I. Introduction
When ground freezes in cold region, water isinduced to flow towards the freezing front aslenses form and frost heave occurs. Frost heavedamages roads, buildings and irrigation-drainage
systems in a farmland. To overcome such
frost-action damages, it is necessary to clarify frost
heave mechanism.
Many researchers have studied the frost heavemechanism. For instance, Miller 1) proposed amodel which is based on heat and mass transport
through a partially frozen zone called frozen fringe.
Introducing the concept of segregation potential,
Konrad 2) proposed a frost heave model which isbased on the observation that the velocity of water
intake is proportional to temperature gradient in thefrozen fringe. These models have emphasized theimportance of the frozen fringe. The frozen fringe
is assumed to consist of unfrozen water, soil
particles and a network of pore ice extending fromthe base of the active ice lens3). However, few
experimental studies have been carried out toclarify actual structure of the frozen fringe. In thispaper, we report an experimental study onmicrostructure near the freezing front observedwith a microscope in 10μm scale-resolution
during soil freezing.

Table1 Sample Velocity Vs (μm/sec) andtemperature gradient α (℃/mm)
αVs

0.2

0.125

0A0

B00.4

A1

B1

0.6

A2

B20.8

A3

B3

II. Experimental Method
The soil used here was Fujinomori clay. The soil
consisted of 15% sand , 61% silt and 24% clay.
The dry density of the soil is 1.18 g/cm3 . The
specific surface area of the soil is 24.5m2 /g. Thesoil was mixed with distilled water to make slurry
and deaired by a vacuum pump. The slurry wasplaced in an acrylic cylinder with 10 cm diameter
and was consolidated at an overburden pressure of
1 MPa for a week. A 3 mm-thick rectangularsample was obtained by cutting the consolidated
soil and placed between a pair of microscope slide
glasses as shown in figure 1. The sample cell had
a water reservoir at the warmer side to supply
water into the freezing front. Both sides of thesample cell were sealed with glue to keep saturated
condition. Vaseline was applied to the slide

76mm
26mm

SampleWater reservoir section

Thermocouples

Fig.1 Schematic diagram of sample cell for direct
observation
glasses to reduce friction between soil and glass.
Two copper-constantan thermocouples wereinserted into the sample cell for the measurement oftemperature. The sample cell was lighted up by
using a cold light during the experiment.
A schematic diagram of our experimental
apparatus is shown in figure 2. The sample cell
was placed in a teflon cell holder indicated by a star
mark ; ☆. The temperature of each end of thesample cell was controlled by thermo electriccooling devices. Thus during the experiment, aconstant temperature gradient, α, was maintained.
The sample cell holder was moved toward the coldside at a constant velocity from 0 to 40 μm/sec by
a computer-controlled pulse motor. Eight series ofexperiments were conducted with two different
temperature gradients and four different sample
velocities, Vs. When Vs was zero, the isotherms
moved immediately after lowering the temperature
at cold side. When Vs was not zero, the freezing
velocity, Vf, was equal to the sample velocity, Vs.
The experimental conditions on temperature
gradients at steady state and sample velocities areshown in table 1.

VTRCCD
CameraDuring each experiment, the apparatus waslocated in the ambient temperature of 5.0 ℃; sothat the initial temperature of the sample was 5.0 ℃.
Each observation was made after a constanttemperature gradient was given to the sample forone hour. Ice segregation and crystal growth near
the freezing front were observed with a microscope(40 magnification). The microscope was equippedwith a charge coupled device (CCD) camera and avideo system. Sample images were captured in
one-minute interval. The sample images wasdivided with 20 μm mesh by a computer and thecrystal growth rate was measured from a relative
coordinate of the growing surface. And thetemperature of ice segregation was determined bytracing the measured temperature profiles on theimage.
III. Experimental Results(1) Freezing experiment with zero sample velocity(A0 and B0)
Figure 3 shows an image of the freezing process
in the condition that sample A0 at a velocity of 0μm/sec and a temperature gradient of 0.2 ℃/mm.
It was observed that ice lenses segregatedrhythmically from the cold side and that thewarmest ice lens was formed at a point below the0 ℃ isotherm. Neither pore ice larger than 10 μm
nor a displacement of soil particles was found in
the region between the warmest ice lens and 0 ℃
isotherm. The warmest ice lens started to segregate
at -0.55 ℃ and grew 1.7 mm-thick during time
period of 400 minutes. The temperature at theinterface between the warmest ice lens and soilparticles increased gradually and reached -0.2 ℃.
Figure 4 shows the change in thickness of thewarmest ice lens with time for specimens A0 andB0. Specimen A0 was frozen at a larger
temperature gradient than specimen B0 (see Table1). The elapsed time was counted from start ofMicroscope
Stepping motor

