Research ArticleUnloading Creep Characteristics of Frozen Clay Subjected toLong-Term High-Pressure K0 Consolidation before Freezing

Jinbo Jia 1 Yansen Wang 12 and Yangguang Leng 2

1State Key Laboratory for Geomechanics and Deep Underground EngineeringChina University of Mining Science and Technology Xuzhou 221116 China2School of Mechanics and Civil Engineering China University of Mining Science and TechnologyXuzhou 221116 China

Correspondence should be addressed to Yansen Wang yswangcumteducn

Received 30 May 2019 Revised 12 August 2019 Accepted 31 August 2019 Published 18 September 2019

Academic Editor Emanuele Brunesi

Copyright copy 2019 Jinbo Jia et al (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Artificial ground freezing has been widely applied in the construction of vertical shafts in deep and thick alluvia As an importantfactor the in situ creep behavior of deep frozen soil affects the mechanical properties of frozen walls and the safety and stability ofshaft linings Acquiring creep characteristics and deep soil parameters by methods that ignore the engineering and geologicalsituations is currently inadvisable A series of triaxial unloading tests were conducted with frozen clay subjected to long-term high-pressure K0 consolidation before freezing to research the unloading creep characteristics creep strength and other parameters ofthe clay and the results indicated the following (1) (e creep behaviors of frozen clay are affected by the consolidation time andconsolidation stress Long-term high-pressure K0 consolidation reduces the creep strain and creep rate of frozen clay (2) (edecrease in the ice and the unfrozen water contents of frozen clay caused by the prolongation of consolidation time result in anincrease in the long-term strength and instantaneous strength Consolidation time has an obvious effect on long-term strengthand weakens the creep property of frozen clay Consolidation stress significantly affects the instantaneous strength (3) (edeformation resistance capability of frozen clay is enhanced by compaction thus E1 η1 and η2 increase with prolongedconsolidation and the nonlinearity of the accelerated creep increases

1 Introduction

Artificial ground freezing is frequently prescribed for con-structing vertical shafts in deep and thick alluvia Evidencesuggests that interactions between the frozen soil and shaftlining which are subjected to the effect of creep are among theimportant factors controlling stability (erefore it is essentialfor the stability of shaft construction to evaluate the creepproperties of frozen deep clay In an investigation into deepclay Cui [1] found that the creep properties of frozen deep claycannot be obtained accurately by traditional soil mechanicstests because the high density low ice content and specialmicrostructure exhibited under long-term high K0 stress (iswork is especially complex because creep properties are affectedby sedimentary conditions and consolidation-freeze modes [2]

the acquired creep characteristics and parameters would beinaccurate if these factors were ignored

To date a considerable number of studies have beenpublished on the creep behavior characteristics of frozensoils Ladanyi [3] and Takegawa et al [4] studied the creepcharacteristics of frozen clay and the results indicated thatnonattenuated and attenuated creep occurred in frozensoil subjected to different stresses due to the strengtheningand weakening effects caused by the damage and healing ofthe microstructure Zhu and Carbee [5] performed creeptesting the results of which showed that nonattenuatedcreep occurred due to the predominance of structuralstrengthening in frozen soil when the stresses were lessthan the long-term strength attenuated creep occurredowing to the prominence of the weakening effect under

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 7192845 18 pageshttpsdoiorg10115520197192845

stresses greater than the long-term strength (erefore itis necessary to study the long-term strength in more detailYang et al [6] proposed that the long-term strength firstdecreased and then increased with increasing ice contentbased on the results of uniaxial tests of frozen soil with icecontents of 40ndash120 Fish [7] established an equationthat described the decrease in the long-term strength offrozen soil with creep time Nadezhdin and Sorokin [8]investigated the strength characteristics of deep frozenclay by the method of freezing before K0 consolidationand the results revealed that preloading had different ef-fects on the ultimate long-term strength and instantaneousstrength the ultimate long-term strength of soil increasedbut the instantaneous strength decreased Roman andKrivov [9] conducted uniaxial compression and sphericalplate indentation tests to determine the long-term strengthof frozen soil and a reasonable prediction equation wasselected to describe the variation in the long-termstrength (e initial moisture content freezing tempera-ture and creep stress were regarded as influence factors ina number of investigations about the creep and strengthproperties of deep frozen clay Reconstituted frozen soilsthat underwent ephemeral consolidation under highpressure before freezing were mostly used in these testsHowever the initial consolidation state engineering stresspath and test mode should be considered comprehen-sively in the study of deep frozen clay Otherwise theapplicability of test results will be limited Hence theinfluence of high-pressure K0 consolidation age should notbe neglected

To define the creep mechanism of frozen soils manyscholars have made important contributions to the creepconstitutive model of frozen soils Component combinationtheory was frequently applied to studies on creep models offrozen soils eg the Kelvin model the Burgers model andthe Nishihara model [10] Li et al [11] proposed that theparabolic yield criterion was suitable for artificially frozensoil under high and complex stress and established a creepmodel based on viscoelastic-plastic damage theory [12]Subsequently numerical simulations and laboratory testswere conducted and the results illustrated the applicabilityof the strength criterion and the rationality of this creepmodel [13 14] Li et al [15] proposed an improved Nishiharamodel that considered the effects of hardening and weak-ening caused by temperature and external stress duringcreep which could produce a reasonable prediction of threecreep stages of frozen soil Nevertheless the effects ofconsolidation stress and consolidation age on creep modesand parameters have not been thoroughly considered

When studying the creep properties of deep artificiallyfrozen clay it is crucial to consider the characteristics oflong-term high-pressure consolidation and then freezing(us in this paper the variation rules of the unloading creepcharacteristics and the long-term strength of deep frozenclay are analyzed with consideration of the consolidationtime and stress by the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo In addition the improved Nishiharamodel is applied to reasonably describe the creep behavior

and the influences of the consolidation time on the creepparameters are analyzed (is study provides a basis forfurther revealing the creep mechanism of deep artificiallyfrozen clay

2 Experimental Program

21 Materials and Experimental Apparatus (e clay in-vestigated in the present study was derived from amine shaftat a depth of approximately 520ndash550m and the physicalparameters are listed in Table 1(e reconstituted specimenswere prepared as cylinders with diameters of 618mm andheights of 125mm (e initial water content and the drydensity of the specimens tested were 278 and 149 gcm3respectively (ese specimens were saturated with air-freewater under vacuum for 24 hours to achieve a saturation of098

Consolidation tests of reconstituted clay specimens wereconducted on an SKA-1 K0 consolidation instrument and acustom high-pressure lever-type loading system (005ndash60kN)and theK0 values weremonitored aDL-4050 cryogenic coolingcirculating pump (minus 40ndash0degC) was applied to freeze the speci-mens under constant axial load in addition constant axialpressure and unloading confining pressure creep tests of frozenclay specimens were conducted with the TATW-500 subzerodynamic and static high-pressure triaxial test system whoseconfining and axial pressure can be controlled simultaneouslyto a maximum axial pressure and confining pressure of 500 kNand 20MPa respectively (e schematic diagrams of the testapparatus are shown in Figures 1 and 2

22 Experimental Procedure and Conditions

(1) (e unfrozen specimens underwent K0 consoli-dation tests to simulate the formation of deep clayin alluvia Meanwhile the K0 value and watercontent were measured (e consolidation time (tc)and pressure (σ1) were 3ndash28 days and 8ndash10MParespectively

(2) After the specimens had been consolidated for thepredetermined time loading-freezing tests wereconducted at minus 15degC In these tests the temperature ofthe internal central position and the axial frostheaving deformation of the specimens were moni-tored After the temperature and the axial de-formation stabilized freezing lasted for almost24 hours to ensure uniformity (e frozen specimensremoved from the mold were preserved in a ther-mostat box (e rebound deformations were verysmall before and after stripping in these tests

(3) (e frozen specimen was placed into the pressure cellof the TATW-500 high-pressure triaxial test systemand silicone oil was used as a filler (en the testtemperature was recovered by the circulating cryo-genic liquids and kept for 12 hours Furthermoreduring the creep tests a constant temperature wasmaintained (ereafter a triaxial pressure state was

2 Advances in Civil Engineering

applied to the frozen specimen to recover the K0stress state

(4) According to the test requirements the confiningpressure was unloaded in three steps (e loadvalues were determined based on kiσs where σsrepresents the difference between the instantaneousshear strength and the initial deviator stress of afrozen specimen under the same condition whichwere obtained from the shear strength test underthe triaxial unloading stress path and the K0

consolidation test respectively and ki is the stresscoefficients (ie ki 02 04 and 06 or ki 03 05and 07) After maintaining the target deviatorstress for 10 hours the next stage of unloading wasperformed (e test ended when the specimen hadbeen destroyed or a test time of 30 hours had beenreached

