effects of diatomite and sbs on freeze-thaw resistance of

Research ArticleEffects of Diatomite and SBS on Freeze-Thaw Resistance ofCrumb Rubber Modified Asphalt Mixture

HaibinWei Ziqi Li and Yubo Jiao

College of Transportation Jilin University Changchun 130025 China

Correspondence should be addressed to Yubo Jiao jiaoybjlueducn

Received 20 February 2017 Revised 26 April 2017 Accepted 30 April 2017 Published 21 May 2017

Academic Editor Gianluca Cicala

Copyright copy 2017 Haibin Wei et al This 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 is properly cited

Asphalt mixture is susceptible to moisture damage under the effect of freeze-thaw (F-T) cycles In this paper crumb rubber (CR)was used to modify stone mastic asphalt (SMA) and the effects of diatomite and styrene butadiene styrene (SBS) on antifreezingperformances of crumb rubber modified SMA (CRSMA) were investigated Regression analysis and modified grey model (MGM)were used to construct the prediction models for properties of modified mixtures CRSMA CR and diatomite modified SMA(CRDSMA) and CR and SBS modified SMA (CRSSMA) were prepared in laboratory respectively Process of F-T cycles wasdesigned Air void indirect tensile strength (ITS) and indirect tensile stiffness modulus (ITSM) were measured to evaluate theantifreezing performances of CRSMA CRDSMA and CRSSMA Results indicate that air voids increase with the increasing of F-Tcycles ITS and ITSM all decrease with the increasing of F-T cycles The addition of diatomite and SBS can reduce the air void andimprove the ITS and ITSMof CRSMA CRSSMApresents the lowest air void highest tensile strength and largest stiffnessmoduluswhich reveals that CRSSMA has the best F-T resistance among three different kinds of mixtures Moreover MGM (1 2) modelspresent more favorable accuracy in prediction of air void and ITS compared with regression ones

1 Introduction

Reuse of waste materials can reduce the consumption ofnatural resources Moreover it can alleviate the waste accu-mulation which can cause serious environmental problem[1ndash3] Therefore reuse of waste materials has got great atten-tionWith the rapid development of automotive industry thenumber of vehicles increases and then amount of scrap tiresalso increases According to the statistical data over 1 billiontires are sold each year all around the world and millionsof waste tires are generated [4 5] Waste tires are not easilydisposed of and lead to great threat to public health andenvironment Many solutions have been proposed for reuseof scrap tires [6ndash9]

Scrap tires can be recycled in the form of crumb rubber(CR) which is a profitable practice La Rosa et al [9]demonstrated that the addition of 50 phr of ground tirerubber (GTR) in styrene-isoprene-styrene (SIS) formulationpresents favorable environmental benefits Life cycle assess-ment (LCA) results indicate that the effects of virgin rubber(471) and carbon black (343) on environmental impacts

of GTR are more obvious than tire grinding process (4)Farina et al [10] investigated the environmental performanceof using crumb rubber in bituminous mixtures based onLCA Results reveal that asphalt rubber obtained throughwet process presents significant benefits for energy savingenvironmental impact human health preservation of ecosys-tems andminimization of resource depletionThe reductionsof gross energy requirement and global warming potentialrange between 36 and 45 compared with standard pavingsolutions Furthermore CR can be used to modify asphaltwhich is an effective method to consume them Previousresearches have demonstrated that CR is a successfulmodifierfor asphalt mixture because of favorable compatibility andinteraction between rubber and asphalt [5] CR modifiedasphalt andmixture havemany advantagesThey can improvethe rutting resistance at high temperature crack resistance atlow temperature fatigue resistance and elastic performance[4 11ndash13] Moreover Liang et al [14] investigated the viscousproperties storage stability and morphology of recycled tirescrap rubber modified asphalt (TSRMA) The results revealthat the addition of crumb rubber can increase viscosity of

HindawiAdvances in Materials Science and EngineeringVolume 2017 Article ID 7802035 14 pageshttpsdoiorg10115520177802035

2 Advances in Materials Science and Engineering

asphalt and improve rutting deformation resistance How-ever it presents poor stability with the increasing of rubberparticle size Navarro and Gamez [4] presented the effect ofcrumb rubber on bearing capacity and cohesion of asphaltmixture The results show that crumb rubber can increasethe stiffness and stability of mixture while it slightly reducestensile strength De Almeida Junior et al [15] evaluatedthe properties of asphalt modified by rubber and styrenebutadiene styrene (SBS) respectively The findings indicatethat rubber has the potential performance to substitute SBSin pavementmaterials However it does notmeet some of therequirements in standard specifications

Diatomite is a widely used mineral with low cost andconsiderable storage which has high absorptive capacityand stability [16ndash22] It has been widely used for asphaltmodification in China [16ndash21] Mohamed Abdullah et al[17 18] studied the properties of diatomite modified asphaltThe results indicate that there is no chemical reactionbetween asphalt and diatomite Diatomite can improve therutting resistance of asphalt at high temperature The agingresistances of modified asphalt are superior to pure oneCheng et al [19] demonstrated the antiaging properties ofdiatomite modified asphalt The results reveal that diatomiteis helpful for improving the high temperature stability andantiaging property of asphalt Tan et al [21] investigatedthe low temperature property of diatomite modified asphaltThe results show that diatomite particles distribute well inasphalt and diatomite modified mixture possesses better lowtemperature performance than neat one

Currently SBS copolymer is the most widely used modi-fier for asphalt which can absorb the oil fractions and swellthem [23ndash25] It can improve both high and low temperatureperformances of mixture Khodaii and Mehrara [26] con-ducted dynamic creep tests for unmodified and SBSmodifiedasphalt SBS modified mixture possesses lower temperaturesusceptibility and higher compactibility Sun et al [27] foundthat reactive blending of SBS and asphalt can improve thehot storage stability rheological properties elasticity anddeformation resistance of modified asphalt The limitationsfor SBS modified asphalt lie in its lower workability higherproduction cost and being easy to aging [28 29] Thereforeit is crucial to have some other waste materials to partiallysubstitute for SBS in modified asphalt CR can reduce thecost and possess favorable performances which is a favorablesubstitute In order to meet the requirements of high graderoad pavement modified asphalt with better performancescan be prepared using CR and SBS composite modifierDong et al [30] investigated the rheological behavior ofSBSCR composite modified asphalt The results reveal thatthe addition of CR and SBS can effectively improve theviscoelastic property and temperature sensitivity of asphalt

In addition freeze-thaw (F-T) cycle is an important factorto influence the performances of road pavement in seasonalfrozen regions which cover 535 of Chinarsquos land area Roadpavement in this region is exposed to at least one F-T cycleeach year [31] CR has beenwidely used in concrete to provideF-T protection [32] Meanwhile Zhang et al [33] foundthat rubber modified asphalt mixture has better antifreezingperformance than the neat one Current research results

indicate that CR is an effective additive to improve the F-Tresistance for road materials

Grey theory was proposed by Deng in 1982 [34] whichhad been widely used in many fields for factor analysisand forecasting Grey relational analysis (GRA) was widelyused to evaluate the influential degrees of factors [35 36]Grey model is another important aspect in grey theorywhich can achieve high prediction accuracy for uncertainsystems It can realize the prediction of system behavior usingfewer data and less complicated mathematical calculation[37] Ren et al [38] predicted the long-term cumulativeplastic deformation of subgrade under cyclic loads using greymodel Wang and Li [39] adopted grey model for pavementsmoothness prediction Grey model was also used for thepredictions in environmental vulnerability assessment [40]natural disasters [41] and road traffic [42] and so forth GM(1 1) (Grey Model First-Order One Variable) is one of themost widely used grey models in practical application [43]However the limitation existing in traditionalGM(1 1) is thatit needs equal interval for time series data It cannot be usedfor time series data with nonequal interval [44]

As discussed above reuse of CR and diatomite possessesfavorable economic and environmental benefits Further-more F-T action has significant effect on the properties ofasphalt pavement in seasonal frozen regions It will reducethe pavement life severelyThe compoundmodified effects ofCR and diatomite CR and SBS on asphalt mixture under F-T actions are still unknown In order to improve the freezingresistance of asphalt pavement crumb rubber modifiedstone mastic asphalt (CRSMA) crumb rubber and diatomitemodified stonemastic asphalt (CRDSMA) and crumb rubberand SBS modified stone mastic asphalt (CRSSMA) wereprepared respectively Effects of F-T cycles on three differentkinds of asphalt mixtures were tested and evaluated usingair voids indirect tensile strength (ITS) test and indirecttensile stiffness modulus (ITSM) test Meanwhile predictionanalysis was used to construct the relationships betweenproperties and F-T cycles in order to improve the conveniencefor performance analysis of mixture Modified grey modelMGM (1 2) was applied for prediction of air void and ITS

