Lang_Triaxial Tests on Dry, Naturally Occurring Snow

8/2/2019 Lang_Triaxial Tests on Dry, Naturally Occurring Snow

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ELSEVIER Cold Reg ions Sc ience and Techno logy 23 ( 1995 ) 191-199

cold regionsscienceand technology

T r i a x i a l t e s t s o n d r y , n a t u r a l l y o c c u r r i n g s n o wR.M. Langa, W.L. Harr ison b

aU.S. Ar m y Cold Regions Research a nd Eng ineer ing Laboratory , 72 Ly m e Road, Hanover , NH 03755-1290, USAbUnivers i ty o f Utah, Dept . of Geography, 270 Orson Spencer Hall, Sa l t Lak e City , UT 84112, USARece ive d 27 M ay 1993; accep ted a f t e r rev i s ion 18 March 1994

Abs t rac t

T h i s s t u d y p r e s e n t s a n d d i s c u s s e s t h e r e s u l t s o f t r i a x i a l t e s ts c o n d u c t e d o n d r y , n a t u r a l l y o c c u r r i n g s n o w . T h ea p p l i e d s t r a i n r a t e fo r t h e f r e s h s n o w w a s 1 .0 1 1 0 - 5 s - ~ a n d t h e c o n f i n i n g p r e s s u r e w a s v a r i e d f r o m 0 t o 4 1 .3 7k P a . S t r e s s - d e f o r m a t i o n c u r v e s a r e p r e s e n t e d a n d s n o w b e h a v i o r i s r e p r e s e n t e d w i t h i n t h e c o n t e x t o f a c r i ti c a ls t at e m o d e l ( R o s c o e e t a l. , 1 9 63 ). U n d e r t h e s e s p ec i fi c l o a d i n g c o n d i t i o n s t h e s t r e s s - d e f o r m a t i o n c u r v e s d e m o n -s t r a t e t h a t s n o w e x h i b i t s a n i n s t a n t a n e o u s r e s p o n s e w h i c h c a n b e c h a r a c t e r i z e d a s a n i s o t r o p i c , n o n l i n e a r , e l a s t i c -p l a s ti c s t r a in h a r d e n i n g m a t e r i a l f o r c o m p u t a t i o n a l p u r p o s e s . T h e l o a d i n g c o n d i t i o n s d i d n o t p r o m o t e t h e v i s c o u sb e h a v i o r o f th e s n o w a n d v i s c o u s e f f e c ts a r e n o t c o n s i d e r e d . W h e n t h e r e s u l t s a r e c o r r e c t e d t o t r u e s t r es s , t h e s n o wc o n t i n u e s t o d e f o r m w i t h o u t a n i n c r e a s e i n l o a d b e y o n d t h e l i m i t l o a d . A l so , t h e e f f ec t o f i n c r e a s e d u l t i m a t e s t r e n g thw i t h i n c r e a s e d c o n f i n i n g p r e s s u r e w a s , i n g e n e ra l , a p p a r e n t f o r s n o w .

1. Introduct ionData concerning the mechanical response of

snow to measured, applied loads are very lim-ited. The mechanical response o f snow to an ap-plied load is of interest in diverse fields of study,e.g. from the natur e o f flowing snow in an ava-lanche to the problems encountered intrafficability.

The mathematic al description of any materi-al's mechanical behavior is always idealized andthe idealization is formulated for the specificloading condition under consideration. A goodexample is the behavior of metals, which in ma nystructural loading scenarios may be sufficientlydescribed as a Hookean material but in othercases as perfectly plastic or perhaps hardeningoccurs outside the initial, linear portion of thestress-strain curve. When one considers the range

of deformations, deformation rates, tempera-tures, etc., to which a materia l in the solid statemay be subjected, it becomes obvious that a con-stitutive law can only serve to approximate amaterial's response to loading in an appropri-ately restricted range. Formul ating the appropri-ate, idealized constitutive behavior for any ma-terial is never a trivial or simple process.Snow does not conform to simple modelling inthe same manner as a material like metals, assnow behavior is affected by hydrostatic pres-sure, and behaves differently unde r compressionand tension. Unde r the specific, applied loadingconditions that were considered in this paper,snow demonstrates an instantaneous responsethat may be interpreted as an elastic-plasticstrain hardening behavior. This approach, ormaterial model, is not in tende d to be used as anaccurate model for the detailed behavior o f the

016 5-232 X/95 /$09 . 50 1995 E ls ev ie r Sc ience B . V. A l l r igh t s re s e rvedS S D I 0 1 6 5 - 2 3 2 X ( 9 4 ) 0 0 0 0 5 - I


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192 R.M. Lang, W..L. Harrison / Cold Regions Science and Technology 23 (1995) 191-199

