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Research ArticleExperimental Research on Frost Heave Characteristics ofGravel Soil and Multifactor Regression Prediction

Xiaoyong Long Guoping Cen Liangcai Cai and Yue Chen

Aeronautics Engineering College Air Force Engineering University No 1 Baling Road Baqiao District Xirsquoan China

Correspondence should be addressed to Xiaoyong Long 18509270709163com

Received 16 April 2018 Revised 16 July 2018 Accepted 25 October 2018 Published 12 December 2018

Academic Editor Antonio Caggiano

Copyright copy 2018Xiaoyong Long et alis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Gravel soil is usually considered to be insensitive to frost heave However many frost heave deformations of foundation inseasonal frozen region indicate that gravel soil may also produce frost heave under certain special conditions In order to gain adeep insight into the frost heave characteristics of gravel soil a series of laboratory experiments on one-dimensional frost heavewere conducted under the open- and closed-water replenishing condition using an improved experiment apparatuse influenceof various factors including initial moisture content clay content compactness overlying load and water replenishing on frost-heaving ratio of gravel soil were analyzed And the basic frost heave characteristics including frost heave amount frost heavespeed frozen depth freezing speed and moisture content distribution after freezing in a gravel soil sample were analyzed ecorrespondingmechanisms were also discussed Results showed that in the open water replenishing condition there exists a linearrelationship between initial moisture content overlying load and frost-heaving ratio and a quadratic polynomial relationshipbetween clay content compactness and frost-heaving ratio Frost-heaving ratio in the open water replenishing condition can befound to increase over three times than that under the closed water replenishing condition Multifactor regression empiricalformula was obtained by multiple regression analysis to predict the frost-heaving ratio of gravel soil under certain collocation offactors and levels under the closed water replenishing conditione significant effects on frost-heaving ratio were in order waterreplenishing gt initial moisture content gt clay content gt compactness gt overlying load

1 Introduction

Coarse-grained soils which can show outstanding perfor-mance in compaction shearing intensity water perme-ability and liquefaction under dynamic load and having theadvantages of rich reserves easy access and economical arewidely used as natural foundation materials in foundationengineering construction such as highways railways air-ports dams and excavations Traditionally coarse-grainedsoils are usually identified as frost heave insensitive materialsbecause of the large grain size small grain surface energyweak hydrophilic performance little film water large po-rosity unapparent capillarity and weak water migrationand water is easy to freeze into ice in situ [1ndash4] Howeverbased on the observation of frost heave of subgrade ofHarbin-Dalian high-speed railway in Northeast China andpavement structure foundation of Guoluo Airport locatedat Qinghai Airport China Liu et al [5 6] Zhang [7] and

Liu et al [8] found that the coarse-grained soils can alsoproduce obvious frost heave phenomenon under the com-bination of certain clay content (the mass fraction of theparticle with a diameter less than 0075mm) initial moisturecontent and temperature in seasonal frozen regionus it issignificant to comprehensively research the frost heavecharacteristics of coarse-grained soil for effectively preventingfrost heave deformations of coarse-grained soil foundation

It has always been a focus and hot spot to conduct re-search on soil frost heave characteristics Since Everett [9]proposed the first frost theory and Miller [10] put forwardsecond frost theory there has been a lot of research [11ndash19]in frost-heaving mechanism and achieved certain resultsWith the deepening of the understanding on frost-heavingmechanism in permafrost the frost-heaving fillers especiallythe frost heave characteristics of the coarse-grained soil arealso studied After that in 1988 the experimental studies ofChen et al [20] showed that in the open water replenishing

HindawiAdvances in Materials Science and EngineeringVolume 2018 Article ID 5682619 13 pageshttpsdoiorg10115520185682619

condition the frost-heaving ratio of sand gravel increaseswith the decreased freezing rate as a power function becauseit favours cryosuction [21 22] Also as a small amount ofpowdered clay was mixed into the sand gravel the frostheave sensitivity of gravel in the open water replenishingcondition increases with the increase of particle viscosityVinson et al [23] and Chen and Wang [24] have found thatthe increase in the content of fine-grained soil and thecontent of clay minerals will increase the frost heave sen-sitivity of the coarse-grained soil Among them Vinson et al[23] further studied the influence of fine particle size on thefrost-heaving susceptibility of coarse-grained soil estab-lished the correlation between frost-heaving ratio and seg-regation potential and then pointed out that the smaller theparticle size the greater the correlation coefficient roughlaboratory experiment Xu [25] pointed out that when thecontent of powder and clay in granular soil is less than 12even under full water saturation condition the frost-heavingratio is no more than 2 As the content of powder andclay are greater than 12 the frost-heaving ratio increasesobviously Viklander [26] has found that porosity is animportant factor affecting the frost heave when researchingthe frost heave characteristics of the rocks in the freeze-thawcycle Konrad and Lemieux [27 28] thinks that when thecontent of fine-grained soil in coarse-grained soil is lessthan 7 the frost heaving of coarse-grained soil is relativelysmall but the amount of water supplement is very obviousand the frost-heaving ratio of 1 is the standard to dis-tinguish frost heave sensitivity of coarse-grained soil bylaboratory freezing tests Arenson and Sego [29] determinedthe position of unfrozen water film during the freezingprocess of coarse-grained soil by using the fluorimetrictracing method According to the classification character-istics of railway subgrade filling material and the criterion ofmaintenance for railway track Ye et al [30] pointed out thatgravel with fine grain content less than 15 belong to frostheave insensitive materials and can be used to build theantifreezing layer of subgrade Lai et al [31] studied the frostheave and thawing characteristics of a new type embank-ment and coarse-grained embankment rough the indoorfrost heave experiment Nie et al [32] pointed out that thefrost heave characteristics of graded crushed stone as thefiller on the surface of the foundation bed were affected bymoisture content porosity and fine particle content andthe moisture content was the dominant factor affecting thefrost heave of graded crushed stones rough the orthog-onal experiment and grey correlation analysis of gradationcrushed stone in the cold region Zhao et al [33] and Wanget al [34] pointed out that the main factor affecting the frost-heaving ratio of graded crushed stones was moisture con-tent followed by fine particle content compactness andcold end temperature and the correlation degree betweenthem was not significant

To sum up the combination of some factors and levels ofcoarse-grained soil also produces certain frost heave efactors affecting the frost heave of coarse-grained soil in-clude the following aspects the gradation of soil particlesthe content of fine particles and their mineral compositionwater content density permeability coefficient capillary

action and external load [35ndash37] However the researchresults on the impact laws of various factors on the coarse-grained soil frost heaving and its interpretation differ greatlyIn particular the understanding of frost heave character-istics under various factors is not clear enough Furtherresearch is needed on the interaction and correlation be-tween various factors on frost-heaving ratio of coarse-grained soil e relationships between the research re-sults and the actual engineering need to be strengthenederefore it is necessary to systematically research the frostheave characteristics of coarse-grained soil e researchgroup has devoted to the research of frost damage in sea-sonal frozen region of Qinghai-Tibet Plateau for many yearsespecially the systematic and continuous monitoring of frostheave in gravel soil foundation of Guoluo airport pavementstructure [8 38] erefore the gravel soil in the seasonalfrozen region of Qinghai-Tibet Plateau was selected as therepresentative research object to research the frost heavecharacteristics of coarse-grained soil Based on the uniqueclimate and soil characteristics of the area (see the 21 sectionin detail) a series of laboratory experiments on the frost-heaving ratio of gravel soil were carried out under the open-and closed-water replenishing conditions using an improvedexperiment apparatus to research the frost heave char-acteristics systematically e influence laws of factors in-cluding initial moisture content clay content compactnessoverlying load and water replenishing on frost-heaving ratiowere summarized and discussed And the basic frost heavecharacteristics including frost heave amount frost heavespeed frozen depth freezing speed and moisture contentdistribution after freezing in a gravel soil sample were an-alyzed and discussed In order to predict the frost-heavingratio of gravel soil under certain collocation of factors andlevels under the closed water replenishing condition themultifactor regression empirical formula was obtained bymultiple regression analysis Finally effective suggestionswere put forward for frost heave prevention and control ofcoarse-grained soil in seasonal frozen area

