DynamicShearPropertiesofRecycledWasteSteelSlagUsedasa Geo ... · ResearchArticle...

Research ArticleDynamic Shear Properties of Recycled Waste Steel Slag Used as aGeo-Backfill Material

Liyan Wang 1 Jiatao Yan2 Qi Wang2 Binghui Wang 2 and Wenxue Gong 3

1Professor (Ph D) School of Civil and Architectural Engineering Jiangsu University of Science and TechnologyNo 2 Mengxi Road Zhenjiang Jiangsu Province China2Master Student (Ba) School of Civil and Architectural Engineering Jiangsu University of Science and TechnologyNo 2 Mengxi Road Zhenjiang Jiangsu Province China3Associate Professor (Ph D) School of Civil and Architectural Engineering Jiangsu University of Science and TechnologyNo 2 Mengxi Road Zhenjiang Jiangsu Province China

Correspondence should be addressed to Liyan Wang wly_yzu163com

Received 15 July 2018 Revised 24 November 2018 Accepted 22 April 2019 Published 2 June 2019

Academic Editor Giuseppe Petrone

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

Waste steel slag is a recycled industrial solid waste and is sometimes used as backfills but the dynamic shear properties of wastesteel slag have not been researched at present To understand the dynamic shear properties of waste steel slag the resonancecolumn tests were carried out to investigate the dynamic shear modulus and damping ratio of the steel slag considering the effectof the relative density of steel slag and confining pressure e maximum dynamic shear modulus was discussed and the dynamicmodel of the steel slag was constructed by the HardinndashDrnevich model e regression analysis of the normalized dynamic shearmodulus ratio and damping ratio of the steel slag showed that the dynamic model was very fit for the steel slage comparisons ofthe dynamic shear properties of the steel slag with those of Nanjing fine sand and Fujian standard sand showed that the steel slaghad similar dynamic shear resistance to Fujian standard sand and had potential to become a substitute for sand in the practicalgeotechnical engineering in the future

1 Introduction

With the rapid development of society there are more andmore industrial solid wastes which include some recycledresources such as waste steel slag Steel slag is a by-product ofthe steelmaking process and the annual output increasescontinuously with the increase of the steel output It is thesecond largest waste in metallurgical industry If waste steelslag could not be utilized effectively it will result in a largenumber of dumping the occupation of farmland andpollution of the environment e discarded steel slag isshown in Figure 1 Recycled study on industrial solid wastesin civil engineering has recently become a new trend in theworld and the application of the four kinds of industrialwastes in Britain in asphalt pavement was summed up in-cluding waste slag [1] Many sustainable recycled wastes inthe area of Taiwan were analyzed including waste slag [2]

Steel slag has similar characteristics to sand and has highcompressive strength After eight-month aging the perfor-mance of steel slag has been basically stable and aged steel slagcan be used as a kind of shallow-layer backfill material ebasic requirements of using steel slag as a geotechnical en-gineering material are that the steel slag must be aged the rateof powdering shall be lower than 5 some proper gradingshall be adopted and the diameter of the largest particle shallbe small than 5mmewater content of steel slag is low andthe permeability of the steel slag is good According to ourresearch the permeability coefficient is in the range of10minus3sim10minus2e content of Fe2O3 in the waste steel slag sampleis very lowerefore the aged waste steel slag would not rustover time and would not be reacted with water

Steel slag pile was initially applied to composite foundation[3] which showed steel slag was superior to the traditionalgravel pile foundation in technical economic and social

HindawiShock and VibrationVolume 2019 Article ID 6410362 11 pageshttpsdoiorg10115520196410362

benefits A mixture of steel slag and lime soil was formed andhad good frost resistance and corrosion resistance Aftercompaction the strength index even reached concrete strength[4]Main influence factors of the expansion and powder of steelslag includedmaximumparticle size porosity and free calciumoxide content [5] Steel slag was mixed into graded crushedstone subbase to make the foundation form a good earlystrength and higher shear resistance [6] Mixed sand with steelslag formed mixed soil material and could effectively improvethe bearing capacity of foundation and reduce the settlement offoundation [7]e deformation and strength characteristics oflightweight soil mixed with waste steel slag and foamed plasticswere studied by considering the influence of the steel slagmixing ratio and curing age [8]

e expansive soil by mixing the steel slag of 10sim20was studied and some conclusions were achieved that thesteel slag could significantly reduce the expansion rate liquidlimit and plastic index of expansive soil and that the steel slagof 10sim20 could improve particle distribution and strengthcharacteristics of expansive soil [9] e effect of quantity ofsteel slag on the mechanical properties of blended mixes withcrushed limestone aggregate was evaluated and a theoreticalanalysis was employed to estimate the resistance for failurefactors such as vertical deformations vertical and radialstresses and vertical strains of subbase under overweighttrucks loads [10] e results indicated that the mechanicalcharacteristics and the resistance factors were improved byadding steel slag to the crushed limestone Blast furnace slagin the granulated formwas applied as a granular fill overlay onsoft subgrade soil [11] Stainless steel reducing slag (SSRS) inproduction of the soil-based controlled low-strength material(CLSM) was used as a cement substitute Testing resultsindicate that SSRS with the specific surface area of 4551 cm2gcan substitute for Portland cement up to 30 in production ofexcavated CLSM Based on the testing data an analyticalmodel for predicting compressive strength of the CLSM fromone to 56 days has been developed with high reliability [12]e waste slag was applied into the underground deep wallmethod [13] e carpet waste fibers and steel slag as envi-ronmental friendly additives were applied to overcome theswelling and weakness of the expansive soil [14] e resultsshowed that both chemical modification and mechanicalreinforcement by adding fibers and slag are efficient methodsto improve general properties of expansive clayey soil e

permeability of steel slag and steel slag modifying silt soil asnew geo-backfill materials was studied in detail [15]