2 Materials

21 Raw Materials Base asphalt AH-90 and SBS modifiedasphalt used for experiments were fromPanjin PetrochemicalIndustry Liaoning Province of China Physical propertiesof AH-90 asphalt were measured and listed in Table 1Properties of SBS modified asphalt were tested and givenin Table 2 Aggregate and mineral filler were obtained fromChangchun Municipal Mixing Plant in Jilin Province ofChina Physical properties of andesitemineral aggregate weregiven in Table 3 Limestone powder was chosen as mineralfiller Corresponding properties of filler were listed in Table 4Crumb rubber particle was obtained from Changchun Yux-ing Rubber Materials Co Ltd Jilin Province China Itsproperties were shown in Table 5 Diatomite was producedby Changchun Diatomite Products Co Ltd Jilin ProvinceChina Its physical properties and particle distribution werelisted in Tables 6 and 7

Advances in Materials Science and Engineering 3

Table 1 Properties of neat asphalt

Property Value Technical criterion ()Penetration (25∘C 01mm) 84 80sim100Penetration index PI minus101 minus15sim+10Softening point TRampB (∘C) 44 ge42Ductility (15∘C cm) 150 ge100Specific gravity (15∘C gcm3) 105 mdashAfter TFOTMass loss () minus03 leplusmn08Penetration ratio (25∘C ) 64 ge57Age ductility (10∘C cm) 14 ge8

Table 2 Properties of SBS modified asphalt

Property Penetration(25∘C 01mm)

Softeningpoint TRampB

(∘C)

Ductility(5∘C cm)

Viscosity(60∘C Pasdots)

Value 50 71 40 86

22 Asphalt Mixture Stone mastic asphalt (SMA) was devel-oped in Germany during the 1960s It has been used as thepremium pavement surfacing course for heavy-duty pave-ments high-speed motorways and highways in AmericaEurope China and several other countries due to its excellentrutting resistance fatigue resistance durability and lowernoise characteristics comparedwith dense graded asphalt [4546] In this research SMA-13 gradation was designed basedon the Course Aggregate Void Filling (CAVF) method [47]The designed gradation was shown in Figure 1 Accordingto previous research results the diatomite content 15 byweight of asphalt and crumb rubber content 3 by weight ofaggregate were adopted [15] Optimum asphalt contents weredetermined by Marshall method They are 63 65 and66 for CRSMA CRDSMA and CRSSMA respectively

In order to make crumb rubber and diatomite dispersehomogeneous in the mixture the preparation process wasoptimized The designed preparation process for CRSMAwas shown in Figure 2 Similar to the process in Figure 2CRDSMA would be produced if filler was replaced withfiller and diatomite CRSSMA was obtained if neat asphaltwas replaced with SBS modified asphalt Detailed steps wereexplained as follows

Step 1 Crumb rubber and aggregate were heated for 4 h at180∘C respectivelyThey were blended together using mixingpot (BH-10 Beijing Zhonghangkegong Instrument Co LtdChina)The blending temperature is 165∘C speed is 80 rminand time is 90 sThis step is identical for CRSMA CRDSMAand CRSSMA

Step 2 Asphalt was heated to 165∘C and added to themixtureof crumb rubber and aggregate They were blended togetherat 165∘C for 90 s using mixing pot The mixing speed is alsoset to be 80 rmin In this step neat asphalt was used forCRSMA andCRDSMA while it was SBSmodified asphalt forCRSSMA

Sieve size (mm)

Upper limitLower limit

0

20

40

60

80

100

Perc

ent p

assin

g (

)

007

5

015 03

06

118

236

475

95

132 16

CAVF design

Figure 1 CAVF design gradation for SMA-13

Step 3 Filler was heated for 4 h at 180∘C and added to themixture consisting of crumb rubber aggregate and asphalt(neat one for CRSMA and CRDSMA and SBS modified onefor CRSSMA) They were blended together at the speed of80 rmin and 165∘C for 90 s using mixing pot In this stepmineral powder was used for CRSMA and CRSSMA whilemineral powder and diatomite were used for CRDSMA

Then CRSMA CRDSMA and CRSSMA were preparedfor testing Marshall samples (101mm diameter and 635mmheight) were prepared byMarshall hammermethod For eachsample its weight is 1200 g According to the determinedmixture proportion aggregate 98429 g mineral powder10937 g crumb rubber 3281 g and neat asphalt 7353 g wereused for preparation of each CRSMA sample while aggregate97302 g mineral powder 10811 g crumb rubber 3243 g neatasphalt 7516 g and diatomite 1128 g were used for eachCRDSMA sample and aggregate 98123 g mineral powder10902 g crumb rubber 3271 g and SBS modified asphalt7704 g were used for each CRSSMA sample The height ofeach sample was controlled to be (635 plusmn 13)mm

3 Experimental and Analytical Methods

31 Process of Freeze-Thaw In this research the detailedprocesses of freeze-thaw were designed and listed as follows

(1) The samples were divided into several groups Eachgroup consisted of three samples One group of sam-ples was placed at room temperature Other groupsof samples were immersed into water and placed invacuum drying box for 15min under vacuum degree980 kPa Then vacuum drying box was adjusted toatmospheric condition The samples were immersedinto water for another 05 h

(2) Each sample was taken out of the tank and placedinto plastic bag with 10ml water The bag was put in


Table 3 Properties of aggregate

Sieve size (mm) 132 95 475 236 118 06 03 015 0075Apparent density (gcm3) 2811 2796 2786 2710 2678 2675 2628 2627 2618Absorption coefficient of water () 089 101 143 mdash mdash mdash mdash mdash mdash

Table 4 Physical properties of mineral powder

Property Hydrophilic coefficient Apparent density (gcm3) GradationSieve size (mm) Passing ()

Value 086 272006 100015 9660075 809

CRSMA

Filler 180∘C

Neat asphalt 165∘C

Crumb rubber 180∘CAggregate 180∘C

Blending 90 s 165∘C



Figure 2 Designed preparation process for CRSMA

refrigerator for 16 h at minus20∘C until all the water inplastic bag was frozen

(3) The samples were removed from plastic bags andplaced into water tank for 8 h with constant tempera-ture 60∘C until all the water was melted

After (1) (2) and (3) one F-T cycle was completed Inthis study the number of F-T cycles was 15 for ITS test and10 for air void and ITSM tests After F-T cycles the sampleswere removed from plastic bags and placed into water tankfor 24 h with constant temperature 60∘CThen they were putinto water tank for 2 h with constant temperature 25∘C andsample spacing was bigger than 10mm The treated sampleswere used for air void ITS and ITSM tests

32 Air Void Test In this paper air voids for sampleswere tested by surface-dry condition method accordingto standard AASHTO T-166 [48] Firstly Marshall speci-mens (101mm diameter and 635mm height) were preparedthrough compaction method with 75 blows on each sideof cylindrical samples Secondly masses for samples in drywater and surface-dry conditions were measured respec-tively Bulk specific gravity for samples can be calculated by

120574119891 = 119898119886(119898119891 minus 119898119908) (1)

where 119898119886 119898119908 and 119898119891 are masses of sample in dry waterand surface-dry conditions respectivelyThen the theoreticalmaximum specific gravity (120574119905) of samples was tested throughvacuum sealing method Finally air voids of samples can beobtained by

119881119881 = (1 minus 120574119891120574119905 ) times 100 (2)

Change ratio of air void was calculated by

Δ119881119881119894 = (119881119881119894 minus 119881119881119894minus1)119881119881119894 times 100 (3)

where119881119881119894 is the air void of mixture after 119894 times of F-T cycles119894 = 1 2 1033 Indirect Tensile Strength (ITS) Test ITS test is an effec-tive measure to evaluate the anticracking ability of asphaltmixture under low temperature [4 21] In this research thetest was carried out according to standard AASHTO T-283at temperature of minus10∘C [48] It is performed using a mate-rial testing machine (MQS-2) produced by Nanjing NingxiInstrument Co Ltd Jiangsu Province China Loading ratewas 1mmmin Marshall specimens (101mm diameter and635mm height) were placed in the chamber at minus10∘C for 6 hbefore testsThe failure loadswere recorded at the end of testsITS can be calculated by

ITS = (2119875)(120587119863119905) (4)

where ITS is the tensile strength of specimen 119875 is the failureload 119863 is the diameter of specimen 119905 is the height ofspecimen

In order to evaluate the F-T resistance ability of CRSMACRDSMA andCRSSMA change ratio of ITS before and afterF-T cycles is given by

ΔITS119894 = (ITS119861 minus ITS119860119894 )ITS119861

times 100 (5)

where ΔITS119894 is the change ratio of ITS after 119894 times of F-Tcycles ITS119861 is ITS without F-T cycles and ITS119860119894 is ITS after 119894times of F-T cycles


Table 5 Properties of crumb rubber particle

Property Sauer A hardness(∘)

Apparent density(gcm3)

Moisture content()

GradationSieve size(mm)

Passing()