2 Materials and Methods

21 Soil Samples Preparation Guoluo Airport which islocated in Qinghai-Tibetan Plateau seasonal frozen soilregion was chosen as the research background and pro-totype in this paper [39] e climate of Guoluo Airport ischaracterized by low air temperature (the annual averagetemperature is about minus4degC) Abundant rainfall (snow) (theannual average precipitation is 400ndash760mm and the annualprecipitation days are 118ndash175 days) long negative tem-perature period (even more than 8 months) large frozendepth (the maximum frozen depth is about 25m) smallcooling rate and long retention time of freezing fronts insoil Accordingly this kind of regional climatic condition isapt to intensify moisture migration and frost heave All soilsamples were collected from the field experiment section atQinghai Guoluo Airport e filling section of GuoluoAirport was mainly filled with natural gravel soil but asusual in a construction process some surface silt can bemixed in leading to an uneven distribution of clay content

2 Advances in Materials Science and Engineering

Because there were some difficulties of taking trans-portation and saving of undisturbed soil samples this re-search adopted the reshaping disturbed soil by baggingfreight impurities filtration and air dry We chose thenatural gravel soil as the major experiment subject andselected the surface silt as the reference object rough thescreening test the clay content of natural gravel soil is 69and the clay content of surface silt was 50e average claycontent of the soil base of Guoluo Airport pavement was97 the clay content of somemeasured points even reachedabout 20 erefore we chose four kinds of clay content10 15 20 25 to study the effect of clay content onfrost heave characteristics of gravel soil and choose 45 as acomparison group Five kinds of soil samples with claycontent of 10 15 20 25 and 45 were obtained bymixing the two soil samples (natural gravel soil and surfacesilt) uniformly according to the different proportions

22 Physical Characteristics Test of Gravel Soil According tothe test requirement (Test Methods of Soils for HighwayEngineering) the grading curve of the above two soilsamples was obtained by the grain size analysis test which isshown in Figure 1 It is known from Figure 1 that the contentof fine particles in natural gravel soil is less while the fineparticle content in surface silt is more Moreover it could beobtained that the coefficient of nonuniformity and thecurvature of natural gravel soil (the values are 47 and 21) areall larger than that of surface silt (the values are 25 and 14)e coefficient of nonuniformity of surface silt is not lessthan 5 and the curvature is between 1 and 3 indicating thatthe gradation of surface silt is good However the coefficientof nonuniformity of natural gravel soil is too large in-dicating the absence of intermediate particles and the badgradation In the actual construction process the surface silttends to be doped in natural gravel soil and not only makesthe clay content of soil foundation increased but also tosome extent to fill the missing natural gravel soil middlediameter is effect makes the frost-heaving phenomenonof grit soil foundation more serious

According to the methods described in Soil SamplesPreparation five kinds of soil samples containing 10 1520 25 and 45 silt were prepared respectively and theresults are shown in Table 1 From Table 1 it could beobtained that the optimum initial moisture content in-creased with clay content while standard maximum drydensity decreased with clay content

e relative density of the two kinds of soil samples was271 indicating that the influence of grain composition onrelative density of soil grain was very small and all kinds ofclay content of gravel soil can use the same value (271) erelative density of the soil sample of clay content of 10 wasmeasured by a jar and the soil sample of clay content of 45was measured by a pycnometer

23 Experiment Principle e frost heave amount and frost-heaving ratio are the main parameters to measure the frostheave properties of soil e frost heave amount is thevertical displacement of the soil which is caused by soil

freezing While the later (also known as the frost heavecoefficient) is the ratio of the increment of the longitudinalheight to the original height of the specimen under thecondition of nonlateral deformation and one-dimensionalfreezee frost-heaving ratio is usually expressed as follows

η ΔhHf

times 100 (1)

where η is the frost-heaving ratio Δh is the frost heaveamount at the end of the freeze (mm) and Hf is the frozendepth (cm) (Test Methods of Soils for Highway Engineering)

e frozen depth can be determined with Equation (2)

Hx H i +tminusi

11138681113868111386811138681113868111386811138681113868

tminusi1113868111386811138681113868

1113868111386811138681113868 + t+i+1

1113888 1113889 (2)

where Hx is the frozen depth H is the spacing of tem-perature measuring element (H 20 cm) i is the layernumber of temperature measuring element from the surfaceto calculate |tminusi | is the absolute value of negative temperatureof level i and t+

i+1 is the absolute value of positive tem-perature of level i + 1 and the calculating diagram is in-dicated in Figure 2

24 Experiment Apparatus Improvement According toTest Methods of Soils for Highway Engineering JTG E40-2007 [40] the traditional frost heave experiment apparatus

100

80

60

Part

icle

size

per

cent

()

40

20

00001 001 01

Natural gravel soilSurface silt

Particle size (mm)1 10 100

Figure 1 Gradation curve

Table 1 Results of standard compaction test

Clay content () Standard maximumdry density (gcm3)

e optimum initialmoisture content ()

10 236 66915 233 70020 229 76625 225 82745 2 1302

Advances in Materials Science and Engineering 3

consists of a soil sample box a pressure system a waterreplenishing system a displacement monitoring system atemperature control system and a calorstat e schematicdiagram of traditional frost heave experiment apparatus isshown in Figure 3

However due to the small size of the apparatus thestandard rule is only applicable to the small size soil such ascohesive soil and sandy soil but not suitable for the de-termination of the frost-heaving ratio of the gravel soil withlarger particle size In addition the traditional frost-heavingratio experiment apparatus also has some defects thereforethe following improvements have been made (1) Size of thesoil sample box was increased According to the principle ofsimilarity the inside diameter was increased from 10 cm to15 cm the height was increased from 10 cm to 16 cm and thespacing of temperature sensors was increased from 1 cm to2 cm (2) A modified pressure system was used in the ex-perimente weight pressure was replaced with air cylinderpressure and the range of pressure was increased to makethe adjustment more convenient e new pressure systemconsists of an air compressor pressure regulating valves anair cylinder and a connecting pipe (3) Data acquisitionsystem has been improved e dial indicator with an ac-curacy of 005mm was replaced by a displacement sensorwith an accuracy of 0001mm for observing the changes inthe frost heave amount All sensors could collect the signalsof displacement and temperature automatically and thesignals were recorded and saved automatically by computer(4) Cold bath system has been improved In the traditionalfrost-heaving ratio experiment apparatus the cold bathsystem only set a fixed freezing temperature which wasinconsistent with the actual law of atmospheric coolingerefore a cold bath system with automatic coolingfunction was adopted to make the freezing temperaturemore in line with the actual situation In addition the coldside was set at the bottom in the traditional frost-heavingratio experiment apparatus which does not match the actualof top-down cooling of the foundation In the improvedfrost-heaving ratio experiment apparatus the cold side wasset at the top in line with the actual situation (5) Waterreplenishing system has been improved e Maddox waterreplenishing bottle was used to keep water level constantand the water import was charged from top to bottom foradapting the actual groundwater replenishing e dis-placement sensor collecting and saving data automaticallywas used to observe change of the water level in the waterreplenishing system After the improvement the new frostheave experiment apparatus consists of soil a sample boxconstant temperature environment of box and temperature

control system the temperature monitoring system dis-placement acquisition unit monitoring system data acqui-sition unit pressure system and water replenishing systemjust as shown in Figures 4 and 5

e temperature sensor displacement sensor and dataacquisition terminal used in the experiment were all high-precision equipment All the experiment units had beencalibrated before the experiment began which ensured theaccuracy of the experimental results At the same time theupper and lower sides of the cylinder wall were tightened inorder to reduce the error caused by deformation of thesample cylinder itself e soil sample box was surroundedby thermal insulation material for preventing temperatureloss Two filter papers were put on top and bottom of the soilsample in order to prevent moisture loss during the ex-periment Moreover in order to verify the reliability of theimproved frost heave experiment apparatus several groupsof tests were carried out in comparison with the traditionalfrost heave experiment apparatus

Specifically the laboratory tests on one-dimensionalfrost heave were carried out by the traditional experimentapparatus and the improved experiment apparatus re-spectively under the conditions of the same soil sample (claycontent 45) the same test factor index (compactness 95

