Research Article Critical State of Sand Matrix Soils

Research ArticleCritical State of Sand Matrix Soils

Aminaton Marto1 Choy Soon Tan1 Ahmad Mahir Makhtar1 and Tiong Kung Leong2

1 Faculty of Civil Engineering Construction Research Centre Universiti Teknologi Malaysia (UTM)81310 Johor Bahru Johor Malaysia

2 Faculty of Management and Human Resource Development Universiti Teknologi Malaysia (UTM)81310 Johor Bahru Johor Malaysia

Correspondence should be addressed to Choy Soon Tan cstan8liveutmmy

Received 10 January 2014 Accepted 16 February 2014 Published 16 March 2014

Academic Editors J Lian and J R Rabunal

Copyright copy 2014 Aminaton Marto et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The Critical State Soil Mechanic (CSSM) is a globally recognised framework while the critical states for sand and clay are both wellestablished Nevertheless the development of the critical state of sand matrix soils is lackingThis paper discusses the developmentof critical state lines and corresponding critical state parameters for the investigated material sand matrix soils using sand-kaolinmixtures The output of this paper can be used as an interpretation framework for the research on liquefaction susceptibility ofsand matrix soils in the future The strain controlled triaxial test apparatus was used to provide the monotonic loading onto thereconstituted soil specimens All tested soils were subjected to isotropic consolidation and sheared under undrained condition untilcritical state was ascertain Based on the results of 32 test specimens the critical state lines for eight different sand matrix soils weredeveloped together with the corresponding values of critical state parameters119872 120582 and Γ The range of the value of119872 120582 andΓ is 0803ndash0998 0144ndash0248 and 1727ndash2279 respectively These values are comparable to the critical state parameters of riversand and kaolin clay However the relationship between fines percentages and these critical state parameters is too scattered to becorrelated

1 Introduction

Recent field evidences of ground failure in sand with lim-iting percentages of fines during strong earthquakes havehighlighted the need to better characterize the stress-strainbehaviour of saturated soils in a broader range from puresand to sand matrix soils Although the recent study trendfocuses more on the investigation of sand with limitingpercentages of fines the situation is more worsening whenthere is still no clear conclusion that could be drawn at thismoment to describe the roles of fines in liquefaction suscep-tibility of sand matrix soils In the absence of a fundamentalunderstanding of the seismic behaviour of sand matrix soilsthe usability of the currently used liquefaction susceptibilityassessment criteria the Modified Chinese Criteria that solelyrelies on the interpretation of few earthquake events isactually questionable [1ndash3]

The shear strength and the deformation behaviour of soilare so depended to the combination of changes in volume and

confining stress But the research approach in geotechnicalfield is to lump together those related postreconnaissancedata to formulate new empirical assessment criteria withoutcapturing their true characteristic through fundamental soilmechanics interpretationWithout implicitly considering thefundamental basis of soil mechanics applicability of theseempirical guidelines which is nonuniversally applicable isarguable These empirical data only provide limited insightto existing state of art

The stress-strain behaviour of soils could be either stimu-lated through constitute models or interpreted within classi-cal plasticity models such as Mohr-Coulomb Among thesemodels Critical State Soil Mechanic (CSSM) developed bySchofield and Wroth [4] is the most robust framework toexplain the fundamental behaviour of different soil materialsThe fact that a loose soil is compressible while a dense soil isdilatants is in general agreement Density well presented thesoil behaviour especially for granular soils Therefore CSSMis a powerful tool able to explain the behaviour of soil

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 290207 7 pageshttpdxdoiorg1011552014290207

2 The Scientific World Journal

Table 1 Overall developments of CSSM with respect to soil liquefaction

Year Researchers Developments

1940 Casagrande [11] Introduced critical void ratio the same void ratio where contractedloose soil and dilated dense soil approach after sheared to large strains

1956 Taylor [12] Showed experimentally that dilatancy is stress dependent

1958 Roscoe et al [13] Defined critical state as the ultimate state at which a soil continues todeform at constant stress and constant void ratio

