Pressures developed during the unidirectional freezing of water-saturated porous materials

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Pressures developed during the unidirectional freezing of

water-saturated porous materials

Penner, E.

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FROM

Physics

of

Snow

and

Ice

Proceedings of the International Conference on Low Temperature Science, 1966

VOLUME I

Part

2

Edited

by

Hirobumi

~ U R A

THE INSTITUTE OF LOW TErvlPERATURE SCIENCE

HOKKAIDO UNIVERSITY

Pressures Developed during the Unidirectional Freezing

o f Water-Saturated Porous Materials

Experiment and T h e o r y

Edward

PENNER

Soil Alcclirr~ric..~ Scctio~r, 1)iz~i.siior

of'

121tilcli~iy. Itc,.secr~-clr 1\51tio~rcrl It(,.sccr~-cl, Cororcil, Ottcreurr, O~itrr~-io, Ccr~rrrclrr

Abstract

A new experimental apparatus is being used that permits the measurement of developing pressures during the freezing process in the environment of a small temperature gradient. Studies with pads of nearly uniform-size glass beads (in the micron range) indicate that after an ice lens h ~ s developecl the ice-water interfacial energy, computed from the measured pressures and the pore geometry of glass bead pads, ranges between 30 and 35 ergs/cm2. T h e supporting theory assumes that such pressures arise because of the curved interfaces between the ice lens ancl water, ice ancl porous solid, and water and solid according to Everett's model.

Freezing experiments \\,it11 pads of well-graded spheres (1-30 /!) show the significance of thc smaller pores in the porous system in determining the magnitude of prcssurcs devclopccl during ice lens growth. T h c study has been extended to soils and some common building materials.

I. Introduction

Frost heave experiments show that pressures developed a t an ice-water boundary beneath a n ice lens are related to t h e pore dimensions of t h e soil (Penner, 1958, 1963). In the absence of all confining pressures, t h e maximum suction (negative pressure) is developed in t h e water phase if the porous system does not have access to an external water supply. T h i s suction is also related to the pore dimensions (Penner, 1957). I t is possible also to halt ice lensing by a combination of suction and confining pressure (Penner, 1958).

r .

I h e geometry of most porous materials is normally too complex f o r t h e investi- gation of theories that predict a precise relation between the heaving pressure induced by ice lensing ancl the geometry of t h e solid structure with its attendant pore system. T h e present paper describes freezing experiments with glass beads (which have only

a small size variation and a r e in a close-pack array) to test m o r e rigorously than has been d o n e previously t h e prediction of heaving pressures by Everett and I-Iaynes (1965). Based o n t h e experimental technique devised and the agreement shown between theory and experiment, t h e studies have been extended to more complex porous systems, which contain a wide r a n g e in pore size distribution, in order to ascertain the significance of this size distribution o n ultimate pressures. Such studies have been conducted in a preliminary way o n a silty soil of lcnown frost heave characteristics, o n bricks, a cement mortar, and a sandstone.

11.

Theory r .

I h e temperature at which ice will propagate through a pore restriction of given size in a water-saturated porous medium is given by the following equation (Sill and Sltapslri, 1956), provided the suction in the water is zero :

where

7-i is radius of curvature of the ice-water interface and also

pore radius,

Pi density of the ice,

Qf

latent heat of fusion,

T ,

temperature of melting a t zero curvature of the solid-liquid interface at standard pressure,

T

temperature at which freezing takes place with radius of curvature, r, in contact with water,

o i , ice-water interfacial energy.

Everett and Naynes (1965) have predicted heaving pressures in porous materials based on pore size, the parameter used previously by others (Penner, 1957, 1958, 1963) with the important addition that the geometry of the systems is defined precisely. r .

I h e case of special interest in the present paper is the close-pack array of uniform-size spheres (Everett and I-Iaynes, 1965). This porous body is overlain by a continuous ice lens, as depicted in the schematic drawing of Fig. 1 a and

b.

T h e pressure difference across the ice-water interface is given by

where

7-i is r a d i ~ ~ s of curvature of the ice-water interface,

pi

pressure on the ice,

p'

pressure in the water, and oi, interfacial energy term.