Value 60 1321 05475 06236 986118 08

Table 6 Properties of diatomite

Property Color PH Specific gravity (gcm3) Bulk density (gcm3) Loss on ignition () Content of SiO2 () Content of Fe3O2 ()Value Orange 8sim10 2152 037 le025 ge871 le11

34 Indirect Tensile StiffnessModulus (ITSM) Test In order toinvestigate the bearing capacity of asphalt mixture ITSM testwas performed according to standard AASHTO TP-31 [48]ITSM test was widely used to analyze the tensile propertiesof mixture which can be further related to the crackingperformance of pavement In this research a multifunctionaltesting machine (NU-14) was used which was producedby Cooper Research Technology Ltd United Kingdom Inorder to investigate the antifreezing performance of modifiedasphalt mixtures the tests were conducted at 5∘C and Mar-shall specimens (101mm diameter and 635mm height) wereadopted The specimens were placed in the chamber at thetest temperature for 6 h before tests The schematic diagram[4] for load pulse was shown in Figure 3 Rise time was124ms and duration period was 30 s The target deformationin horizontal direction was 5 120583mThe peak load was adjustedaccording to the test value of target deformation during thetest The stiffness modulus can be obtained by

119878119898 = 119865 sdot (120583 + 027)ℎ sdot 119885 (6)

where 119878119898 is the stiffness modulus MPa 119865 is the peak loadN 120583 is Poisson ratio which is 025 at 5∘C ℎ is the height ofspecimen mm 119885 is the measured deformation in horizontaldirection mm

Change ratio of 119878119898 before and after F-T cycles wascalculated by

Δ119878119898119894 = (119878119861119898 minus 119878119860119898119894)119878119861119898 times 100 (7)

where Δ119878119898119894 is the change ratio of stiffness modulus after 119894times of F-T cycles 119878119861119898 is stiffnessmoduluswithout F-T cyclesand 119878119860119898119894 is stiffness modulus after 119894 times of F-T cycles

35 Modified Grey Method MGM (1 119898) Traditional GM(1 1) can realize prediction of time series data with equalinterval It cannot be used for time series data with nonequalinterval In this research time series data is the numberof F-T cycles which is 0 1 3 6 10 and 15 with nonequalintervalsTherefore the modified grey model (MGM) is usedto construct the prediction model of air void and ΔITSThe prediction procedure usingMGM (1 119898) (Modified Grey

a

c

b

Figure 3 Load pulses in ITSM test 119886 peak load 119887 duration time119888 rise time

Model First-Order m Variables) is briefly introduced in thispaper and listed in Appendix

4 Results and Discussion

41 Air Voids Air void is an important characteristic ofinternal structure that affects the moisture damage of asphaltmixture Air voids of CRSMA CRDSMA and CRSSMAunder 0 1 2 10 times of F-T cycles were tested respec-tively Corresponding Δ119881119881119894 (119894 = 1 2 10) were calculatedThree specimens were measured for each case For thesemeasurements mean value and standard deviation (SD) werecalculated respectively Corresponding estimation of verticalerror bar was determined for each case which represents thestandard deviation Results of air voids (Mean plusmn SD) andΔ119881119881 for CRSMA CRDSMA and CRSSMA before and afterF-T cycles are shown in Figures 4 and 5

As can be seen from Figure 4 there is no significantincrease or decrease in air void amplitude for each case Airvoids of CRSMA CRDSMA and CRSSMA are all below7 after 10 times of F-T actions Air voids increase withthe increasing of F-T cycles which agrees with the resultobtained by Xu et al [49] Air void of CRSMA increases from426 to 671 after 10 times of F-T cycles compared withthat without F-T effect It increases from 408 to 635 forCRDSMA and 409 to 601 for CRSSMA The reasons liein that F-T cycles can lead to not only expansion of existingvoids but also formation of new voids [49] Furthermoreair voids of CRSMA are generally larger than CRDSMAor CRSSMA while air voids of CRSSMA are the lowestAccording to the result by Song et al [20] diatomite has


Table 7 Particle distribution of diatomite

Particle size (120583m) lt5 10sim5 20sim10 40sim20 gt40Percentage () 193 280 207 210 110

CRSMACRDSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

CRSSMA

Figure 4 Air voids (Mean plusmn SD) of CRSMA CRDSMA andCRSSMA before and after F-T cycles

1 2 3 4 5 6 7 8 9 10F-T cycle (times)

0

2

4

6

8

10

12

14

16

18

ΔVV

()

CRSMACRDSMACRSSMA

Figure 5 Change ratio of air void for CRSMA CRDSMA andCRSSMA

larger void and absorption properties than mineral fillerIt can effectively absorb the lower molecular group andlower polar aromatic molecules of asphalt to form thickerasphalt film and anchorage structure around aggregates andcrumb rubber particles which can increase the contact areaand decrease the air voids between aggregates and rubberparticles According to the results of SBS modified asphalt byLarsen et al [23] and Adedeji et al [24] polymer phase and

asphalt phase exist together Polymer globules are dispersedhomogenously in the continuous asphalt phase which forma stable network structure It can strengthen the adhesionbetween aggregate and rubber particle and decrease the airvoids

As shown in Figure 5 Δ1198811198811 are the largest for CRSMAand CRDSMA It reveals that rapid expansion of existingvoids and formation of new voids happen after the firstF-T cycle However change ratio of air void for CRSSMAincreases before 5 times of F-T cycles It is induced by thestrong network structure formed by two twisted continuousphases [22] which delays the growth of air void Changeratios of air voids for CRSMA CRDSMA and CRSSMA tendto be stable after several times of F-T actions It is because theexpansion of existing voids and formation of new voids cometo steady state

The analysis of variance (ANOVA) is themost commonlyused statistical method to determine the significant effectsof factors [50] ANOVA and F-T tests were conducted todetermine statistically significant process parameters of F-Tcycles on air voids for CRSMA CRDSMA and CRSSMAANOVA results were listed in Table 8

According to ANOVA results 119865 values of CRSMACRDSMA and CRSSMA are all greater than 119865001 Theprobability is 99 that F-T cycle possesses significant effectson air voids of CRSMA CRDSMA and CRSSMA Besides 119865value of CRSMA is the largest while 119865 value of CRSSMA isthe smallest The results indicate that F-T cycle presents themost statistically significant effect on air void of CRSMA andlowest one on CRSSMA The additions of SBS and diatomitecan reduce the influence of F-T cycles on air void

42 ITS Results ITS and ΔITS were calculated for CRSMACRDSMA and CRSSMA after F-T cycles 0 1 3 6 10 and15 Three specimens were measured for each case For thesemeasurements mean value and standard deviation (SD) werecalculated respectively Corresponding estimation of verticalerror bar was determined for each case which represents thestandard deviation Results of ITS (Mean plusmn SD) and ΔITS areshown in Figures 6 and 7

As can be seen from Figures 6 and 7 ITS for three differ-ent kinds of asphalt mixtures all decrease with the increasingof F-T cycles and decrease rates become smaller MeanwhileΔITS of CRSMA CRDSMA and CRSSMA increase with theincreasing of F-T cycles The reasons lie in that repetitive F-T actions increase the air voids which is conducive to waterflow Effect of water frost will cause microcrack formationand propagation in asphalt mixture These kinds of seriousdamage lead to the reduction of ITS With the increasing ofF-T cycles air voids tend to be stable Therefore the frosteffect of water slows down Moreover ITS of CRSSMA is thehighest while ITS of CRSMA is the lowest Slowing trendsfor CRDSMA and CRSSMA are more obvious than CRSMAWith the increasing of F-T cycles ΔITS of CRSSMA is the


Table 8 Analysis of variance (ANOVA) of F-T cycles on air void

Asphalt mixtures Degree of freedom Sum of square fordeviance 119865 value 119865001 Significance

CRSMA10

17695 143264326

lowastlowastCRDSMA 15257 120106 lowastlowastCRSSMA 13589 118599 lowastlowastlowastlowastCorrelation is significant at the 001 level

CRSMACRDSMACRSSMA

03

04

05

06

07

08

09

1

ITS

(MPa

)

3 6 9 12 150F-T cycle (times)

Figure 6 Relationship between ITS (Mean plusmn SD) and F-T cycles

CRSMACRDSMACRSSMA

0

10

20

30

40

50

60

ΔIT

S (

)

3 5 7 9 11 13 151F-T cycle (times)

Figure 7 Relationship between ΔITS and F-T cycles

smallest while it is the biggest for CRSMAThe reasons lie inthat diatomite has good absorption ability of asphalt whichmakes the adhesion capability of asphalt mortar increase andalso the asphalt film thickness on aggregate surface [20 35]Therefore the cohesion among aggregates is strengthened

and the anti-F-T ability of mixture improves which enhancesthe resistance to internal damage of mixture For SBS itselastomeric phase can absorb the oil fraction of asphalt andswell it A continuous polymer phase forms that can improvethe performances of asphalt [23 24]Thenetwork structure ofSBS modified asphalt is more stable than diatomite modifiedone

