Dependence of Snow Hardness on Specific Gravity

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Dependence of Snow Hardness on Specific Gravity

N A T I O N A L RESZARCI-I C K Y C I L

C AYAEA

THR TIRPENDENCE

OF

SNOW HARDNESS

Oi\T S P L C I F I Z Gl:AVITY

by

Lorne $1. Gold ANALYZED Report N6.

54

of the

Divisicn

of

Building Research

O t t a w a

PREFACE

R e s e a r c h i n t o t h e problems r e l a t e d t o snow and i c e i s a most i m p o r t a n t p a r t of t h e work of t h e L i v i a i o n o f 3 u i l d i n g R e s e a r c h s i n c e it i s so p e c u l i a r l y a Canadian

problem,

The D i v i s i o n h a s j u s t had completed 2 s p e c i a l

c o l d room which was d e s i g n e d a s a snow and i c e laboraa.tory

-

one of t h e f i r s t s u c h l a b o r a t o r i e s e v e r t o be b u i l t , The work h a s a l r e a d y s t a r t e d i n t h i s l a b o r a t o r y and t h e L i v i s i o n loolcs f o r w a r d t o u s i n g t h i s s p e c i a l f a c i l i t y f o r an i m v e d i n t e -

a t t a c k on t h e more u r g e n t r e s e a r c h pro'blems i n t h i s f i e l d . I n advance o f t h e c o m p l e t i o n of t h i s f a c i l i t y ,

Yr.

Lorne Gold, t h e IIead of t h e Snow and I c e R e s e a r c h Z e c t i o n , h a s been c a r r y i n g o u t t h e o r e t i c a l s t u d i e s and '?.as been u s i n g a l s o t h e r e s u l t s of t h e snow s u r v e y of Canada f o r i n v e s t i s a t - t o n a l work. The snow s u r v e y was i n i t i a t e d by- a n d _is c a r r i e d o l ~ t t h r o u g h t h e A s s o c i a t e Committee on S o i l and Snow ?,,?ech::nj.cs.

T h i s p a p e r ("The Uependence o f Snow B a r d n e s s on S p e c i f i c , G r a v i t y t ' ) p r e s e n t s t h e r e s u l t s o f some of t h e s e

p r e l i m i n a r y s t u d i e s and i s a companion p a p e r t o 1 ~ ~ t i . X . 3 e p o r t ?To.

55

("The S t r e n g t h o f Snow i n Compression under l ~ y n a m i c ~ o z d s " ) . These two p a p e r s a r e c i r c u l a t e d i n t h i s p r e l i m i l i a r y

Tor3

f o r c r i t i c i s m and comment. It i s hoped t h a t t h e 2 rnag

b e p u b l i sh.ed when sui ta'uly amended i n t h e li.il;ht o f coci:-,ient s

r e c e i v e d .

Ottawa

TII:: LhPETJDENCG

OF

SNOW IIAHLNESS

OM

SPECIT'II: Gl<liVTTY b y L o r n e

W.

