Introduction

The determination of SP requires the measurement ofthe water intake velocity and the temperature gradientin the frozen fringe (e.g., Konrad, 1980). Because of therelative simplicity of the theory and the test methodrequired to obtain SP, the concept has been applied tosolve many practical field problems (e.g., Nixon, 1982;Saarelainen, 1992). Further, the SP concept can providea very powerful basis to develop soil frost heave sus-ceptibility criteria (Reike et al., 1983; Vinson et al., 1984).

However, the procedure to obtain SP from a simplestep freezing test has not been completely standardized.For example, the heave velocity (divided by 1.09) isvery often used in place of water intake velocitybecause an accurate method to continuously measurewater intake is lacking. Further, in many cases SPchanges rapidly near the end of transient freezing; the

determination of the end of transient freezing greatlyinfluences the evaluation of SP. A more sophisticatedmethod employing a ramped freezing test is highly rec-ommended to determine SP by Penner (1986) andKonrad (1988), but the test equipment to performramped freezing tests is not available to most practi-tioners. In addition, the many factors which influenceSP have sometimes raised questions regarding its accu-rate determination (Gassen and Sego, 1993).

Statement of purpose

The purpose of the research reported herein is to iden-tify improvements to the step freezing frost heave testso that one can obtain consistent and reproducible val-ues of SP. The scope of the work presented includes (1)a description of the test methods and laboratory pro-gram conducted to verify the improvements, and (2) adiscussion of the significance of the improvements.

Abstract

Although the Segregation Potential (SP) concept has contributed greatly to an engineering approach for frostheave, there is still concern regarding the consistency and reproducibility of SP in a laboratory freezing test.This arises from the uncertainty in the evaluation of SP from a step freezing test. In order to facilitate a consis-tent and reproducible measurement of SP, a laboratory research program was conducted in which threeimprovements were made to the conventional step freezing test. The improvements included: (1) the use of anaccurate water intake measurement with an electric balance, (2) a shallower temperature gradient, and (3) theaddition of a cold bath to facilitate ice nucleation. Based on the test results obtained, it was concluded that theimprovements resulted in an accurate, consistent and reproducible determination of SP. In addition, a conti-nuously recorded water intake velocity can provide useful information to identify the formation of the final icelens.

Yuzuru Ito, et al. 509

AN IMPROVED STEP FREEZING TEST TO DETERMINE SEGREGATIONPOTENTIAL

Yuzuru Ito1, Ted S. Vinson2, J. F. (Derick) Nixon3, Douglas Stewart4

1. Dept. of Civil Engineering, Setsunan University 17-8, Ikeda-Nakamachi, Neyagawa, Osaka 572, JAPAN

e-mail: cito@civ.setsunan.ac.jp

2. Dept. of Civil, Construction, and Environmental EngineeringOregon State University, 107 Apperson Hall, Corvallis, Oregon 97331-2302, U.S.A.

e-mail: vinsont@ccmail.orst.edu

3. Nixon Geotech Ltd.Box 9, Site 9, RR6, Calgary, Alberta, T2M4L5,CANADA

e-mail:derickn@cadvision.co.ca

4. Dept. of Civil EngineeringThe University of Leeds, Leeds, LS2 9JT,UNITED KINGDOM

e-mail:cengdis@civil.leeds.ac.uk

Laboratory evaluation of SP

In a step freezing test, SP is defined as (e.g. Konrad,1980)

[1]

where, SP(t) is the segregation potential at

time t,v(t) is the water intake velocity, andgradTf(t) is the overall temperature gradient of the

frozen fringe.

Following the method proposed by Konrad (1987), atypical procedure to evaluate SP from a step freezingtest is illustrated in Figure 1. A step freezing test is con-ducted and the amount of heave (Figure 1a) and tem-perature distribution (Figure 1b) are recorded. The totalheave (H) is obtained directly from an LVDT reading.The segregation heave (hs) and the water intake velocity(v) (Figures 1a, 1c) are calculated from the readingobtained with a water intake monitoring device (e.g., aburet) . The temperature distribution (Figure 1b) can beused to estimate the temperature gradient of the frozenfringe (Figure 1d) and the frozen depth, which is thelocation of the 0¡C isotherm. Next the rate of cooling ofthe fringe (Figure 1e) is computed as:

[2]

where X is the frozen depth.