43 ITSM Results 119878119898 of CRSMA CRDSMA and CRSSMAwere tested and corresponding Δ119878119898 were calculated Threespecimens were measured for each case and the mean valuewas regarded as the result Results for 119878119898 and Δ119878119898 are listedin Table 9

As shown in Table 9 119878119898 for CRSMA CRDSMA andCRSSMA decrease with the increasing of F-T cycles Δ119878119898increase with the increasing of F-T cycles The reasons liein that stiffness modulus is used to evaluate the bearingcapacity of mixtures Formation of microcrack under F-Taction changes the internal structure andweakens its integrityof asphalt mixture [49] which reduces the bearing capacityWith the increasing of F-T cycles the influence of internaldamage is more obvious Furthermore CRSSMA possessesthe highest stiffness modulus value while CRSMA has thelowest one It is because diatomite modified asphalt and SBSmodified one have higher cohesion ability than the neat one[23] which can lower the degree of internal damage and alsothe bearing capacity for mixture Similarly network structureof SBS modified asphalt presents superior performance thandiatomite modified one119878119898 and ITS are important characteristics to represent themechanical properties of asphalt mixture Their correlationsneed to be demonstrated which are shown in Figure 8 Itcan be observed that 119878119898 and ITS present favorable linearrelationships It can provide reference for the evaluation ofmechanical properties of mixtures

44 Performance Prediction In practice processes of F-Tair void ITS and ITSM tests are complicated and time-consuming They make the evaluation of mixture propertiesinconvenient Prediction analysis can be used to constructthe relationships between mixture properties and F-T cycleswhich is convenient for performance analysis of mixture Inthis paper predictionmodels of air void and ITS for CRSMACRDSMA and CRSSMA were established based on regres-sion analysis and MGM (1 2) respectively The predictioneffects of two models were compared and analyzed

441 Regression Analysis Model The regression analysis hasbeen one of the most popular methods for performance


Table 9 119878119898 and Δ119878119898 for CRSMA CRDSMA and CRSSMA before and after F-T cycles

F-T cyclesITSM results119878119898 (MPa) Δ119878119898 (MPa)

0 5 10 5 10CRSMA 6896 5080 4094 2633 4063CRDSMA 7532 5614 4930 2548 3456CRSSMA 7969 6332 5465 2055 3143

CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP

Figure 8 Relationship between 119878119898 and ITS

prediction in many fields from decades [51ndash53] Regressionanalysis consists of fitting a function to the data to discoverhow one or more variables (dependent variable) vary as afunction of another (independent variable) In this studyindependent variable is F-T cycles dependent variables areair void and ΔITS respectively

For CRSMA ΔITS is signed as variable 1199101198621 and air voidis 1199101198622 For CRDSMA ΔITS is signed as variable 1199101198631 and airvoid is 1199101198632 For CRSSMA ΔITS is signed as variable 1199101198781 andair void is1199101198782 Regressionmodels forCRSMACRDSMA andCRSSMA are established based on the results of air voids andΔITS after 0 1 3 6 and 10 times of F-T cyclesThey are shownin Figures 9 and 10

As can be seen from Figures 9 and 10 two order poly-nomials were used to construct the prediction models ofΔITS for CRSMA CRDSMA and CRSSMA 1198772 values ofthe models for ΔITS were higher than 097 Linear regressionmodels were adopted for the prediction of air void forCRSMA andCRSSMA and two order polynomials were usedto for CRDSMA 1198772 values of the models for air void werehigher than 095 All these models revealed close agreementsbetween experimental results and predicted ones

The prediction results of ΔITS (1199101198621 1199101198631 1199101198781) and airvoid (1199101198622 1199101198632 1199101198782) are calculated by use of the establishedregression models The relative errors are obtained for ΔITS

0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407

Figure 9 Regression models of ΔITS for CRSMA CRDSMA andCRSSMA

and air void after 15 times of F-T cycles which can becalculated by

120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)

where 120578 is relative error between test value and predicted one119910119894 and 119910119894 are test value and predicted one after 119894th F-T cyclesrespectively

Corresponding root-mean-square error (RMSE) is alsocalculated which is a frequently used measure of the differ-ences between values predicted by a model and the valuesactually tested The smaller RMSE is the higher the predic-tion accuracy of model presents RMSE can be calculated by

RMSE = radicsum119899119894=1 (119910119894 minus 119910119894)2119899 (9)

where 119899 is the number of samplesThe prediction results of regression models are listed in

Tables 10ndash12As shown in Tables 10 11 and 12 the relative errors for1199101198621 and 1199101198622 after 15 times of F-T cycles are 115 and

309 respectively They are 298 and 1994 for 1199101198631 and1199101198632 and 200 and 508 for 1199101198781 and 1199101198782 The prediction


Table 10 Prediction results of 1199101198621 and 1199101198622 for CRSMA based on regression model

F-T cycle 1199101198621 1199101198621 120578 () RMSE () 1199101198622 1199101198622 120578 () RMSE ()0 0 1541 mdash

078

426 459 775

018

1 20 2013 065 488 482 1233 29 2860 138 536 527 1686 40 3890 275 594 596 03410 47 4812 238 671 687 23811 mdash 4962 mdash mdash 709 mdash12 mdash 5080 mdash mdash 732 mdash13 mdash 5165 mdash mdash 755 mdash14 mdash 5218 mdash mdash 778 mdash15 53 5239 115 776 800 309

Table 11 Prediction results of 1199101198631 and 1199101198632 for CRDSMA based on regression model


196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914

Figure 10 Regression models of air void for CRSMA CRDSMAand CRSSMA

accuracy of1199101198632 is close to 20 which is unsatisfactory As forthe maximum relative error they are 275 775 22551994 1108 and 508 for 1199101198621 1199101198622 1199101198631 1199101198632 1199101198781 and1199101198782 respectively They are more than 5 except 1199101198621 In theaspect of RMSE they are 078 018 196 058 123and 017 for 1199101198621 1199101198622 1199101198631 1199101198632 1199101198781 and 1199101198782 respectively

442 MGM (1 2) Model For CRSMA ΔITS is signed asvariable 119883(0)1198621 and air void is 119883(0)1198622 MGM (1 2) models forCRSMA are established based on the results of air voids andΔITS after 0 1 3 6 and 10 times of F-T cycles

For MGM (1 2) models of CRSMA the first-orderdifferential equation is

119889119883(1)1198621119889119905 = minus04925119909(1)1198621 + 37466119909(1)1198622 minus 04624119889119883(1)1198622119889119905 = minus00133119909(1)1198621 + 01254119909(1)1198622 + 41781

(10)

Time response functions for ΔITS and air void after 15times of F-T cycles can be obtained as

119883(1)119862 (15) = 119890[ minus04925 37466minus00133 01254 ](15minus0) ([ 0426] + [1317173 ])

minus [1317173 ] (11)

The restored values for ΔITS and air void after 15 times ofF-T cycles can be calculated by

119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)


Table 12 Prediction results of 1199101198781 and 1199101198782 for CRSSMA based on regression model


123

409 404 122

017

1 12 1333 1108 421 426 1193 22 2107 minus423 458 468 2186 31 3024 minus245 542 532 18510 36 3791 531 601 617 26611 mdash 3901 mdash mdash 639 mdash12 mdash 3979 mdash mdash 660 mdash13 mdash 4025 mdash mdash 681 mdash14 mdash 4038 mdash mdash 703 mdash15 41 4018 200 689 724 508

Table 13 Prediction results of119883(0)1198621 and119883(0)1198622 for CRSMA based on MGM (1 2)

F-T cycle 119883(0)1198621 119883(0)1198621 120578 () RMSE () 119883(0)1198622 119883(0)1198622 120578 () RMSE ()0 0 000 000

101

426 426 000

003


The prediction results of ΔITS (119883(0)1198621) and air void (119883(0)1198622)are calculated by use of the establishedMGM(1 2)modelTherelative errors and RMSE are calculated for ΔITS and air voidafter 15 times of F-T cyclesThe prediction results of MGM (12) model are listed in Table 13

Prediction models of air voids and ΔITS for CRDSMAand CRSSMA are also established based on MGM (1 2)according to the calculation procedure of CRSMA ForCRDSMAΔITS is signed as variable119883(0)1198631 and air void is119883(0)1198632The prediction results of ΔITS (119883(0)1198631) and air void (119883(0)1198632) arecalculated by use of the established MGM (1 2) model Therelative errors and RMSE are calculated for ΔITS and air voidafter 15 times of F-T cyclesThe prediction results of MGM (12) model are listed in Table 14

For CRSSMA ΔITS is signed as variable119883(0)1198781 and air voidis 119883(0)1198782 The prediction results of ΔITS (119883(0)1198781 ) and air void(119883(0)1198782 ) are calculated by use of the established MGM (1 2)model The relative errors and RMSE are calculated for ΔITSand air void after 15 times of F-T cyclesThe prediction resultsof MGM (1 2) model are listed in Table 15

