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Weather in relation to winter concreting
Ser
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RIIEM SYMPOSIIIM: Itlnter Concretlng IMATTMR IN REI./I.fION TO WINTER CONCRETING
A N A L Y Z ' ; D
by E . G . S w e n s o nNATIONAI RESEARCH COI'NCII.
. Canada.
S e g s l o n A General Report
WEATIIER IN RIIATION TO WINTER CONCRITING by E . G . S w e n s o n S U M M A R Y T h l s r e p o r t a l e a l s w i t h t h e v a r i o u s factors whi.ch l n f l u e n c e t h e c o o l i n g o f c o n c r e t e e x p o s e d t o winter weather ancl with the quantitati,ve roethocls by which weather data may b e a p p l i e d i n p r a c t i c a l c a s e s . T h e o v e r a f l s i t u a t i o n i s e x a m i n e d o n t h e b a s i s o f t h e two general problerns: t h e p r e c l i c t l o n o f t h e e n v i r o n r n e n t a l c o n d i t i o n s t o w h i c h a c o n c r e t e m a s s w i l l b e s u b j e c t e d , a n d t h e p r e d i c t i o n o f t h e r e s u l t i n g c o n d i t l o n s t h r o u g h o u t t h a t m a s s .
C a s e s a r e c j _ t e d a n c l t h e c o n p o n e n t s of the basic heat exchange between the concrete mass ancl its environnent are i d e n t l f l e c l . T h e e l e m e n t s a n d f a c t o r s o f c l i m a t e a r e
c o n s i d e r e d o n t h e b a s i s o f t h e i r role in cocling, and winter w e a t h e r d a t a a r e a s s e s s e d . T h e e f f e c t s o f v a r i o u s l o c a l f a c t o r s o n t h e p e r t i n e n t w e a t h e r e l e m e n t s a r e c o n s i d e r e d i n r e l a t i o n t o t h e c o o l i n g o f c o n c r e t e . T h e u s e t h a t c a n b e m a c l e o f s t a t l s t i c a l w e a t h e r - d a t a , o f f o r e c a s t i n f o r m a t i o n , a n c l o f a k n o w l e d g e o f t h e i n f l u e n c e of nicroclimatic f a c t o r s 1 s d i s c u s s e d i n t e r m s o f t h e size and. duratlon of a job.
T h e p r o b l e n o f p r e d l c t i n g t e n p e r a t u r e s w i t h i n t h e c o n c r e t e l s r e c o g n i s e d b a s i c a l l y a s a h e a t e x c h a n g e s l t u a t i o n . H e a t t r a n s r n i s s i o n p h e n o m e n a a r e r e v i e w e d b r l e f l y , a n d i t i s n o t e d t h a t c o n v e c t l o n a n d radiation c a n b e d e a l t w i t h b y m o d i f l c a t i o n s t o s i x q p l e c o n d u c t i o n t h e o r y , t h u s g r e a t l y s i n p l i f y i n g t h e e q u a t i o n s a n d c a l c u l a t i o n s . A r e v l e w i s g i v e n o f q u a n t l t a t i v e n e t h o d s a l r e a d y d e v e l o p e d f o r p u r p o s e s o f p r e d i c t i o n o f c o n c r e t e t e n p e r a t u r e s . I t 1 s s u g g e s t e d t h a t l a b o r a t o r y i n v e s t l g a t i o n s a r e useful prinarily 1n the determination of quantities anal c o e f f i c l e n t s r e q u l r e d i n c a l c u l a t l o n s , t o t h e s t u d y o f phenonena, and to assessing the approximations that nay be enployetl .
R d S U M d l e r a p p o r t p r d p a r d p a r l r a u t e u r p r d c i t d a t r a i t a u x d i v e r s f a c t e u r s q u i i n f l u e n c e n t 1 e r e f r o i d i s s e n e n t d u b d t o n e x p o s e i a u x i n t e m p d r i e s d e 1 ' h i v e r , a i n s i q u r a u x m d t h o d e s q u a n t i t a t i v o s e r v a n t A a p p l i q u e r d d e s c a s p r a t i q u e s l e s t l o n n d e s s u r I a t e m p d r a t u r e . L r a u t e u r a x a m i n e 1 ' e n s e m b l e d e la sltuation en se basant sur 1es tleux problEmes gdndraux s u i v a n t s : a ) 1 a p r d d i c t i o n d e s c o n d i t i - o n s d u m i l i e u au-.cque11es une masse tle bdton sera soumise et b) 1a p r d d l c t i o n d e s c o n d i t l o n s q u i e n r d s u l t e r o n t d a n s t o u t e l a n a s s e . M o n s i e u r S w e n s o n c i t e c e r t a i n s c a s e t i d e n t i f i e d e s d l d r o e n t s c l e 1 ' d c h a n g e c a i o r i f i q u e d e b a s e q u i s e p r o d u i t e n t r e l a r n a s s e d e b d t o n e t s o n a n b i a n c e . 1 1 c o n d i d d r e 1 e s 6 l d n e n t s e t 1 e s f a c t e u r s d u c l l n a t e n s e b a s a n t s u r l e u r r o l e f o r s c l u r e f r o i d i s s e m e n t ; 1 1 d v a l u e a u s s i 1 e s d o n n d e s s u r l a t e u r p d r a t u r e d ' h i v e r . L ' e f f e t e x e r c d p a r d i - v e r s f a c t e u r s l o c a u x s u r l e s d l d m e n t s p e r t i n e n t s d e t e m p d r a t u r e s o n t a u s s i 1 ' o b j e t d ' u n e d t u d e p a r r a p p o r t a u r e f r o i d l s s e m e n t d r . r b d t o n . I ' a u t e u r d j - s c u t e , e n o u t r e , e n t e r m e s d e I ' d t e n d u e e t d e 1 a d u r d e d r u n p r o j e t r l r e m p l o i q u ' o n p e u t f a i r e d e s s t a t i s t i q u e s s u r I a t e r n p d r a t u r e , c l e s p r d d i c t i o n s e t d e l a c o n n a i s s a n c e c l e l - r i n f f u e n c e c l e s f a c t e u r s m i c r o c l i m a b d r i - q u e s . I , e p r o b l b m e d e l a p r d d i c t i o n d e s t e n p d r a t u r e s d l r i n t d r i e u r d u b e i t o n e s t r e c o r u n u f o n t l a m e n t a l e m e n t c o m m e u n c a s c l ' d c h a n g e c a l o r i f i q u e . I ' a u t e u r e x a m i n e r a p i d e m e n t 1 e s p h d n o n b n e s c l e t r a n s r n i s s i o n c a l o r i f l q u e e t n o t e q u ' o n p e u t c o n s i d r i r e r l a c o n v e c t i o n e t l - a r a d i a t i o n c o n m e d e s m o c l i f i c a t i o n s d e I a t h d o r i e d e c o n d u c t i o n s i m p l e r c e q u i s i - m p l i f i e g r a n d e m e n t 1 e s e i q u a t i o n s e t l e s c a 1 c u 1 s . l r a u t e u r f a i t u n e r e v u e d e s m d t h o d e s q u a n t i t a t i v e s q u i o n t d d ; l d t d m i - s e s a u p o i n t p o u r p r , J d i r e 1 e s t e n p d r a t u r e s d u b d t o n . I 1 i n d i q u e q u e 1 e s r e c h e r c h e s l e l a b o r a t o i r e s e r v e n t s u r t o u t d l a d d t e r r n i n a t i o n d e s q u a n t i t 6 s e t d e s c o e f f i c i e n t s r e q u i s p o u r l e c a f c u l , a i - n s i q u ' ) . l r d t u d e d e s p h d n o m d n e s e t d 1 ' e i v a l u a t i o n d e s a p p r o x i n a t i o n s q u ' o n p e u t u t i l i s e r . a.
