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Highway Research Board Bulletin, 225, pp. 1-22, 1959-12-01

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The mechanism of frost heaving in soils

Penner, E.

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Ser

TH1

N21r2

no.

87

c. 2

NATIONAL RESEARCH COUNCIL

CANADA

DIVISION O F BUILDING RESEARCH

The Mechanism of Frost Heaving in Soils

BY

E . PENNER

REPRINTED FROM BULLETIN NO. 225

HIGHWAY RESEARCH BOARD, 1959

P.

1-22

RESEARCH P A P E R No.

87

of the

DIVISION O F BUILDING RESEARCH

PRICE 50 CENTS

OTTAWA

DECEMBER 1 9 59

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The Mechanism of Frost Heaving in Soils

E. PENNER, Division of Building Research, National Research Council, Ottawa, Ontario

The "mechanism of f r o s t heaving" involves the interaction of the three f r o s t action factors: a water supply, a f rost-susceptible soil, and below-freezing temperatures.

The propagation of ice between soil particles depends on pore size, that i s , the s m a l l e r the pores and channels between pores, the lower the temperature necessary before the ice front can ad- vance. This provides a means f o r supercooling the pore water be- neath an actively growing ice lens. The subsequent release of en- ergy in such systems i s utilized to c r e a t e a moisture suction gra- dient which induces a moisture flow to the ice front and also to de- velop a positive p r e s s u r e to raise the overburden and provide a space f o r the ice lens. Consistent with the theory, i t can be shown that compact clay soils, which have the greatest resistance to ice propagation, can develop the largest moisture suction and heaving p r e s s u r e in a closed system and coarse-grained soils, the lowest.

In the over-all phenomenon of f r o s t heaving the most difficult combination of related processes to treat, even on a semi-quanti- tative basis, i s the heat and moisture flow. This difficulty a r i s e s not only f r o m the complexity of the mathematics but a l s o from the lack of experimental measurements of heave rates, heat flow, moisture flow, temperature distributions, and moisture tensions while ice lensing i s in progress. In the absence of such informa- tion the quantitative treatment of the combined heat and moisture flow appears impossible.

F R O S T ACTION in soils consists of two different phenomena. It involves f r o s t heaving resulting mainly from the accumulation of moisture in the form of ice lenses a t the freezing plane in the soil and also the decrease of supporting strength when thawing takes place.

F r o s t action i s contingent on the existence of a combination of f r o s t action factors. These factors a r e a frost-susceptible soil, a moisture supply, and sufficiently low soil temperatures to cause some of the soil water to freeze. The process which re- sults from the interaction of these factors during the freezing period i s commonly re- f e r r e d to a s the "mechanism" of f r o s t heaving. The other phenomenon involved in f r o s t action, the decrease of supporting strength of the soil during the thawing period, i s particularly important in the performance of highways and airports. This problem, however, has not received much attention by r e s e a r c h workers.

This paper i s devoted to the interaction of the f r o s t action factors in frost heaving and not to the details of any one factor.

Although some basic research has been c a r r i e d out in the field of frost heaving the mechanism i s still not completely understood. This has been and still is a real ob- stacle to the complete solution of problems of f r o s t damage to engineering s t r u c t u r e s constructed of soil o r other porous material. In recent y e a r s a number of research workers have made important contributions on certain aspects of the frost heaving process, but the early published work on the mechanism of f r o s t action by T a b e r and Beskow still stands a s the most complete coverage of the subject.

Since the f r o s t heaving process i s extremely complicated and much experimental work i s still needed, the theory outlined i s tentative and may be changed o r modified a s more information becomes available. Nevertheless, it i s based on the work pub- lished by others and the results of research c a r r i e d out in recent years by the author and his colleagues.

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The material in this paper i s divided into two sections. The f i r s t section deals with the phenomena of soil freezing based on experimental evidence obtained mostly in the laboratory. The second section i s mainly concerned with the theory of f r o s t heaving in an attempt to explain the ob- served phenomena.

PHENOMENA OBSERVED DURING FREE ZING

In Soils That Support Ice Lens Growth Ice Lensing and F r o s t Heave. The cause of f r o s t heaving can be attributed mainly to the formation of ice lenses in the soil. This was f i r s t shown in 1916 by Taber

( I )

at a time when the popular belief was that f r o s t heaving resulted solely from the volume change of water in changing from a liquid to a solid.

Ice lenses normally grow parallel to the ground surface and perpendicular to the direction of heat flow. The f o r m e r i s not always true since there a r e a number of different ice f o r m s known; the latter, however, i s always true. The thickness of the ice mav va-& from s m a l l hairline lenses to those se;eral inches thick (Fig. 1) depending on a number of factors to be discussed later.

The heave in a saturated non-compres- sible soil in a closed system originates from the expansion of the water frozen in situ plus the volume of water moved to the freezing zone and i t s expansion. It i s noted that the volume change of water on freezing i s in the direction of the heat flow. In a closed system containing a compressible soil which i s saturated be- fore freezing the volume increase due to ice segregation i s offset, except f o r the 9 percent expansion, by the consolidation of the soil. This i s true in the region where the shrinkage curve i s linear. If, on the other hand, additional water i s supplied to the specimen f r o m an outside

source (open system) the shrinkage may Figure

1.

Small ice lenses Fn

be more than offset. s i l t y s o i l (above). I c e l e n s , approxi-

The soil between successive ice lenses mately 5 ~ n . thick, in s i l t y s o i l .

i s often relatively dry. Whether some of the soil water in these l a y e r s i s frozen

depends on the moisture status of the l a y e r s and the temperature. The l a t t e r i s pri- marily determined by i t s position in the f r o z e n soil profile.

Induced Suction and Moisture Flow. The flow of moisture to the freezing zone in relatively moist soils appears to s t a r t immediately after crystallization of the water begins. The effect i s s o pronounced that i t can be observed some distance away from

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T I M E H O U R S

Figure 2. S o i l moisture s u c t i o n increase due t o i c e lensing a s a function of time in a

closed system containing P o t t e r s f l i n t . Cold s i d e temperature -3 C, warm s i d e tempera- t u r e 1.5 C.

the freezing zone. This indicates that a suction gradient i s set up in the soil water. The phenomenon can be demonstrated by connecting a mercury manometer through a water connection to the soil water in the specimen. Measurements such a s this have been made by several observers

(2,

3).

The actual rate at which suction increases in a closed system i s a function of a num- ber of variables such a s the suction-moisture content relationship, moisture permea- bility, and rate of heat extraction. The results shown in Figure 2 give the time-suc- tion relationships during ice lens growth in a sample of Potters flint. This material i s composed of about 6 percent clay-size particles with the remainder in the silt-size range. The temperature on the cold side of the specimen was held at -3 C with the warm side at +11/2 C. Crystallization was mechanically induced at the cold end of the specimen at approximately -2 C.

The suction developed at the ice lens induces a suction gradient in the soil moisture. This i s the main driving force f o r water movement to the ice lens. Since the driving force i s a suction gradient, a s opposed to a positive pressure gradient, the principles of unsaturated permeability apply. This type of flow should not be confused with sat- urated permeability. The significant difference lies in the fact that the unsaturated permeability coefficient is not a constant but i s rather a function of the average suction, decreasing a s the average suction increases. This principle i s illustrated in Figure 3 showing the unsaturated permeability coefficient and the moisture content a s functions of the average moisture suction.