(5) (e confining and axial pressures were graduallyreleased the samples were removed and the stepsabove were repeated to continue the tests

(e detailed unloading creep test arrangements are listedin Table 2

3 Experimental Results and Analysis

31 Axial Creep StrainCharacteristics Figures 3(a)ndash3(c) and4(a)ndash4(d) demonstrate variations in axial creep strain andaxial creep rate with time for specimens that were frozen atminus 15degC and subjected to various consolidation conditionsFrom these figures the following conclusions can bereached

(1) (e specimens subjected to various consolidationconditions show both attenuation creep and non-attenuation creep as the deviator stress varies Whenthe deviator stress is low the creep strain presentsobvious attenuation characteristics (e non-attenuation creep occurs with high deviator stress

Table 1 (e basic physical properties of the clay specimens

Gs ρd (gmiddotcmminus 3)Composition of grains ()

wL () wp ()gt025mm 025sim01mm 0sim0075mm 0sim0045mm lt0045mm

271 149 3 632 271 611 8186 5883 2893

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(a)

(1)

(2)

(4)(3) (5)

(6)

(b)

Figure 1 High-pressure consolidation and loading-freezing equipment (a) SKA-1 K0 consolidation instrument (1) Axial loadingbar (2) pressure cell (3) oil inlet (4) oil outlet (5) drainage channel (6) specimen (7) hydraulic sensor (b) Loading-freezing system(1) Consolidation load (2) steel consolidometer (3) cryogenic coolant (4) thermostatic bath (5) specimen (6) thermocouple

(1)

(2)(3)

(4)(5)

(6)

(7)

(10) (9)

(8)

Figure 2 Triaxial creep test system for frozen soil (1) Axial loadingcell (2) antiforce frame (3) pressure cell (4) cryogenic coolant (5)specimen (6) thermocouple (7) thermostatic bath (8) confiningpressure controller (9) axial loading controller (10) computer

Advances in Civil Engineering 3

Table 2 Arrangements of triaxial unloading creep test on frozen clay

Number σ1 (MPa) T (degC) tc (d) σ1 minus σ3 (MPa)1 8 minus 15 3 3540452 8 minus 15 7 3540503 8 minus 15 14 4045504 10 minus 15 3 3540455 10 minus 15 7 4347516 10 minus 15 14 4550557 10 minus 15 28 424752

Stra

in (

)

35 MPa

45 MPa 40 MPa

35 MPa

45 MPa 40 MPa

Cr

eep

rate

(middoth

ndash1)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

0

2

4

6

8

10

12

2 4 6 8 10 120Time (h)

(a)

Stra

in (

)

35 MPa

50 MPa 40 MPa

35 MPa

50 MPa 40 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 3 Continued

4 Advances in Civil Engineering

(e creep strain and creep rate increase with thedeviator stress at the same creep time

(2) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of the specimensunder the same deviator stress at the same creeptime

(e average creep rate based on the steady creep stage inthe creep rate curve is taken as the steady creep rate _εs (esteady creep rates of each specimen under various deviatorstresses are listed in Table 3

(e relationship between the creep rate and the deviatorstress of frozen clay can be described with the exponentialequation (1) [16 17] According to the data on the steadycreep rate of the specimens with various consolidationconditions the regression curves of _εsminus (σ1 minus σ3) were de-termined as shown in Figure 5 and the regression pa-rameters are listed in Table 4

_εs aeb σ1minus σ3( ) (1)

where _εs represents the steady creep rate σ1 minus σ3 is the creepdeviator stress and a and b are the material constants relatedto the consolidation time and consolidation stress

For frozen specimens subjected to long-term high-pressure K0 consolidation before freezing the steady creeprate increases with creep deviator stress under the samedeviator stress the steady creep rate decreases with theextension of the consolidation time (e regression pa-rameter a increases with the extension of the consolidationtime while b decreases on the contrary a decreases with theincrease in the consolidation stress whereas b increases

32 Long-Term Strength During the exposure duration ofthe shaft excavation section the long-term strength of theartificially frozen deep clay has an important influence on

the long-term mechanical stability of the frozen wallHowever human error makes it very difficult to determinethe stress inflection point of frozen clay accurately with theconventional stress-strain isochronal curve method Moreaccurate long-term measurements of strength are obtainedfrom the creep tests in this paper by applying the re-lationship between the experimental steady creep rate andcreep deviator stress and the method of equal intervaltangent to eliminate human error

(e specific methods for this approach are as follows

(1) According to the creep tests the steady creep rateunder different deviator stresses was obtained

(2) (e exponential equation shown as equation (1) wasapplied to fit the relationship between steady creeprate and deviator stress

(3) Tangent lines were drawn every 5deg in the range from5 to 85deg on the fitting curve (e intersection pointsof each tangent line with the deviator stress axis weremarked as A B C D E and so on (e upper andlower limits of the long-term strength correspond tothe two creep deviator stresses of the intersectionpoints with the smallest spacing

(4) Tangent lines were drawn every 1deg between the twointersection points with the smallest spacing on thefitting curve Step (3) was repeated to obtain a moreaccurate range of the long-term strength and thenthe average value was taken as the long-term strengthof the frozen clay specimen

A schematic diagram of this method is shown inFigure 6

K0 values moisture contents instantaneous strengthslong-term strengths and strength decay rates based on thehigh-pressure K0 consolidation tests triaxial shear tests andtriaxial creep tests of frozen clay were determined as listed in

Stra

in (

)

40 MPa

50 MPa 45 MPa

40 MPa

50 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

Figure 3 Variations in axial creep strain and axial creep rate with time (σ1 8MPa) (a) tc 3 d (b) tc 7 d and (c) tc 14 d

Advances in Civil Engineering 5

35 MPa 40 MPa 45 MPa

35 MPa 40 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(a)

43 MPa 47 MPa 51 MPa

43 MPa 47 MPa 51 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 4 Continued

6 Advances in Civil Engineering

45 MPa 50 MPa 55 MPa

45 MPa 50 MPa 55 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

42 MPa47 MPa52 MPa

42 MPa47 MPa52 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(d)

Figure 4 Variations in the axial creep strain and axial creep rate with time (σ1 10MPa) (a) tc 3d (b) tc 7d (c) tc 14d and (d) tc 28d

Table 3 (e steady creep rate of the frozen clay specimens (minus 15degC)

SpecimenPrimary deviator stress Secondary deviator stress Tertiary deviator stress

σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1)

8MPa-3 d 35 0159 40 0313 45 06818MPa-7 d 35 0111 40 0184 50 07188MPa-14 d 40 0181 45 0325 50 058210MPa-3 d 35 0143 40 0266 45 059110MPa-7 d 43 0215 47 0364 51 061810MPa-14 d 45 0221 50 0401 55 072910MPa-28 d 42 0120 47 0207 52 0355

Advances in Civil Engineering 7

Table 5 σf represents the instantaneous strength and σfinfinrepresents the long-term strength (e strength decay rate isexpressed as σ ie σ (σf minus σfinfin )σf

To analyze the evolution and mechanisms of the in-stantaneous and long-term strengths their variations andrates of increase are shown in Figures 7 and 8 respectivelyFigure 9 shows the variations in the strength decay rates

(e following conclusions were reached

(1) (e instantaneous and long-term strengths of thespecimens subjected to consolidation under 8MPaincrease by 053MPa and 067MPa respectively

which are within consolidation times of 1 to 14 daysand those under 10MPa increase by 081MPa and114MPa with consolidation times of 1 to 28 days(e strengths increase rapidly for consolidationtimes of 3 to 7 days and as the consolidation timeincreases the rates of increase in the strengths tendto be stable

(2) (e long-term strengths and instantaneousstrengths of specimens consolidated under10MPa are higher than those consolidated under8MPa

Stea

dy-s

tate

cree

p ra

te (

middothndash1

)

3 d 7 d 14 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(a)St

eady

-sta

te cr

eep

rate

(middoth

ndash1)

3 d 7 d

14 d 28 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(b)

Figure 5 (e regression curves of _εsminus (σ1 minus σ3) (a) σ1 8MPa and (b) σ1 10MPa

Table 4 (e regression parameters of _εsndash(σ1 minus σ3)

Parameters8MPa 10MPa

3 d 7 d 14 d 3 d 7 d 14 d 28 da 0000839 0001031 0001714 0000674 0000736 0001033 0001257b 1488 1309 1165 1506 1320 1192 1086