SP (Figure 1f) can be evaluated as the ratio ofthe water intake velocity (Figure 1c) to the temperaturegradient of the fringe (Figure 1d). The time when therate of cooling becomes zero is considered as the end oftransient freezing. SP at this time is most frequentlyused for field frost heave prediction.

Concerns regarding the evaluation of SP

There are three major concerns regarding the methodpresently used to evaluate SP. The first concern is rela-ted to the water intake measurement. SP is defined bythe ratio of water intake velocity to the temperaturegradient of the frozen fringe. To date, a volume changedevice such as a buret, or a pressure transducer hasbeen used to measure the water intake velocity.However, the accuracy of these devices is limited to1/10 ml. This is equivalent to approximately 0.01 mmof heave for a 10 cm diameter specimen. On the otherhand, if the heave rate is used to establish SP, an LVDTmay be used with a precision of 0.001 mm. It is appa-

rent that SP based on water intake velocity will fluc-tuate to a much greater extent than SP based on heave velocity.

It is possible to estimate the water intake velocityfrom the heave data if the amount of water whichchanges phase below 0¡C is known, using the followingequations:

[3]

[4]where, H(t) is the total heave measured at time t,hs(t) is the segregation heave ,hi(t) is the in-situ heave,X(t) is the frozen depth from the original surface,n is the porosity, Æt is the time interval, ande is the amount of water changing phase below 0 ¡C

expressed as a decimal fraction.

The strict use of Equation 4 requires knowledge of theamount of water which changes phase at the frost front (e).

The 7th International Permafrost Conference510

SP tv t

gradT tf

( )( )

( )=

dT

dtgrad T

dX

dtf

f= ·

Figure 1. Flow-chart for Evaluation of SP.

H t h t h ts i( ) ( ) ( )= +

v tdh t

dt

H t t H t t n X t t X t t

ts( )

.( ) ( ( ) ( )) . ( ( ) ( ))

. •= · =

+ - - - · · + - -11 09

0 092 18

D D D DDe

The second concern is the determination of the end oftransient freezing or the time when a final ice lens startsto form. Since SP at this time is most often used for fieldpredictions, the determination of this time is veryimportant. The end of transient freezing is determinedfrom the rate of cooling of the frozen fringe, which iscomputed from the temperature distribution along thecell wall. It is likely that some uncertainty may exist inthe rate of cooling, since the temperature along theinner walls of the frost heave cell is not exactly the tem-perature inside the specimen. In fact, the rate of coolingof the fringe usually fluctuates due to heat flow fromoutside the test cell. This uncertainty is of greatest con-cern when SP changes rapidly in the freezing test.

The third concern is the boundary temperature condi-tion of the test. In a step freezing test to obtain SP, thetemperature gradient is generally much steeper thanthe field temperature gradient. In a laboratory stepfreezing test, the temperature in a specimen rapidlydecrease during transient freezing and only become sta-ble at the end of transient freezing. This thermal regimeis completely different from that which exists whenfrost heave occurs in the field. It is reasonable to specu-late that the use of a shallower temperature gradientwould reduce the discrepancy between the laboratoryand the field condition.

Improved step freezing frost heave test system

Three improvements were made to the procedure andequipment commonly used to determine SP. The firstimprovement was made in the measurement of waterintake. The method used to establish water intakevelocity utilizes an electric balance to obtain a continu-ous record of weight change in place of a volumechange device. The electric balance ensures a precisionof 0.01 ml of water intake which is equivalent to 0.001mm of heave for a 10 cm diameter specimen. Thisallows a direct and precise computation of SP fromwater intake velocity and temperature gradient.

