Mechanisms discussion of frost heave and test verifications of moisture migration

Chang Yuan,ChengSong Yang ,LianHai Zhang

State Key Laboratory of Frozen Soil Engineering,Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Sciences,Lanzhou,Gansu 730000,China

1 Introduction

The phenomenon of frost heave was first researched in the late 17thcentury,but the main cause,moisture migration,was not found until the 20thcentury (Liet al.,2000).In cold regions,frost heave attacks various engineering constructions.In Canada,the Canadian Oil (Canol) petroleum pipeline constructed in 1943 was abandoned the next year due to the destruction caused by frozen heave.The Qinghai-Tibet Highway was started in 1954,but frost problems on the Qinghai-Tibet Plateau quickly drew the attention of the Ministry of Communications and Railways (Zhou,2000),as 85% of the roadbed problems were caused by thaw collapse and 15% were caused by frost heave and frost boiling (Wuet al.,2002),and many bridges and culverts were destroyed by frost heave.One of the most frequent disasters on the Qinghai-Tibet Railway is frost heave (Cheng and Ma,2006;Cheng and Yang,2006).

Regarding the mechanisms of frost heave,the frozen fringe theory proposed by Miller (1972) is generally accepted,which is also called the second frost heave theory:between the freezing front and the warm side of the ice lens there exists a zone with low water content,low conductivity,and no frost heave,which is called the frozen fringe.Many subsequent researchers have hypothesized about the mechanisms of ice lens formation based on the frozen fringe theory,including Gilpin(1980),Konrad and Morgenstern (1981),O’Neill (1983)and Sheng (1995).They conducted a great deal of researches on frozen fringe as related to temperature,pore water pressure,unfrozen water content,moisture conductivity,ice pressure,and so on.

Herein a freeze-thaw cycle experiment was conducted with clay silt from the Qinghai-Tibet Plateau simulating the field environment and adopting advanced apparatuses to measure various parameters involving soil-water potential,temperature,and water supplement.And the relations among these parameters were analyzed to verify the moisture migration theory.

2 Unfrozen water content and its measurement

Unfrozen water content is an important index with which not only to evaluate the characteristic of moisture migration,but also to perform thermotechnical calculations of frozen soil.Under conditions below 0 °C,the free energy of water in soil reduces,but there still exists some liquid water because of soil particles’interface energy and the pore structure among particles,that is called unfrozen water (Cannell and Gardner,1959;Miller,1980;Dashet al.,1995;Watanabe and Mizoguchi,2002).In the processes of freeze-thaw cycles,unfrozen water migrates along the temperature gradient,and the existence of unfrozen water and its phase change affect the heat transformation and mass transportation,causing the moisture,salinity,and colloidal particles to redistribute.The variation of unfrozen water content changes the hydraulic characteristics of frozen soil,and this adversely affects the flow of water in the soil.The relation between temperature and unfrozen water content is a fundamental feature in simulating the characteristics of water dynamics (Watanable and Wake,2009).The strength of frozen soil could be affected by unfrozen water,the changes in which would cause the mechanical properties of frozen soil to vary obviously and even fiercely.

Currently,there are many methods to measure unfrozen water content,including pulsed nuclear magnetic resonance (NMR),time-domain reflectometry(TDR),calorimetry,thermometry,the sublimation method,and CT imagery.

Pulsed NMR measures the free-induction decay(FID) of protons in a magnetic field.The FID value of water is proportional to the amount of water in the sample.Because the FID signal of ice decreases more rapidly than that of liquid water,the amount of unfrozen water in a sample can be determined by its FID value,when the signals can be separated (Watanabe and Wake,2009).NMR is a fast and accurate method for determining the unfrozen water content in frozen soil in the laboratory (Smith and Tice,1988;Ishizakiet al.,1996;Watanabe and Mizoguchi,2002),but the necessary equipment and facility are expensive.The expression derived from this technique could be(Kujala,1991):

whereWu(%) is the unfrozen water content of frozen soil,W0(%) is the water content of unfrozen soil,αandβare parameters related to the soil characteristics.