Heaving P r e s s u r e s . When vertical displacement i s prevented in a frost-heaving soil a positive p r e s s u r e is developed at the ice-water interface. This pressure i s known a s the heaving pressure. Such pressures can be sufficiently high to destroy foun- dations and lift buildings.

The author has measured the heaving p r e s s u r e a s a function of dry density f o r Pot- t e r s flint. At constant moisture suction the heaving pressure increased with increas-

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ing density (Fig. 4). In another experi- ment using a different preparation of Pot- t e r s flint the increase in p r e s s u r e was measured a s a function of time with a suitably mounted ring dynamometer. An adequate supply of water was assured by maintaining the water table at the base of a 3-in. specimen throughout the experi- ment. On the basis of Figure 4 this mois- ture condition should be potentially the most favorable f o r the development of maximum p r e s s u r e . Figure 5 shows the relationship between time and pressure. The p r e s s u r e eventually terminates the ice lensing process. At this point the heaving p r e s s u r e is at a maximum.

ate

of F r o s t Heave. Beskow (4) demonstrated that the heaving rate-was not always influenced by the r a t e of f r o s t penetration a s shown by Figure 6. In his experiments the temperature was varied between -2 C and -10 C above the sample without affecting the heave rate. Beskow pointed out that the maximum rate of heave was achieved when the cold

I ; : U RATED P E R M E A B I L I T Y 10 - SUCTION-MOISTURE C O N T E N T 2 8 3 . * 7 > != 6 W I LI w 5 RELATIONSHI S I L T 7

-

-

-

- - a -

-

CLA ?,' 100 2 0 0 3 0 0 4 0 0 5 0 0 SOIL M O I S T U R E SUCTION C M WATER

side temperature of the specimen was Figure 3. Unsaturated permeability and -2 C. Colder temperatures down to -10 suction-moisture content relationship. C, although increasing the r a t e of f r o s t

did not increase the heaving

rate. It i s evident, however, that, over a certain range of temperatures, increasing the rate of f r o s t penetration by applying lower cold-side temperatures does increase the heave rate (Fig. 7). Two different cold-side temperatures were used, -3 and -6 C.

Figure 4. Relationship between s o i l moisture tension, overburden pressure, and d r y den- s i t y when heaving ceased.

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C 6

1600

TIME HOURS

F i g u r e 5. Heaving p r e s s u r e i n c r e a s e due t o i c e l e n s i n g a s a f u n c t i o n of time measured w i t h a r i n g dynamometer i n a s a t u r a t e d sample of P o t t e r s f l i n t . Cold s i d e temperature

-3 C, w a r m s i d e temperature 1.5 C.

The specimen consisted of a homogeneous mixture of 45percent silt and 55percent clay /BOTTOM WATER TEMPERATURE compacted t o a d r y density of 1.26 g/cc. F r e e

L

t o - - - - - - ' water was provided continually a t the base of the 3 -in. specimen. The rate of heave was a function of the r a t e of heat removal. Increas- ing the temperature gradient within a certain AIR TEMPERATURE

-4-

-range i n c r e a s e s the r a t e of heave. If the heav- ing r a t e reaches a maximum value a s Beskow suggests, i t is still a matter of speculation whether the rate of heave stays constant o r de- c r e a s e s a s the t e m p e r a t u r e gradient is still f u r t h e r increased. Suchmaximum values of heat removal may well lie beyond those en- countered under natural conditions.

T h e r e appears to b e general agreement on the influence of overburden p r e s s u r e and/or soil moisture suction level on the

- r a t e of heaving. Beskow's r e s u l t s (Fig. 8)

i l l u s t r a t e what h a s been generally observed, 0

o 5 0 100 150 ZOO that is, increasing either the overburden

TIME IMIN I p r e s s u r e o r soil moisture suction simul-

F i g u r e 6. Another example showing t h a t taneously o r independently reduces the

f r o s t heave i s independent of r a t e of r a t e of heaving.

f r e e z i n g . s o i l - v e r y f i n e s i l t , pressure- At this stage it should be pointed out 410 g / s q cm

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-

I I I I I I I I I I I I 4 1400 1200

-

-

0 -

-

/ ' O / O

-

I U 0 1000

-

-

-2

W LZ 3 m 800

-

-

m W u a 600

-

-

Z - > 4 W I

-

-

I I I I I I I I I 2 3 4 5

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that the heave rate i s dependent not only on the rate of heat removal f r o m the freezing zone but i s intimately associated with the unsaturated permeability and the induced suction gradient. This will be discussed more fully later.

In Soils That Do Not Support Ice Lens Growth

There i s very little information available 011 the freezing behavior of soils that do

not show ice segregation. Two different phenomena were recognized when saturated specimens of this kind were subjected to unidirectional freezing. Even under rather small loads some laboratory-prepared specimens exuded water from the unfrozen end to accommodate the volume increase a s the initial freezing occurred. The amount of water exuded has not been measured. The phenomenon i s also mentioned by Beskow

(4). - In all c a s e s the exudation of water coincided with active penetration of the freez-

ing zone.

Other specimens showed heaving during the initial freezing which terminated when the freezing plane stopped penetrating. Soils that exhibit this second type of phenome- non a r e thoughttobe borderline with respect to frost damage. How these soils react to different r a t e s of freezing has not been determined experimentally.

FUNDAMENTAL FEATURES OF THE ICE LENSING PROCESS

The growth of ice lenses in soils i s a fascinating subject and has recently caught the attention of a number of research workers who have made useful contributions

5 4 A V) W s 3 0 Z

-

-

W > u W I 2 I 0 0 I 2 3 4 TIME (HOURS)

Figure 7. The amount of heave a s a flmction of time f o r two d i f f e r e n t c o l d side tem- peratures. The specimens were prepared a t a dry density of 1.26 g/cc from crushed a i r

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T I M E ( M I N . )

Figure 8. Diagram showing f r o s t heaving r a t e f o r different pressures, surface load o r capillary pressure. For any given pressure there i s a c e r t a i n slope of t h e curve, i.e., a d e f h i t e r a t e of heave. For each slope the corresponding pressure i s given

in g/sq cm. S o i l pure fractions, 0.01

-

0.005 mm.

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(6,

- - -

7, 8). As has been pointed out, some disagreement still exists about the mechan- ism but this s t e m s from a lack of experimental results. Any consideration of the fun- damental features of the ice lensing process in nature i s therefore somewhat specula- tive. An attempt has been made in this paper to support the theory by experimental results wherever possible and to include the opinions expressed in the literature par- ticularly where general agreement exists.

Pore Size a s a Mechanism f o r Supercooling

In the unidirectional freezing of a saturated soil the dimensions of the interconnect- ing channels determine the temperature at which ice propagation may proceed. This effect of channel o r pore size provides a means f o r the supercooling of the soil water below the freezing point near the ice-water interface. The freezing of soil water at supercooled temperatures was suggested by Taber

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and Jackson et al. (6) a s a nec- e s s a r y feature of the ice lensing process, a s it provides the energy f o r thedevelop- ment of heaving p r e s s u r e and the creation of a suction gradient.

