4. Observation of ice lensing and frost heaving (Exp. 1. 2)

When a porous medium consisting of water and fine particles, such as soil, isfrozen unidirectionally, the water sometimes forms regions of ice that are almost devoidof particles.

These regions are called ice lenses, and repetition of the process results inthe formation of intermittent layers.

The formation of ice lenses is recognized as anecessary condition for frost heave.

In this case, there are some questions we must

consider, that is, how the ice lens generates, grows and forms the layer, what are factorsthat mainly affect the ice lensing, and what kind of microstructure do ices make nearfreezing front.

To clarify these questions, in this chapter, images of the samples infreezing process were directly observed by using unidirectional freezing apparatus
equipped with microscope. Such experiment, which can observe formation of theintermittent layers in freezing sample continuously and microscopically, has not carriedout except a few experiments.

4.1 Sample and method
Samples used here were the sample 1, 4 and 5.

The sample 1 was mixed with

distilled water to make slurry and deaired by a vacuum pump.

The slurry was placedin an acrylic cylinder with 10-cm diameter and consolidated at an overburden pressureof 1 MPa for a week.

A 3 mm-thick rectangular sample was obtained by cutting theconsolidated sample. The samples 4 and 5 were mixed with distilled water and deairedby boiling.

Water contents of prepared samples 1 and 4 were 46% and 80%,

respectively.

The samples 2-5 hardly have plastic condition.

of these samples drastically change at their liquid limit.

Consistency condition

Then, two types of watercontents were prepared for sample 5; one was the fluidized sample with water content- 57 -

of 35% (sample 5s), and other was non-fluidized sample with water content of 33%(sample 5c). In this connection, we can say that the sample 4 was fluidized sample.
These prepared samples were placed into sample cell as shown in figure 14.
The cell was composed of a pair of slide glasses (Matunami S-1111) and acrylic spacers.
The cell had a capacity of 20.0 × 70.0 × 3.0 mm 3.

Both sides of the cell were sealedwith silicone to keep saturated condition, except for a small hole on one side to relievepressure.

The cell for the sample 1 and 5 had a water reservoir at the warmer side to

supply water and had two pair of copper-constantan thermocouples with diameter of 0.2mm, calibrated with an accuracy of 0.03 ˚C to measure temperature.
When different temperatures were given to each end of the sample cell, theisotherm advance in the sample until a steady state was attained.
the experiment two stages.

Then, we separated

In the first stage (Exp. 1), we observed the vicinity of a

growing ice lens immediately after temperature gradient was applied until the warmest
ice lens almost stopped growing.
are listed in Table 2.

The final temperature gradients α given to the cellThis kind of freezing would correspond to frost penetration in

actual field in which freezing rate decreases gradually.

In the second stage (Exp. 2),

the cell was moved toward cold side at a constant rate of Vs after a temperature gradient
was given to a sample cell for 1 hour.

Since the advancing rate of the isotherm had

decreased to enough low for 1 hour, the V s gave a constant freezing rate V f to thesample (Vf = - V s).

Then, we observed the vicinity of ice growing surface for duration

until the cell was moved by 20-mm distance.

The condition on the temperature

gradient α at steady state, and sample moving rate Vs are listed in Table 2.
Temperatures at two points, which were apart 4 mm and sandwiched the freezing front,
were measured.

Each temperature gradient was calculated from the temperatures.

When the sample applied extremely rapid V s, pore water would freeze there; i.e. ice lenscould not form.

Therefore, V s were applied within the range which ice lens can form.

- 58 -

This kind of freezing can be regarded as frost heave under a constant freezing rate.
During each experiment, the apparatus was located in the ambient temperatureof 5.0 ˚C, so that the initial temperature of the sample was 5.0 ˚C.

Ice segregation and

ice lens growth near the freezing front were observed with a microscope (40magnification).

The microscope was equipped with a charge coupled device (CCD)

camera and a video system. Sample images were captured in one-minute interval.
The sample images was divided with 20-µm mesh by a computer and the ice lens
growth rate was measured from a relative coordinate of the growth surface.