Stea

dy cr

eep

rate

Stea

dy cr

eep

rate

A B C D E F Deviator stress

e minimum interval

B C Deviator stress

e minimum interval

Long-termstrength

Figure 6 (e method used to obtain the long-term strength

8 Advances in Civil Engineering

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

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applied to the frozen specimen to recover the K0stress state

(4) According to the test requirements the confiningpressure was unloaded in three steps (e loadvalues were determined based on kiσs where σsrepresents the difference between the instantaneousshear strength and the initial deviator stress of afrozen specimen under the same condition whichwere obtained from the shear strength test underthe triaxial unloading stress path and the K0

consolidation test respectively and ki is the stresscoefficients (ie ki 02 04 and 06 or ki 03 05and 07) After maintaining the target deviatorstress for 10 hours the next stage of unloading wasperformed (e test ended when the specimen hadbeen destroyed or a test time of 30 hours had beenreached

(5) (e confining and axial pressures were graduallyreleased the samples were removed and the stepsabove were repeated to continue the tests

(e detailed unloading creep test arrangements are listedin Table 2

3 Experimental Results and Analysis

31 Axial Creep StrainCharacteristics Figures 3(a)ndash3(c) and4(a)ndash4(d) demonstrate variations in axial creep strain andaxial creep rate with time for specimens that were frozen atminus 15degC and subjected to various consolidation conditionsFrom these figures the following conclusions can bereached

(1) (e specimens subjected to various consolidationconditions show both attenuation creep and non-attenuation creep as the deviator stress varies Whenthe deviator stress is low the creep strain presentsobvious attenuation characteristics (e non-attenuation creep occurs with high deviator stress

Table 1 (e basic physical properties of the clay specimens

Gs ρd (gmiddotcmminus 3)Composition of grains ()

wL () wp ()gt025mm 025sim01mm 0sim0075mm 0sim0045mm lt0045mm

271 149 3 632 271 611 8186 5883 2893

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(a)

(1)

(2)

(4)(3) (5)

(6)

(b)

Figure 1 High-pressure consolidation and loading-freezing equipment (a) SKA-1 K0 consolidation instrument (1) Axial loadingbar (2) pressure cell (3) oil inlet (4) oil outlet (5) drainage channel (6) specimen (7) hydraulic sensor (b) Loading-freezing system(1) Consolidation load (2) steel consolidometer (3) cryogenic coolant (4) thermostatic bath (5) specimen (6) thermocouple

(1)

(2)(3)

(4)(5)

(6)

(7)

(10) (9)

(8)

Figure 2 Triaxial creep test system for frozen soil (1) Axial loadingcell (2) antiforce frame (3) pressure cell (4) cryogenic coolant (5)specimen (6) thermocouple (7) thermostatic bath (8) confiningpressure controller (9) axial loading controller (10) computer

Advances in Civil Engineering 3

Table 2 Arrangements of triaxial unloading creep test on frozen clay

Number σ1 (MPa) T (degC) tc (d) σ1 minus σ3 (MPa)1 8 minus 15 3 3540452 8 minus 15 7 3540503 8 minus 15 14 4045504 10 minus 15 3 3540455 10 minus 15 7 4347516 10 minus 15 14 4550557 10 minus 15 28 424752

Stra

in (

)

35 MPa

45 MPa 40 MPa

35 MPa

45 MPa 40 MPa

Cr

eep

rate

(middoth

ndash1)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

0

2

4

6

8

10

12

2 4 6 8 10 120Time (h)

(a)

Stra

in (

)

35 MPa

50 MPa 40 MPa

35 MPa

50 MPa 40 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 3 Continued

4 Advances in Civil Engineering

(e creep strain and creep rate increase with thedeviator stress at the same creep time

(2) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of the specimensunder the same deviator stress at the same creeptime

(e average creep rate based on the steady creep stage inthe creep rate curve is taken as the steady creep rate _εs (esteady creep rates of each specimen under various deviatorstresses are listed in Table 3

(e relationship between the creep rate and the deviatorstress of frozen clay can be described with the exponentialequation (1) [16 17] According to the data on the steadycreep rate of the specimens with various consolidationconditions the regression curves of _εsminus (σ1 minus σ3) were de-termined as shown in Figure 5 and the regression pa-rameters are listed in Table 4

_εs aeb σ1minus σ3( ) (1)

where _εs represents the steady creep rate σ1 minus σ3 is the creepdeviator stress and a and b are the material constants relatedto the consolidation time and consolidation stress

For frozen specimens subjected to long-term high-pressure K0 consolidation before freezing the steady creeprate increases with creep deviator stress under the samedeviator stress the steady creep rate decreases with theextension of the consolidation time (e regression pa-rameter a increases with the extension of the consolidationtime while b decreases on the contrary a decreases with theincrease in the consolidation stress whereas b increases

32 Long-Term Strength During the exposure duration ofthe shaft excavation section the long-term strength of theartificially frozen deep clay has an important influence on

the long-term mechanical stability of the frozen wallHowever human error makes it very difficult to determinethe stress inflection point of frozen clay accurately with theconventional stress-strain isochronal curve method Moreaccurate long-term measurements of strength are obtainedfrom the creep tests in this paper by applying the re-lationship between the experimental steady creep rate andcreep deviator stress and the method of equal intervaltangent to eliminate human error

(e specific methods for this approach are as follows

(1) According to the creep tests the steady creep rateunder different deviator stresses was obtained

(2) (e exponential equation shown as equation (1) wasapplied to fit the relationship between steady creeprate and deviator stress

(3) Tangent lines were drawn every 5deg in the range from5 to 85deg on the fitting curve (e intersection pointsof each tangent line with the deviator stress axis weremarked as A B C D E and so on (e upper andlower limits of the long-term strength correspond tothe two creep deviator stresses of the intersectionpoints with the smallest spacing

(4) Tangent lines were drawn every 1deg between the twointersection points with the smallest spacing on thefitting curve Step (3) was repeated to obtain a moreaccurate range of the long-term strength and thenthe average value was taken as the long-term strengthof the frozen clay specimen

A schematic diagram of this method is shown inFigure 6

K0 values moisture contents instantaneous strengthslong-term strengths and strength decay rates based on thehigh-pressure K0 consolidation tests triaxial shear tests andtriaxial creep tests of frozen clay were determined as listed in

Stra

in (

)

40 MPa

50 MPa 45 MPa

40 MPa

50 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

Figure 3 Variations in axial creep strain and axial creep rate with time (σ1 8MPa) (a) tc 3 d (b) tc 7 d and (c) tc 14 d

Advances in Civil Engineering 5

35 MPa 40 MPa 45 MPa

35 MPa 40 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(a)

43 MPa 47 MPa 51 MPa

43 MPa 47 MPa 51 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 4 Continued

6 Advances in Civil Engineering

45 MPa 50 MPa 55 MPa

45 MPa 50 MPa 55 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

42 MPa47 MPa52 MPa

42 MPa47 MPa52 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(d)

Figure 4 Variations in the axial creep strain and axial creep rate with time (σ1 10MPa) (a) tc 3d (b) tc 7d (c) tc 14d and (d) tc 28d

Table 3 (e steady creep rate of the frozen clay specimens (minus 15degC)

SpecimenPrimary deviator stress Secondary deviator stress Tertiary deviator stress

σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1)

8MPa-3 d 35 0159 40 0313 45 06818MPa-7 d 35 0111 40 0184 50 07188MPa-14 d 40 0181 45 0325 50 058210MPa-3 d 35 0143 40 0266 45 059110MPa-7 d 43 0215 47 0364 51 061810MPa-14 d 45 0221 50 0401 55 072910MPa-28 d 42 0120 47 0207 52 0355

Advances in Civil Engineering 7

Table 5 σf represents the instantaneous strength and σfinfinrepresents the long-term strength (e strength decay rate isexpressed as σ ie σ (σf minus σfinfin )σf

To analyze the evolution and mechanisms of the in-stantaneous and long-term strengths their variations andrates of increase are shown in Figures 7 and 8 respectivelyFigure 9 shows the variations in the strength decay rates

(e following conclusions were reached

(1) (e instantaneous and long-term strengths of thespecimens subjected to consolidation under 8MPaincrease by 053MPa and 067MPa respectively

which are within consolidation times of 1 to 14 daysand those under 10MPa increase by 081MPa and114MPa with consolidation times of 1 to 28 days(e strengths increase rapidly for consolidationtimes of 3 to 7 days and as the consolidation timeincreases the rates of increase in the strengths tendto be stable