1968 Schofield and Wroth [4] Brought together stress-dependent strength and dilatancy to introducecritical state soil mechanics with Cam-Clay model

1969 Castro [14] Observed three different types of stress-strain behaviour (liquefactionlimited liquefaction and dilation) in monotonic loading tests

1975 Casagrande [15] Developed steady state line from both drained and undrained tests andnoticed that dense sand can be liquefying under sufficient high load

1981 Poulos [16]Formalised the concept of steady state of deformation (continuallydeformation under four constant conditions volume normal effectivestress shear stress and velocity)

1985 Poulos et al [17] Recognised that steady-state line is useful for identifying thesusceptibility of flow liquefaction

1985 Been and Jefferies [18] Proposed state parameter the void ratio difference between current stateand critical state at same mean stress

1991 Been et al [19]Showed that critical state and steady state of sands are equivalent andindependent of stress path sample preparation method and initialdensity

Critical state linePeak point

Critical stateCritical state

Axial strain 120576

Dev

iato

r stre

ss q

Mean effective stress p998400

Figure 1 Idealised behaviour of loose particular soil in undrained triaxial shear [10]

at various density states It is a globally recognised frameworkthat the critical states for sand and clay are both wellestablishedNevertheless the development of the critical stateof sand matrix soils is lacking

Moreover CSSM also rooted the basic theoretical frame-work of soil liquefaction yet most available findings withinthe current literature were outside this critical state con-text Table 1 summarizes the overall developments of criticalCSSM with respect to soil liquefaction study This paperaims to discuss the development of the critical state line andcorresponded critical state parameters for the investigatedmaterial sand matrix soils using sand-kaolin mixtures Theoutput of this paper will be used as an interpretation frame-work for the research of liquefaction susceptibility of sandmatrix soils in future

2 The Critical State of Sand

To date quite a number of granular soils have been tested toestablish for their critical state Figure 1 shows the undrainedbehaviour of loose sand under triaxial testing The steadystate is exactly representing the critical void ratio under

CSSM interpretation The critical state line (CSL) shows theunique relationship between the deviator stress (119902) the meannormal effective stress (1199011015840) and the specific volume (]) Therelationship is as follows

119902119891= 119872119901

1015840

119891

]119891= Γ minus 120582 ln1199011015840

119891

(1)

in which the subscripts ldquo119891rdquo denote the ultimate failure atthe critical states119872 denote the critical stress ratio 120582 denotethe gradient of the critical state line Γ denote the interceptof the critical state line The parameters of 119872 120582 and Γ areregarded as constants for a particular soil and the values forsome typical soils are given in Table 2

Jefferies and Been [5] had summarised some of theimportant results as shown in Table 3 In fact the criticalstate line is not always in its linear relationship especially atstresses higher than 1000 kPa However the range of interestin engineering community is lower than 500 kPa it is true totreat the critical state line in linear form

Several researchers try to correlate index properties ofgranular soils with critical state parameter including fines

The Scientific World Journal 3

Table 2 Critical state parameters of some soil types [20]

Soil Indexes LL PL 120582 Γ 119873 119872 1206011015840

120581120582

Fine-grained clay soilsLondon clay 75 30 016 245 268 089 23∘ 039Kaolin clay 65 15 019 314 326 100 25∘ 026Glacial till 35 17 009 181 198 118 29∘ 016

Coarse-grained soilsRiver sand 016 299 317 128 32∘ 009Decomposed granite 009 204 217 159 39∘ 006Carbonate sand 034 435 480 165 40∘ 001

Table 3 Critical state properties of some soils (after Jefferies and Been [5])

