Mechanisms of rock breakdown by frost action: An experimental approach

Cold Regions Science and Technology, 17 ( 1990 ) 253-270 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

253

M E C H A N I S M S OF ROCK BREAKDOWN BY FROST ACTION: AN EXPERIMENTAL APPROACH Norikazu Matsuoka Institute of Geoscience, University of Tsukuba, Ibaraki 305 (Japan)

(Received June 8, 1989; revised and accepted July 14, 1989)

ABSTRACT

cesses on frost shattering may depend on the surface area per unit volume of the rocks.

Freezing behavior and frost shattering ofrocks were studied in the laboratory. Rates of frost shattering were determined for 4 7 different samples of saturated tvcks partially immersed in water by a decreasing rate of the longitudinal wave velocity during fi'eeze-thaw cycles. The ratio of surface area per unit volume to tensile strength gives a good estimation of the fi'ost shattering rate. This indicates that water migration caused by adsorptive suction participates in the frost shattering, as well as the 9% volumetric expansion. Frost shattering occurred in porous rocks despite the lower saturation level than the theoretical value derived from the volumetric expansion theory. Furthermore, the open system was much more effective in fi'ost shattering than the closed system was. Such moisture effects also demonstrate the large role of water migration in fi'ost shattering. The linear strain of some saturated rocks during a freeze-thaw cycle was measured with foil strain gauges, hnmersion in water increased the fi'eezing expansion of tuffs, although it affected the strain of a shale and an andesite only little. Low cooling rates resulted in small freezing expansion of rocks placed under the closed system because of creep of pore ice. These results suggest that the fi'eezing expansion of a rock consists of three components: two positive strains due to the 9% volumetric expansion of water, and water migration controlled by adsorptive suction, and a negative strain due to creep of ice. The frost shattering of the tufts would be primarily controlled by the water migration, and that of the shale and andesite is probably caused by the volumetric expansion. The relative contribution of the two pro-

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INTRODUCTION Frost shattering, or rock breakdown by freezing of water present in pore spaces and joints, has been considered as the prevailing weathering process in cold regions (e.g. French, 1976; Washburn, 1979). Both laboratory and field studies have yielded considerable data on this subject. Nevertheless, the mechanisms of frost shattering are not well understood (McGreevy, 1981; Lautridou, 1988 ). A number of recent literature studies have attributed the cause of frost shattering to either the volumetric expansion of freezing water, or water migration due to either capillary or adsorption force and the resultant ice segregation. The 9% volumetric expansion which accompanies the phase change of water to ice has been regarded long as the prime cause responsible for the frost shattering (e.g. O1lier, 1969; French, 1976). This theory was also supported by Davidson and Nye ( 1985 ) who found that the ice in a 1-mm-wide slot made in lucite produced p r e s s u r e s u p to 11 bar by volumetric expansion. Because this value is greater than the tensile strength of some porous rocks, the volumetric expansion must be a cause of frost shattering. An alternative mechanism w a s first proposed by Everett ( 1961 ) who regarded capillary suction as t h e c a u s e of water migration into the freezing front and of rock breakdown. Walder and H a l l e t ( 1 9 8 5 ) developed a theoretical model of crack growth in freezing rock. Their model is based on Gilpin's

© 1990 Elsevier Science Publishers B.V.

254

(1980) frost-heave theory which explains the water migration in terms of adsorptive suction. Such water migration through freezing porous rocks was observed also by laboratory experiments (Fukuda and Matsuoka, 1982; Fukuda, 1983). Thus, water migration must also be responsible for frost shattering, although, whether the capillary or adsorptive suction causes the migration has not yet been verified. These evidences lead to a hypothesis that a combination of both processes, i.e. volumetric expansion and water migration, controls frost shattering, as suggested by Tharp (1987). Nevertheless, there is no experimental evidence supporting this hypothesis. The present study was intended to evaluate the relative contribution of the two processes to the rate of frost shattering. For this purpose, a series of laboratory experiments were conducted: (1) freeze-thaw tests for relating rock properties to the frost shattering rate; (2) freeze-thaw tests for evaluating the moisture controls of frost shattering; and (3) measurements of linear strain during a freezethaw cycle. Factors affecting the frost shattering rate were discussed on the basis of these experimental results.

F R E E Z E - T H A W TESTS FOR V A R I O U S ROCKS IN S A T U R A T E D OPEN S Y S T E M S A number of rocks were subjected to the repetition of freeze-thaw cycles under the same moisture conditions. The frost shattering rates of these rocks were determined by the ultrasonic method. The validities of previous theories concerning the mechanism of frost shattering were discussed through the investigation of responsible rock properties for the frost shattering rate.

NORIKAZU MATSUOKA

Hence, temperature oscillations above and below 0 ° C may result in the shattering of such rocks, not by frost action but by hydration of adsorbed water ( D u n n and Hudec, 1966; Fahey, 1983). To eliminate the influence of hydration shattering, the rocks readily damaged by wetting-drying were precluded from the tests. Several physical and mechanical properties of rock samples, expected to control the rate of frost shattering, were measured or indirectly calculated. These properties are porosity, dry bulk density, specific surface area, mean pore radius, tensile strength, longitudinal wave velocity, anisotropic factor and Young's modulus. Methods for their determination are described in the Appendix, together with lists of determined values for all samples. Experimental procedures Boulder-sized samples were cut into cubic specimens with an edge of 5 cm length. About five "intact" specimens without visible fractures were used for the freeze-thaw tests. After saturation with water in a vacuum chamber for 72 h, the specimens were placed in a small metallic container, and submerged in water for one third of their heights; then, they were covered with gauze to prevent drying. Such a treatment enabled the specimens to be held under a "saturated closed system" condition during the tests. The container, in which specimens were placed, was transferred to a climatic cabinet and then subjected to the repetition o f half-daily freeze-thaw cycles: the maximum and minimum room temperatures were + 20 ° C and - 20 ° C (Fig. 1 ). This temperature cycle is useful to facilitate rock breakdown and hence data collection, despite the greater range

Samples ~

,,

Forty-seven boulder-sized rock samples were collected from various localities. They consist of twenty-eight sedimentary, eighteen igneous and one metamorphic rocks. Geological ages range from Paleozoic to Quaternary. They also show wide variation in physical and mechanical properties. Pore water in some argillaceous rocks did not freeze even at a temperature as low as - 2 0 ° C .