H

H

Hxtindash

t+i+1

0

i

i + 1Temperature sensor

Temperature sensor

Temperature sensor

Figure 2 Schematic diagram of frozen depth calculation

Soil sample

1

2

3

4

5

6

7

Figure 3 Traditional frost heave experiment apparatus (1) Waterreplenishing apparatus (2) Dial indicator of heave (3) ermalinsulation material (4) Pressure apparatus (5) Positive tempera-ture circulative liquid import and export (6) ermistor tem-perature measuring point (7) Negative temperature circulativeliquid import and export


overlying load 20 kPa) and the same cooling environmente results of the contrast tests are shown in Figure 6 Itcould be seen that the results of the two groups of test resultsalmost coincide verifying the reliability of the improvedfrost heave experiment apparatus erefore the improvedfrost heave experiment apparatus could be used to test thefrost-heaving ratio of coarse-grained soils

25 Experiment Program and Procedures e initial watercontent clay content compactness and overlying loadwere selected as 4 factors and the multifactor experimental

design was carried out e initial moisture content wasdesigned according to the optimum initial moisture contentto the above 5 kinds of soil clay content in the size of the3ndash18 corresponding to the 3ndash5 levels Considering thatthe compactness of the actual airport foundation was gen-erally controlled at around 90ndash98 we chose 85 9095 and 100 as compaction indexes e overlying loadwas selected as 4 levels such as 10 kPa 20 kPa 30 kPa and40 kPa In order to explore the order of influence of variousfactors on frost-heaving ratio and to obtain the multifactorregression empirical formula for predicting the frost-heaving ratio of gravel soil under certain collocation of

SoilsampleTemperature

acquisition unit

Displacementacquisition unit

Pneumaticbalance device

Temperaturecontrol system

Displacement sensor

Warm bottom

Thermal insulationmaterial

Temperature sensor

Cold top Cold bath circulation port

Temperature sensor

Pressure system Water replenishing apparatus

Displacement sensor

Computer

Figure 4 Schematic diagram of the improved frost heave experiment apparatus

Figure 5 Improved frost heave experiment apparatus (a) Altai measurement and control system (b)ermostat (c) Data acquisition unit(d) Cryostat (e) Pneumatic balance apparatus (f ) Soil sample box (g) Maddox water replenishing bottle


factors and levels the multifactor analysis was conducted onthe basis of single factor test results

e temperature of cold bath and the calorstat was set to1degC for 6 h to ensure that the internal temperature of thesample reached 1degC at which point the freezing process wasinitiated During the freezing process the temperature of thecold bath declined from 1degC at the speed of 02degCh lastingapproximately 72 h until stability of deformation to simu-late the law of atmospheric cooling [41] After the freezingthe sample was removed immediately from the soil samplebox and then equally divided into 7 pieces by slicesMoisture distribution in the sample was measured by dryingmethod

3 Results and Analysis

31 Influence of Various Factors on Frost-Heaving Ratio

311 Initial Moisture Content e influence of variousinitial moisture contents on frost-heaving ratio is shown inTable 2 Frost-heaving ratio increases with initial moisturecontent when clay content remains unchangede reason isconsidered as follows the increase of moisture contentmakes the water bonding in the soil sample more tight andthe continuous movement of water is more obvious As wecan see from the fitting curves frost-heaving ratio and initialmoisture content indicated unary linear relation e sizeorder of slope of fitting curve is 25 gt 45 gt 15is maybe attributed to that the dry density of the soil sample of claycontent 45 was the least among the three (refer to theresults of standard compaction test) e more loose the soilstructure is the bigger the soil pore is the more the iceaccommodates and the less the frost-heaving ratio is edry density of the soil sample of clay content 25 is biggerthan the one of clay content 45 and the moisture mi-gration was more obvious because of the less soil pore edry density and the cohesive force between soil particles of

soil samples with clay content of 15 are all the largestamong the three erefore it is the most likely to produceoverlapping and thickening combined water film whichmakes the permeability of soil decrease and the channel ofwater migration narrow

312 Clay Content e influence of various clay contents onfrost-heaving ratio is shown in Table 3 As we can see from thefitting curves the frost-heaving ratio increases with claycontent corresponding to a polynomial function when degreeof saturation remains unchanged e reason is considered asfollows the increase of clay content leads to the increase oftotal surface area and surface energy of soil particles andmore surface energy makes the soil particles absorb morewater film e water film between soil particles is inter-connected to form a thin film channel conducive to con-tinuous moisture migration As the clay content is fixed thefrost-heaving ratio increases with the increase of saturatione reason is considered as follows besides the reason that theinitial moisture content increases with the increase of thesaturation the volume of the soil pore decreases with theincrease of the saturation and the pore is more easily filledwith frozen ice which is more likely to cause the frost heavedisplacement of the soil particles Comparing the coefficientsof the three fitting curves in Table 3 it is known that the frost-heaving ratio and the clay content are nonlinear increasingrelation and the growth rate decreases gradually When theclay content is small the frost-heaving ratio increases rapidlyWhen the clay content is large the growth rate of frost-heaving ratio gradually slows down

313 Compactness e influence of various compactnesson frost-heaving ratio is shown in Table 4 Frost-heavingratio increased first and then decreased with the increase ofcompactness in the form of polynomial function andapproached its maximum at the compactness of 95 whenoverlying load initial moisture content and clay contentremain unchanged When the compactness is less than 95the film continuity of nonfrozen moisture increases with thecompactness which contributes to moisture migration andfreezing and lead to the increase of frost heave intensionWhen the compactness reaches to some critical value wherethin film channel is least frost heave intension approachesits maximum However with the increase of compactnessthe frost-heaving strength of soil decreases is is due to thereduction of pore volume in soil and the increase of effectivecontact area between soil particles resulting in the super-position of the water film on the periphery and the ob-struction of moisture migration during freezing

314 Overlying Load e influence of various initialmoisture contents on frost-heaving ratio is shown in Table 5Frost-heaving ratio decreases with overlying load whichindicates that the overlying load has inhibitory effect onfrost-heaving ratio rough the three fitting curves in Ta-ble 5 it is found that the frost-heaving ratio gently decreasedlinearly with the increase of overlying load

25

20

15

Fros

t-hea

ving

ratio

()

10

0510 12 14

Moisture content ()16 18

Traditional experiment apparatus

Improved experiment apparatus

Figure 6 e contrast test between improved experiment appa-ratus and traditional experiment apparatus


315 Water Replenishing e relationship between thefrost-heaving ratio and water replenishing is shown inFigure 7 In contrast to the closed and open water replen-ishing condition the frost-heaving ratio in the open waterreplenishing condition could be found to increase severaltimes more than that of the closed water replenishingcondition is may be attributed to that the pore pressure

which is formed by moisture migration drive replenishingwater to the freeze frontal surface then grow ice lens causedthe sharp increase of frost-heaving ratio It is fully indicatedthat the external water replenishing is the main factorcausing the frost heave of gravel soil foundation In theprevention and control of frost heave measures preventingwater replenishing is more important than other factors

Table 2 Influence of various initial moisture contents on frost-heaving ratio

Test no Compactness()

Overlyingload (kPa)

Claycontent ()

Initial moisturecontent ()

Frost-heavingratio () Fitting curve R2

1

95 20

15

3 043

y 0093x + 0137 09522 5 0623 7 0714 9 1025

25

643 081

y 0244x minus 0767 09916 735 0997 827 1288 919 1469

45

10 088

y 0173x minus 0802 099510 12 13211 14 16412 16 19813 18 228

Table 3 Influence of various clay contents on frost-heaving ratio


Overlyingload (kPa) Saturation Clay

content ()Frost-heavingratio () Fitting curve R2

1

95 20

08

10 010

y minus00012x2 + 01012x minus 0791 12 15 0463 20 0754 25 0995

09

10 019

y minus00025x2 + 01589x minus 11395 099726 15 0717 20 1018 25 1289

1

10 028

y minus00042x2 + 02258x minus 1559 110 15 08811 20 12812 25 146

Table 4 Influence of various compactness on frost-heaving ratio

Test no Overlyingload (kPa)


Claycontent ()

Compactness()