T h e pressure difference across the ice-solid interface a t A is given by

where r is the radius of curvature of the solid.

Comparing eqs. (2) and (3) gives the pressure at point A as

In the region of the water-solid interface at

B

PRESSURES DURING FREEZING

brought close t o C, is given by

2ui, 2

Ap

=

p:\

-

p>

= - --

+

- - : ( ~ i s - ~ ~ s ) .

7-i

Introducting t h e Young-Dupre equation

uis -UIvs = uiw COS H

,

I - 1

and defining

B'

a s

--,

eq. (6) may be rewritten in the f o r m ri cos H 201, cos H (1

+

B')

A p

= . . .. I- H e a t F l o w I c e - w a t e r l n l e r f a c e I C r i t i c a l R a d i u s r . e t w e e n T h r e e T o u c h i n g S p h e r e s W a t e r S e c t i o n A - A - S C H E M A T I C D R A W I N G O F I C E - W A T E R I N T E R F A C C P R I O R T O P R O P A G A T I N G T H R O U G H I ' O K C R E S T R I C T I O N B E T W E E N T H R F E T O U C H I N G S P H E R E S

Fig. 1. ( a ) Spheres in close-pack array

(b) Schematic drawing of ice-water interface prior to propagating through pore restriction between three touching spheres

T h e critical radius of curvature a t which a non-wetting phase displaces a completely wetting phase through t h e triangular shaped hole between three touching spheres has recently been investigated experimentally by Everett a n d Haynes (1965). I t may be noted that geometrically t h e radius of t h e smallest sphere that can pass t h r o u g h s u c h a hole is given by

I -

- 6.41

.

I-; ( 9 )

T h e reason for questioning t h e validity of t h e geometry in eq. (9) is that the interface between spheres is n o t a surface of revolution. Everett and Haynes determined t h e ratio of t h e sphere radius t o critical radius of curvature by a series of experiments involving capillary rise between close-pacli cylindrical rods, maximum bubble pressure between three spheres in mutual contact, and drainage of liquid f r o m a pyramid of

steel balls in a cubic close-pack arrangement. It was concluded from these experi- ments that the critical radius of curvature was approximately

-ADJUSTABLE (LOWER CELL 4 REQUIRED TEFLON ONLY) SLIDES L E D GLYCOL I N L E T T EXCHANGER ER PLASTIC C E L L (COLD) BRASS SUPPORTING COOLED GLYCOL , MILLIVOLT RECORDER ADJUSTABLE TEFLON SLIDES COOLING LIQUID LOWER (SLIDING) BRASS P L A T E

Fig. 2. (a) Ileave pressure cell - t o p elevation (b) Heave pressure cell - side elevation

PRESSURES DURING FREEZING

where ,- is radius of spheres as before,

and 7-1 critical radius of curvature at the narrowest constriction of

three touching spheres.

T h e concept of Everett and I-Iaynes recognizes two contributions to the heaving f o r c e : one, the increase in pressure on the ice that is required for the ice to pass through a narrow constriction; the other equalling Z ; r ~ o i , which is taken into account in the development of eq. (8) by considering the difference in the interfacial tensions between water-solid and ice-solid.

111. Experimental Investigation

T h e apparatus used to measure 11eavi1 upper cell is the cold side and is held in rests on a sensitive force transducer, wllich is fixed to the lower plate. T h e upper and lower plates a t the extremities of the cells are held together with four Invar rods 1.27 c m in diameter. Fluctuations in room temperature, which would give rise to small movements are avoided by circulating a liquid at constailt temperature through the Invar rods and end plates.

T h e specimeil is placed in a sample holder between the two cells in the centre section so that it will be in direct contact with the finned metal heat exchangers. T h e temperature of the glycol solution cir- culating round the finned heat exchangers of the two cells iillposes the temperature gradient across the specimen.

T h e sample holder has a sinall porous plate at the lower end for water transmis- sion to the specimen and the external water level lceeps the specimen water-saturated during the growth of the ice lens. Temper-

; forces is shown in Figs. 2 and 3. T h e

. fixed position ; the lower cell (warm side)

atures, which were monitored continuously Fig. 3. Photograph of frost heave pressure apparatus a t the ends of the specimen, showed fluctu-

ations of less than O.Ol°C over periods of several d a y s ; over shorter periods the variations were considerably less. Temperature variations at the freezing front were imperceptibly small as is indicated by the constancy of heaving pressures a t equilibrium. T h e experimental procedure with unconsolidated materials such as glass beads and soils was as follows.