ColdChamber

HotChamber☆

Fig.2 Schematic diagram of direct observation
apparatus

Fig.3 Image of Fujinomori clay in freezing
process for A0THICKNESS (MM)1.510.5000.4A0B00.2A 0.20 ℃/mm
B 0.125℃/mm

100200300
ELAPSED TIME (MIN.)

0.1
400

Fig.4 The relationship between the thickness ofthe warmest ice lens and time
segregation of the warmest ice lens. The warmest
ice lens grew rapidly in the beginning, and grew
more slowly at later time stages. After 400
minutes, a thicknesses of warmest ice lenses were
1.7 mm and 1.3 mm for A0 and B0, respectively.
These results indicate that the thickness of ice lensincrease more at the larger temperature gradient andthat the growth of ice lens stabilized with time.
The difference in the thickness of ice lens between
A0 and B0 came from the difference in the growth
rates in the early stages of the experiment.
Figure 5 shows temperatures at the growthsurface of the warmest ice lens. The temperatures
increased with time and were gradually
approaching -0.2 ℃. The temperatures at which
the warmest ice lenses started to form were -0.55℃ and -0.4℃ for A0 and B0, respectively. Whenthe temperature gradient was steeper, the warmest
ice lens started to form at a lower temperature.

0TEMPERATURE (℃)

A 0.20 ℃/mm
B 0.125℃/mm-0.2B0-0.4-0.6

00.3

GROWTH RATE (μm/s)

0.5

20-0.6 -0.5 -0.4 -0.3 -0.2 -0.1
TEMPERATURE (℃)

0Fig.6 The relationship between growth rate of thewarmest ice lens and temperature at the growthsurfaceand 3 experiments at conditions B0. No ice lenses
grew at temperature above -0.2 ℃. This indicatesthat the growth rate of ice lens is determined by thetemperature at the growth surface. These results
agreed well with the result reported by the Ishizaki
et al.4) .
(2) Freezing experiments with different sample
velocities (A1 to A3 and B1 to B3)
Figure 7 shows an image of freezing process for asample which was moving at a velocity of 0.6 μm/sec towards the freezing element at a temperature
gradient of 0.2 ℃/mm (condition A2). Rhythmic
ice lenses were observed near the freezing front
during freezing. In this series of experiments, each
ice lens was formed in a similar interval and had
similar thickness. Once a new ice lens segregatedon the warm side, previously formed ice lenses
stopped growing. This ice lens also stopped
growing when a more recent ice lens started tosegregate on the warm side. In the case of A2, thesegregation and the growth of ice lens wereobserved at -0.5℃.

A0100
200300400
ELAPSED TIME (MIN.)

Fig.5 Temperature at growth surface of thewarmest ice lens as a function of time
Figure 6 shows growth rate of the ice lenses at thegrowth surface of the warmest ice lens as afunction of temperature. The results in Fig. 6were obtained from 7 experiments at conditions A0A01A02
A03
A04
A05
A06
A07
B01
B02
B03

Fig.7 Image of Fujinomori clay in freezing
process with applying a sample speed (A2)

3
2
100

0.5
0.4
0.3
0.2
0.1

50
100
150200ELAPSED TIME (MIN.)