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O. 0. C.F i g . 1. S c h e m a t i c o f t r i a x i a l t e s t a p p a r a t u s . ( a ) C h a m b e r p r e s s u r e c o n t r o l , ( b ) t r i a x i a l c e ll , ( c ) c o n s t a n t p r e s s u r e p o r e v o l u m ec h a n g e m e a s u r e m e n t d e v i ce .i n t e rn a l p h y s i c a l n a t u r e o f sn o w , b u t a s a c o m -p u t a t i o n a l t o o l f o r v a r i o u s m a c r o s c o p i c p r o b -l e m s i n s n o w s c i en c e . T h e s e d a t a a r e o f p a r t ic u -l a r i n t e r e s t f o r u s e i n f i n i t e e l e m e n t a n d f i n i t ed i f f e r e n c e m o d e l s . T h e e x p e r i m e n t a l d a t a a r e t h er e s u l t o f t r i a x i a l t e s t s o n s n o w . T h e c h o i c e o ft r i a x ia l t e s t in g r e s u l t s f r o m t h e i n h e r e n t a s s u m p -t i o n t h a t s n o w r e s p o n s e c a n b e d e s c r i b e d b y ap l a s t i c i t y t h e o r y f o r t h e l o a d i n g s c e n a r i o o f i n t e r -e s t, a s s n o w e x h i b i t s t h e p r o p e r t y o f c o n t i n u i n gd e f o r m a t i o n a t a c o n s t a n t s t r e s s l e v e l b e y o n ds o m e t h r e s h o l d l o a d ( e l a s ti c l im i t ) , w h i c h d e -p e n d s o n t h e c o n f i n i n g p r e s s u r e . T h i s i s t h e c l as -s i c a l d e f i n i t i o n o f " i d e a l l y p l a s t i c " o r " p e r f e c t l yp l a s t i c " b e h a v i o r ( s e e , f o r e x a m p l e , C h e r t, 1 9 7 5 ) .

2. Exp er imental re sul ts2 .1 . T e s t a p p a ra t u s a n d m e t h o d o l o g y

T h e t r i a x ia l a p p a r a t u s u s e d t o p e r f o r m t h e e x -p e r i m e n t s w i t h s n o w w a s a d a p t e d f r o m t h a t u s e d

f o r s o i l s . M o d i f i c a t i o n s w e r e n e c e s s a r y t o a c -c o m m o d a t e t h e l ow c o m p r e s s i v e s tr e ng t h o fs n ow , m e a s u r e m e n t a t t e m p e r a t u r e s b e l o wf re e z in g , a n d t h e u s e o f a c o m p r e s s i b l e p o r e f lu i d .T h e t r i a x ia l c e l l i s o f t h e N o r w e g i a n t y p e ( A n -d r e s e n e t a l. , 1 9 5 7 ; A n d r e s e n a n d S i m o n s , 1 9 6 0 )( s e e F ig . 1 ) , w h i c h w a s m o d i f i e d t o a c c o m m o -d a t e a lo a d t r a n s d u c e r i n s i d e t h e c h a m b e r s o t h a tt h e f r i c ti o n o f t h e l o a d i n g p i s t o n p a c k i n g w o u l dn o t e f f e c t t h e s t r es s m e a s u r e m e n t s . F o r s n o w ,d e v i a t o r i c ( a x i a l ) s t r e s s e s o f l e s s t h a n 0 .1 M P aa r e o f i n t e r e s t ( N a i t o , 1 9 7 3 ) . T h e f r i c t i o n a lf o r ce s d u e t o t h e p i s t o n p a c k i n g w e r e e s t i m a t e dt o b e o f t h e o r d e r o f 0 .0 4 M P a ( A n d r e s e n e t al .,1 9 5 7 ) w h i c h i s u n a c c e p t a b l y h i g h f o r m e a s u r e -m e n t o f t h e s t r es s l e v el s o f i n t e re s t w i t h o u t p u t -t i n g t h e l o a d m e a s u r i n g d e v i c e i n s i d e t h e c e l l .A l s o , i t i s n e c e s s a r y f o r t h e c o n f i n e m e n t m e m -b r a n e t o h a v e a n e g l i g i b l e r e s i s t a n c e t o d e f o r -m a t i o n w h e n c o m p a r e d w i t h th e f o r ce s re q u i re dt o d e f o r m s n o w .T h e u s e o f a ir a s th e w o r k i n g f l u i d i n t h e


