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Highway Research Record, 393, pp. 56-64, 1972-10-01
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Influence of freezing rate on frost heaving
Penner, E.
https://publications-cnrc.canada.ca/fra/droits
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https://nrc-publications.canada.ca/eng/view/object/?id=22aeb3d5-8d38-4aa8-9b6f-aab553b198e4 https://publications-cnrc.canada.ca/fra/voir/objet/?id=22aeb3d5-8d38-4aa8-9b6f-aab553b198e4NATIONAL RESEARCH COUNCIL O F CANADA CONSEIL NATIONAL DE RECHERCHES DU CANADA
Influence of Freezing Rate o n Frost Heaving
N A T ~ O ~ A L RESEARCH COUNCiL
Reprinted f r o m
Highway R e s e a r c h Record No. 393 1972, p. 56
-
64 R e s e a r c h P a p e r No. 538 of the Division of Building R e s e a r c h OTTAWA October 1972 P r i c e 25 c e n t s NRCC 12868L'INFLUENCE DU TAUX DE G E L SUR LES
SOULEVEMENTS DUS AU G E L
SO MMAIRE
L ' a u t e u r e x a m i n e l e s p r i n c i p a u x f a c t e u r s t h e r m i q u e s q u i influencent l e
m h c a n i s m e de s o u l k v e m e n t d e s s o l s dG a u gel. L e m h c a n i s m e d u gel
s e m b l e i n f l u e n c e r c o n s i d h r a b l e m e n t l e s e x p 6 r i e n c e s de l a b o r a t o i r e
v i s a n t
5
p r 6 d i r e l e d e g r 6 de s u s c e p t i b i l i t h d e s s o l s a u gel. L a c o m p a r a i s o ~
de l a s u s c e p t i b i l i t 6 a u gel de d i f f 6 r e n t s s o l s s e m b l e t r o m p e u s e l o r s q u ' e l l e
s e fonde s u r d e s e x p h r i e n c e s m e n h e s a u mEme taux de p k n h t r a t i o n de l a
ligne de gel. L ' u t i l i s a t i o n d u mGme taux d ' e n l k v e m e n t de l a c h a l e u r
s e m b l e p e r m e t t r e d e s c o m p a r a i s o n s p l u s s i g n i f i c a t i v e s de l a s u s c e p t i -
bilit6 a u gel. E n g6n6ra1, l ' a u g m e n t a t i o n d u taux d ' e n l k v e m e n t d e l a
c h a i e u r f a i t m o n t e r
5
s o n niveau m a x i m u m l e taux de soul'evement, s u i v i
d'une r 6 d u c t i o n qui c r o i s e l a ligne d ' e x p a n s i o n in s i t u d u changement d e
p h a s e d e l ' e a u d e s p o r e s .
L ' a u t e u r p r 6 s e n t e l e concept d'Arakawa a u s u j e t d e l ' e f f i c a c i t h d e l a
s 6 g r 6 g a t i o n d e l a g l a c e e t e n 6tudie l ' u t i l i t h dans l a d 6 t e r m i n a t i o n du
d e g r 6 d e s u s c e p t i b i l i t h a u gel.
L e r a p p o r t d ' e f f i c a c i t 6 E de l a s h g r b g a t i o n
d e l a glace indique l a f r a c t i o n d e c h a l e u r q u i e s t enlev6e du f r o n t de
p r o p a g a t i o n d u g e l d a n s l e s o l e t q u ' o n peut a t t r i b u e r d i r e c t e m e n t
5
l a
f o r m a t i o n de l e n t i l l e s d e glace. L o r s q u e E
=1 , l a c h a l e u r t o t a l e p r o d u i t e
p r o v i e n t du changement d e p h a s e l o r s de l a f o r m a t i o n d e s l e n t i l l e s de
g l a c e . L o r s q u e
0<
E
<
1 , une p a r t i e s e u l e m e n t d e l a c h a l e u r p r o d u i t e
p r o v i e n t d e l a f o r m a t i o n d e s l e n t i l l e s de glace. Enfin, l o r s q u e E
=
0,il
n'y a p a s d e l e n t i l l e s d e g l a c e . Enfin, on s u g g 5 r e quelques
amelioration^e n c e q u i c o n c e r n e l e s e x p h r i e n c e s s u r l a s u s c e p t i b i l i t h a u gel effectuhes
e n l a b o r a t o i r e .