According to the above literature review at present thedynamic shear resistance characteristics of waste steel slag as ageo-backfill material have not been studied Recently manyresearches were carried out on dynamic shear properties ofsoils or soils mixed with other solid waste [16ndash22] e shearmodulus and damping ratio of a backfill material are twoessential indexes for the seismic performance analysis andsafety performance evaluation of backfill materials [23ndash29]Dynamic properties of steel slag improved with sand-tireshreds admixture had been studied [30] In this paper thedynamic shear modulus and damping ratio of waste steel slagwould be investigated by resonance column tests

2 Experimental Work

21 Test Material e aged waste steel slag in the test wasproduced by the Yonggang Company in ZhangjiagangChina which is shown in Figure 1e chemical compositionof the waste steel slag is shown in Table 1 e content of freecalcium oxide was 32 and less than 5 and the ignition losswas 78 and less than 8 [31] which showed that the wastesteel slag could be applied in geotechnical backfill

e grain size distribution of the waste steel slag is shownin Figure 2 e bulk density of the waste steel slag wasapproximately 22 gcm3e gradation characteristics of thesteel slag are as follows d60 10mm d30 047mm andd10 012mm the coefficient of uniformity (Cu) was 83 andthe coefficient of curvature was 18 (Cc) erefore the steelslag was classified as the well-graded material

22 Test Method e test equipment used in this paper is aGZZ-50-type resonant column instrument which is shownin Figure 3 According to the basic principle of the resonantcolumn the equipment could test dynamic shear strain (c)dynamic shear modulus (G) and damping ratio (λ) of soil bythe method of torsion vibration e test sample size is50mm (empty)times 100mm (H) e instrument can be used tostudy the dynamic properties of unbroken samples in a smallshear strain range of 10minus6sim10minus4

In the resonance column test the main influence factors ofthe dynamic shear behavior of steel slag include relative density(Dr) and confining pressure (σ) In order to study the re-lationship between the relative density of steel slag and itsdynamic shear characteristics the resonant column tests of thesteel slag samples with different relative densities were carriedout Samples were prepared according to Geotechnical TestMethod Standard [3] e maximum dry density is determinedby the vibration hammer method and the minimum drydensity is determined by the funnel and cylinder method emaximumdry density and theminimumdry density of the steelslag were respectively 258 gcm3 and 196 gcm3

Samples were prepared according to the standard for thesoil test method e quality of the single sample was cal-culated according to the relative density of the steel slag erelationship between the control density and the relativedensity can be expressed as follows

Figure 1 Tested steel slag

2 Shock and Vibration

ρd ρdmaxρdmin

ρdmax minusDr ρdmax minus ρdmin( ) (1)

where Dr ρmax ρmin and ρd represent the relative densitythe maximum dry density the minimum dry density andthe control density respectively

In the sample test the relative density of steel slag wasselected for 30 50 and 70 respectively because steel slagis applied as a kind of the shallow-layer backll material esteel slag with a water content of 6 is thought in a naturalstate Furthermore when the water content is 6 the steel slagis apt to form the test sample erefore the water content inthe test sample was set as 6 e loading density (ρ) wascalculated using the following equation

ρ ρd(1 + w) (2)

where ω represents the water content of steel slag especic test parameters are shown in Table 2 e controldensity and the loading density of the test samples are alsoshown in Table 2 GZ1simGZ3 respectively represent the testsample with the relative density of 30 50 and 70

e test sample and loading process in the resonantcolumn apparatus are shown in Figure 4

3 Results and Discussion

31 Eect of RelativeDensity e relationships between thedynamic shear modulus (G) and the shear strain (c) of thesteel slag with dierent relative densities are shown inFigure 5 when the conning pressures (σ) were re-spectively 100 kPa 200 kPa and 300 kPa e G-c curvesof the steel slag accorded with hyperbolic characteristicse dynamic shear modulus decreased with the increase ofshear strain for all of the samples with dierent relativedensities When the shear strain was small and in the rangeof 1 times 10minus6 lt clt 1 times 10minus5 the dynamic shear modulus of thesteel slag decreased with the increase of the shear strain ofthe steel slag but the magnitude of the decrease was smallHowever the shear strain increased beyond 1 times 10minus5 thedynamic shear modulus decreased rapidly with the in-crease of shear strain and the decrease magnitude wasgreat

e greater the relative density of the steel slag is thelarger the dynamic shear modulus of the steel slag is and theoverall relationships between dynamic shear modulus andshear strain were upward with the increase of the relativedensity of the steel slag e relationship between themaximum dynamic shear modulus (Gmax) and dierentrelative densities is shown in Figure 6 when the conningpressure was 200 kPa e maximum dynamic shear mod-ulus of the steel slag increased with the increase of therelative density of steel slag When the relative density of thesteel slag was 70 the maximum dynamic shear modulus ofthe steel slag was the maximum

e relationships between the damping ratio (λ) and theshear strain of the steel slag with dierent relative densitiesare shown in Figure 7 when the conning pressures were100 kPa 200 kPa and 300 kPa respectively

e relative density of the steel slag had little eect on thedamping ratio of the steel slag e overall variation ten-dency between the dynamic shear modulus and shear strainwas basically the same under dierent relative densitiesey were staggered and had nearly no oset

When the shear strain was small and in the range of1times 10minus6lt clt 1times 10minus5 the damping ratio of the steel slagincreased with the increase of shear strain but the increasein magnitude was small When the shear strain increasedbeyond 1times 10minus5 the damping ratio of the steel slag increasedrapidly with the increase of shear strain e reason for thisphenomenon was that the steel slag was in an elastic state