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Fig. 2. Stress -defo rmati on curves from the first season tests, with p the snow density, P the confining pressure and Tth e temper-ature. Dash ed line is correc ted for the d iamete r increase in the sample (true stress ). zJ P'gives the corresponding value o f volumechange due to axial (t rue) stress for the indicate d stress-displa cement value at 15% strain.c h a m b e r a n d p o r e s p a c e s e l i m i n a te d t h e p r o b -l e m o f f i n d in g a f l u i d c o m p a t i b l e w i t h s n o w . T h eu s e o f a c o m p r e s s i b l e fl u id d o e s n o t i n t r o d u c e a n yp r o b l e m s w h e n v o l u m e c h a n g e s ar e m e a s u r e d a tc o n s t a n t p r e s s u r e , b u t w h e n t h e p r e s s u r e v a r i e s ,B o y l e s L a w ( B r a d y a n d H u m i s t o n , 1 9 7 8 ) m u s tb e a p p l i e d . A c c u r a t e m e a s u r e m e n t s o f t h e i n it i alp o r e v o l u m e a n d o f t h e p o r e v o l u m e c h a n g e a r ea l s o r e q u i si t e. T h e p o r e v o l u m e c h a n g e m e a s u r e -m e n t d e v i c e i s a U - t u b e m a n o m e t e r w i th a s ta -t i o n a r y a r m a n d a s p r i n g s u s p e n d e d a r m c o n -n e c t e d b y f l e x ib l e t u b i n g . T h e v o l u m e c h a n g e i sr e a d o n t h e s t a t io n a r y a r m w h i c h i s g r a d u a t e d i nO . l m l d i v i s i o n s. T h e s p r i n g s u s p e n d e d p o r t i o n

o f t h e m a n o m e t e r p o s i t i o n s i t s e lf t o c o r r e c t t h ei m b a l a n c e i n m e r c u r y l e v e l s c a u s e d b y v o l u m ec h a n g e s . I n o r d e r t o d o t h i s , t h e s p r i n g c o n s t a n t ,K, i sK = A c P n g / ( 2 - - P a / P H g ) - - kw h e r e A c i s 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 s u s -p e n d e d m e r c u r y r e s e r v o ir , Pr ig i s t h e d e n s i t y o fm e r c u r y , P a i s t h e d e n s i t y o f a i r a n d k i s t h e w e i g h to f f le x i bl e t u b i n g a n d m e r c u r y p e r c e n t i m e t e r . Ac h a n g e i n v o l u m e o f t h e s y s t e m c a u s e s a s l ig h tp r e s s u r e d i f f e r e n t i a l a c r o s s t h e a r m s o f t h e m a -n o m e t e r . T h e m e r c u r y f l o w s s o a s t o e q u a l i z e t h ep r e s s u r e a n d t h e s p r i n g a d j u s t s t o t h e c h a n g e i n


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displacement (cm)F i g. 3 . S t r e s s - d e f o r m a t i o n c u r v e s f r o m t h e f i r s t s e a s o n te s t s, w i t h p th e s n o w d e n s i t y , P t h e c o n f i n i n g p r e ss u r e a n d T t h e t e m p e r -a t u r e . D a s h e d l i n e i s c o r r e c t e d f o r t h e d i a m e t e r i n c r e a s e i n t h e s a m p l e ( t r u e s t r e s s ) . A V g i v e s t h e c o r r e s p o n d i n g v a l u e o f v o l u m ec h a n g e d u e t o a x i a l ( t r u e ) s t r e s s f o r th e i n d i c a t e d s t r e s s - d i s p l a c e m e n t v a l u e a t 1 5 % s tr a i n .weight, maintain ing the preset pressure across thedevice. The volume change is recorded as achange in level of mercury in the fixed manom-eter arm. An x - y recorder was used to record theaxial load and deformation. Pressure and flowcontrol regulators allowed complete control o f thechamber air supply and pressure. A So i l t e s t brandprecision motorized compression device wasused in the field to control and apply the axialload.

The snow samples were cylindrical with a vol-ume o f 391 cm 3, a length o f 14.95 cm and a di-ameter of 5.77 cm. After weighing for density,the samples were encased in a confining mem-brane with a solid circular cap on top and a po-rous platen on the bottom. The porous platen al-lowed interaction of the pore air with the air inthe pore volume meas uremen t device.Tests conducted at atmospheric pressure in thechamber were performed with and withoutmembranes to determine effects of the mem-brane. No effects were discernible.

2 .2 . S n o w p r o p e r t ie sThe field laboratory was located in Albion

Basin, Alta, Utah. Alta is well known for the con-sistent precipitation of dry, low density snowduring the winter season. The snow samples usedfor the natura lly occurring snow tests during thefirst test season were collected and tested aftersundown when the a mbient temperature was be-low freezing. The grain size displayed negligiblegradation. The densities of the samples rangedfrom 170 k g / m 3 t o 376 k g / m 3. The seasonalsnowpack depth was subnormal (approximatedepth o f 1 m) for the test area during the firsttest season. The pack contained snow whichranged in age from 2 weeks to 3 months, allwithin the 1 m depth. The snowpack conditionsfor the second test season were normal for thearea.The grain size distribution was studied in or-der to assess the structural properties o f a snow-pack sample in relation to the critical density of


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F i g . 4 . S t r e s s - d e f o r m a t i o n c u r v e s f r o m t h e s e c o n d s e a s o n t e st s , w i t h p t h e s n o w d e n s i t y , P t h e c o n f i n i n g p r e s s u r e a n d T t h et e m p e r a t u r e .

