Microscopic Observation of Ice Lensing and Frost Heaves in Glass Beads
Yoshiko MUTOU*, Kunio WATANABE*,
Takeshi ISHIZAKI** and Masaru MIZOGUCHI**Department of Bioresources, Mie University, 1515 Kamihama Tsu, Mie, 514, Japan**Tokyo National Research Institute of Cultural Properties, Tokyo, 13-27 Uenokouen,Higashi-Ku, Tokyo, 110, Japan

Abstract
Frost heave in soil is a complex solidification phenomenon which involves movement of water throughunfrozen soil to the freezing front. In order to clarify the frost heave mechanism, microscopic ice lensing inglass beads has been observed by using an apparatus which can control the temperature gradient and freezing
velocity independently. As a result, it was found that artificial ice lenses were formed in the glass beads aswell as soil and that thickness of the ice lenses depended on freezing velocity. In addition, exclusion andencapsulation of glass beads particles have been observed in freezing water-particles systems by using thesame apparatus. The results suggest that particle size and freezing velocity are important factors for ice
lensing. Observing the ice lensing microscopically will help to understand the mechanism of frost heave.

INTRODUCTION
Frost heave occurs when ice formation
segregates the soil structure. This process iscalled ice lensing. Although a lot of models
and theories about the frost heave (eg. Miller,
1978; Konrad and Duquennoi, 1993; Gillpin,1980) have been proposed, details of themechanism remain unknown. Frost heave insoil is a complex solidification phenomenon
that is caused by various water-related factors.
Soil is so heterogeneous in terms of texture,
particle shape, electrical charge and chemicalcomposition that it is difficult to clarify which
is important for ice lensing. Because of thissoil complexity, few microscopic observations
have been carried out to visualize ice lensing.
Ice lensing is known to occur in someporous media (Ozawa and Kinosita, 1989;
Wilen and Dash, 1995). If frost heave in an
ideal porous medium is observed directly, it
would be helpful to reveal the factors
responsible for frost heave. There are two
types of ice growth in the water system
containing a few foreign particles; one is icegrowth that encapsulates the particles and theother is ice growth that pushes the particles
ahead. The criteria of the ice formations in thesystem are affected by interaction between theice growing surface and a particle (Uhlmannand Jackson, 1966; Körber et al., 1992). Fromthe view point of the exclusion of particles, theice lensing in porous media may belong to thelatter ice growth. Therefore, it is valuable tocompare the ice lensing in a porous medium tothe ice growth which excludes foreign particles
in the water system.
In this study, we observed ice lensing inglass beads instead of soil through microscopeby using a directional freezing apparatus(Somboonsuk, Mason and Trivedi, 1984) which
can control a temperature gradient and afreezing velocity independently.
And weobserve isolated particles near ice growing
surface by using the same apparatus. Then, we
discuss influence of temperature gradient,
freezing velocity and particle size on frost
heave.
METHODS
DirectionalFreezing ApparatusA
directional
freezingapparatus(Somboonsuk, Mason and Trivedi, 1984) is
schematically shown in Figure 1.

PACKED PARTICLES SYSTEMGDEFDCA BCVs = V fDDFigure 1. Experimental apparatus
Freezing velocity, Vf, and temperature gradient A, arecontrolled independently. A: sample cell, B: teflon cellholder, C: copper blocks, D: thermo-electric devices, E:
computer-controlled pulse motor, F: translational stage

A sample, illustrated as the shaded portion, wasplaced in a teflon cell holder. To give atemperature gradient to the sample cell, eachend of the sample was held at different
temperatures, T H and TL, by two copper blocks
kept at constant temperatures by thermo-electricdevices.
The cell holder connected to atranslational stage with a computer-controlled
pulse motor was moved at a constant velocity,
Vs. Ice lensing and ice-water interface wereobserved through a microscope which wasequipped with a charge coupled device (CCD)
camera and a video tape recorder (VTR) system.
Sample images were captured in one-minuteinterval and analyzed to measure the rate of ice
lensing.
Materials and Experimental Conditions
Two kinds of in situ observations weremade. One was the observation of ice lensing
in the glass beads contacting each other (packedparticles system) and the other was theobservation of pushing or encapsulating theglass beads dispersing in water (isolatedparticles system).

