Ice Lensing Mechanism
during Soil Freezing

Graduate School of Bioresources, Mie University
Kunio Watanabe
December, 1999

Kunio Watanabe, Ice Lensing Mechanism during Soil Freezing
Nougyo-Doboku, Graduate School of Bioresources, Mie University
1515 Kamihama Tsu, Mie 5148507, Japankunio@dobokuPc4.bio.mie-u.ac.jp

This edition is translated from an original Japanese thesis, which submitted to theGraduate School of Bioresources, Mie University, for the degree of Doctor ofPhilosophy.

ABSTRACTIce Lensing Mechanism during Soil Freezing
Kunio WATANABE
Mie University, 1999
When soil is cooled under 0 ˚C, soil water solidifies with decreasing
temperature.

This is known as soil freezing.

In Japan, the ground is frozen

seasonally in Hokkaido, Tohoku, and some mountain areas.

Short-term frozen groundis even found in the western part of Japan. Soil freezing is estimated to occur inalmost 70 per cent of the Earth’s land surface.

Furthermore, soil is sometimes frozen

artificially for use. There are many situations in which soil freezes.
If soil expands when it freezes, the volume change is called frost heave.
When heaving occurs, some of the ice layer formed near the ground surface is present
as seems of pure segregated ice; this ice layer is called an ice lens. The ground surface
sometimes expands dozens of centimeters due to the ice lensing.

It causes muchdamage to paved road, drainage system in farmland, foundation, and so on.

Thegrowth of ice lenses induces soil water to flow from the unfrozen zone to the surfacezone.

In this case, some solutes illuviate to near the ground surface with the water

flow. To overcome such frost-action damage, it is important to clarify the mechanismof ice lensing during soil freezing. Furthermore, ice lensing is not a phenomenon
limited to soil.

It has also been observed in various porous materials.

Knowledge ofthe mechanism of ice lensing will be applied to fields that involve these frozen materials,including physical chemistry, biology, material science, food processing, and medicine.
Numerous studies with the intention of clarifying the mechanism of ice lensing
have been reported.

Presently, one of the theories most often used is the secondary

frost heave theory. In this theory, presence of partially frozen region near growing
surface of ice lens is assumed.

The intermittent formation of ice lenses is thenexplained from calculating stresses in the region.
has not been confirmed experimentally.

However, the partially frozen region

And the stress partition factor, which isimportant for calculating the neutral stress, has not been theoretically verified.
Summarizing the historical studies, there are two problems associated with clarifying

mechanism of ice lensing.

One is to clarify the microstructure near the freezing front,

i.e. to clarify water conditions and particle migration in the partially frozen region.
The other is to explain the dynamic mechanism of ice lensing, in which the generationand growth of an ice lens is repeated to form intermittent layers.

In order to solvethese problems, we performed three series of freezing experiment using a unidirectional
freezing apparatus.

In the first experiment, ice lensing in soil and porous media

consisting of fine particles were microscopically observed, then, following results wereobtained. Ideal ice lenses for modeling can be made using uniform sized glass beads.
The growth of ice lens is dependent on supercooling of the growth surface.

Thefreezing rate influences the ice lens growth more than temperature gradient. It issuggested that freezing rate, supercooling degree at growth surface of ice lens andparticle condition near growing ice lens were important factors for considering ice
lensing model.

From the second experiment, in which ice interface in water withdispersed glass particles was observed, the criteria for exclusion and encapsulation ofparticles during ice formation with respect to particle size and freezing rate was shown.
The relationship between particle size and critical freezing rate was explained by
Köber’s theory.

It is suggested that the critical freezing rate was important for thegeneration of ice lens.

In the third experiment, microstructure in the vicinity of icelens is observed using Raman spectroscopy. It is obtained that no ice was found in any
pore warmer than the warmest ice lens in the porous media and the ice lens grew
without penetrating the warmer pores.
Based on the experimental results, we then presented a model for simulating
the formation of ice lenses during freezing of unconfined uniform porous media ispresented.

The main notions of the model are that generation and jump are dependent

on the freezing rate, and growth is dependent on supercooling.

The critical freezing

rate is assumed to vary with changes in the number of particles near the ice lens as itgrows.

The model was demonstrated for the unidirectional freezing of a porous

medium consisting of fine glass particles.

The numerical results show that this model

can represent the formation of intermittent layers of ice lenses in such a system.

Thismodel can be applied to ice formation in unconfined water-soaked porous media.
As mentioned above, we clarified the microstructure near the freezing front inwater-saturated porous media experimentally and made a model, which can explain theformation of intermittent layers of ice lenses.

ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to Dr. Masaru Mizoguchi and Dr.
Takeshi Ishizaki for their numerous invaluable guidance during this study.