With the TDR method,the relative permittivity of soil,rε,can be calculated from the TDR waveform(Toppet al.,1980),to determine the unfrozen water content by building a function between the volatile water content and the permittivity.This method is fairly easy and is usually used to determine the unfrozen water of soil at its original position in the field(Watanabe and Wake,2009).The TDR method is generally accepted in measuring water content in unfrozen soil,but more research is needed in applying this method to frozen soil (Wanget al.,1998;Zhou and Chen,2003;Chenet al.,2004).

The CT image method measures the unfrozen water content of frozen soil by obtaining the gray value in the process of frozen soil thawing,during which phase change occurs.Experimental results (Li,2011) have shown that the gray value rises obviously over time when the temperature rises and the frozen soil thaws;at the moment the thawing finishes,the time-gray value figure appears as an obvious turning point,which signal the end of the thawing of the frozen soil.

Calorimetry is a classic method for measuring unfrozen water content (Haeberli,1978).A frozen soil sample with a stable subzero temperature is put into calorimetric water,and after a period of heat transformation,the sample and the calorimetric water would achieve a heat balance.According to the law of conservation of energy,the heat absorbed by the sample is equal to the heat released by the calorimetric water and each part of the calorimetric device,then the ice content could be calculated out and the unfrozen water content could be computed.This method is complex in both operation and computation,but its principle is clear,its accuracy is high,it accumulates abundant experience and it is generally used.Its expression is:

whereCcw,Cd,Cware,respectively,the special heat of the calorimetric water,the dry soil,and the water in the soil,cal/(g·°C);Wi,Wu,Wcw,Wd,Ww,Wc,Wpare,respectively,the percentage content of ice,unfrozen water,calorimetric water,dry soil,ice and water together,cup,and nitrolacquer,%;andt'0,t'n,t'sare,respectively,the original temperature of the calorimetric water,the mean temperature of the calorimetric water after amendment,and the original temperature of the frozen soil sample,°C.

Thermometry is a quick method to acquire the unfrozen water content,which is determined by the soil properties (including the mineral chemical components of the soil particles,dispersity,water content,density,and the components and concentration of the aqueous solution),the external conditions (including temperature and pressure) and the freeze-thaw history,and the steady dynamic equilibrium between the unfrozen water content and the subzero temperature.It is expressed as (Xuet al.,1985b):

whereWuis the unfrozen water content,%;θis the negative temperature’s absolute value,°C;eandfare empirical coefficients of the soil properties.In engineering applications,one-point and two-point prediction models are used to quickly measure the unfrozen water content (Xuet al.,1985a).

3 Frozen fringe

The frozen fringe is a partial frozen zone between the warm side of the ice lens and the freezing fringe with low water content,low moisture conductivity and no frost heave.It is a transition zone with pore ice from unfrozen soil to frozen soil,where the unfrozen moisture migration occurs.This layer is divided into three regions,the frozen zone,the frozen fringe and the unfrozen zone,of which the frozen fringe is most closely related to ice segregation.

After the frozen fringe zone was first proposed,researchers began to conduct experiments and simulations to explore its structures.For example,Akagawal (1988) used X-rays to analyze the frost heave ratio,water absorption rate,and the thickness and temperature of frozen fringe.Watanableet al.(1997) used a high-resolution CCD camera to dynamically shoot the freezing front to observe the frozen fringe’s microstructure.Liet al.(1999) used a cryogenic copy membrane from a controlled freezing test to research the characteristics of the frozen fringe and they combined the data of frost heave observation to assess change in specific parameters of the frozen fringe.The structure of the frozen fringe is shown in figure 1.

The thickness of the frozen fringe is defined as the distance between the freezing front and the warm side of the segregated ice layer (Xuet al.,1997):

whereDsis the thickness of the frozen fringe (cm);Hfis the position of the freezing front (cm);Hsis the position of the warm side of the segregated ice layer (cm).

