s t a r t i n g 3 months l a t e r w i t h a s l o p e

of + 2 0 ° ~ / m o n t h is equivalent ta a temperature curve t h a t decreases

linearly f o r 3 _{mnths and then remains c o n s t a n t thereafter. S i n c e the}

heat conduction equation i s l i n e a r , t h e v a r i a t i o n o f t h e soil surface

temperature is j u s t t h e sum o f t h e effects caused by each component o f

t h e air temperature a c t i n g independently.

The temperature, Ts, at the surface sf a semi-infinite s o l i d w i t h a

when TA = T + Ct, where

T

0 A

Temperature at a l l depths

i n

h r

soi 1

Y

K s o i l

2 2

For values of y t less than 0.2 the function FCy t] is very well

represented by t h e simpler expression

Example :

T~ drops 2On/month f o r 3 months, remains constant at -20°F for 1

month, then rises at 2 0 " / m n t h .

Find the depth o f straw needed to keep the soil surface temperature

from

K 2

st raw = 0.5 Btu/hr ft (OF/in.) 2

( a ) F o r 2 - f t l a y e r o f straw

K

s traw

B = _R

,

s t r a w T i m e ₃ Months 0 1 2 3 4 5 T = C o n s t a n t 40 0 4 0 4 0 40 40 40 40 40 Ramp I 0 - 20 -40 - 60 - 80 - 100 -120 - 140 Ramp 2 _{0 0 0 0} 20 4 0 60 80 Ramp 3 0 0 0 0 0 20 40 60

The c o n s t a n t plus the t h r e e ramp functions produce t h e required time v a r i a t i o n af the ambient temperature

TA.

temperature is j u s t t h e sum

of

component o f t h e ambient temperature acted independently.

The surface temperature r e s u l t i n g f r o m a ramp with slope 2o0/month

For y2 = 0.0176 months-' t 2 months T t F ( T ~ ~ I S o i l Surface Ternpehature Time 11_3 Months 0 T = C o n s t a n t 0 40 40 40 40 40 40 40 Ramp 1 0 -1 86 -5.00 - 8 . 8 7 - 1 3 . 4 2 -18.54 - 2 2 . 4 1 Ramp 2 0 0 0 0 + 1.86 + 5.00 + 8.87 Ramp 3 0 0 0 0 0 + 1 . 8 6 +5,100 Sum = T S 40' 38-14" 35.00" 31.13' 28.44O 2 8 - 3 2 " 3 1 - 4 6 "

(b) For 3 ft straw y2

=

-

R

v

o.ao

-

These r e s u l t s i n d i c a t e t h a t just over 3 ft of straw would b e enough

to keep t h e ground surface f m m f r e e z i n g i f the

m i n i m u m mean

temperature is - 2 0 " ~ and the ground is at + 4 0 ' ~ when the straw i s spread.

The thickness o f t h e i n s u l a t i o n needed depends

on the

from the

.

Thus

2

2 K i n s u l a s o i l

x 10 5 i n s o l 1 -

]

Anather generalization can be made. The i n s u l a t i o n should b e a p p l i e d

when t h e heat c o n t e n t o f t h e ground is a t i t s annual maximum. T h i s is

usually t h e l a t e r p a r t o f August. If the i n s u l a t i o n is a p p l i e d this e a r l y

t h e

To w i l l

fact, 2 ft of s t r a w applied at the end of August would probably be

adequate t o keep the ground unfrozen in those parts of Canada where the minimum mean monthly temperature is t h e order o f - 2 0 " ~ .