A specialthanks to my supervisor, Dr. Masahiro Aragaki, for his useful comments andencouragement, and also my sincere thanks to Dr. Hideki Kiyosawa for his invaluableadvice.
Most of the experiments for this paper were carried out at the Institute of Low
Temperature Science, Hokkaido University.

I gratefully acknowledge Dr. Masami

Fukuda, Dr. Takeo Hondoh and Akira Hori, who provided me with a chance to do theexperiments.

Special thanks are also expressed to Ms. Yoshiko Muto to staffs at theinstitute and staffs at the Laboratory of Agricultural physics, Mie University, for theircontinuing support to the study.
I would like to thank Dr. Yoshinori Furukawa and Dr. Kazushige Nagashima
for the development of unidirectional freezing apparatus and their comments at theexperiments.

I also thank Dr. Hiroshi Fukazawa and Dr. Tomoko Ikeda for the use ofRaman spectroscopy and thank Dr. Satoshi Takeya for the use of X-ray system.

I alsowish to acknowledge Dr. Satoshi Akagawa, Dr. Yoshiaki and Mr. Yutaka Minami fortaking electron micrographs and measuring grain size distribution and specific surfacearea.
I also wish to acknowledge Dr. Fujio Tuchiya, Dr. Kazuo Takeda, Takahiro
Ohrai, and member at frozen ground section of Japanese Society of Snow and Ice for
their suggestion and discussion. I extend my appreciation to Dr. Yuji Kodama, Dr.
Toshio Sone, Dr. Yoshiyuki Ishi, and Dr. Jorge Strelin, who have been very
encouraging.
Thanks are also due to the Japan Society for the Promotion of Science for
grants awarded for this study. Finally, I am pleased to acknowledge my wife andpeasants.

CONTENTS

1.

2.

3.

Introduction1.1
Soil freezing
1.2
The importance of studying soil freezing
1.3
Ice lensing and the purpose of this study
Factors and theories of ice lensing
2.1
Introduction
2.2
Main factors considered in soil freezing
2.2.1
Unfrozen water
2.2.2
Ice formation
2.2.3
Water flow during soil freezing
2.2.4
Heat transfer during soil freezing
2.3
Ice lensing theories and models
2.3.1
Capillary theory
2.3.2
Hydrodynamic model
2.3.3
Secondary frost heave theory
2.3.4
Osmotic model
2.3.5
Takashi’s theory
2.3.6
Adsorption force theory2.3.7
Segregation potential concept
2.3.8
Kinetic model
2.3.9
Thermomolecular pressure model
2.3.10 Thermodynamics approach
2.4
Problems for theories and models of ice lensing
Materials and apparatus
3.1
Characteristics of samples and grain-size distribution
3.2
Surface conditions
3.3
Specific surface area and distribution of pores
3.4
Unfrozen water content
3.4.1
NMR methods
3.4.2
Test procedure
3.4.3
Unfrozen water content
3.4.4
Effect of solute on unfrozen water content
3.5
Unidirectional freezing apparatus

page1
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27
27
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2930
31
33
36
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4.

5.

6.

7.

8.

Observation of ice lensing and frost heaving (Exp. 1. 2)
page
4.1
Sample and method
57
4.2
Experimental results
61
4.2.1
Freezing experiment with zero sample rate
61
4.2.2
Freezing experiment with constant sample rate74
4.3
Discussion
85
4.4
Summary88
Observation of freezing of dispersed glass beads in water (Exp. 3)
5.1
Sample and method
89
5.2
Experimental results
90
5.3
Discussion
93
5.4
Summary
94
Observation of the vicinity of ice lens by Raman spectroscopy (Exp. 4)
6.1
Sample and method
95
6.2
Raman spectroscopy
100
6.3
Experimental results
100
6.4
Discussion
101
6.5
Summary102
A Model for the Formation of Ice Lenses in an Unconfined, Watersaturated, Porous Medium consisting of Spherical Particles
7.1 Model
103
7.1.1
System and conditions
103
7.1.2
Generation of an ice lens
103
7.1.3
Growth of the ice lens
105
7.1.4
Heat transfer
106
7.1.5
Number of particles near the growth surface
107
7.1.6
Ice lensing
109
7.2
Simulation
112
7.3Discussion
115
7.4
Summary118
Summary and conclusions

References

LIST OF FIGURES
Figure caption

pageFig. 1. Schematic diagram of soil freezing and ice lensing.

7

Fig. 2. Ice lensing observed in soil and in porous medium consisting

9

uniform sized glass particles.
Fig. 3. Schematic drawing of ice-water interface prior to propagating

20

through pore restriction between three touching spheres.
Fig. 4. Schematic diagram of the frozen fringe, with ice lens.

23

Fig. 5. Principles of the secondary frost heave theory.

24

Fig. 6. Grain size accumulation curves for the samples.

35

Fig. 7. Electron micrographs of samples.

37

Fig. 8. Distribution curves of nano pores of the samples.