Therefore,the thickness of the frozen fringe is determined by two parameters:the positions of the freezing front and the warm side of the segregated ice layer.Under the coefficient actions of these two parameters,the thickness of the frozen fringe varies with time in three scenarios:(1) the thickness of the frozen fringe increases with time when the freezing front moves faster than the warm side of the segregated ice layer;(2) the thickness does not change when the moving speed of the freezing front is equal to that of the warm side of the segregated ice layer;(3) the thickness decreases with time when the freezing front moves slower than the warm side of the segregated ice layer.

The freezing front is a moving interface between frozen soil and unfrozen soil,and its position is generally at or slightly lower than the position of 0 °C,whose moving velocity is related to the temperature gradient.When the temperature gradient increases,the freezing front moves quickly downward,but when the temperature gradient decreases,the freezing front moves slowly downward,or even stays at a certain depth because of the resistance of latent heat released from the phase change from water to ice (Qiuet al.,1994).

Figure 1 Structure of the frozen fringe

The temperature of the warm side of the segregated ice lens is called the segregated temperature,and it is another frequent research object.Ice segregation appears easily where there is no construction joint,when the segregated temperature is only determined by temperature (i.e.,the segregated temperature decreases when temperature of the cold side decreases).At the construction joint,the segregated temperature is determined by the material’s shearing strength;when the shearing force caused by the temperature difference is greater than the material’s shearing strength,shear failure occurs and segregated ice appears (Xuet al.,1997).

From the freezing front to the warm side of the ice lens in the frozen fringe zone,the temperature decreases from the freezing point to the segregated temperature,and the pore water pressure,unfrozen water content,and moisture conductivity all decrease as the temperature decrease (Shenget al.,1995).With no upper load,the segregated temperature and pore water pressure satisfy the Clapeyron equation (Konrad,1989),and the unfrozen water content and moisture conductivity decrease exponentially with decreasing temperature (Anderson and Tice,1973).This makes it more difficult for water to migrate to the warm side of the ice lens,and when the segregated temperature decreases to a critical valueTsm,the water migration stops.At the same time,ice pressure gradually increases to the separated ice pressure,the separated ice pressure gradually increases to the upper load pressure,and the effective stress gradually decreases to zero,which signs the initiation of a new ice lens (Gilpin,1980;Konrad and Morgenstemm,1980;O’Neill and Miller,1982).

4 Mechanism of frost heave and experimental verification

4.1 Frost heave and its mechanism

When water in soil freezes to ice,its volume increases by 9%;this is called the frost heave of water.When the frost heave of water leads to the volume expansion of soil,this is called the frost heave of soil.In the freezing process,moisture migration could cause water concentration,which is the main cause of frost heave (Qiuet al.,1994).

There are three processes in frost heave:(1) a dynamic process between the ice lens and the water film outside the soil particles (water phase change and suction);(2) water transport from the underground water level to the water film;(3) latent heat transformation in the phase change of water.Frost heave is a macro phenomenon in frozen soil caused by moisture migration,and the driving force for moisture migration is the negative pressure gradient derived from the temperature gradient in the frozen fringe (Sheng,1994).

Frost heave includes in-situ frost heave and segregated frost heave.In in-situ frost heave,the pore water in freezing soil,or unfrozen water in frozen soil freezes in the process of the freezing front moving forward;this keeps cooling the frozen soil,and leads to the soli volume increasing by 9%.In-situ frost heave occurs under the condition of quick freezing that is too rapid for gaseous water and liquid water to migrate,for gas to sublimate to ice or for liquid water to freeze to colloidal ice at the interface between soil particles or in the pores as ice crystal monomers.