Figure 3 Resonant column apparatus (GZZ-50)

Table 1 Chemical composition of waste steel slag in the testComposition SiO2 CaO MgO Fe2O3 Al2O3Content α () 1128 4800 486 524 1138

Composition Na2O K2OAlkalicontent f-CaO Ignition loss

Content α () 006 008 011 32 78

Steel slag

0102030405060708090

100

By m

ass p

assin

g (

)

10 01 0011Grain size (mm)

Figure 2 Grain distribution of test steel slag

Table 2 Test schemes

Samplenumber

Conningpressure σ

(kPa)

RelativedensityDr

Controldensityρd (gcm3)

Watercontentω ()

Loadingdensity ρ(gcm3)

GZ1 100 200 300 30 211 6 224GZ2 100 200 300 50 223 6 236GZ3 100 200 300 70 236 6 250

Shock and Vibration 3

when the shear strain was small and the dynamic energy losswas relatively smaller When the shear strain of the steel slagincreased the stress wave resistance became larger and theenergy consumption became large e damping ratio at theconfining pressure of 300 kPa and 30 relative density had adifferent tendency compared with others e possiblereason is that the water content of steel slag was high forloose steel slag with the relative density of 30 and the pore

water viscosity was greater than that of the pore water indense steel slag under the dynamic loads especially when theshear strain was in the range of 10minus5 and 10minus4 for highconfining pressure

32 Effect of Confining Pressure e relationships betweenthe dynamic shear modulus and the shear strain of the steel

(a) (b) (c)

Figure 4 Test sample in the resonant column apparatus (a) formed sample (b) loading sample (c) sample covered with the pressurechamber

Dr = 03Dr = 05Dr = 07

30

60

90

120

150

180

Dyn

amic

shea

r mod

ulus

(MPa

)

10ndash6 10ndash4 10ndash310ndash5

Shear stain

(a)

Dr = 03Dr = 05Dr = 07

40

80

120

160

200

240

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

Dr = 03Dr = 05Dr = 07


Shear stain

80

120

160

200

240

280

320

Dyn

amic

shea

r mod

ulus

(MPa

)

(c)

Figure 5 Effect of relative density on the G-c curve of steel slag (a) σ 100 kPa (b) σ 200 kPa (c) σ 300 kPa


slag with dierent conning pressures are shown in Figure 8when the relative densities of the steel slag were respectively30 50 and 70

e overall trend lines ofG-cwere basically the same andupward with the increase of conning pressure e greaterthe conning pressure was the larger the dynamic shear

02 03 04 05 06 0807170

180

190

200

210

220

Fitted value

Max

imum

dyna

mic

shea

r mod

ulus

(MPa

)

Relative density

Figure 6 Relationship between the maximum dynamic shear modulus and relative density (σ 200 kPa)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()

10ndash310ndash410ndash6 10ndash5

Shear stain

(a)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(b)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(c)

Figure 7 Eect of the damping ratio on the λ-c curve of steel slag (a) σ 100 kPa (b) σ 200 kPa (c) σ 300 kPa


modulus was e reason was that the increase of conningpressure made the internal pore volume of the steel slagnarrow and the bite forces between steel slag particles in-crease and the shear deformation resistance of the steel slagwas enhanced

33 Maximum Dynamic Shear Modulus At present themaximum dynamic shear modulus (Gmax) is determined bythe laboratory test data

e relationship between the reciprocal of the dynamicshear modulus (Gminus1) and the shear strain (c) is linearaccording to the hyperbolic model of HardinndashDrnevich emaximum dynamic shear modulus (Gmax) could be obtainedfrom the tted lines of Gminus1 and c e maximum dynamicshear modulus was the intercept of the Gminus1-c line e ttedlines of Gminus1 and c are shown in Figure 9 and the ttingparameters are shown in Table 3

With the increase of conning pressure the overall trendof the G-1-c lines was downward As can be seen fromTable 3 with the increase of relative density the maximumdynamic shear modulus of the steel slag had been

signicantly improved With the increase of conningpressure the maximum dynamic shear modulus of the steelslag with dierent relative densities also increased Forexample GZ1 was compared to GZ3 when the conningpressure was 100 kPa Gmax increased from 108MPa to162MPa and increased approximately by 50 when theconning pressure was 300 kPa Gmax increased from235MPa to 280MPa and only increased by 195 isnding showed that the relative density had greater eect onthe maximum dynamic shear modulus of the steel slag withlow conning pressure than with high conning pressureerefore the steel slag in a dense state would have betterseismic shear resistance when the steel slag is applied intoshallow foundation improvement

4 Dynamic Model of the Steel Slag

ere are three typical hyperbolic models including Davi-denkov model HardinndashDrnevich model and RambergndashOsgood model that could describe soil dynamic propertiesvery well RambergndashOsgood model and Davidenkov model

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

50

100

150

200

250

300

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(c)

Figure 8 Eect of conning pressure on the G-c curve of steel slag (a) Dr 03 (b) Dr 05 (c) Dr 07


have many experimental parameters and are usually used tofit the dynamic properties of soil under complex stressconditions For the steel slag the experimental parametersare less and the dynamic shear properties could be describedby the HardinndashDrnevich model

e test range of shear strain in the resonant columnequipment was generally in a range of 10minus4sim10minus6 e dy-namic shear modulus and the damping ratio in a large strainrange (larger than 50times10minus4) could be obtained by the fittingcurve of the small strain dynamic model

00 10 times 10ndash4 20 times 10ndash4 30 times 10ndash4 40 times 10ndash4000

001

002

003G

ndash1 (M

Pandash1

)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(a)


001

002

003

Gndash1

(MPa

ndash1)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(b)