The relationship between the s i z e of a stable spherical c r y s t a l in i t s own melt and the absolute temperature can be shown by:

in which

r = radius of the crystal (cm);

p. = density of the ice (g/cc);

1

U. = interfacial energy (ergs/sq cm);

1W

Qf = latent heat of fusion (ergs/g);

T = tfmperature of melting a t zero curvature of the solid-liquid interface

( K); and

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Figure 9. An enlarged schematic diagram showing a section of t h e i c e l e n s with respect t o t h e s o i l p a r t i c l e and s o i l pore.

Eq. 1 recently used by Sill and Skapski (9) f o r the determination of the surface ten- sion of solids in thin wedges, s t a t e s that theproduct of the curvature radius and f r e e z - ing point depression i s a constant determined by the interfacial tension and the bulk properties of the substance.

Assuming that the s i z e of the soil pore determines the s i z e of the advancing ice crystal the quantity r in Eq. 1 may be interpreted a s the radius of the pore. A part of the soil pore i s occupied by the adsorbed phase which probably places additional size limitations on the ice crystal. This mechanism appears to be responsible f o r the growing of the ice phase a t the supercooled temperatures necessary to r e l e a s e the energy required f o r the work involved in heaving and moisture movement. Accordingly, the s m a l l e r the pore radius, r , the lower the temperature necessary f o r the ice front

1

to advance, that i s , ATa? Measurements of heaving p r e s s u r e and suction pressure indicate that these quantities do increase a s the pore size of the porous material i s reduced. The difficulty with a more rigid application of Eq. 1, although desirable, i s beset with many difficulties since a gradation of pore s i z e s normally e x i s t s in soils. P r e s s u r e Relationships a t the Ice-Water Interface

The heaving p r e s s u r e s that a r e developed a t the ice-water interface depend to a large extent on the moisture status of the soil. When the soil system i s maintained completely saturated, given sufficient time, the maximum heaving p r e s s u r e possible f o r a given soil i s developed because under these conditions the suction p r e s s u r e in the water i s essentially zero. According to F i g u r e 4 increasing the suction reduced the ultimate heaving pressure. In the absence of any overburden p r e s s u r e the maximum suction p r e s s u r e i s possible. An attempt will be made in this part of the paper to jus- tify theoretically this relationship. Figure 9 i s a schematic drawing showing the ice phase and water phase in relation to the s o i l pore and soil particle. Attention i s drawn to the intimate contact that exists between the ice and water phases a s this i s of some importance in developing the theory.

The temperature atwhich the ice phase grows depends on the p r e s s u r e imposed. The p r e s s u r e may be imposed on the water phase, o r on both the ice and water phases simultaneously o r on the ice phase alone. In each case the equilibrium freezing tem- perature i s different. The complete development of the pressure-freezing point de- pression equations a r e given by Edlefsen and Anderson

(10).

The final equations de- veloped by Edlefsen and Anderson a r e a s follows.

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Case 1. The total change in p r e s s u r e on the ice is always equal to the total change in p r e s s u r e on the water.

in which

d P t = total change in p r e s s u r e ; Q = latent heat of fusion;

f

v = specific volume of water; w

v. = specific volume of ice;

1

T = the absolute temperature a t which the phase change occurs; and dT = change in freezing point temperature.

Substitution of the proper values f o r vi, v T , and Qf shows that the freezing w'

point i s lowered by 0.00748 C per atmosphere of p r e s s u r e increase.

Case 2. The p r e s s u r e on the water remains constant while the p r e s s u r e on the ice is changed.

where d p . i s the p r e s s u r e change on the ice; the other symbols a r e the s a m e a s pre- 1

viously designated. In this c a s e the freezing point is lowered by 0.0899 C per atmos- phere of p r e s s u r e increase.

Case 3 . The p r e s s u r e on the i c e remains constant while the p r e s s u r e on the water i s changed.

In this case a positive p r e s s u r e r a i s e s the freezing point temperature by 0. 0824 C per atmosphere of p r e s s u r e , but a decrease in p r e s s u r e lowers the freezing point.

In the light of the different relationships between p r e s s u r e and freezing point de- pression it is necessary to assume the actual disposition of the water relative t o the ice phase and soil grains. It is believed that in a saturated system the relationship that applies i s given in Case 1. The fact that the characteristics of ice lensing show no abrupt change in going f r o m a completely saturated to a partially saturated system s e e m s to indicate that an intimate contact between the water phase and the ice phase extends into the unsaturated range. One need not exclude the possibility of moisture transfer in the vapor phase to the ice lens but i t must be accepted that, a t the f a c e of the growing ice lens, the water and ice phases exist in contact with each other.

If p r e s s u r e i s applied to the ice phase the water between the ice and soil particles i s placed in a state of compression. The pore water i s not affected if a rigid non-com- pressible material is being considered. Applying suction to the pore water would place the pore ice in a state of tension and consequently Case 1 s t i l l s e e m s to apply. The Mechanism of Ice Lens Growth

The mechanism of ice lens growth together with the development of heaving p r e s - s u r e s and suction in the soil moisture can be described a s follows, assuming that Eqs. 1 and 2 apply. If the system i s saturated, a s depicted in Figure 9, the absorption f o r c e s a r e fully satisfied. This means that if it was not inside a soil pore the outer- most layer of water around the particle would f r e e z e at nearly the temperature of bulk water. It i s believed that the initial crystallization of water begins either i n the soil pore a t the ground surface of the s o i l and propagates downward o r , in the c a s e of ice

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lenses separated by relatively dry layers, crystallization begins most easily in large pores o r discontinuities in the soil.

After crystallization has occurred i t s subsequent growth into an ice lens involves the manifestations of heaving p r e s s u r e s and suction p r e s s u r e s that accompany the pro- cess. Referring to Figure 9, the ice front will be temporarily prevented from prop- agatingdownward between the soil particles until the temperature has been lowered sufficiently to satisfy Eq. 1. Before this occurs part of the adsorbed water above the particle will freeze. As water i s being removed f r o m the adsorbed l a y e r into the ice phase it i s replaced from below and an equilibrium thickness of water i s maintained around the soil particle by continual replacement with supercooled water molecules. This i s really no more than film adjustment around the particle and will continue until the temperature drops sufficiently f o r the ice front to propagate through the soil pore. The mechanism really hinges on the existence of supercooled water in contact with the adsorbed phase and continual replacement of water to the adsorbed phase a s more water molecules enter the i c e phase. It can also be seen that the existence of the ad- sorbed phase i s a vital link in the movement of water f r o m a supercooled state into the adsorbed phase and hence into the ice phase. Similarly it may be noted that if the propagation of ice occurred at the freezing temperature of bulk water, 0 C, the evolu- tion of energy necessary to cause heaving and moisture movement would not occur. This i s well supported by experimental evidence and i s the justification f o r replacing fine-grained soils with gravels when f r o s t heaving cannot be tolerated. In going from porous systems containing s m a l l pores to those containing large pores no abrupt change in the heaving tendency i s predicted but would be in accordance with the amount of su- percooling possible which i s proportional to the radius of the pores according to Eq. 1.