Segregated frost heave is a heave phenomenon in which moisture concentrates at the rear of the moving freezing front (the warm side of the ice lens) to generate a segregated ice lens.Even after soil is frozen,there still exists some unfrozen water film resulting from the surface energy of soil particles.The water film migrates from a high-temperature position to a lower-temperature position induced by the temperature gradient,and water being gathered behind the freezing front generates a segregated ice lens to cause frost heave.In order to recover the water film’s adsorption capacity and pressure balance outside the soil particles,it has to adsorb the water film constrained by the particles in the unfrozen soil to supplement the migrated water,providing water to the freezing front and ice lens generation (Wenget al.,1999).Segregated frost heave occurs under the condition of abundant water supply and slow freezing,and it could lead to volume increasing by 1.09 times,which is the main component of frost heave (Xu and Deng,1991;Xuet al.,1995;Xuet al.,1997).

In terms of the liquid-solid ice generating modes proposed currently,there are some main patterns involving mechanisms of segregated ice generation,colloidal segregated ice generation,resegregated ice generation and intrusive ice generation.Self-purification of ice (Cheng,1983) means that impurities including solute,soil particles,tiny solid particles,are expelled by ice crystals during segregation;the more fierce this purification phenomenon is,the slower the crystallizing is.This is the reason why the soil particles at the front of the freezing interface move and layers of ice lens become stacked to cause frost heave (Yu,2006).

In the process of freezing,unfrozen water content and moisture conductivity are not only important indexes to evaluate the moisture migration characteristics,but also two significant parameters in the frost heave models (Sheng,1994).In the second frost heave mechanism,the amount of frost heave depends on the speed of heat release,pore size,segregated temperature,and moisture conductivity in the frozen fringe,the temperature gradient in the frozen fringe,the thickness of the frozen fringe,the original moisture tension in the unfrozen soil,the moisture conductivity in the unfrozen soil,the compressibility of the unfrozen soil and the upper load pressure (Tian,2008).

4.2 Experimental verification

4.2.1 Experimental conditions and methods

Under the conditions of no salt,no pressure and an open system,freeze-thaw cycle experiments were conducted with Qinghai-Tibet Plateau clay silt,controlling the top and bottom boundary temperatures of the samples to simulate the field circumstance and measuring the soil-water potential and temperature in the samples.The experiment used a freeze-thaw cycle test installation,CR3000 (Campbell Scientific (Canada) Corp.,Edmonton,Alberta) and DT-80 (Thermo Fisher Scientific Australia Pty Ltd,Scoresby,Australia)data acquisition instruments,PF-Meter soil-water potential probes (Stevens Water Monitoring systems,Inc.,Portland,OR),Thermal-109 temperature probes(Campbell Scientific (Canada) Corp.,Edmonton,Alberta) and an organic glass column jar of 20 cm inner diameter and 30 cm height (Figure 2).

Figure 2 Organic glass column jar being filled with soil

The test temperature boundaries were the bottom temperature set as +1 °C and kept it,the top set as-10 °C.The top temperature was maintained for 48 h and then changed to +10 °C and then kept for 12 hours,and then the operation was repeated.PF-Meter probes were set in the soil layers at 2–5 cm and 8–11 cm from the bottom to top,two probes in each layer.The Thermal-109 probes were set at 2,5,8,and 11 cm from the bottom to top,one probe in each position.A pressure probe was set on the water supplement tube to acquire the amount of water supplement and record it every 4 hours.

The whole freeze-thaw experiment was sustained for 473 hours,spanning seven cycles.When the experiment was finished,small soil samples were collected at different heights to measure their water contents.

4.2.2 Results and analysis

The temperature gradient in the frozen fringe induces soil-water potential,providing the driving force for moisture migration which leads to water redistribution.In the open system,water supplement was provided to the freeze-thaw cycle experiment,and the pressure probe on the tube recorded the supplement trend.Figure 3 shows the data of the 8–11 cm soil layer as an example.