As shown in Tables 13 14 and 15 the relative errors for119883(0)1198621 and 119883(0)1198622 after 15 times of F-T cycles are 377 and090 respectively They are 426 and 335 for 119883(0)1198631and 119883(0)1198632 and 210 and 174 for 119883(0)1198781 and 119883(0)1198782 It revealsthat the established MGM (1 2) models possess favorableaccuracy in performance prediction of CRSMA CRDSMAand CRSSMA As for the maximum relative error they are

377 090 564 335 382 and 284 for 119883(0)1198621 119883(0)1198622 119883(0)1198631 119883(0)1198632 119883(0)1198781 and 119883(0)1198782 respectively They are less than 5except 119883(0)1198631 In the aspect of RMSE they are 101 003091 011 061 and 009 for119883(0)1198621 119883(0)1198622 119883(0)1198631119883(0)1198632119883(0)1198781 and119883(0)1198782 respectively

Compared with regression models the relative errorsof MGM (1 2) models in prediction of air void and ΔITSafter 15 times of F-T cycles are more stable and reliable Themaximum relative errors and RMSE of MGM (1 2) modelsare much lower than regression ones except for ΔITS ofCRSMA The results indicate that the differences betweenvalues predicted byMGM (1 2) model and the values actuallytested are smaller than regression model MGM (1 2) modelpresents more favorable accuracy in performance predictionof CRSMA CRDSMA and CRSSMA

5 Conclusions

Reuse of waste materials is conducive to the protection ofnatural resources and environment In this paper CR anddiatomite were recycled to modify SMA CR diatomite andSBS were used to prepare CRSMA CRDSMA and CRSSMAF-T effects on thesemixtures were investigatedThe followingconclusions can be obtained

(1) Air voids of CRSMA CRDSMA and CRSSMA allincrease with the increasing of F-T cycles The addi-tion of diatomite into CRSMA can reduce its air void


Table 14 Prediction results of119883(0)1198631 and119883(0)1198632 for CRDSMA based on MGM (1 2)


091

408 408 0

011


Table 15 Prediction results of119883(0)1198781 and119883(0)1198782 for CRSSMA based on MGM (1 2)


061

409 409 000

009


because diatomite can effectively absorb the lowermolecular group and lower polar aromatic moleculesof asphalt to form thicker asphalt film and anchor-age structure around aggregates and crumb rubberparticles As for the effect of SBS it can also reducethe air void of CRSMA because of the strong networkstructure of SBS modified asphalt CRSSMA presentsthe lowest air voids during the test ANOVA resultsreveal that F-T cycle presents the lowest statisticallysignificant effect on air void of CRSSMA

(2) Indirect tensile strength for three different kinds ofasphalt mixtures all decrease with the increasingof F-T cycles Diatomite and SBS present enhance-ment effects for indirect tensile strength of CRSMAAnchorage structure of diatomite modified asphaltand continuous polymer phase of SBS modifiedasphalt can improve the cohesion among aggregatesand enhances the resistance of mixture to internaldamage Results for change ratio of tensile strengthbefore and after F-T cycles reveal that CRSSMA is thesmallest and CRSMA is the biggest

(3) Indirect tensile stiffness modulus of CRSMACRDSMA and CRSSMA decreases with the increas-ing of F-T cycles Diatomite and SBS can effectivelyimprove the stiffness modulus of CRSMA which isbecause diatomitemodified asphalt and SBSmodifiedone have higher cohesion abilities than the neat one

CRSSMA possesses the highest stiffness modulusvalue Stiffness modulus and indirect tensile strengthpresent favorable linear relationship

(4) The differences between values predicted byMGM (12) model and the values actually tested are smallerthan regression model It indicates that MGM modelpresents more favorable accuracy and can be used forperformance prediction of asphalt mixtures

In summary the network structure of SBS modifiedasphalt is more stable than diatomitemodified one Pavementconstructed using CRSSMA will have the better antifreezingperformance than that usingCRSMAorCRDSMAHoweverthe pavement constructed using CRDSMAwill be a favorablechoice considering its environmental and economic advan-tages It not only presents good antifreezing performance butalso realizes the reuse of waste materials including CR anddiatomite

Appendix

Modified Grey Method MGM (1 119898)The prediction procedure usingMGM (1 119898) (Modified GreyModel First-Order 119898 Variables) is briefly introduced asfollows

Step 1 Assume that the original series of data with 119898variables are


119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[

119909(0)1 (1198961) 119909(0)1 (1198962) sdot sdot sdot 119909(0)1 (119896119899)119909(0)2 (1198961) 119909(0)2 (1198962) sdot sdot sdot 119909(0)2 (119896119899) 119909(0)119898 (1198961) 119909(0)119898 (1198962) sdot sdot sdot 119909(0)119898 (119896119899)

]]]]]]]]

(A1)

where 119883(0) is the nonnegative original time series data 119898is the number of variables 119883(0)119895 (119895 = 1 2 119898) is the 119895thvariable with nonequal interval 119899 is the number of time seriesdata for variables119883(0)119895 (119896119894) is the data at time 119896119894Step 2 One time accumulating generation operational se-quences (1-AGO sequences) for119883(0)1 119883(0)2 119883(0)119898 are

119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)

where 119883(1)119895 is the AGO sequence of 119883(0)119895 119909(1)119895 (119896119894) =sum119894119897=1 119909(0)119895 (119896119897)Δ119896119897 Δ119896119897 is the interval between 119896119897 and 119896119897minus1Step 3 MGM (1119898) model can be obtained by the followingfirst-order differential equation

119889119883(1)1119889119905 = 11988611119909(1)1 + 11988612119909(1)2 + sdot sdot sdot + 1198861119898119909(1)119898 + 1198871119889119883(1)2119889119905 = 11988621119909(1)1 + 11988622119909(1)2 + sdot sdot sdot + 1198862119898119909(1)119898 + 1198872

119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)

Assume 119860 = [11988611 11988612 sdotsdotsdot 119886111989811988621 11988622 sdotsdotsdot 1198862119898 1198861198981 1198861198982 sdotsdotsdot 119886119898119898

] 119861 = [[11988711198872119887119898

]]

Then (A3) can be expressed by

119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)

where119883(1) = 119883(1)1 119883(1)2 119883(1)119898 119879Step 4 The solution of (A4) is

119883(1) (119896119894) = 119890119860(119896119894minus1198961) (119883(1) (1198961) + 119860minus1119861) minus 119860minus1119861 (A5)

which is called the time response function In (A5) matrix119860and vector 119861 are undetermined

Step 5 Solution of 119860 and 119861 The generating sequence fornearest-neighbor mean value with nonequal interval is

119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)

where 119911(1)119895 (119896119894) = 05(119909(1)119895 (119896119894minus1) + 119909(1)119895 (119896119894))Difference equation for (A5) can be obtained after dis-

cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)

Least squares estimation sequence for MGM (1119898) is

119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[

119911(1)1 (1198962) 119911(1)2 (1198962) sdot sdot sdot 119911(1)119898 (1198962) 1119911(1)1 (1198963) 119911(1)2 (1198963) sdot sdot sdot 119911(1)119898 (1198963) 1

119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)

Matrix 119860 and vector 119861 can be calculated by

119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)

Step 6 Time response function of difference equation119909(0)119895 (119896119894) = sum119898119897=1 119886119895119897119911(1)119897 (119896119894) + 119887119895 is119883(1) (119896119894) = 119909(1)1 (119896119894) 119909(1)2 (119896119894) 119909(1)119898 (119896119894)119879

= 119890119860(119896119894minus1198961) (119883(1) (1198961) + 119860minus1119861) minus 119860minus1119861 (A11)

Step 7 The restored values can be obtained as follows

119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)


Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

The authors express their appreciations for the financialsupports of National Natural Science Foundation of Chinaunder Grants nos 51408258 and 51578263 China Postdoc-toral Science Foundation Funded Project (nos 2014M560237and 2015T80305) Fundamental Research Funds for the Cen-tral Universities (JCKYQKJC06) Transportation Science andTechnology Project of Jilin Province (2015-1-11) and Scienceamp Technology Development Program of Jilin Province

References

[1] L D Poulikakos C Papadaskalopoulou B Hofko et al ldquoHar-vesting the unexplored potential of european waste materialsfor road constructionrdquo Resources Conservation and Recyclingvol 116 pp 32ndash44 2017

[2] Y Zhang Q Guo L Li P Jiang Y Jiao and Y Cheng ldquoReuseof boron waste as an additive in road base materialrdquoMaterialsvol 9 no 6 article 416 2016

[3] M A Mull K Stuart and A Yehia ldquoFracture resistancecharacterization of chemically modified crumb rubber asphaltpavementrdquo Journal of Materials Science vol 37 no 3 pp 557ndash566 2002