(2) (e long-term strengths and instantaneousstrengths of specimens consolidated under10MPa are higher than those consolidated under8MPa

Stea

dy-s

tate

cree

p ra

te (

middothndash1

)

3 d 7 d 14 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(a)St

eady

-sta

te cr

eep

rate

(middoth

ndash1)

3 d 7 d

14 d 28 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(b)

Figure 5 (e regression curves of _εsminus (σ1 minus σ3) (a) σ1 8MPa and (b) σ1 10MPa

Table 4 (e regression parameters of _εsndash(σ1 minus σ3)

Parameters8MPa 10MPa

3 d 7 d 14 d 3 d 7 d 14 d 28 da 0000839 0001031 0001714 0000674 0000736 0001033 0001257b 1488 1309 1165 1506 1320 1192 1086

Stea

dy cr

eep

rate

Stea

dy cr

eep

rate

A B C D E F Deviator stress

e minimum interval

B C Deviator stress

e minimum interval

Long-termstrength

Figure 6 (e method used to obtain the long-term strength

8 Advances in Civil Engineering

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

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Table 2 Arrangements of triaxial unloading creep test on frozen clay

Number σ1 (MPa) T (degC) tc (d) σ1 minus σ3 (MPa)1 8 minus 15 3 3540452 8 minus 15 7 3540503 8 minus 15 14 4045504 10 minus 15 3 3540455 10 minus 15 7 4347516 10 minus 15 14 4550557 10 minus 15 28 424752

Stra

in (

)

35 MPa

45 MPa 40 MPa

35 MPa

45 MPa 40 MPa

Cr

eep

rate

(middoth

ndash1)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

0

2

4

6

8

10

12

2 4 6 8 10 120Time (h)

(a)

Stra

in (

)

35 MPa

50 MPa 40 MPa

35 MPa

50 MPa 40 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 3 Continued

4 Advances in Civil Engineering

(e creep strain and creep rate increase with thedeviator stress at the same creep time

(2) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of the specimensunder the same deviator stress at the same creeptime

(e average creep rate based on the steady creep stage inthe creep rate curve is taken as the steady creep rate _εs (esteady creep rates of each specimen under various deviatorstresses are listed in Table 3

(e relationship between the creep rate and the deviatorstress of frozen clay can be described with the exponentialequation (1) [16 17] According to the data on the steadycreep rate of the specimens with various consolidationconditions the regression curves of _εsminus (σ1 minus σ3) were de-termined as shown in Figure 5 and the regression pa-rameters are listed in Table 4

_εs aeb σ1minus σ3( ) (1)

where _εs represents the steady creep rate σ1 minus σ3 is the creepdeviator stress and a and b are the material constants relatedto the consolidation time and consolidation stress

For frozen specimens subjected to long-term high-pressure K0 consolidation before freezing the steady creeprate increases with creep deviator stress under the samedeviator stress the steady creep rate decreases with theextension of the consolidation time (e regression pa-rameter a increases with the extension of the consolidationtime while b decreases on the contrary a decreases with theincrease in the consolidation stress whereas b increases

32 Long-Term Strength During the exposure duration ofthe shaft excavation section the long-term strength of theartificially frozen deep clay has an important influence on

the long-term mechanical stability of the frozen wallHowever human error makes it very difficult to determinethe stress inflection point of frozen clay accurately with theconventional stress-strain isochronal curve method Moreaccurate long-term measurements of strength are obtainedfrom the creep tests in this paper by applying the re-lationship between the experimental steady creep rate andcreep deviator stress and the method of equal intervaltangent to eliminate human error

(e specific methods for this approach are as follows

(1) According to the creep tests the steady creep rateunder different deviator stresses was obtained

(2) (e exponential equation shown as equation (1) wasapplied to fit the relationship between steady creeprate and deviator stress

(3) Tangent lines were drawn every 5deg in the range from5 to 85deg on the fitting curve (e intersection pointsof each tangent line with the deviator stress axis weremarked as A B C D E and so on (e upper andlower limits of the long-term strength correspond tothe two creep deviator stresses of the intersectionpoints with the smallest spacing

(4) Tangent lines were drawn every 1deg between the twointersection points with the smallest spacing on thefitting curve Step (3) was repeated to obtain a moreaccurate range of the long-term strength and thenthe average value was taken as the long-term strengthof the frozen clay specimen

A schematic diagram of this method is shown inFigure 6

K0 values moisture contents instantaneous strengthslong-term strengths and strength decay rates based on thehigh-pressure K0 consolidation tests triaxial shear tests andtriaxial creep tests of frozen clay were determined as listed in

Stra

in (

)

40 MPa

50 MPa 45 MPa

40 MPa

50 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

Figure 3 Variations in axial creep strain and axial creep rate with time (σ1 8MPa) (a) tc 3 d (b) tc 7 d and (c) tc 14 d

Advances in Civil Engineering 5

35 MPa 40 MPa 45 MPa

35 MPa 40 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(a)

43 MPa 47 MPa 51 MPa

43 MPa 47 MPa 51 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 4 Continued

6 Advances in Civil Engineering

45 MPa 50 MPa 55 MPa

45 MPa 50 MPa 55 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

42 MPa47 MPa52 MPa

42 MPa47 MPa52 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(d)

Figure 4 Variations in the axial creep strain and axial creep rate with time (σ1 10MPa) (a) tc 3d (b) tc 7d (c) tc 14d and (d) tc 28d

Table 3 (e steady creep rate of the frozen clay specimens (minus 15degC)

SpecimenPrimary deviator stress Secondary deviator stress Tertiary deviator stress

σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1)

8MPa-3 d 35 0159 40 0313 45 06818MPa-7 d 35 0111 40 0184 50 07188MPa-14 d 40 0181 45 0325 50 058210MPa-3 d 35 0143 40 0266 45 059110MPa-7 d 43 0215 47 0364 51 061810MPa-14 d 45 0221 50 0401 55 072910MPa-28 d 42 0120 47 0207 52 0355

Advances in Civil Engineering 7

Table 5 σf represents the instantaneous strength and σfinfinrepresents the long-term strength (e strength decay rate isexpressed as σ ie σ (σf minus σfinfin )σf

To analyze the evolution and mechanisms of the in-stantaneous and long-term strengths their variations andrates of increase are shown in Figures 7 and 8 respectivelyFigure 9 shows the variations in the strength decay rates

(e following conclusions were reached

(1) (e instantaneous and long-term strengths of thespecimens subjected to consolidation under 8MPaincrease by 053MPa and 067MPa respectively

which are within consolidation times of 1 to 14 daysand those under 10MPa increase by 081MPa and114MPa with consolidation times of 1 to 28 days(e strengths increase rapidly for consolidationtimes of 3 to 7 days and as the consolidation timeincreases the rates of increase in the strengths tendto be stable

(2) (e long-term strengths and instantaneousstrengths of specimens consolidated under10MPa are higher than those consolidated under8MPa

Stea

dy-s

tate

cree

p ra

te (

middothndash1

)

3 d 7 d 14 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(a)St

eady

-sta

te cr

eep

rate

(middoth

ndash1)

3 d 7 d

14 d 28 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(b)

Figure 5 (e regression curves of _εsminus (σ1 minus σ3) (a) σ1 8MPa and (b) σ1 10MPa

Table 4 (e regression parameters of _εsndash(σ1 minus σ3)

Parameters8MPa 10MPa

3 d 7 d 14 d 3 d 7 d 14 d 28 da 0000839 0001031 0001714 0000674 0000736 0001033 0001257b 1488 1309 1165 1506 1320 1192 1086

Stea

dy cr

eep

rate

Stea

dy cr

eep

rate

A B C D E F Deviator stress

e minimum interval

B C Deviator stress

e minimum interval

Long-termstrength

Figure 6 (e method used to obtain the long-term strength

8 Advances in Civil Engineering

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

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(e creep strain and creep rate increase with thedeviator stress at the same creep time

(2) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of the specimensunder the same deviator stress at the same creeptime

(e average creep rate based on the steady creep stage inthe creep rate curve is taken as the steady creep rate _εs (esteady creep rates of each specimen under various deviatorstresses are listed in Table 3

(e relationship between the creep rate and the deviatorstress of frozen clay can be described with the exponentialequation (1) [16 17] According to the data on the steadycreep rate of the specimens with various consolidationconditions the regression curves of _εsminus (σ1 minus σ3) were de-termined as shown in Figure 5 and the regression pa-rameters are listed in Table 4