Soils Fines () 119890max 119890min Γ 12058210

119872

Castro sand B 0 0840 0500 0791 0041 122Castro sand C 0 0990 0660 0988 0038 137Monterey 0 0820 0540 0878 0029 129Nevada 75 0887 0511 0910 0045 12Ottawa 0 0790 0490 0754 0028 113Toyoura 0 0873 0656 1000 0039 124Erksak 33007 07 0747 0521 0816 0031 127Erksak 3201 1 0808 0614 0875 0043 127Erksak 3553 3 0963 0525 0848 0054 118Chek Lap Kok 05 0682 0411 0905 013 mdash

content [6] void ratio [7] and liquidity index [8] Howeverfindings show that these index properties on their own onlygive scatter relationship to be correlated with critical stateparameters These findings therefore are too irrelevant to bepractically used However the intrinsic properties of sandincluding grain size distribution do actually show theirsignificance influence to the critical state line Clean sandwith rounded grains would have a lower value of 120582 (120582 about003) compared to silty sands with angular shape (120582 about02)

3 Experiment Testing

In order to establish the critical state line and the critical stateparameters for the investigated material monotonic triaxialcompression tests have been performed The discussion inthis paper based on a total of 32 triaxial tests was carriedout on sand-kaolinmixtures at several percentages by weightThe parent sand is uniformly graded medium sand (SP) withspecific gravity of 263 It was obtained from a river in JohorBahru Malaysia In order to obtain clean sand it was firstrinsed with water to remove impurities before proceedingwith the sieve analysis White kaolin with a specific gravity of262 plastic limit of 38 and liquid limit of 25 manufacturedby Kaolin (Malaysia) Sdn Bhd were added to parent sandto create sand matrix soils with various fines percentagesby weight The index properties of the tested sand matrixsoils are presented in Table 4 The specific gravity of all sandmatrix soils is therefore also as 263 Based on the criteria

00

200

400

600

800

1000

0060 0600

Pass

ing

()

Particle size (mm)

SA1SK1SK2SK3

SK4SK5SK6SK7

Figure 2 Particle size distribution of the tested soils

of coefficient of uniformity (Cu) and coefficient of curvature(Cc) in Unified Soil Classification System all of the sandmatrix soils are classified under uniformly graded soils (SP)Particle size distribution is shown in Figure 2

The testing conditions were set constantly to increasethe precision All tested specimens have an approximately100mm height by 50mm diameter cylindrical size Mono-tonic triaxial compression tests were carried out on straincontrolled triaxial apparatus under undrained conditionThespecimens were prepared under dry deposition methods to


Table 4 Compositional characteristic of tested sand matrix soils

Tested soils Weight percentages () Density (Mgmminus3) Void ratio GradingSand kaolin Min Max Min Max Cu Cc

SA1 100 0 137 159 0920 0649 41 15SK1 95 5 139 166 0894 0582 48 17SK2 90 10 141 170 0867 0550 50 12SK3 85 15 143 176 0841 0491 54 12SK4 80 20 145 180 0815 0462 57 08SK5 75 25 147 187 0788 0409 57 04SK6 70 30 139 176 0894 0491 54 03SK7 60 40 128 163 1051 0615 46 03

0

200

400

600

800

0 500 1000

Dev

iato

r stre

ss (k

Pa)

Mean effective stress (kPa)

(a)

0

200

400

600

800

0 10 20 30

Dev

iato

r stre

ss (k

Pa)

Axial strain ()

(b)

50 kPa100 kPa

200 kPa400 kPa

minus100

0

100

200

00 100 200 300Pore

wat

er p

ress

ure (

kPa)

Axial strain ()

(c)

0

100

200

300

400

0 20 40

Und

rain

ed sh

ear s

treng

th (k

Pa)

Percentages of fines ()50 kPa100 kPa

200 kPa400 kPa

(d)

Figure 3 (a) Stress path (b) peak deviator stress (c) pore pressure developments (d) undrained shear strength of tested sand matrix soils

a relative density of 50 The mould was gently tapped todensify the sand to the required void ratio The specimenswere saturated by being initially flushed with deaired waterand followed by increasing the back pressure of 100 kPa Aneffective stress of approximately 10 kPa was maintained onthe specimen during back pressure saturation To enhance

the consistency of the testing condition the test was termi-nated if the specimen could not reach a 119861 value of at least096 at this stage The strain rate of the shearing process is02mmmin The specimens were then isotropically consoli-dated at various effective confining stresses of 50 kPa 100 kpa200 kPa and 400 kPa The moisture content was measured