d r y s n o w . C r i ti c a l d e n s i t y i s d e f i n e d a s t h e d e n -s i ty t h a t i s r e a c h e d t h r o u g h u n c o n f i n e d c o m p a c -t i o n w h e r e v o l u m e c h a n g e c e a s e s ( s e e , f o r e x -a m p l e , D r u c k e r , 1 9 6 7 ) . I n o r d e r t o d e t e r m i n eg r a in s iz e d i s t ri b u t i o n , a 5 0 0 c c s a m p l e o f s n o ww a s g e n t l y s e p a r a t e d a n d p l a c e d i n t h e t o p o f as t a c k o f t w o s i e v e s 2 . 3 8 m m , a n d 0 . 8 4 m m , a n da p a n t o r e t a i n a n y g r a i n s p a s s i n g t h e 0 . 8 4 m ms i ev e . T h e s t a c k w a s a g i t a te d f o r 5 m i n u t e s a n di n s p e c t e d . T h e r e s u lt w a s a g e n e ra l r e g r o u p i n g o ft h e p a r t i c l e s w i t h l i tt l e e x h i b i t i o n o f p a r t i c l e d i s -t r i b u t i o n . T e m p e r a t u r e c o n t r o l h a d b e e n c a r e -f u ll y m a i n t a i n e d a n d i t w a s c o n c l u d e d t h a t g r a ins e p a r a t i o n w o u l d h a v e o c c u r r e d o n l y i f t h e a g i-t a t i o n h a d b e e n s e v e r e . D u r i n g t h e s e c o n d t e s ts e a s o n a t A l t a , i t w a s n o t e d t h a t t h e g r a i n s i z ep r o fi le o f t h e s n o w p a c k w a s u n i f o r m e x c e p t f o rt h e l ay e r o f d e p t h h o a r a t t h e g r o u n d - s n o w p a c k

i n t e rf a c e . T h i s w a s 0 . 4 5 m i n d e p t h i n a t o t a l p a c kd e p t h o f 3 . 0 m a t t h e t e s t s i te .2.3 . Te st resu l t s

T h e s t r e s s - s t r a i n c u r v e s o f t h e u n d i s t u r b e df i e l d s a m p l e s a r e s h o w n i n F ig s . 2 t h r o u g h 4 . T h ed e n s i t i e s p , c h a m b e r p r e s s u r e s P , v o l u m e t r i cc h a n g e s A V , a n d a m b i e n t t e m p e r a t u r e s f o r e a c hs a m p l e a r e g i v e n i n T a b l e 1 . R 2 is t h e s t r e s s a t 2c m d e f o r m a t i o n ( 1 3 .5 % s tr a i n ) . T h e v o l u m e t r i cc h a n g e s A V a r e e x p r e s s e d a s t h e v a l u e a t t h e a p -p l i e d c o n f i n in g p r e s s u r e f o l l o w e d b y t h e v a l u e a t1 5 % s tr a i n . T h e s t r a i n r a t e f o r t h e c u r v e s i n F i g s .2 t h r o u g h 4 w a s 1 .0 1 1 0 - 5 s - ~. O n e s a l i e n t f e a -t u r e o f t h e s n o w u n d e r l o a d i n g w a s t h e c o n t i n u -o u s s m o o t h d e f o r m a t i o n o f t h e s a m p l e , i .e ., n oi n d i c a t i o n o f c o l l a p s e - r e g a i n p a t t e r n s a s re -


6/9

196 R.M. Lang, W.L. Harrison / CoM Regions Science and Technology 23 (1995) 19 I- 199Table 1Paramete rs for dry, naturally occurring snow testsTest No. p P AV~ R2 T(kg/m 3) (kPa) (mE) (kPa) (C)770330-1 168 0 0/ 3. 6 b 29.3 - 4770330-2 178 10.34 c 28.9 - 4770409-1 306 0 c 68.0 - 2770409-2 328 10.34 9.4/ 9.8 82.0 - 2770409-3 328 20.68 7.7 /14 .4 110.0 - 2770409-4 284 31.03 15.8/5.7 80.0 -2770409-5 312 d 0 0/3.5 43.0 - 2770410-3 328 0 0/10 .4 90.0 - 2770410-4 328 13.79 2.6/10.9 97.0 -2770410-5 320 27.58 11.3/7 .5 104.0 - 2770410-6 320 41.37 17.2/ 7.0 110.0 - 2770410-8 376 34.47 13.1/e - - 2770410-9 320 0 0/1 0.0 83.0 - 2770410-10 320 6.89 3.7/14.8 70.0 -2780221-1 258 0 - 75.0 - 9780221-3 230 0 - 43.0 - 8780221-5 232 0 - 36.0 - 8780221-5 282 0 - 85.0 - 6780221-6 276 0 - 84.0 - 6aA Vbefore "/ " is due to confining pressure only; AVafter " / " is the value at 15% strain.bCorrugated membrane .CMembrane leakage.dVertical sample .eVirgin compr essi ve test only.