Fig.8 Total heave when the sample was moved
Figure 8 shows total heave as a function of time
for different sample velocities. The total heave wasdetermined by movement of a soil particle on thesample images. In this series, the elapsed time wascounted from the start of the sample cellmovement. Heave increased linearly with time foreach specimen. The total heave increased withincreasing freezing velocity.
Figure 9 shows relationship between heaving rateand sample velocity. The solid line is the best fit
for the experimental values for series A (α= 0.2℃/mm) and the dashed line for series B (α=0.125 ℃/mm).
Figure 10 shows the segregation temperature forthe ice lenses. The segregation temperature is here
defined as the temperature of the interface at whichan ice lens is growing. Each ice lens started tosegregate at a constant temperature. When thefreezing velocity and the temperature gradient werehigh, ice lens segregated at a lower temperature.
These results indicate that the segregation
temperature was dependent on the freezing velocity
than the temperature gradient.
IV. Discussions
We will discuss here a frost heave model by using
the experimental results. At first, we examine thefrost heave model based on a partially frozen zone,
so called frozen fringe.
In the frozen fringe model, frost heave isdetermined by the coupled of heat and water flowin the frozen fringe. Soil water would flow
through the frozen fringe with permeability
coefficient, K, from the unfrozen zone to thesurface of the growing ice lenses due to thepressure gradient, dP/dx. If all water flowing toice lens contributes to the warmest ice lens growth,
the growth rate of the warmest ice lens, Vg, isgiven byVg = - K dP
ρ i g dx ,(1)0HEAVE RATE Vh (μm/s)

HEAVE (mm)4A1A2A3
B1
B2
B3

A 0.20 ℃/mm
B 0.125℃/mm
ABVh = -0.04 + 0.6Vf
Vh = -0.02 + 0.6Vf

00.2 0.4 0.6 0.81SAMPLE VELOCITY Vs (μm/s)

Fig.9 The relationship between frost heave rateand sample velocity

0-0.2-0.4-0.6-0.8-10TEMPERATURE (℃)

5A1A2A3B1B2
B350100
150200ELAPSED TIME (MIN.)

Fig10 Temperature at growth surface of ice lens
where ρi is the density of ice and g is thegravitational constant. Gilpin 3) and Nixon 5) haveassumed that pore ice would grow so that unfrozen
water content would decrease. They haveexpressed the permeability of the frozen fringe, K,
as a function of temperature:
K = K0α ,(2)(-T)
where K0 is the permeability of frozen ground at-1 ℃, T is the temperature in the frozen fringe andα is an empirical constant. Equation (2) meansthat the permeability of the frozen fringe decreases
exponentially with decreasing temperature of thefrozen fringe. Consequently, the growth rate of
the warmest ice lens calculated by eq. (1) should
decrease.
In our experiment, the growth rate of the warmest
ice lens decreased with increasing temperature at
the growth surface of ice lens as shown in figure.
6. The experimental result corresponds to not thefrozen fringe model by Gilpin and Nixon but theexperimental results by Vignes et al.6) , Biermans etal.7) and Ozawa et al.8) . This discrepancy may
come from the postulation that there would be poreice in the frozen fringe. Actually, we did notobserve any pore ice larger than 10 μm could beobserved (e.g. figure. 3, figure. 7).
If we assume that there is no pore ice in the frozen
fringe, the frozen fringe has a constant permeability
and the soil water flows to the surface of growing
ice lens through the frozen fringe due to atemperature difference. By applying generalized
Clausius-Clapayron equation, pressure of the soil
water on the growth surface of ice lens is given by∆P = 1.23(Ts -Tm)+0.11∆Pi +Π [MPa]9), (3)where ΔP is the pressure difference between thesoil water and an atmosphere, Ts is the temperature
at the growth surface of ice lens and Tm is themelting point of ice at an atmospheric pressure, Δ
Pi is the pressure difference between ice lens andthe atmosphere, and Π is the osmotic pressure of
the soil water. For soil freezing without
overburden pressure, ice pressure in the soil may
be at the atmospheric pressure. In addition, theosmotic pressure may be negligible for salt freesoil. Then eq. (3) becomes∆P = 1.23(Ts -Tm)[MPa] .