Gold I n a p r e v i o u s p a p e r ( I ) i t w a s shown t h a t snow h a r d n e s s , a s m e a s u r e d w i t h t h e Y a t i o n a l R e s e a r c h C o u n c i l h a ~ d n e s s g a u g e , was a d i r e c t m e a s u r e o f t h e u l t i m a t e s t r e n g t h of v i r g i n snow i n c o m p r e s s i o n . A n a l - y s i s o f r e s u l t s f r o m t h e C a n a d i a n snow s u r v e y showed t h a t h a r d n e 3 s d e p e n d e d p r i m a r i l y o n t h e s p e c i f i c g r a v i t y o f t h e snow a n d s i g n i f i c a n t l y o n t h e sncw ~emperatl- re and t h e b o n d i n g b e t w e e n snow p a r t i c l e s . The f a c t that t h e c h a r a c t e r i s t i c s o f t h e snow d e p e n d o n t h e i n t e g r a t e d - - ~ e t e o r o l o ~ L c a 1 f a c t o r : : l e d t o n hi,;h. d e ~ r e e of u - a r i a b i l i t y i n sncrs h a r d n e s s uncier n o r m a l l y s p e c i f i e d c o n d i - t i : 2 n s m It i s t h e p u ~ p o s e o f t h i s p a p e r t o d i s c u s s f ~ ~ r t h e r tl_e d e p e n d - e n c e o f snow h a r d n e s s o n s p e c i f ' i c g r a v i t y and t o a t t c x p t t o s h e d rnore l i ~ h t o n t h e f a c t o r s w h i c h c o n t r i b u t e t o t h e v a r i a ; - , r i l l . t y of- t h e s t r e n g t h p r o p e r t i e s o f snow p a r t i c l - ~ l a r l y i n r > e l a . t i o n ko t h . e b o n d i n s b e t w e e n c r y s t a l s .

I n o r d e r t o u n d e r s t a n d t h e behaviou.l- of' snow o n a p h e n o m e n o l o ~ i c a l s c a l e , it i s n e c e s s a r y t o

?a;'

some a t t e n t i o n t o t h e s t r u c t u r e o f t h e snow a t t h e s i n g l e n a r t i c l e l e v e l 3f o b s e r v a t i o n . B e f o r e s r r i v i n g a t t h e g r o u n d , :, n o w p a r t i c l e Inas n sFa3e d e t e r m i n e d b y i t s i n t e r n a l c r y s t c l l i n e s t r u c t u r e

and t h e e n v i r o n m e n t i n w h i c h i t h a s grown. The s i n g l e c r y s t a l s h a v e a h e x a g o n a l symmetry and may b e b a s i c a l l y c l e n d r i t i c ,

p l a t e - l i k e o r c o l i m a r i n s h a p e . T h e s e c ~ y s t a l s , wit:? t h e i r i i e t z i l e d s u r f a c e s h a p e when a r r i v i n g a t t h e z r o u n d , a r e v e r y u n s t a b l e t h e r m o d y ~ ~ m i i c a l l y i n t h e i r new e n v i r o n r ~ e n t

( 2 , 3

)

.

A

clecag and g r o w t h p r o c e s s f o l l o w s w h i c h m o d i f i e s t i l e s71.ape

cf escl?. i r d i v i d u a l c r > y s t a l . The c r y s t a l s h e z i n t o l o s e t h e i r c ' l i a r a c t e r i s t i c c r y s t a l l i n e d e v e l o p m e n t a n d t e n d t o a common d e n o m i n a t i o n ctt' g r a i n s w i t h smooth s u . r f a c e f e a t u r e s . I n i t i a l l y , t h e d e t a i l e d s t r u c - t u r e o f cr: ~ - k . ~ l l s i n i n t i r r l a t e c o n t a c t o n t h e g r o u n d l e a d s t o t h e development o f b o n d s b e t w e e n t l - ~ e c : r y s t a l s d u r i n g t h e decay and. g r o w t h p r o c e s s . As t h e p r b o c e s s c o n t i n u e s , b o n d s a r e d e s t r o y a d , t h e snow s e t t l e s a l l o w i n g more i n t i m a t e c o i l t a c t and furt?!.ep : ) o i l d . ~ ape d e v e l o p e d . It i s n o t u n r e a s o n a b l e t o assnrnc .I;.%al; wi.i.;l.i. a l l o t h e r f a c t o r s i d e n t i . c a 1 - , a c r y s t a l w i t h p r o j e c t i o n : : Trr~;?: i t s s v r f a c e 3.s l i k e l y t o d e v e l o p more and s t r o n g e r b o n d s l ~ e t w s e n a d j a c e n t c r y s t a l s t h a n o n e w i t h a smooth r e g u l a r ? s u r f a c e . A l s o , t h e s m a l l e r t h e d i s t a n c e b e t w e e n a d j a c c n t c x . y s t a l s u r f a c e s a n d t b e l a r g e r t h e s u r f a c e available; f o r boulciiizg, t h e nmrc l i k e l y w i l l b o n d s d e v e l o p . I t c a n x o t hr