The growth of such an ice lens may be halted in two ways. Firstly, if the ice lens i s loaded, causing a p r e s s u r e a t the ice-water interface above the soil p a r t i c l e , the f r e e z - ing point of the water would drop according to Eq. 2. The limiting p r e s s u r e to stop ice growth would occur when the freezing point of the water above the particle has been lowered (by positive p r e s s u r e s ) to the same temperature a s i s necessary f o r ice to propagate through the pore constriction. The experimental justification i s shown in Figure 5 which shows that ice lens growth can be stopped i n a saturated s o i l by loading the soil.

Ice lensing may also be halted by applying suction to the water in the p o r e system. A suction o r negative p r e s s u r e in the pore water r a i s e s the temperature a t which ice can propagate through a pore of given size. This i s based on Eq. 2. At the same time application of suction has the effect of drawing the ice-water interface toward the soil particle. This induces a s t a t e of compression at the ice-water interface above the soil particle and a lowering of the temperature at which freezing occurs.

Based on these considerations it i s thought possible that the maximum overburden p r e s s u r e s to stop ice lensing should be about twice a s great a s the maximum suction. F r o m limited experimental evidence using P o t t e r s flint a s the soil media this appears to be the c a s e (11).

Under naturaTconditions in the field the positive p r e s s u r e s on the ice-water inter- face a r e the naturally occurring overburden p r e s s u r e s due to the weight of frozen soil. The suction o r negative p r e s s u r e gradient i s induced by the i c e lens in the soil water. The induced suction gradient will never be g r e a t e r than that required to supply the de- mands of the growing ice lens. When the demand f o r water i s great the suction gra- dient increases. This tends to lower the unsaturated permeability coefficient, however,

resulting in a diminishing water supply. It follows therefore that the most favorable conditions f o r frost heaving i n any frost-susceptible soil i s when the f r o s t line i s close to the surface (low overburden p r e s s u r e ) and when the water table i s high (low suction).

HEAT AND MOISTURE FLOW AS RELATED TO ICE LENSING

In the over-all phenomenon of f r o s t heaving the most difficult combination of related processes to t r e a t , even on a semi-quantitative basis, i s the heat and moisture flow. This difficulty a r i s e s not only f r o m the complexity of the mathematics but also from the lack of experimental measurements of heave rates, heat flow, moisture flow,

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temperature distributions, and moisture tensions while i c e lensing is in p r o g r e s s . In the absence of such information, the quantitative treatment of the combined heat and moisture flow a p p e a r s impossible.

Some attempt a t a quantitative theoretical t r e a t m e n t f o r s o i l s was f i r s t made by Winterkorn (12). Following Winterkorn's method of reasoning, P o w e r s

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m a d e some tentative c a l c ~ l a t i o n s of relative r a t e s of heat flow due to conduction and heat flow a- r i s i n g f r o m the latent heat of fusion in the f r e e z i n g of green concrete. Although these authors have indicated the type of information that is necessary, the c o r r e c t n e s s of the computations depends on whether valid coefficients were used. These coefficients a r e not constants but vary a s the s y s t e m changes. P e r h a p s all that can be done a t this stage is to point out the various f a c t o r s that a r e known to b e involved and to specu- late on the p r o g r e s s of a continually changing s y s t e m .

A s the moisture tension i n c r e a s e s in the unfrozen zone beneath the ice l e n s t h e un- saturated permeability coefficient may a l s o change. In relatively uniform s a n d s and s i l t s the change i s abrupt and o c c u r s a t relatively low moisture tensions consistent with the s i z e of the p o r e s . In well-graded s a n d s and s i l t s the change is l e s s abrupt but d e c r e a s e s continuously with increasing m o i s t u r e tension (Fig. 3). The varying permeability coefficient is known to be related to the desaturation of these s y s t e m s without any consolidation occurring. In s y s t e m s consisting of compressible s o i l s the permeability coefficient is a l s o a function of the tension but the r a t e of change is l e s s abrupt due to the consolidation of the clay. Because the tension o r suction gradient is

thought to be the driving f o r c e f o r liquid moisture flow in frost-heaving s o i l s , i t can be assumed that the unsaturated permeability coefficient will a l s o change during i c e lens- ing if the tension changes.

A portion of the moisture flow during i c e l e n s i c g is attributable to flow in the vapor phase if s o m e of the voids a r e a i r filled. T h e r e f o r e unsaturated permeability coeffi- c i e n t s determined normally under isothermal conditions cannot b e strictly applied.

The t h e r m a l conductivity of f r o z e n s o i l is higher than that of unfrozen s o i l a t mois- t u r e contents above about 10 p e r c e n t according to Kersten

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The ratio f o r frozen to unfrozen soil i n c r e a s e s to values exceeding 1. 5 a s the m o i s t u r e content i n c r e a s e s . Referring now to the t h e r m a l conductivities of a frozen l a y e r of s o i l above a n unfrozen l a y e r i t may be c o r r e c t to a s s u m e a constant conductivity f o r t h e frozen l a y e r but a s the moisture content beneath the i c e l e n s changes s o does the t h e r m a l conductivity. In addition, the changing dimensions of the specimen due to heaving and the l a y e r i n g of the i c e phase with i t s unique t h e r m a l conductivity must a l s o be taken into account. Superimposed on this complicated s y s t e m is the climate-controlled temperature fluc- tuation which adds f u r t h e r to the difficulty of unravelling the phenomenon a s i t o c c u r s under field conditions. Complicated a s i t may be the consecutive formation of i c e l e n s e s i s , nevertheless, the product of the combined heat and moisture flow patterns.

Much speculation surrounds the phenomenon of consecutive.ice lens formation. The growth of a n i c e l e n s is thought to terminate when the r a t e of heat removal exceeds the total heat a r r i v i n g a t the lens. T h i s can be shown to be the c a s e if a reduced rate of moisture flow, resulting f r o m increased tensions, is postulated. The reduction in flow r a t e of m o i s t u r e is not entirely necessary f o r consecutive i c e lens formation. In- c r e a s i n g the r a t e of heat removal may a l s o d r i v e the freezing zone f u r t h e r into the m a t e r i a l until a m o r e favorable heat and m o i s t u r e flow balance is encountered. An important difference e x i s t s between the two c a s e s . When t h e r e is a reduced r a t e of moisture flow and desaturation o c c u r s beneath the ice lens, i c e c r y s t a l nucleation must precede the formation of a new i c e lens. In t h e c a s e where the r a t e of heat removal i s suddenly i n c r e a s e d , ice propagation p r o c e e d s through the p o r e system and t h e nucle- ation of i c e c r y s t a l s a t the new s i t e is not involved. This has been observed by the author in unidirectional f r e e z i n g of saturated s o i l specimens.

P r a c t i c a l Considerations Based on Basic P r i n c i p l e s

The amount of guidance that the practicing engineer can obtain f r o m basic consider- ations i s limited a t this s t a g e i n the understanding of basic phenomenon of f r o s t heav- ing. In many instances the suggestions which s t e m f r o m a fundamental approach

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support the measures that a r e used in practice based on experience i n the field and laboratory freezing experiments.