_εs aeb σ1minus σ3( ) (1)

where _εs represents the steady creep rate σ1 minus σ3 is the creepdeviator stress and a and b are the material constants relatedto the consolidation time and consolidation stress

For frozen specimens subjected to long-term high-pressure K0 consolidation before freezing the steady creeprate increases with creep deviator stress under the samedeviator stress the steady creep rate decreases with theextension of the consolidation time (e regression pa-rameter a increases with the extension of the consolidationtime while b decreases on the contrary a decreases with theincrease in the consolidation stress whereas b increases

32 Long-Term Strength During the exposure duration ofthe shaft excavation section the long-term strength of theartificially frozen deep clay has an important influence on

the long-term mechanical stability of the frozen wallHowever human error makes it very difficult to determinethe stress inflection point of frozen clay accurately with theconventional stress-strain isochronal curve method Moreaccurate long-term measurements of strength are obtainedfrom the creep tests in this paper by applying the re-lationship between the experimental steady creep rate andcreep deviator stress and the method of equal intervaltangent to eliminate human error

(e specific methods for this approach are as follows

(1) According to the creep tests the steady creep rateunder different deviator stresses was obtained

(2) (e exponential equation shown as equation (1) wasapplied to fit the relationship between steady creeprate and deviator stress

(3) Tangent lines were drawn every 5deg in the range from5 to 85deg on the fitting curve (e intersection pointsof each tangent line with the deviator stress axis weremarked as A B C D E and so on (e upper andlower limits of the long-term strength correspond tothe two creep deviator stresses of the intersectionpoints with the smallest spacing

(4) Tangent lines were drawn every 1deg between the twointersection points with the smallest spacing on thefitting curve Step (3) was repeated to obtain a moreaccurate range of the long-term strength and thenthe average value was taken as the long-term strengthof the frozen clay specimen

A schematic diagram of this method is shown inFigure 6

K0 values moisture contents instantaneous strengthslong-term strengths and strength decay rates based on thehigh-pressure K0 consolidation tests triaxial shear tests andtriaxial creep tests of frozen clay were determined as listed in

Stra

in (

)

40 MPa

50 MPa 45 MPa

40 MPa

50 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

Figure 3 Variations in axial creep strain and axial creep rate with time (σ1 8MPa) (a) tc 3 d (b) tc 7 d and (c) tc 14 d

Advances in Civil Engineering 5

35 MPa 40 MPa 45 MPa

35 MPa 40 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(a)

43 MPa 47 MPa 51 MPa

43 MPa 47 MPa 51 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 4 Continued

6 Advances in Civil Engineering

45 MPa 50 MPa 55 MPa

45 MPa 50 MPa 55 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

42 MPa47 MPa52 MPa

42 MPa47 MPa52 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(d)

Figure 4 Variations in the axial creep strain and axial creep rate with time (σ1 10MPa) (a) tc 3d (b) tc 7d (c) tc 14d and (d) tc 28d

Table 3 (e steady creep rate of the frozen clay specimens (minus 15degC)

SpecimenPrimary deviator stress Secondary deviator stress Tertiary deviator stress

σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1)

8MPa-3 d 35 0159 40 0313 45 06818MPa-7 d 35 0111 40 0184 50 07188MPa-14 d 40 0181 45 0325 50 058210MPa-3 d 35 0143 40 0266 45 059110MPa-7 d 43 0215 47 0364 51 061810MPa-14 d 45 0221 50 0401 55 072910MPa-28 d 42 0120 47 0207 52 0355

Advances in Civil Engineering 7

Table 5 σf represents the instantaneous strength and σfinfinrepresents the long-term strength (e strength decay rate isexpressed as σ ie σ (σf minus σfinfin )σf

To analyze the evolution and mechanisms of the in-stantaneous and long-term strengths their variations andrates of increase are shown in Figures 7 and 8 respectivelyFigure 9 shows the variations in the strength decay rates

(e following conclusions were reached

(1) (e instantaneous and long-term strengths of thespecimens subjected to consolidation under 8MPaincrease by 053MPa and 067MPa respectively

which are within consolidation times of 1 to 14 daysand those under 10MPa increase by 081MPa and114MPa with consolidation times of 1 to 28 days(e strengths increase rapidly for consolidationtimes of 3 to 7 days and as the consolidation timeincreases the rates of increase in the strengths tendto be stable

(2) (e long-term strengths and instantaneousstrengths of specimens consolidated under10MPa are higher than those consolidated under8MPa

Stea

dy-s

tate

cree

p ra

te (

middothndash1

)

3 d 7 d 14 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(a)St

eady

-sta

te cr

eep

rate

(middoth

ndash1)

3 d 7 d

14 d 28 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(b)

Figure 5 (e regression curves of _εsminus (σ1 minus σ3) (a) σ1 8MPa and (b) σ1 10MPa

Table 4 (e regression parameters of _εsndash(σ1 minus σ3)

Parameters8MPa 10MPa

3 d 7 d 14 d 3 d 7 d 14 d 28 da 0000839 0001031 0001714 0000674 0000736 0001033 0001257b 1488 1309 1165 1506 1320 1192 1086

Stea

dy cr

eep

rate

Stea

dy cr

eep

rate

A B C D E F Deviator stress

e minimum interval

B C Deviator stress

e minimum interval

Long-termstrength

Figure 6 (e method used to obtain the long-term strength

8 Advances in Civil Engineering

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

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35 MPa 40 MPa 45 MPa

35 MPa 40 MPa 45 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(a)

43 MPa 47 MPa 51 MPa

43 MPa 47 MPa 51 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(b)

Figure 4 Continued

6 Advances in Civil Engineering

45 MPa 50 MPa 55 MPa

45 MPa 50 MPa 55 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

42 MPa47 MPa52 MPa

42 MPa47 MPa52 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(d)

Figure 4 Variations in the axial creep strain and axial creep rate with time (σ1 10MPa) (a) tc 3d (b) tc 7d (c) tc 14d and (d) tc 28d

Table 3 (e steady creep rate of the frozen clay specimens (minus 15degC)

SpecimenPrimary deviator stress Secondary deviator stress Tertiary deviator stress

σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1)

8MPa-3 d 35 0159 40 0313 45 06818MPa-7 d 35 0111 40 0184 50 07188MPa-14 d 40 0181 45 0325 50 058210MPa-3 d 35 0143 40 0266 45 059110MPa-7 d 43 0215 47 0364 51 061810MPa-14 d 45 0221 50 0401 55 072910MPa-28 d 42 0120 47 0207 52 0355

Advances in Civil Engineering 7

Table 5 σf represents the instantaneous strength and σfinfinrepresents the long-term strength (e strength decay rate isexpressed as σ ie σ (σf minus σfinfin )σf

To analyze the evolution and mechanisms of the in-stantaneous and long-term strengths their variations andrates of increase are shown in Figures 7 and 8 respectivelyFigure 9 shows the variations in the strength decay rates

(e following conclusions were reached

(1) (e instantaneous and long-term strengths of thespecimens subjected to consolidation under 8MPaincrease by 053MPa and 067MPa respectively

which are within consolidation times of 1 to 14 daysand those under 10MPa increase by 081MPa and114MPa with consolidation times of 1 to 28 days(e strengths increase rapidly for consolidationtimes of 3 to 7 days and as the consolidation timeincreases the rates of increase in the strengths tendto be stable

(2) (e long-term strengths and instantaneousstrengths of specimens consolidated under10MPa are higher than those consolidated under8MPa

Stea

dy-s

tate

cree

p ra

te (

middothndash1

)

3 d 7 d 14 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(a)St

eady

-sta

te cr

eep

rate

(middoth

ndash1)

3 d 7 d

14 d 28 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(b)

Figure 5 (e regression curves of _εsminus (σ1 minus σ3) (a) σ1 8MPa and (b) σ1 10MPa

Table 4 (e regression parameters of _εsndash(σ1 minus σ3)

Parameters8MPa 10MPa

3 d 7 d 14 d 3 d 7 d 14 d 28 da 0000839 0001031 0001714 0000674 0000736 0001033 0001257b 1488 1309 1165 1506 1320 1192 1086

Stea

dy cr

eep

rate

Stea

dy cr

eep

rate

A B C D E F Deviator stress

e minimum interval

B C Deviator stress

e minimum interval

Long-termstrength

Figure 6 (e method used to obtain the long-term strength

8 Advances in Civil Engineering

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

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45 MPa 50 MPa 55 MPa

45 MPa 50 MPa 55 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12St

rain

()

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(c)

42 MPa47 MPa52 MPa

42 MPa47 MPa52 MPa

Cree

p ra

te (

middothndash1

)