o v e r - e r q p h n s l z e d tl:!at t h e thermod;rnamic i n s t , a ' L i l - i t y ~i:j~i.c;'n a l l o w s t h e c r y s t a . 1 ~ t o 'be r n o d i f i e d t o s a t ; - s f ' g t i l e c o n s i d e l - e d s i t u . a t i o n s i s h i g h l y s e n s i t i v e t o p a s t and p r e s e n t m e t e o r o - l o s i c a l f a c t o r s .

The main body of t h e i n d i v i c i u a l c r y s t a l i s q u i t e s",-o-ng aanc'i. c e r t a i ? ~ l y much s t r o n g e r t h a n t h e bonds r.dhlc;l :!czu? between t i l e c r y s t a l s s i m p l y i'rorn c r B o s s - s e c t i o ~ a l a r e a

c o i - i s i d e r a t io n s . T h e r e f o r e , u n d e r c o n d i t i o n s of r a p i d deforsl-a a t i o n t h e c r y s t a l i t s e l f d o e s n o t l i l - 2 l y p l a y a s i g n i f i c a n t ole i r l !Lets,-mining t h e s t r e n g t h of s!.~oc.r u-nt il a c l j a c e z ~ t

c r y s " L 1 ~ a r e i n d i r e c t c o n t a c t . It :'LS t h e f a c t t7:lut ri:;~.'Li1

bed;; o f t l - ~ e c r y s t a l i s n o t i n d i r e c t c o n t a c t r,.~it?;; i t s f:-;l);ledi.ate ilciglzbor s t ~ l i i c h d i f f e r e n t i a t e s snow from rnost o t h e r n i s t e r i a l s and I s a d s t o t h e h i s h l y v a ~ i a b l e s t r e n g t h p r o p e r t i e s . ';lke;n a load i:. a p p l i e d , t h e r e l a t l i v e l y weak i n t e r c o n n e c t r i i ~ ; T:o;-tds

. > '-, -

n.;..l~ f a i l f i i . r n t . I f t h e l o a d i n g whicn l e a d s t o the c o l l a p s e

i s r.al2id e . n > u ~ h , v e r y l i t t l e o r no r e - g r o w t l ~ of ;,oncis brill- c)cc1.1r and !;he snow s t r u c t u r e must c o l l a p s e u n t i l t h e l o a d ca:l b e s a r y L e d b y d i r e c t c o n t a c t between t h e body of t h e c r y s t a l s o r t h e i r p r c j e c t i o n s . I n t h i s p r o c e s s , tile coil.- t r i k ! u t i o n .:.ue t o e l a s t i c and p l a s t i c d e f ' o r m a t i o : ~ i s i n - s i g n i f i c a n t

&en

compared t o t h e novercent c a u s e d Ly t h e c o l l a p s e o f t h e s t r ~ x c t u r e . T l i e r e f o r e , i n summary, f ' o ~ dynamlc l o a d s one would e x p e c t a v e r y r a p i d 1oaGi.n:; .to 21:~: b r e a k i i i g p o i n t o f bonds between c r y s t a l s ,

a

sub seqi.: e n t

c o l l a p s e o f t h e s t r w c t u r e and c o a s o l i d a t i o l l 1eaclirl.i;

to

a s;?ecif i c g Y a v i t y de-t er:?~.ined by t h e l o a d anc' t h e a s s o c l r , t e 5 kineniat ic. s.