A

water-saturated specimen inside a thin walled lucite sample holder was inserted between two cells and a thermal gradient established, with the upper side slightly below

0°C

and the lower side slightly above the freezing temperature.

Freezing was initiated by seeding the cold side with a frosted wire. After a 24-llr period, while the pressure was increasing, the freezing plane was stationary within the sample. On stabilization the pressures were reduced to zero by adjustment of the nuts holding the upper and lower cells together. This was repeated several times until the ice lens was estimated to be about 2 mm thick. Maximum forces in the vertical direction were then allowed to develop fully and were monitored on a millivolt recorder from the output of the force transducer. T h e whole process was repeated, each run taking several days, depending somewhat on the liind of sample used and on t h e magnitude of the forces developed. As would be expected, equilibrium was approached slowly as the forces approached a maximum.

During pressure build-up the temperature at each end of the specimen was not permitted to vary, so that t h e forces to be measured would rise only at the ice-water interface below the ice lens and not as a result of expansion of water freezing at reduced temperatures behind the ice lens.

IV. Resrilts

Heaving p?-essz~l-e nzeas~~?-enzents i ? ~ pads of glass bends. Glass beads were size fractionated by sedimentation in water to obtain size uniformity. Figure 4, curve A,

gives the size distribution of the original stocli from which the fractionations were made. T h e degree of variation was established by preparing smears on glass slides and photographing them at random. Some 800 to 900 beads were measured and counted in each size range to establish this variation. T h e results are plotted in Fig. 4.

4 8 12 1 6 20 24 2 8 3 2

S I Z E O F B E A D ( D I A I , M I C R O N S

PRESSURES DURING FREEZING 1407

I n curves

I3

_and C t h e median was used for calculations where the size of t h e particles was involved. I t may be seen that the median diameter of t h e s~llaller fraction was 12.0 kt; t h e median diameter of the larger size fraction was 19.4 i.1. T h e heaving force was also measured o n pads of t h e original stoclc of beads.

T h e size varied f r o m 9 to 19 kt (diam.) in the batch of smaller beads. From Fig. 4 it may be seen that some 10% were between 9 and 10 I.!, that another 10% were from 1 5 t o 19 61, and that 80% were between 10 and 1 5 LI. T h e larger beads ranged in size f r o m 1 5 to 27 /I, but 80% of them were between 17 and 22 kt. Five percent of t h e unsorted beads were smaller than 1 kt, and the largest were 30 p.

T h e Everett and Haynes relation (eq. (8)) relating bead radius to heaving pressure is plotted in Fig. 5 for t h e two oiw values of 30 and 40. T h e experimental relations between bead radius and heaving pressure a r e indicated o n t h e same figure. T h e value for the 1 2 kt diameter beads is an average of 1 0 different heaving force measurements; for the 19.4 kt size it consists of two different measurements.

I , , , , , , , I l l _{l ' l ' l '} " 6 = 30 2 U i w c o s tl I l t B ' ) A P - _r

-

6 ; 4 0 - - - U n s o r t e d B e a d s . 4 3 0 p 0 1 a - - 1 9 . 4 ~ B e a d s - - I l l 1 1 1 1 I l 1 1 ~ 1 1 1 1 1 1- 1 2 4 6 8 1 0 1 2 1 4 16 1 8 2 0 r , R A D I U S O F S P H E R E S , M I C R O N S

Fig. 5 . Everett ancl Haynes equation relating heaving pressure to sphere ri~clius

T h e experimental results give values for oi,, of 30 and 35. A t this point in the studies it was assumed that 35 is the more reliable value because t h e experiments were repeated a greater number of times for t h e 12 kt beads. Another assumption in t h e preparation of the bead pads was that a close-pack assemblage had been achieved, since it was f o r this geometry that t h e equation held. T h c pads were prepared by both jarring and tamping t h e sediment. Because t h e ice f r o n t has some capacity for rearranging t h e material at t h e freezing front, it is believed that something very close to a close-pack array was achieved at t h e interface between t h e particles and t h e ice lens. T h e values for o i , obtained in this experiment compare favourably with the most reliable results reported in t h e literature f r o m o t h e r methods of obtaining values for

It is believed that the experimental technique used is sufficiently refined for use in exploring ice lens pressures for materials of more complicated pore geometry. An attempt has been made to assess which pore sizes are predominant in establishing the maximum force attainable when a large pore size variation exists.