0

200

400

600

800

0 200 400 600 800

Dev

iato

r stre

ss q

(kPa

)

Mean effective stress p998400 (kPa)

SA1SK1SK2SK3

SK4SK5SK6SK7

(a) Critical state line in 119902-1199011015840 space

130

140

150

160

170

180

0 200 400 600 800

Spec

ific v

olum

e 120592


SA1SK1SK2SK3

SK4SK5SK6SK7

(b) Critical state line in V-1199011015840 space

130

140

150

160

170

180

1 10

Spec

ific v

olum

e 120592

SA1SK1SK2SK3

SK4SK5SK6SK7


(c) Critical sate line in log form

080

090

100

0 10 20 30 40

Criti

cal s

tate

par

amet

er M

Fines ()

(d) Critical state parameters

Figure 4 Critical state line and critical state parameters of tested sand matrix soils

at the end of monotonic tests to enable the specific volumeat particular mean normal effective stress to be backedcalculated

4 Results and Discussion

Figure 3(a) shows the typical stress path of the tested soilsperformed in this study particularly the clean sand specimen(SA1) The peak deviator stress is correspondingly increasingat higher effective confining stress as shown in Figure 3(b) Itcan be observed in Figure 3(c) that the dense specimens (atrelative density of 50) develop negative pore pressure andthus increase the final shear strength In factmost researchersprefer to use loose state specimen in establishing the criticalstate line because of the noticeable peak strength and residuestate However the existence of quasi-steady state is soconfusing and may lead to conservative conclusion Hencea dense specimen was considered in this study Figure 3(d)shows the peak deviator stress of all 32 monotonic undrainedtriaxial testings The hyperbolic curve and the noticeable

drop at 25 of kaolin added in sand have been justified incompanion paper [9] The additional of fines will initiallyfacilitate grain separation At the point of threshold finescontent where the fines already fully occupy the interstitialspace between the sand grains it forces a return of the sandmatrix soils to far less compressible behaviour

Based on the results of monotonic undrained triaxialtesting the critical state lines of 8 different sand matrix soilsare plotted in two different spaces These critical state linesare parallel to one another In fact the straight line throughthe origin in Figure 4(a) (119902-1199011015840 space) and the curved linein Figure 4(b) (V-1199011015840 space) are corresponded when trans-forming the V-1199011015840 space into log form as in Figure 4(c) thevalues of Γ and 120582 could be obtained Table 5 summarised thecritical state parameters of the tested soils in this study Therange of the value of119872 120582 and Γ is 0803ndash0998 0144ndash0248and 1727ndash2279 respectively These values are comparable tothe critical state parameters of river sand and kaolin clay asshown in Table 2 To compare these critical state parametersat different percentages of fines for example Figure 4(d) was


Table 5 The critical state parameters

Soils 119872 Γ 120582

SA1 0998 2279 0248SK1 0926 2180 0232SK2 0969 2094 0221SK3 0970 1956 0189SK4 0940 1840 0166SK5 0803 1727 0148SK6 0882 1829 0144SK7 0940 1944 0269

plotted particularly the value of119872 across fines percentagesHowever there is not an apparent relationship that couldbe drawn between fines percentages and these critical stateparameters The relationship between fines percentages andthese critical state parameters are too scattered to be corre-lated In addition other compositional characteristics includ-ing both coefficient of curvature and uniformity limitingvoid ratio and void ratio range are also able to uniquelydescribe the behaviour of sand matrix soils of different finespercentages The general indexes that have been usually usedto describe the compositional characteristics are not sufficientenough to give good correlations in quantifying the trends ofcritical state parameters across different percentages of finesadded in parent sand Loosely speaking the plastic behaviourdue to the presence of kaolin as the plastic fines is a verypotential cause for such variation The plasticity of higherpercentages of kaolin existing within parent sand should havehigher values compared to lower percentages Although itis important to find out which intrinsic factor is actuallycorresponding to such changes it is beyond the aims andscope of this paperTherefore more researches are warrantedin future