And thetemperature of ice segregation was measured from the temperature profile that was
traced on the image.

Table 2. Experimental conditions (Exp. 1 and Exp. 2).
SampleNo. Vs
Exp.1
Exp.2

0.4
0.6
0.8

α

1,4,5
0.2
A0
A1
A2
A3

* Vs (µm/sec): α (˚C/mm)- 59 -

1
0.125
B0
B1
B2
B3

4
0.28
C0
C1
C2
C3

4
0.33
D1
D2
D3
D4

Thermocouple s
Water reservoir sectio nSampleFig. 14. Schematic diagram of sample cell for unidirectional freezing experiment.

- 60 -

4.2 Experimental results
4.2.1 Freezing experiment with zero sample rate (Exp. 1)(1) Image of the sample in freezing process
Figure 15a shows the image of the freezing sample 1 (Fujinomori soil) under
the condition of A0 (Vs = 0 µm/sec, α = 0.20 ˚C/mm).

It was observed that ice lenses

segregated from the cold side (from up to down in the figure) and formed intermittent
layers.

An ice lens was thicker as it was at warmer location.

And it was also

observed that the warmest ice lens formed at a point below 0 ˚C isotherm.

Neitherpore ice larger than 10 µm nor a displacement of soil particles due to pore ice formation
was found in the region between the warmest ice lens and 0 ˚C isotherm.

Under thecondition of A0, the warmest ice lens started to segregate at -0.55 ˚C and grew 1.7 mm
thick during time period of 400 minutes. The temperature at the growth surface of thewarmest ice lens increased gradually and reached -0.2 ˚C.
Figure 15b shows the image of the freezing sample 4 (water saturated uniform
size glass particles) under the condition of D0 (Vs = 0 µm/sec, α = 0.33 ˚C/mm).
Black and white portions are ice lenses and glass particles, respectively.

Ice lenses

segregated from the cold side (from up to down in the figure) and formed intermittent
layers, just same as in sample1.

An ice lens was thicker as it formed later.

Such icelensing was observed in other experiments under different temperature gradients for Vs= 0 µm/sec.

Under the condition of D0, the warmest ice lens grew to 3.5 mm thick for

10 hours.

The growth surface of ice lenses in the sample 4 was flatter than in thesample 1.

The ice lenses in the sample 4 made clearer layer in the perpendicular toheat flow than the ice lenses in the sample 1. And a boundary of ice lens observed in
the sample 4 was much clearer than in the sample 1.

These observations show thatfrost heave may occur in glass particles as well as in soil.

Therefore, observing ideal

ice lensing in the sample 4 will be useful to make ice lensing model.

- 61 -

Figure 15c shows the image of the freezing sample 5s (water saturated nonuniform size glass particles) under the conditions of A0 (Vs = 0 µm/sec, α = 0.20
˚C/mm).

The sample was freezing from up to down in the figure.

also observed in this sample as it as in other samples.

Ice lensing wasUnder the condition of A0, thewarmest ice lens started to segregate at -0.37 ˚C and grew 1.4 mm thick during time
period of 400 minutes. The temperature at the interface between the warmest ice lensand particles increased gradually and reached-0.08 ˚C.

Comparing ice lens insample 5 with that in the sample 1 and 4, ice lens in the sample 5s has medium
roughness of the growth surface and clearness of the boundary.

When an ice lens was

growing, aggregated particles sometimes moved through the ice lens to warmer side.
Such migration of aggregated particles in the sample 5s was similar to that in the sample
1 than that in the sample 4.

It is suggested that the difference of uniformity of particle

size and frame structure of particles affect to disturb shape of the ice lenses.
Here, we observed the growth of the warmest ice lens in each sample andmeasured the temperatures at growth surface observed in the samples 1 and 5.

(2) Thickness of the warmest ice lensFigure 16a shows the change in thickness of the warmest ice lens in the sample
1 for specimens A0 and B0.

Specimen A0 was frozen at a larger temperature gradientthan specimen B0 (Table 2).

The elapsed time was counted from start of segregationof the warmest ice lens.