The sample used here was glass beads withthe diameter of 2.2 µm. The glass beads weremixed with distilled and deaired water at thewater content of 80% by weight and compacted
in a sample cell with 3 mm thickness. The cell
was composed of a pair of 26 x 76 x 1 mm 3
slide glasses and a spacer.
When the different temperatures weregiven to each end of the sample cell, theisotherm advanced in the sample until a steadystate was attained. We made two types offreezing experiment.
In the first experiment we observed thevicinity of a growing ice lens immediately after
temperature gradient was applied until thewarmest ice lens stopped growing. The final
temperature gradients given to the cell are
shown in Table 1.
Table 1 Experimental conditions for packed
particles system
Vf (µm/s)
A (°C/mm)
Exp. 1
Exp. 2
0.20
0.28
0.33

-*
-*
-*

0.4 0.6 0.8
0.4 0.6 0.8
0.4 0.6 0.8

A: Temperature gradient,
Vf : Freezing velocity, *:Vs = 0 (µm /sec)
In the second experiment, after atemperature gradient was given to a sample cellfor 1 hour, the cell was moved toward cold sideat the constant velocity of Vs. Since theadvancing velocity of the isotherm had
decreased rapidly to low enough for 1 hour, thecell velocity of Vs gave a constant freezing
velocity, Vf, to the sample (V f = - V s ). We
observed the vicinity of ice growing surface fora duration until the cell was moved by 20 mmdistance. The condition on the temperature
gradient at steady state, A, and freezing velocity,Vf, are shown in Table 1.

ISOLATED PARTICLES SYSTEM
The sample used here was three types ofglass beads with different diameter, 2.2, 5.3 and9.7 µm. Each sample was a mixture with thewater content of 1000g-water per 1g-glass
beads. The mixture was compacted in asample cell with 100 µm thickness. After thetemperature gradient of 0.33 °C/mm was givenfor half an hour, the cell was moved at aconstant velocity. Then the vicinity of ice
growing surface was observed until the cell wasmoved by 5 mm distance. The condition on
the freezing velocity, Vf, and the particles
diameter are shown in Table 2.

ICE LENS
3.5 mmFigure 2. Final ice lens formed in the packed particles
system under A = 0.33 (°C/mm),Vf = 0 (µm/sec) and Ø =2.2 (µm) Ice lens are black and glass beads are white.
Final ice lens is the thickest ice lens.
Right: cold, Left:warm.

Table 2 Experimental conditions forisolated particles system
Particle diameter
Freezing velocity(Ø, µm)(Vf , µm/s)
9.7
4.0,3.0,2.0, 1.5
5.3

5.0,4.0,3.0, 2.5, 2.0

2.25.0, 4.5, 4.0, 3.5, 3.0, 2.5, 2.0

ICE LENS

0.1mm
RESULTS AND DISCUSSION
Packed Particles System
Figure 2 shows an image of ice lenses
under the temperature gradient of 0.33 °C/mm
for Vs =0. Black and white portions are ice
lenses and glass beads, respectively. The ice
lenses stratified in the direction of heat flow(from right to left in figure). An ice lens was
thicker as it was formed later. The warmest
ice lens grew to 3.5 mm-thick for 10 hours.
Such ice lensing was observed in otherexperiments under different temperature
gradients for Vs =0.
These observations show that frost heave
may occur in glass beads as well as in soil.
The freezing experiment for Vs =0 corresponds
to frost penetration in nature in which freezing
velocity decreases gradually and the thickest icelens is found near the final 0°C isotherm.

Figure 3. Ice lenses formed in the packed particles
system under A= 0.20, Vf = 0.8 and Ø = 2.2.
Ice lenses are black and glass beads are white. Right: cold,Left: warm. An ice lens starts to grow at the location ofsolid circle.

Therefore, observing artificial ice lensing in theglass beads will be useful in understanding offrost heave.
Figure 3 shows ice lenses under thetemperature gradient of 0.20 °C/mm for Vs =0.8 µm/sec. Stratified ice lensing with same
thickness and same space grew from cold towarm sides (from right to left in figure). Eachice lens started to grow at the same location (atthe same temperature) in the visual field ofmicroscope. The warmer end of the ice lens
moved toward cold side with growing ice lens,i.e. pushing glass beads ahead at the colder endof the ice lens. This indicates that the growthrate of an ice lens was slower than Vf and thatthe temperature at the warmer end of theTHICKNESS OF ICE LENS (mm)5Isolated Particles System
A = 0.20 (°C/mm)
A = 0.28 (°C/mm)
A = 0.33 (°C/mm)

432
100

0.2

0.4
0.6Vf ( µm/s)

0.8Figure 4. Relationship between freezing velocity andthickness of ice lens.
Thickness of ice lens depends on freezing velocity.