1

20

7 15

85 051

y minus00022x2 + 04158x minus 18939 099912 90 0663 95 0714 100 0645

827 25

85 098

y minus00031x2 + 05869x minus 26515 098716 90 1187 95 1288 100 1179

18 45

85 208

y minus00023x2 + 04329x minus 18105 0970710 90 22111 95 22812 100 218


32 6e Basic Characteristics of Typical Frost Heave Process

321 Frost Heave Amount and Frost Heave Speed In orderto gain a deep insight into the basic laws of typical process ofthe frost heave of gravel soil we selected a set of typical frostheave processes from all the experimental results In ourexperiment the sample (initial moisture content 9 siltcontent 15 and compactness 95 overlying load 20 kPa)was chosen as a group of typical specimens e variation offrost heave amount with time is shown in Figure 8 and therelationship between frost heave speed and time during thefreezing is shown in Figure 9

From the process of frost heave of gravel soil it can beseen that there are approximately four phases (i)e frozen-shrink phase the frost heave amount and the frost heavespeed were very small and developed slowly even showed asnegative value e frost heave amount not only did notincrease but decreased due to the shrinkage of soil particle atlow temperature (ii) e fast-increasing phase as freezingtime continues the frost heave amount increased rapidly

e frost heave speed rose rapidly and reached the peakdue to the intense ice segregation during this period in-dicating that soil frost heave deformation rapidly increased(iii) e slow-increasing phase over time the frost heavespeed gradually decreased and frost heave amount increased

Table 5 Influence of various overlying load on frost-heaving ratio



Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen

5 7Moisture content ()

9

Figure 7 Relationship between water replenishing and frost-heaving ratio

125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72

Figure 8 Variation of frost heave amount with time

020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72

Figure 9 Variation of frost heave speed with time


slowly is may be attributed to that the migration ofmoisture to the ice lens would decrease due to insufficientmoisture supply under the closed water replenishing con-dition as well as the low permeability of the frozen fringe[34] e slow growth of the thickness of ice lens and degreeof succession lead to the decrease of growth speed of frostheave amount (iv) e relatively stable phase during thisphase the frost heave speed reached 0 and lasted to the endof the experiments Although there were fluctuations whichmay be caused by unstable voltage the frost heave speedvaried within quite narrow limits than those in phases (2)and (3) [42] e amount of unfrozen moisture decreasedresulting in decreasing in moisture migration and stoppinggrowing of ice lens e moisture migration is primarilydriven by the difference in soil moisture potential around thefrost front under a closed water replenishing condition [34]Correspondingly frost heave amount decreased eventuallyreaching a near constant value

322 Frozen Depth and Freezing Speed e relationshipbetween frozen depth and time during the freezing is shownin Figure 10 e frozen depth was observed to gradually shiftdownward from the top of the sample (initial moisturecontent 9 clay content 15 and compactness 95 andoverlying load 20 kPa) at the beginning of the freezing processwhen cooling was applied As freezing time continues thevariation gradient of frozen depth becomes smaller andsmaller After a certain period of time the soil sample reacheda stabilization phase with small change in frozen depth erate of frost front advance and maximum frozen depth werefound to be dependent on initial moisture content thermalconductivity and cooling temperature [43]

e relationship between freezing speed and time duringthe freezing is shown in Figure 11 e freezing speed wassignificantly greater during the phases (1) and (2) than thosein phases (3) and (4) As freezing time continues thefreezing speed gradually decreases It is believed that thefreezing speed is one of main factors affecting the devel-opment of frost heave [42] Comparing Figures 8 and 11 thefreezing speed in phase (1) where the frost heave speed wasnegative was less than that in phase (2) due to frozen-shrinkphenomenon e frost heave increased rapidly due to thelarger frost heave speed and freezing speed in phase (2) Asthe frost heave speed and freezing speed keep decreasing therate of development of frost heave slowed down in phase (3)and reached the minimum until the last phase It was ob-served that the tendency of the changes of frost heave speedand freezing speed was similar this is consistent with theconclusion of Zhou et al [18]

323 Moisture Content Distribution in Soil after FreezingAfter freezing for different durations we cut the soil sampleby slice and then measure the moisture content of slice bydrying method e relationship between the moisturecontent distribution and time after freezing is shown inFigure 12 for the same sample It was assumed that initialmoisture content in the sample is uniformly distributed (thecurve of 9 in Figure 12) e depth of 0 in Figure 10

indicates the cold side while the depth of 14 cm indicates thewarm side e moisture content on the cold side wassignificantly larger than that on the warm side which in-dicated that moisture migration during freezing occurred inthe gravel soil sample e moisture content in the frozensection was also considerably greater than initial moisturecontent Conversely the moisture content in the nonfrozensection was significantly lower than the initial moisturecontent e moisture distribution after different freezingtimes (4 h 12 h 36 h and 72 h) was found to be similar intrend and follow an S-shape e different frozen depths(2 cm 6 cm 10 cm and 12 cm) after corresponding freezingtimes ((4 h 12 h 36 h and 72 h) (refer to Figure 10)) whichserved as the dividing line between the frozen section and thenonfrozen section distinguished between an increase and adecrease in moisture content e moisture content in-crement at the cold side and the maximum frozen depthwere observed to be greater compared with other positionsin the sampleis may be attributed to the larger porosity ofthe gravel soil and the soil moisture potential produced bythe temperature gradient resulted in a migration of moisture

0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72

Figure 10 Variation of frozen depth with time

060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72

Figure 11 Variation of freezing speed with time


near the frost front to the ice lens at the beginning offreezing Over time an increase in the frozen depth andreduction in moisture near the frost front were observedand led to a decrease in the permeability of the frozen frontand a reduction in moisture migration e moisture movedupward to the frost front due to the reduced moisturemigration near the warm side at the beginning of freezingresulting in a greater increment in moisture content aroundthe maximum frozen depth [34] e moisture incrementbetween the cold side and warm side was small due tominimal moisture migration in gravel soil under a closedwater replenishing condition Over time the moisturecontent near the freezing front increased markedly whereasthe moisture content in the frozen zone away from thefreezing front varied slightly

33 Multifactor Regression Analysis e multifactor re-gression equation was built with initial moisture content claycontent compactness and overlying load as independentvariables and with frost-heaving ratio as dependent variablebased on MATLAB

η 014765ωm + 012152ωs minus 000208ω2s minus 004818K

+ 000032K2 minus 000274P

(3)

Correctional goodness of fit R2 099 F-test F

54276gtF005(4 36) 265 the infective of the regressionequation together with the regression coefficient were dis-tinctness by significance testing e fitting accuracy is highis suggested that under the closed water replenishing con-dition the importance order of the factors is initial moisturecontent gt clay content gt compactness gt overlying load eapplication range of regression prediction formula is initialmoisture content (3 18) clay content (10 45)

compactness (85 100) and overburden load (10 kPa40 kPa) Fitting values were obtained through the multi-factor regression equation and then compared with fittingvalues as indicated in Figure 13 It is known from Figure 13that the fitting degree of formula (3) is high indicating thatthe model has a high accuracy and a certain validity eapplication of this regression model can predict the frost-heaving ratio under the comprehensive influence of differentfactors and has a certain application value in the design ofantifrost heave in building engineering

4 Discussion

e frost-heaving ratio of gravel soil increases linearly withthe increase of water content which has been confirmed bymany researches [44] e frost-heaving ratio of 1 is con-sidered as a criterion for determining the frost heave sensi-tivity of coarse-grained soil [27 28] Coarse-grained soil withclay content less than 15 is generally considered to be a frostheave insensitive soil When the clay content is over 15 thefrost heave of coarse-grained soils is more obvious [30] eexperiment results in this paper are consistent with theseconclusions When the clay content is 15 even though theoptimal moisture content is 7 (Table 1) the frost-heavingratio of gravel soil is still less than 1 When the clay contentis 10 the frost-heaving ratio is not more than 03 evenwhen the saturation is 1 When the clay content is 25 thefrost-heaving ratio of gravel soil is almost 1erefore it canbe believed that gravel soil with less than 15 of clay contentis a frost heave insensitive soil It is suggested that 15 of theclay content should be used as the control standard of thegravel soil frost-heaving ratio in the actual project