The ice lens grew rapidly in the beginning, and grew more

slowly at later time stages.

After 400 minutes, thicknesses of the ice lenses were 1.7mm and 1.3 mm for A0 and B0, respectively.

These results indicate that the thicknessof ice lens increase more at the larger temperature gradient and that the growth of ice
lens stabilized with time.

The difference in the thickness of ice lens between A0 andB0 came from the difference in the growth rates in the early stages of the experiment.

- 62 -

Fig. 15a.

An image of the freezing sample 1 (Fujinomori soil) under the condition of

A0 (Vs = 0 µm/sec, α = 0.20 ˚C/mm).

- 63 -

Fig. 15b. A image of the freezing sample 4 (glass particles) under the condition of D0(Vs = 0 µm/sec, α = 0.33 ˚C/mm).

- 64 -

Fig. 15c.

An image of the freezing sample 5s (water saturated non-uniform size glass

particles) under the conditions of A0 (Vs = 0 µm/sec, α = 0.20 ˚C/mm).

- 65 -

Thickness (mm)

2
1.5

A0

1

B0

0.5
0

Fig. 16a.

0

A 0.20 K/mm
B 0.125K/mm
100
200
300
Elapsed time (min)400

The change in thickness of the warmest ice lens in the sample 1 forspecimens A0 and B0.

- 66 -

Thickness (mm)2
1.5

sample 4
sample 5s
sample 5c

1
0.5
0

0

100
200
300
Elapsed time (min)400

Fig. 16b. The change in thickness of the warmest ice lens in the samples 4, 5s and 5c.

- 67 -

Figure 16b shows the change in thickness of the warmest ice lens in thesamples 4, 5s and 5c.

The axes are same as in the figure 16a. All of the warmest ice

lenses were grew rapidly in the beginnings, and grew more slowly at later time stages as
it as in the sample 1.

After 400 minutes, thicknesses of the warmest ice lenses were

1.4 mm, 1.4 mm and 0.8 mm for the samples 4, 5s and 5c.

The thickness of thewarmest ice lens in the sample 4 and 5s were thinner than in sample 1. And, fluidized
sample (sample 5s) has thicker ice lens than non-fluidized sample (sample 5c).

These

results indicate that the thickness of ice lens will be changed by the slight difference ofpacking condition of particles and temperature condition than uniformity of particles.

(3) Temperature at growth surface of the warmest ice lensFigure 17a shows temperatures at the growth surface of the warmest ice lensobserved in sample 1.
approaching -0.2 ˚C.

The temperatures increased with time and were gradually

The temperatures at which the warmest ice lenses started to form

were -0.55 ˚C and -0.4 ˚C for A0 and B0, respectively.

When the temperature gradient

was steeper, the warmest ice lens started to form at a lower temperature.

Figure 17b

shows temperatures at the growth surface of the warmest ice lens observed in sample 5s
under the condition of A0.

The ice lens started to form and grew at warmer

temperature than in sample 1.
Figure 18 shows growth rate of ice lenses observed in sample 1 as a function oftemperature at the growth surface.

The results in figure 18 were obtained from 7

experiments at conditions A0 and 3 experiments at conditions B0.
at temperature above -0.21 ˚C.

No ice lenses grewThis figure indicates that the temperature at the growthsurface determines the growth rate of ice lens. The best fit for the relationship between
the growth rate of the ice lens Vil and the temperature is given by- 68 -

Vil = 1.0 ∆Til ,(21)

where supper cooling degree ∆Til is the temperature difference between the growthsurface of ice lens and -0.21 ˚C.
Figure 19 shows growth rate of ice lenses observed in the sample 5 as afunction of temperature at the growth surface.

Supercooling degree ∆Til for the sample

5 was the temperature difference between the growth surface of ice lens and -0.05 ˚C.
The solid line is the best fit for sample 1 (equation 21).

The relationship between

growth rate and supercooling degree at the growth surface of the sample 5 was similar
to the relation of the sample 1.

These results indicate that not only the growth rate of

the ice lens in sample 1 but also that in sample 2-5 can be expressed by same equation(21), if the supper cooling degree were accurately decided.