WEATHER IN RNT,ATION TO W]NTER CONCRXT]NG I n o r d e r t o a c h i e v e t h e p r o p e r c u r i n g e n v l r o n x c e n t f o r f r e s h c o n c r e t e i t i s n e c e s s a r y t o e n p l o y t r e a n s o f m o d i f y i n g o r c o n t r o l l i n g t h e e f f e c t s o f w e a t h e r , r e g a r d l e s s o f s e a s o n . V / i n t e r c o n c r e t i n g p o s e s t h e s p e c i a l _ p r o b l e n o f p r o t e c t i n g t h e c o n c r e t e f r o m t h e e f f e c t s o f b e l o w - f r e e z i - r r g t e m p e r a t u r e s u n t i f i t h a s a t t a i n e d t h e n e c e s s a r y r t f r e e z i n g r e s i s t a n c e r ' . D e s p i t e t h e d l f f i c u l t i e s l n v o l v e d j . n w i n t e r c o n s t r u c t j . o n d u e t o 1 o w t e r n p e r a t u r e e , s n o w , s h o r t d a y l i g h t p e r i o d s a n d g e n e r a l i n c o n v e n i e n c e a n d d i s c o r o f o r t , building t e c h r o l - o g y m a k e s y e a r - a r o u n c l c o n s t r u c t i o n p r a c t i c a l a n d m o d e r n n e e d s r n a k e i t n e c e s s a r y . T h e a d d e d c o s t s a r e o f t e n b a l - a n c e d b y s u c h a d v a n t a g e s a s t h e g r e a t e r a v a i l a b i l i t y o f n a t e r i a l s a n d l a b o u r a n d t h e e a s e o f t r a n s p o r t a t i o n o v e r f r o z e n g r o u n d ( 1 ) . p r o p e r p r o t e c t i o n o f c o n c r e t e i n c o l d . w e a t h e r c a n a l s o p r o v l d e r n o r e u n i f o m c u r i n g c o n d i t i o n s t h a n a r e o f t e n o b t a i n e d l n s u m m e r w o r k ( 2 ) . T h e p r o t e c t i o n r e q u i r e d d u r i n g w i n t e r c o n c r e t i n g h a s t h u s f a r b e e n s e l e c t e d a l - m o s t e n t i r e l y o n t h e b a s i s o f r u l e -o f - t h u n b m e t h -o d s d e r i v e d f r -o m f l e l d e x p e r i e n c e . W e a t h e r i n f l u e n c e h a s b e e n c o n s l d e r e d p r i n a r i l y i n t e r m s o f a t m o s p h e r i c t e m p e r a t u r e w i t h l i t t l e o r n o r e g a r d f o r o t h e r e n v i r o n m e n t a l f a c t o r s . I t h a s o r r l y r e c e n t l y b e e n r e c o g n i z e d t h a t c o n c r e t e c a n h a r d e n s a t i s f a c t o r l l y a t r e l _ a t i v e l y 1 o w t e m p e r a t u r e s . I t i s n o w r e a f i z e c l t h a t p r o t e c t i o n h a s o f t e n b e e n e x c e s s i v e . T h e m i n i m u n c o n d l t i o n s u n d e r w h i c h a c c e p t a b l e c u r i n g i s a c h j - e v e d a r e n o w b e i n g d e f i n e d , a n d i t i s p o s s J . b i - e t o d e v e l o p q u a n t i t a t i v e n e t h o d s f o r t h e r a t i . o n a l d e s i g n o f p r o t e c t i o n f o r f r e s h c o n c r e t e p l a c e d u n d e r w i n t e r c o n d i - t i - o n s . I t i s t h e p u r p o s e o f t h j _ s p a p e r t o e x a m j - n e w i n t e r w e a t h e r c o n d i t i o n s a n d t h e r e l a t i o n s h l p s b e t w e e n t h e r n a n d t h e t h e r m a ] a n d r n o i s t u r e e n v i r o n m e n t o f f r e s h c o n c r e t e .
II TIIE BASIC PROBI,EM
An excellent exanple of concretlng under extremely
severe winter condltlons was the oonstrubtlon of a concrete
brldge at Saskatoon, Canadar twenty-four years ago.
Continuous temperature records ln thle case llLustrate the
remarkable retention of heat in nass concrete wlth
relatively 11ttle protection, and the positlve moaleratlng
lnfluence of a water bcdy (l). lhe concrete in thls bridge
1s in excellent cond.ltlon todaY.
Thle brldge, shown 1n figure 1, was bu1lt uncler condltione whlch calletl for the provlslon of a naximum of
wlnter enploynent. fhe use of naoblnery was restrlctecl a:ccl
the concrete hatl to be wheeled by labourers from the mlxerg to the plers as far as 10OO feet away' regartlless of weather c o n d t l t i o n s .
tr'igure 2 shows the tenperature recordlnge in one of the plers, the concrete for whlch was placecl ln an excavation when the dally nininum alr temperature was as low as -looF' 0n1y the formwork served as protection up to the ice Ievel o f t h e r i v e r . T h e 2 5 - f o o t s e c t i o n a b o v e l c e l e v e l w a s h o u s e a t a n d h e a t e t l . D e e p l t e w l n t l s p e e d s o f u p t o 2 0 n . p ' h . t the thernorneters against the forne never reatl below 50oF.
The roatlway ancl sitlewalk slabs were placed untler
sinllar extreme conditlons. The stalewalk concrete was
protected by hot sand, sawclust, and tarpaper. the roa'Iway
concrete was kept above freezing for more than three ctays
by runnlng hot water over it contlnuously ilay ancl night ' Flgure J shows the teroperatures recortled in another pler, in the sprlnging arch sectlon attached to 1tr and in tbe roatlway slab. The river water, at 52oF, hatl a
reroarkable moderating effect on the temperatures 1n the
pier. Thie effect extendetl through the arch ring ancl even
tto the crown' a hunclrecl feet from the pler anal at an
elevation of ?5 feet above the water 1lne. Ihe ternperatures
in the roatl-deck followed the a1r tenperature qulte closelyt but the rtthernelly attacheclrt arch ring showeal a much lower
r e s p o n s e t o a n b l e n t t e m p e r a t u r e s . A s i n l l a r b u t o p p o s i t e
effect was recorded during the hot sunmer. Although the
tlata shown 1n figure I were obtained in hardeneil concrete, t h e y s e r v e a s a g o o d l l l u s t r a t i o n o f t h e i n f l u e n c e w h i c h c o n t a c t w l t h l a r g e m a s s e s c a n h a v e , i n t h e c a s e of newly p l a c e d c o n c r e t e , i n p r o v i d i n g f o r a flow of heat whieh may o f f s e t i n l a r g e m e a s u r e t h e c o o l i n g p r o i l u c e d b y 1 o w a i r t e m p e r a t u r e s .
I n t h e c a s e o f s n a l - l c o n c r e t e s t r u c t u r e s o r e l e m e n t s , t h e h e a t s t o r e d a n d t h e h e a t g e n e r a t e d p e r cubic foot are
the sane as in the larger structures. Ihe saroe phenomena
a r e i n v o l v e d b u t t h e r e d u c t i o n i n s l z e increases the s u r f a c e t o - v o l - u n e r a t i o , t h u s g r e a t l y j _ n c r e a s i n g the rate at w h i c h t e m p e r a t u r e c h a n g e s c a n t a k e p I a c e . f n c r e a s e d p r o t e c t i o n 1 s r e q u i r e d t o p r o v i d e t h e s a r : e c u r i n g c o n d i t i o n s . T h e i n f l u e n c e o f s i z e i s i l f u s t r a t e d b y f i g u r e 4 , T w o c o n c r e t e c u b e s , p r o t e c t e d o n l y b y 2 - i n c h l u n b e r f o r m s , w e r e e x p o s e d t o f r e e z i n g c o n d l t i o n s , w i t h a t h e r m o m e t e r p l a c e d a t t h e c e n t r e of the face next to the f o r r n ( 4 ) . T h e f a c e t e n p e r a t u r e o f t h e l - f o o t c u b e d r o p p e d b e l - o w f r e e z i n g i n 5 t h o u r s , w h e r e a s t h e f a c e t e m p e r a t u r e of t h e J - f o o t c u b e r e m a i n e d a b o v e 50oF after l5 hours.
T h e c a s e s j u s t c i t e d s h o w t h a t t h e t e m p e r a t u r e c o n d i t i o n s w i t h i n a c o n c r e t e m a s s a r e n o t a l o n e d e t e r m i n e d b y t h e e x t e r n a l w e a t h e r c o n d i t i o n s , b u t c a n b e g r e a t l y l n f l u e n c e d b y t h e e f f e c t s o f s c a l e a n d o f h e a t e x c h a n g e w l t h c o n n e c t i n g m a s s e s . O t h e r i m p o r t a n t f a c t o r s a r e t h e d e g r e e o f i n s u l a t i o n i n t e r p o s e d b e t w e e n t h e c o n c r e t e a n d t h e w e a t h e r , a n d t h e r a t e a n d a n o u n t o f h e a t g e n e r a t j _ o n within t h e c o n c r e t e m a s s . T h e p r e d i c t i o n o f t e r n p e r a t u r e s i n t h e c o n c r e t e i - n v o f v e s r e c o g n j _ t l o n o f a b a s i c h e a t exchange s i t u a t i o n j - n which temperatures can change only through c h a n g e s i n t h e s t o r e o f h e a t e n e r g y w l t h i n t h e xoass.
r , l . e a t h e r e l e m e n t s c a n i _ n f lu e n c e t h e t e m p e r a t u r e of c o n c r e t e o n l y i n s o f a r a s t h e y c h a n g e the store of internal h e a t . T h e i r i m p o r t a n c e a n d i n f l u e n c e a r e d e t e r m i n e d b y t h e e x t e n t t o w h i c h t h e y a f f e c t t h e v a r i o u s c o m p o n e n t s o f t h e
over-al-l heat exchange between the concrete naas and lts surrounclings.