T h e important role of the smaller beads in the unsorted batch ranging up to 30 can be seen from the heaving pressures developed. T h e beads in Fig. 4, curve A, gave a heaving pressure of 1.28 lcg/cm2, which corresponds to bead size radius of 3.5 /-t

using a value of 35 for o i , ~ .

P r e l i ~ n i n a r y ice lensixg pl-essul-e nzens~~r-elner~ts 071 the surface of stzturntcd po1-OLLS solids.

Bricks. Frost action deterioration of building materials in structures has not been associated with the ice lensing mechanism until recently (Garden, 1965). It is, however, of real value to be able to understand the mechanism and so to be able to predict the possible range of stresses to which structural components can be subjected, due solely to freezing. In the context of this paper the practical significance is simply referred to, since the main objective is to relate ihe magnitude of the heaving stresses due to lens growth with the pore geometry.

Four briclis, as received f r o m the manufacturer, have been studied. Two were prepared by the extrusion method, one was a "pressed" briclc, and the last was a soft mud variety. Samples were cut to fit the sample holder of the heaving pressure apparatus described previously. T h e specimens were short cylinders 1.905 cm diameter and 0.635 cm long. T h e samples were talcell at least 1.27 cm from any outside surface i i ~ order to avoid slcin effects.

Sample preparation simply involved water saturation under vacuum. At the com- pletion of the ice lens pressure ineasurements the same specimens were oven-dried and again saturated under vacuum in order to obtain total porosity. Finally, they were oven-dried and their pore size distribution determined down to 0.1 /-t (diam.) with a mercury porosimeter.

T h e freezing technique was much the same as that described earlier, except that the ice lens was grown at the surface. T h e briclc samples were not, in fact, frozen, but were merely in coiltact with a growing ice lens. Again, the crystallization of the water was induced with a frosted wire. T h e pressure was lrept sufficiently low for a lens from 2 to 4 mm to develop rapidly, after which maximum forces were allowed to develop.

For the purpose of calculating the critical size of the pores involved a pore geometry has been assumed consisting of cylindrical capillary openings to the surface. T h e equation

2oiw

p = --

I.1

'

(11)

is assumed to apply, where 1-1 is the radius of the pore constriction of the briclr in

direct contact with the ice lens.

Based on the area exposed to the ice and the heaving force measured experimentally, the heaving pressure calculated was 0.95 lcg/cm2 f o r the soft mud briclc; 1.75 kg/cm2 f o r the pressed briclc ; 2.12 kg/cmVor one extruded type ; and 1.84 kg/cm2 for the other.

PRESSURES DURING FREEZING 1409 T h e pore size distribution f o r the bricks is shown in Fig. 6 ; other pertinent information is given in Table 1. I t may be noted that the porosimeter that was used is capable of filling pores down to 0.1 /* diameter and gives almost complete saturation f o r the bricks studied.

1 ' 2 3 4 5 6 7 8

P O R E R A D I U S , M I C R O N S

Fig. 6. Pore size distribution curves for bricks

Table 1. Percentage of pore volume and pore size properties of bricks

Total pore vol, pore vol, greater Limiting pore size'" Pore size smaller ~ ~identity i ~ of k sample vol. 0.05 active ill lensing than active in

by eq. (11) lensing (%) (%) ~ .

(!.O

(%) 1 soft mud 37.73 34.66 0.75

-.