- 69 -

Temperature (℃)

0
A 0.20 K/mm
B 0.125K/mm
-0.2
B0
-0.4
A0
-0.6
0

Fig. 17a.

100
200
300
Elapsed time (min)400

Temperatures at the growth surface of the warmest ice lens observed insample 1.

- 70 -

Temperature (℃)

0
-0.2
-0.4
-0.6
0

Fig. 17b.

100
200
300
400
Elapsed time (min)Temperatures at the growth surface of the warmest ice lens observed insample 5s.

- 71 -

Growth rate (μm/s)

0.5
A01
A02
A03
A04
A05
A06
A07
B01
B02
B03

0.4
0.3
0.2
0.1
0
-0.6

Fig 18.

-0.4-0.2
Temperature (℃)

0Relationship between growth rate of the warmest ice lens and temperature at

the growth surface.

- 72 -

Growth rate (μm/s)

0.12
0.8

0.4

sample 1
sample 5

Vf = 1.0∆T0

Fig. 19.

0

0.1
Supercooling ∆T

0.2

Relationship between the growth rate of ice lens and supercooling degree atthe growth surface.

- 73 -

4.2.2 Freezing experiment with constant sample rate (Exp. 2)(1) Image of sample in freezing process
Figure 20a shows the image of freezing process for the sample 1 which wasmoving at constant rate of 0.60 µm/sec towards the frozen side with the temperature
gradient of 0.2 ˚C/mm (A2).

The sample was freezing from up to down in the figure.

When the constant moving rate was applied, ice lenses rhythmically formed at the same
location (at the same temperature) in the visual field of microscope.

In this series ofexperiments, each ice lens was formed in a similar interval and had similar thickness.
Once a new ice lens segregated on the warmer side, previously formed ice lenses
stopped growing.

This ice lens also stopped growing when a more recent ice lensstarted to segregate on the warmer side.

In the case of A2, the segregation and thegrowth of ice lens were observed -0.5 ˚C.
Figure 20b shows the image of freezing process for the sample 4 under thecondition of A3 (V s = 0.80 µm/sec, α = 0.20 ˚C/mm).

It was observed as it as insample 1 that ice lenses with same thickness and same interval grew from cold side towarm side. The ice lens grew with pushing glass particles ahead at the growth surface.
This growth surface moved toward cold side in the view field of microscope.

Thisindicates that the growth rate of an ice lens was slower than Vf and that the temperature
at the warmer end of the growing ice lens was lower than the temperature at which theice lens started to grow.

When the growth surface of ice lens moved by a distancefrom the location, at which the ice lens started to grow, the ice lens stopped growing anda new ice lens started to grow at the previous location.

Figure 21 shows relationshipbetween thickness of ice lens and sample moving rate.

The thickness of ice lensdecreased as the freezing rate increased.

- 74 -

Figure 20c shows the image of freezing process for the sample 5 under thecondition of A2 (Vs = 0.60 µm/sec, α = 0.20 ˚C/mm).
rhythmically formed as it as in other samples.

Stratified ice lenses

Although thickness and interval of ice

lens observed in sample 4 were almost constant, they were in mess in the sample 4,
sample 5 and sample 1 in that order. Figure 22 shows relationship between meaninterval of ice lens and sample moving rate.
the freezing rate increased.

The mean interval of ice lens decreased as

And the mean interval in the sample 5 was between that in

the samples 1 and 4.
Here, we measured the total heave amount and occurring temperature of ice
lens observed in sample 1.

(2) Total heave amountFigure 23 shows total heave as a function of time for different sample moving
rates.

When sample was freezing, volume of the sample would be expanding. This

expanded volume was called total heave. And it almost equals to the sum of thicknessof all ice lenses in the sample.

The total heave was determined by measuring

movement of a soil particle on the images. In this series, the elapsed time was counted
from the start of the sample cell movement.
for each specimen.

Total heave increased linearly with time

The total heave increased with increasing freezing rate.

24 shows relationship between heaving rate Vh and sample moving rate Vs.