According to the research of Xu [25] the content ofpowder clay in granular soil is less than 12 and the frost-heaving ratio is not more than 2 even under sufficientwater saturation As the content of powder clay is greaterthan 12 the frost-heaving ratio increases obviously It isshown in Table 3 that the frost-heaving ratio is not morethan 03 even when the saturation is 1 with the claycontent of 10 When the clay content is more than 15even under unsaturated conditions the frost-heaving ratio isstill more than 05 is fully reflects the significant effectof the clay content on the frost-heaving ratio and validatesthe applicability of the control standard of 15 clay content

Chen et al [20] show that in an open water replenishingcondition the frost-heaving ratio of sand gravel increasesexponentially with the increase of the content of fine grainsoil Under the closed water replenishing condition of thisresearch the frost-heaving ratio of gravel soil increases withthe increase of clay content in a nonlinear increasing relation(Table 3) In addition to the reasons for water replenishmentthe general trend of the two is consistent except for thedifferent rate of growth and change Under the open waterreplenishing condition the frost-heaving ratio is easy toreplenish more moisture when the clay content is largeresulting in a significant increase in the frost-heaving ratioUnder the closed water replenishing condition the growthrate of frost-heaving ratio decreases with the limited watercontent

082 84 86 88

Moisture content ()90 92 94 96 98

2

4

6

8

10

12

14

Initial moisture content ()4h moisture content () 12h moisture content ()

36h moisture content ()72h moisture content ()

Dep

th (c

m)

Figure 12 Moisture content distribution in soil after freezing ofdifferent duration


e results of this paper show that 95 of compaction isthe maximum threshold of gravel soil frost-heaving ratiowhich is similar to the results obtained from the relatedresearch results [45] In airport pavement foundationconstruction the compaction is generally controlled withinthe range of 95sim98 Based on the 95 threshold obtainedfrom the experimental results we propose to increase theconstruction compactness to 98 so as to reduce the frost-heaving ratio

e research results of Li and Zhu [44] and Bao et al[46] confirmed the suppressing effect of overlying load onfrost heave Bao et al [46] thinks that the inhibition isrelated to water migration caused by consolidation anddrainage and freezing In this experiment the overlyingload leads to the consolidation and drainage trend fromthe top to the bottom of the soil e cold side on the topcauses the moisture migration trend from the bottom to thetop of the soil e two effects cancel each other whichresults in the inhibition of the overburden load on the frost-heaving ratio By curve fitting of the data of the threegroups it can be found that the frost-heaving ratio de-creases with overlying load in a negative exponential formBy investigating the slope of fitting curve of frost-heavingratio and overlying load variation (Table 5) we find thatwith the increase of overlying load the decrease of frost-heaving ratio is relatively small indicating that this in-hibition effect is smaller is may be attributed to that theexternal load is much less than the huge frost-heaving forcegenerated by the frost heaving inside the soil so therestraining effect of the overlying load on frost-heavingratio is very small

It is documented that the basic process of frost heave offine-grained soils was also divided into four phases [42]However because of the different physical characteristics ofcoarse-grained soil and fine-grained soil the basic frostheave characteristics of the two basic processes of frostheaving are different As we can see from Figures 8ndash12 the

dividing line between the four stages of the basic process offrost heave of the gravel soil was different from that of fine-grained soile frost heave amount and frost heave speed ofgravel soil was also different from that of fine-grained soilFor the basic process of frost heave of gravel soil the frostheave amount and frost heave speed of the four phases aredifferent By calculating the average frost heave speed at eachstage we can get the order of the frost heave speed in fourstages the second phase the third phase the first phase andthe fourth phase which is in accordance with the actual frostheave process e speed of frost heave in each phase es-sentially reflects the intensity of moisture migration in thesoil and is also closely related to the temperature gradient[34] In the early period of freezing with the influence of thetemperature gradient the moisture migration is obviousunder the effect of the stronger temperature gradient thusthe greater frost heave increment is produced In the middleand late freezing period with the limited water under theclosed water replenishing condition decreasing themoisturemigration is obviously eased even under the larger tem-perature gradient and the frost heave amount graduallytends to be gentle In order to effectively treat the frost heavedeformation in occurrence considering the different stagesof the frost heave process of various soil samples we thinkthat the appropriate time points should be selected based onthe basic characteristics of different soil frost heave and theexternal water supplement should be cut off as far as possibleto reduce the water migration in the soil

e regression prediction formula shows that the initialwater content has the most significant influence on the frost-heaving ratio of sand and gravel soil e research results ofNie et al [32] on the frost heave characteristics of gradedmacadam also confirmed that water content is the dominantfactor affecting the frost heave of graded crushed stoneWang et al [34] and other researchers pointed out that themain factors affecting the frost-heaving ratio of gradedcrushed stones were moisture content followed by fineparticle content compactness and cold end temperaturee regression analysis shows that the significant order ofinfluence on the frost-heaving ratio of gravel soil is watercontent clay content compactness and overlying load iswill help us to better understand the factors that affect thefrost heave of gravel soil and provide suggestions for theantifrost heave of the engineering foundation

5 Conclusions

e conclusions of this research are summarized as follows

(1) Under the closed water replenishing condition thefrost-heaving ratio increased with initial moisturecontent linearly rose with clay content corre-sponding to a polynomial function gently decreasedlinearly with the increase of overlying load increasedfirst and then decreased with the increase of com-pactness in the form of polynomial function andapproached its maximum at the compactness of 95Under the open water replenishing condition thefrost-heaving ratio of gravel soil can be found to

25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number

Experimental valuesFitted values

30 36

Figure 13 Contrast of experimental and fitting values of frost-heaving ratio


increase several times more than that of the closedwater replenishing condition

(2) From the process of frost heave of gravel soil it canbe seen that there are approximately four phases thefrozen-shrink phase the fast-increasing phase theslow-increasing phase and the relatively stablephase e frost heave speed and the freezing speedof each phase are closely related Moisture contentdistributions after freezing indicated that moisturemigration during freezing occurred in the gravel soilsample e moisture content in the frozen frontsection was significantly greater than initial moisturecontent indicating the migration of moisture to thefreezing front during freezing

(3) Multifactor regression forecast formula was obtainedby the multifactor regression analysis It can be seenthat the initial water content and clay content havegreat influence on the frost-heaving ratio of gravelsoil under the closed water replenishing conditione application of this regression model can predictthe frost-heaving ratio under the comprehensiveinfluence of different factors and has certain engi-neering application value

(4) e effects of various factors on the frost-heaving ratioare water replenishing gt initial water content gt claycontent gt compactness gt overlying load ereforein the engineering practice the control of waterreplenishing initial water content and clay content isthe key method to conduct the antifreeze design Wesuggest that the clay content of the soil foundationshould be controlled below 15 and the compactnessshould be controlled over 98 so as to reduce thefrost-heaving deformation of the gravel soil

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

We declare that the authors have no conflicts of interest orother interests that might be perceived to influence theresults andor discussion reported in this paper

Authorsrsquo Contributions

Xiaoyong Long and Guoping Cen conceived and designedthe research Xiaoyong Long and Liangcai Cai carried outthe experiment and analyzed the experiment resultsXiaoyong Long and Yue Chen wrote the manuscriptXiaoyong Long Guoping Cen Liangcai Cai and Yue Chenreviewed and edited the manuscript All authors read andapproved the manuscript

Acknowledgments

is research was supported by China Civil AviationAdministration Research Project (MHRD20140216)

References

[1] H M Dai and X L Wang ldquoFrost heave susceptibility ofhighway bridge foundation in seasonal frost regionrdquo Cold Re-gions Science and Technology vol 20 no 2 pp 141ndash146 1992

[2] A Y Li Y H Niu F J Niu and H Liu ldquoResearch status offrost heaving properties and controlling measures of coarsegrained soilrdquo Journal of Glaciology and Geocryology vol 1no 37 pp 202ndash210 2015

[3] R A Peterson and W B Krantz ldquoDifferential frost heavemodel for patterned ground formation corroboration withobservations along a North American arctic transectrdquo Journalof Geophysical Research Biogeosciences vol 113 no G3pp 250ndash258 2014

[4] M W Smith and D E Patterson ldquoDetailed observations onthe nature of frost heaving at a field scalerdquo Canadian Geo-technical Journal vol 26 no 2 pp 306ndash312 1989