9 2 pressed 42.68 39.13 0.41

=

11 4 extruded 34.11 33.92 0.34 r 7 7 extruded 37.42 35.08 0.39 2.11

*

radius of pores

T h e limiting radii calculated from heaving pressures did not vary greatly f r o m brick to brick. Bricks Nos. 1 and 2, which were the soft mud and pressed varieties, had a larger percentage of pores in the large size range and these gave lower heaving pressures, particularly brick No. 1. Almost all of the pores in the two extruded bricks were smaller than 1 /A r a d' ius.

T h e last column in Table 1 shows the approximate percentage volume, consisting of pores smaller than the pore size calculated from the maximum heaving pressure.

This shows the importance of the smaller pores in assuming an active role in the ice lensing mechanism. T h e maximum pressure measured did not in any of the cases studied correspond to the smallest pores of the bricks.

O t h e r P o ? - ~ L L S ~ ? ~ ~ t e l - i ~ z l . s . Ice lens heaving pressures were measured also in a sand- stone and in a cement mortar. T h e pore size distribution down to 0.05 ,L( radius is

given in Fig. 7. Equation (11) gave the limiting pore size radius active in heaving as 0.20 / ( for the cement mortar. Comparing total pore volume with the volume of pores

greater than 0.05 1.t shows that half the total volume of pores in the cement mortar is less tllan 0.05 1.t. In sandstone, limiting heaving radius 0.20, only 4 % of the total pore volume was contained in pores smaller than 0.05 p. T h e heaving pressures measured in the cement mortar were 3.51 kg/cm2 and in the sandstone, 3.57 kg/cm2.

- - C e m e n t M o r t a r - T o t a l P o r e V o l 3 4 . 9 0 % - L i m i t i n g H e a v i n g R a d i u s f o r M o r t a r a n d S a n d s t o n e - - S a n d s t o n e T o t a l P o r e V o l 1 4 . 8 2 % a - N o t e

-

R a d i u s o f P o r e C a l c u l a t e d f r o m M a x i m u m I c e L e n s P r e s s u r e - M o r t a r 0 . 2 0 4 ~ S a n d s t o n e 0 . 2 ~ -. - 0 - I I I * 1 2 3 4 5 6 7 8 P O R E R A D I U S , M I C R O N S

Fig. 7. M e r c u r ) ~ l ~ o r o s i ~ n e t e r pore distribution curves for s;~ndstone and cement mortar

Ice l e ~ ~ s i l z g . ~ I - P S S L L ? - C S i ? ~ silty soil. T h i s particular soil, described elsewhere (Penner,

1960), has been shown to be highly frost-susceptible. I t contains abount 9% clay size, 43% silt, and 48% sand. Samples were prepared at two different densities to compare behaviour at radically different pore size ranges. T h e less dense sample (1.87 g/cm3) was prepared by compaction in a normal compaction apparatus. T h e highly dense sample was compressed at 9 000 kg/cm2 for 10 min in the air-dry state. T h e samples were then oven dried and trimmed to the correct size f o r the heaving measurements. They were allowed to saturate from one direction prior to the start of freezing.

Figure 8 shows mercury porosimeter values for both densities in the air-dry state, and shows the radically different porosities and pore size distributions for the two

PRESSURES DURING FREEZING 1.111 samples. T h e total pore volu~lle d e t e r ~ n i n e d by water saturation was 32.0% of the total sample volunle for the compacted sample and 15.7% for the compressed s a ~ n p l e .

Heaving pressures of 1.43 lig/cni"or the high density s:unple and 1.23 lig/cm2 for the low density sample were measured, giving a critical pore size value, using eq. (111, of 0.5 and 0.6 cc, respectively. T h e r e is, therefore, some influence of density, as was shown previously (Penner, 1955), but because of the similarity in heaving pressures the main effect appears to Ile derived from t h e finest particles.

Fig. 6. T'ore size rlistril)utioi~ in sill ;it I\\.(, rlensilics in Ihc oven tlry stntc

It was obvious that o n wetting t h e nlaterial before {rewing some swelli~lg occurred aud that the curves shown in Fig. 8 would not apply exactly; but in many ways this preliminary method of pore size evaluation had merit. Iiegardless of how t h e sample is preparecl. the freezing front modifies the distribution of particles to some extent, as 1121s been shown by C o r t e (19fi2), :untl some tloubt remains as to how applicable bulk properties a r e to the situation a t the contact between the ice lens and the particles ;ut the freezing front.