The conponents of the basic heat exchange between the concrete mags ancl its environment are shown dlagramnatically ln flgure 5. The store of heat wlthln the concrete ls nade up of sensible heat ln an amoult which le reflectetl dlrectly by the tenperature. To this store is attaleal the heat of hydration the rate of release of whlch is a functlon of tine and temperature for a glven mix. The heat exchange with c o n n e c t i n g b o d i e e m a y b e e i t h e r a g a l n o r a l o s s b u t r a s i e the case with all heat flows, can take place only 1n the c l i r e c t i o n o f d e c r e a s i n g t e m p e r a t u r e s .
C o n d u c t j - o n - c o n v e c t i o n e x c h a 4 g e , w h i c h i s f r e q u e n t l y t h e m o s t i r n p o r t a n t o n e , t a k e s p l a c e b e t w e e n t h e c o n c r e t e m a s s ancl the air, antl is affected by air tenperature anal air
s p e e d . f n w l n t e r t h i s w i l l n o r m a l l y b e a h e a t l o s s . A further component of heat exchange fron the surface of the c o n c r e t e o r i t s e n c l - o s u r e o c c u r s a s a n e t r a d i a t i o n e x c h a n g e with the sun and sky. When the sun is shining there nay be a heat gain regartlless of the temperature of the concrete, a heat gain or loss on cloudy days, ancl a loss on clear nlghts to the sky. During the daytine there can be diffuse ratliation produeed by the scattering antl reflection of some of the tlirect radiation coming from the sun by natter in the a t m o s p h e r e , b y t h e g r o u n d , a n d b y s u r r o u n d i n g o b i e c t s ' I n acldition there can be a radiation exchange between the concrete anat 1ts surrounalings, the alirection of whj-ch is d e t e r n i n e d b y t h e r e s p e c t i v e t e m p e r a t u r e s .
The component of heat exchange due to change of state of water is the only one shown that tloes not result in the clirect transfer of heat energy. Evaporation occurring on or within the concrete takes up the latent heat of vaporization whlch is then carried off by the escaping vapour.
Conversely, during a contlensation process, thJ.s latent heat is carrietl in the vapour and ie glven up at the condensing surface as heat energy. This conponent of the heat exchange will be affected by the vapour pressure differences between
t h e c o n c r e t e a n d t h e a t m o s p h e r e , a n d b y a i r m o v e m e n t . T h e evaporation-cond.ensation exchange enters not only into the t h e r r n a l p i c t u r e a s J u s t c l i s c u s s e d . , b u t a f f e c t s a l s o t h e n o l . s t u r e s t o r e l e a d . i n g t o a l r y i n g , o r , i n s p e c i - a I c a s e s , t o w e t t j . n g , d e p e n d i n g o n t h e d l r e c t i o n o f t h e d r i v i n g
p o t e n t i a l .
A t t e n t l o n h a s b e e n d i r e c t e d t h u s f a r m a i n l y t o t h e exchange of heat between the concrete and 1ts sumoundlngs. There will also be a flow of heat from one part of the c o n c r e t e t o a n o t h e r , a c c o r d i n g t o a p a t t e r n d e t e r r n i n e c l b y the temperatures produced throughout the mass, and by the t h e r n a l p r o p e r t l e s o f t h e c o n c r e t e i t s e l f . T h e a s p e c t o f w i n t e r c o n c r e t i n g w l t h w h i c h t h i s s e s s i o n i s c o n c e r n e c l i s e s s e n t i a l l y t h a t o f p r e d i c t i n g t h e c o n d i t i o n s w h l c h t h e c o n c r e t e w 1 1 1 e x p e r i e n c e d u r i n g i t s c u r i n g p e r i o d . , a n d m a y b e c o n s i d e r e c l i n t w o d l s t i n c t p a r t s : ( a ) p r e d i c t i o n o f t h e e n v i r o n m e n t a l c o n d i t i o n s t o w h l c h t h e c o n c r e t e n a s s w i l l b e s u b j e c t e t l , a n d ( b ) p r e t t i - c t l o n o f c o n d i t i o n s t h r o u g h o u t t h e c o n c r e t e
resulting from a given set of environrnental c o n d i t i o n s . R e f j - n e m e n t i n t h e s e l e c t j - o n o f p r o t e c t i o n d e p e n c l s u p o n t h e a c c u r a c y w i t h w h i c h t h e c o n d i t i o n s , w h i c h t h e c o n c r e t e i e I 1 k e 1 y t o e x p e r i e n c e , c a n b e p r e d l c t e c l i - n a c l v a n c e o f t h e c u r i n g p e r i o d . T h l s w i l l i n v o l r r e a n a t t e m p t t o p r e d l c t w e a t h e r c o n c l l t i o n s s i n c e o t h e r Q n v i r o n m e n t a l f a c t o r s w i l l b e known or can be determined.
]II GENEzuI CHARACTERISTICS OF W]NTER WEATI]ER
1. The Nature of V{eather
'lVeather and cllmate are determlnecl prlnarlly by the heat balance between the atmosphere and the surface of the e a r t h , a n d a l l c h a n g e s t h a t o c c u r i n w e a t h e r c a n b e t r a c e c i t o t h e s l n g l e p h y s i c a l f a c t o r : h e a t ( 5 ) . T h e e a r t h a c t s a s a heat reservoir and its surface is an j-ntermediary in al1
heat transactlons between it and the atnosphere.
Radiatlon is the priroary process governing the warming and the cooling of the earthrs surface. In sunmer the surface gains heat from solar racllatlon by day and loses heat by outgoing racliation at nlght, the amount varying with the type of surface. In winter, the lnconing racllation ls realuced by day owing to the recluced angle of inciclentle of the sunrs raysr, their longer path through atnospherer and the shorter perlod of sunlight. The amount of inconlng racllatlon reachlng the earth nay be realucecl to a snall quantlty through reflection by clouds. The actual- amount absorbed nay be reclucetl Bubstantlally by snow cover. 0n a winter nlght the outgoing ratllatlon ls also small due to the reduceal temperature of the earthrs surface fron whlch the heat nust be drawn. Under conditlons l-eading to a net loss outward the grouncl surface temperature may be reducecl below t h a t o f t h e a d j a c e n t a i r a n d t h e e o 1 l l a y e r s .
The nost irnportant observ'etl and neasured physlcal p r o p e r t l e s o f w e a t h e r a r e a i r t e n p e r a t u r e , w i n d r Y a p o u r c o n t e n t , a 1 r p r e s s u r e , s t a t e o f s k y r a l d p r e c i p l t a t i o n . These are the fluctuating components of weather antl clinate. The relatively static influencee on large-sca1e weather are the geographical factors auch as latltude, altltutler lancl anat water distrlbutionr vegetati.on, antl nature of the soi1.
The characteristics of weather ancl clinate rnay be clefinect by the indivltlual elementa ae they vary wlth tirne o f t l a y , s e a s i n , a n d p l a c e . C e r t a l n p r o p e r t i e s a r e m o r e usefully tlescribecl by calculatetl values lnvolving
conbinations of one or nore of the simple elernents. These a r e r e f e r r e a l t o a s c o n b l n e d e l e m e n t s , e x a m p l e s b e i n g :
relative hurnlclity, equivalent temperature, cooling power ancl t l r y l n g p o w e r . S p e c l a l c h a r a c t e r l g t l c s s u c h a s v a r i a b i f i t y , frequency and probabllity are calfecl derivecl elements antl a r e o b t a i n e c l f r o m s t a t i s t i c a l a n a l y s e s o f w e a t h e r d a t a .
The recortling of weather clata is usually carriecl out uncler truntlisturbecl contlltionsrr, w611 above the surface of the ground, in ortler to tlescribe conditions over a large
r e g l o n . L o c a l i n f l u e n c e s a r e , t h e r e f o r e , l a r g e l y e l i n i n a t e d . T h e p h y s i c a l c o n d i t i g n o f t h e a t m o s p h e r e , d e s c r i b e d b y t h e s e d a t a , a t a given time and p1ace, c o n s t i t u t e s t h e w e a t h e r . T h e a v e r a g e s t a t e o f t h e
a t n o s p h e r e i n a g i v e n r e g i o n , a s reflected by the average of c l a t a e x t e n d l n g o v e r n a n y y e a r s , constitutes t h e c l i m a t e o f t h a t r e g i o n .