0

2

4

6

8

10

12

Stra

in (

)

00

04

08

12

16

20

24

2 4 6 8 10 120Time (h)

2 4 6 8 10 120Time (h)

(d)

Figure 4 Variations in the axial creep strain and axial creep rate with time (σ1 10MPa) (a) tc 3d (b) tc 7d (c) tc 14d and (d) tc 28d

Table 3 (e steady creep rate of the frozen clay specimens (minus 15degC)

SpecimenPrimary deviator stress Secondary deviator stress Tertiary deviator stress

σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1) σ1 minus σ3 (MPa) _εs (middothminus 1)

8MPa-3 d 35 0159 40 0313 45 06818MPa-7 d 35 0111 40 0184 50 07188MPa-14 d 40 0181 45 0325 50 058210MPa-3 d 35 0143 40 0266 45 059110MPa-7 d 43 0215 47 0364 51 061810MPa-14 d 45 0221 50 0401 55 072910MPa-28 d 42 0120 47 0207 52 0355

Advances in Civil Engineering 7

Table 5 σf represents the instantaneous strength and σfinfinrepresents the long-term strength (e strength decay rate isexpressed as σ ie σ (σf minus σfinfin )σf

To analyze the evolution and mechanisms of the in-stantaneous and long-term strengths their variations andrates of increase are shown in Figures 7 and 8 respectivelyFigure 9 shows the variations in the strength decay rates

(e following conclusions were reached

(1) (e instantaneous and long-term strengths of thespecimens subjected to consolidation under 8MPaincrease by 053MPa and 067MPa respectively

which are within consolidation times of 1 to 14 daysand those under 10MPa increase by 081MPa and114MPa with consolidation times of 1 to 28 days(e strengths increase rapidly for consolidationtimes of 3 to 7 days and as the consolidation timeincreases the rates of increase in the strengths tendto be stable

(2) (e long-term strengths and instantaneousstrengths of specimens consolidated under10MPa are higher than those consolidated under8MPa

Stea

dy-s

tate

cree

p ra

te (

middothndash1

)

3 d 7 d 14 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(a)St

eady

-sta

te cr

eep

rate

(middoth

ndash1)

3 d 7 d

14 d 28 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(b)

Figure 5 (e regression curves of _εsminus (σ1 minus σ3) (a) σ1 8MPa and (b) σ1 10MPa

Table 4 (e regression parameters of _εsndash(σ1 minus σ3)

Parameters8MPa 10MPa

3 d 7 d 14 d 3 d 7 d 14 d 28 da 0000839 0001031 0001714 0000674 0000736 0001033 0001257b 1488 1309 1165 1506 1320 1192 1086

Stea

dy cr

eep

rate

Stea

dy cr

eep

rate

A B C D E F Deviator stress

e minimum interval

B C Deviator stress

e minimum interval

Long-termstrength

Figure 6 (e method used to obtain the long-term strength

8 Advances in Civil Engineering

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

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Submit your manuscripts atwwwhindawicom

Table 5 σf represents the instantaneous strength and σfinfinrepresents the long-term strength (e strength decay rate isexpressed as σ ie σ (σf minus σfinfin )σf

To analyze the evolution and mechanisms of the in-stantaneous and long-term strengths their variations andrates of increase are shown in Figures 7 and 8 respectivelyFigure 9 shows the variations in the strength decay rates

(e following conclusions were reached

(1) (e instantaneous and long-term strengths of thespecimens subjected to consolidation under 8MPaincrease by 053MPa and 067MPa respectively

which are within consolidation times of 1 to 14 daysand those under 10MPa increase by 081MPa and114MPa with consolidation times of 1 to 28 days(e strengths increase rapidly for consolidationtimes of 3 to 7 days and as the consolidation timeincreases the rates of increase in the strengths tendto be stable

(2) (e long-term strengths and instantaneousstrengths of specimens consolidated under10MPa are higher than those consolidated under8MPa

Stea

dy-s

tate

cree

p ra

te (

middothndash1

)

3 d 7 d 14 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(a)St

eady

-sta

te cr

eep

rate

(middoth

ndash1)

3 d 7 d

14 d 28 d

0

1

2

3

4

5

6

3 4 5 6 7 82Deviator stress (MPa)

(b)

Figure 5 (e regression curves of _εsminus (σ1 minus σ3) (a) σ1 8MPa and (b) σ1 10MPa

Table 4 (e regression parameters of _εsndash(σ1 minus σ3)

Parameters8MPa 10MPa

3 d 7 d 14 d 3 d 7 d 14 d 28 da 0000839 0001031 0001714 0000674 0000736 0001033 0001257b 1488 1309 1165 1506 1320 1192 1086

Stea

dy cr

eep

rate

Stea

dy cr

eep

rate

A B C D E F Deviator stress

e minimum interval

B C Deviator stress

e minimum interval

Long-termstrength

Figure 6 (e method used to obtain the long-term strength

8 Advances in Civil Engineering

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

5 10 15 20 25 30000

004

008

012

016

020

dσfd

t c an

d dσ

finfindt c

MPa

middotdndash1

Consolidation time (d)

8 MPa instantaneousstrength

8 MPa long-termstrength

10 MPa instantaneousstrength

10 MPa long-termstrength

(a)

dσfd

σ 1 an

d dσ

finfindσ 1

2 4 6 8 10 12 1400

01

02

03

04

Instantaneous strengthLong-term strength

Consolidation time (d)

(b)

Figure 8 Variations in the rates of increase in the instantaneous and long-term strengths of the frozen clay (a) dσfdtc and σfinfindtc vs tc and(b) dσfdtc and σfinfindtc vs tc

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Insta

ntan

eous

stre

ngth

(MPa

)

5 10 15 20 25 300Consolidation time (d)

(a)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

24 25 26 27 28 29 3023Water content ()

(b)

8 MPa instantaneous strength10 MPa instantaneous strength

8 MPa long-term strength10 MPa long-term strength

3

4

5

6

7

8

Long

-term

stre

ngth

(MPa

)

060 062 064 066 068 070 072058K0

(c)

Figure 7 Variations in the long-term and instantaneous strengths of the frozen clay (a) σf and σfinfin vs tc (b) σf and σfinfin vs w and (c) σf andσfinfin vs K0

Table 5 Instantaneous and long-term strengths of the frozen clay

Specimen w () K0 σf (MPa) σfinfin (MPa) σ ()8MPa-3 d 2957 0701 555 381 31358MPa-7 d 2701 0657 593 428 27828MPa-14 d 2590 0593 608 448 263110MPa-3 d 267 0699 568 391 312810MPa-7 d 2541 0661 619 449 274610MPa-14 d 2427 0609 637 474 257010MPa-28 d 2377 0590 649 505 2049

Advances in Civil Engineering 9

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(3) (e water contents of saturated specimens subjectedto long-term consolidation at 8MPa and 10MPa are259ndash2957 and 2377ndash267 respectively (eincrease in dry density caused by the prolongation ofconsolidation time results in the decrease in thesaturated ice content of the specimen Meanwhilethe cohesion and friction between soil particles in-crease as well as the cementation between the soiland ice (e contribution of compaction to the in-stantaneous and long-term strengths of the frozenspecimens increases gradually and the effect on thelong-term strength is prominent

(4) (e K0 values decrease with the consolidation timeConsequently with the decrease in excess pore waterpressure and the increase in effective stress betweenclay particles the unfrozen water content in frozenspecimens decreases Meanwhile the friction force ofthe soil particles increases and the relative motionunder the deviator stress decreases As indicated by thetest results the instantaneous and long-term strengthsdecrease with the K0 value

(5) (e consolidation time-related increase rates in theinstantaneous and long-term strengths graduallydecrease with the extension of the consolidation timeIn addition the increase rates of the long-termstrength are higher than those of the instantaneousstrength ie the long-term strength of frozen clay ismore greatly affected In contrast the consolidationstress-related increase rates of the instantaneous andlong-term strengths increase with the consolidationtime In addition the instantaneous strength is af-fected more than the long-term strength

(6) (e long-term strengths of the specimens consoli-dated under 8MPa and 10MPa are 3135ndash2631and 3128ndash2049 less than the instantaneousstrengths respectively (e decay rates of strengthare reduced with the consolidation time and thestrengths of the specimens consolidated under8MPa decay more drastically It can be inferred that

the creep time effect on the strength of frozen clay isweakened by long-term high-pressure consolidationbefore freezing ie the creep property weakens