5 Conclusion

An experimental study with undrained monotonic triaxialcompression test has been conducted on sand-kaolin mix-tures (sandmatrix soils) and the results were used to establishthe critical state of the soils together with correspondingcritical state parameters Based on the results the followingconclusions are achieved

(1) The range of the value of119872 120582 and Γ is 0803ndash09980144ndash0248 and 1727ndash2279 respectively

(2) Neither the fines percentages nor other correspond-ing compositional characteristics are adequate to becorrelated with the critical state parameters of sandmatrix soils

(3) More researches are warranted in future to find outwhich intrinsic factor significantly contributes to thechanges to the critical state parameters of sandmatrixsoils across different fines percentages

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors gratefully acknowledged the financial supportby the Ministry of Education Malaysia (MOE) under theFundamental Research Grant Scheme (Vot 4F316) and alsothe Universiti Teknologi Malaysia (UTM) through Zamalahprogram in undertaking the research to publish the resultsThe support from the Construction Research Centre andConstruction Research Alliance UTM is also acknowledged

References

[1] R W Boulanger and I M Idriss ldquoLiquefaction susceptibilitycriteria for silts and claysrdquo Journal of Geotechnical and Geoenvi-ronmental Engineering vol 132 no 11 pp 1413ndash1426 2006

[2] S Prakash and V K Puri ldquoRecent advances in liquefaction offine grained soilsrdquo inProceedings of the 5th International Confer-ence onRecentAdvances inGeotechnical Earthquake Engineeringand Soil Dynamics San Diego Calif USA 2010

[3] A Marto and C S Tan ldquoShort review on liquefaction suscepti-bilityrdquo International Journal of Engineering Research and Appli-cations vol 2 pp 2115ndash2119 2012

[4] A Schofield and C P Wroth Critical State Soil MechanicsMcGrawHill London UK 1968

[5] M Jefferies and K Been Soil Liquefaction A Critical StateApproach Taylor amp Francis London UK 2006

[6] CA Stamatopoulos ldquoAn experimental study of the liquefactionstrength of silty sands in terms of the state parameterrdquo SoilDynamics and Earthquake Engineering vol 30 no 8 pp 662ndash678 2010

[7] A Papadopoulou and T Tika ldquoThe effect of fines on criticalstate and liquefaction resistance characteristics of non-plasticsilty sandsrdquo Soils and Foundations vol 48 no 5 pp 713ndash7252008

[8] B Muhunthan and D LWorthen ldquoCritical state framework forliquefaction of fine grained soilsrdquo Engineering Geology vol 117no 1-2 pp 2ndash11 2011

[9] A Marto C S Tan A M Makhtar N Z M Yunus and AAmaludin ldquoUndrained shear strength of sand plastic fines mix-turesrdquoMalaysian Journal of Civil Engineering vol 25 no 2 pp189ndash199 2013

[10] K Been and M Jefferies ldquoStress-dilatancy in very loose sandrdquoCanadian Geotechnical Journal vol 41 no 5 pp 972ndash989 2004

[11] A Casagrande ldquoCharacteristics of cohesionless soils affectingthe stability of slopes and earth fillsrdquo Contributions to SoilsMechanics pp 1925ndash1940 1940

[12] D W Taylor Fundamentals of Soil Mechanics John Wiley ampSons London UK 1956

[13] K H Roscoe A Schofield and C P Wroth ldquoOn the yielding ofsoilsrdquo Geotechnique vol 8 no 1 pp 22ndash53 1958

[14] G Castro Liquefaction of sands [PhD thesis] Harvard Univer-sity Cambridge 1969