2 . W i n t e r W e a t h e r C h a r a c t e r i s t i c s a n d D a t a
( a ) T e m p e r a t u r e s . - T h e r o o s t i n p o r t a n t w e a t h e r e l e m e n r i n w i n t e r c o n c r e t i n g i s t e m p e r a t u r e . T h e d a i l y and annual temperature variations follow closely t h e c h a n g e s o n t h e e a r t h ' s s u r f a c e w h j _ c h a r e , i n t u r n , d e t e r m i n e d b y t h e h e a t e x c h a n g e p r o c e s s e s a l r e a d y n e n t i o n e d . D e s p i t e t h e l o w e r d e g r e e o f racllation heat exchange in winter, its influence i s s t i 1 l m a r k e d . T h i s i s l f l u s t r a t e d i n f i g u r e 6 in which the temperature amplitude is shown to i l e c r e a s e c o n s i d e r a b l y w i t h t h e o c c u r r e n c e of c l o u d s w h i c h r e f l - e c t a n d a b s o r b b o t h i n c o m i n g and o u t g o j . n g r a d i a t l o n ( 5 ) . T e m p e r a t u r e a m p l i t u d e l s a l s o a f f e c t e d b y l a t i t u d e , a l t i t o d e , a n c l n e a r n e s s t o l a r g e b o d i e s o f w a t e r . 0 f p a r t i c u l a r c o n c e r n i n w j - n t e r c o n c r e t e w o r k are minimun temperatures. The monthly averages of daily minimun temperatures indj_cate only generally t h e s e v e r i t y o f w l n t e r c o n i l l t i o n s .
S u c h d a t a m a y b e i n a d e q u a t e s i n c e t h e v a r i a t i o n f r o m m e a n v a l u e s m a y b e v e r y g r e a t . E x a m p l e s o f s u c h v a r i a t i o n s a r e g i v e n i n T a b l e I .
llhe lowest tenperature on recorcl for the t h i r t y - y e a r p e r i o a l f o r t h e n o n t h o f D e c e m b e r , for exarnple, differs ty 48ol' fron the trean daily nini-num, and by 21oF from the mean nonthly m i n l m u m . S u c h l a r g e d e v i a t i o n s a r e n o t u n u s u a l , p a r t i c u l a r l y 1 n c o n t i n e n t a l - t y p e c l i m a t e s .
tenperatures is the rate Efnd degree of tenperature change. The anplltudee shown by claily marches of tenperature are baseal on average values and again cleviations nay be very great. Cases of very rapicl temperature changes occut iust eaet of the Rocky Mountains in Weatern Canada where the severe contlnental winter weather ls frequently nodlfied by warm Chlnook (ufoehnn) wlncls descending eastward over the mountalns to the plains. Temperature rlses of 4OoF ln 15 nlnutes are not unusual, antl 1n extreme cases the thernometer has been loxown to rlse JooF ln three ninutee (5). Temperature clrops, although less rapltlr can be aluoet as uarketl. Such weather phenomena are often assoclatecl wlth hlgh altitudes antl certaln inlantt regions. 0n the other hancl, sutltlen changes froro trcoltl spellsrr to trwarn spellstt are nore often aesoclateal wlth the tlme of year ln certai-n areas.
Duratlon and frequency of below-freezlng ternperatures, antl Itthreghold[ datea showlng the p r o b a b l e f i r s t o c c u r r e n c e o f f r o s t , a r e o f s p e c i a l lnterest in wlnter concretlng. Figure 7 shows the march of minlmum tenperatures for the nonth of October 1n ldontreal basetl on recorcls fron 1874 to L954 (71. The average mlnlmurn ternperature remains above 52oF for the whole month, but the low
mlninum falls below the freezing polnt for most of thlo perloct. Ihe probablllty when frost nlght flrst be expected ls October Jrd' ancl a clrop in temperature below 25oF la not to be expectett unt11 October 17th. Weather records also proviale alata fron whlch the frequency of |tfrost-tlaystt ancl the duration of froet-free perlode can be calculated. (b) Wlncl. - The irnportant charaoterlstics of wlncl are
speecl and cllrectlon, both of whlch roay show great vartabillty, ancl both of whlch are dlrectly
connected wlth changee 1n weather. Moet weather L 2
statj_on alata show a falrly regular ala1ly varlation l n d l r e c t i o n . A t h l g h a l t i t u c l e s , o r n e a r l a r g e b o d l e s o f w a t e r , t h l s n a y o c c u r a s one prevalllng wind during the day and an opposlte one at night. In mountaj-nous regions a regular cycle of two
opposlng winds, one downhllI and one uphl11, can
r e e u l t f r o r a e f f e c t s o f s o l a r r a c l i a t l o n . T h e direction of a prevallj_ng wind nay vary
consialerably through the influence of such factors
a s l o c a l t o p o g r a p h y .
Variations from mean wind speeds may be very
g r e a t , a s i l l u s t r a t e c l i n T a b l e I I .
The variatlon from Eonth to raonth is very snall but the clifference between the nean and the maxinun for each of the winter months is very g r e a t .
(c) low Temperatures anrl High ivinals. - The severlty of w i n t e r w e a t h e r , f r o n t h e p o i n t of vj.ew of cooling,
is greatly accentuated by the slmultaneous
occur?ence of hlgb winals and 1ow tenperaturee. It
b e c o m e s n e c e s s a r y , t h e r e f o r e , t o c o n s l c l e r p a r t i c u l a r v a l u e s o f w i n d s p e e d w i t h v a r i o u s t e n p e r a t u r e s . S u c h c l a t a a r e n o t a v a i l a b l e f r o n
indepenclent records of tenperature and wind, and
can only be obtained fron records obtained
s i n u l t a n e o u s l y 1 n p o i n t o f t 1 m e . S u c h c o r o b i n a t i o n s o f d a t a , a l t h o u g h r e q u i r e d f o r c e r t a l n p u r p o s e s , p a r t i c u l a r l y f o r e s t a b l i s h l n g c o o l i n g e f f e c t s , a r e
obtalned fron norroal weather records through
rather laborious analyses. Such an analysls was
nade to compare the severlty of wlnter weather 1n
t w o C a n a d l a n c i t i e s , C h u r c h i l l a n d S a s k a t o o n . I n figure 8 is plotted the average frequency
d i s t r i b u t i o n o f w i n c l s a t v a r l o u s s p e e d s f o r l O o F t e m p e r a t u r e r a n g e f o r t h e s e t w o l o c a l i t i e s , b a s e d o n t h e p e r i o d i n d i c a t e d . f t c a n b e s e e n t h a t a t S a s k a t o o n p r a c t i c a l l y a l l t h e w t n d s p e e d
occurrences during December, January and February f a l t 1 n t h e r a n g e 0 t o 1 9 n . p . h . r t h e w J , n d s p e e t l a v e r a g e b e i n g 1 0 . 7 n . p . h . A t C h u r c h i l l t h e o c c u m e n c e s a r e s p r e a a l o v e r o t o 1 4 m . p . h . r t h e a v e r a g e f o r t h e s a m e p e r i o d b e i n g 1 4 . 7 n . p . h . I t 1 s t o b e n o t e d t h a t t h e f r e q u e n c y o f w i n d s p e e d o c c u r r e n c e i s g r e a t e r a t l o w t e m p e r a t u r e s f o r C h u r c h i f l t h a n f o r S a s k a t o o n . f t i s t h e r e f o r e e v i d e n t t h a t t h e r e i s a m u c h g r e a t e r p r o b a b i l i t y
of the simultaneous occurrence of hlgh winds antl
1 o w t e n p e r a t u r e s a t C h u r c h i l l t h a n a t S a s k a t o o n . ( d ) O t h e r E l e m e n t s . - H u n l d i t y ' c l o u d i . n e s s ' a n d
p r e c i p i t a t l o n a r e g e n e r a l l y o f s e c o n d a r y
i n p o r t a n c e t o t h e w i n t e r e n v i r o n m e n t o f c o n c r e t e . S n o w c o v e r r ' h o w e v e r , t e n d s t o a c c e n t u a t e e x t r e m e g
of temperature by ractiating strongly at night and
r e f l e c t i n g i n c o m j - n g r a d i a t i o n s t r o n g l y d u r i n g t h e d a y . I h i s p r o p e r t y o f s n o w a l s o t e n d s t o p r o l o n g l o w t e m p e r a t u r e s i n e a r l y s p r i n g . S n o w c o v e r d e c r e a s e s d e p t h o f f r o s t p e n e t r a t i o n b u t , e x c e p t
in continental clines r variability in anount ancl
d i s t r i b u t i o n i s s o g r e a t t b s t p r e d i c t i o n i s d i f f i c u l t . T h e d u r a t l o n o f s n o w c o v e r a n d frequency of snowfal'l are, however, signlficant f a c t o r s . T h e m o d e r a t i n g e f f e c t o f c l o u d i n e s s t
nentioned before r may waxrant the use of data on
cluration antl frequency of sunshj-ne during winter m o n t h s .