I n o r d e r t o d e r i v e a r e l a t i o n s h i n ~ e t w c : ~ n tl,c c l t i r n a t e corn-71-essive c.t:rength of' snow and tlie s:2ccrif l c ;;i'svit;y o f t h e snow? one must mn!;e c e r t a i - 1 2 s i m p l i f y i n 2 assurflptioi::s c o n c e T n i n g t h e bonding betwen t h e c r y s t a l s . 1 3 e c a ~ oe o f t h e n a t u r e of snow, t h e s e a s s u m p t i o n s c a n o n l y b e vel->-y ~ ; ~ v . d e . I n t h e n e x t s e c t i o n t h e a s s u m p t i o n s w i l l be l i s t e d and t h e

r>es1;11;5nz deyendence o f t h e h a r d n e s s , wllich i s a m c a -,urned

_.

'

i d c , ? . i t i c a l ->.ri.t% t h e u l t i m a t e con-pessi.ve s t r e ~ l g t ? ~ : , 3n spec:if L!::

~ p 2 , - i t \ - d e p t v e d .

L e t u s c o n s i d e r a s m a l l group o f s r y s t a l s i:i t h a

::;r;gw s t r u c t:~:~re and t h e bonds which i n t eracon:iec41; c.:~.2 s e c r y si;als

( p l i , * 1 . Suppose t h e r e a r e 0;- t h e a v e r a g e n c r y s - L a l s p . s r

u n i t area ia t h e snow. L e t t h e t o t a l I.o;?.J t r a n s m l t t e c l -i;'~youyh

G ~ Cof' t h e s e c r y s t a l s be P i . T h e r e f o r e , t h e a v e r a g e s t r s e s

s c t i n g on a p l a n e p e r p e n d i c u l a r t o tlhe d i r e c t i o n of s t r e s s rlrould t e g i v e n by

T h i s l o a d must b e t r a n s n ~ i t t e d from c r 3 y s t n l t o c r y s t a l t h r o u g h t h e i n t e r c o n n e c t i n g bonds.

f o l l o w i n g assuinptions i d i l l b e made:

Thc snow i s u n i l ' o r ~ and hortlop;eneous t h r o u g h o u t

The a v e r a g e number o f p a r t i c l e s i n any u n i t

area

l o c a t e d i n t h e snow i s n

T l ~ e axa3;Agc numbera of' p a r t i c l e s p e r u n i t volume i s ITa?

n

z If6 %"

The a v e r a g e mass of

a

s i n g l e c r y s t a l i s t h a t d e r i v e d Ly

Bader ( 2 ) and i s g i v e n a p p r o x i m a t e l y by ma

= 0.5

da

3

7,dciere da i s t h e a v e r a g e c r y s t a l s i z e .

T l ~ e r e f o r e , Na i s g i v e n a p p r o x i m a t e l y by

where Ps i s t h e s p e c i f i c g r a v i t y of t h e snow and jPs t h e d e n s i t y

Each bond which c o n t r i b u t e s t o

Pi

i s u n d e r compression o n l y and behaves

a s

a column.

The b e b a v i o u r of e a c h column under compression i s governed by R a n k i n e ' s formula:

where

O

= t o t a l ?i>?d <:ri

-31-

A = c r o s s - s e c t i o n a l a r e a of column k = r a d i u s of g y r a t i o n of a r e a A

=

r f o r s o l i d c i r c u l a r c r o s s - s e c t i o n of r a d i u s r

2

L

=

l e n g t h of t h e column C and b a r e c o n s t a n t s t o be d e t e r m i n e d .

L i s lrnovsn a s t h e s l e n d e r n e s s r a t i o of t5e column,

-

k

FOP a c i r c u l a r column, L

=

2L

-

Under c o n d i t i o n s of r a p i d l o a d i n g , e a c h column b e h a v e s e l a s t i c a l l y t o f a i l u r e

The coiumns have a c i r c u l a r c r o s s - s e c t i o n

The a v e r a g e number of bonds, n i , e f f e c t i v e i n t r a n s m i t t i n g

Pi

i s p r o p o r t i o n a l t o t h e number of p a r t i c l e s p e r u n i t . a r e a n and t o t h e s u r f a c e a r e a o f t h e a v e r a g e p a r t i c l e .