F r o s t Susceptibility Based on Grain Size and Grain-Size Distribution. According to theory, grain size i s not a s important a s the resultant pore size but there i s a rela- tionship between the two. In relatively uniform soils pore s i z e increases with grain size. The theory predicts that the maximum moisture suctions and heaving pressures should d e c r e a s e with increasing pore size. The importance of pore size i s implicit in the f r o s t action c r i t e r i a commonly used which permit a l a r g e r percentage of fines in uniformly graded material than in well-graded material. The theory therefore supports the practice of using coarse-grained materials with gradation limitations such a s the Casagrande criteria. No rigid guidance, however, can be obtained from the theory a s to the exact grain size o r grain-size distribution above which no frost heaving will oc- c u r under favorable moisture supply. It would seem reasonable to categorize soils in practice according to the degree of f r o s t susceptibility recognizing no abrupt deline- ation based on grain-size considerations between frost-heaving and non-frost-heaving soils. The influence of grain s i z e on the r a t e of moisture movement must also be ta- ken into account if the r a t e of heave i s considered. Although the maximum moisture suctions possible increase with decreasing grain size, the moisture permeability i s decreased. Consequently, a s i s observed in the field, heavy clays will heave at a much slower rate than s i l t s and the total amount of heave during one winter season would be much less. In coarse-grained soils, the moisture suctions will b e low o r negligible and the permeability parameter need not be considered. Silts which a r e notoriously treacherous f r o m a frost action point of view have a combination of mois- ture suction and permeability which lead to an extremely high f r o s t susceptibility and a r e avoided when possible in current practice.

Density and F r o s t Susceptibility. The effect of increasing the density i s similar to decreasing the grain size, that i s , the soil p o r e s a r e reduced in size. High densities may be desirable and necessary in achieving the required bearing capacity but at the same time soils which a r e borderline with respect to f r o s t susceptibility would become more f r o s t susceptible with increasing density.

Homogeneity and Differential Heave. A non-frost-susceptible material containing pockets of silt o r clay which a r e f r o s t susceptible may show characteristic differential heaving when intercepted by the f r o s t line. It has been shown that normally non-frost- susceptible soils can act very effectively in transmitting moisture (3). There a r e other reasons f o r differential heaving; variations in soil texture i s one of the more im- portant.

Moisture Supply and F r o s t Susceptibility. Without moisture no soil i s f r o s t suscep- tible. Normally the assessment of f r o s t susceptibility i s made under the most favor- able moisture supply. It i s shown theoretically that the lower the moisture supply (high suctions) the s m a l l e r the maximum heaving p r e s s u r e s and the lower the rate of heave (Figs. 4 and 5). An expression of f r o s t susceptibility f o r a given s o i l should al- s o be based on the moisture status likely to be encountered a t a given site. Drainage and the dissipation of seepage f o r c e s i s therefore most significant. Hydrostatic p r e s - s u r e s which result in the supply of f r e e water to the freezing plane will increase the maximum heaving p r e s s u r e s possible and increase the r a t e of heaving. T h i s will also lead to differential heaving with the s a m e outward manifestations a s non-homogeneous soils. F r o s t heaving will not occur, however, even with adequate water supply unless the soil pores a r e sufficiently small to induce some supercooling. When the soil con- s i s t s of c o a r s e uniform sands and gravels, no amount of water can possible result in heaving.

CONCLUSIONS

The mechanism of f r o s t heaving and a l l i t s ramifications a r e still not completely understood. This i s particularly true in resolving the combined heat and moisture flow in f r o s t heaving systems.

In some aspects of the mechanism the p r o c e s s i s fairly well known. T h i s applies to the understanding of how heaving p r e s s u r e s and suction potentials develop. The

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independent role of liquid m o i s t u r e flow under suction potential g r a d i e n t s and t h e vari- ation of flow with a v e r a g e suction is a l s o reasonably well understood. In t h e develop- ment of consecutive i c e l e n s f o r m a t i o n s and the r a t e of i c e growth the m e c h a n i s m can b e only qualitatively d e s c r i b e d and a m o r e rigid mathematical development would be useful.

T h e a s s i s t a n c e t h e p r a c t i c i n g engineer c a n expect f r o m b a s i c s t u d i e s is mostly qualitative in nature. In many i n s t a n c e s the t h e o r y s u p p o r t s t h e kind of solutions de- veloped f r o m many y e a r s of field experience. At the s a m e t i m e it offers a reasonable tentative working b a s i s and f u t u r e s t u d i e s c a n b e m o r e d i r e c t e d toward finding s o l u - tions to f r o s t heaving in s o i l s and f r o s t action generally.

ACKNOWLEDGMENTS

T h i s is a contribution f r o m the Division of Building R e s e a r c h , National R e s e a r c h Council, Canada, and is published with the approval of the D i r e c t o r of the Division.

REFERENCES

1. T a b e r , S., "The Growth of C r y s t a l s under E x t e r n a l P r e s s u r e . " American J o u r n a l of Science, Vol. 41, pp. 544-545 (1916).

2. Jumikis, A. R., "The Soil F r e e z i n g Experiment. " HRB Bull. 135, pp. 150-165 (1956).

3. P e n n e r , E., "Soil Moisture T e n s i o n and Ice Segregation.

"

HRB Bull. 135, pp. 50- 64 (1956).

4. Beskow, G., "Soil F r e e z i n g a n d F r o s t Heaving with Special Application to Roads and Railroads. " (1935), t r a n s l a t e d by J. 0. O s t e r b e r g , Technological In-

stitute, Northwestern University (1947).

5. T a b e r , S., " F r o s t Heaving." J o u r n a l of Geol., Vol. 37, No. 1 , pp. 428-461 (1929). 6. Jackson, K. A., C h a l m e r s , B., and McKay, G., "Study of I c e Formation in Soils."

Tech. Rep. No. 65, A r c t i c Construction and F r o s t Effects L a b o r a t o r y , Boston (1956).

7. Gold, L. W., "A P o s s i b l e F o r c e Mechanism Associated with t h e F r e e z i n g of Water in P o r o u s M a t e r i a l s . " HRB Bull. 168, pp. 65-72 (1957).

8. Martin, R. T . , "Rhythmic I c e Banding i n Soil. " HRB Bull. 218 (1958).

9. Sill, R. C., and Skapski, A. S., "Method f o r t h e Determination of Surface T e n s i o n of Solids f r o m t h e i r Melting P o i n t s in Thin Wedges. " Journal, Chem. Phys, Vol. 24, NO. 4, pp. 644-651 (1956).

10. Edlefsen, N. E., and Anderson, A.B. C., "Thermodynamics of Soil M o i s t u r e . " Hilgardia, Vol. 15, pp. 31-268 (1943).

11. P e n n e r , E., " P r e s s u r e s Developed in a P o r o u s Granular S y s t e m a s a R e s u l t of I c e Segregation. " HRB Special Report 40 (1958).

12. Winterkorn, H. F . , "Discussion to Suction F o r c e in Soils upon Freezing. " Amer. Soc. Civ. Eng., Vol. 81, S e p a r a t e 656, pp. 6-9 (1955).

13. P o w e r s , T . C., "Resistance of Concrete to F r o s t a t E a r l y Ages." P r o c e e d i n g s , RILEM Symposium on Winter Concreting Theory a n d P r a c t i c e , Sessior? C, General Report, Copenhagen (1956).