3 . C o n b i n e c l E l e m e n t s
0n1y a few combined eleuents have been developed on a
q u a n t i t a t i v e b a s i s . A n e x a r n p l e o f a u s e f u l c o r n b i n e d e l e m e n t i s r e l a t l v e h u m i d i t y . O t h e r s o f i n t e r e s t j . n certain
connections are cooling power and drying power. Forrnulae
f o r t h e s e c o m b i n e c l e l e m e n t s f o r p a r t i c u l a r s i t u a t i o n s a r e r e v i e w e d b y C o n r a d a n d P o f l a k ( 8 ) a n a l a n d s b e r g ( 5 ) .
S u c h e q u a t i o n s a r e o f i n t e r e s t . b e c a u s e t h e y itlustrate
how two or more individual eleroents may be combined to
p r o d u c e a s i n g l e v a L u e f o r use in place of the origlnal e l e m e n t s i n c l e t e r n i n i n g a h e a t l n g or coollng rate for a s p e c i f i c s e t o f c i r c u m s t a n c e s t a k e n i n t o a c c o u n t in the e q u a t i o n . T h e y r n u s t n o t , h o w e v e r , b e a p p l i e d to situations o t h e r t h a n t h o s e f o r w h l c h t h e y a r e intencled.
Certain instruments such as the Kata-Thermometer anal
t h e D a v o s t r ' r l g o r i n e t e r ( 5 ) , m e a s u r e c o o l i n g p o w e r s usefuf in c e r t a i n s p e c i f i c a p p l i c a t i o n s w h i c h a r e d e f i . n e d b y t h e c h a r a c t e r i s t l c s o f i n s t r u m e n t s c o n s t r u c t e d i n a s t a n d a r d w a y . S i n i l a r i n s t r u m e n t s m i g h t b e u s e d o n a c o n t i n u o u s r e c o r c l b a s i s t o p r o v i d e a s i n g l e strean of data, thus
avoiding the laborlous procedure required j.n combinlng
s e v e r a l i n d l v l d u a l e ] e m e n t s t h r o u g h a n e q u a t i o n . T h e f o r m u l a e f o r c o o l - i n g p o w e r a r e , i n e f f e c t ,
e x p r e s s i o n s f o r t h e r a t e o f h e a t l o s s under a particular s e t o f c i r c u m s t a n c e s , t h e i n c l u d e d w e a t h e r e f e m e n t s a l o n e b e r _ n g c o n s i d e r e d a s v a r y i _ n g . A s u b s t a n t j _ a l _ nunber of varlabLes o t h e r t h a n w e a t h e r e l e n e n t s c a n a l s o affect the rate .of heat l o s s f r o m a c o n c r e t e r n a s s a n d m u s t be taken into account. E a c h c o m b i n a t i - o n o f t h e s e e l e m e n t s woulcl requlre a separate c o o l i n g p o w e r e q u a t i o n a n d t h e v a l u e of conbi_ning the
w e a t h e r e l e m e n t s i n t o a s i n g l e e x p r e s s i o n no longer serves a u s e f u l p u r p o s e f o r t h e g e n e r a l c a s e . I t b e c o m e s m o r e
c o n v e n i e n t t o i n t r o d u c e t h e s e l e c t e d values of the weather e l e m e n t s i n t o t h e h e a t f l o w e q u a t i o n s . A s i m i l a r s i t u a t i o n e x j , s t s w i t h r e s p e c t t o t h e a p p l l c a t i o n o f d r y i n g p o w e r e q u a t i o n s . U n l i k e h e a t f 1 o w , h o w e v e r , s a t l s f a c t o r y
e q u a t i o n s f o r m o l s t u r e f l _ o w f o r the general case have yet to b e d e v e l o p e d .
MICROCIIMATIC AND OTHER INVIRONI,/ENTAI INFTUXNCES
1 . G e n e r a f F e a t u r e s o f S m a l _ l - s c a l e C l _ i n a t e T h e w e a t h e r d a t a o b t a i n e d f r o m m e t e o r o l o s i c a l
obgervations under rrundigturbetl conclitlonsrr are va11cl only for large-sca1e cllmate. They tlo not represent the actual conclltions near the grouncl or near some loca1 botly or structure whlch may exert a conslderably nodifylng influence on the weather elements. The equallzlng lnfluences that operate in the upper atmosphere cllninlsh progressively with increaeing proxlnity to the ground. Near the ground the air layer is a zone of disturbances antl variations due to such v a r l a b l e f a c t o r s a s v e g e t a t l o n , s o 1 1 c o n t l i t i o n s r t o p o g r a p h y t ancl bulltl1ngs.
The dimensions and range of srnall--scaIe climate are ateternined by the particular envlronmental situatlon' Geiger
( 9 ) c o n s i d e r s t h e a i r l a y e r u p t o t w o m e t r e s a b o v e t h e ground surface as the zone that ie influencetl by variations of the ground and other sumoundings, antl refers to this envir.onment as the mlcroclimate. In this zone a particular o b J e c t , s u c h a s a m a s s o f c o n c r e t e , l s c o n i l i ' t i o n e c l b y t h i s environment which nay cliffer substantlally fron the
u n d l s t u r b e t l w e a t h e r . T h e m o r e f a n i l l a r t e r m s r r l o c a l r r t ilurbanrt (10) and rrspotrt climates (5) are comnonly enployetl f o r s p e c i f i c a r e a s a f f e c t e d p r i n c l p a l l y b y p e c u l i - a r i t i e s o f t o p o g r a p h y r t r e e s ' w a t e r b o c l l e s , a n d g r o u p s o f b u i l d i - n g s
( 1 0 ) . I ' S i t e r r climate is useal to tlescrlbe'the e n v i r o n m e n t a t a s b u i l c l i n g s l t e w h e r e t h e a t l d i t l o n a l f a c t o r s o f s i z e '
shape, and nearness of buildings exert a special i'nfluence o n w e a t h e r ( 5 ) .
A signlflcant feature of snall ecale climate is the g r e a t v a r i a t l o n t h a t c a n e x i s t i n a r e l a t i v e l y s n a l l a r e a ' An lllustration of this 1s the frequently quotecl example of winter teroperature differences 1n Toronto shown in flgure 9
( 1 1 ) . T h e t o p o g r a p h l c a n d t e m p e r a t u r e p r o f i l e s s h o w t h e g r a d u a l d e c r e a s e o f t e m p e r a t u r e w l t h c i t s t a n c e f r o n t h e l a k e shore, ancl the remarkable temperature rrlowrr in the va11ey seven niles away, the clifference betrveen thls temperature ancl the lakeshore temperature being Jootr'.
2 . C h a r a c t e r i s t i c s o f M i c r o c l i m a t e
Ternperature, more than any other cllnatic element,
r e a c t s s e n s i t i v e l y t o t h e n a t u r a l s e t t i n g . N e s t t o i t w i n c l s p e e d 1 s s u b j e c t t o v e r y l a r g e n i c r o c l f u o a t i c v a r i a t i o n s ( 1 2 ) .
The ground surface warros through lncoming radiation ancl
c o o l s b y o u t g o i n g r a d i a t l o n a t n l g h t . T h e a i r l a y e r n e x t t o t h e g r o u n d , a s a r e s u l t o f r a d i a t i o n g a i n s a n d l o s s e s a t t h e
surface, shows a greater tenperature amplitude than the
h i g h e r l a y e r s o f a l r . T e m p e r a t u r e s t a k e n a t t h e t o p o f a w e a t h e r s t a t i o n t o w e r n a y , t h e r e f o r e , b e c o n s i d e r a b l y h l g h e r
at night than those near the ground surface, and
correspondingly lower cluring the day.