1 0 )

P i

i s d i v i d e d e v e n l y among t h e n i bonds.

il) ' ~ ' n e r a d i u s r o f a column i s some f u n c t i o n o f d, and L. The l a r g e r t h e a r e a on which t h e i n t e r c o n n e c t i n g column c a n grow, t h e l a r g e r t h e c r o s s - s e c t i o n a l a r e a o f t h e c o l u t m w i l l b e ; t h e f a r t h e r a p a r t t h e p a r t i c l e s a r e , t h e s m a l l e r t h e c r o s s - s e c t i o n a l a r e a of t h e column w i l l b e ; t h e c l o s e r t h e p a r t i c l e s a r e t o g e t h e r b , t h e more i n - s e n s i t i v e t h i s a r e a w i l l b e t o change? i n L. T h e r e f o r e , 1.ot

r2

=

₉

cj:

I

+j

c)'

64

(5)

where $ i s a c o n s t a n t . 1 2 ) As the s p e c i f i c g r a v i t y of t h e snow i n c r e a s e s , t h e p a r a t i c l e s move c l o s e r t o g e t h e r and b e g i n t o i n t e r f e r e w i t h e a c h o t h e r . T h a t i s , some of t h e s t r e s s w i l l b e t r a n s m i t t e d b e t w e e r p a r t i c l e s by d i r e c t c o n t a c t . L e t a f a c t o r be introdl.lced t o talce c a r e of - t h i s e f f e c t .

rJo1,r, t h e number of' p a r t i c l e s l y i n g on a l i n e o f u n i t l e n g t h i n t h e snow i s g i v e n a p p r o x i m a t e l y by

The dlstsnce of s e p a r a t i o n between c r y s t a l c e n t e r s i s t h u s g i v e n b y

i

=

( O a 5 day

l / 3

I n .$igurc 2, L i s p l o t t c d a s a f u n c t i o n of f o ~ l;tl;acc v ~ l i i e s c f

d,.

It i s seen t ? ; a t L ap;oroacT~es 0 a t

p s sql:cLl

t o

apprc,ximately 0.5. Also,

at

any one s p e c i r l c gi-avit) ,

L

i n c r e a s e s d i t h da, For a c i r c u l a l a c r o s s - s e c t i o n

2

.

"3 L e t - 0 . 8

h i - 1 ~ 3

Then j

5

(+j2

i s p l o t t e d a g a i n s t

Ps

i n 1 % ~ .

3.

The s t r e s s P t r a n s : - r ~ i t t e d by t h e snow i s givci?, by

p

=

rn

P; i: r

? C A

2

P,' =

Q n ,

=

A d d ,

I

*

b(+V

s i n c e n i i s t h e a v e r a g e number o f b o n d s ~F:I.-- ~!hl,t:,~1.~:.. S u b s t i t u t i n g

6 ,

11,

13

and

1b.

i n 1 2

f

dL?

]

[

+

L,

j

, 2.

-rr

c

;?

[

-.. . . , . . - . . . a i. i d <.. P = d : +

1"

(

t.;;

-. . . _ _ _ _ _ _ _ _ _ _ I _ _ I I _ _ _ _ _ - --.

---

- - - '

[

,

+

3 k- x !, 1

.+

.

-)I

I . . 4

-

0 1 :

d , ;

3 Let. .

'j

'Ti

C

(3

4-

J I

When t h e snow f a i l s , P =

Kp,

t h e u l t i m a t e s t r e n g t h . o f snow i n c o m p r e s s i o n

T h e r e f o r e ,

k-

=

H a r d n e s s d a t a o b t a i ~ e d from R e s o l u t e , 1J.W.T.; Al.clavik, N. \J.T. ; Gander, Newfoundland and Ottawa, Onta-vio i l l

t h e Canadian snow z u r v e y m c u t i l i z e d t o o b t a i n F i g ,

I!.