00 10 times 10ndash4 20 times 10ndash4 30 times 10ndash4

Gndash1

(MPa

ndash1)

000

001

002

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(c)

Figure 9 Fitted lines of Gminus1 and c under different relative densities (a) Dr 03 (b) Dr 05 (c) Dr 07

Table 3 Fitting parameters of Gminus1

Sample number Relative density Confining pressure (kPa) B A Gmax (MPa) R2

GZ1 30100 39897 001115 108 095200 37212 000681 176 097300 19829 000512 235 094

GZ2 50100 39172 000957 125 095200 35087 000641 187 099300 19283 000488 246 092

GZ3 70100 38686 000741 162 095200 35697 000549 219 099300 19202 000428 280 098


e relationship between the dynamic shear modulusand the shear strain was expressed as equation (3) [32] andthe relationship between the damping ratio and the shearstrain was expressed as equation (4)

G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)

where c cr Gmax and λmax represent the dynamic shearstrain reference shear strain maximum shear modulus andmaximum damping ratio respectively Based on the dy-namic shear modulus damping ratio and shear strain of thesteel slag tested by the resonant column equipment theregression analysis of the normalized dynamic shear mod-ulus ratio (GGmax) and damping ratio was performedaccording to equations (3) and (4) e fitting results arelisted in Figure 10 and in Table 4 As could be seen fromTable 4 with the increase of the relative density and con-fining pressure themaximum dynamic shear modulus of thesteel slag increased It showed that the reference shear straincould be improved by increasing the relative density andconfining pressure

Figure 10 showed that with the increase of the confiningpressure the fitting curves of GGmax-c moved upward andthe fitting curves of λ-c moved downward but not obviouserefore all of the normalized dynamic shear modulusunder different relative densities could be gathered into onefigure which is shown in Figure 11 With the increase of therelative density the fitting curves of GGmax-c moved up-ward but also not obvious ree fitting curves were closetogether and the fitting effect was great showing that it wasappropriate to use equations (3) and (4) to fit the normalizeddynamic shear modulus and the damping ratio of the steelslag

e reference shear strains under different confiningpressure are listed in Table 5 In the fitted hyperbolicmodel the reference shear strain increased with the in-crease of confining pressure e linear fitting analysis ofthe reference shear strain under different confiningpressures of the steel slag is shown in Figure 12 e linearfitting equation is shown in equation (5) e resultsshowed that the linear fitting effect was perfect between thereference shear strain and confining pressure

cr 209 times 10minus7 middot σ3 + 128 times 10minus4 (5)

Considering the influence of confining pressures andcombing equations (3) and (5) the HardinndashDrnevichmodel of the steel slag dynamic properties was estab-lished e dynamic model is shown in the followingequation

G

Gmax

11 + c209 times 10minus7 middot σ3 + 128 times 10minus4( 1113857

(6)

e test range of the steel slag shear strain in the resonantcolumn equipment was in a range of 10minus4sim10minus6 e dy-namic shear modulus and the damping ratio of the steel slag

in a large strain range (larger than 50times10minus4) would beobtained by the dynamic triaxial test

5 Comparisons of Dynamic ShearModulus with Sand

To understand the shear resistance of the steel slag underdynamic loading the maximum dynamic shear modulus ofthe steel slag was compared with those of Nanjing fine sandand Fujian standard sande comparison results when theconfining pressure is respectively 100 kPa 200 kPa and300 kPa are shown in Table 6 In this instance Gmax rep-resents fitted values Figure 13 is the comparison of themaximum dynamic shear modulus for three materials emaximum dynamic shear modulus data of Nanjing finesand when the confining pressure was 300 kPa were lacking[33]

e maximum dynamic shear modulus of the steel slagwas far greater than Nanjing fine sand no matter what theconfining pressure was Furthermore the maximum dy-namic shear modulus of steel slag was similar to that ofFujian sand in the manuscript except for low confiningpressure e maximum dynamic shear modulus of wastesteel slag was close to Fujian sand under low confiningpressure e reason is maybe that steel slag is a porousmaterial and sand is a crystal structure Porosity character ofsteel slag is obvious under low confining pressure and dy-namic loads Especially when the confining pressure washigh and reached 300 kPa the maximum dynamic shearmodulus of the steel slag was in the range of those of Fujianstandard sand erefore the steel slag has good dynamicshear resistance and had potential to become a substitute forsand in the practical geotechnical engineering in the future

6 Conclusion

e dynamic shear characteristics of the steel slag wereinitially studied by resonance column tests and the fol-lowing conclusions were obtained

(1) e dynamic shear modulus of the steel slag de-creased with the increase of shear strain and thedamping ratio increased with the increase of shearstrain e overall variation tendency between thedynamic shear modulus and shear strain was basi-cally the same under different relative densities andconfining pressure

(2) e greater the relative density of the steel slag wasthe larger the dynamic shear modulus of the steel slagwas e overall trend lines of G-c were upward withthe increase of the relative density and confiningpressure e confining pressure and relative densityhad remarkable influence in a small strain range onthe dynamic shear modulus of the steel slag

(3) e maximum dynamic shear modulus of the steelslag had a good linear relationship with the rela-tive density of the steel slag With the increase ofthe relative density and confining pressure the


maximum dynamic shear modulus of the steel slagincreased

(4) e regression analysis of the normalized dynamicshear modulus ratio and damping ratio was per-formed very well according to the HardinndashDrnevichmodel e reference shear strain could be im-proved by increasing the relative density and

confining pressure e linear fitting effect wasperfect between the reference shear strain andconfining pressures

(5) e dynamic shear modulus of the steel slag was fargreater than Nanjing fine sand no matter what theconfining pressure was and was similar to those ofFujian standard sand Especially when the confining

10ndash6 10ndash5 10ndash4 10ndash300

02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)