The water intake and heave velocities represent anoverall condition of the freezing soil. Using a reliablewater intake velocity the end of transient freezing canbe evaluated by considering the relationship to theheave velocity. For a saturated soil at the end of tran-sient freezing the following relationship should exist:

[5]

Equation 5 indicates that the water intake velocityequals the heave velocity divided by 1.09 when thefrost front stops advancing and the in situ heave veloci-

ty (hi) approaches zero (Figure 2). Further, if a Mariotdevice (e.g., McCabe and Kettle, 1985) is used in con-junction with an electric balance, it is possible to con-duct a test with constant water pressure at the unfrozenend of the specimen.

The second improvement was the use of a shallowertemperature gradient for the step freezing test. Thethird improvement was the addition of a cold bath tofacilitate ice-nucleation under a shallower temperaturegradient.

The test system used in the research program wasoriginally fabricated by Reike et al. (1983) and wasmodified for use in the test program (Figure 3). Thethermistors were placed along the length of each half ofthe cell, in the chamber and on the top and bottomboundary plates.

Speciment preparation

Naturally occurring Calgary silt was used for all thefrost heave tests. The properties of Calgary silt are asfollows: liquid limit = 23.7 %; plastic limit = 15.4 %;passing no. 200 = 84 %; % clay size = 26 %. The soil wasinitially prepared as a slurry at a water content of about1.5 to 2 times the liquid limit. The slurry was thenallowed to stand overnight in a container. Finally, a va-cuum was applied to the container for one day.

Consolidation of the slurry to 300 kPa was performedin four stages in a consolidometer. After consolidation,

Yuzuru Ito, et al. 511

v tdh t

dt

dH t

dtor

dh t

dts i( )

.( )

.( ) ( )

= = =1

1 091

1 090

Figure 2. Approximate Relationship Between Heave Velocities, Rate ofCooling

the 10 cm diameter sample was extruded from the con-solidometer and trimmed. The test specimen wasplaced on the bottom of the freezing cell and the sideswere coated with silicon grease. A thin rubber mem-brane was placed over the specimen and the surface ofthe membrane was again coated with silicon grease.Finally, the two halves of the frost heave cell wereclamped together to enclose the specimen.

Test procedure

The SP tests were conducted under three differenttemperature gradients at a constant overburden pres-sure of 45 kPa. A step freezing method was used andthe specimens were frozen from the bottom end to thetop.

Following the application of the overburden pressurethe specimen temperature was allowed to equilibrate atapproximately +0.5 to +1.5¡C by circulating antifreezeat a constant temperature from the warm bath throughthe top and bottom plates. Next, antifreeze at -10¡C wascirculated through the bottom plate to initiate ice nucle-ation. After observing a slight change in the electric ba-lance and the load cell readings, the circulation throughthe bottom plate was changed to the cold bath at the

prescribed temperature. The LVDT, electric balance,load cell, and thermistors were monitored at 10 or 15 min. intervals during the test.

Analysis of test data

The water intake velocity at time t can bedirectly computed from the water intake reading:

[6]

where,Ww(t)is the weight of the water tank at time t,A is the cross sectional area of the specimen, andÆt is the time interval.

The segregation heave or heave due to water intakefrom the unfrozen part of the soil (hs(t)) is also compu-ted directly from the water intake reading.

On the other hand, the total heave velocity divided by1.09 or the rate of water changing phase in the freezingsoil is computed from the LVDT reading:

[7]

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Figure 3. Improved Step Freezing Test System.

v tW t t W t

A tw w( )( ) ( )

=- -

·D

D

V tH t H t t

tHw ( )( ) ( )

. •=

- - DD1 09

Using the total heave measured with the LVDT andthe segregation heave, the in-situ heave is calculatedfrom Equation 3. The fraction of water which changesphase below 0¡C can also be computed from vand VHw.

The SP was determined from Equation 1 as the ratioof the exact water intake velocity v(t) and the tempera-ture gradient of the frozen fringe or grad Tf(t).Assuming a segregation freezing temperature Ts = - 0.3¡C, grad Tf(t) was computed following the pro-cedure explained by Konrad (1987).

Test results

TEST WITH A STEEPER TEMPERATURE GRADIENT

Figure 4 presents the results for test C-6 in which an 8cm specimen was frozen under the boundary tempera-ture condition of -3.7 and +1.6¡C. To illustrate theadvantage of the electric balance to monitor waterintake, SP at the end of the transient state was estima-ted using two different procedures.