p o r t e d b y o t h e r s ( K i n o s i t a , 1 9 67 ; S h i n o j i m a ,1 9 6 7 ) F o r t h e a p p l i e d s t r a in r a t e , th e s n o w s a m -p l e s d e f o r m e d c o n t i n u o u s l y , f i rs t e x h i b it i n g l in -e a r b e h a v i o r i n a v e r y n a r r o w r a n g e u p t o t h el i m i t lo a d . T h e b e h a v i o r a f t e r t h e li n e a r p o r t i o no f t h e c u r v e s i s th a t o f a p l a s ti c s t r a i n - h a r d e n i n gm a t e r i a l w i t h a d e p e n d e n c e o n c o n f i n i n g p r e s -s u r e ( F i g s . 2 a n d 3 ) . T h e d a s h e d l i n e s i n d i c a t et h a t t h e s t re s s e s h a v e b e e n c o r r e c t e d f o r t h e i n -c r e a s e i n d i a m e t e r , i . e . c o n v e r t e d t o a " t r u es t r e s s " . T h e " t r u e s t r e s s " - d e f o r m a t i o n c u r v e sw o u l d i m p l y t h a t t h e s n o w i s a p p r o a c h i n g p l a s t i cb e h a v i o r a s t h e s n o w s a m p l e s c o n t i n u e t o d e -f o r m a l t h o u g h t h e a p p l i e d s t r e s s l e v e l i s n o ti n c r e a s i n g .I n g e n e r a l , i n c r e a s i n g t h e c o n f i n i n g p r e s s u r ei n c r e a s e d t h e u l t i m a t e s t r e n g th o f t h e s n o w s a m -p i es . T h i s b e h a v i o r i s n o t d i s p l a y e d i n t h e t r a n-s i ti o n fr o m t e s t # 7 7 0 4 0 9 - 3 a n d # 7 7 0 4 0 9 - 4 . T h et e s t p r e s s u r e w a s i n c r e a s e d f r o m 2 0 . 6 8 k P a t o3 1 . 0 3 k P a , b u t t h e d e n s i t y o f t h e s a m p l e i n

# 7 7 0 4 0 9 - 4 i s 1 3 % l o w e r . A l t h o u g h d e n s i t y is n o ta n i d e a l i n d i c a t o r o f s t r e n g th , i t m a y h a v e r e -s t r i c t e d t h e u l t i m a t e s t r e n g t h i n t h i s p a r t i c u l a rs a m p l e .F i g . 4 s h o w s t h e s e c o n d s e a s o n t e s t s ( s e r i e s 7 8 )w h i c h w e r e a l l c o n d u c t e d w i t h z e r o c o n f i n i n gp r e s s u r e . U l t i m a t e s t r en g t h s v a r y f r o m 4 0 k P a t o9 7 k P a w i t h d e n s i ti e s v a r y i n g o n l y 1 8% ( p l u s o rm i n u s 2 6 kg /cm 3 ) . T h e l o w e r v a l u e s o f s t re n g t hd o c o r r e s p o n d w i t h t h e l o w e r d e n s i t i e s a n d t h eh i g h e s t v a l u e s w i t h t h e h i g h e s t v a l u e s o f d e n s i t y .T h e s e r i e s 7 8 t e s t s h a v e n o t b e e n c o r r e c t e d f o rd i a m e t e r c h a n g e s i n t h e s a m p l e s a s m e a s u r e -m e n t s o n d i a m e t e r c h a n g e s w e re n o t r e c o r de d .T h e v o l u m e t r i c c h a n g e , A V , i n T a b l e 1 i s s h o w na s t w o v a l u e s f o r a l l t e s t s e x c e p t f o r n u m b e r7 7 0 4 1 0 - 8 w h i c h w a s a v i r g i n c o m p r e s s i o n t e s t( p u r e h y d r o s t a t i c s t r e s s ) . T h e n u m b e r p r e c e d -i n g t h e " / " g i v e s t h e v o l u m e c h a n g e d u e t o ce l lp r e s s u r e P ( v i rg i n c o m p r e s s i o n ) a n d t h e v a l u ef o l lo w i n g t h e " / ' " g i v e s t h e v o l u m e c h a n g e d u e


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vo l u m e t r i c h a n g e , V m l )F i g . 5. V i r g i n c o m p r e s s i o n l i n e s ( V C L ) o f t h e s a m p l e s i n t h ep r e s s u r e - v o l u m e p l a n e . S a m p l e d e n s i t ie s a r e i n d i c a te d . T e s tt e m p e r a t u r e w a s - 2 C .