=L o

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-20 i

Time (h)

Fig. ]. The temperature cy¢|c used for freeze-thaw tests.

255

MECHANISMS OF ROCK BREAKDOWN BY FROST ACTION

and shorter period compared with the diurnal freeze-thaw cycles held in the field. The temperature record at the center of a tuff-b specimen indicates that both freezing and thawing penetrate into the center of specimen within a temperature cycle (Fig. 1 ). The longitudinal wave velocity Vp of a rock specimen was measured every 2-10 cycles for porous rocks and every 50-100 cycles for compact rocks. The deterioration of the specimen was detected through a reduction in Vp. The specimen has been subjected to up to 1000 freeze-thaw cycles, unless completely broken before 1000 cycles.

Rf was calculated by fitting a straight line to the

curve of Fp within the limit of measurement. For anisotropic rocks with an anisotropic factor Ai of more than 1.10, Rfwas calculated as the mean value for the three axes of a cube. The mean values of Rf are cited in the Appendix. The value of Rr is nearly proportional to the rate of disintegration determined from a reduction in dry weight (Matsuoka, 1988). This indicates that Rf predicts the rate of subsequent weight reduction. If it was possible to determine Rfeven for a rock which shows no visible breakage, Rrwould be a better scale of the frost shattering rate than the rate of weight reduction.

Scale of frost shattering rate Figure 2 shows changes in Vp during 300 freezethaw cycles for the nine sandstones (sandstones ai ). Rocks with low initial values of Vp draw steeply descending curves of Vp, whereas those with higher initial values show rather gentle curves. Because Vp reduces with enlarging cracks and pores in the specimen, the rate of such microscopic breakage is expressed by the decreasing rate of Vp, which is given by the following value of Rr: R f - ( Vpo - Vpk )

( 1)

V~ok

where k is the number of freeze-thaw cycles, Vpk is the value of Vp after k cycles and Vpo is the initial value of Vp. When the specimen is considerably broken, Vp can not be determined any further. In such an instance, 6~E

{a

5 4 3

~g '

140

i 240 ' 340 Number of freeze-thaw cycles

Fig. 2. Reductions of longitudinal wave velocity Vpof sandstone specimens during 300 freeze-thaw cycles.The letters in this figure show the type of sandstone.

Relationships between rock properties and frost shattering rate Some previous studies proposed empirical criteria for evaluating the frost susceptibility, or the frost shattering rate, in terms of rock properties. Fukuda ( 1974 ) suggested that rocks with a porosity of more than 20% were frost susceptible, because such rocks were completely broken within 30 freeze-thaw cycles. Lautridou and Ozouf (1982) found that rocks with a porosity of less than 6% were little damaged after several hundreds of freeze-thaw cycles. Litvan (1973), in his freeze-thaw experiments on bricks, concluded that good resistance was expected from the bricks with a specific surface area of less than 5 × 102 m 2 kg- ). Figure 3 shows the relationships between Rf and four rock properties, i.e. the porosity n, tensile strength St, specific surface area Sw and mean pore radius g. These relations are summarized as follows. ( 1 ) The value of Rf tends to increase in proportion to n. Many igneous rocks, however, show low Rrvalues despite high porosities. Thus, both Fukuda's (1974) and Lautridou and Ozouf's (1982) criteria give only a rough estimation of frost susceptibility. (2) Rocks with higher St values generally have lower Rf values, or are more resistant against frost shattering. Nevertheless, several igneous rocks show low Rf values despite low St values. (3) There is only a weak correlation between Rf and S,, although Litvan's (1973) criterion gives a rough estimation of frost susceptibility.

256

NORIKAZU

10 °

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Fig. 3. The frost shattering rate Rfas a function of the porosity n, tensile strength St, specific surface area Sw and mean pore radius F. The letters, A, B and C show critical values suggested by Lautridou and Ozouf ( 1981 ), Fukuda (1979) and Litvan (1973), respectively. (4) Little correlation is found between Rr and f. As a result, the frost shattering rate can not be indicated by any of the above-mentioned rock properties alone, but may be dependent upon combination of several properties. Mechanisms o f frost shattering should be considered for further discussion. Application

of volumetric

expansion

theory

When pore water completely freezes in a saturated closed system o f porosity n, its 9% volume increase produces the potential linear-freezing strain ~v such that (Mellor, 1970):

~lv = 0 . 0 3 n

(2)

This equation assumes that pore ice in the sample is subject to no constraint from pore walls. Because the frost shattering is regarded as a tensional failure (e.g. Everett, 1961; Winkler, 1968; Mellor, 1970), the shattering force originating from the volumetric expansion, Fv, takes the form: Fv = ElvEt = 0.03nEt

(3)

where Et is Young's modulus in tension. When the shattering force exceeds the tensile strength o f a rock, the rock fails. The rock breakdown, however, may occur in spite o f Fv < St. This

MECHANISMS

OF ROCK BREAKDOWN

BY FROST ACTION

257

Application of the capillary force theory

10 0

• Sedimentary rocks o Igneous rocks

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Iv Fig. 4. Relationship between the frost shattering rate Rr and the parameter I~=0.03 n Ed/S, derived from the volumetric expansion theory. A metamorphic rock is included in igneous rocks.