Influence of Freezing
Rate
on
Frost Heaving
INFLUENCE OF FREEZING RATE O N FROST HEAVING
Edward Penner, National Research Council of CanadaThe major t h e r m a l influences on the frost-heaving p r o c e s s in s o i l s a r e reviewed. Laboratol'y experiments that a r e designed to predict the f r o s t susceptibility of soil in the field a r e shown to be strongly influenced by the freezing procedure. I t is believed to be misleading to compare the f r o s t susceptibility of different s o i l s based on freezing t e s t s that a r e c a r r i e d out at the s a m e r a t e of f r o s t line penetration. Applying the s a m e r a t e of heat removal is thought to give more meaningful comparisons of frost susceptibility. Ingeneral, increasing the r a t e of heat removal c a u s e s the heaving r a t e t o r i s e to a maximum followed by a reduction that intercepts the in-place p o r e w a t e r phase change expansion line. Arakawa's concept of ice segregationefficiency is introduced, and i t s usefulness f o r a s s e s s i n g f r o s t susceptibility i s discussed. The ice segregation efficiency ratio, E, gives the fraction of the heat removed f r o m the freezing front in the s o i l that i s directly attributable to ice l e n s formation. When E = 1, the total heat evolved is f r o m the phase change involved in i c e l e n s formation; when when 0 < E < 1, only a p a r t of the heat evolved is derived f r o m ice l e n s formation; and when E = 0, no icelensing occurs. Finally, suggestions a r e made f o r the improvement of frost-susceptibility t e s t s in the laboratory. .A SATISFACTORY laboratory t e s t method h a s not yet been devised that s e r v e s a s a reliable b a s i s f o r the a s s e s s m e n t of f r o s t susceptibility of s o i l s for a l l conditions. T h e variability of the natural environment complicates simulation of the conditions. The procedure up t o the present has been t o c r e a t e favorable conditions f o r f r o s t heaving in the laboratory, where it h a s not been possible t o simulate the d e s i r e d conditions effectively. However, by using t h i s method, s o i l s can be distinguished that a r e border- line with respect to f r o s t susceptibility and that may cause unexpected f r o s t action problems in the field.
The nature of the porous media, water supply, and t h e r m a l conditions a r e the t h r e e principal f r o s t action f a c t o r s and, of these, the f i r s t factor i s probably t h e e a s i e s t to simulate. Representative s a m p l e s may be taken f r o m the s i t e in question, pretreated, and compacted to simulate t h e field condition. T h i s can be done easily when the freez- ing zone-is confined within e a r t h s t r u c t u r e s such a s f i l l s and embankments but may be more difficult f o r undisturbed s o i l s .
Because the amount and r a t e of lensing i s dependent on w a t e r supply, the most favor- able condition f o r heaving i s normally simulated. Laboratory specimens a r e usually presaturated before freezing, and in the c a s e of open s y s t e m s additional moisture i s made available at the base of the soil sample. The ice lensing s y s t e m in the field may operate a s an open s y s t e m f r o m a high water table o r a s a closed system if the water table is a t g r e a t depth. These a r e the extremes, which can be created easily in the laboratory, but the ordinary c a s e s a r e m o r e difficult to simulate.
This paper i s particularly concerned with the third f r o s t action factor-thermal con- ditions. The importance of the r a t e at which the s o i l specimen is frozen and i t s effect on mobilizing moisture flow i s an essential factor that influences frost-susceptibility a s s e s s m e n t s f o r field conditions. T h i s i s supported by many experiments c a r r i e d out recently in various laboratories. Finally, a method f o r quantifying the influence of heave rate with respect to the t h e r m a l condition imposed is discussed. This method is based on an efficiency ratio concept recently introduced by Arakawa (1).