V.

Summary

1. Pressures resulting from ice lens g r o w t h have been measured on pads of glass beads. which sire believed to be sufficiently uniform t o test the equation of Everett and IIaynes (1965). T h e pressures predicted from the equation correspond to experimental heaving pressures and give values for u , , between 30 ant1 35. 'The inost reliable value is considered to be 35.

2. Heaving pressure measurenlents with unsorted glass beads show t h e significance of the smaller beads in producing the ultimate ice lens pressures.

materials such as bricks, a cement mortar, anti 21 s:unclstone show that pore size clistri- bution is a significant factor. Brick No. 1, \vhich hacl a large percentage of large pores, gave considerably lower pressures. F r o m 7 to 11% of the pore volume, based

o n the total volume of the samples, hat1 a snlaller radius than that corresponding to thc maximum heaving pressure, using eq. !11).

ibi Of the porous solids studied celllent mortar ant1 sanclstone gave the highest pressures corresponcling to critical operative radii of about 0.2 ,I!.

ic) Pressures in a silty soil measured a t two densities indicate the influence of the finest particles in establishing heaving pressures a t the ice lens f r o n t in silty soils.

Acknowledgments

T h e a u t h o r wishes to ackno\\?!edge the assistance of his many colleagues, in particular

P.

.I. Sereda ancl

'T.

Iiitchie, and also D. Eldrecl f o r his patience in assisting \\it11 the m a n y hours of measurements involved in the various experiments. T h i s paper is a contribution f r o m the Ilivision of U ~ ~ i l c l i n g Iiesearcli, National Research Council. Canada, ancl is p ~ ~ b l i s h e d wit11 the approval of the P i r e c t o r of the Division.

Itef erences

1) COWI.:, 11. 1:. 1'362 \'ertic~ll migr;ltion o l particles in lront o l :L ~ n o \ . i n g Ircczing plane.

,T. (;(~of)/r.\~.i. lZo.~., 67, 1085-1090,

2 ) 1 < 7 1 ~ , 1 . I . n c - I \ Y N s .I. I . 1 Capillary [ ~ r o p c r t i c s oi some morlcl l)orc s y s t c n ~ s \vith special relerence t o I ~ - o s l tl;lmage. lZ11,l:"~l 1j11ll. S c , . ? c ) S(,I.., 27, 31-38.

1

0

(;.\IIDIIN, C;. I<. 19(i5 I);~niage to blesonry Constructions 1))- the Ice-Lensing Mechanism. I'rescncecl at [he I:ILI:4I~Cil3 Symposium on "bloisturc Pro1)lcms in 13uiltlings." I-lclsinlii. I:inl:untl, 8 pp.

4) I-'ESSI;R, IS. 1957 Soil nioislurc tcnsion ant1 ice scgrcg:~tion. I I ( ~ I I T S Y I \ , /(L'.Y. /:CI(II.(/ 1h1//. 168. 50-($4.

51 PI:NXI;R. I-. 1958 Pressures tlevclol~etl in :I granulnr system a s a result o l ice-segrcg;~tion. 1 li~y/r.x~<ry ~Z(J.Y. fio(11~1 S'f)i,(.itr/ lZ1y~t., 4 0 , 1511 --195).

ti\ PI'SXER, I-. 1%iO 'I'he importance of Ircczirlg rate in lrost action in soils. 1'1-01.. . ~ I , / C I . . So(.. / o r 'fi,.iti~rg. rr~rrl Jltrt(~~-iczl.\,, 60, 1151-ll(j5.

7) P E N N I X , I<. 1965 Frost heaving in soils. Procceclings o l the I'crmalrost. Intcrn:~tional Conference, A \ i ~ t . l(.c~tl. S(.i.-lVtrt. 1Zr.i. C:orl~rc.il. !'I//>/. 1287, 197-20".

8j SII.~.,

R.

C. and SIL\PS~CI, A. S. 1956 Mcthotl f o r the determination o l the surfilcc tension of solicls. f r o m their melting 1)oints in thin \vetlgcs. .T. C'/I~,III. I1/r)~.s., 2 4 , (jfll!l-(i51.