The amount of frost heave in fine grained soils exceeds usually the value predicted by the volumetric expansion theory (e.g. Taber, 1929). This is due to water migration from the unfrozen layer towards the freezing front. Such water migration was observed also in the freezing of a porous rock (Fukuda and Matsuoka, 1982; Fukuda, 1983). If the volume increase due to water migration is much greater than that due to the phase change of pre-existing water, the shattering force would be practically controlled by the former process. The capillary force theory is one of the theory concerning water migration during freezing, first formulated by Everett ( 1961 ). This theory predicts that a suction force causing water migration is determined by the pressure difference at the curved meniscus of the ice-water interface. The suction force is regarded to be equivalent with the heaving (or the shattering) force (Everett, 1961 ). Assuming that ( 1 ) the pores are initially saturated with water, and (2) both pores and the ice-water inter10 0

is because heterogeneous structures in rocks permit stress concentration to some weak pores or cracks, and also repeated freeze-thaw action leads to a fatigue failure. Thus, a rather realistic condition for the rock breakdown is that the frost shattering rate depends on the ratio of the shattering force to the tensile strength. Then, substituting the dynamic Young's modulus Ed for E t o n the assumption that Et 7:Ed, the ratio is given by a dimensionless parameter Iv: Iv - nE..______jd 0.0 3

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In general, Ed is significantly greater than Et (Jaeger and Cook, 1979 ). Figure 4 indicates that Rr increases in proportion to Iv. This relation, however, is clear only for sedimentary rocks: many igneous rocks have low Rrvalues despite high Iv values. Thus, the 9% volumetric expansion on freezing may be responsible for a part of the shattering force causing the rock breakdown, but it can not be the unique cause of frost shattering.

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258

NORIKAZU MATSUOKA

face are spherical, the shattering force produced by the capillary suction F¢, or the maximum suction force at equilibrium P . . . . is expressed by:

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Figure 5 shows the relationship between rr and Ic, where a~,v=3.3×10 -8 MN m -I (Hobbs, 1974) is used. Although Rr is proportional to Ic as a whole, the correlation between the two is poor. The capillary force theory, therefore, can not explain the whole mechanism of frost shattering.

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Since a much larger heaving force than the calculated value of Fc was observed in soil freezing experiments (e.g. Loch and Miller, 1975; Takashi et al., 1981 a ), the capillary force theory has been suspected and replaced by the adsorption force theory. The latter theory states that the freezing film water adsorbed on soil particles, trying to retrieve the loss of its thickness, generates a suction force (Takagi, 1980). The shattering force due to adsorptive suction Fa, however, has not yet been formulated. The simplest assumption is that Fa is proportional to the surface area per unit volume of rock Sv, because an increase in & is responsible for increasing the amount of unfrozen film water (Dillion and Andersland, 1966; Anderson and Tice, 1972) and hence for increasing the heaving (or the shattering) force (Takashi et al., 1981b). Then, disregarding the time effect, F~ is written as:

Fa :,:&

(7)

where Sv =Pd Sw; Pd is the dry bulk density. Accord-

10 9

(MN'lm)

Fig. 6. Relationship between the frost shattering rate Rr and the parameter la=Sv/S, derived from the adsorption force theory. ingly, the ratio of the shattering force to the tensile strength is given by a parameter I~:

la-

Application of the adsorption force theory

......

o/~ee o :°/~b //o •

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i

/

where P~ is the pore ice pressure, Pw is the pore water pressure, a~w is the interfaeial free energy between ice and water (constant) and r~ is the radius of the ice-water interface (Everett, 1961 ). The value ofr~ can be replaced by : (e.g. Everett, 1961; Blachere and Young, 1972). Then, the frost shattering rate must be a function of the ratio of the shattering force to the tensile strength such that: 20"iw

o

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rc

/c =

•

/

Sv

S,

(8)

A fairly good correlation is found between Rrand la except a few data points (Fig. 6). The correlation between the two axes in Fig. 6 is higher than that in Fig. 5 where the shattering force is expressed by the capillary suction; and is also higher than that in Fig. 4 where the force is derived from the volumetric expansion, because the relation in Fig. 6 fits both sedimentary and igneous rocks. The dashed line in Fig. 6 indicates that Rr is expressed by a power function such that:

(Sv) '.2

Rr::c\ & j

(9)

These freeze-thaw tests for the saturated open system, therefore, indicate that the frost shattering force of a majority of tested rocks is primarily influenced by the water migration due to the adsorptive suction generated in unfrozen film water; and that the 9% volumetric expansion may also participate in the shattering of several rocks.

MECHANISMS OF ROCK BREAKDOWN BY FROST ACTION FREEZE-THAW TESTS MOISTURE CONDITIONS

UNDER

259

DIFFERENT

The saturated open system taken in the freezethaw tests is a rather unusual condition in field locations. Effects of other moisture conditions, i.e. unsaturation and closed systems, should also be considered. Although the moisture conditions have been regarded as an important control of frost shattering (McGreevy and Whalley, 1985; Hall, 1986), there are few detailed laboratory studies on this subject. Effects of two moisture variables, initial water content and water-supply conditions were examined in the present tests. Three kinds of rocks, tuffb, tuff-c and sandstone-g (see Appendix), were used for the tests. All of them are little resistant to frost action. Experimental

procedure

For each rock type nine cubic specimens with an edge of 5 cm in length were prepared. After the dry weight, Wd, and saturated weight, ~ , were determined, saturated specimens were exposed to air for different time spans, except one was kept at the saturation point. The specimens were set to various water contents through such a differential desiccation. The water content is expressed by the degree of saturation, S~:

s~-

( Wn-- Wd)

(Ws- H~)

system: the latter was already described in the previous section on "Freeze-thaw tests for various rocks in saturated open systems". Effect

of initial water

tering

rate

content

on frost

shat-

The repetition of freeze-thaw cycles resulted in a significant reduction in Vp when Sr is greater than 0.75 (Fig. 7). Above this critical value, the frost shattering rate increases lineary with St. Visible damages also appeared, but only in rocks with high Sr values (Fig. 8 ). Fagerlund ( 1979 ) found that concrete and bricks are damaged by frost action when Sr is greater than 0.80. He called this value the critical degree of saturation. The present tests showed that the critical degree of saturation of some porous rocks lies around 0.75, close to the Fagerlund's value. The volumetric expansion theory implies that the rock is possibly damaged when further expansion occurs after ice has filled all pore spaces. High saturation levels are required for this situation, because at low saturation levels the expanding ice escapes into other open spaces and hence exerts no shattering force to the rock. Assuming that the 9% volumetric expansion is the only cause of rock breakdown, the potential linear freezing strain for an unsaturated rock eTv is expressed by: •

t/

e~v=~(1.O9Sr- 1 )