-
The dependency of heave r a t e on the freezing r a t e has not always been recognized. Beskow (2) found that, f o r a constant p r e s s u r e (load on the soil), "the r a t e of heaving i s independent of the r a t e of freezing." He f u r t h e r stated that "it should be noted, however, that this i s completely valid only f o r relatively permeable soil." Beskow recognized that, f o r s o i l s where the f r o s t line was stationary, various heave r a t e s w e r e possible and dependent on heat flow (a relatively unique condition), thus t h i s dependence did not hold f o r a penetrating f r o s t line (more common in the field). Similarly, the U. S. Army C o r p s of Engineers (9) stated that " r a t e of heave h a s been found to be relatively in- dependent of r a t e of f i e e z i n g over a range of freezing r a t e s employed in the investiga- tion." This was the b a s i s f o r t h e i r frost-susceptibility classification that i s valid f o r freezing r a t e s between
'/4
and5/4
in. of f r o s t penetration p e r day.Higashi (4) studied the r a t e of heaving in the laboratory and found an inverse relation with f r o s t - l 6 e penetration, a r e s u l t quite contradictory to previous findings. Although this i s difficult t o understand, the author believes that the highly restrictive w a t e r supply influenced the r e s u l t s attributed to t h e r m a l conditions by Higashi. In m o r e recent laboratory expeiments by Penner (7) and Kaplar (5, 6), the heaving r a t e w a s found to be directly dependent on heat flow, i.e., i n c r e a s i n g n e t heat flow and f r o s t - penetration r a t e increased the heave r a t e .
Haas (3) concluded f r o m r e s u l t s of field studies that, when the f r o s t line was not penetrating, the heave r a t e was essentially proportional t o the heat conduction difference between the frozen zone and the unfrozen zone. This observation i s s i m i l a r to Beskow's findings. Field data w e r e a l s o presented f o r the c a s e when the f r o s t line w a s actively penetrating, and the heave r a t e was found t o be inversely proportional t o the f r o s t pene- tration r a t e . In a published discussion to t h e paper by Haas, Penner (8) w a s able t o
show that no s t a t i s t i c a l significance existed between t h e two variables,-frost-penetration r a t e and heave rate, because of s c a t t e r in the data.
HEAT FLOW AND FROST PENETRATION STUDIES
The method used by Penner (7) to study the influence of the r a t e of heat flow on the heave r a t e w a s to m e a s u r e h e a t i n and heat out with calibrated heat t r a n s d u c e r s placed a t opposite ends of a 3-in. long and 6-in. diameter specimen. At the s a m e time, heave r a t e and moisture-influx r a t e w e r e a l s o measured under conditions of unidirectional heat flow. The relevant aspects of this investigation a r e summarized a s follows.
T h r e e s o i l s w e r e studied: a clay (Leda clay) with 64 percent clay-size p a r t i c l e s and 36 percent s i l t - s i z e particles; a s i l t (PFRA s i l t ) with 9 percent clay-size particles, 43 percent silt-size, and 48 percent sand-size; and a sandy s o i l (Lindsay sand) with 7 percent clay-size particles, 13 percent silt-size, and 80 percent sand-size, based on the MIT grain-size classification. The d r y densities w e r e 91, 110, and 137 lb/ft3 respec- tively; a l l the samples w e r e presaturated before freezing. The saturated m o i s t u r e contents averaged 33.2 percent, 19.2 percent, and 8.2 percent respectively.
The prefreezing procedure w a s t o impose a t h e r m a l gradient of about 0.35 C/in. a c r o s s the water-saturated specimen with the cold end n e a r 0 C. When t h e r m a l equilibrium was established, the t e m p e r a t u r e of the cold end w a s reduced t o just below 0 C and crystallization of the w a t e r was artificially induced. The heat flow was then controlled to give a constant r a t e by manual adjustment of the t e m p e r a t u r e on the cold side. When a constant heave r a t e was established, the t h e r m a l gradient was increased to give a different r a t e of heat extraction by lowering the cold-side temperature.
Figure 1 (from a previous paper by t h e author, 7) shows the r e s u l t s of t h r e e r a t e s of heat removal f r o m one of the soils, Lindsay s a d . The figure shows the net heat removal (difference between heat in and heat out) and the moisture influx values ex- p r e s s e d in t e r m s of the heat released upon freezing. All t h r e e s o i l s showed a positive i n c r e a s e in heaving r a t e when the heat flow w a s increased.
The r e s u l t s shown in Figure 2 (from a previous paper by the author, 7) w e r e obtained somewhat differently but lead t o the s a m e conclusions, In t h i s s e r i e s ofexperiments, a new sample was prepared f o r each heat flow r a t e ; at t h e s a m e time, the moisture flow r a t e s into the sample w e r e also measured. As before, moisture flow w a s plotted in t e r m s of latent heat of fusion by using standard values of 80 cal/g of w a t e r o r 144
Figure 1. Cumulative values of net heat flow and moisture flow versus time.