Figure 10 Fitted curves of GGmax-c and λ-c under different mixing ratios (a) Dr 03 (b) Dr 05 (c) Dr 07

Table 4 Fitting results of test parameters

Sample number Relative density Confining pressure (kPa) Gmax (MPa) λmax () cr R2

GZ1 30100 108 0247 139times10minus4 098200 176 0249 167times10minus4 098300 235 0251 184times10minus4 093




pressure reached 300 kPa the maximum dynamicshear modulus of the steel slag was in the numericalrange of those of Fujian standard sand e com-parison showed the steel slag had similar dynamicshear resistance to Fujian standard sand and had

potential to become a substitute for sand in thepractical geotechnical engineering in the future

Data Availability

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

Conflicts of Interest

e authors declare that they have no conpoundicts of interest

Acknowledgments

is research was nancially supported by the NaturalScience Foundation of Jiangsu Province (Grant noBK20161360) the SixMajor Talents Peak in Jiangsu Provincein China (Grant no 2016-JZ-020) and Postgraduate Re-search and Practice Innovation Program of Jiangsu Province(Grant no SJCX17_0609)

References

[1] Y Huang R N Bird and O Heidrich ldquoA review of the use ofrecycled solid waste materials in asphalt pavementsrdquo ResourcesConservation and Recycling vol 52 no 1 pp 58ndash73 2007

[2] W-T Tsai ldquoAnalysis of the sustainability of reusing industrialwastes as energy source in the industrial sector of TaiwanrdquoJournal of Cleaner Production vol 18 no 14 pp 1440ndash14452010

00

02

04

06

08

10

100kPa (Dr = 03)300kPa (Dr = 03)200kPa (Dr = 03)100kPa (Dr = 05)200kPa (Dr = 05)300kPa (Dr = 05)

100kPa (Dr = 07)200kPa (Dr = 07)300kPa (Dr = 07)

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ

Figure 11 Fitted curves of GGmax-c under dierent conningpressures

y = 209 times 10ndash7 σ3 + 128 times 10ndash4 R2 = 094

Fitted valueCurve fitting

100 200 300 4000Confining pressure (kPa)

12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain

Figure 12 Fitted curves between reference shear strain andconning pressure

Table 5 Reference shear strains under dierent conningpressures

Sample number Conning pressure Reference shear strainGZ1 30 147times10minus4GZ2 50 176times10minus4GZ3 70 188times10minus4

Table 6 Comparisons ofGmax for steel slag ne sand and standardsand

Conning pressure (kPa)Gmax (MPa)

100 200 300Nanjing ne sand [33] 47sim54 66sim74 Fujian standard sand [32] 126sim197 174sim272 211sim323Steel slag 108sim125 162sim219 235sim280

Steel slagFujian standard sandNanjing fine sand

0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100

Confining pressure (kPa)

Figure 13 Comparison of the maximum dynamic shear modulusof steel slag with traditional sands


[3] T Huang X ZWang Y GWu et al ldquoExperimental researchand application of Yubei steel slag pile composite founda-tionrdquo Chinese Journal of geotechnical engineering vol 21no 3 pp 72ndash77 1999

[4] Z H Liao Guide to Application of New Materials in HighwayEngineering China Communications Press Beijing China2004

[5] C Yan S Y Liu and Y F Deng ldquoExperimental research forthe application of mining waste in the trench cutting remixingdeep wall methodrdquo Advances in Materials Science and En-gineering vol 2015 Article ID 202848 9 pages 2015

[6] M Z Hu ldquoe application of steel slag in Lou-Lian highwayrdquoHighway and Car Transport vol 10 no 2 pp 52-53 2006in Chinese

[7] W Li H L Wang Li F Li et al ldquoMechanical property tests ofmixed soil materials of waste steel slag and sandrdquo Journal ofShenyang Construction University (NATURAL SCIENCEEDITION) vol 16 no 5 pp 794ndash799 2008

[8] L Y Wang P Gao and G X Chen ldquoExperimental studies onthe compressive deformation and strength characteristics ofnew mixed lightweight sand blended with waste steel slagrdquoChinese Journal of Geotechnical Engineering no S2pp 204ndash209 2013 in Chinese

[9] S Shulin J Tang and Q H Zheng ldquoExperimental study ofexpansive soil improved with granulated blast furnace slag(GBFS)rdquo Rock and Soil Mechanics vol 33 no 7 pp 1940ndash1944 2012

[10] A E brahim and A E-M Behiry ldquoEvaluation of steel slag andcrushed limestone mixtures as subbase material in flexiblepavementrdquo Ain Shams Engineering Journal vol 4 no 1pp 44ndash53 2013

[11] Y Laxmikant and R K Tripathi ldquoEffect of the length ofgeogrid layers in the bearing capacity ratio of geogrid rein-forced granular fill-soft subgrade soil systemrdquo Proce-diamdashSocial and Behavioral Sciences vol 104 pp 225ndash2342013

[12] Y-N Sheen L-J Huang H-Y Wang and D-C Le ldquoEx-perimental study and strength formulation of soil-basedcontrolled low-strength material containing stainless steelreducing slagrdquo Construction and Building Materials vol 54pp 1ndash9 2014

[13] Y Chao L Songyu and D Yongfeng ldquoExperimental researchfor the application of mining waste in the trench cuttingremixing deep wall methodrdquo Advances in Materials Scienceand Engineering pp 1ndash9 2015

[14] M Shahbazi M Rowshanzamir S M Abtahi andS M Hejazi ldquoOptimization of carpet waste fibers and steelslag particles to reinforce expansive soil using responsesurface methodologyrdquo Applied Clay Science vol 142pp 185ndash192 2017