Figure 3 Temperature and soil-water potential during the first and second cycles

As shown in figure 3,when the temperature was higher than a critical value around 0 °C,the soil-water potential was almost zero;when the temperature dropped to a critical value around 0 °C,the soil-water potential increased rapidly and then stabilized with only small fluctuations;when the temperature rose back to a critical value around 0 °C,the soil-water potential decreased rapidly to almost zero.The initiation of frozen fringe started with the frozen temperature that was the temperature of freezing front,and ended with the segregated temperature.In a given sample and boundary temperature range,the segregated temperature,the frozen temperature and the thickness of the frozen fringe were almost constant;therefore,a stable temperature gradient was provided by the frozen fringe to induce a stable soil-water potential.

Table 1 Physical properties of soil sample

Within the boundary temperatures,the soil-water potential changed cyclically with the temperature variation.

Because of soil-water potential,moisture in the soil sample migrates from the high-temperature position to low,and the water content redistributes.The water content distributions at different heights before and after the experiment are shown in figure 4.

Figure 4 Water content distributions over the various heights

As shown in figure 4,the water was distributed uniformly before the experiment,but it redistributed more to the upside than to the downside.An abnormal phenomenon appears at the bottom of the curve,which was the effect of moisture absorption.In the process of the freeze-thaw cycles,moisture migrates upward consistently,driven by the soil-water potential,leading to the water content redistribution.

In order to measure the amount of water supplement,a water supplement tube was installed at the back of the test case,accompanied with a pressure probe.The supplement trend is shown in figure 5.

Figure 5 Water supplement trend in a single freeze-thaw cycle

Figure 5 shows a whole cycle.The pressure in the tube reflected the trend of water supplement,which was increased constantly:when the temperature was high,water was supplied slowly or even not supplied;when the temperature was low,water was supplied quickly.At the same time,ice segregated quickly and it needed a large amount of water.The trends of water supplement in freezing or thawing were respectively uniform,corresponding to the stable soil-water potential in figure 3,which provided the driving force for steady moisture migration.

The amount of water supplement could be observed directly by the scale on the water supplement tube during the process,as shown in figure 6.

Figure 6 Water supplement

At the beginning of the cycles,the water supplement was almost zero,while the moisture migration was limited to the water in the sample itself.As the cycles proceeded,the amount of water supplement increased gradually,but the supplement gradient in the freezing process was greater than that in the thawing process.The total trend of the supplement gradients consistently increased,but the increment of the gradients gradually decreases.This is because the cycles made the soil structure looser,and extended the pore size,leading to an increase in moisture conductivity.The moisture conductivity in saturated soil increased after each cycle,and the increment was most notable in the first cycle,when the soil particles were fine and the dry density was high.The moisture conductivity unltimately approached to a constant (Deng and Xu,1991),which suggests that the water supplement gradient would also approach a critical value.

The driving force for moisture migration derives from soil-water potential caused by the temperature gradient in the frozen fringe.To verify this,the position of the freezing front could be estimated by measuring the temperature,assuming the temperature at the freezing front was 0 °C.The temperature varied linearly along its height,as shown in figure 7.

As shown in figure 8,the position of the freezing front varied cyclically.In the process of freezing,freezing started at the top and the freezing front moved downward.On the initiation of the frozen fringe,soil-water potential increased rapidly to a stable value,and it did not increase as more frozen fringe was generated and the freezing front moved downward.In the process of thawing,the freezing front moved upward quickly,but a stable soil-water potential still existed if there was a frozen fringe in the sample.At the time the frozen fringe disappeared,the freezing front moved to the top and the soil-water potential disappeared.It can thus be inferred that the temperature gradient inside the frozen fringe that induced the soil-water potential,which provided a driving force for moisture migration.

Figure 7 Temperature and soil-water potential

Figure 8 Height of the freezing front position

5 Conclusions

The frozen fringe has been a focus of much research in frozen soil physics,and researchers have used various advanced apparatuses to observe the microstructure of the frozen fringe,validating various hypotheses about the frozen fringe.In admitting the existence of the frozen fringe,a freeze-thaw cycle experiment was conducted to verify the mechanisms of frost heave and a key characteristic of the frozen fringe,its unfrozen water content.This fundamental research on the mechanisms of frost heave provides theoretical support for building frost heave models.