[4] F M Navarro andM C R Gamez ldquoInfluence of crumb rubberon the indirect tensile strength and stiffness modulus of hotbituminousmixesrdquo Journal ofMaterials inCivil Engineering vol24 no 6 pp 715ndash724 2012

[5] A I B Farouk N A Hassan M Z Mahmud et al ldquoEffectsof mixture design variables on rubberndashbitumen interactionproperties of dry mixed rubberized asphalt mixturerdquoMaterialsand Structures vol 50 no 1 article 12 2017

[6] M F Azizian P O Nelson P Thayumanavan and K JWilliamson ldquoEnvironmental impact of highway constructionand repair materials on surface and ground waters case studyCrumb rubber asphalt concreterdquo Waste Management vol 23no 8 pp 719ndash728 2003

[7] M Bueno J Luong F Teran U Vinuela and S E PajeldquoMacrotexture influence on vibrationalmechanisms of the tyre-road noise of an asphalt rubber pavementrdquo International Journalof Pavement Engineering vol 15 no 7 pp 606ndash613 2014

[8] G A J Mturi J OrsquoConnell S E Zoorob and M De Beer ldquoAstudy of crumb rubbermodified bitumen used in South AfricardquoRoadMaterials and Pavement Design vol 15 no 4 pp 774ndash7902014

[9] A D La Rosa G Recca D Carbone et al ldquoEnvironmentalbenefits of using ground tyre rubber in new pneumatic for-mulations a life cycle assessment approachrdquo Proceedings of theInstitution of Mechanical Engineers Part L Journal of MaterialsDesign and Applications vol 229 no 4 pp 309ndash317 2015

[10] A Farina M C Zanetti E Santagata and G A Blengini ldquoLifecycle assessment applied to bituminous mixtures containingrecycled materials crumb rubber and reclaimed asphalt pave-mentrdquo Resources Conservation and Recycling vol 117 pp 204ndash212 2017

[11] H H Kim and S-J Lee ldquoEvaluation of rubber influence oncracking resistance of crumb rubber modified binders with wax

additivesrdquo Canadian Journal of Civil Engineering vol 43 no 4pp 326ndash333 2016

[12] H Ziari A Goli and A Amini ldquoEffect of crumb rubbermodifier on the performance properties of rubberized bindersrdquoJournal of Materials in Civil Engineering vol 28 no 12 ArticleID 04016156 2016

[13] Z Xie and J Shen ldquoPerformance of porous European mix(PEM) pavements added with crumb rubbers in dry processrdquoInternational Journal of Pavement Engineering vol 17 no 7 pp637ndash646 2016

[14] M Liang X Xin W Fan H Sun Y Yao and B XingldquoViscous properties storage stability and their relationshipswith microstructure of tire scrap rubber modified asphaltrdquoConstruction and Building Materials vol 74 pp 124ndash131 2015

[15] A F De Almeida Junior R A Battistelle B S Bezerra and RDe Castro ldquoUse of scrap tire rubber in place of SBS in modifiedasphalt as an environmentally correct alternative for BrazilrdquoJournal of Cleaner Production vol 33 pp 236ndash238 2012

[16] H Wei Q He Y Jiao J Chen and M Hu ldquoEvaluation of anti-icing performance for crumb rubber and diatomite compoundmodified asphaltmixturerdquoConstruction and BuildingMaterialsvol 107 pp 109ndash116 2016

[17] N A Mohamed Abdullah N Abdul Hassan N A MohdShukry et al ldquoEvaluating potential of diatomite as anti cloggingagent for porous asphalt mixturerdquo Jurnal Teknologi vol 78 no7-2 pp 105ndash111 2016

[18] P Cong N Liu Y Tian and Y Zhang ldquoEffects of long-termaging on the properties of asphalt binder containing diatomsrdquoConstruction and BuildingMaterials vol 123 pp 534ndash540 2016

[19] Y Cheng J Tao Y Jiao Q Guo and C Li ldquoInfluence ofdiatomite and mineral powder on thermal oxidative ageingproperties of asphaltrdquo Advances in Materials Science and Engi-neering vol 2015 Article ID 947834 10 pages 2015

[20] Y Song J Che and Y Zhang ldquoThe interacting rule of diatomiteand asphalt groupsrdquo Petroleum Science and Technology vol 29no 3 pp 254ndash259 2011

[21] Y Q Tan L Zhang and X Y Zhang ldquoInvestigation of low-temperature properties of diatomite-modified asphalt mix-turesrdquoConstruction and BuildingMaterials vol 36 pp 787ndash7952012

[22] Q Guo L Li Y Cheng Y Jiao and C Xu ldquoLaboratory eval-uation on performance of diatomite and glass fiber compoundmodified asphalt mixturerdquo Materials amp Design vol 66 pp 51ndash59 2015

[23] D O Larsen J L Alessandrini A Bosch and M S Cor-tizo ldquoMicro-structural and rheological characteristics of SBS-asphalt blends during their manufacturingrdquo Construction andBuilding Materials vol 23 no 8 pp 2769ndash2774 2009

[24] A Adedeji T Grunfelder F S Bates C W Macosko MStroup-Gardiner and D E Newcomb ldquoAsphalt modified bySBS triblock copolymer structures and propertiesrdquo PolymerEngineering and Science vol 36 no 12 pp 1707ndash1723 1996

[25] R Blanco R Rodrıguez M Garcıa-Garduno and V MCastano ldquoRheological properties of styrene-butadiene copoly-mer-reinforced asphaltrdquo Journal of Applied Polymer Science vol61 no 9 pp 1493ndash1501

[26] A Khodaii and A Mehrara ldquoEvaluation of permanent defor-mation of unmodified and SBSmodified asphalt mixtures usingdynamic creep testrdquo Construction and Building Materials vol23 no 7 pp 2586ndash2592 2009


[27] D Sun F Ye F Shi and W Lu ldquoStorage stability of SBS-modified road asphalt preparation morphology and rheologi-cal propertiesrdquo Petroleum Science and Technology vol 24 no 9pp 1067ndash1077 2006

[28] SWen andDD L Chung ldquoDouble percolation in the electricalconduction in carbon fiber reinforced cement-basedmaterialsrdquoCarbon vol 45 no 2 pp 263ndash267 2007

[29] S S AwantiM S Amarnath andAVeeraragavan ldquoLaboratoryevaluation of SBS modified bituminous paving mixrdquo Journal ofMaterials in Civil Engineering vol 20 no 4 pp 327ndash330 2008

[30] F Dong X Yu S Liu and J Wei ldquoRheological behaviors andmicrostructure of SBSCR composite modified hard asphaltrdquoConstruction and Building Materials vol 115 pp 285ndash293 2016

[31] H Liu F Niu Y Niu Z Lin J Lu and J Luo ldquoExperimentaland numerical investigation on temperature characteristics ofhigh-speed railwayrsquos embankment in seasonal frozen regionsrdquoCold Regions Science and Technology vol 81 pp 55ndash64 2012

[32] A Richardson K Coventry V Edmondson and E DiasldquoCrumb rubber used in concrete to provide freeze-thaw protec-tion (optimal particle size)rdquo Journal of Cleaner Production vol112 pp 599ndash606 2016

[33] L Zhang T-S Li and Y-Q Tan ldquoThe potential of usingimpact resonance test method evaluating the anti-freeze-thawperformance of asphalt mixturerdquo Construction and BuildingMaterials vol 115 pp 54ndash61 2016

[34] J L Deng ldquoThe control problems of grey systemsrdquo Systems ampControl Letters vol 1 no 5 pp 288ndash294 1982

[35] D-H Shen and J-C Du ldquoApplication of gray relational analysisto evaluate HMA with reclaimed building materialsrdquo Journal ofMaterials in Civil Engineering vol 17 no 4 pp 400ndash406 2005

[36] P Zhang C Liu and Q Li ldquoApplication of gray relationalanalysis for chloride permeability and freeze-thaw resistance ofhigh-performance concrete containing nanoparticlesrdquo Journalof Materials in Civil Engineering vol 23 no 12 pp 1760ndash17632011

[37] J R San Cristobal F Correa M A Gonzalez et al ldquoA residualgrey prediction model for predicting s-curves in projectsrdquoProcedia Computer Science vol 64 pp 586ndash593 2015

[38] X-W Ren Y-Q Tang J Li and Q Yang ldquoA prediction methodusing grey model for cumulative plastic deformation undercyclic loadsrdquo Natural Hazards vol 64 no 1 pp 441ndash457 2012

[39] K C P Wang and Q Li ldquoPavement smoothness predictionbased on fuzzy and gray theoriesrdquo Computer-Aided Civil andInfrastructure Engineering vol 26 no 1 pp 69ndash76 2011

[40] S Sahoo A Dhar and A Kar ldquoEnvironmental vulnerabilityassessment using grey analytic hierarchy process based modelrdquoEnvironmental Impact Assessment Review vol 56 pp 145ndash1542016