(11)

(LO)

where IV, is the weight after desiccation. After S~ was determined, the longitudinal wave velocity of the specimens was also measured. Then, they were sealed in aluminum-foil so that their water content were kept constant; hence, they were placed under the closed system condition. The specimens were subjected to 50 freeze-thaw cycles: the temperature curve is the same as in Fig. 1. Every 10 to 20 cycles, their Vp values were remeasured. The frost shattering rate is indicated here by the ratio of Vpso (the value of Vp after 50 cycles) to Vpo (the initial value of Vp). The influence of water supply was evaluated by a comparison between the reduction in Vp of the saturated specimen under the closed system and that under the open

1.0

I~-°-"~|

°

"h

O

$ o.5 • Tuff-b • Tuf f-c • Sandstone-g 0

'

'

'

' 0~5. ~ ~ '

~ 10.f

Sr

Fig. 7. Relationship between the frost shattering rate Vpso/l~o and the degree of saturation St.

260

NORIKAZU MATSUOKA

(-

¢0 E

2.5 2

I

Tuff-b Tuff-c .

0

1.5 l ~

Open Closed system system o o ¢ -" ~. ~, ~L J.

~

- ~ =

~-

1.0 0.5 I

0

i

I

I

i

10 20 30 40 50 Number of freeze-thaw cycles

Fig. 9. Reductions of longitudinal wave velocity lip of rocks during 50 freeze-thaw cycles: comparisons between open and closed systems.

Fig. 8. The state of tuff-c specimens after freeze-thaw tests. (a) The specimens have different degrees of saturation Sr. (b) Both specimens were saturated with water but tested for different water-supply conditions. Thus, at least Sr>0.92 is required for the breakdown of rocks. However, as shown in Fig. 7, frost damage occurred in these rocks with St< 0.92. Furthermore, some rocks expanded significantly during freezing even if St was about 0.5 or well below 0.92 (Mellor, 1970). These results also suggest that the 9% volumetric expansion is not the unique cause of frost shattering.

Effect of water-supply condition on frost shattering rate In spite of identical saturated rocks (St= 1.0 ), the water-supply condition greatly affected their frost shattering rates. The submerged specimens reduced Vp rapidly during first several freeze-thaw cycles (Fig. 9 ), and were completely shattered before ten cycles (Fig. 8b). By contrast, the sealed samples reduced Vp much slowly (Fig. 9), and lost not more than 50% of their initial weights even after 50 cycles.

Thus, the open system is much more favorable to frost shattering than the closed system. In the open system, an increase in ice volume due to water migration leads to large damage of the rock; whereas in the closed system, only pre-existing water redistributes within the rock and hence the resultant damage would be rather small. These results also suggest that the water migration accompanied with freezing plays a large role in the frost shattering of some porous rocks.

M E A S U R E M E N T S OF FREEZING STRAIN USING STRAIN GAUGE The freeze-thaw tests revealed that at least two processes, i.e. the 9% volumetric expansion, and water migration, participate in the frost shattering of rocks. However, the relative contribution of these processes to the frost shattering rate has yet to be evaluated. The detailed investigation of rock behavior during a freeze-thaw cycle enables such an evaluation to be made. With the progress of freeze-thaw cycles, the repetition o f expansion and contraction leads to the accumulation of strain in a rock (Douglas et al., 1987 ) and subsequently to the failure of the rock. This

MECHANISMS OF ROCK BREAKDOWN BY FROST ACTION

I

Gauge leads Connector ~

261

~

strs,n

Rock specimen

ilicone rubber V~////BL~//A p o x y c e m e n t -I~_/_Z/_Z/J_J_~ ] Rock specimen [

Wetproof

putty

'

Fig. 10. Attachment and water-proofing of a strain gauge. The thermistor sensor monitors the rock temperature at l cm depth.

suggests that the amount of expansion produced during freezing affects the frost shattering rate of the rock. From this viewpoint, the freezing strain o f several rocks was measured with strain gauges and analyzed in the light of the theories of frost shattering.

Experimental procedures The temperature and strain of rocks were recorded simultaneously as functions of time. Effects of water-supply conditions and cooling rates were examined. Tested rocks are shale-g, tufts-b, -c, -g and andesite-e (see Appendix). The size of specimens is the same as the freeze-thaw tests. The freezing strain was measured with a foil strain gauge: Kyowa KFL-type gauge with a length of 5 m m , a resistance of 120 ohms, and a gauge factor of 2.1%. This gauge is self-compensated against tem-

peratures ranging from - 2 0 0 to + 30 ° C, so that an error is limited to less than _+ 1.8 × 10 -6 ° C - t within the compensated range. Variations in temperature may also provide the error by changing the resistance of a lead wire. An apparent strain due to such a change was minimized using the three-lead-wire system (Fig. 10). These wires were connected to a strain recorder whose scale can be read to the order to 10 -6 strain. Attachment and coating of the gauge are illustrated in Fig. 10. The details were described in Matsuoka (1988). For sedimentary rocks, the gauge was attached perpendicular to bedding planes so that the m a x i m u m strain could be recorded. The coated specimen, being saturated with water under vacuum, was tested either for the saturated closed or for the saturated open system. Rock temperature was monitored with a thermistor sensor 2.0 m m in diameter installed in the specimen. The mean temperature of the specimen was represented by the value at a depth of 1 cm. The accuracy of the therm o m e t e r is 0.2°C. In the tests for evaluating the influence of moisture condition, the room temperature was controlled as in Fig. 1 la: the specimen is cooled and heated with a rate of 6 ° C h - J. In the tests for evaluating the cooling rate effects, the room temperature was controlled as in Fig. 1 lb: on freezing initiation, a brief thermal shock was given by rapid cooling so that a delay of freezing due to supercooling might be avoided; and then the specimen was cooled with a rate of either 2 or 6°C h -~. The latter tests were conducted only for the closed system.