33 Long-Term MohrndashCoulomb Strength Parameters Inprevious studies the strength criterion of frozen soil undertriaxial stress paths followed the MohrndashCoulomb strengthcriterion [18] Based on triaxial shear tests and triaxial creeptests of frozen clay strength envelopes following the MohrndashCoulomb strength criterion are shown in Figure 10 and theMohrndashCoulomb strength parameters are listed in Table 6

From the analysis the following results were found

(1) As shown in Figure 11 the instantaneous and long-term MohrndashCoulomb strength parameters increasedwith the consolidation time and the instantaneousinternal friction angles and cohesions are greaterthan the long-term internal friction angles andcohesions

(2) (e decay rates of the long-term internal frictionangles and cohesions compared to those of theinstantaneous internal friction angles and cohesionsare reduced by long-term consolidation beforefreezing It is illustrated that the creep property offrozen clay is weakened under these conditions

4 Creep Equation of Deep Frozen Clay

Consisting of a Hooke body viscoelastic body and visco-plastic body the Nishihara model can describe the variationin different creep types thus reflecting the internal char-acteristics and creep mechanism of frozen clay (e me-chanical model is shown in Figure 12 where E0 representsthe elastic modulus of the Hooke body E1 is the elasticmodulus of the viscoelastic body η1 and η2 are the viscositycoefficients of the viscoelastic and viscoplastic bodies andσinfin is the long-term strength of the frozen clay

(e creep equations corresponding to the triaxial stressstate are shown in the following equation

0 5 10 15 20 25 3020

22

24

26

28

30

32

34

Consolidation time (d)

8MPa10MPa

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)

(a)

8MPa10MPa

23 24 25 26 27 28 29 3020

22

24

26

28

30

32

34

Water content ()

Dec

ay ra

te o

f lon

g-te

rmstr

engt

h (

)(b)

8MPa10MPa

058 060 062 064 066 068 070 07220

22

24

26

28

30

32

34

Dec

ay ra

te o

f lon

g-te

rmSt

reng

th (

)

K0

(c)

Figure 9 Variations in the strength decay rate of the frozen clay (a) strength decay rate vs tc (b) strength decay rate vs w and (c) strengthdecay rate vs K0

10 Advances in Civil Engineering

24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

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24

28

32

36

0 2 4 6 8 10 12(σ1 + σ3)(2)(MPa)

3d7d14d

σ f (2

)(M

Pa)

(a)

(σ1 + σ3)(2)(MPa)

3d7d14d

16

2

24

28

0 2 4 6 8 10 12

σ finfin

(2)(

MPa

)

(b)

Figure 10 Strength envelopes of frozen clay (a) instantaneous strength and (b) long-term strength

Table 6 Instantaneous and long-term MohrndashCoulomb strength parameters

tc (d) c (MPa) φ (deg) cinfin (MPa) φinfin (deg) cminus cinfinc () φ minus φinfinφ ()3 d 2586 2079 1740 1546 3270 25597 d 2623 3986 1817 3207 2991 248414 d 2652 4586 1908 3497 2805 2375

10

20

30

40

50

Fric

tion

angl

e (deg)

φφinfin

4 8 12 160Consolidation time (d)

(a)

ccinfin

14

18

22

26

30

Cohe

sion

(MPa

)

4 8 12 160Consolidation time (d)

(b)

Figure 11 Variations in instantaneous and long-term MohrndashCoulomb strength parameters vs tc (a) friction angle and (b) cohesion

E0

E1

η1

σinfin

η2

Figure 12 (e Nishihara model

Advances in Civil Engineering 11

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E0

+σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2t σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(2)

A power function that reflects the nonlinearity of theviscoplastic body is applied to improve the creep constitutiveequations (see equation (3)) where e is the nonlinearaccelerated creep index In addition the variation rules of

the attenuation creep stable creep and acceleration creepstages are mainly analyzed in this paper Instantaneouscreep the instantaneous deformation under triaxial deviatorstress is neglected in this study to facilitate analysis

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

35MPa tested50MPa tested

40MPa testedPredicted

0 2 4 6 8 10 120

2

4

6

8

10

12

Stra

in (

)

Time (h)

(b)

Time (h)

40MPa tested50MPa tested

45MPa testedPredicted

Stra

in (

)

0 2 4 6 8 10 120

2

4

6

8

10

12

(c)

Figure 13 Comparisons between the experimental and calculation results (σ1 8MPa) (a) 3 d (b) 7 d and (c) 14 d

12 Advances in Civil Engineering

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 σ1 minus σ3 lt σfinfin

ε σ1 minus σ33E1

1 minus exp minus2E1

η1t1113888 11138891113890 1113891 +

σ1 minus σ3 minus σfinfin( 1113857

η2te σ1 minus σ3 ge σfinfin

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(3)

(e improved model is verified through the data of creeptests and shown as Figures 13 and 14 (e fitting parametersare listed in Table 7

Variations in the creep regression parameters of thefrozen clay with the deviator stress are shown in Figures 15and 16 Considering that the deviator stress of each grouptest is different as is the long-term strength the variations in

creep parameters with σ1 minus σ3 minus σfinfin taken as abscissa areanalyzed

Taking the case of the specimen consolidated for 7 daysbefore freezing viscoelastic deformation and viscoplasticdeformation are analyzed under different deviator stressesaccording to the improved creep model (e results areshown in Figure 17

0 2 4 6 8 10 120

2

4

6

8

10

12

Time (h)

35MPa tested45MPa tested

40MPa testedPredicted

Stra

in (

)

(a)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

43MPa tested51MPa tested

47MPa testedPredicted

Stra

in (

)

(b)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

45MPa tested55MPa tested

50MPa testedPredicted

Stra

in (

)

(c)

Time (h)0 2 4 6 8 10 12

0

2

4

6

8

10

12

42MPa tested52MPa tested

47MPa testedPredicted

Stra

in (

)

(d)

Figure 14 Comparisons between the experimental and calculation results (σ1 10MPa) (a) 3 d (b) 7 d (c) 14 d and (d) 28 d

Advances in Civil Engineering 13

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

Table 7 (e improved creep model parameters

σc (MPa) tc (d) σ1 minus σ3 (MPa) σ1 minus σ3 minus σfinfin (MPa) E1 (GPa) η1 (GPamiddoth) η2 (GPamiddoth) e

8

335 minus 031 0239 1784 mdash mdash40 019 0269 1952 2267 135845 069 0221 1568 2040 1135

735 minus 078 0265 2124 mdash mdash40 minus 028 0273 2160 mdash mdash50 072 0256 1772 3322 1324

1440 minus 048 0277 2310 mdash mdash45 002 0309 2412 4149 225750 052 0292 2002 3703 1381

10

335 minus 041 0266 1988 mdash mdash40 009 0289 2076 2474 160145 059 0247 1728 1984 1089

743 minus 018 0304 2313 mdash mdash47 022 0317 2366 3448 140651 062 0305 1980 3225 1340

1445 minus 024 0310 2458 mdash mdash50 026 0339 2473 3841 141055 076 0326 2083 3547 1378

2842 minus 085 0311 2486 mdash mdash47 minus 035 0342 2544 mdash mdash52 015 0374 2606 4545 2163

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

3 d 7 d 14 d

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 15 Continued

14 Advances in Civil Engineering

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

18

22

26

30

34

38

42

η2

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(c)

10

12

14

16

18

20

22

24

e

02 04 06 08 1000

3 d 14 d

σ1 ndash σ3 ndash σ finfin

(d)

Figure 15 (e variation in creep parameters (σ1 8MPa) (a) E1 (b) η1 (c) η2 and (d) e

3 d 7 d 28 d

14 d

E1

020

024

028

032

036

040

ndash05 00 05 10ndash10σ1 ndash σ3 ndash σ finfin

(a)

14

18

22

26

30

η1

ndash05 00 05 10ndash10

3 d 7 d 28 d

14 d

σ1 ndash σ3 ndash σ finfin

(b)

Figure 16 Continued

Advances in Civil Engineering 15

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

(e analysis results above suggest the followingconclusions

(1) On the basis of Figures 15(a) and 16(a) E1 firstincreasing and then decreasing reflect that the creepdeformation of frozen clay under a low deviatorstress is composed of only viscoelastic deformationand strengthening effects occur Viscoelastic de-formation and viscoplastic deformation coexist andthe ratio of deviator stress to viscoelastic strain (E1)increases when the deviator stress exceeds the long-

term strength With a continual increase in thedeviator stress the effect of strengthening is weak-ened therefore the viscoelastic deformation in-creases and E1 decreases accordingly