LINDSII SAND 16.WO
14.000 TERMS OF LATENT 12.000 HEAT OF CRVSTILL12ATION l0,OOO q = n . 0 0 0
2
6 , 0 0 0 4 , 0 0 0 2 . 0 0 0 0 4 8 12 16 2 0 2 4 28 32 36 4 0 TIME, nrFigure 2. Cumulative value of net heat flow and moisture flow versus time.
5 0 I I I I I I I I I
LINDSAY SAND 12,000
TIME, hr LEGEND:
-
UEAT OUT MINUS UEAT IN -MOISTURE MOVED INTO S-E IN TERMSBtu/lb of w a t e r . It w a s possible t o establish and maintain a constant heat extraction r a t e a f t e r a s h o r t period, a s may be s e e n f r o m F i g u r e 2. The apparatus w a s dismantled, and the thickness of the frozen l a y e r w a s m e a s u r e d to calculate the average f r o s t - penetration r a t e .
The influence of r a t e of f r o s t - l i n e penetration on heave r a t e h a s been s u m m a r i z e d f o r these s t u d i e s in Figure 3 . The upper c u r v e s show the total heave due t o (a) the ex- pansion of the in situ w a t e r a s the f r o s t line penetrated and (b) the additional w a t e r moved into the freezing zone. The lower c u r v e s give the heave r a t e s that c a n be a s - signed t o the in-place expansion of in s i t u w a t e r when it f r e e z e s .
K a p l a r ' s (5) r e c e n t studies support t h e positive influence of frost-penetration r a t e on frost-heave r a t e ( ~ i g . 4; f r o m Kaplar, 6) in laboratory-conducted experiments. Ex- p e r i m e n t s w e r e a l s o c a r r i e d out by ~ a p l a r (6) w h e r e the frost-heaving r a t e was mea- s u r e d f o r different but constant freezing t e m p e r a t u r e s in the freezing cabinet above the s a m p l e s . Summary r e s u l t s a r e shown in Figure 5 (from Kaplar, 5) f o r f o u r dif- f e r e n t s o i l s , f r o m which Kaplar concludes "that t h e heave r a t e i s dependent on o r con- trolled by the r a t e of heat extraction (up t o s o m e unknown c r i t i c a l r a t e dependent upon the availability of w a t e r and the capability of the s o i l t o conduct the water)."
The frost-line penetration r a t e i s , therefore, a n important consideration when decid- ing on the freezing procedure t o be used f o r determining t h e f r o s t susceptibility of s o i l s in the laboratory. F i g u r e s 3, 4, and 5 show, however, that the dependence of the heave r a t e on heat extraction r a t e ( o r frost-line penetration r a t e ) is different f o r each soil. T h i s dependence cannot a s yet be predicted and must apparently be determined experi- mentally. Yet t h e c r i t e r i o n c u r r e n t l y used exclusively t o evaluate quantitatively f r o s t susceptibility i s the r a t e of heaving. It i s unfortunate that t h i s important c r i t e r i o n i s s o sensitive t o the r a t e at which f r e e z i n g i s c a r r i e d out. Some effort h a s been made t o understand t h e d e g r e e of f r o s t susceptibility in t e r m s of other f a c t o r s s u c h a s heav- ing p r e s s u r e s , but f u r t h e r work i s n e c e s s a r y before t h e s e can be applied with con- fidence t o field problems.