(a)

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2

i

i

4

I

i

6

Time (h)

0

2

4

6

Time (h)

Fig. 11. Room temperature regime used for measurements of freezing strain, for testing the influences of moisture conditions (a); and of cooling rate Rc (b).

262

NORIKAZU MATSUOKA

The strain gauge involves an error of less than + 1.8× 1 0 - 6 ° C - l if the rock has a coefficient of thermal expansion of 10.8× 10-6°C - ' . The error enlarges as the deviation of the coefficient increases from 1 0 . 8 × 1 0 - 6 ° C - ' . Such an apparent strain produced by a change in temperature was eliminated from the measured strain curves for wet rocks, using calibration curves drawn for dry rocks which show no freezing expansion (Matsuoka, 1988 ). The strain just before freezing is defined to be zero, and the expansion is indicated by the positive. E f f e c t of w a t e r - s u p p l y strain

c o n d i t i o n on f r e e z i n g

A typical data for tuff-b in the closed system is shown by two illustrations (Fig. 12 ). After the initial freezing the specimen expanded rapidly with descending temperature. The expansion slowed down below - 5 ° C, and virtually stopped at about - 1 0 : C . The thawing contraction drew a nearly symmetrical curve to the freezing expansion. Thus, both expansion and contraction occurred mostly between 0°C and - 5 °C. The same rock, placed under the open system, showed similar behavior to that under the closed system, except for the difference in the total expansion (Fig. 13 ). A comparison between Figs. 12 and 13 indicates that the m a x i m u m freezing strain EL m a x of tuff-b in the open system is about twice as great i

lO

i

i

I

as that in the closed system. This result is consistent with the preceding result that tuff-b, when subjected to freeze-thaw action, was much more rapidly broken under the open system. This is probably due to water migration from the exterior to the frozen rock, which causes greater expansion and hence more rapid breakage by cyclic freeze-thaw action. Typical results for other rocks are shown together in Fig. 14. All rocks expanded rapidly between 0°C and - 5 °C. This temperature range coincides with the period during which most of pore water freezes in rocks, releasing the latent heat. This result, however, disagrees with the theoretical prediction by Walder and Hallet ( 1985 ) who stated that freezing is most effective in producing crack growth between - 4 ° C and - 15 ° C. Such a disagreement may be because the rock properties assumed in their calculation are quite different from those used in the present tests. The values of EL max obtained from the open system tests for the three tufts are about 1.5 times as great as those from the closed system tests (Table 1 ). This indicates that water migration greatly affects the frost shattering rate of these tufts. By contrast, there appeared to be no significant effect o f the availability of water on eL max of andesite-e and possibly shale-g (Fig. 14, Table 1 ). This suggests that, despite the open system condition, the external water migrates little into these rocks during freezing and hence contributes scarcely to the freezI

i

(a)

(b) 4

3~

?

a~ o x

Q)

-lO

E

G) k-

09

1

-20

o -3O

0

i

I

r

I

I

2

4

6

8

10

Time (h)

I 12

-20

I

I

-10

i

I

0 Temperature (°C)

-1 10

Fig. 12. Typical strain data for a saturated tuff-b specimen during a freeze-thaw cycle: a closed system test with a cooling rate Rc= 6 °C h-~. (a) Temporal variations in rock temperature and strain. (h) Strain versus rock temperature.

MECHANISMS

OF ROCK BREAKDOWN

r

r

BY FROST ACTION

~

1

/"

263

r

5

i

i

(b) <~:~~

I

i

4 A

A

-

o

o

3~

3

==

-10

I- -20

2

Strain--

j

C

'

._=

2

t~ t/)

1

-30 =

0

2

4

6

8

10

12

,

I

-20

14

-10

Time (h)

i

i

o Temperature(°C)

-1

10

Fig. 13. Typical strain data for a saturated tuff-b specimen during a freeze-thaw cycle: an open system test with a cooling rate R ¢ = 6 ° C h - t . (a) Temporal variations in rock temperature and strain. (b) Strain versus rock temperature. i

i

t

i

Shale-g

Tuf

Tuff-c

-

~

TII

II

Tuff-g

Tuff-g

Andesite-e

I

-20

I

-liO

0 10 Temperature (°C)

(a) Closedsystem

-20

I

-10

0 10 Temperature (°C)

(b) Opensystem

Fig. 14. Strain curves for several rocks against rock temperature: comparisons between closed and open systems.

NORIKAZU MATSUOKA

264 TABLE 1 Measured maximum freezing strain ( X 10- 3 ) for different water-supply conditions Cooling rate 6°C h Run

Tuff-b

Shale-g

Tuff-c

Andesite-e

Tuff-g

closed

open

closed

open

closed

open

closed

open

closed

open

1 2 3 4 5

1.52 3.99 5.70 3.50 2.20

3.71 5.03 2.22 2.06

3.29 2.97 3.06 2.43 3.25

4.93 4.86 5.58 6.14 5.30

2.82 2.13 1.45 1.72 2.05

3.75 2.82 3.24

4.39 5.20 4.07 2.60

5.52

1.40 1.32 0.71 1.20

1.34 1.15

Mean

3.38

3.26

3.00

5.36

2.03

3.27

4.07

5.52

1.16

1.25

(a)

(b)

10

R c = 6 °C h -1

R c = 6 °C h"1

Rc = 2 °C h -1

Rc =

Tem

4

2 °C h"1

x

-10

x~X i~. -20 train

,Z

3 o

¢.2

CO 1 0

-30 0

I

l

I

I

I

2

4

6

8

10

I

12

Time (h)

-20

-'mio

I

-1 10

0

Temperature

(*C)

Fig. 15. Effect of cooling rate Rc on freezing strain of saturated tuff-b: closed system tests. (a) Temporal variations in rock temperature and strain. (b) Strain versus rock temperature.

ing strain. In other words, these two rocks are believed to be shattered mostly by the 9% volumetric expansion. Pore water pressure during freezing was monitored by Fukuda and Matsuoka (1982) and Fukuda (1983), using tuff-b and andesite-e. These studies showed that during the freezing process of tuff-b the matric suction in the unfrozen layer rose with approaching freezing front, thus suggesting that pore water moved toward the frozen layer. By contrast, the matric suction in the unfrozen layer remained constant during the freezing process of andesire-e; hence, water moved little toward the frozen layer. This contrast coincides with the present mea-

surements of freezing strain and thus supports the idea that water migration is responsible for the frost shattering of tuff-b, whereas only the volumetric expansion contributes to the shattering of andesite-e.