W h e n c o n d i t i o n s a r e s u c h a s t o p r o d u c e a n e t l o s s o f h e a t b y r a d i a t i o n f r o m t h e g r o u n d s u r f a c e , a s i t u a t i o n w h i c h o c c u r s o n a c l e a r w i n t e r n i g h t , t h e a i r l a y e r n e x t t o t h e g r o u n d b e c o n e s a s t a b l e l a y e r o w j _ n g to t h e g r e a t e r denslty o f c o l c l e r a i r . f h i s a c c o u n t s f o r t h e f r e q u e n t l o w e r l n g o f w i n d s p e e d w l t h d e c r e a s l n g t e n p e r a t u r e i n w i n t e r . T h e s t a b i l i t y o f t h i s s t r a t i f i c a t i o n i s d i s t u r b e d b y a n y w a r m i n g p r o c e s s t h r o u g h t h e l n i t i a t i o n o f c o n v e c t i o n . E v e n c l u r i n g c o o l i n g s o m e n l x i n g o c c u r s t h r o u g h s o - c a l l e a l r r c o l d n e s s c o n v e c t i o n r r c a u s e d b y t h e c l e s c e n t o f c o o l e t l a i r a n a l d u s t p a r t i c l e s ( 9 ) . T h e o c c u r r e n c e o f w i n d d e s t r o y s t h e s t r a t l f i c a t i o n a n d t h e r e s u l t a n t m l x i n g r a i s e s t h e g r o u n d s u r f a c e t e m p e r a t u r e . A i r s t r a t i f i c a t i o n l e a d s t o t h e o c c u r r e n c e o f I ' c o l d a i r d a m s t r a n a l r t f r o s t h o l e s " w h e r e
temperatures may be very considerably below the normal ai.r
tenperature s .
I n t h e c o o l i n g p r o c e s s a i i c o n v e c t i o n o r w i - n d o p e r a t e s i n t w o w a y s . A s p r e v i o u s l y n e n t i o n e d i t t e n d s t o d e s t r o y s t r a t l f i c a t i o n a n t l t h e r e b y r e d u c e s t h e h a z a r t l o f f r o s t .
However, wind increases the heat transfer rate from a
s u r f a c e t o t h e a d j a c e n t a i r , t h u s i n c r e a s i n g t h e c o o l i n g rate for a glven temperature.
' ) .
I n t e n s l f i c a t i o n o f F r o s t
Freezing tenperatures become more extr.eme on a
m i c r o c l i m a t i c s c a l e a s a r e s u l t o f a n u m b e r o f f a c t o r s ( 9 ) .
A clear slqr on a winter nlght favours outwartl radlatlon and
r e s u l t s i n l o w e r s u r f a c e t e m p e r a t u r e s . A r e d u c t i o n o f t h e m o i s t u r e c o n t e n t h a s t h e s a n e e f f e c t s i n c e w a t e r v a p o u r i n c r e a s e s t h e c o u n t e r - r a d i a t i o n o f t h e a t m o s p h e r e a t n i g h t . S t i l l a i r f o s t e r s a i r s t r a t l f i c a t l o n w l t h t h e c o l d e s t a i r n e x t t o t h e h o r l z o n t a l s u r f a c e . P o o r h e a t c o n c l u c t l v i t y o f
the soil prevents daytine storage of heat and retarcls heat
f l o w t o t h e s u r f a i e d u r i n g c o o l l n g . R a p i d c o o l i n g a l u e t o s t r o n g e v a p o r a t i o n i s a c o n t r l b u t o r y f a c t o r . C o I d a i r f l o o d s d u e t o l o c a 1 a c l v e c t i o n , a s n e n t i o n e d e a r l i e r r a r e a l s o f a c t o r s i n i n t e n s i f i c a t l o n o f f r o s t . T h e a b s e n c e o f n a t u r a f p r o t e c t i o n a f f o r c l e d b y v e g e t a t i o n a l s o c o n t r i b u t e s to lower ground surface teroperatures.
4 . S i t e C l l m a t e
0n a winter concreting iob the environmental factors
are the natural topography ancl vegetation antt the man-nade
structures ancl excavations. A clearing in a foresteal area
or a site surrounclecl by buildings 1n a city is provided with
a winal break. Heated bullclings provide heat which may
p r e v e n t e x c e s s i v e l y 1 o w t e m p e r a t u r e s o n a c o l c l w i n t e r n i g h t .
They also supply heat to the grouncl. The pollution of air
over a city is also a rooclifying influence through
c o u n t e r - r a d i a t i o n e f f e c t s .
T h e c l e a r i n g o f s n o w c o v e r t e n c l s t o i n t e n s i f y e x t r e n e s o f s u r f a c e t e m p e r a t u r e s , w h e t h e r g r o u n d r r o c k , o r o t h e r n a t e r i a l . T h e g e n e r a l a c t i v i t i e s o n a i o b s l t e n a y c o n t r i b u t e t o t h e m o c l i f i c a t i o n o f w e a t h e r c o n d i t l o n s .
Builclings anal clearings mayr through unfavourabfe
o r i e n t a t i o n , a e c e n t u a t e w i n c l s p e e c l , o r m a y a c t a s I ' c o l d air a l a m s r r . n x c a v a t i o n s b e c o m e r r f r o s t h o l e s t ' i f l e f t e x p o s e d f o r
some time, but if fresh, may exert a motlerating influence on
the change in temperature of a material placed in contact
wlth it. Gu111es anal ravines nay tlrain away cold air or
b u l l d u p c o l d a i r c l a m s , d e p e n c l i n g o n o r i e n t a t i o n . I n
general, convex sutifaces have a moderate roicroclimate and
concave surfaces have an extrene one in wi.nter.
5 . G r o u n d a n d R o c k T e n p e r a t u r e s
The thernal conductlvity ancl the heat storage p r o p e r t i e s o f s o i L a n d e x p o s e d r o c k a r e f r e q u e n t l y o f i n p o r t a n c e t o w i n t e r c o n c r e t e w o r k ( 1 t ) . C o n c r e t e m a y b e p l a c e d d i r e c t l y i n a n e x c a v a t i o n o r o n r o c k , a n d roay either gai-n or lose heat dependlng on the relative ternperatures. I t l s c o m n o n p r a c t i c e t o w a r m s u c h s u r f a c e s b e f o r e p l a c i n g c o n c r e t e o n t h e m 1 n c o l d w e a t h e r .
E v e n i n e x t r e m e w i n t e r c l i m a t e s the frost penetratlon i s u s u a l l y l i n i t e d t o a f e w f e e t . F i g u r e 1 0 s h o w s s o 1 1 t e m p e r a t u r e s a t v a r i o u s d e p t h s d u r i n g a cold wj-nter in W e s t e r n C a n a d a ( 1 4 ) . D e s p i t e t h e v e r y l o w a l r t e n p e r a t u r e s , t h e d e p t h o f f r o s t p e n e t r a t i o n i s o n l y 6 f e e t . A c o v e r l n g of vegetatlon, snow or straw will appreciably lower the d e p t h o f f r o s t p e n e t r a t i o n ( 1 5 ) .
Figure 11 shows aj.r and rock tenperatures cluring February, March and April at a Job site 1n Eastern Canada. The rock was kept bare of overburden and snow for a 5_foot r a d i u s ( 4 ) . A l t h o u g h a i r t e m p e r a t u r e s w e r e f a i r l y 1 o w , f r o s t p e n e t r a t l o n w a s l l m i t e d t o l e s s t h a n J f e e t .
Cases where ground temperatures are of inportance in w i n t e r c o n c r e t e w o r k a r e p e r h a p s limitecl. T h e y a r e , h o w e v e r , n o t r e s t r l c t e d t o c a s e s o f c l i r e c t c o n t a c t o r e n b e d m e n t 1n the ground, but nay be of lmportance in situations where heat exchange nay take place with the ground through an i n t e r m e d i a t e b o d y o r s t r u c t u r e .
V IIEAT FIOW WITH S?XCIAI REFERNNCE TO COOIING CONCRITE O n c e t h e c o n d i t i o n s o f e x p o s u r e o f a c o o l i n g c o n c r e t e mass have been establisheat, which ls the firet half of the p r o b l e r n o f p r e d l c t i n g c o n d i t l o n s w i t h i n t h e c o n c r e t e , t h e r e remains the problen of analysing the heat flow condition w h l c h w 1 1 1 b e p r o d u c e d b y a n y g i v e n sltuation. O n c e i t i s p o s s l b l e t o p r e d i c t the result of any given situation, t h e s e l e c t i o n o f s o m e f o r n o f p r o t e c t i o n , o r t h e d e t e r m l n a t i o n
of the noallflcatlons to the contlltione whlch w111 lead to a cleslrecl result, can folIow readily.
1. Heat Transfer by Conductlon
Heat flow wlthin a concrete naas can be aseunetl to take plaoe entlrely by conductlon. Ihe one posslble exceptlon to thle is the transfer of lateat heat carrled by vapour
dlffuslng wlthln the concrete maos. Heat flow by conduction ls always asauned to follow a 61x[p].e flow 1aw as statetl by Fourler:
o - - t S- d r
where, 1n Eagllsl unltst
q = B t u Per sq. ft. P€r br. t = temperatuie 1n oF.
x = d i s t a n c e i n t h e t l i r e o t l o a o f f l o w r f t . i< = coefflcient of conttuotivity.