14. K e r s t e n , M. S., "Laboratory R e s e a r c h f o r the Determination of the T h e r m a l Prop- e r t i e s of Soils." R e s e a r c h L a b o r a t o r y Investigations, Eng. Exp. Station, University of Minnesota (1949).

Discussion

R. TORRENCE MARTIN, R e s e a r c h Associate, Soil Engineering Division, Massachu- s e t t s Institute of Technology-It is not the p u r p o s e of a d i s c u s s e r to introduce new evi- dence with the a i m of e i t h e r substantiating o r refuting the t h e s i s of the author. On the o t h e r hand, c r i t i c i s m alone i s not sufficient. T o admit a competitive hypothesis to the working l i s t is a c o n c r e t e f o r m of e x p r e s s i n g a doubt, while a t the s a m e t i m e r e - specting existing hypotheses, and s e r v e s b e t t e r than a b s t r a c t c r i t i c i s m toward unravel- ling the intertwined complexities of nature. In brief the w r i t e r a c c e p t s T . C. Chamber-

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l a i n ' s s y s t e m of multiple working hypotheses a s f u r n i s h i n g the m o s t wholesome condi- tions f o r r e s e a r c h and that any additional hypothesis not i n itself i n c r e d i b l e will b e welcomed.

In o r d e r to keep the d i s c u s s i o n within t o l e r a b l e l i m i t s , the r e m a r k s s h a l l be con- fined to possible a l t e r n a t i v e i n t e r p r e t a t i o n r e g a r d i n g the significance of (1) pore s i z e (Eq. 1 i n M r . P e n n e r ' s p a p e r ) and (2) p r e s s u r e upon f r e e z i n g point d e p r e s s i o n (Eq. 2 i n M r . P e n n e r ' s p a p e r ) , relative t o the theory of i c e lens formation. At the outset i t m u s t b e c l e a r l y s t a t e d and with e m p h a s i s , that the author's hypothesis con- cerning Eq. 1 and Eq. 2 a p p e a r s to b e completely r a t i o n a l and self-consistent with the e x p e r i m e n t a l d a t a p r e s e n t e d . T h e r e f o r e , the a u t h o r ' s a r g u m e n t s m u s t be r e s p e c - ted, a t l e a s t f o r the p r e s e n t , a s one of a group of working hypotheses.

P o r e Size

T h e author a t t r i b u t e s to t h e s m a l l p o r e s and the even s m a l l e r p o r e c o n s t r i c t i o n s two vital effects r e l a t e d t o t h e mechanism of i c e l e n s f o r m a t i o n : (1) supercooling and (2) r e t a r d a t i o n of i c e f r o n t advance.

Supercooling, AT, is the t e m p e r a t u r e difference between the actual t e m p e r a t u r e a t which t h e i c e is forming, Tx, and the equilibrium t e m p e r a t u r e , T e' a t which the liquid phase under i t s existing activity could c o e x i s t with the s o l i d phase; i. e., A T = T

-

T

e x'

Supercooling is frequently confused with f r e e z i n g point depression. F r e e z i n g point d e p r e s s i o n , dT, is the t e m p e r a t u r e difference between t h e equilibrium t e m p e r a t u r e f o r the activity of the liquid i n the s y s t e m u n d e r consideration, T and t h e equilibrium

e'

t e m p e r a t u r e f o r p u r e liqu'id u n d e r no r e s t r a i n t , T ' i. e., d T = T

-

T F o r pure wa-

0' o e '

t e r T = 0.00 C, w a t e r in a c l a y s o i l s y s t e m may have a f r e e z i n g t e m p e r a t u r e , T e , of

0

- 5 C; t h e r e f o r e , if the w a t e r i n such a s o i l s y s t e m is being converted l o i c e a t a tem- p e r a t u r e , T of -6 C, the supercooling f o r the s y s t e m is -1 C and t h e f r e e z i n g point

x

'

d e p r e s s i o n is -5 C.

T h e full realization conerning the meaning of t h e s e definitions i s e s s e n t i a l . P e n n e r c o r r e c t l y defines d T in Eq. 1 a s a f r e e z i n g point d e p r e s s i o n ; however, he then s t a t e s "This m e c h a n i s m ( r e f e r r i n g t o Eq. 1)' a p p e a r s t o b e r e s p o n s i b l e f o r the growing of the i c e p h a s e a t the supercooled t e m p e r a t u r e s n e c e s s a r y t o r e l e a s e t h e e n e r g y r e - quired f o r the work involved i n heaving and m o i s t u r e movement

.

.

.

" which c a n hardly b e t r u e s i n c e d T of Eq. 1 is a f r e e z i n g point d e p r e s s i o n and not a supercooling.

F u t h e r , v e r y p u r e w a t e r i n bulk h a s b e e n supercooled t o a t l e a s t -39 C; if this be f a c t , then s m a l l p o r e s a r e not a n e c e s s a r y p r e r e q u i s i t e f o r supercooling. Neverthe- l e s s , the p o r e s i z e h a s a profound influence upon supercooling because p o r e size con- t r o l s the s t a t i s t i c a l probability of obtaining sufficient i c e nucleation to r e a c h a m e a s - urable growth r a t e . T o i l l u s t r a t e t h i s concept, the following hypothetical example is given-Case A: ten l a r g e w a t e r filled p o r e s e a c h p o r e having one nucleus f o r i c e f o r - mation; the t e m p e r a t u r e is lowered until i c e s t a r t s to nucleate. Ice growth is rapid b e - c a u s e t h e volume of w a t e r a t the p r o p e r t e m p e r a t u r e , instantaneously available t o each i c e nucleus, is v e r y l a r g e . C a s e B: u s e the s a m e volume, the s a m e water, and the s a m e n u m b e r of nuclei a s i n C a s e A b u t n o w with a p o r o u s s y s t e m containing 1,000 p o r e s . H e r e t h e r e is a nucleus in only one p o r e p e r 100. T h e t e m p e r a t u r e is lowered and a t about the s a m e t e m p e r a t u r e a s in C a s e A i c e nuclei f o r m i n the 1 0 p o r e s ; how- e v e r , the volume of w a t e r a t the p r o p e r t e m p e r a t u r e available to e a c h i c e nucleus is now what i t was in C a s e A. T o t a l i c e growth i s v e r y s m a l l ; t h e r e f o r e , the t e m - p e r a t u r e m u s t be lowered ( o r additional w a t e r supplied) b e f o r e a n a p p r e c i a b l e growth r a t e is reached.

Cooling c u r v e s ( t e m p e r a t u r e v s t i m e ) on v a r i o u s p o r o u s s y s t e m s with different p o r e fluids should provide t h e d a t a n e c e s s a r y i n o r d e r to decide the p r o p e r relation- s h i p between p o r e s i z e and supercooling.

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Retardation of ice front advance i s clearly demonstrated by Eq. 1; however, there i s an equally valid counter-proposal which s t a t e s that the ice front has no d e s i r e to ad- vance through the pore constriction provided that a supply of water can be maintained a t the ice front. Then, by the time the ice front wants to advance i t i s too late, i c e formation has already begun further down in the soil.