First, according to the rate of cooling of the fringedefined by the cell wall temperature measurements(Figure 4a), transient freezing ended between approxi-mately 600 and 1250 min. Considering the range of timewhich could be used to define the end of transientfreezing, SP could be evaluated as 0.0016 to 0.0025 mm2/(s¥¡C) (Figure 4c).

The second procedure utilized the relationshipbetween water intake and heave velocities (Figure 4b).The heave velocity divided by 1.09 (VHw) equals thewater intake velocity(v) when the frost front stopsadvancing. After this time there is no further in situfreezing (hi). This time may be considered as the end oftransient freezing when the final ice lens starts to form.Following this procedure, Figure 4b suggests that theend of transient freezing could conservatively be esti-mated as 600 to 950 min. Therefore, SP could be evalu-ated as 0.0019 to 0.0025 mm2/(s¥¡C) (Figure 4c). Since itis considered that the frost front may progress a little,and a small amount of water remaining unfrozen in thefrozen fringe will freeze after the formation of the finalice lens, it is reasonable to assume that the final ice lensmay begin to form at approximately 600 min.Consequently, SP was interpreted as 0.0025 mm2/(s¥¡C) at 600 min. It was obvious that SPestimated by the water intake velocity was much moredefinitive than SP estimated by the rate of cooling.

Further, it was observed that while the rate of coolingwas disturbed by the cyclic fluctuation in temperaturereadings due to the heat flow from outside the cell, bothVHw and v showed no such disturbance. This meansthere was substantially no effect in the freezing testresult caused from the thermal disturbance due toimproper insulation.

TESTS WITH SHALLOWER TEMPERATURE GRADIENTS

Figure 5 presents the results for test C-11 in which a 10cm specimen was frozen under the boundary tempera-ture condition of -2.4 and +0.8 ¡C. This is about one halfthe gradient used in test C-6. In this test the insulationof the freezing cell was greatly improved. As a result,there was less fluctuation in the temperature basedinformation such as the rate of cooling (Figure 5a). Butthe end of transient freezing is still difficult to identify

Yuzuru Ito, et al. 513

Figure 4. Results From Test C-6 (Steep Temperature Gradient).

from Figure 5a. The cooling rate indicates that the endof transient freezing was between 600 and 1100 min and SP was estimated as 0.0024 to 0.0025 mm2/(s¥¡C). However, according to Figure 5b,VHw equals v at 850 min and SP was evaluated as

0.0025 mm2/(s¥¡C). The advantage of the accuratewater intake measurement was again demonstrated.

Another significant advantage associated with theshallow temperature gradient may be observed by com-paring Figures 4c and 5c. The SP was approximatelyconstant over a relatively wide range of time (SPchanged only about 5 % at between 600 and 1100 min,Figure 5c) under a shallow temperature gradient. Onthe other hand, SP decreased substantially (approxi-mately 30 % between 600 and 1100 min, Figure 4c)

under a steeper temperature gradient. The differencecan be explained by the fact that in a test with a shal-lower temperature gradient, freezing progresses moreslowly and SP also changes more slowly.

Figure 6 presents the results from test C-14 in whichan 11 cm specimen was frozen under the boundarytemperature condition of -1.3 and +0.4¡C. This isapproximately one half the gradient used in test C-11.Figure 6a suggests that the end of transient freezingwas between 350 to 1250 min, while Figure 6b indicatesthat VHw and v are approximately equal between 750and 1250 min. The SP was about 0.0034 mm2/(s¥¡C) foreither of the possible ranges of the end of transientfreezing (Figures 6a and 6b). Significantly, the time pe-riod over which SP was constant was substantiallylonger than reported in the previous tests C-6 and C-11.

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Figure 5. Results From Test C-11(Intermediate Temperature Gradient). Figure 6. Results From Test C-14 (Shallow Temperature Gradient).