[5] H Liu F J Niu Y H Niu Z J Lin J H Lu and J LuoldquoExperimental and numerical investigation on temperaturecharacteristics of high-speed railwayrsquos embankment in sea-sonal frozen regionsrdquo Cold Regions Science and Technologyvol 81 pp 55ndash64 2012

[6] H Liu F J Niu Y H Niu and X F Yang ldquoStudy on thermalregime of roadbed-culvert transition section along a highspeed railway in seasonal frozen regionsrdquo Cold Regions Sci-ence and Technology vol 106-107 pp 216ndash231 2014

[7] X J Zhang ldquoAnalysis of frost heave laws in subgrade onHarbinndashDalian high-speed railway and its influence factorsrdquoRailway Standard Design vol 7 pp 8ndash12 2013

[8] J Y Liu G P Cen and Y Chen ldquoStudy on frost heavecharacteristics of gravel soil pavement structures of airport inAlpine regionsrdquo RSC Advances vol 7 no 40 pp 24633ndash24642 2017

[9] D H Everett ldquoe thermodynamics of frost damage toporous solidsrdquo Transactions of the Faraday Society vol 57pp 1541ndash1551 1961

[10] R D Miller ldquoLens initiation in secondary frost heavingrdquo inProceedings of International Symposium on Frost Action inSoils Lulea Sweden February 1977

[11] N Matsuoka K Moriwaki and K Hirakawa ldquoDiurnal frost-heave activity in the Soslashr-Rondane Mountains AntarcticardquoArctic and Alpine Research vol 20 no 4 pp 422ndash428 1988

[12] N Matsuoka M Abe and M Ijiri ldquoDifferential frost heaveand sorted patterned ground field measurements and alaboratory experimentrdquo Geomorphology vol 52 no 1-2pp 73ndash85 2003

[13] R L Michalowski ldquoA constitutive model of saturated soils forfrost heave simulationsrdquo Cold Regions Science and Technologyvol 22 no 1 pp 47ndash63 1993

[14] T F Azmatch D C Sego L U Arenson and K W BiggarldquoNew ice lens initiation condition for frost heave in fine-grained soilsrdquo Cold Regions Science and Technology vol 82pp 8ndash13 2012

[15] J B Murton ldquoermokarst sediments and sedimentarystructures Tuktoyaktuk Coastlands western Arctic CanadardquoGlobal and Planetary Change vol 28 no 1ndash4 pp 175ndash1922001

[16] J B Murton J C Ozouf and R Peterson ldquoHeave settlementand fracture of chalk during physical modelling experimentswith temperature cycling above and below 0degCrdquo Geo-morphology vol 270 pp 71ndash87 2016

[17] D Sheng S Zhang Z Yu and J Zhang ldquoAssessing frostsusceptibility of soils using PCHeaverdquo Cold Regions Scienceand Technology vol 95 pp 27ndash38 2013


[18] J Z Zhou C F Wei H Z Wei and L Tan ldquoExperimentaland theoretical characterization of frost heave and ice lensesrdquoCold Regions Science and Technology vol 104-105 pp 76ndash872014

[19] H Zheng S Kanie F J Niu and A Y Li ldquoree-dimensional frost heave evaluation based on practicalTakashirsquos equationrdquo Cold Regions Science and Technologyvol 118 pp 30ndash37 2015

[20] X B Chen Y Q Wang and P He ldquoFrost susceptibility ofsandy gravel during freezingrdquo Chinese Journal of GeotechnicalEngineering vol 10 no 3 pp 23ndash29 1988

[21] S Taber ldquoFrost heavingrdquo Journal of Geology vol 37 no 5pp 428ndash461 1929

[22] J Aguirre-Puente M Fremond and G Comini ldquoCongelationdes sols-etude physique et modeles mathematiquesrdquo In-ternational Journal of Refrigeration vol 1 no 2 pp 99ndash1071978

[23] T S Vinson F Ahmad and R Rieke ldquoFactors important tothe development of frost heave susceptibly criteria for coarse-grained soilsrdquo Transportation Research Record vol N1089pp 124ndash131 1986

[24] X B Chen and Y Q Wang ldquoControl of frost heave ingeotechnical engineeringrdquo in Proceedings of Eighth Interna-tional Conference on Offshore Mechanics and Arctic Engi-neering American Society of Mechanical Engineers (ASME)New York NY USA March 1989

[25] X Z Xu ldquoProgress of frost heave research in Chinardquo Advancein Earth Sciences vol 9 no 5 pp 13ndash19 1994

[26] P Viklander ldquoLaboratory study of stone heave in till exposedto freezing and thawingrdquo Cold Regions Science and Tech-nology vol 27 no 2 pp 141ndash152 1998

[27] J M Konrad and N Lemieux ldquoInfluence of fines on frostheave characteristics of a well-graded base-course materialrdquoCanadian Geotechnical Journal vol 42 no 2 pp 515ndash5272005

[28] J M Konrad ldquoFreezing-induced water migration in com-pacted base-course materialsrdquo Canadian Geotechnical Jour-nal vol 45 no 7 pp 895ndash909 2008

[29] L U Arenson and D C Sego ldquoe effect of salinity on thefreezing of coarse-grained sandsrdquo Canadian GeotechnicalJournal vol 43 no 3 pp 325ndash337 2006

[30] Y S Ye Z J Wang A J Cheng and M Y Luo ldquoFrost heaveclassification of railway subgrade filling material and thedesign of anti-freezing layerrdquo China Railway Science vol 28no 1 pp 1ndash7 2007

[31] Y M Lai S M Zhang and W B Yu ldquoA new structure tocontrol frost boiling and frost heave of embankments in coldregionsrdquo Cold Regions Science and Technology vol 79-80pp 53ndash66 2012

[32] Z H Nie Y Liu and X Wang ldquoExperimental study onfrozen-heave influence factors for graded gravel in surfacelayer of passenger dedicated linerdquo Journal of Railway Scienceand Engineering vol 10 no 4 pp 59ndash62 2013

[33] H X Zhao Z Q Wu and Z Y Li ldquoExperimental study onfrost heave of silty clay in seasonally frost soil regionsrdquoProcedia Engineering vol 28 pp 282ndash286 2012

[34] Q Z Wang J K Liu X X Zhu J Y Liu and Z Y Liu ldquoeexperiment study of frost heave characteristics and graycorrelation analysis of graded crushed rockrdquo Cold RegionsScience and Technology vol 126 pp 44ndash50 2016

[35] J P Bilodeau G Dore and P Pierre ldquoGradation influence onfrost susceptibility of base granular materialsrdquo InternationalJournal of Pavement Engineering vol 9 no 6 pp 397ndash4112008

[36] K D Eigenbrod ldquoEffects of cyclic freezing and thawing onvolume changes and permeability of soft fine-grained soilsrdquoCanadian Geotechnical Journal vol 33 no 4 pp 529ndash5371996

[37] R Tester and P Gaskin ldquoEffect of fines content on the frostsusceptibility of a crushed limestonerdquo Canadian GeotechnicalJournal vol 33 no 4 pp 678ndash680 1996

[38] G P Cen X Y Long G Hong J Y Liu and H L LildquoInfluence of fine content on frost heaving properties of gravelsoilrdquo Science and Technology Review vol 5 no 33 pp 78ndash822015

[39] X Y Long C P Cen L C Cai and J Y Chen ldquoModelexperiment of uneven frost heave of airport pavementstructure on coarse-grained soils foundationrdquo Constructionand Building Materials vol 188 pp 372ndash380 2018

[40] JTG E40-2007 Test Methods of Soils for Highway EngineeringMinistry of Communication of the Peoplersquos Republic ofChina Beijing China 2007

[41] W J Hou ldquoAnalysis on the characteristic of temperaturechange in Dawu Town Guoluo Prefecturerdquo Guoluo Tech-nology no 1 pp 87ndash91 2007

[42] L L Yu and X Y Xu ldquoExperimental study on rate of frostheave by artificial freezingrdquo Chinese Journal of GeotechnicalEngineering vol 12 no 31 pp 1902ndash1906 2009

[43] T L Wang Z R Yue C Ma and Z Wu ldquoAn experimentalstudy on the frost heave properties of coarse-grained soilsrdquoTransportation Geotechnics vol 1 pp 137ndash144 2014