This additional hypothesis a r i s e s from a consideration of crystal growth rate inde- pendent of anypore constrictions. The f i r s t condition, for a c r y s t a l of a given s i z e in i t s own melt, i s that the rate of crystal growth increases a t a fantastic rate a s the temperature i s lowered below the equilibrium temperature (for this case T e = To). The second condition, given a fixed amount of supercooling, i s that the larger the crys- tal size the more rapid the growth rate. Returning to a soil system, suppose that a small crystal (a whisker) i s attempting to grow perpendicular to a large pore crystal, any water available will go to the large pore crystal rather than the whisker because (a) the pore crystal i s larger and thus grows f a s t e r , and (b) the pore crystal i s colder, thus i t grows f a s t e r . Both of these situations rob the small whisker in favor of the large pore crystal since the l a r g e r crystal i s energetically more stable than the whisker.

One may phrase the question another way. Which requires the least expenditure of energy, water transport o r ice front advance? A crude calculation from very meager data indicates that water transport requires only a fraction of the expenditure of en- ergy required f o r i c e front advance. This energy consideration is not an additional hypothesis, but should provide a means of testing between different hypotheses when better experimental data become available. Data needed a r e temperature and p r e s - s u r e measurements in both phases a t a freezing ice front. Some way must be devised to differentiate between freezing point depression and supercooling. In fact, P e n n e r t s hypothesis and the alternatives herein suggested, both tacitly assume that supercooling does occur. There can be no doubt but that supercooling will provide the energy re- quired; however, if experiments show that there i s no supercooling then some other source of energy must be found and any acceptable working hypothesis will have t o be modified to include the new information. Since ice lensing i s a rate process in which the rate i s definitiely finite, there must be some infinitesimal amount of supercooling to provide a gradient in o r d e r to prevent the r a t e f r o m going to zero.

P r e s s u r e upon Freezing Point Depression

The author prefers Case 1 where the total p r e s s u r e change on the ice i s always e- qual to the total p r e s s u r e change on the water because of

".

.

.

the intimate contact that exists between the ice and the water phases.

"

That there i s intimate contact be- tween the phases has been verified by numerous workers since Taber's original work (author's ref. 5). Penner has very carefully measured the tension (-P) in the water phase during ice lensing; if Case 1, Eq. 2, i s applicable i t s e e m s to imply that the ice phase can withstand no lateral s t r e s s .

Does intimate contact necessarily require that the p r e s s u r e on the two phases be equal? Taber did not think so, he envisioned the adsorbed water film (which may be only a few molecular layers thick) a s a two-dimensional liquid able to withstand nor- mal s t r e s s e s and a t the same time retain relative f r e e mobility laterally. In their discussion of p r e s s u r e effects upon freezing point depression Edlefson and Anderson (author's ref. 10) were of the opinion that Case 2 and Case 3, Eqs. 3 and 4, would be the appropriate-solutions f o r freezing a soil system provided that the percent a i r voids was greater than zero. It i s certainly a r a r e soil where the voids a r e 100.0 percent water-f illed.

Penner mentions

". . .

that the characteristics of ice lensing show no abrupt change in going from a completely saturated2 to a partially saturated system .

.

.

"

Applica- '1t i s assumed that Penner i s using saturation a s previously defined by him (HRB Bull. 135, p. 109) which states, "At saturation the tension i s zero, although in the c a s e of light textured soils the soil pores may be partially filled with a i r .

"

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tion of the combination of Case 2 and C a s e 3 likewise would provide a perfectly smooth transition. I t might a l s o be added that the freezing point depression would be increased 10 t i m e s f o r the s a m e p r e s s u r e change.

T a b e r (author's ref.

2)

performed freezing experiments with benzene and nitroben- dT

zene where

-

d P f r o m Case 1, Eq. 2 would b e positive r a t h e r than negative a s f o r water. The organic liquid s y s t e m s gave marked "ice" lensing and appear to v a r y with p r e s - s u r e in the s a m e manner a s the water s y s t e m s . By the u s e of C a s e s 2 a n d 3, Eqs. 3 and 4, one would expect s i m i l a r behavior between the organic liquid and w a t e r s y s t e m s . Because t h e r e is appreciable m a s s t r a n s f e r , whether the volume change f r o m liquid to solid is positive o r negative is probably of no consequence.

F r o m the p r e s e n t data, the p r o and con arguments concerning the importance of p r e s s u r e on freezing point depression a r e inconclusive; however, the organic liquids may prove advantageous toward obtaining definite data regarding the effect of p r e s s u r e

d T

because the

-

coefficients a r e much l a r g e r than f o r water. The coefficients f o r ben- d P

zene and nitrobenzene a r e compared below with the water coefficients given by Penner.

dT

in C/atm. calculated f r o m d P

Fluid Eq. 2 Eq. 3 Eq. 4

Water -0.00748 -0. 089 +O. 0824 Benzenea +O. 040 -0.22 +O. 25 Nitrobenzenea +O. 023 - 0 . 2 5 +O. 27 a

T e m p e r a t u r e of freezing, latent heat, and specific volumes necessary f o r these cal- culations w e r e obtained f r o m the International Critical T a b l e s .

In conclusion, one of P e n n e r ' s m a j o r points should be reiterated. F r o s t heaving is a dynamic unsteady s t a t e p r o c e s s ; t h e r e f o r e , in any experiment designed to t e s t any portion of any hypothesis concerning i c e lensing, one must always k e e p in mind that a l l the v a r i a b l e s a r e v e r y strongly interrelated. F o r example, suppose one were to a r b i t r a r i l y change the overburden p r e s s u r e . In o r d e r to ascertain what effect this will have on i c e lensing one m u s t consider a t the very l e a s t what happens t o (1) the freezing temperature, (2) the nucleation point, (3) water transport, and (4) heat t r a n s - f e r through the soil and ice. Then, in turn, how each of t h e s e changes effects and is effected by the induced changes in the other t h r e e variables.

A. R. JUMIKIS, P r o f e s s o r of Civil Engineering, Rutgers, The State University, New

Brunswick, N. J. -The a i m of P e n n e r ' s p a p e r i s , like that of the p a p e r s by the other authors partaking in t h i s symposium, the review and a s s e s s m e n t of the p r a c t i c a l util- ity of the currently available knowledge a s i t p e r t a i n s to t h e freezing of w a t e r in s o i l s , mainly in relation to highway engineering. The author p r e s e n t s his p a p e r i n three principal sections, the l a s t of which can be described a s follows:

1. Phenomena observed by the author with his s o i l f r e e z i n g experiments in the lab- oratory;

2. A condensed theory of f r o s t heaving which s e r v e s h e r e partly f o r t h e purpose of explaining the phenomena observed in the a u t h o r ' s studies; and

3 . P r a c t i c a l considerations based on fundamental principles.

Water, T e m p e r a t u r e , Undercooling, Interaction-Important F a c t o r s

In general two things s t r i k e one immediately upon s t a r t i n g to study a freezing soil system and t h e s e a r e , f i r s t , the profound influence of t e m p e r a t u r e upon t h e soil mois- t u r e , and, second, the observation that the substance w a t e r contributes considerably to the performance of the soil, particularly when under f r e e z i n g conditions. These

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two factors-temperature, o r rather heat exchange with the surroundings of the f r e e z - ing soil system on the one hand, and soil moisture migration induced by a thermal po- tential on the other hand-interact mutually, an interaction which endows the freezing soil system with great complexity, and consequently makes it very difficult to study.