[41] B-J Qiu J-H Zhang Y-T Qi and Y Liu ldquoGrey-theory-basedoptimization model of emergency logistics considering timeuncertaintyrdquo PLoS ONE vol 10 no 9 Article ID e0139132 2015

[42] B Twala ldquoExtracting grey relational systems from incompleteroad traffic accidents data the case of Gauteng Province inSouth Africardquo Expert Systems vol 31 no 3 pp 220ndash231 2014

[43] B Zeng G Chen and S-F Liu ldquoA novel interval grey predic-tion model considering uncertain informationrdquo Journal of theFranklin Institute vol 350 no 10 pp 3400ndash3416 2013

[44] C Li J Qin J Li and Q Hou ldquoThe accident early warningsystem for iron and steel enterprises based on combinationweighting and Grey Prediction Model GM (11)rdquo Safety Sciencevol 89 pp 19ndash27 2016

[45] K Yan D Ge L You andXWang ldquoLaboratory investigation ofthe characteristics of SMA mixtures under freeze-thaw cyclesrdquoCold Regions Science and Technology vol 119 pp 68ndash74 2015

[46] H Y Katman M R Ibrahim M R Karim S Koting and N SMashaan ldquoEffect of rubberized bitumen blending methods onpermanent deformation of SMA rubberized asphalt mixturesrdquoAdvances inMaterials Science and Engineering vol 2016 ArticleID 4395063 14 pages 2016

[47] Z Chunxiu and T Yiqiu ldquoStudy on anti-icing performance ofpavement containing a granular crumb rubber asphaltmixturerdquoRoadMaterials and Pavement Design vol 10 pp 281ndash294 2009

[48] AASHTO American Association of State Highway and Trans-portation Officials American Association of State Highway andTransportation Officials 2006

[49] H Xu W Guo and Y Tan ldquoInternal structure evolution ofasphalt mixtures during freezendashthaw cyclesrdquo Materials andDesign vol 86 pp 436ndash446 2015

[50] O Kelestemur S Yildiz B Gokcer and E Arici ldquoStatisticalanalysis for freezendashthaw resistance of cement mortars contain-ing marble dust and glass fiberrdquo Materials and Design vol 60pp 548ndash555 2014

[51] A M Bagirov A Mahmood and A Barton ldquoPredictionof monthly rainfall in Victoria Australia clusterwise linearregression approachrdquoAtmospheric Research vol 188 pp 20ndash292017

[52] A K Yadav and S S Chandel ldquoIdentification of relevant inputvariables for prediction of 1-minute time-step photovoltaicmodule power using artificial neural network and multiplelinear regression modelsrdquo Renewable and Sustainable EnergyReviews 2017

[53] J J Cannon T Kawaguchi T Kaneko T Fuse and J ShiomildquoUnderstanding decoupling mechanisms of liquid-mixturetransport properties through regression analysis with structuralperturbationrdquo International Journal of Heat and Mass Transfervol 105 pp 12ndash17 2017

Submit your manuscripts athttpswwwhindawicom

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MaterialsJournal of



asphalt and improve rutting deformation resistance How-ever it presents poor stability with the increasing of rubberparticle size Navarro and Gamez [4] presented the effect ofcrumb rubber on bearing capacity and cohesion of asphaltmixture The results show that crumb rubber can increasethe stiffness and stability of mixture while it slightly reducestensile strength De Almeida Junior et al [15] evaluatedthe properties of asphalt modified by rubber and styrenebutadiene styrene (SBS) respectively The findings indicatethat rubber has the potential performance to substitute SBSin pavementmaterials However it does notmeet some of therequirements in standard specifications

Diatomite is a widely used mineral with low cost andconsiderable storage which has high absorptive capacityand stability [16ndash22] It has been widely used for asphaltmodification in China [16ndash21] Mohamed Abdullah et al[17 18] studied the properties of diatomite modified asphaltThe results indicate that there is no chemical reactionbetween asphalt and diatomite Diatomite can improve therutting resistance of asphalt at high temperature The agingresistances of modified asphalt are superior to pure oneCheng et al [19] demonstrated the antiaging properties ofdiatomite modified asphalt The results reveal that diatomiteis helpful for improving the high temperature stability andantiaging property of asphalt Tan et al [21] investigatedthe low temperature property of diatomite modified asphaltThe results show that diatomite particles distribute well inasphalt and diatomite modified mixture possesses better lowtemperature performance than neat one

Currently SBS copolymer is the most widely used modi-fier for asphalt which can absorb the oil fractions and swellthem [23ndash25] It can improve both high and low temperatureperformances of mixture Khodaii and Mehrara [26] con-ducted dynamic creep tests for unmodified and SBSmodifiedasphalt SBS modified mixture possesses lower temperaturesusceptibility and higher compactibility Sun et al [27] foundthat reactive blending of SBS and asphalt can improve thehot storage stability rheological properties elasticity anddeformation resistance of modified asphalt The limitationsfor SBS modified asphalt lie in its lower workability higherproduction cost and being easy to aging [28 29] Thereforeit is crucial to have some other waste materials to partiallysubstitute for SBS in modified asphalt CR can reduce thecost and possess favorable performances which is a favorablesubstitute In order to meet the requirements of high graderoad pavement modified asphalt with better performancescan be prepared using CR and SBS composite modifierDong et al [30] investigated the rheological behavior ofSBSCR composite modified asphalt The results reveal thatthe addition of CR and SBS can effectively improve theviscoelastic property and temperature sensitivity of asphalt

In addition freeze-thaw (F-T) cycle is an important factorto influence the performances of road pavement in seasonalfrozen regions which cover 535 of Chinarsquos land area Roadpavement in this region is exposed to at least one F-T cycleeach year [31] CR has beenwidely used in concrete to provideF-T protection [32] Meanwhile Zhang et al [33] foundthat rubber modified asphalt mixture has better antifreezingperformance than the neat one Current research results

indicate that CR is an effective additive to improve the F-Tresistance for road materials

Grey theory was proposed by Deng in 1982 [34] whichhad been widely used in many fields for factor analysisand forecasting Grey relational analysis (GRA) was widelyused to evaluate the influential degrees of factors [35 36]Grey model is another important aspect in grey theorywhich can achieve high prediction accuracy for uncertainsystems It can realize the prediction of system behavior usingfewer data and less complicated mathematical calculation[37] Ren et al [38] predicted the long-term cumulativeplastic deformation of subgrade under cyclic loads using greymodel Wang and Li [39] adopted grey model for pavementsmoothness prediction Grey model was also used for thepredictions in environmental vulnerability assessment [40]natural disasters [41] and road traffic [42] and so forth GM(1 1) (Grey Model First-Order One Variable) is one of themost widely used grey models in practical application [43]However the limitation existing in traditionalGM(1 1) is thatit needs equal interval for time series data It cannot be usedfor time series data with nonequal interval [44]

As discussed above reuse of CR and diatomite possessesfavorable economic and environmental benefits Further-more F-T action has significant effect on the properties ofasphalt pavement in seasonal frozen regions It will reducethe pavement life severelyThe compoundmodified effects ofCR and diatomite CR and SBS on asphalt mixture under F-T actions are still unknown In order to improve the freezingresistance of asphalt pavement crumb rubber modifiedstone mastic asphalt (CRSMA) crumb rubber and diatomitemodified stonemastic asphalt (CRDSMA) and crumb rubberand SBS modified stone mastic asphalt (CRSSMA) wereprepared respectively Effects of F-T cycles on three differentkinds of asphalt mixtures were tested and evaluated usingair voids indirect tensile strength (ITS) test and indirecttensile stiffness modulus (ITSM) test Meanwhile predictionanalysis was used to construct the relationships betweenproperties and F-T cycles in order to improve the conveniencefor performance analysis of mixture Modified grey modelMGM (1 2) was applied for prediction of air void and ITS

2 Materials

21 Raw Materials Base asphalt AH-90 and SBS modifiedasphalt used for experiments were fromPanjin PetrochemicalIndustry Liaoning Province of China Physical propertiesof AH-90 asphalt were measured and listed in Table 1Properties of SBS modified asphalt were tested and givenin Table 2 Aggregate and mineral filler were obtained fromChangchun Municipal Mixing Plant in Jilin Province ofChina Physical properties of andesitemineral aggregate weregiven in Table 3 Limestone powder was chosen as mineralfiller Corresponding properties of filler were listed in Table 4Crumb rubber particle was obtained from Changchun Yux-ing Rubber Materials Co Ltd Jilin Province China Itsproperties were shown in Table 5 Diatomite was producedby Changchun Diatomite Products Co Ltd Jilin ProvinceChina Its physical properties and particle distribution werelisted in Tables 6 and 7







(∘C)

Ductility(5∘C cm)


Value 50 71 40 86





Sieve size (mm)


0

20

40

60

80

100

Perc

ent p

assin

g (

)