[15] A Casagrande ldquoLiquefaction and cyclic deformation of sandsa critical reviewrdquo in Proceedings of the 5th Panamerican Con-ference on Soil Mechanics and Foundation Engineering BuenosAires Argentina 1975


[16] S J Poulos ldquoThe steady state of deformationrdquo Journal of theGeotechnical Engineering Division vol 107 no 5 pp 553ndash5621981

[17] S J Poulos G Castro and J W France ldquoLiquefaction evalua-tion procedurerdquo Journal of Geotechnical Engineering vol 111 no6 pp 772ndash792 1985

[18] K Been and M G Jefferies ldquoState parameter for sandsrdquoInternational Journal of RockMechanics andMining Sciences andGeomechanics Abstracts vol 22 no 6 1985

[19] K Been M G Jefferies and J Hachey ldquoThe critical state ofsandsrdquo Geotechnique vol 41 no 3 pp 365ndash381 1991

[20] J H AtkinsonAn Introduction to theMechanics Soils and Foun-dations Through Critical State Soil Mechanis McGraw-HillLondon UK 1993

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Hindawi Publishing Corporation httpwwwhindawicom

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Table 1 Overall developments of CSSM with respect to soil liquefaction

Year Researchers Developments

1940 Casagrande [11] Introduced critical void ratio the same void ratio where contractedloose soil and dilated dense soil approach after sheared to large strains

1956 Taylor [12] Showed experimentally that dilatancy is stress dependent

1958 Roscoe et al [13] Defined critical state as the ultimate state at which a soil continues todeform at constant stress and constant void ratio

1968 Schofield and Wroth [4] Brought together stress-dependent strength and dilatancy to introducecritical state soil mechanics with Cam-Clay model

1969 Castro [14] Observed three different types of stress-strain behaviour (liquefactionlimited liquefaction and dilation) in monotonic loading tests

1975 Casagrande [15] Developed steady state line from both drained and undrained tests andnoticed that dense sand can be liquefying under sufficient high load

1981 Poulos [16]Formalised the concept of steady state of deformation (continuallydeformation under four constant conditions volume normal effectivestress shear stress and velocity)

1985 Poulos et al [17] Recognised that steady-state line is useful for identifying thesusceptibility of flow liquefaction

1985 Been and Jefferies [18] Proposed state parameter the void ratio difference between current stateand critical state at same mean stress

1991 Been et al [19]Showed that critical state and steady state of sands are equivalent andindependent of stress path sample preparation method and initialdensity

Critical state linePeak point

Critical stateCritical state

Axial strain 120576

Dev

iato

r stre

ss q

Mean effective stress p998400

Figure 1 Idealised behaviour of loose particular soil in undrained triaxial shear [10]

at various density states It is a globally recognised frameworkthat the critical states for sand and clay are both wellestablishedNevertheless the development of the critical stateof sand matrix soils is lacking

Moreover CSSM also rooted the basic theoretical frame-work of soil liquefaction yet most available findings withinthe current literature were outside this critical state con-text Table 1 summarizes the overall developments of criticalCSSM with respect to soil liquefaction study This paperaims to discuss the development of the critical state line andcorresponded critical state parameters for the investigatedmaterial sand matrix soils using sand-kaolin mixtures Theoutput of this paper will be used as an interpretation frame-work for the research of liquefaction susceptibility of sandmatrix soils in future

2 The Critical State of Sand

To date quite a number of granular soils have been tested toestablish for their critical state Figure 1 shows the undrainedbehaviour of loose sand under triaxial testing The steadystate is exactly representing the critical void ratio under

CSSM interpretation The critical state line (CSL) shows theunique relationship between the deviator stress (119902) the meannormal effective stress (1199011015840) and the specific volume (]) Therelationship is as follows

119902119891= 119872119901

1015840

119891

]119891= Γ minus 120582 ln1199011015840

119891

(1)

in which the subscripts ldquo119891rdquo denote the ultimate failure atthe critical states119872 denote the critical stress ratio 120582 denotethe gradient of the critical state line Γ denote the interceptof the critical state line The parameters of 119872 120582 and Γ areregarded as constants for a particular soil and the values forsome typical soils are given in Table 2