Each p o i n t was found by c a l c u l a t i n z t h e mean e n e c i f ' i c g r a v i t y f o r e a c h g r o u p o f h a r d n e s s r e a d i n g s , The :,roups went i n

s t e p s of 1 0 f o r h a r d n e s s from 1 0 t o 1 0 0 , i n s t e p s of 100 f o r h a r d n e s s 100 t o 1000 and i n s t e p s o f 1000 f o r h a r d n e s s f'pon, 1000 t o 10,000. It was f e l t t h a t by t h i s rnetllod t l l c ,;enclanl depencie.?_ce of h a r d n e ~ s o 1 s p e c i f i c g r a v i t y c o u l d b c ol=i;:~?_;~cd from d a t a wkich had a s p r e a d i n l l a r d n e s s v a l u e s o f v p 'LO a

f a c t o r o f 1000 a t any one s p e c i f i c g r a v i t y . T h e s p r e a d i n s p e c i f i c g r a v i t y a t any one h a r d n e s s was much l e s s

( i z

t h e o r d e r of 2 ) .

From F i g .

4,

v a l u e s were o b t a i n e d f o r bl 22d c i . l ' h e s e were founci t o be

I n P i g ,

4,

t h e d e r i v e d c u r v e i s shown dashed.

The r e l a t i o n s h i p between h a r d n e s s and s p e c i f l c g r a v i t y i s v e r y n e a r l y a s t r a i g h t l i n e on t h e l o g

-

l o g d i s p l a y . If we l e t t h e s p e c i f i c g r a v i t y c o r r e s p o n d i n g t o

narchiess K - ~ .

,

b s Ps., end s i r f o r K p 2 b e

PSp

- .i

-

-

T h i s v e r y clw-delg sl?ows how s e n s l t i.ve t h 3 a t r ' c n g t h propcrdt i e s ~f :,he sno~.J ape t o q , a l ; i f ' i c g r a v i t y .

T'nouglrl e q u a t i o n

1 6

i s i n good a g r e c r n e n t w i t h t h e a v e r a g e d e p e i i d e n c e o f h a r d n e s s o n s p e c l f ' i c g r a v i t y , i t rUoes

o-t s'- l . ~ j + j fh.3 f.;<-l;r~p.e aa-pj.ab j - 1 j . t ~ ifi hayil;c 3 s c ; l l ; s ~ r ~ v ~ , i : , i c n s .

It

bras shoi,fi-- I n ( i ) iz'rlat; si-,r:le o f t h i s v a r i : ; l s j . l i t y c o l ~ l d b e attr:ibix.ced. ~ C J tem;,lera'i,ure e f f e c 4 ; s . The eff s ~ t , of'

t

er;perat,ul-e

i s 70i; f~pl>z-r~Z?^Lt i n ~ q l l a t i c r ~ 7 _ & T O P

_tw,

r e a s o z s f

7 1

,'

C

.

- i ~ ? ~ i c h e ~ l > o d i s s t h e e i a s t 5,; p r o p a r ~ t i e s

or i c e , was ase~~::rlcd c o n s t a r i t and.

21 t:?e i;rowth. and d e c a y o f i . o n d s d u e t o t e ~ * : p e l t i ~ ' : ~ i n g e s w a s il.e;lected.