FigureThe solidline is the best fit for the experimental values for series A (α = 0.20 ˚C/mm) and thedashed line is for series B (a = 0.125 ˚C/mm).
moving rate.

- 75 -

Heaving rate was about 60% of theFig. 20a.

An image of the freezing sample 1 (Fujinomori soil) under the condition ofA2 (Vs = 0.6 µm/sec, α = 0.20 ˚C/mm).

- 76 -

Fig. 20b.

An image of the freezing sample 4 (glass particles) under the condition of

D2 (Vs = 0.8 µm/sec, α = 0.20 ˚C/mm).

- 77 -

Fig. 20c.

An image of the freezing sample 5s (water saturated non-uniform size glass

particles) under the conditions of A2 (Vs = 0.6 µm/sec, α = 0.20 ˚C/mm).

- 78 -

Thickness of ice lens (mm)5
○ α=0.20 (K/mm)△ α=0.28 (K/mm)□ α=0.33 (K/mm)

4
3
2
1
0

0

0.2

0.4
0.6
Vs (μm/s)

0.8

Fig. 21. Relationship between freezing rate and thickness of ice lens.

- 79 -

Spacing (mm)1.0Sample 4
Sample 5
Sample 1

0.8
0.6
0.4
0.2
0
0.5

1.0
Vs(μm/s)

1.5

Fig. 22. Relationship between freezing rate and spacing between ice lenses.

- 80 -

Heaving amount (mm)

5

A1
A2
A3
B1
B2
B3

4
3
2
1
0

Fig. 23.

0

50
100
150
Elapsed time (min)200

Total heaving amount when a sample was moving with constant rate (sample

1).

- 81 -

0.5

A 0.20 K/mm
0.4 B 0.125K/mm
0.3
0.2

Vh = -0.04 + 0.6Vs
Vh = -0.02 + 0.6Vs

0.1
0

0

B

A

0.2

0.4

0.6

0.8

1

Vs (μm/s)

Fig. 24. Relationship between heaving rate and sample moving rate.

- 82 -

Temperature (℃)

0
-0.2
-0.4
-0.6
A1
A2
A3

-0.8
-1
0

B1
B2
B3

50
100
150
200
Elapsed time (min)Fig. 25. Temperature at growth surface of ice lenses.

- 83 -

Temperature (℃)

-0.2
B

A

-0.4
-0.6

A 0.20 K/mm
B 0.125K/mm

-0.8
-1

0

0.4
0.8
Vs (μm/s)

Fig. 26. Relationship between freezing rate and ice lens generation.

- 84 -

(3) Temperature at growth surface of ice lensFigure 25 shows the segregation temperature for the ice lenses.

The

segregation temperature was defined as the temperature of the interface at which an ice
lens started to grow. Each ice lens started to segregate at a constant temperature.
Figure 26 shows relationship between the occurring temperature and the freezing rate.
When the freezing rate and the temperature gradient were high, ice lens segregated at alower temperature.

This figure also indicate that the segregation temperature wasdependent on the freezing rate than the temperature gradient

4.3 Discussion
We will discuss here a frost heave model by using the experimental results ofthis chapter.

At first, we examine the frost heave model based on a partially frozen

zone, so called frozen fringe.
In the frozen fringe model, frost heave is determined by the coupled of heat
and water flow in the frozen fringe (e.g. Miller, 1980; Gilpin, 1980).

It was assumed

that soil water would flow through the frozen fringe with hydraulic conductivity K fromthe unfrozen zone to the growth surface of the ice lenses due to the pressure gradientdP/dx. If all water flowing to ice lens contributes to the warmest ice lens growth, theheave rate Vh is given bydp,
Vh = - Kρwg dx(22)

where ρi is the density of ice and g is the gravitational constant.

Gilpin (1980) andNixon (1991) have assumed that pore ice would grow so that unfrozen water content
would decrease.

They have expressed the hydraulic conductivity of the frozen fringe

K as a function of temperature:- 85 -

K=

K0(- T)β,(23)

where K0 is the hydraulic conductivity of frozen sample at –1 ˚C, T is the temperature in
the frozen fringe and β is an empirical constant.