t o t h e " t r u e s t r e s s " a t 1 5 % s t r a i n . T h i s s e c o n dv a l u e o f A V i s a l so g i v e n i n F i gs . 2 a n d 3 a n dc o i n c i d e s w i t h t h e 1 5% s t r a i n ( v e r t i c a l l i n e ) .F i g . 5 s h o w s t h e v i r g i n c o m p r e s s i o n l i n e s( V C L ) o f t h e s am p l e s in t h e P - V p l a n e , f o r t h er a n g e o f s n o w d e n s i t i es t e s te d . T h e s i g n i f ic a n c eo f t h e v i r g i n c o m p r e s s i o n l i n es i s t h e a b i l i ty t op r e d i c t ( e x t r a p o l a te ) t h e v o l u m e t r ic r es p o n s e o ft h e s n o w u n d e r a n i n c r e a se i n p r e s s u re f o r a g i v e ni n i t i a l de ns i t y r a nge . T h e t yp i c a l s o i l r e s po ns e i sa l i n e a r r e l a t i o n s h i p b e t w e e n t h e n a t u r a l l o g a -r i t h m o f i n c re a s in g h y d r o s t a t i c p r e s su r e a n d d e -c r e a s i n g v o i d r a t i o ( s e e C h e n , 1 9 75 , f o r e x a m -p l e ) . F i g. 6 s h o w s t h e r e l a t i o n s h i p o f in i t ia lv o l u m e m i n u s t h e v o l u m e t r i c c h a n g e , V-AV,v e r s u s t h e n a t u r a l l o g a r i t h m o f t h e s p h e r i c a lp r e s s u r e , P , c o n t a i n i n g t h e c r i ti c a l s ta t e l i n e a n dt he v i r g i n c om p r e s s i on l i ne u s i ng a l l pos s i b l e da t aa c c u m u l a t e d d u r i n g t h e f i r s t s ea s o n o f A l t a t es t s( 7 7 s e r i e s ) . T h e b e s t f i ts f o r t h e v i r g i n c o m p r e s -s i o n l i n e a n d c r i t i c a l s t a t e l i n e m a y b e i n t e r -p r e t e d t o d i s p l a y li n e a r r e s p o n s e . I n c o n s i d e r i n gt h e V C L , t h e i m p l i c a t i o n i s th a t i f t h e s n o w i s a t

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n a tu r a l o g a h th m f the sphehcal pmseum, I n P k P a )F i g . 6 . I n i t i a l v o l u m e m i n u s t h e v o l u m e t r i c c h a n g e , V-ztV,v e r s u s t h e n a t u r a l l o g a r i t h m o f t h e s p h e r i c a l p r e ss u r e , P , f ir s ts e a s o n o f A l t a t e s t s ( 7 7 s e r i e s ) . C ~ is t h e e x t r a p o l a t e d v o l -u m e a t u n i t p r e s s u r e o n t h e c r i t i c a l s t a t e l i n e a n d V~ i s t h ee x t r a p o l a t ed v o l u m e a t u n i t p r e s su r e o n t h e v i r g i n c o m p r e s-s i o n l i n e . L i n e s a r e b e s t f i t .

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F i g . 7 . P r o j e c t i o n o f t h e c r it i c a l s t a t e l in e ( C S L ) a n d t h e v i r -g i n c o m p r e s s i o n l i n e ( V C L ) i n t h e P - V p l a n e u s i n g t h e d a t af r o m t h e f i r s t s e a s o n A l t a t e s t s ( 7 7 s e r i e s ) .


8/9

198 R.M. Lang, W..L. Harrison / Cold Regions Science and Technology 23 (1995) 191-199s o m e c u r r e n t p r e s s u r e o n t h e V C L a n d i t i s t h el a rg e s t v a l u e t h a t h a s b e e n a p p l i e d t o t h e s n o w ,t h e n u p o n t h e a p p l i c a t i o n o f a p r e s s u re i n c r e a s et h e s n o w w i l l l o a d a l o n g t h e V C L . I f t h e p r e s s u r ei s r e m o v e d , t h e s n o w w i ll u n l o a d a l o n g s o m eo t h e r p a t h u n d e r t h e V C L a t a r e d u c e d v a l u e f o rt h e v o l u m e , b u t u p o n r e a p p l i c a t i o n o f a p r e ss u r ew h i c h e x c e e d s t h e i n i t i a l v a l u e , t h e r e l o a d i n g r e -s p o n s e s h o u l d i n t e r s e c t t h e V C L a n d p r o c e e d t or e s p o n d l i n e a r l y a lo n g t h e V C L . I d e a l ly , th e V C Lw o u l d b e i n t e r s e c t e d u p o n r e l o a d in g a t t h e s a m ep o i n t o f u n l o a d i n g , b u t r e a l is t i c a ll y t h e i n t e r s e c -t i o n w i ll b e m a d e a t a n d e c r e a s e d v a l u e o f v o l-u m e a n d a c o r r e s p o n d i n g i n c r e a s e d v a l u e o f t h en a t u r a l l o g a r i t h m o f P .