93 = t"tperature gradlent ox
Thls slmple equation, when integratetl for the slnple case of a steatly-state flow in one dlrectlonr leatls to the e q u a t i o n :
o = E ( t = - + \ L \ - L - u 2 "
givi-ng the flow rate 1n Btu per square foot per hour through tr feet of material having a coefflcient of concluctlvlty k and with tenperatures tt and t, naintainecl on elther side. The case of a combination of plane slabs of dlfferent materials through which the heat nust flow in a nornal d i r e c t i o n , 1 . e . r t h r o u g h t h e m a t e r i . a l e i n s e r i e s r c a n b e hanctletl readily by the acloption of the resistance concept. The concluctances of each of a number of layers is glven by ki k2
j t and their reepectj-ve reglstances by. the !1 tJ2
rdclprocale of tbese conductaaoes. The equatlon for n layers becones
q . = c ( t l - t 2 ) , where
C = conductance of the conblnatlon, and
I/C = resLstance of the combination
= 3 *'r --- *
lr,
*r k2 kn
The steaily-state equation 1s used extensively in the
c a l c u l a t i o n o f h e a t t r a n s f e r t h r o u g h b u i l d l n g s e c t i o n s .
There are extensive data on the coefficients for various
m a t e r i a l s . T h e o n l y n a j o r c o u p l l c a t l o n i n s u c h
c a l c u l a t l o n o , w h e n d e a l l n g w i t h s t e a d y - s t a t e c o n d u c t l o n i n o n e d l m e n s l o n i n s o l i d s , i s t h a t c r e a t e d b y t h e p r e s e n c e o f m o l s t u r e . M o s t o f t h e c o e f f i c i e n t s a v a i l a b l e h a v e b e e n t l e t e r n i n e d f o r d r y m a t e r i a l s . C o e f f i c i e n t s a r e q u o t e d f o r
some wet materials on the aseumption that the role of
moisture can be accounted for simply by the use of an
i n c r e a s e d c o e f f i c i e n t i n t h e c o n d u c t i o n e q u a t i o n . T h i s u r a y
lead to serious error lf the tenperature gradient gives to a
nigration of noisture through a process of evaporation and
c o n d e n s a t i o n w i t h i n t h e n a t e r i a l . T h i s m o r e c o m p l l c a t e d s l t u a t i o n i s o n l y n o w b e i n g w e l l r e c o g n l z e d , a n d h a s n o t y e t b e e n r e d u c e c l t o a w o r k i n g b a s l s f o r c a l c u l a t i o n . M u c h
attention has been paict to the role of rnoisture 1n heat
t r a n s m i s s i o n b y C a m m e r e r ( 1 5 ) J o h a n s g o n ( 1 ? ) , a n A o t h e r s .
The aaldeal mechanisn of latent heat transfer 1s unlikely
to be inportant in wet, setting concrete, but rnay play an
inportant role in the heat transfer through materials used
ag fornwork, or as insulating or protective coveri.ng, which
a r e I i k e l y t o c o n t a i n m o i s t u r e . T h i s n e c h a n i s m n e e d n o t b e c o n s i d e r e c l f u r t h e r , b e y o n d r e c o g n l z i n g i t a s a c o m p l i c a t i o n , a n d t h a t i t i s s t i l l a n a t t e r f o r r e s e a r c h .
Heat Transfer by Convectlon and Radiation
The additional roechanisma of heat transfer, convection
r a d i a t i o n , o p e r a t e a l o n g w i t h c o n d u c t l o n 1 n n o s t c a a e s .
2 .
Thls conblnect eltuatlon exlstg at an a1r boundary or across an a1r apace or an air cell withln a material or combination of materials. There usuatly exlsts a temperature gradient withln the surface air filn whlch' becauge of the clifference 1n ilensity created, leads to a circulation of the a1r which then acts as a transport mechanlen for heat. Meanwhilet sone conductlon also occurs fron one alr layer to the next. When occurring naturally over eurfaces in a stil1 air field't ln which the air notion ls protluoed solely by the lnfluence of the surface temperaturer thls mechanlsm 1s known as free convection antl is expressetl by an equation of the forn:
- L / +
" $ / 4
9 c - u \ u A - ' S / I
where
Q " = B t u P e ! s q . f t . P e r h r . t
b = constant for any given arrangementt t" = air tenperature 1n unclisturbecl airt t s = s u r f a c e t e m P e r a t u r e .
This heat transfer nay be expressetl by an equivalent contluction equation form:
^ = l r / + - + \ q c - u c \ u a - v s , '
where
h " = b ( t . - t J r / 4 .
Ihe heat exchange occurring by radlation between a bocly surface and another surface at a clifferent tenperature is given bi the Stefan-Boltzmann equation:
Q r = o r { t t 4 - t 1 4 ) , where
c = constant
F = factor introtluced to account for the geometric relationshlp between the two surfaces exchanglng radlant enerryr ancl for the effects of the deviation of the surfaces fron blaok-bocly condltlone.
T , a n d T , a r e t h e a b s o l u t e tempdratures
surfaces exchanging energy.
This nay also be reduced to the forn of e ouat i-on . where Q " = h " ( T 1 - T 2 )
h " = c r r ' ( I r 2 + r r 2 ) ( T , + T r ) .
1 , C o n b i n e c l F i l n C o e f f i c i e n t s T h e h e a t t r a n s f e r b y c o n d u c t i o n - c o n v e c t j _ o n a n d b yradiatlon at the a1r boundary of a body can be handled by a
s i m p l e c o e f f i c i e n t h = h c + h a w h i c h , w h e n m u l t i p l i e c l b y t h e a i r - t o - s u r f a c e t e u r p e r a t u r e c i i f f e r e n c e , g i v e s t h e h e a t t r a n s f e r r a t e . T h i s i s r a t i o n a l i f t h e t e m p e r a t u r e o f t h e e x t e r n a l r a d i a t j - n g s u r f a c e , T 2 1 i s e q u a l t o a i r t e m p e r a t u r e . T h e c o e f f l c i e n t s h " a n d h r a r e n o t t r u e c o e f f i c i e n t s s l n c e t h e y a r e f u n c t i o n s o f t e m p e r a t u r e , b u t t h e y , o r t h e i r s u m , c a n b e a s s i g n e d c o n s t a n t v a l u e s f o r c e r t a i n ranges of c o n d i t i o n s w i t h 1 i t t 1 e l o s s i n p r e c i s i o n . A v a l u e o f 2 . 0 i s c o m m o n l y a s s i g n e a l t o t h e c o n d u c t a n c e o f a s u r f a c e f o r s t i l l a i r c o n d i t i o n s a t e x t e r i o r b u i l c l i n g s u r f a c e s , a n d w j . t h s u r r o u n d i n g b o d l e s at alr ternperature. U n c l e r s i r o l l a r c o n d i t j - o n s , b u t w l t h w i n d which produces a r r f o r c e d convectionl at the surface, in combination wlth
radiation exchange, the surface conductance 1s given
approxlmately by the relationshlp
where
h = 2 + 0 . 4 V
V = w i n d . s p e e t l in m . p . h . ( 1 8 ) .
T h e m a r k e d e f f e c t o f w i n d i n i n c r e a s i n g t h e c o n d u c t a n c e n a y b e n o t e d , a 2 0 m . p . h . w i - n d increaslng the effective
c o n d u c t a n c e f r o m 2 t o 1 0 .
Evaporation from a wet surface can result 1n an
increased transfer of heat as a result of water taking up
of the two a conductance
t h e l a t e n t h e a t o f v a p o r l z a t i o n a e i t i s e v a p o r a t e d . T h i s
is the action which produces the lowerecl temperature when a
therrnorneter ie fitteal with a wetted wick around the bulb.
l l t t l e h a s b e e n d o n e a s y e t i n t h e d e v e l o p r n e n t o f a r a t i o n a l b a s i s f o r c a l c u l a t l o n o f h e a t t r a n s f e r f r o m w e t t e d s u r f a c e s .
The reduction of convection ancl racliation to equivalent
conductances becomes a great convenlence j-n Eany probleros s l n c e t h e o v e r - a l l h e a t t r a n s f e r c a n b e t r e a t e c l a s a c o n t i u c t i o n t h r o u g h o u t . S u c h a r e d u c t i o n i s u s u a l l y r e a t l i l y
acconplished when the radiation exclrange is with surroundlng
bodies, but the combined mechanlsms become much more
difflcult to hantlle when the racllatlon exchange 1s with the
s k y . S o l u t i o n s b y t r i a l - a n d - e r r o r a r e p o s s i b l e b u t a r e i n m a n y c a a e s n o t p r a c t i c a l . I t 1 s n e c e s s a r y i n u s i n g t h e n t o
asoume a surface temperature, then to calculate the heat
exchanges between the surface at that temperature and the
air and slqr, and to check this with the heat flow in the
botly to the surface, correcting the assumeil surface
temperature until a balance is obtained. This procedure
becones unpractieal when the heat flow is translent or
p e r i o d i c .