:7ra0:?i t h e 3reli;.r1i1121r:li d i s c c 1 s ~ i o n and t h e z.ssi~.n~p)t,fc;!.ir; n c c e s s a l - y 'lo s'"L:;.~?l..ify t 3 d e r i v a t i o n o f e q . ~ . a t i o n 1.6:, -Che r 3 l e o f t b . e

l;.i-';e~>corine~=tlli;; koncis i l l d e t er>r;~i-.llng t ne s'cw.cr,;-,ti-?- o f E ~ : I M

Lieco:ne s (!ii?lt6 c l . e n l a . It i..s :il.so sppar>ent, t1:1s

t

a s t h e s p c c % . f ic

g ~ a v 3 . t ~ i n c r e a s e s , and If' t h e snow i s con:S'lnod, t h e b o n d s b e h a v e l e s I. il;e s i e n G e r ccsluxcrls a:qi:l 1-i:ore 14!:-:: sklor't co;urnns,

1 c . .,6 i I:;., .--. -- t ,o ~ , ~ t ' a t s r ~ s t r e n g t h 217d s t 8 t : i l i t - y

~f

the s t ~ ~ c t u r e

a~-:d u.iti-nately n nc;rma.l L e e - l i k e be;--[avi.o:ir.

T-,- , ,,.e d i s c u s s i o n and d . e r i v a t i o n i-:ave :?.I E O S ~ I O L J ~

$-I- i s ! , q . ~ 1 1 6 . : ~ ~ ' e r - ~ g t h of s;l.or,~ is i n d e p e n d e i ~ t to t h e f'i:=st orcler o n c u . > - s ~ : ! l s i z e

(I),

A11 e f f e c t of' r , r . y s t a l s i z e i s i n h e r e n t

:'in

t h e ass_::ilaptio~z:: f o r 8.t any oae s p e c l . f i c i;;rsvS.tj,

the

l a r g e r t h e c r y s t , c l s , t h e i->;reatera w i l l be the s e ~ ) a r a . t , - i o n ( L ) , , t h e :iiuni;l?er o f 2:u-lri:edfiate neigtjl2E;ors w i l l . d e c r e a s e a n d tiy.erei'ore t!.1~2 t)onc:.i,~g w i l l I:IC weal..:er, These e f f e c t s must b e n3arl.g ' b r i a l l c e d : i r l :rla.i;iipi) by tile l r l c r e a s e d s.[:r.~f a c e elaca

cbf" t h e c r : ; y z t i i l a v a i l a i - _ l l e f o r 1:)onclinp;. Tliese f a c t s a l s o

? nc;?.cata t;:;it; ~ l i j nd- blown o r n r o c e s z e d snow c a n ?-lave I!.i;;ll

--

styenil;tl? cl-;ay:?.::c,ei.ist:ics ;?ot a i ~ l y - f'rom pe~y:r,:?wtll dl.~.? t o

t':ey:;.;o(I;;na?j:i;; u g l ~ a l a n c e -2v.t b y i n c r e n ~ . e d bo!lc:..in:.:: - :iue t o mol.9

i _T+,' ,

*;--

..

t .A

- .

I,, , c o n t ~ , c t , and rincr.eased p r o j e c t i o n s bet.weer-! i i r ~ i ~ ~ l i Lol?ds

, A 'a

.

I* J T h e i.Qcl-eEi e e i n p r o j e c t f o n s o r e v e n i n n z t i : s l .

;,~i-,-l;i_(-;le ;cnlr;$~eys i s dl:-n, t o f r a c t ~ ~ l r i . t i p . 4 12~1 t'iie :-~ec?.:?~nlll:al. cjy

rl.;~:;t:rai prszs sin;;. -

I n c o l i c l i ~ s i o n lit nust b e p ~ i n t e d o u t t h a t the

:'or?sgofng is v a l i d o n l y o v e r t h e s p e c i f i c g r a v i t ~ i _J raRr;e u p t , ~ 7

0 ~ 1 ~ ;

a t t k e m o s t . \ ) . e n t h e s p e c i f i c p a v r i . t y 1.s in t h e r.a:1z,ge o f

Ct.!;.

o r ::rester,, t h e snow b e g i n s t o appxaoacb t h e

s t a t e o f ac: t u a l c o n . t a c t b e t w e e n n a r t i c l e s r e s u l . t i n ~ ; : i n a