I n o r d e r t o d e s c r i b e t h e g e n e r a l s t a t e o f s t r e s so f a s n o w s a m p l e i n t h e t r i a x i a l t e s t , i t i s a ll o w a -b l e t o p o s t u l a t e t h a t i n a t h r e e d i m e n s i o n a l s p a c eo f t h e s p h e r i c a l s t re s s P , t h e s e c o n d i n v a r i a n t o ft h e d e v i a t o r i c s t r e s s H ' ~ , a n d t h e v o i d r a t i o e v o rv o l u m e V , a u n i q u e s t a t e b o u n d a r y s u r f a c e c a nb e c o n s t r u c t e d f r o m t h e t r ia x i a l t e s t d a t a ( f o r ac o m p l e t e d i s c u s s io n s e e R o s c o e a n d B u r la n d ,1 9 6 8 o r C h e n , 1 9 7 5 ) . A d m i s s i b l e s t a t e p o i n t s l ieb e l o w th e s u r f a c e a n d r e p r e s e n t t h e i n i t ia l l i n e a rr e g i on o f m a t e r i a l r e s p o n s e . P o i n t s o n t h e s t a t eb o u n d a r y s u r fa c e r e p r e s e n t h a rd e n i n g a n d i n a d -m i s s i b l e p o i n t s l i e a b o v e t h e s u r f a c e . T h e c r i t i c a ls t a t e l i n e i s a l i n e o n t h i s s t a t e b o u n d a r y s u r f a c ew h e r e u n l i m i t e d d i s t o r t i o n a l s t r ai n m a y o c c u rw i t h o u t a n a c c o m p a n y i n g c h a n g e i n v o l u m e o rs t a t e o f s tr e s s . T h e c r i t i c a l s t a t e l i n e p r o j e c t i o ni n t o th e l n P v s . V - A V p l a n e f o r th e s n o w s a m -p l e s is d e p i c t e d i n F i g . 6 . T h e d e p i c t e d p a r a m e -t e r , C 1 , i s t h e e x t r a p o l a t e d v o l u m e a t u n i t p r e s -s u r e o n t h e c r i t i c a l s t a t e l i n e a n d t h e p a r a m e t e rV ~, i s t h e e x t r a p o l a t e d v o l u m e a t u n i t p r e s s u r eo n t h e v i rg i n c o m p r e s s i o n l in e .

F i g . 7 s h o w s th e p r o j e c t i o n o f t h e c r i t i c a l s t a t el i n e ( C S L ) a n d t h e v i r g i n c o m p r e s s i o n l i n e( V C L ) i n t h e P - V p l a n e u s in g t h e d a ta f r o m th ef i rs t s e a s o n A l t a t e s t s ( 7 7 s e r i e s ) .

3 . C o n c l u s i o n s

C o n s t a n t s t r a i n r a t e t r i a x ia l t e s t s w e r e p e r -f o r m e d o n d r y , n a t u r a l l y o c c u r r i n g s n o w . T h e

t e c h n i q u e f o r t e s ti n g s n o w w a s d i r e c tl y a d a p t e df r o m m e t h o d s t h a t a r e u s e d t o o b t a i n t h e m e -c h a n i c a l p r o p e r t i e s o f s o il s a n d o t h e r g r a n u l a rm e d i a s u b j e c t e d t o t h re e d i m e n s i o n a l s t re s ss t a t es .I n i t ia l d e n s i t i e s w e r e l o w t o i n t e r m e d i a t e ( 1 7 0k g / m 3 t o 3 7 6 k g / m 3 ) a n d s i g n if i ca n t v o l u m ec h a n g e s o c c u r r e d u n d e r t h e a p p l i e d l o a d s . T h es t r e s s - d e f o r m a t i o n c u r v e s e x h i b i t e d a n i n i t i a ll i n e a r p o r t i o n o f t h e c u r v e t o i n t e r n a l f a i lu r e , i .e .l o s s o f c o h e s i o n , a n d t h e p l a s t i c h a r d e n i n g p o r -t io n . A d e p e n d e n c e o n c o n f i n i n g p r e s s u r e is a p -p a r e n t . U l t i m a t e s t r e n g t h i n c r e a s e s f r o m a p -p r o x i m a t e l y 6 0 t o 1 3 0 k P a a t z e r o c o n f i n i n gp r e s s u r e t o v a l u e s i n e x c e s s o f 1 6 0 k P a a t h i g h e rp r e s s u r e s . I n g r a n u l a r i c e, t h e r o le o f c o n f i n i n gp r e s s u r e i s t o i n h i b it t h e g r o w t h o f c ra c k s a n dc o m m u n i c a t i o n b e t w e e n c ra c k s ( K a l i f a e t a l. ,1 9 9 2 ) . T h e m e c h a n i s m i n s n o w i s p r o b a b l y s i m -i la r , i. e ., t h e c o n f i n i n g p r e s s u r e m a y s e r v e t o r e -p r e s s t h e f a i lu r e o f t h e i n t e r g ra n u l a r b o n d s i ns n o w . I n p l o t t i n g t h e v i r g i n c o m p r e s s i o n l i n e s o ft h e s n o w w h i c h w a s t e s t e d , r e s u lt s e x h i b i t e d t h et y p i c a l s o i l r e s p o n s e o f a l i n e a r r e l a t i o n s h i p b e -t w e e n t h e n a t u r a l l o g a r i t h m o f in c r e a s in g h y d r o -s t a t i c p r e s s u r e a n d d e c r e a s i n g v o i d r a t i o o rv o l u m e .A l t h o u g h t h e s e d a t a d o n o t p r o v i d e a s t a t i s t i -c a l b a s i s f o r t h e m e c h a n i c a l p r o p e r t i e s o f s n o w ,t h e y d o s e r v e to p r o v i d e g u i d e l in e s f o r th e l o a dr e s p o n s e o f d r y sn o w . I n a d d i t io n , m e c h a n i c a lp r o p e r t i e s f o r u s e i n m o d e l l i n g c a n b e e a s i l y i n -f e r re d f o r c o m p a r a b l e l o a d i n g r a te s .