Frost heave is affected by many factors and its mechanisms are complex,and herein only two factors are taken into account.More parameters should be considered to analyze the coupled effects on moisture migration and ice segregation,and comprehensive research on the effects of those parameters and their trends is needed.Improved experimental apparatuses and methods could not only measure more parameters,but also simulate field circumstances more effectively,making the experimental data more practical.

The authors would like to thank the following for their financial support:the Project of the Natural Science Foundation of China (No.41271087);the Independent Foundation of the State Key Laboratory of Frozen Soil Engineering (Grant No.O9SF102011).

Akagawa S,1988.Experimental study of frozen fringe characteristics.Cold Regions Science and Technology,15(3):209–223.

Anderson DM,Tice AR,1973.The unfrozen interfacial phase in frozen soil water systems.In:Physical Aspects of Soil Water and Salts in Ecosystems.Springer,New York,pp.107–124.

Cannell GH,1959.Walter H Gardner.Freezing-point depressions in stabilized soil aggregates,synthetic soil,and quartz sand.Soil Science Society of America Journal,23(6):418–422.

Chen XF,Du Y,Zhang YL,2004.Reliability of calibration curves measured by TDR in frozen soils verified by NMR.Journal of Glaciology and Geocryology,26(6):642–655.

Cheng GD,1983.The mechanism of repeated segregation for the formation of thick layered ground ice.Cold Regions Science and Technology,8:57–66.

Cheng GD,Ma W,2006.Permafrost engineering problems in the construction of Qinghai-Tibet Railway.Journal of Nature,28(6):315–320.

Cheng GD,Yang CS,2006.The permafrost mechanical problems in construction of the Qinghai-Tibet Railway.Mechanics in Engineering,28(3):1–8.

Dash JG,Fu HY,Wettlaufer JS,1995.The premelting of ice and its environmental consequences.Reports on Progress in Physics,58(1):115.

Deng YS,Xu XZ,1991.Hydraulic conductivity of unsaturated soil and its changing regularity in saturated soil after freezing-thawing cycles.Journal of Glaciology and Geocryology,13(1):51–60.

Gilpin RR,1980.A model for the prediction of ice lensing and frost heave in soils.Water Resources Research,16(5):918–930.

Haeberli W,1978.Special aspects of high mountain permafrost methodology and zonation in the Alps.Proceedings of the Third International Conference on Permafrost,National Research Council of Canada,Ottawa,1:378–384.

Ishizaki T,Maruyama M,Furukawa Y,et al.,1996.Premelting of ice in porous silica glass.Journal of Crystal Growth,163(4):455–460.

Konrad JM,1989.Influence of cooling rate on the temperature of ice lens formation in clayey silts.Cold Regions Science and Technology,16(1):25–36.

Konrad JM,Morgenstern NR,1980.A mechanistic theory of ice lens formation in fine-grained soils.Canadian Geotechnical Journal,17(4):473–486.

Konrad JM,Mogenstern NR,1981.The segregation potential of a freezing soil.Canadian Geotechnical Journal,18(4):482–491.

Kujala K,1991.Factors Affecting Frost Susceptibility and Heaving Pressure in Soils.Ph.D.Dissertation,University of Oulu,Oulu,Finland.

Li DY,2011.Experiment and theoretical research on a new test method to measure unfrozen water content in frozen soil.Ph.D.Dissertation,China University of Mining and Technology,Beijing,pp.111–127.

Li P,Xu XZ,Chen FF,2000.State and progress of research on the frozen fringe and frost heave prediction models.Journal of Glaciology and Geocryology,22(1):90–95.

Li P,Xu XZ,Pu YB,et al.,1999.Analysis of characteristics of frozen fringe by using the digital technique of picture.Journal of Glaciology and Geocryology,21(2):175–180.

Miller RD,1972.Freezing and heaving of saturated and unsaturated soils.Highway Research Record,393:1–11.

Miller RD,1980.Freezing phenomena in soils.In:Applications of Soil Physics.Daniel Hillel,New York,pp.254–299.