I1

more norrr.alV bel1avi:-i-~:1r~. The n a r t i c l e s e p a r e t i c ? l i l'ias

d e c r e a s ? d t o s u c h a n e x t e n t t11o.t t h e assump-ti.on o f t h e Scnd

bi:'r-iavi~i..:: as colulnns be;!;ilis t o b r e a k G o m , Under nax~rnal a y r p l i c n t i o n s , , S a n ? , - i n e s f'or?rnu.la .telxds t o i:,ive t;oo l a r g e a v n l l i e .;'o:r2 t h e ult.ii-rlat e s t r e n g t h a t s m a l l s l e n d e r l i e s s r a t i o s .

Ref e r e l i c e s

(1.) G o l d , LLd. The St-re.tl:gth. o f Snow i n C o r ! p r c s s i o q u i ~ t ~ e r

12

Lgilal.il.f c Load 2 , Eenor*t

Nc

,

L i v i F i o ; ~ of i_ic i l u i n c -

b~

F:eses.rc~h, I : i a t i o n a l liesearacli. Col:-ncii, Ottawa. Zecep."-- Lt,b.,er, 1 9 5 4 .

( 2 ) Badep:, :I, ,

R,

Eiaefel.1,

U,

Iiucher., 6, iJe:-~sr, 9. 4c!".6;1,

..pd 2 j . ; r y T : 1 8 3 ~ ~ z 3 0 5 ~ a z d i t 7 'F~~Ietcii~ox.~:.!:.?.siii. TI.::,-.:sla-i:ior?. . Zce and P a r m a f r o st R e aeai:~cl-L :!:,sta'ul i :::-imc.r;i,;,

C o r p s of' Jj,l _{c -} q + n e c r s , U, Fie A . p r , g - , W i : , l ~ 4 t & , I ~ . ~ ~ ? I Q - % S .

19540

(3)

d 3 Qaeir;.?lin, I'C,!f. S n o t ~ a.s a C r y s t a l l l ~ z e A&:>r>e:,ats.

rI~ r a - r l s l a - ; , i o n 2 1 ,

Snow,

I c e and Terrnafrosr, Researzi-1

1:,Ls,aliii:::~rient, .

.

+- z C o r p s o f Er-:i:zciers,. U.S. A r m y , W i l m e t t e , I l i . i n o i s ,

1954~

I N T E R C O N N E C T I N G BONDS

FIGURE I

SNOW PARTICLES AND THEIR

INTERCONNECTING BONDS

m m ~ n .

S P E C I F I C G R A V I T Y fs

FIGLIRE 2 SEPARAl'ION L BETWEEN SNOW PARTICLES AS A FUNCTION SPECIFIC GRAVITY

CURVE OBTAINED FROM RESULTS OF SNOW SURVEY 10000 _{- 1} 8 0 0 0

-

-

Y

- ' 0 0 6 0 0 0 - 0 +-DERIVED CURVE - - 8 0 4 0 0 0 - - 60 - _- 4 0 2 0 0 0 - - _{2 0} 1000 - _- 8 0 0 - - - _{I 0} 6 0 0 - E "E - 8

-,I"

- - i1.i 4 0 0 - V) V) V) W - W z 0 w - 4 E w u u I 2 0 0 - I - ₂ 100 - _- 8 0 - - - ₁ 60 - _- 0 8 - 4 0 - - 3.6 - 0 - 0 4 I 2 0 - '10 10 1 " ' 1 1 I 1.0 0 . 8 0.6 0 . 4 0 . 2 0.1 S P E C I F I C G R A V I T Y fi F I G L I R E 4 H A R D N E S S A S A F U N C T I O N O F S P E C I F I C G R A V I T Y A S O B T A I N E D F R O M O B S E R V A T I O N S M A D E A T R E S O L U T E

,

A K L A V I K , GANDER A N D O T T A W A .