ICE SEGREGATION EFFICIENCY RATIO
The author, in previous s t u d i e s (7), m e a s u r e d the induced w a t e r flow into the s a m p l e during ice lensing a s well a s the n e c h e a t flow (heat out minus heat in). Arakawa (1) t e r m e d t h e r a t i o of t h e s e quantities the ice segregation efficiency ratio, which i s dzfined by the following equation:
w h e r e U L gives the heat evolved a t the f r e e z i n g front based on the moisture flow r a t e (ice l e n s growth r a t e ) and t h e denominator i s the net heat flow out of the sample, that is, heat out minus heat in. The symbols in t h e equation a r e defined a s follows:
5 = ice segregation r a t e , m a s s of i c e p e r unit a r e a p e r unit t i m e a t the f r o s t line;
L = latent heat of fusion;
K1 = t h e r m a l conductivity, frozen l a y e r ;
Kz = t h e r m a l conductivity, unfrozen l a y e r ;
a
T , / ~ x = t h e r m a l gradient in frozen l a y e r ; anda
T ~ / ? x = t h e r m a l gradient in unfrozen layer.The ice segregation efficiency r a t i o s have been calculated f r o m the r e s u l t s shown in Figure 2. In t h e f i r s t instance, t h e efficiency r a t i o h a s been plotted a s a function of net heat flow (Fig. 6). In Figure 7, t h e r a t i o h a s been plotted a s a function of r a t e of f r o s t penetration f o r the s a m e e x p e r i m e n t s with the aid of F i g u r e 3. F i g u r e s 6 and 7 both show the s a m e tendency f o r the i c e segregation efficiency r a t i o t o d e c r e a s e a s t h e r a t e of heat removal o r f r o s t penetration r a t e i n c r e a s e s . Within t h e range of r a t e s of heat extraction of 0 t o 20 ~ t u / h r ft2 o r f r o s t penetration r a t e s of 0 t o 3 in./day, t h e r a t e of m o i s t u r e flow into the s a m p l e (hence t h e heaving r a t e ) i n c r e a s e d when the r a t e of heat
60
Figure 3. Heave rate versus frost-penetration rate.
,*
' / I
:
-V O l D W A T E R
0 I 2 3 4 5
A V E R A G E F R O S T P E N E T R A T I O N R A T E , I N C H E S / D A Y
Figure 4. Heave rate versus rate of frost penetration.
G R A V E L L Y S A N D . 5 % C O 0 2 , 1 " M A X L O A D 0 5 P S I k
1
/"---..
'\ W A R M ' \ . H R I V lE/
V O l D WATER HEAVE PATE I (SATUPATED) I I I I I I I I 0 4 8 1 2 1 6 F R O S T P E N E T R A T I O N , I N / D A YFigure 5. Summary of multi-ring freezing tens. Figure 6. The ice segregation efficiency ratio as a function of net heat flow (heat out minus heat in).
I I I I I I I 1 I L I N D S A Y S A N D P F R A S I L T L E D A C L A Y -
-
- - 0-
I I 1 I I I 1 I I A I R I E M P E R A T U R E A B O V E S P E C I M E N . "F 0 0 0 0 2 0 4 0 6 0 8 1 0 E F F I C I E N C Y R A T I O MANCHESTER FINE SANDI I a I I
Figure 7. The ice segregation efficiency ratio as a
function of frost-penetration rate.
3 2 28 2 4 2 0 1 6 1 2 8
Figure 8. The influence of net heat flow on frost penetration.
F R O S T P E N E T R A T I O N R A T E , I N C H E S / D A Y
r e m o v a l w a s i n c r e a s e d (Fig. 2). Doubling the r a t e of heat removal, however, does not double the heave r a t e . T h i s d e c r e a s e in ice lensing efficiency is depicted in the ice segregation efficiency r a t i o and is an indication that the moisture permeability, even in s a t u r a t e d samples, is too low to hold t h e efficiency ratio constant f o r s o m e soils a s the freezing r a t e i s increased. In Lindsay sand i t appeared t o r e m a i n relatively con- stant u p t o 1 in./day of f r o s t penetration (in t h i s c a s e equivalent t o about 9 Btu/hr ft2) and then d e c r e a s e d . Sufficient data a r e not available f o r the o t h e r s o i l s t o determine whether t h i s t r e n d applies m o r e generally.
T h e r e i s a s p e c i a l c a s e of f r o s t heaving with a stationary f r o s t line and, a s pointed out by Haas (3) and others, it may o c c u r o v e r a r a n g e of values of net heat flow. If w e ignore the s m a l l amount of heat extraction due t o cooling of the w a t e r a s it moves in the t h e r m a l field,
a
T ~ / ~ X , the efficiency r a t i o E equals 1, that is,despite the fact that the heaving r a t e may v a r y depending on the net heat flow. Arakawa c a l l s i t perfect segregation when E = 1 and imperfect segregation when 0 < E < 1. F o r a s o i l that does not heave, E equals 0 because o i s z e r o when no i c e segregation o c c u r s .