(4)

This equation means that the pressure difference
can be expressed as a linear function of thetemperature at the growth surface of ice lens. If it
is assumed that the hydraulic conductivity of thefrozen fringe and kinetic coefficient at the growthsurface of ice lens are constant, the calculated ice
lens growth rate would increase with decreasing
the temperature at the growth surface of ice lens.
This relationship between the growth rate and thetemperature is consistent with our experimental
results in figure 6. Nevertheless the ratio
calculated from eq. (4) is one order larger than ourexperimental result. To explain the difference
between the calculation and the experiment, twopossibilities can be considered; one is thathydraulic conductivity of soil between 0℃
isotherm and growth surface of ice lens might be
1-order lower than that of unfrozen soil, and theother is that an unfrozen water film on the growthsurface of ice lens would have some resistance tosupply water into ice crystal. The former
possibility may come from either the viscosity ofwater affected by local changes of temperature,pressure and solute concentration or the clogging
of pore by bubbles which would be formed oninterface. This possibility, however, will be low
because frost heave was observed in theexperiment using deaired pure water and glass
beads. The latter possibility will come from kinetic
process during interface growing. The kinetic
process is a process which deals with a dependenceof molecular incorporation to an interface on theinterface growth rate. The interface kinetics is oneof the fundamental factors which decide a crystal

growth shape.
For the discussion of the kinetic process in frost
heave, however, more studies will be needed
considering non-equilibrium process. In any
possibility, our experimental results indicate thatthe ice segregation rate is determined by the kinetic
process at the segregating surface rather than thehydraulic conductivity in partially frozen zone
(frozen fringe).
V. Conclusions
Microstructure near freezing front during soil
freezing was observed directly by using an one
dimensional freezing apparatus. From theexperiments, the following results are obtained;(1) No pore ice was formed in the frozen fringe.
(2) The frost heave depends on the freezing
velocity. (3) The heaving rate depends on thetemperature at the growth surface of the warmest
ice lens. (4) The temperature of ice lenssegregation depends on the freezing velocity.
It was concluded that the temperature at thegrowth surface of the warmest ice lens is an
important factor for the frost heave mechanism.
We will need more studies on the microscopic
process near the freezing front to clarify the frost
heave mechanism.
Acknowledgments
The authors would like to acknowledge helpful
suggestions for making the experimental apparatus
by Dr. Takeda and Mr. Okamura.
References
1) Miller R. D.: Frost Heaving in Non-colloidal
soils, Proc. 3rd Inter. Conf. Permafrost, pp.
707-713, (1979)
2) J. M. Konrad and C. Duquennoi : A Model for
Water Transport and Ice Lensing in Freezing
Soils, Water Resources Res., pp. 3109-3124,(1993)
3) Gillpin R. R. : Model for Prediction of Ice
Lensing and Frost Heave in Soils, Water
Resources Res., pp. 918-930, (1980)
4) T. Ishizaki and N. Nishio : Experimental studyof final ice lens growth in partially frozen
saturated soil, Fourth International Symposium
on Ground Freezing, pp. 71-78, (1985)
5) J. F. Nixon : Discrete ice lens theory for frost
heave in soils, Can. Geotech. J., pp. 834-859,(1991)
6) M. Vignes and K. M. Dijkema : A Model for
Freezing of Water in a Dispersed Medium, J.

Colloid and Interface Sci., pp. 165-172, (1974)
7) M. B. G. M. Biermans, K. M. Dijkema and D.
A. De Vries : Water Movement in Porous Media
towards an Ice Front, J. Hydrology, pp.
137-148, (1978)
8) H. Ozawa and S. Kinosita : Segregated Ice
Growth on a Microporous Filter, J. Colloid andInterface Sci., pp.113-124, (1989)
9) M. Mizoguchi : A Derivation of Matric Potential
in Frozen Soil, The Bulletin of the Faculty ofBioresources, Mie University, No.10, pp.175182, (1993)