Effect of cooling rate on freezing strain The freezing strain of tuff-b was measured for two kinds of cooling rate Re. Figure 15 indicates that the higher cooling rate ( R c = 6 ° C h -~ ) results in both more rapid expansion and a somewhat greater value Of ELmax than the lower rate ( R ~ = 2 ° C h - l ). On average, eemax for the higher rate is about 1.4 times as great as that for the lower one (Table 2).

MECHANISMSOF ROCKBREAKDOWNBYFROSTACTION TABLE 2 Measured maximum freezing strain (X 10-s) of tuff-b for different cooling rates Run

Cooling rate ( °C h-i ) 6

2

1 2 3 4 5

2.05 2.62 3.07 2.62 3.31

1.89 1.76 1.18 2.56 2.38

Mean

2.73

1.95

5 oT-

0

.c_

Andeslle-e

~-5

ffl

265 at - 10°C for 24 h. The contraction was recorded in both rocks for a long period (Fig. 16). Rates of contraction decreased with time. This behavior can be explained by the creep of pore ice constrained from the rock body, because of the similarly with the primary creep curve of frozen soils (Andersland et al., 1978). The alternative explanation is due to ice extrusion into the void spaces involved in unsaturated rocks (Tharp, 1987). However, such an extrusion occurs unlikely in saturated rocks like the present case, because there is no space for ice to escape. This result indicates that at least the contraction of rocks due to the creep of pore ice is responsible for decreasing the freezing expansion. Because the contraction progresses with time, high cooling rate is favorable to an increase in ELmax of the rock in closed systems. In open systems, however, low cooling rates may favor frost shattering because prolonged freezing periods enable continuous water supply (e.g. Walder and Hallet, 1985 ).

-10 Tuff-b

-15

-200

|

5

i

10

I

15

I

20 Time

25

FACTORS AFFECTING FREEZING STRAIN A N D F R O S T S H A T T E R I N G R A T E OF ROCKS

(h)

Fig. 16. Contraction of two rocks maintained at - 10°C after freezing with a cooling rate Rc= 6 °C h- ~:closed system tests. Blachere and Young (1974) pointed out that ELmaxof ceramics in the closed system increases with increasing cooling rate. They attributed this to the plastic deformation (or creep) of ice, because they also found that the ceramics contracted slowly when held at a constant subzero temperature. Similar contraction behavior was also observed in frozen concrete (Litvan, 1972). Tharp (1987) stated that the ice pressure exerted to rocks is also relaxed through the ice deformation. Nevertheless, there has been no laboratory evidence supporting the relaxation of ice pressure in rocks. In order to check whether such a relaxation appears in frozen rocks placed under the closed system, temporal variations in strain were measured at a constant subzero temperature, using tuff-b and andesite-e. After a saturated specimen was cooled to - 10°C with Rc = 6 °C h - t , the room temperature was held

The volumetric expansion theory predicts that the maximum freezing strain for a saturated closed system is calculated by Eq. 2 on the assumption of no constraint from the rock. The calculated values of EL max, however, are several times as great as the measured ones for the saturated closed system (Table 3), as pointed out by Mellor (1970); and they are even greater than those for the saturated open system. This suggests that the assumption is not TABLE 3 Comparison between calculated and measured maximum freezing strains Rock type

Calculated

Measured

(xlO

(xlO

Shale-g

10.1

Tuff-b Tuff-c Tuff-g Andesite-e

11.8 13.7 13.6 6.75

-3)

3.38 3.00 2.03 4.07 1.16

-3)

266

NORIKAZU MATSUOKA

necessarily correct, and hence that the freezing strain is significantly reduced by the contraction of the rock. Because the elastic contraction of ice is estimated to be negligible in comparison with eL max (Mellor, 1970), the greatest part of the contraction would be produced by the plastic deformation of ice. Another possibility to decrease the calculated freezing strain is due to the unfrozen water which still exists below 0°C, because such water does not contribute to the freezing expansion. Low et al. ( 1968 ) estimated the amount of unfrozen water in soils from the relationship between freezing point depression and water content. This method was applied to three rocks (shale-g, tuff-b and andesite-e ); and as a maximum 20% of pore water in a saturated rock was estimated to be still unfrozen at - 2 0 ° C (Matsuoka, 1988). However, even though the calculated values in Table 3 are cut by 20%, they are still several times greater than the measured ones. Thus, the contraction due to the creep of ice must reduce a large part of the freezing expansion produced by both volumetric expansion and water migration. As a result, the linear freezing strain eL of a rock is written as: EL = ELV + ELW + ELD

( 12 )

where ELy is a positive strain due to the 9% volumetric expansion of pre-existing water, ELWis a pos-

itive strain due to water migration, and ELOis a negative strain due to the creep of ice and possibly to ice extrusion. Then, the frost shattering rate is expressed as a function of a parameter If: If--

(ELy +~LW + ~LD)E,

&

(13)

The linear strain due to the 9% volumetric expansion for an unsaturated rock was given by e~_v in Eq. 11. Introducing the unfrozen water content 0,, Eq. 11 is rewritten by: ELv= ~ ( 1.09Sr - 1 ) (n-O,)

(14)