[15] L Y Wang J T Yan Q Wang B H Wang and A IshimweldquoStudy on permeability of steel slag and steel slag modifyingsilt soil as new geo-backfill materialsrdquo Advances in CivilEngineering vol 2018 2018 In press

[16] G X Chen X Z Liu D H Zhu et al ldquoExperimentalstudies on dynamic shear modulus ratio and damping ratioof recently deposited soils in Nanjingrdquo Chinese Journal ofGeotechnical Engineering vol 28 no 8 pp 1023ndash10272006

[17] G Chen Z Zhou T Sun et al ldquoShear modulus anddamping ratio of sandndashgravel mixtures over a wide strainrangerdquo Journal of Earthquake Engineering vol 2017no 10 2017

[18] X Z Ling F Zhang Q L Li L S An and J H WangldquoDynamic shear modulus and damping ratio of frozencompacted sand subjected to freeze-thaw cycle under multi-stage cyclic loadingrdquo Soil Dynamics and Earthquake Engi-neering vol 76 pp 111ndash121 2015

[19] P H H Giang P O V Impe W F V Impe P Menge andW Haegeman ldquoSmall-strain shear modulus of calcareoussand and its dependence on particle characteristics andgradationrdquo Soil Dynamics and Earthquake Engineeringvol 100 pp 371ndash379 2017

[20] K Senetakis A Anastasiadis and K Pitilakis ldquoDynamicproperties of dry sandrubber (SRM) and gravelrubber(GRM) mixtures in a wide range of shearing strain ampli-tudesrdquo Soil Dynamics and Earthquake Engineering vol 33no 1 pp 38ndash53 2012

[21] W Zhou Y Chen GMa L Yang and X Chang ldquoAmodifieddynamic shear modulus model for rockfill materials under awide range of shear strain amplitudesrdquo Soil Dynamics andEarthquake Engineering vol 92 pp 229ndash238 2017

[22] H Zhuang R Wang G Chen Y Miao and K Zhao ldquoShearmodulus reduction of saturated sand under large liquefaction-induced deformation in cyclic torsional shear testsrdquo Engi-neering Geology vol 240 pp 110ndash122 2018

[23] L-Y Wang H-L Liu P-M Jiang and X-X Chen ldquoPre-diction method of seismic residual deformation of caissonquay wall in liquefied foundationrdquo China Ocean Engineeringvol 25 no 1 pp 45ndash58 2011

[24] L Y Chen S K Chen and P Gao ldquoResearch on seismicinternal forces of geogrids in reinforced soil retaining wallstructures under earthquake actionsrdquo Journal of Vibroen-gineering vol 16 no 4 pp 2023ndash2034 2014

[25] L Wang G Chen and S Chen ldquoExperimental study onseismic response of geogrid reinforced rigid retaining wallswith saturated backfill sandrdquo Geotextiles and Geomembranesvol 43 no 1 pp 35ndash45 2015

[26] L Y Wang G X Chen P Gao et al ldquoPseudo-static cal-culation method of the seismic residual deformation of ageogrid reinforced soil retaining wall with a liquefied backfillrdquoJournal of Vibroengineering vol 17 no 2 pp 827ndash840 2015

[27] G Q Kong L D Zhou Z T Wang G Yang and H LildquoShear modulus and damping ratios of transparent soilmanufactured by fused quartzrdquo Materials Letters vol 182pp 257ndash259 2016

[28] W-x Gong L-y Wang J Li and B-h Wang ldquoDisplacementcalculation method on front wall of covered sheet-pile wharfrdquoAdvances in Civil Engineering vol 2018 Article ID 503705713 pages 2018

[29] Y Chuancheng C Wenxia and D Haiyue ldquoResearch oncomparison of the maximum dynamic shear modulus testrdquoProcedia Engineering vol 28 pp 230ndash234 2012

[30] L Y Wang X T Cao Q Wang and B H Wang ldquoDy-namic properties of steel slag improved with sand-tireshreds admixturerdquo Proceedings of the Institution of CivilEngineersmdashGround Improvement vol 2018 pp 1ndash17 2018

[31] L Y Wang B T Huang and P Gao ldquoA new geo-materialconsisting of industrial wastes and its preparation and ap-plicationrdquo China No Patent ZL20131 0186058 2013

[32] X M Yuan and J Sun ldquoModel of maximum dynamic shearmodulus of sand under anisotropic consolidation and revisionof Hardinrsquos formulardquo Chinese Journal of Geotechnical Engi-neering vol 3 pp 264ndash269 2005

[33] B H Wang G X Chen and Q X Hu ldquoExperiment ofdynamic shear modulus and damping of Nanjing fine sandrdquoWorld Earthquake Engineering vol 26 no 9 pp 7ndash15 2010


International Journal of

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Shock and Vibration


Civil EngineeringAdvances in

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Journal of

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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Journal ofEngineeringVolume 2018

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Submit your manuscripts atwwwhindawicom

benefits A mixture of steel slag and lime soil was formed andhad good frost resistance and corrosion resistance Aftercompaction the strength index even reached concrete strength[4]Main influence factors of the expansion and powder of steelslag includedmaximumparticle size porosity and free calciumoxide content [5] Steel slag was mixed into graded crushedstone subbase to make the foundation form a good earlystrength and higher shear resistance [6] Mixed sand with steelslag formed mixed soil material and could effectively improvethe bearing capacity of foundation and reduce the settlement offoundation [7]e deformation and strength characteristics oflightweight soil mixed with waste steel slag and foamed plasticswere studied by considering the influence of the steel slagmixing ratio and curing age [8]