In studying frost effects upon soil it must also be remembered that there i s some- thing else involved than merely the solid particles of the soil, viz., soil texture (refer to the textural criterion of frost-susceptible soils, for example). As just mentioned, in the soil freezing process an important factor, among others, i s the soil moisture and, what seems to be more important, the interaction of physical forces between the surface of soil particles and the soil moisture films surrounding the soil particles. This i s of particular significance in studying the soil moisture transfer in the film phase upon freezing.

From what i s thus f a r known from literature, f r o m the research work by the author, the discusser of the author's paper, and others, i t seems that the key to the s e c r e t s of the freezing soil system lies in the substance water itself and in the understanding of the undercooling phenomenon taking place in the freezing soil system. Thus the liquid phase of the soil i s not just an important constituent part of the soil a s it con- cerns the performance of the soil under load, but it also plays a n important role when subjected to temperature changes. Temperature, it i s known, changes the properties of water. Variation in temperature s t a r t s a thermal potential which induces the soil moisture to migrate, and to induce between the ends of the freezing soil system a n electrical potential. The influence of the latter on the other processes taking place in a freezing soil system seems a t present to be very obscure.

Method of Study

Referring to the contents of the paper under discussion, it can be observed that the author and the discusser both study the freezing soil system in i t s entirety. The ob- vious reason for using this method i s that unfortunately a t present there a r e no satis- factory scientific tools available f o r handling all of the interior details of the system. Hence the author's working method i s very advantageous f o r i t s simplicity and practi- cal applications. This method comprehends all the factors and potentials-although some of them may be masked out-which might contribute to the net amount of the up- ward flow of soil moisture upon freezing and consequent frost heaving.

The author states, rightly it is felt, that the mechanism of f r o s t heaving is s t i l l not completely understood. To this can be added that in the soil freezing system m o r e than one mechanism is operative; besides the f r o s t heaving mechanism there act also simul- taneously several moisture transfer mechanisms, some of which a r e more effective than others, depending upon the degree of porosity of the soil. The details of the mois- ture transfer, too, a r e not too well understood. The lack of such knowledge, in the words of the author, is indeed a r e a l obstacle to the complete solution of the f r o s t ac- tion problem in highway, foundation and earthwork engineering. This i s then one of the major reasons why the author studies the freezing soil system experimentally.

One also observes that Penner's manner of treating the soil moisture transfer re- lates to the mechanism of soil moisture transfer in the film phase.

Moisture Transfer

The moisture transfer through a homogeneous, isothermal porous medium i s com- monly characterized by the coefficient of permeability, k. In a freezing soil system where temperature varies with depth below the ground surface, the soil moisture film i s also a t different points below the ground surface a t a correspondingly different temperature. It is gratifying to observe that this idea has also found i t s way into Pen- ner's work. The author realizes that "the unsaturated permeability coefficient is not a constant but is rather a function of the average suction

.

. .

"

It is felt appropriate to say a t this point that the prime cause of the processes in the soil system under study

is the freezing thermal gradient, o r simply thermal potential, the suction being just a function of the temperature difference acting on the soil system. Because the tempera- ture changes with depth, the soil moisture transfer characteristic is not a constant.

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F o r this reason it would probably be better to speak of a coefficient of the system's transmissibility, k which v a r i e s with depth rather than permeability. In the case of

s

'

moisture migration in soil in the vapor phase, the coefficient of vapor diffusion applies. The degree of concentration of electrolytes, keeping in view the relationship of film flow to the zeta-potential, which acts a c r o s s the electric diffuse double layer, may also have i t s effect upon the amount of soil moisture transferred upon free'zing. It is

understood that electrolytes have a great influence upon the amount of soil moisture transferred to the frozen zone: the fewer electrolytes the more moisture transferred. Ice Lensing

Relative to the topic of ice lensing in soil, the following can be added to the author's presentation: the thickness of the ice layers depends, among other things, upon the rapidity of cooling and the concentration of the soil moisture a s an electrolyte, a s well a s upon p r e s s u r e conditions. Also, the amount of banded ice layers in a soil system (number of layers p e r unit thickness of the frozen zone, thickness of the i c e layers and distribution of visible ice layers) depends very much upon the r a t e of nucleation, which in i t s turn leads to the subject of undercooling. Generally, it lias been observed by the d i s c u s s e r ' s soil freezing experiments, and it is also known from physics and geology, that when the soil system i s frozen quickly the crystals, viz., i c e layers, a r e very thin, o r even invisible by the unaided eye, even if the whole soil sample i s frozen solid throughout. Slow crystallization, viz., freezing of s o i l moisture, brings about large, clearly visible crystals, viz., ice layers.

According to Tammann, the degree of undercooling i s a function of temperature and s o is the rate of nucleation. In undercooled water only molecules with sufficiently low kinetic energy a r e able to form nuclei upon which ice crystals can form. With the decrease in temperature the rate of nucleation increases, but only up to a certain point, when the viscosity of the water (which increases exponentially with the decrease in tem- perature) slows down the molecular movement to such a degree that the r a t e of nuclea- tion decreases.

Crystallization velocity of undercooled soil moisture is frequently facilitated by col- loidal substances the particles of which a r e non-spherical. Spherical particles, a s well a s truly dissolved substances, lower the velocity of crystallization.

The condition of unfrozen water in freezing o r frozen s o i l also depends, of course, upon pressure.

Density and F r o s t Susceptibility

The author's view on this topic i s fully in accord with the discusser's view, namely, that one should consider the dry density-optimum moisture relationship of a soil ac- cording to which there is a maximum dry density at a certain optimum moisture con- tent. With increase in moisture content beyond the optimum the dry density decreases. As to the heat transfer through a freezing soil, the thermal diffusivity, a =

,

de-

c * P

pends upon the coefficient of thermal conductivity, K, specific heat, c , and the unit weight of the soil, p . Usually c does not vary widely; therefore, in large-scale field operations, little can be done to improve this factor. If K i s decreased, a decreases automatically, but again in large-scale compaction operations K can be decreased rel- atively little. The only f a c t o r here which s e e m s to affect the decrease of the thermal diffusivity, a, i s the unit weight of the soil, p. The g r e a t e r p i s , the l e s s a is. This implies that the compacted soil would have a decreased diffusivity, but only up to the maximum compacted density, which i s limited by the optimum moisture content. After the optimum moisture content i s reached, the density of s o i l decreases and consequently the coefficient of thermal diffusivity increases, with the result of quick f r o s t penetra- tion into the soil. Of course, the increase in moisture content past the optimum has more total latent heat, which upon freezing is released and retards somewhat the frost penetration rate and total depth.

Figure

Figure  2.  S o i l  moisture  s u c t i o n   increase  due  t o   i c e   lensing  a s   a  function  of  time  in  a  closed  system  containing  P o t t e r s   f l i n t
Figure  4.  Relationship  between  s o i l  moisture  tension,  overburden  pressure,  and d r y   den-  s i t y  when  heaving  ceased
Figure  7.  The  amount  of  heave  a s   a  flmction  of  time  f o r   two  d i f f e r e n t   c o l d   side  tem-  peratures
Figure  8.  Diagram  showing  f r o s t   heaving  r a t e   f o r   different  pressures,  surface  load  o r   capillary  pressure
+2

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