The value of 0u is also a function of temperature and specific surface area (Anderson and Tice, 1972). More complicating factors seem to control the other two strain components. The results described in the section on "Freeze-thaw tests for various rocks in saturated open systems" suggests that the surface area per unit volume controls the adsorp-

tive suction and hence the value of ELW. Additionally, if the water migration is ruled by Darcy's law, ELW would also depend on such factors as the hydraulic conductivity o f the rock and the duration of the freezing phase. The third term, ELD, is probably controlled by the stress applied to pore ice and the cooling rate, as suggested in the section on "Measurement of freezing strain using strain gauge". Equation 13 indicates that the prime cause of frost shattering varies with rock type, depending on the relative magnitude between the two positive strains, ELV and ELW. For instance, the frost shattering of shale-g and andesite-e is attributed to the 9% volumetric expansion, because their ELw values seem negligible (Table 1 ). Rocks with small value of Sv including these two rocks may produce little adsorptive suction; hence, they would also be shattered by the volumetric expansion. By contrast, the prime cause of the shattering o f the tufts and probably rocks with large Sv values is believed to be water migration, because the effect of ~LW seems significant (Table 1).

CONCLUSIONS The freezing strain of rocks consists of three components: two positive strains, i.e. due to the 9% volumetric expansion of pre-existing water and, due to water migration controlled by the adsorptive suction, and a negative strain due to the creep of pore ice. The rate of frost shattering depends on Young's modulus, tensile strength and the factors controlling these three strain components. These factors include: surface area per unit volume, porosity, degree of saturation, availability o f water and cooling rate; and possibly hydraulic conductivity, duration of freezing phase and unfrozen water content. The prime cause of frost shattering depends on the relative magnitude between the two positive strains. Rocks with a large surface area per unit volume like tufts are characterized by much greater freezing expansion as well as higher frost shattering rate in open systems than in closed systems; hence, they are shattered largely due to the adsorptive suction. By contrast, rocks with small surface area show no significant difference in the maximum freezing expansion between the closed and open systems;

267

MECHANISMSOF ROCKBREAKDOWNBYFROSTACTION TABLE 4 Some physical and mechanical properties and frost shattering rate of sedimentary rocks used for experiments Rock type t

Ch-a Ls-a Ls-b Ss-a Ss-b Ss-c Ss-d Ss-e Ss-f Ss-g Ss-h Ss-i SI-a Sh-a Sh-b Sh-c Sh-d Sh-e Sh-f Sh-g Sis-a Tu-a Tu-b Tu-c Tu-d Tu-e Tu-f Tu-g

Geological age2

Cret Pal Cret Cret Cret Cret Pag Pag Neo Neo Neo Neo Neo Pal Cret Cret Pag Pag Pag Neo Cret Neo Neo Neo Neo Neo Neo Neo

n ×

10 - 2

1.10 1.15 1.53 0.26 3.55 12.0 8.43 13.4 5.77 28.0 32.2 32.9 16.6 0.67 3.30 1.42 5.49 9.07 12.2 33.7 1.25 36.2 39.3 45.5 46.3 51.0 37.8 45.3

Yd >( 103 (kgm -3)

S,, X 103 (m2kg - I )

r X 10-a (m)

St

Vp

(MNm -2)

(kms - I )

2.67 2.75 2.74 2.68 2.58 2.30 2.43 2.31 2.50 1.65 1.86 1.86 2.23 2.74 2.66 2.71 2.75 2.43 2.34 1.68 2.73 1.54 1.47 1.50 1.39 1.23 1.35 1.60

0.230 0.406 0.830 0.299 4.66 5.88 10.3 5.64 4.46 3.68 23.3 16.7 17.5 0.592 2.06 5.08 9.25 11.8 13.2 6.49 0.883 14.4 17.5 19.1 23.0 26.7 20.9 33.5

5.37 3.09 2.02 0.973 0.886 2.66 1.01 3.09 1.55 13.8 2.23 3.18 1.28 1.24 1.81 0.840 0.647 0.949 1.18 9.27 1.56 4.90 4.58 4.76 4.34 4.46 4.02 2.54

11.9 4.9 7.2 14.7 6.3 2.9 4.5 4.7 7.8 0.40 2.6 0.98 3.0 13.0 10.5 6.7 5.5 8.3 3.4 1.6 11.7 0.36 0.78 0.53 0.48 0.29 0.24 0.38

5.23 3.35 3.34 5.80 4.51 3.01 3.48 3.50 4.39 1.65 2.93 2.12 3.28 5.65 4.63 5.23 4.50 4.18 3.53 2.52 5.00 2.22 2.34 2.11 1.94 2.18 1.87 2.08

Ai

Ed X 103 (MNm -2)

Rf × 10-3 (cycle -I )

1.00 1.00 1.05 1.00 1.00 1.00 1.24 1.20 1.06 1.12 1.04 !.04 1.17 1.05 1.39 1.26 1.13 1.15 1.15 1.27 1.54 !.16 1.09 1.15 1.04 1.00 1.04 1.17

56.4 32.6 30.4 55.2 43.6 21.2 28.2 25.0 51.8 5.6 11.1 6.9 20.6 59.6 42.8 40.0 31.4 38.2 23.6 10.2 41.4 4.9 5.1 1.1 1.6 1.3 0.78 2.3

0.072 0.22 0.16 0.033 1.17 6.66 3.71 6.86 1.15 141 70.2 131 8.56 0.041 0.12 0.18 0.76 4.31 8.91 27.5 0.067 178 80.9 69.7 53.7 41.7 140 175

LCh = chert, Ls = limestone, Ss = sandstone, SI = sandy shale, Sh = shale, Sis = siliceous shale, Tu = tuff. 2pal = Paleozoic, Cret = Cretaceous, Pag = Paleogene, Neo = Neogene.

therefore, only the 9% v o l u m e t r i c e x p a n s i o n participates in the frost s h a t t e r i n g o f these rocks.