e expansive soil by mixing the steel slag of 10sim20was studied and some conclusions were achieved that thesteel slag could significantly reduce the expansion rate liquidlimit and plastic index of expansive soil and that the steel slagof 10sim20 could improve particle distribution and strengthcharacteristics of expansive soil [9] e effect of quantity ofsteel slag on the mechanical properties of blended mixes withcrushed limestone aggregate was evaluated and a theoreticalanalysis was employed to estimate the resistance for failurefactors such as vertical deformations vertical and radialstresses and vertical strains of subbase under overweighttrucks loads [10] e results indicated that the mechanicalcharacteristics and the resistance factors were improved byadding steel slag to the crushed limestone Blast furnace slagin the granulated formwas applied as a granular fill overlay onsoft subgrade soil [11] Stainless steel reducing slag (SSRS) inproduction of the soil-based controlled low-strength material(CLSM) was used as a cement substitute Testing resultsindicate that SSRS with the specific surface area of 4551 cm2gcan substitute for Portland cement up to 30 in production ofexcavated CLSM Based on the testing data an analyticalmodel for predicting compressive strength of the CLSM fromone to 56 days has been developed with high reliability [12]e waste slag was applied into the underground deep wallmethod [13] e carpet waste fibers and steel slag as envi-ronmental friendly additives were applied to overcome theswelling and weakness of the expansive soil [14] e resultsshowed that both chemical modification and mechanicalreinforcement by adding fibers and slag are efficient methodsto improve general properties of expansive clayey soil e

permeability of steel slag and steel slag modifying silt soil asnew geo-backfill materials was studied in detail [15]

According to the above literature review at present thedynamic shear resistance characteristics of waste steel slag as ageo-backfill material have not been studied Recently manyresearches were carried out on dynamic shear properties ofsoils or soils mixed with other solid waste [16ndash22] e shearmodulus and damping ratio of a backfill material are twoessential indexes for the seismic performance analysis andsafety performance evaluation of backfill materials [23ndash29]Dynamic properties of steel slag improved with sand-tireshreds admixture had been studied [30] In this paper thedynamic shear modulus and damping ratio of waste steel slagwould be investigated by resonance column tests

2 Experimental Work

21 Test Material e aged waste steel slag in the test wasproduced by the Yonggang Company in ZhangjiagangChina which is shown in Figure 1e chemical compositionof the waste steel slag is shown in Table 1 e content of freecalcium oxide was 32 and less than 5 and the ignition losswas 78 and less than 8 [31] which showed that the wastesteel slag could be applied in geotechnical backfill

e grain size distribution of the waste steel slag is shownin Figure 2 e bulk density of the waste steel slag wasapproximately 22 gcm3e gradation characteristics of thesteel slag are as follows d60 10mm d30 047mm andd10 012mm the coefficient of uniformity (Cu) was 83 andthe coefficient of curvature was 18 (Cc) erefore the steelslag was classified as the well-graded material

22 Test Method e test equipment used in this paper is aGZZ-50-type resonant column instrument which is shownin Figure 3 According to the basic principle of the resonantcolumn the equipment could test dynamic shear strain (c)dynamic shear modulus (G) and damping ratio (λ) of soil bythe method of torsion vibration e test sample size is50mm (empty)times 100mm (H) e instrument can be used tostudy the dynamic properties of unbroken samples in a smallshear strain range of 10minus6sim10minus4

In the resonance column test the main influence factors ofthe dynamic shear behavior of steel slag include relative density(Dr) and confining pressure (σ) In order to study the re-lationship between the relative density of steel slag and itsdynamic shear characteristics the resonant column tests of thesteel slag samples with different relative densities were carriedout Samples were prepared according to Geotechnical TestMethod Standard [3] e maximum dry density is determinedby the vibration hammer method and the minimum drydensity is determined by the funnel and cylinder method emaximumdry density and theminimumdry density of the steelslag were respectively 258 gcm3 and 196 gcm3

Samples were prepared according to the standard for thesoil test method e quality of the single sample was cal-culated according to the relative density of the steel slag erelationship between the control density and the relativedensity can be expressed as follows

Figure 1 Tested steel slag


ρd ρdmaxρdmin




ρ ρd(1 + w) (2)












Content α () 006 008 011 32 78

Steel slag

0102030405060708090

100

By m

ass p

assin

g (

)




Samplenumber

Conningpressure σ

(kPa)

RelativedensityDr


Watercontentω ()


GZ1 100 200 300 30 211 6 224GZ2 100 200 300 50 223 6 236GZ3 100 200 300 70 236 6 250





(a) (b) (c)


Dr = 03Dr = 05Dr = 07

30

60

90

120

150

180

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

Dr = 03Dr = 05Dr = 07

40

80

120

160

200

240

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

Dr = 03Dr = 05Dr = 07


Shear stain

80

120

160

200

240

280

320

Dyn

amic

shea

r mod

ulus

(MPa

)

(c)





02 03 04 05 06 0807170

180

190

200

210

220

Fitted value

Max

imum

dyna

mic

shea

r mod

ulus

(MPa

)

Relative density


Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(a)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(b)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(c)










σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

50

100

150

200

250

300

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(c)






001

002

003G

ndash1 (M

Pandash1

)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(a)


001

002

003

Gndash1

(MPa

ndash1)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(b)


Gndash1

(MPa

ndash1)

000

001

002

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(c)




GZ1 30100 39897 001115 108 095200 37212 000681 176 097300 19829 000512 235 094

GZ2 50100 39172 000957 125 095200 35087 000641 187 099300 19283 000488 246 092

GZ3 70100 38686 000741 162 095200 35697 000549 219 099300 19202 000428 280 098



G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)






G

Gmax


(6)






6 Conclusion











02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ρd ρdmaxρdmin




ρ ρd(1 + w) (2)












Content α () 006 008 011 32 78

Steel slag

0102030405060708090

100

By m

ass p

assin

g (

)