T h e r e i s one component of the total heave that is not taken into account in the ice segregation efficiency. In a frost-susceptible soil, the expansion of the existing pore o r void w a t e r adds t o the total heave if the f r o s t line i s penetrating. T h e amount of heave in t h i s c a s e r e s u l t s simply f r o m the phase change of p o r e w a t e r t o ice, which gives about a 9 percent volume i n c r e a s e . Kaplar and P e n n e r have both shown the amount t h i s contributed to the total heave ( F i g s . 4 and 3). T h e calculation of heave r e s p o n s e t o the expansion of the void w a t e r when it f r e e z e s has been based on a l l the w a t e r f r e e z i n g a t 0 C. T h i s i s known to introduce an e r r o r in t h e total heave, but o t h e r e x p e r i m e n t s would have t o be undertaken t o evaluate t h i s c o r r e c t l y f o r a l l t h r e e s o i l s . Although t h e latent heat of fusion i s the s a m e f o r both the void w a t e r and "outside" w a t e r moved to the freezing zone, the amount of heave resulting i s vastly different. T h e amount of heave resulting simply f r o m phase change expansion of the void w a t e r may be, in s o m e soils, a considerable portion of the total heave. F o r Lindsay sand at a f r o s t penetration r a t e of 3 in./day, i t amounts t o about 9 . 5 percent a s shown in F i g u r e 3 . At p r e s e n t t h e r e d o e s not s e e m t o be a s a t i s f a c t o r y way of incorporating t h i s contribution into the ice segregation efficiency ratio. Nonetheless, i t should not be overlooked in the t o t a l a s s e s s m e n t of f r o s t susceptibility.
T h e heave r a t e tends t o i n c r e a s e t o a maximum a s the r a t e of f r e e z i n g i s i n c r e a s e d and then f a l l s off and i n t e r s e c t s the h e a v e - r a t e curve, which r e s u l t s solely f r o m the void w a t e r phase change. T h i s t r e n d i s shown in F i g u r e 4. Under v e r y high r a t e s of f r o s t penetration, mobilization of w a t e r apparently is not possible. It i s also unlikely that under field conditions t h e f r o s t penetration r a t e would be high enough t o produce the maximum heave r a t e attainable in the laboratory. T h e a v e r a g e f r o s t penetration r a t e i s m o r e likely to be l e s s than 1 in./day in a r e a s of s e a s o n a l f r o s t in Canada.
Finally, i t is misleading t o c o m p a r e the f r o s t susceptibility of v a r i o u s s o i l s based on f r e e z i n g t e s t s c a r r i e d out at t h e s a m e r a t e of frost-line penetration. Different s o i l s exposed to the s a m e f r e e z i n g conditions will f r e e z e at different r a t e s . T h i s i s shown f o r t h r e e s o i l s (Fig. 8) f o r which heat flow data and frost-penetration r a t e s w e r e avail- able. A s a n example, f o r a heat extraction r a t e of 10 Btu/hr ft2, the a v e r a g e f r o s t penetration in the laboratory w a s 0.5 in./day f o r Leda clay, 1 in./day f o r Lindsay sand, and 1.20 in./day f o r PFRA s i l t . T h e s a m p l e s w e r e fully s a t u r a t e d and had a m o s i t u r e content of 33.2 percent, 8.2 percent, and 19.2 p e r c e n t respectively. Under s i m i l a r t h e r m a l conditions, the main f a c t o r s that d e t e r m i n e the f r o s t penetration r a t e in f r o s t - susceptible s o i l s a r e the in situ m o i s t u r e content and t h e i c e segregation r a t e . O t h e r l e s s e r influences placed on the foregoing s a m p l e s a r e such f a c t o r s a s density and t h e t h e r m a l conductivity and specific heat of the s o i l solids.