ACKNOWLEDGEMENTS

APPENDIX: PHYSICAL A N D MECHANICAL PROPERTIES OF ROCK SAMPLES T h e porosity n a n d the dry b u l k d e n s i t y pd are calculated by formulas: n=

A part of this study was c o n d u c t e d u s i n g the climatic c a b i n e t s at the N a t i o n a l I n s t i t u t e o f P o l a r Research. I would like to t h a n k Y. Y o s h i d a a n d K. M o r i w a k i for p e r m i s s i o n to use e x p e r i m e n t a l apparatuses. I a m also grateful to M. I n o k u c h i , M. F u kuda, Y. Ono, T. S u n a m u r a , Y. M a t s u k u r a a n d E. Yatsu for their helpful suggestions.

( w s - Wd)

(ws-ww) pwWd

Pd-(ws- Ww)

(hi) (i2)

where Pw is the d e n s i t y o f water ( c o n s t a n t ) , Wjd is the dry weight, w~ is the saturated weight a n d Ww is the saturated weight o f the s p e c i m e n s u b m e r g e d in

268

NORIKAZUMATSUOKA

TABLE 5 Some physical and mechanical properties and the frost shattering rate of igneous and metamorphic rocks used for experiments Rock type ~ Geological age 2

n X I 0 -2

Ya XI0 3 ( k g m -3)

S,,, Xl0 3 (m2kg - t )

f X I 0 -8 (m)

St

Vr,

( M N m -2)

(kms -I)

Ai

Ed Xl0 3 ( M N m -2)

Rr X I 0 -3 (cycle - t )

And-a And-b And-c And-d And-e And-f And-g Bas-a Bas-b Dac-a Dia-a Gab-a Gne-a

Neo Neo Neo Neo Quat Quat Quat Quat Quat Quat Unk Cret Neo

6.07 28.4 51.7 52.3 22.5 25.8 37.3 25.4 12.6 3.84 0.99 0.12 1.47

2.49 1.97 1.25 1.22 2.05 1.97 1.66 2.04 2.39 2.75 2.82 2.86 2.63

1.26 3.41 6.33 18.8 5.50 1.75 2.08 0.088 0.186 0.377 1.06 0.039 0.639

5.80 12.7 19.6 6.84 5.99 22.5 32.4 424 85.0 11.1 0.994 3.24 2.62

4.0 2.9 0.12 0.10 1.8 1.6 0.96 1.5 2.1 4.9 16.6 14.1 5.6

2.73 3.15 1.74 1.45 2.86 2.06 1.81 3.72 2.52 2.97 4.71 6.40 3.24

1.15 1.10 1.12 1.00 1.04 1.09 1.06 1.00 1.00 1.00 1.00 1.00 1.06

17.0 12.1 0.51 0.22 11.3 4.8 2.8 7.1 11.4 33.4 61.0 71.2 30.0

1.77 2.67 52.4 55.0 3.35 1.10 1.77 0.12 0.15 0.046 0.051 0.055 0.077

Gra-a Gra-b Rhy-a Rhy-b Rhy-c Ser-a

Cret Neo Cret Quat Quat Unk

2.22 1.42 1.84 13.1 50.1 2.78

2.55 2.60 2.62 2.23 1.21 2.64

0.939 0.205 0.346 0.952 1.23 14.6

2.78 7.99 6.09 18.5 101 0.216

4.8 7.9 11.6 4.5 2.0 7.9

2.89 3.23 4.69 2.46 2.47 5.36

1.00 1.00 1.02 1.02 1.00 1.17

33.4 35.5 50.2 15.5 6.2 44.4

0.13 0.10 0.10 0.21 45.9 0.049

tAnd=andesite, Bas=basalt, Dac=dacite, Dia=diabase, Gab=gabbro, Ser= serpentinite. 2Cret = Cretaceous, Neo = Neogene, Quat = Quaternary, Unk = unknown.

water. The value of Wd was measured after the specimen has been dried in an over for 48 h at 105°C. The value of Ws and Ww were measured after the specimen has been submerged in water in a vacuum chamber for 72 h. Equation Al demonstrates that n gives "effective" porosity in which only hydraulically-linked pores are included. The specific surface area Sw, i.e.the internal surface area per unit mass, was determined by nitrogen adsorption (BET m e t h o d ) . Specimens weighing 0.5-3.0 g were examined. The mean pore radius r was calculated from the other measured properties. If pores are spherical, f is expressed by (Matsuoka, 1988): r=

3n pdSw

(A3)

The resistance against shattering force is given by the tensile strength S . because the frost shattering is a kind of tensile failure (e.g. Everett, 1961; Mellor, 1970). The value of St was determined by the

Gne=gneiss,

Gra=granite,

Rhy=rhyolite,

diametrical compression of a disk specimen, 3 cm in diameter (e.g. Jaeger and Cook, 1979). For anisotropic rocks with preferred joints or beddings, the mean values of $I were calculated from the values for various directions. Measurements of the longitudinal wave velocity, Vp, enabled us to find structural properties o f rocks such as the size, a m o u n t and orientation o f pores or cracks without damage of rocks. This velocity was determined by the pulse propagation test using a Pwave of 200 kHz and measured in dry state, where the effect of pores or cracks appeared more clearly than in wet state. For anisotropic rocks, the mean values of Vp were calculated from the values for various directions. Intensity of anisotropy was also evaluated with the anisotropic factor Ai: m~x

Zi -- ~-~min

(A4)

where Vp max and Vp mi. are the m a x i m u m and mini m u m values of Vo, respectively.

MECHANISMSOF ROCKBREAKDOWNBYFROSTACTION Y o u n g ' s m o d u l u s was d e t e r m i n e d by a d y n a m i c m e t h o d . If three properties, the dry u n i t weight 7d, the l o n g i t u d i n a l wave velocity a n d t r a n s v e r s e wave velocity Fs, are k n o w n , the d y n a m i c Y o u n g ' s m o d ulus, Ea, can be given by (Jaeger a n d Cook, 1979): Ed _Yd V~(3

V~/V~- 4 )

g( v ~ / v ~

(A5)

- l)

where g is the acceleration due to gravity. T h e value o f Vs was also d e t e r m i n e d by the pulse p r o p a g a t i o n test. These properties a n d the frost s h a t t e r i n g rate o f rock s a m p l e s are listed in Tables 4 a n d 5.

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