007

5

015 03

06

118

236

475

95

132 16

CAVF design













Value 086 272006 100015 9660075 809

CRSMA

Filler 180∘C











120574119891 = 119898119886(119898119891 minus 119898119908) (1)


119881119881 = (1 minus 120574119891120574119905 ) times 100 (2)




ITS = (2119875)(120587119863119905) (4)




times 100 (5)






Moisture content()


Passing()

Value 60 1321 05475 06236 986118 08




119878119898 = 119865 sdot (120583 + 027)ℎ sdot 119885 (6)



Δ119878119898119894 = (119878119861119898 minus 119878119860119898119894)119878119861119898 times 100 (7)



a

c

b









CRSMACRDSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

CRSSMA


1 2 3 4 5 6 7 8 9 10F-T cycle (times)

0

2

4

6

8

10

12

14

16

18

ΔVV

()

CRSMACRDSMACRSSMA












CRSMA10

17695 143264326


CRSMACRDSMACRSSMA

03

04

05

06

07

08

09

1

ITS

(MPa

)



CRSMACRDSMACRSSMA

0

10

20

30

40

50

60

ΔIT

S (

)

3 5 7 9 11 13 151F-T cycle (times)












CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP






0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407



120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)










078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of








(∘C)

Ductility(5∘C cm)


Value 50 71 40 86





Sieve size (mm)


0

20

40

60

80

100

Perc

ent p

assin

g (

)

007

5

015 03

06

118

236

475

95

132 16

CAVF design













Value 086 272006 100015 9660075 809

CRSMA

Filler 180∘C











120574119891 = 119898119886(119898119891 minus 119898119908) (1)


119881119881 = (1 minus 120574119891120574119905 ) times 100 (2)




ITS = (2119875)(120587119863119905) (4)




times 100 (5)






Moisture content()


Passing()

Value 60 1321 05475 06236 986118 08




119878119898 = 119865 sdot (120583 + 027)ℎ sdot 119885 (6)



Δ119878119898119894 = (119878119861119898 minus 119878119860119898119894)119878119861119898 times 100 (7)



a

c

b









CRSMACRDSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

CRSSMA


1 2 3 4 5 6 7 8 9 10F-T cycle (times)

0

2

4

6

8

10

12

14

16

18

ΔVV

()

CRSMACRDSMACRSSMA












CRSMA10

17695 143264326


CRSMACRDSMACRSSMA

03

04

05

06

07

08

09

1

ITS

(MPa

)



CRSMACRDSMACRSSMA

0

10

20

30

40

50

60

ΔIT

S (

)

3 5 7 9 11 13 151F-T cycle (times)












CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP






0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407



120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)










078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of







Value 086 272006 100015 9660075 809

CRSMA

Filler 180∘C











120574119891 = 119898119886(119898119891 minus 119898119908) (1)


119881119881 = (1 minus 120574119891120574119905 ) times 100 (2)




ITS = (2119875)(120587119863119905) (4)




times 100 (5)






Moisture content()


Passing()

Value 60 1321 05475 06236 986118 08




119878119898 = 119865 sdot (120583 + 027)ℎ sdot 119885 (6)



Δ119878119898119894 = (119878119861119898 minus 119878119860119898119894)119878119861119898 times 100 (7)



a

c

b









CRSMACRDSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

CRSSMA


1 2 3 4 5 6 7 8 9 10F-T cycle (times)

0

2

4

6

8

10

12

14

16

18

ΔVV

()

CRSMACRDSMACRSSMA












CRSMA10

17695 143264326


CRSMACRDSMACRSSMA

03

04

05

06

07

08

09

1

ITS

(MPa

)



CRSMACRDSMACRSSMA

0

10

20

30

40

50

60

ΔIT

S (

)

3 5 7 9 11 13 151F-T cycle (times)












CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP






0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407



120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)










078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of






Moisture content()


Passing()

Value 60 1321 05475 06236 986118 08




119878119898 = 119865 sdot (120583 + 027)ℎ sdot 119885 (6)



Δ119878119898119894 = (119878119861119898 minus 119878119860119898119894)119878119861119898 times 100 (7)



a

c

b









CRSMACRDSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

CRSSMA


1 2 3 4 5 6 7 8 9 10F-T cycle (times)

0

2

4

6

8

10

12

14

16

18

ΔVV

()

CRSMACRDSMACRSSMA












CRSMA10

17695 143264326


CRSMACRDSMACRSSMA

03

04

05

06

07

08

09

1

ITS

(MPa

)



CRSMACRDSMACRSSMA

0

10

20

30

40

50

60

ΔIT

S (

)

3 5 7 9 11 13 151F-T cycle (times)












CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP






0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407



120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)










078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





CRSMACRDSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

CRSSMA


1 2 3 4 5 6 7 8 9 10F-T cycle (times)

0

2

4

6

8

10

12

14

16

18

ΔVV

()

CRSMACRDSMACRSSMA












CRSMA10

17695 143264326


CRSMACRDSMACRSSMA

03

04

05

06

07

08

09

1

ITS

(MPa

)



CRSMACRDSMACRSSMA

0

10

20

30

40

50

60

ΔIT

S (

)

3 5 7 9 11 13 151F-T cycle (times)












CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP






0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407



120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)










078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





CRSMA10

17695 143264326


CRSMACRDSMACRSSMA

03

04

05

06

07

08

09

1

ITS

(MPa

)



CRSMACRDSMACRSSMA

0

10

20

30

40

50

60

ΔIT

S (

)

3 5 7 9 11 13 151F-T cycle (times)












CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP






0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407



120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)










078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of






CRSMACRDSMACRSSMA

03

04

05

07

09

ITS

(MPa

)

2 09 4

= 5 minus x 0214

2 09 8

= 6 minus x 016

R = 6

y 13 E 4 minus 9

6000 8000S (MP






0

10

20

30

40

50

60

ΔIT

S (

)

R2 = 0991

R2 = 09713

R2 = 09983

CRSMACRDSMACRSSMA

3 5 7 9 11 13 151F-T cycle (times)

yS1 = minus01626x2 + 45196x + 89718

yD1 = minus0219x2 + 5521x + 81758

yC1 = minus01611x2 + 48822x + 15407



120578119894 = 100381610038161003816100381610038161003816100381610038161003816(119910119894 minus 119910119894)119910119894 times 100100381610038161003816100381610038161003816100381610038161003816 (8)










078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





078

426 459 775

018




196

408 432 588

058


CRSMACRDSMACRSSMA

1 2 3 4 5 6 7 8 9 100F-T cycle (times)

3

4

5

6

7

Air

void

s (

)

R2 = 09811

yS2 = 02131x + 40436

R2 = 09502

yD2 = minus00217x2 + 04044x + 43173

R2 = 09672

yC2 = 02275x + 45914






(10)



minus [1317173 ] (11)


119883(0)119862 (15) = 119883(1)119862 (15) minus 119883(1)119862 (10)15 minus 10 = [54996076912 ] (12)




123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





123

409 404 122

017




101

426 426 000

003








5 Conclusions






091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





091

408 408 0

011




061

409 409 000

009








Appendix




119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of



119883(0) =[[[[[[[[

119883(0)1119883(0)2119883(0)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A1)


119883(1) =[[[[[[[[

119883(1)1119883(1)2119883(1)119898

]]]]]]]]

=[[[[[[[[


]]]]]]]]

(A2)



119889119883(1)119898119889119905 = 1198861198981119909(1)1 + 1198861198982119909(1)2 + sdot sdot sdot + 119886119898119898119909(1)119898 + 119887119898

(A3)


] 119861 = [[11988711198872119887119898

]]


119889119883(1)119889119905 = 119860119883(1) + 119861 (A4)





119885(1)119895 = 119911(1)119895 (1198962) 119911(1)119895 (1198963) 119911(1)119895 (119896119899) (A6)


cretization it is

119909(0)119895 (119896119894) = 119898sum119897=1119886119895119897119911(1)119897 (119896119894) + 119887119895 (A7)


119886119895 = (1198861198951 1198861198952 119886119895119898 119895)119879 = (119875119879119875)minus1 119875119879119884119895 (A8)

where

119875 =[[[[[[[[


119911(1)1 (119896119899) 119911(1)2 (119896119899) sdot sdot sdot 119911(1)119898 (119896119899) 1

]]]]]]]]

119884119895 = 119909(0)119895 (1198962) 119909(0)119895 (1198963) 119909(0)119895 (119896119899)119879(119895 = 1 2 119898)

(A9)


119860 = (119886119894119895)119898times119898 119861 = (1 2 119898)119879

(A10)




119883(0) (119896119894) = 119909(0)1 (119896119894) 119909(0)2 (119896119894) 119909(0)119898 (119896119894)119879

= 119883(1) (119896119894) minus 119883(1) (119896119894minus1)Δ119896119894 (A12)




Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of





Acknowledgments


References































































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








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CoatingsJournal of

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effects of diatomite and sbs on freeze-thaw resistance of

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