44

Fig. 9. Schematic diagram of NMR setup.

49

Fig. 10. Unfrozen water content in the frozen samples

50

Fig. 11. Unfrozen water curves of samples 1 saturated with NaCl,51

KCl and MgCl2 solutions.
Fig. 12. Schematic diagram of unidirectional freezing apparatus.

54

Fig. 13. Schematic diagram of temperature gradient and freezing

56

rate given to the sample on the unidirectional freezing apparatus.
Fig. 14. Schematic diagram of sample cell

60

Fig. 15. Images of the freezing samples under the conditions of A0 and D0.

63

Fig. 16. The change in thickness of the warmest ice lens in each sample.

66

Fig. 17. Temperatures at the growth surface of the warmest ice lens.

70Fig. 18. Relationship between growth rate of the warmest ice lens and72
temperature at the growth surface.
Fig. 19. Relationship between the growth rate of ice lens and supercooling73

degree at the growth surface.
Fig. 20. Images of the freezing samples under the conditions of A2 and D2.

76

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

79

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

80

Fig. 23. Total heaving amount when a sample was moving with constant rate. 81

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

82

LIST OF FIGURES
Figure caption

pageFig. 25. Temperature at growth surface of ice lenses.

83

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

84

Fig. 27. An image of the vicinity of ice growing surface in water91

with dispersed glass particles.
Fig. 28. Physical factors on a spherical particle ahead of the growing surface. 92
Fig. 29. The Raman spectra obtained from samples at room

97

temperature and the temperature of liquid nitrogen.
Fig. 30. A computer-processed image of the vicinity of the growth98

surface of the ice lens monitored using the Raman system.
Fig. 31. A series of the Raman spectra obtained from pores.

99

Fig. 32. Schematic description model system.

104

Fig. 33. Schematic description change in number of particles near ice lens.

108

Fig. 34. Schematic description freezing rate.

111

Fig. 35. Growth amount of ice lenses.

114

Fig. 36. Schematic description of the vicinity of the ice lens.

117

LIST OF TABLES AND PHOTOGRAPHS
Figurecaption

page

Photograph 1.

Frost damage to paved roads (Kushiro, 1997).

3

Photograph 2.

Ice lenses in actual soil (James Ross Island, 1998).

8Photograph 3.

A pulsed NMR instrument PRAXIS-2.

48

Photograph 4.

Unidirectional freezing apparatus.

53

Photograph 5.

Raman spectroscopy.

96

Table 1.

Characteristics of the samples 1-5.

34

Table 2.

Experimental conditions (Exp. 1 and Exp. 2).

59

Table 3.

Experimental conditions (Exp. 3).

89

LIST OF SYMBOLS
symbolAunit
meaning2marea-2 -1
m s
coefficienta0m
average molecular distance in liquid
-1 -1
B
ms K
coefficientC
mol kg-1 molality
J K-1kg-1 specific heatm-5
coefficient
-2 -1
Dm s
self diffusion coefficient of water moleculedmdistancemmean particle diameter
EJinternal energyFηΝ
viscous drag forceFγ
Νrepulsive force
GJGibbs free energy-2gms
gravitational acceleration
HJ
enthalpy
Js-1m-2
flux of water molecule-1Kms
hydraulic conductivity-1
Kf
K kg mol molar freezing point constantkW m-1K-1 thermal conductivityk
J K-1
Boltzman coefficient-1
LJ kg
latent heat of fusion
mkg
mass-3Nm
number of particles per unit volumepPa
pressure
QW
heat flux
Rmradius of particle
-1 -1
Rf
Jm s
resistance from freezing processRh
J m-1s-1
resistance from water flowrm
curvature radiusrpm
radius of pore
-1
SJK
entropySPm2K-1s-1 segregation potential
TK, ˚C
temperaturet, tpstime
TmK, ˚C
melting temperature of bulk waterUc
coefficient of uniformity
Uc’coefficient of curvature-1
Vc , Vc’ m scritical rate of progress of freezing front-1
Vfms
rate of advancing of freezing front

LIST OF SYMBOLS
symbolVhVilVsxzαβχ∆Τf ,∆Τ∆µγηιννRΠ
ρσsubscriptefH
hiilLlnpqsuwunitm s-1m s-1
m s-1mm
K m-1
K, ˚CJJ m-2
N s m-2
m-1
m-1
Pakg m3Pa

meaningheaving rate
rate of ice lens growthrate of moving of sample cell = - Vf v m3
coordinate
coordinate
temperature gradientconstantstress partition factor
temperature difference from Tmchemical potential
interfacial energy
coefficient of viscosity
van't Hoff coefficientnumber of vibration
Raman shift
osmotic pressure
density
stressmeaning
effective
frozen, freezing
highheave
ice
ice lens
lowliquidneutralpore
quasi-liquid
solid, soil, sample
unfrozenwater

specific volume