R e f e r e n c e sAndresen, A. and Simons, N.E., 1960. Norwegian TriaxialEquipment and Technique. Norwegian Geotechnical In-stitute, Publication #35.Andresen, A., Bjerrum, L., Dibiago, E. and Kjaernsli, B., 1957.

Norwegian Geotechnical Institute, Publication #21.Bennett, W.D., 1973. Documentation of Snow Characteris-tics for Over-snow Vehicle Validation Tests. CRREL TN.Brady, J.E. and Humiston, G.E., 1978. General ChemistryPrinciples and Structure. Wiley, Chichester, 2nd Ed.Chen, W.F., 1975. Limit Analysis and Soil Plasticity. Else-vier, Amsterdam.Drucker, D.C., 1967. Introduction to Mechanics of Deform-able Solids. McGraw-Hill, Englewood Cliffs.


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R.M. Lang, W.L. Harrison / Cold Regions Science and Technology 23 (1995) 191-199 19 9Ha r r i so n , W.L . , Be rg e r , R .H. a n d Ta k a g i , S . , 1 9 7 5 . On th eAp p l i c a t i o n o f Cr i t i c a l S t a t e So i l Me c h a n ic s t o Dry Sn o w .CRREL 1 R-4 7 3 .Ka l i f a , P . , Ou i l i o n , G . a n d Du v a l , P . , 1 9 92 . M ic ro c ra c k in ga n d th e f a i l u re o f p o ly c ry s t a l l in e ic e u n d e r t r i a x i a lc o m p re ss io n . J . Gla c io l . , 3 8 (1 2 8 ) : 6 5 -7 6 .Kin o s i t a , S. , 1 9 6 7. Co m p re ss io n o f sn o w a t c o n s t a n t sp e ed .I n : H . O u r a ( E d i t o r ) , P h y s i cs o f S no w a n d I ce : In t . C o n f .on L ow Te mp . Sc i . , 1966, Proc . , Vol . I, P t . 2 . Inst . o f LowTe m p . Sc i . Ho k k a id o Un iv . , Sa p p o ro , p p . 9 1 1 -9 2 7 .Na i to , M . , 1 9 7 3 . Me c h a n ic a l Ch a ra c t e r i s ti c s o f Sn o w I I .( R e p o r t # 5 ) T R D I , J a p a n D e f e n se A g e n cy , E x p e r i m e n -t a l Se c ti o n , Sa p p o ro E x p e r im e n ta l S t a t io n .Ra m se ie r , R .O. , 1 9 6 3 . So m e p h y s i c a l a n d m e c h a n ic a l p ro p -

e r t i es o f p o l a r sn o w. J . Gla c io l . , 4 (3 6 ) .Ro sc o e , K .H. a n d Bu r l a n d , J .B . , 1 9 68 . On th e G e n e ra l i z e dS t r e s s - S t r a in B e h a v i o r o f W e t C l a y . In : J . H e y m a n a n dF .A. Le c k ie (Ed i to r s ) , En g in e e r in g P l a s t ic i t y . Ca m b r id g eU n i v . P r e ss , L o n d o n , p p . 5 3 5 - 6 0 9 .Ro sc o e , K .H. , Sc h o f i e ld , A .N. a n d Th u ra i r a j a h , A . , 1 9 6 3. Ane v a lu a t i o n o f t e s t d a t a fo r se l e c t in g a y i e ld c r i t e r i o n fo rso i l. Sp ec . Te c h . Pu b l . AST M, 3 6 1 :1 1 1 -1 2 8 .Sh in o j im a , K. , 1 9 67 . S tu d y o n t h e Vi sc o l a s ti c De fo rm a t io no f S n ow . I n : H . O u r a ( E d i t o r ) , P h y s i cs o f S n o w a n d I c e:In t . Conf . on Low Temp. Sc i . , 1966, Proc . , Vol . I , P t . 2 .In s t . o f Lo w Te m p . Sc i . Ho k k a id o Un iv . , Sa p p o ro , p p .8 7 5 - 9 0 7 .

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