[44] R Y Li and J Zhu ldquoStudy for frost heave characteristics ofdeep overburden in double direction freezing moderdquo CoalTechnology vol 36 no 2 pp 87ndash89 2017

[45] Y Guo Y H Yang and L G Zeng ldquoStudy on frost heavingcharacteristics of subgrade soil of Lanzhou-Xinjiang railwayrdquoSubgrade Engineering vol 149 no 2 pp 149ndash151 2010

[46] J A Bao P Yang and X N Wang ldquoExperimental study onfrost heave properties of cement-improved soilrdquo Journal ofZhengzhou University (Engineering Science) vol 34 no 1pp 5ndash9 2013


CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

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Polymer ScienceInternational Journal of



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Journal ofEngineeringVolume 2018

Applied ChemistryJournal of


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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in



ChemistryAdvances in


Advances inPhysical Chemistry


BioMed Research InternationalMaterials

Journal of


Na

nom

ate

ria

ls


Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

condition the frost-heaving ratio of sand gravel increaseswith the decreased freezing rate as a power function becauseit favours cryosuction [21 22] Also as a small amount ofpowdered clay was mixed into the sand gravel the frostheave sensitivity of gravel in the open water replenishingcondition increases with the increase of particle viscosityVinson et al [23] and Chen and Wang [24] have found thatthe increase in the content of fine-grained soil and thecontent of clay minerals will increase the frost heave sen-sitivity of the coarse-grained soil Among them Vinson et al[23] further studied the influence of fine particle size on thefrost-heaving susceptibility of coarse-grained soil estab-lished the correlation between frost-heaving ratio and seg-regation potential and then pointed out that the smaller theparticle size the greater the correlation coefficient roughlaboratory experiment Xu [25] pointed out that when thecontent of powder and clay in granular soil is less than 12even under full water saturation condition the frost-heavingratio is no more than 2 As the content of powder andclay are greater than 12 the frost-heaving ratio increasesobviously Viklander [26] has found that porosity is animportant factor affecting the frost heave when researchingthe frost heave characteristics of the rocks in the freeze-thawcycle Konrad and Lemieux [27 28] thinks that when thecontent of fine-grained soil in coarse-grained soil is lessthan 7 the frost heaving of coarse-grained soil is relativelysmall but the amount of water supplement is very obviousand the frost-heaving ratio of 1 is the standard to dis-tinguish frost heave sensitivity of coarse-grained soil bylaboratory freezing tests Arenson and Sego [29] determinedthe position of unfrozen water film during the freezingprocess of coarse-grained soil by using the fluorimetrictracing method According to the classification character-istics of railway subgrade filling material and the criterion ofmaintenance for railway track Ye et al [30] pointed out thatgravel with fine grain content less than 15 belong to frostheave insensitive materials and can be used to build theantifreezing layer of subgrade Lai et al [31] studied the frostheave and thawing characteristics of a new type embank-ment and coarse-grained embankment rough the indoorfrost heave experiment Nie et al [32] pointed out that thefrost heave characteristics of graded crushed stone as thefiller on the surface of the foundation bed were affected bymoisture content porosity and fine particle content andthe moisture content was the dominant factor affecting thefrost heave of graded crushed stones rough the orthog-onal experiment and grey correlation analysis of gradationcrushed stone in the cold region Zhao et al [33] and Wanget al [34] pointed out that the main factor affecting the frost-heaving ratio of graded crushed stones was moisture con-tent followed by fine particle content compactness andcold end temperature and the correlation degree betweenthem was not significant

To sum up the combination of some factors and levels ofcoarse-grained soil also produces certain frost heave efactors affecting the frost heave of coarse-grained soil in-clude the following aspects the gradation of soil particlesthe content of fine particles and their mineral compositionwater content density permeability coefficient capillary

action and external load [35ndash37] However the researchresults on the impact laws of various factors on the coarse-grained soil frost heaving and its interpretation differ greatlyIn particular the understanding of frost heave character-istics under various factors is not clear enough Furtherresearch is needed on the interaction and correlation be-tween various factors on frost-heaving ratio of coarse-grained soil e relationships between the research re-sults and the actual engineering need to be strengthenederefore it is necessary to systematically research the frostheave characteristics of coarse-grained soil e researchgroup has devoted to the research of frost damage in sea-sonal frozen region of Qinghai-Tibet Plateau for many yearsespecially the systematic and continuous monitoring of frostheave in gravel soil foundation of Guoluo airport pavementstructure [8 38] erefore the gravel soil in the seasonalfrozen region of Qinghai-Tibet Plateau was selected as therepresentative research object to research the frost heavecharacteristics of coarse-grained soil Based on the uniqueclimate and soil characteristics of the area (see the 21 sectionin detail) a series of laboratory experiments on the frost-heaving ratio of gravel soil were carried out under the open-and closed-water replenishing conditions using an improvedexperiment apparatus to research the frost heave char-acteristics systematically e influence laws of factors in-cluding initial moisture content clay content compactnessoverlying load and water replenishing on frost-heaving ratiowere summarized and discussed And the basic frost heavecharacteristics including frost heave amount frost heavespeed frozen depth freezing speed and moisture contentdistribution after freezing in a gravel soil sample were an-alyzed and discussed In order to predict the frost-heavingratio of gravel soil under certain collocation of factors andlevels under the closed water replenishing condition themultifactor regression empirical formula was obtained bymultiple regression analysis Finally effective suggestionswere put forward for frost heave prevention and control ofcoarse-grained soil in seasonal frozen area

2 Materials and Methods

21 Soil Samples Preparation Guoluo Airport which islocated in Qinghai-Tibetan Plateau seasonal frozen soilregion was chosen as the research background and pro-totype in this paper [39] e climate of Guoluo Airport ischaracterized by low air temperature (the annual averagetemperature is about minus4degC) Abundant rainfall (snow) (theannual average precipitation is 400ndash760mm and the annualprecipitation days are 118ndash175 days) long negative tem-perature period (even more than 8 months) large frozendepth (the maximum frozen depth is about 25m) smallcooling rate and long retention time of freezing fronts insoil Accordingly this kind of regional climatic condition isapt to intensify moisture migration and frost heave All soilsamples were collected from the field experiment section atQinghai Guoluo Airport e filling section of GuoluoAirport was mainly filled with natural gravel soil but asusual in a construction process some surface silt can bemixed in leading to an uneven distribution of clay content








η ΔhHf

times 100 (1)



Hx H i +tminusi

11138681113868111386811138681113868111386811138681113868

tminusi1113868111386811138681113868

1113868111386811138681113868 + t+i+1

1113888 1113889 (2)




100

80

60

Part

icle

size

per

cent

()

40

20

00001 001 01







10 236 66915 233 70020 229 76625 225 82745 2 1302







H

H

Hxtindash

t+i+1

0

i


Temperature sensor

Temperature sensor


Soil sample

1

2

3

4

5

6

7







acquisition unit




Displacement sensor

Warm bottom


Temperature sensor


Temperature sensor


Displacement sensor

Computer













25

20

15

Fros

t-hea

ving

ratio

()

10

0510 12 14










Overlyingload (kPa)

Claycontent ()



1

95 20

15

3 043

y 0093x + 0137 09522 5 0623 7 0714 9 1025

25

643 081

y 0244x minus 0767 09916 735 0997 827 1288 919 1469

45

10 088

y 0173x minus 0802 099510 12 13211 14 16412 16 19813 18 228





1

95 20

08

10 010

y minus00012x2 + 01012x minus 0791 12 15 0463 20 0754 25 0995

09

10 019

y minus00025x2 + 01589x minus 11395 099726 15 0717 20 1018 25 1289

1

10 028

y minus00042x2 + 02258x minus 1559 110 15 08811 20 12812 25 146




Claycontent ()

Compactness()


1

20

7 15

85 051

y minus00022x2 + 04158x minus 18939 099912 90 0663 95 0714 100 0645

827 25

85 098

y minus00031x2 + 05869x minus 26515 098716 90 1187 95 1288 100 1179

18 45

85 208

y minus00023x2 + 04329x minus 18105 0970710 90 22111 95 22812 100 218









Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen


9


125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72


020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72








0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










η ΔhHf

times 100 (1)