One device developecl in bullcting work is that of
s o l - a i r t e m p e r a t u r e . I t i s a l e f i - n e d a s t h e t e n p e r a t u r e o f t h e o u t d o o r a i r , w h i c h 1 n t h e a b e e n c e o f a l l r a t l i a t i o n exchanges, would give the same rate of heat entry into the
surface as woulal exist with the actual combination of
lncldent solar raaliation, radiant energy exchange with the
sky ancl other outiloor surrounclingsr and the convective heat
e x c h a n g e w i t h t h e o u t d o o r a i r ( 1 9 ) . T h e c o m b i n a t i o n o f t h e s o l a r r a d l a t i o n g a l n w l t h t h e c o n d u c t l o n - c o n v e c t i o n a t t h e s u r f a c e l s t h u s d e a l t w i t h a s a c o n d u c t a n c e r u s i n g s o l - a i r
temperature ln place of outdoor temperature in the
c a l c u l a t l o n s .
4 . C o o l i n g o f a C o n c r e t e M a s s
W l t h L n t h e c o n c r e t e n a s s , t o g e t h e r w i t h l t s f o r m w o r k a n d p r o t e c t i v e c o v e r , t h e h e a t t r a n s f e r c a n b e d e a l t w i t h a s
a c o n d u c t i o n . A n y a l r s p a c e s e x i s t i n g w i t h i n t h i s
a r r a n g e m e n t c a n r e a d i l y b e a s s i g n e d . a p p r o p r i a t e c o n d u c t a n c e s a s i s c l o n e f o r a i r s p a c e s i n b u i l d i n g constructions. T h e a c t u a l s i t u a t i o n , h o w e v e r , m a y b e f a r f r o m s i m p l e .
C o n p l i c a t i . o n s a r e i n t r o d u c e c l b y t h e t r a n s i e n t n a t u r e o f t h e f 1 o w , b y t h e p r o d u c t i o n o f h e a t of hydratlon within the mass, a n t l b y t h e t h r e e - d j _ m e n s i o n a l f l o w w h l c h will exist in nost c a s e s . W h i l e t h e d i f f e r e n t l a l e q u a t i o n s f o r c o n d u c t i o n f o r t h e g e n e r a l c a s e c a n b e s e t u p , solutions can be found r e a d . i l y f o r o n l y a l _ i m i t e d n u n b e r o f c a s e s , notably the s i m p l e r c a s e s i n t w o a n d t h r e e d i m e n s i o n s , such as those i n v o l v i n g p i p e s a n d s p h e r e s . M a n y c a s e s o f t w o - c l i m e n s i o n a l s t e a d y - s t a t e f l o w c a n b e d e a l t w i t h b y r e l a x a t i o n m e t h o d s . f n t h e c a s e o f t r a n s i e n t a ^ n d . p e r l o d l c f l o w , s o l u t i o n s a r e a v a i l a b l e f o r a n u m b e r o f t h e s i m p l e r c a s e s i n v o l v i n g flow in one alimension. The case of a slab of a single m a t e r i a l a t o n e t e m p e r a t u r e w i t h o n e o r b o t h p l a n e surfaces
s u c l d e n l y c h a n g e d t o , a n d h e l d a t , s o n e o t h e r t e r n p e r a t u r e , c a n b e s o l v e d . S o l u t i o n s a r e a v a i l a b l e a 1 s o , a n c l h a v e b e e n r e d u c e d t o c h a r t f o r m , f o r t h e c a s e o f s l a b s of irniform material at one temperature sualdenly i-nmersed in a fluid at
s o m e o t h e r t e n p e r a t u r e . T h i s b r i n g s i n f l u i d f i l a r e s i s t a n c e . T h i s m e t h o d e a n b e a p p l i e d t o b r i c k - s h a p e d .objects by c o n b i n i n g t h e r e s u l t s f o u n d f o r t h r e e s l a b s o f t h i c l o r e s s e s e q u a l t o t h e l e n g t h , w l d t h a n c l d e p t h , o r t o a column of r e c t a n g u l a r s e c t i o n b y c o n s i c l e r i n g t w o e q u i v a l e n t s l a b s . T h e c a s e s i n w h i c h t h e t e n p e r a t u r e s o f t h e s o l i c l surfaces a r e n o t h e l - c l c o n s t a n t , a n d a r e n o t d e t e r m i n e d b y i m m e r s i o n i n a c o n s t a n t t e m p e r a t u r e f l u i d b u t f o l l o w s o u e o t h e r p a t t e r n , a n d t h o s e i n w h i c h t h e s l a b i s a c o m p o u n d o f o n e of s e v e r a l m a t e r i a l s h a v i n g d i f f e r e n t p r o p e r t l e s , c a n b e s t b e d e a l t b y a g r a p h i c a l m e t h o d d e v e l o p e c l b y S c h m i d t . A l l o f these methods can be found in stand.ard textbooks provlding c o m p r e h e n s i v e t r e a t u r e n t o f h e a t t r a n s f e r , s u c h a s t h a t o f M c A d a m s (2 0 ) .
C a s e s i n c o n c r e t i n g w j - 1 1 u s u a l l y i n v o l v e b o t h s u r f a c e h e a t e x c h a n g e c o n d i t i - o n s a n d a t l e a s t o n e o t h e r x o a t e r i a l
useal aa fornwork or coverr in atlditlon to the concrete. U n d e r c e r t a l n c o n d l t i o n s , s i m p l l f y i n g a s s u m p t i o n s e n a b l e s o l u t i o n s t o b e f o u n d . I n t h e c a s e o f a p l a n e c o n c r e t e w a l l between forns, for example, the fornwork mayr unaler certain l i n l t e d c o n t l l t l o n s , b e r e d u c e d f o r p u r p o s e s o f c a l c u l a t l o n t o a n e q u l v a l e n t a c l d e d t h l c l a l e s s o f c o n c r e t e . U n c l e r c e r t a l n o t h e r c o n d i t i o n s , w h e n t h e h e a t s t o r a g e c a p a c i t y o f t h e f o r n w o r k o r o t h e r c o v e r i s s m a 1 1 , l t n a y b e c o n s l d e r e d a l o n g wlth the air f11n resistance in an equivalent fluld filot and the ttfluid immersionrt solution usetl .
S t i 1 l a n o t h e r t y p e o f s i n p l l f l c a t i o n n a y b e p o s s i b l e i n the case of heavily insulated bodles, when the conductivlty of the botly is relatively so great that the tenperature
differences throughout the body are never greatr untler the
reducecl heat flow permltted by the cover. Under these
conclitionsr and neglecting heat storage in the coverr a
f a i r l y s i m p l e t r a n s i e n t s o l u t i o n i s p o s s i b l e .
T h e c o e f f l c i e n t s o f c o n t l u c t i v l t y f o r t h e e l e m e n t s o f
the encfosure and for the concrete nust be lmown. When both
heat storage capacity and flow in a material nust be taken i n t o a c c o u n t ' t h e c o e f f i c l e n t , t h e r m a l d l f f u s i v l t y ' g i v e n 6 v 3 m u s t b e k n o w n . T h l s c o e f f i c i e n t e x p r e s s e s t h e r a t i o
" q c
-Po f c o n d u c t i v l t y t o t h e r m a l c a p a c i t y . C o n c l u c t i v i t y d a t a f o r noet bullding materialo, of the type which roight be usecl for f o r u w o r k o r l n s u l a t l o n ' a r e r e a s o n a b l y w e l l e s t a b l i s h e t l t although the presence of water nay be a complicating factor a s p r e v i o u s l y m e n t i o n e t l .
Heat generatecl by hyclration wlthin the concrete adals to the internal heat available to make up the heat lost fron t h e m a s s . T h e r a t e a t w h i c h i t i s r e l e a s e d d e p e n d s h o w e v e r upon the rate of hydration of the cenentr whlch is ln turn a f u n c t l o n o f t e m p e r a t u r e f o r a g l v e n n i x . T h e t o t a l h e a t releasecl up to the developrnent of a given degree of
hydratlon can be deternlned but the introcluctlon of heat release ae a functlon of time and tenperature may be d i f f i c u l t l f n o t i n p o s s i b l e t o h a n d l e l n t h e g e n e r a f c a s e '