Discussion

WATER INTAKE MEASUREMENT

The advantage of using an electric balance for moni-toring water intake was demonstrated. This methodimproved the accuracy of water intake data to the accu-racy of conventional heave data. The three test results(Figures 4b, 5b, 6b) showed that the fluctuations ofheave velocity divided by 1.09 (VHw) and water intakevelocity (v) were of the same order of magnitude. Itwould be difficult to compare VHw and v if v was basedon a measurement from either a buret or a pressuretransducer.

As a result of this improvement, it was possible toevaluate SP directly from the water intake velocity.With accurate water intake data, there is no need to esti-mate the fraction of in situ water changing phase under0¡C (e). Conversely, e can be easily calculated from therelationship of VHw and v . In the test program, e was60% (C-6), 50% (C-11), and 38% (C-14) respectively,indicating it was not constant.

It was also demonstrated that the relationshipbetween VHw and v can be used to evaluate the end oftransient freezing. Since the temperature data is easilyinfluenced by the overall thermal environment, the useof temperature based information to evaluate the end oftransient freezing is questionable. Therefore, it is con-cluded that the use of the relationship between VHwand v to determine the end of transient freezing repre-sents a significant advantage over the use of tempera-ture data.

TEMPERATURE BASED INFORMATION

The three test results presented suggest it is necessaryto examine the dependency of SP on the temperaturedata available. It must be emphasized that although thethermistors in the cell wall were in contact with thefreezing specimen through a very thin membrane, theyactually monitored the cell wall and soil temperature intheir immediate vicinity and not the temperature in theinterior of the specimen. The quality of the cell insula-tion has a substantial influence on the accuracy of thetemperature readings along the cell wall.

The frost heave cell for test C-6 was covered withinsulation, consisting of a styrofoam box and glass woolcovering the outside of the test cell. To improve theinsulation in the box, in tests C-11 and C-14 a thin styro-foam sheet was placed over the glass wool to preventpossible air movement inside the box. As shown inFigure 4a, the temperature fluctuation directly influ-enced the computed rate of cooling and, hence, theevaluation of the end of transient freezing. The end oftransient freezing was difficult to interpret under these

conditions and results in either a greater or smallervalue of SP.

SEGREGATION POTENTIAL

The SP defined by the exact water intake velocity andtemperature gradient at the frozen fringe were plottedin Figures 4c, 5c and 6c. The three figures show that theshallower the temperature gradient, the wider therange over which SP was approximately constant. Therange in which SP was constant started from 250 to 300 min and finished at 700 (Figure 4c), 1600 (Figure 5c)and 2400 min (Figure 6c), respectively. In other words,for the Calgary silt used for this research program, thetest with a shallower temperature gradient facilitatedthe determination of SP compared to the test with asteeper temperature gradient.

If SP was estimated from the heave data, the range ofresponse over which SP was constant would be difficultto determine. Therefore, the step freezing test to obtaina reliable SP should be conducted under a shallowertemperature gradient with continuous monitoring ofwater intake. To facilitate ice nucleation another coldbath should be added to the two existing baths.

Summary and conclusion

Improvements were made to a step freezing test tofacilitate the consistent and reproducible evaluation ofSP. The improvements include the use of an electric bal-ance for the measurement of water intake velocity, theuse of a shallow temperature boundary condition, andan additional cold bath for ice nucleation.

Test results were presented which demonstrated therelationship between VHw and v. These results could beused to estimate the end time of transient freezing orthe formation of the final ice lens. It was also shownthat SP calculated as the ratio of the water intake veloci-ty from the improved water intake measurement andtemperature gradient at the frozen fringe, was constantover a greater time period for a test conducted with ashallow temperature gradient.

Overall, it may be concluded that the step freezingtest to evaluate SP should be conducted with a shallowtemperature gradient, an ice nucleation cold bath, and acontinuous water intake monitoring system. As a resultof the improvements, it was demonstrated that consis-tent and reproducible measurements of SP are possible.

Acknowledgments

The authors would like to thank Mr. Andy Brickmanfor his very precious advice throughout the researchprogram. The financial support for the senior authorprovided by the Japan Highway Public Corporation isgratefully acknowledged.

Yuzuru Ito, et al. 515

The 7th International Permafrost Conference516

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