O’Neill K,1983.The physics of mathematical frost heave models:A review.Cold Regions Science and Technology,6(3):275–291.

O’Neill K,Miller RD,1982.Numerical Solutions for a Rigid-Ice Model of Secondary Frost Heave.Fort Belvoir,VA:Defense Technical Information Center.

Qiu GQ,Liu JR,Liu HX,et al.,1994.Geocryological Glossary.Gansu Science and Technology Press,Lanzhou,China.

Sheng D,Axelsson K,Knutsson S,1995.Frost heave due to ice lens formation in freezing soils,1:Theory and verification.Nordic Hydrology,26(2):125–146.

Sheng DC,1994.Thermodynamics of Freezing Soils:Theory and Application.Lule? University Press,Lule?,Sweden.

Smith MW,Tice AR,1988.Measurement of the unfrozen water content of soils:Comparison of NMR and TDR methods.Report 88–18,U.S.Army Cold Regions Research and Engineering Laboratory,Hanover,NH.

Tian YH,2008.An Experimental Study on Moisture Migration and Frost Action of Fine-Grained Soils during Freezing under Dynamic and State Loading.Ph.D.Dissertation,Beijing Jiaotong University,Beijing,China.

Topp GC,Davis JL,Annan AP,1980.Electromagnetic determination of soil water content:Measurements in coaxial transmission lines.Water Resources Research,16(3):574–582.

Wang GS,Jin HJ,Lin Q,1998.Application of time domain reflectometry (TDR) to determine parameters of frozen soils in cold regions.Journal of Glaciology and Geocryology,20(1):88–92.

Watanabe K,Mizoguchi M,2002.Amount of unfrozen water in frozen porous media saturated with solution.Cold Regions Science and Technology,34(2):103–110.

Watanabe K,Mizoguchi M,Ishizaki T,1997.Experimental study on microstructure near freezing front during soil freezing.Transactions.Japanese Society of Irrigation Drainage and Reclamation Engineering,191:633–638.

Watanabe K,Wake T,2009.Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR.Cold Regions Science and Technology,59(1):34–41.

Weng JJ,Zhou XS,Chen MX,et al.,1999.The underground water migration and consolidation effect of the frozen soil.Underground Engineering and Tunnels,1:2–10.

Wu QB,Liu YZ,Zhang JM,et al.,2002.A review of recent frozen soil engineering in permafrost regions along Qinghai-Tibet Highway,China.Permafrost and Periglacial Processes,13(3):199–205.

Xu XZ,Deng YS,1991.Experiment Study on Water Migration in Freezing and Frozen Soil.Science Press,Beijing,pp.83–85.

Xu XZ,Oliphant JL,Tice AR,1985a.Prediction of unfrozen water content in frozen soils by a two-point or one-point method.Proceedings of the 4thInternational Symposium on Ground Freezing,Sapporo,Japan.A.A.Balkema,Boston,pp.83–87.

Xu XZ,Oliphant JL,Tice AR,1985b.Soil water potential,unfrozen water content and temperature.Journal of Glaciology and Geocryology,7(1):1–14.

Xu XZ,Wang JC,Zhang LX,et al.,1995.The Soil Frost Heaving and Salt Expansion Mechanism.Science Press,Beijing,pp.77–80.

Xu XZ,Wang JC,Zhang LX,et al.,1997.Mechanism of frost heave by film water migration under temperature gradient.Chinese Science Bulletin,42(15):1290–1293.

Yu LL,2006.Experimental study on soil freeze and expansion under artificial freezing.Ph.D.Dissertation,School of Civil Engineering,Harbin Industry and Technology University,Harbin,China,pp.9–10.

Zhou LY,Chen ZX,Li WM,2003.Calibration on measurement of soil water content using time domain reflectrometry (TDR).Acta Pedologica Sinica,40(1):59–64.

Zhou YW,Guo DX,Qiu GQ,et al.,2000.Permafrost in China.Science Press,Beijing.