Hx H i +tminusi

11138681113868111386811138681113868111386811138681113868

tminusi1113868111386811138681113868

1113868111386811138681113868 + t+i+1

1113888 1113889 (2)




100

80

60

Part

icle

size

per

cent

()

40

20

00001 001 01







10 236 66915 233 70020 229 76625 225 82745 2 1302







H

H

Hxtindash

t+i+1

0

i


Temperature sensor

Temperature sensor


Soil sample

1

2

3

4

5

6

7







acquisition unit




Displacement sensor

Warm bottom


Temperature sensor


Temperature sensor


Displacement sensor

Computer













25

20

15

Fros

t-hea

ving

ratio

()

10

0510 12 14










Overlyingload (kPa)

Claycontent ()



1

95 20

15

3 043

y 0093x + 0137 09522 5 0623 7 0714 9 1025

25

643 081

y 0244x minus 0767 09916 735 0997 827 1288 919 1469

45

10 088

y 0173x minus 0802 099510 12 13211 14 16412 16 19813 18 228





1

95 20

08

10 010

y minus00012x2 + 01012x minus 0791 12 15 0463 20 0754 25 0995

09

10 019

y minus00025x2 + 01589x minus 11395 099726 15 0717 20 1018 25 1289

1

10 028

y minus00042x2 + 02258x minus 1559 110 15 08811 20 12812 25 146




Claycontent ()

Compactness()


1

20

7 15

85 051

y minus00022x2 + 04158x minus 18939 099912 90 0663 95 0714 100 0645

827 25

85 098

y minus00031x2 + 05869x minus 26515 098716 90 1187 95 1288 100 1179

18 45

85 208

y minus00023x2 + 04329x minus 18105 0970710 90 22111 95 22812 100 218









Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen


9


125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72


020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72








0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









H

H

Hxtindash

t+i+1

0

i


Temperature sensor

Temperature sensor


Soil sample

1

2

3

4

5

6

7







acquisition unit




Displacement sensor

Warm bottom


Temperature sensor


Temperature sensor


Displacement sensor

Computer













25

20

15

Fros

t-hea

ving

ratio

()

10

0510 12 14










Overlyingload (kPa)

Claycontent ()



1

95 20

15

3 043

y 0093x + 0137 09522 5 0623 7 0714 9 1025

25

643 081

y 0244x minus 0767 09916 735 0997 827 1288 919 1469

45

10 088

y 0173x minus 0802 099510 12 13211 14 16412 16 19813 18 228





1

95 20

08

10 010

y minus00012x2 + 01012x minus 0791 12 15 0463 20 0754 25 0995

09

10 019

y minus00025x2 + 01589x minus 11395 099726 15 0717 20 1018 25 1289

1

10 028

y minus00042x2 + 02258x minus 1559 110 15 08811 20 12812 25 146




Claycontent ()

Compactness()


1

20

7 15

85 051

y minus00022x2 + 04158x minus 18939 099912 90 0663 95 0714 100 0645

827 25

85 098

y minus00031x2 + 05869x minus 26515 098716 90 1187 95 1288 100 1179

18 45

85 208

y minus00023x2 + 04329x minus 18105 0970710 90 22111 95 22812 100 218









Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen


9


125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72


020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72








0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








acquisition unit




Displacement sensor

Warm bottom


Temperature sensor


Temperature sensor


Displacement sensor

Computer













25

20

15

Fros

t-hea

ving

ratio

()

10

0510 12 14










Overlyingload (kPa)

Claycontent ()



1

95 20

15

3 043

y 0093x + 0137 09522 5 0623 7 0714 9 1025

25

643 081

y 0244x minus 0767 09916 735 0997 827 1288 919 1469

45

10 088

y 0173x minus 0802 099510 12 13211 14 16412 16 19813 18 228





1

95 20

08

10 010

y minus00012x2 + 01012x minus 0791 12 15 0463 20 0754 25 0995

09

10 019

y minus00025x2 + 01589x minus 11395 099726 15 0717 20 1018 25 1289

1

10 028

y minus00042x2 + 02258x minus 1559 110 15 08811 20 12812 25 146




Claycontent ()

Compactness()


1

20

7 15

85 051

y minus00022x2 + 04158x minus 18939 099912 90 0663 95 0714 100 0645

827 25

85 098

y minus00031x2 + 05869x minus 26515 098716 90 1187 95 1288 100 1179

18 45

85 208

y minus00023x2 + 04329x minus 18105 0970710 90 22111 95 22812 100 218









Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen


9


125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72


020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72








0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls













25

20

15

Fros

t-hea

ving

ratio

()

10

0510 12 14










Overlyingload (kPa)

Claycontent ()



1

95 20

15

3 043

y 0093x + 0137 09522 5 0623 7 0714 9 1025

25

643 081

y 0244x minus 0767 09916 735 0997 827 1288 919 1469

45

10 088

y 0173x minus 0802 099510 12 13211 14 16412 16 19813 18 228





1

95 20

08

10 010

y minus00012x2 + 01012x minus 0791 12 15 0463 20 0754 25 0995

09

10 019

y minus00025x2 + 01589x minus 11395 099726 15 0717 20 1018 25 1289

1

10 028

y minus00042x2 + 02258x minus 1559 110 15 08811 20 12812 25 146




Claycontent ()

Compactness()


1

20

7 15

85 051

y minus00022x2 + 04158x minus 18939 099912 90 0663 95 0714 100 0645

827 25

85 098

y minus00031x2 + 05869x minus 26515 098716 90 1187 95 1288 100 1179

18 45

85 208

y minus00023x2 + 04329x minus 18105 0970710 90 22111 95 22812 100 218









Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen


9


125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72


020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72








0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








Overlyingload (kPa)

Claycontent ()



1

95 20

15

3 043

y 0093x + 0137 09522 5 0623 7 0714 9 1025

25

643 081

y 0244x minus 0767 09916 735 0997 827 1288 919 1469

45

10 088

y 0173x minus 0802 099510 12 13211 14 16412 16 19813 18 228





1

95 20

08

10 010

y minus00012x2 + 01012x minus 0791 12 15 0463 20 0754 25 0995

09

10 019

y minus00025x2 + 01589x minus 11395 099726 15 0717 20 1018 25 1289

1

10 028

y minus00042x2 + 02258x minus 1559 110 15 08811 20 12812 25 146




Claycontent ()

Compactness()


1

20

7 15

85 051

y minus00022x2 + 04158x minus 18939 099912 90 0663 95 0714 100 0645

827 25

85 098

y minus00031x2 + 05869x minus 26515 098716 90 1187 95 1288 100 1179

18 45

85 208

y minus00023x2 + 04329x minus 18105 0970710 90 22111 95 22812 100 218









Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen


9


125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72


020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72








0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls











Claycontent ()

Overlyingload (kPa)


1

95

669 10

10 022

y minus00021x + 0235 089092 20 0193 30 0164 40 0165

7 15

10 076

y minus00022x + 0775 071186 20 0717 30 0738 40 0689

766 20

10 107

y minus00034x + 1095 0932310 20 10111 30 112 40 096

35

30

25

20

15

10Fros

t-hea

ving

ratio

()

05

003

ClosedOpen


9


125

100

075 I II III IV

050

Fros

t-hea

ving

amou

nt (m

m)

025

000

ndash0250 6 12 18 24 30 36

Time (h)42 48 54 60 66 72


020

015

010 I II III IV

Fros

t-hea

ving

spee

d (m

mh

)

005

000

ndash0050 6 12 18 24 30 36

Time (h)42 48 54 60 66 72








0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









0

2

4

6

8

10Froz

en d

epth

(cm

)

12

14

0 6 12 18 24 30 36Time (h)

42 48 54 60 66 72


060

045

030

015Free

zing

spee

d (deg

Ch)

0000 6 12 18 24 30 36

Time (h)42 48 54 60 66 72






+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







+ 000032K2 minus 000274P

(3)




4 Discussion




082 84 86 88


2

4

6

8

10

12

14



Dep

th (c

m)








5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls









5 Conclusions



25

20

15

Fros

t-hea

ving

ratio

()

10

05

000 6 12 18 24

Number


30 36







Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls








Data Availability






Acknowledgments


References



















































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls






Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




Documents

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