(2) On the basis of Figures 15(b) and 16(b) η1 firstincreasing and then decreasing reflects that com-pared with the stabilization time of viscoelastic de-formation at a low deviator stress the stabilizationtime increases when the deviator stress exceeds thelong-term strength ie η1 increases With a

3 d 7 d 14 d

18

22

26

30

34

38

42

η2

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(c)

3 d 7 d 14 d

10

12

14

16

18

20

22

e

02 04 06 08 1000σ1 ndash σ3 ndash σ finfin

(d)

Figure 16 (e variation in creep parameters (σ1 10MPa) (a) E1 (b) η1 (c) η2 and (d) e

Visc

oela

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(a)

Visc

opla

stic s

trai

n (

)

43 MPa47 MPa 51 MPa

0

2

4

6

8

2 4 6 8 10 120Time (h)

(b)

Figure 17 Viscoelastic and viscoplastic deformation of the frozen deep clay (10MPa-7 d) (a) viscoelastic strain and (b) viscoplastic strain

16 Advances in Civil Engineering

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

continual increase in the deviator stress viscoelas-tic deformation stabilizes more quickly ie η1decreases

(3) When the deviator stress exceeds the long-termstrength viscoplastic deformation increases gradu-ally with the deviator stress thus the deformationresistance and the nonlinearity of the viscoplasticbody decrease gradually which causes the decreasein η2 and e

(4) (e increase in contact between clay particles thethinning of the pore ice and the decrease in theunfrozen water result in the enhancement of long-term deformation resistance with the extension ofconsolidation time which causes the increases in E1η1 and η2 In addition the nonlinear acceleratedcreep index e increases with consolidation time

5 Conclusions

To lay a foundation for research of creep behaviors andrevealing creep mechanism of artificially frozen deep clayunder complex stress states a series of studies on theevolution of creep properties strength and creep parame-ters based on the experimental mode of ldquolong-term K0consolidated-freezing-constant axial pressure and unloadingconfining pressurerdquo have been carried out in this paper (efollowing conclusions can be drawn

(1) Long-term high-pressure K0 consolidation reducesthe creep strain and creep rate of specimens underthe same deviator stress at the same creep time(usconsolidation time and consolidation stress both areimportant factors affecting the creep properties offrozen clay

(2) (e increase in dry density and the decrease in excesspore water pressure caused by the prolongation ofconsolidation time result in the decrease in the iceand the unfrozen water contents of the specimenMeanwhile the cohesion and friction between soilparticles increase in addition to the increased ce-mentation between the soil and ice thus decreasingtheir relative motion under the deviator stress (einstantaneous strengths and long-term strengthsboth increase rapidly with consolidation times from3 to 7 days and as the consolidation time in-creases the variations in the strengths tend to bestable With the extension of consolidation time thedecay rates of strength decrease from 3135 to2631 (σ1 8MPa) and from 3128 to 2049(σ1 10MPa) respectively and the creep propertyweakens

(3) According to the rates of increase in the in-stantaneous and long-term strengths of the frozenspecimens which are related to consolidation timeand consolidation stress the consolidation time hasan obvious influence on the long-term strength offrozen clay and the consolidation stress clearly af-fects the instantaneous strength

(4) (is study presents an improved Nishihara modelthat accounts for the nonlinearity in the acceleratedcreep stage and rationally reflects the creep behaviorcharacteristics of the deep frozen clay With a lowdeviator stress creep deformations are only elasticWhen the deviator stress exceeds the long-termstrength the soil-ice cementation (ie the bondingelement) is weakened soil particles are crushedunfrozen water content is increased and frictionbecomes influential thus viscoelastic and visco-plastic deformation are both observed(erefore theviscoelastic modulus E1 and viscoelastic viscositycoefficient η1 increase in this stage However with acontinued increase in the deviator stress thebonding and friction elements are rapidly destroyedand the viscoplastic deformation increases thus E1η1 and η2 decrease in this deviator stress stage

(5) (e creep parameters E1 η1 η2 and e all increasewith consolidation time thus illustrating thatcompaction before freezing enhances the long-termdeformation resistance of frozen clay and increasesthe nonlinearity of accelerated creep

Data Availability

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

Conflicts of Interest

(e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

(is work was supported by the National Natural ScienceFoundation of China (grant no 51174194) the National KeyResearch and Development Program of China (grant no2016YFC0600903) and the Fundamental Research Fundsfor the Central Universities (grant no 2018ZZCX04)

References

[1] G X Cui ldquoMechanics of frozen soil for deep alluvium-a newfield of frozen soil mechanicsrdquo Journal of Glaciology andGeocryology vol 20 no 2 pp 97ndash100 1998 in Chinese

[2] Y S Wang J B Jia and Y G Leng ldquoUnloading confiningpressure strength properties of long-term K0-consolidatedartificial frozen clay under high pressurerdquo Chinese Journal ofGeotechnical Engineering vol 39 no 9 pp 1636ndash1644 2017in Chinese

[3] B Ladanyi ldquoAn engineering theory of creep of frozen soilsrdquoCanadian Geotechnical Journal vol 9 no 1 pp 63ndash80 1972

[4] K Takegawa A Nakazawa K Ryokai and S AkagawaldquoCreep characteristics of frozen soilsrdquo Developments inGeotechnical Engineering vol 13 no 1-4 pp 197ndash205 1979

[5] Y L Zhu and D L Carbee ldquoCreep behavior of frozen siltunder constant uniaxial stressrdquo Journal of Glaciology andGeocryology vol 6 no 1 pp 33ndash48 1984 in Chinese

[6] Y G Yang Y M Lai and X X Chang ldquoExperimental andtheoretical studies on the creep behavior of warm ice-rich

Advances in Civil Engineering 17

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

frozen sandrdquo Cold Regions Science and Technology vol 63no 1-2 pp 61ndash67 2010

[7] A M Fish ldquoCreep and yield model of frozen soil undertriaxial compressionrdquo in Proceedings of the 5th InternationalOffshore and Polar Engineering Conference pp 11ndash16 (eHague (e Netherlands June 1995

[8] A V Nadezhdin and V A Sorokin ldquoInfluence of preloadingon the strength of frozen soil (discussion)rdquo Soil Mechanicsand Foundation Engineering vol 12 no 3 pp 185-186 1975

[9] L T Roman and D N Krivov ldquoPrediction of long-termstrength for frozen soils of the Bolshezemelnaya Tundrardquo SoilMechanics and Foundation Engineering vol 46 no 5pp 180ndash185 2009

[10] K Sun Z L Chen J Chen et al ldquoA modified creep con-stitutive equation for frozen soil based on Nishihara modelrdquoRock and Soil Mechanics vol 36 pp 142ndash146 2015 inChinese

[11] D-W Li J-H Fan and R-H Wang ldquoResearch on Visco-elastic-plastic creep model of artificially frozen soil under highconfining pressuresrdquo Cold Regions Science and Technologyvol 65 no 2 pp 219ndash225 2011

[12] D W Li J H Chen and Y Zhou ldquoA study of coupled creepdamaged constitutive model of artificial frozen soilrdquoAdvancesin Materials Science and Engineering vol 2018 Article ID7458696 9 pages 2018

[13] D-W Li J-H Fan and R-H Wang ldquoStudying on yield-surface rheological model of artificially frozen soil underunloading statesrdquo Advanced Science Letters vol 13 no 1pp 451ndash456 2012

[14] D Li X Yang and J Chen ldquoA study of triaxial creep test andyield criterion of artificial frozen soil under unloading stresspathsrdquo Cold Regions Science and Technology vol 141 no 9pp 163ndash170 2017

[15] X Li E L Liu B T Song et al ldquoAn improved Nishiharamodel for frozen loess considering the influence of temper-aturerdquo Advances in Materials Science and Engineeringvol 2018 Article ID 9073435 10 pages 2018

[16] X Zhao and G Zhou ldquoExperimental study on the creepbehavior of frozen clay with thermal gradientrdquo Cold RegionsScience and Technology vol 86 no 2 pp 127ndash132 2013

[17] X Zhao G Zhou and G Lu ldquoStrain responses of frozen claywith thermal gradient under triaxial creeprdquo Acta Geotechnicavol 12 no 1 pp 183ndash193 2017

[18] S Y Li Y M Lai S J Zhang et al ldquoAn improved statisticaldamage constitutive model for warm frozen clay based onMohrndashCoulomb criterionrdquo Cold Regions Science and Tech-nology vol 57 no 2-3 pp 154ndash159 2009

18 Advances in Civil Engineering

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

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Chemical EngineeringInternational Journal of Antennas and

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