Equation (23) means that thehydraulic conductivity of the frozen fringe decreases exponentially with decreasing
temperature of the frozen fringe.

Consequently, the growth rate of the warmest ice

lens calculated by equation (22) should decrease.
In our experiment, the growth rate of the warmest ice lens decreased withincreasing temperature at the growth surface of ice lens as equation (21).

The

experimental result corresponds to not the frozen fringe model by Gilpin and Nixon but
the experimental results by Vignes and Dijkema (1974), Biermans et al. (1978), Ishizaki
et al. (1985) and Ozawa and Kinosita (1989).

This discrepancy may come from thepostulation that there would exist pore ice in the frozen fringe.

Actually, no pore ice,

which can change the hydraulic conductivity, larger than 10 µm can be observed (e.g.
figure. 15 and figure. 20).

And another experiment, which we performed by using

electric resistibility, also find no pore ice in the zone between the warmest ice lens and 0
˚C isotherm (Watanabe and Ishizaki, 1995).
If we assume that there is no pore ice in the frozen fringe, the frozen fringe has
a constant hydraulic conductivity and the soil water flows to the surface of growing ice
lens through the frozen fringe due to a temperature difference.

By applying

generalized Clausius-Clapeyron equation, pressure of the soil water on the growthsurface of ice lens (MPa) is given by∆pw = 1.23∆(Til -Tm)+0.11 ∆pi +Π ,(24)

where ∆Pw is the pressure difference between the soil water on the growth surface of ice- 86 -

lens and an atmosphere, Til is the temperature at the growth surface and Tm is themelting point of ice at an atmospheric pressure, ∆Pi is the pressure difference between
ice lens and the atmosphere, and Π is the osmotic pressure of the soil water (Mizoguchi,1993).

For soil freezing without overburden pressure, ice pressure in the soil may beat the atmospheric pressure.

In addition, the osmotic pressure may be negligible forsalt free soil. Then equation (24) becomes∆pw = 1.23∆(Til -Tm) ,(25)

This equation means that the pressure difference can be expressed as a linear function of
the temperature at the growth surface of ice lens.

If it is assumed that the hydraulicconductivity of the frozen fringe and kinetic coefficient at the growth surface of ice lens
are constant, the calculated ice lens growth rate would increase with decreasing thetemperature at the growth surface of ice lens.

This relationship between the growthrate and the temperature is consistent with our experimental results in equation (21).
Nevertheless the ratio calculated from equation (25) is one order larger than our
experimental result.

To explain the difference between the calculation and theexperimental results without considering frozen fringe, two possibilities can beconsidered.

One is that an unfrozen water film on the growth surface of ice lens would

have some kinetic resistance to supply water into ice crystal (surface kinetic effect), andthe other is that crystallization temperature of ice would be changed by particles'
condition near the growth surface (structural supper cooling).

For the discussion of the

kinetic process and supercooling in frost heave, however, more studies will be needed
considering non-equilibrium process.

In any possibility, our experimental results

indicate that the growth rate of ice is determined by the kinetic process at the growthsurface rather than the hydraulic conductivity in partially frozen zone (frozen fringe).

- 87 -

4.4 Summary
In this chapter, ice lensing and microstructure near freezing front was observed
directly by using the unidirectional freezing apparatus.

It was shown that ideal ice

lenses for modeling can be made using uniform size glass particles.
experiments, the following results were obtained.
was formed in the frozen fringe.

From the(1) No pore ice larger than 10 µm(2) The growth amount of ice lens would increase

when the freezing rate and the temperature gradient were high.

In this time, it wasdependent on the freezing rate than the temperature gradient.

(3) The growth rate ofice lens depended on the temperature at their growth surface.

(4) The temperature of

ice lens, which started to segregate, depended on the freezing rate.

In addition, it wasalso suggested that the packing condition of particles near the ice growing surface affectto ice lensing, especially to the intervals and shapes.
It was concluded that freezing rate, supercooling degree at growth surface of
the ice lens and particle condition near growing ice lens were important factors for theice lensing mechanism.

- 88 -