Samplenumber

Conningpressure σ

(kPa)

RelativedensityDr


Watercontentω ()


GZ1 100 200 300 30 211 6 224GZ2 100 200 300 50 223 6 236GZ3 100 200 300 70 236 6 250





(a) (b) (c)


Dr = 03Dr = 05Dr = 07

30

60

90

120

150

180

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

Dr = 03Dr = 05Dr = 07

40

80

120

160

200

240

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

Dr = 03Dr = 05Dr = 07


Shear stain

80

120

160

200

240

280

320

Dyn

amic

shea

r mod

ulus

(MPa

)

(c)





02 03 04 05 06 0807170

180

190

200

210

220

Fitted value

Max

imum

dyna

mic

shea

r mod

ulus

(MPa

)

Relative density


Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(a)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(b)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(c)










σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

50

100

150

200

250

300

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(c)






001

002

003G

ndash1 (M

Pandash1

)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(a)


001

002

003

Gndash1

(MPa

ndash1)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(b)


Gndash1

(MPa

ndash1)

000

001

002

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(c)




GZ1 30100 39897 001115 108 095200 37212 000681 176 097300 19829 000512 235 094

GZ2 50100 39172 000957 125 095200 35087 000641 187 099300 19283 000488 246 092

GZ3 70100 38686 000741 162 095200 35697 000549 219 099300 19202 000428 280 098



G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)






G

Gmax


(6)






6 Conclusion











02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





(a) (b) (c)


Dr = 03Dr = 05Dr = 07

30

60

90

120

150

180

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

Dr = 03Dr = 05Dr = 07

40

80

120

160

200

240

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

Dr = 03Dr = 05Dr = 07


Shear stain

80

120

160

200

240

280

320

Dyn

amic

shea

r mod

ulus

(MPa

)

(c)





02 03 04 05 06 0807170

180

190

200

210

220

Fitted value

Max

imum

dyna

mic

shea

r mod

ulus

(MPa

)

Relative density


Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(a)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(b)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(c)










σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

50

100

150

200

250

300

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(c)






001

002

003G

ndash1 (M

Pandash1

)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(a)


001

002

003

Gndash1

(MPa

ndash1)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(b)


Gndash1

(MPa

ndash1)

000

001

002

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(c)




GZ1 30100 39897 001115 108 095200 37212 000681 176 097300 19829 000512 235 094

GZ2 50100 39172 000957 125 095200 35087 000641 187 099300 19283 000488 246 092

GZ3 70100 38686 000741 162 095200 35697 000549 219 099300 19202 000428 280 098



G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)






G

Gmax


(6)






6 Conclusion











02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




02 03 04 05 06 0807170

180

190

200

210

220

Fitted value

Max

imum

dyna

mic

shea

r mod

ulus

(MPa

)

Relative density


Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(a)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(b)

Dr = 03Dr = 05Dr = 07

0

5

10

15

20

Dam

ping

ratio

()


Shear stain

(c)










σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

50

100

150

200

250

300

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(c)






001

002

003G

ndash1 (M

Pandash1

)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(a)


001

002

003

Gndash1

(MPa

ndash1)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(b)


Gndash1

(MPa

ndash1)

000

001

002

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(c)




GZ1 30100 39897 001115 108 095200 37212 000681 176 097300 19829 000512 235 094

GZ2 50100 39172 000957 125 095200 35087 000641 187 099300 19283 000488 246 092

GZ3 70100 38686 000741 162 095200 35697 000549 219 099300 19202 000428 280 098



G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)






G

Gmax


(6)






6 Conclusion











02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(a)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

40

80

120

160

200

240

280

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(b)

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

0

50

100

150

200

250

300

Dyn

amic

shea

r mod

ulus

(MPa

)


Shear stain

(c)






001

002

003G

ndash1 (M

Pandash1

)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(a)


001

002

003

Gndash1

(MPa

ndash1)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(b)


Gndash1

(MPa

ndash1)

000

001

002

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(c)




GZ1 30100 39897 001115 108 095200 37212 000681 176 097300 19829 000512 235 094

GZ2 50100 39172 000957 125 095200 35087 000641 187 099300 19283 000488 246 092

GZ3 70100 38686 000741 162 095200 35697 000549 219 099300 19202 000428 280 098



G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)






G

Gmax


(6)






6 Conclusion











02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





001

002

003G

ndash1 (M

Pandash1

)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(a)


001

002

003

Gndash1

(MPa

ndash1)

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(b)


Gndash1

(MPa

ndash1)

000

001

002

γ

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

(c)




GZ1 30100 39897 001115 108 095200 37212 000681 176 097300 19829 000512 235 094

GZ2 50100 39172 000957 125 095200 35087 000641 187 099300 19283 000488 246 092

GZ3 70100 38686 000741 162 095200 35697 000549 219 099300 19202 000428 280 098



G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)






G

Gmax


(6)






6 Conclusion











02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



G

Gmax

11 + ccr( 1113857

(3)

λλmax

ccr( 1113857

1 + ccr( 1113857 (4)






G

Gmax


(6)






6 Conclusion











02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







02

04

06

08

10

GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

01

02

03

04

05

γ

λ

(a)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(b)


GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa

00

02

04

06

08

10

00

01

02

03

04

05

γ

λ

(c)










Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References



00

02

04

06

08

10



GG

max

σ3 = 100kPaσ3 = 200kPaσ3 = 300kPa


γ





12 times 10ndash4

14 times 10ndash4

16 times 10ndash4

18 times 10ndash4

20 times 10ndash4

Refe

renc

e she

ar st

rain








0

50

100

150

200

250

300

350

400

Max

imum

dyn

amic

shea

r mod

ulus

(MPa

)200 300100






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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