DISCUSSION AND SUMMARY
T h e major influences on f r o s t heaving that have been s t r e s s e d in t h i s paper can b e attributed directly t o t h e t h e r m a l aspect of freezing t e s t s conducted in t h e laboratory f o r frost-susceptibility evaluation. It h a s been shown that, f o r s a t u r a t e d s o i l s studied i n an open system, the following apply:
1. The heat-removal r a t e influences the heaving r a t e (Figs. 1 and 2).
2. With increasing heat-removal r a t e s , t h e heaving r a t e i n c r e a s e s (Figs. 3, 4, and 5) and a p p e a r s to rise to a maximum; it then d e c r e a s e s and i n t e r s e c t s t h e heave rate based on t h e phase change expansion of t h e p o r e w a t e r (Fig. 4).
3. The r a t e of f r o s t penetration is not t h e s a m e f o r different s o i l s a t t h e s a m e rate
of heat extraction (Fig. 8).
4. The concept of t h e i c e segregation efficiency ratio, E, is a useful indicator of t h e f r o s t susceptibility of a soil; a s the r a t e of f r o s t penetration and heat removal is in- creased, the r a t i o is reduced (Figs. 6 and 7).
5. The heave-rate response t o increasing heat-removal r a t e s is not t h e s a m e f o r all
frost-susceptible s o i l s (Figs. 3, 4 and 5).
6. A considerable portion of the measured heave may be due t o the in situ freezing of t h e p o r e w a t e r (Figs. 3 and 4), but t h e p r e s e n t concept of t h e ice segregation effi- ciency r a t i o does not take t h i s into account.
CONCLUSIONS AND SUGGESTIONS
The work reviewed in t h i s p a p e r suggests that t h e t h e r m a l conditions imposed on laboratory s a m p l e s during laboratory frost-susceptibility experiments a r e an important element of the testing procedure. T h e s e s t u d i e s indicate that t h e r a t e of freezing used should be related to t h e t h e r m a l conditions in t h e field f o r which t h e t e s t s a r e being performed. Because t h e r m a l conditions will v a r y f r o m y e a r t o y e a r in t h e field, it
would be helpful to c a r r y out t h e freezing t e s t s at two r a t e s , one a t less than t h e mini- mum r a t e of freezing and t h e o t h e r at somewhat f a s t e r than t h e maximum r a t e of f r e e z - ing expected. One t e s t conducted with an a r b i t r a r y r a t e of f r e e z i n g is not sufficient t o evaluate t h e response to a different freezing r a t e because t h i s v a r i e s with s o i l type.
The u s e of heat m e t e r s at both e n d s of t h e s o i l sample (along with m e a s u r e m e n t s of m o i s t u r e influx, in s i t u moisture content, and depth of freezing) allows the calculation of a t h e r m a l balance. The i c e segregation efficiency r a t i o can be calculated f r o m t h e s e r e s u l t s . Such a t e s t procedure, although desirable, may be too costly, and t h e infor- mation obtained f r o m exposing t h e s o i l s a m p l e s t o different s u r f a c e t e m p e r a t u r e s t o impose different rates of freezing may be sufficient. If r a t e s of f r o s t penetration a r e both slower and f a s t e r than t h e expected field values, the r e s u l t s should p e r m i t a good evaluation of f r o s t susceptibility of t h e m a t e r i a l under t e s t .
T h e r e does not s e e m to be a need t o c a r r y the f r e e z i n g experiments beyond a 24-hr (or even s h o r t e r ) period. It can be s e e n f r o m the data in Figure 2 that relatively con- s t a n t flow and heaving conditions a r e established in a few hours. More useful informa- tion c a n be obtained by spending e x t r a t i m e and effort on conducting heaving experi- ments at various r a t e s r a t h e r than relying on prolonged m e a s u r e m e n t s a t one r a t e .
Finally, the heaving response to different t h e r m a l conditions h a s been evaluated f o r only a few s o i l s under relatively simple conditions of in s i t u moisture, m o i s t u r e supply, and s a m p l e density. T h i s work does indicate, however, that improvements c a n be effected in frost-susceptibility testing p r o c e d u r e s used in the laboratory.
ACKNOWLEDGMENTS
The author e x p r e s s e s his appreciation t o t h e American Society f o r Testing and Materials f o r p e r m i s s i o n to use F i g u r e s 1 and 2 and t o t h e Highway R e s e a r c h Board f o r Figures 4 and 5. T h i s p a p e r is a contribution f r o m t h e Division of Building Re- s e a r c h , National R e s e a r c h Council of Canada, and is published with t h e approval of t h e D i r e c t o r of the Division.
REFERENCES
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