( a ) Vf = 1.5 µm/sec
Ø = 9.7 µm
ICEFreezing
Front( b ) Vf = 2.0 µm/sec
Ø = 9.7 µm
ICEFreezing
Front
Figure 5. Exclusion (a) and encapsulation (b) ofisolated particles
The right of a dashed line is frozen and the left isunfrozen. White particles are glass beads.
(a) Ice grows with pushing isolated particles ahead:(b) Ice grows with encapsulating isolated particles.

growing ice lens was lower than thetemperature at which the ice lens starts to grow.
When the warmer end of the growing ice lens
moved by a distance from the location at which
the ice lens started to grow, the ice lens stopped
growing and a new ice lens started to grow at
the previous location. This behavior can beregarded as frost heave under a constantfreezing velocity. Figure 4 shows relationshipbetween thickness of ice lens and freezing
velocity. The thickness of ice lens decreased
as the freezing velocity increased.

Figure5shows
exclusion
andencapsulation of isolated particles. Two kindsof ice formations were observed in the isolatedsystem. The right side of a dashed line shownis frozen area and the left is unfrozen. Icegrew with pushing particles ahead at a low
freezing velocity (Figure 5a) while it grew withencapsulating particles at a high freezing
velocity (Figure 5b). In this experiment, theice growing surface stayed at the same locationin the visual field of microscope.
Thebehavior of ice surface shows that the icegrowth rate was equal to the freezing velocity
and that the ice growing surface kept the same
temperature.
Table 2 shows freezing velocities for threekinds of glass beads to examine criteria whether
particles were encapsulated in ice or not.
Underlines denotes the freezing velocity thatparticles were pushed ahead by ice. For 9.7µm-diameter glass beads, ice encapsulatedparticles at the freezing velocities of 4.0, 3.0
and 2.0 µm/sec while ice grew with pushingparticles ahead at the velocity of 1.5 µm/sec.
The critical velocity, Vc, was affected by theparticle size.
Körber et al. (1992) has shown thecriterion for such a particle trapping phenomena.
According to their theory, an isolated particle
pushed to an advancing ice front is subject totwo counteracting forces: an attractive and arepulsive force. The attractive force comesfrom viscous drag due to fluid flow around theparticle which favors entrapment, and therepulsive force originates from van der Waals
forces.
The balance of the two forces
determines whether the particle is encapsulated
or not.
Our experimental results in the isolated
system can be explained by Körber's theory.
However, since this theory deals with the forces
around only one particle, it dose not explain thestratified ice lens observed in the packed
particles system. In fact, we often found that a
new ice started to grow beyond the particles

layer shown in Figure 5a after the particles had
accumulated to a certain thickness. Althoughdetails of the phenomenon were not examined,
the new ice growth in the isolated particles
system must be related to the ice lensing in thepacked particles system. Nevertheless, it isobvious from our experiment in the isolated
system that both particle size and the freezing
velocity are important factors for ice lensing in
the packed glass beads.

Acknowledgments
This experiment was partially carried out
at the institute of low temperature science,
Hokkaido university. The authors would liketo acknowledge for helpful suggestions by Dr.
Fukuda, Dr. Maeno and Dr. Furukawa.

References

CONCLUSION
We observed microscopic ice lensing inglass beads by using an apparatus which cancontrol temperature gradient and freezing
velocity independently. As a result, we foundthat artificial ice lenses were formed in the glass
beads and that thickness of the ice lenses
depended on freezing velocity. In addition, weobserved the criteria for exclusion andencapsulation of glass beads particles during ice
formation with respect to particle size andfreezing velocity. The result suggests thatparticle size and freezing velocity are importantfactors for ice lensing.
In conclusion,
microscopic observation of artificial ice lensing
in the glass beads will be helpful inunderstanding the mechanism of frost heave.

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