Jefferies and Been [5] had summarised some of theimportant results as shown in Table 3 In fact the criticalstate line is not always in its linear relationship especially atstresses higher than 1000 kPa However the range of interestin engineering community is lower than 500 kPa it is true totreat the critical state line in linear form

Several researchers try to correlate index properties ofgranular soils with critical state parameter including fines




120581120582





119872





00

200

400

600

800

1000

0060 0600

Pass

ing

()

Particle size (mm)

SA1SK1SK2SK3

SK4SK5SK6SK7








0

200

400

600

800

0 500 1000

Dev

iato

r stre

ss (k

Pa)


(a)

0

200

400

600

800

0 10 20 30

Dev

iato

r stre

ss (k

Pa)

Axial strain ()

(b)

50 kPa100 kPa

200 kPa400 kPa

minus100

0

100

200

00 100 200 300Pore

wat

er p

ress

ure (

kPa)

Axial strain ()

(c)

0

100

200

300

400

0 20 40

Und

rain

ed sh

ear s

treng

th (k

Pa)


200 kPa400 kPa

(d)





0

200

400

600

800

0 200 400 600 800

Dev

iato

r stre

ss q

(kPa

)


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

0 200 400 600 800

Spec

ific v

olum

e 120592


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

1 10

Spec

ific v

olum

e 120592

SA1SK1SK2SK3

SK4SK5SK6SK7



080

090

100

0 10 20 30 40

Criti

cal s

tate

par

amet

er M

Fines ()










Soils 119872 Γ 120582



5 Conclusion







Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












120581120582





119872





00

200

400

600

800

1000

0060 0600

Pass

ing

()

Particle size (mm)

SA1SK1SK2SK3

SK4SK5SK6SK7








0

200

400

600

800

0 500 1000

Dev

iato

r stre

ss (k

Pa)


(a)

0

200

400

600

800

0 10 20 30

Dev

iato

r stre

ss (k

Pa)

Axial strain ()

(b)

50 kPa100 kPa

200 kPa400 kPa

minus100

0

100

200

00 100 200 300Pore

wat

er p

ress

ure (

kPa)

Axial strain ()

(c)

0

100

200

300

400

0 20 40

Und

rain

ed sh

ear s

treng

th (k

Pa)


200 kPa400 kPa

(d)





0

200

400

600

800

0 200 400 600 800

Dev

iato

r stre

ss q

(kPa

)


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

0 200 400 600 800

Spec

ific v

olum

e 120592


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

1 10

Spec

ific v

olum

e 120592

SA1SK1SK2SK3

SK4SK5SK6SK7



080

090

100

0 10 20 30 40

Criti

cal s

tate

par

amet

er M

Fines ()










Soils 119872 Γ 120582



5 Conclusion







Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













0

200

400

600

800

0 500 1000

Dev

iato

r stre

ss (k

Pa)


(a)

0

200

400

600

800

0 10 20 30

Dev

iato

r stre

ss (k

Pa)

Axial strain ()

(b)

50 kPa100 kPa

200 kPa400 kPa

minus100

0

100

200

00 100 200 300Pore

wat

er p

ress

ure (

kPa)

Axial strain ()

(c)

0

100

200

300

400

0 20 40

Und

rain

ed sh

ear s

treng

th (k

Pa)


200 kPa400 kPa

(d)





0

200

400

600

800

0 200 400 600 800

Dev

iato

r stre

ss q

(kPa

)


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

0 200 400 600 800

Spec

ific v

olum

e 120592


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

1 10

Spec

ific v

olum

e 120592

SA1SK1SK2SK3

SK4SK5SK6SK7



080

090

100

0 10 20 30 40

Criti

cal s

tate

par

amet

er M

Fines ()










Soils 119872 Γ 120582



5 Conclusion







Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

200

400

600

800

0 200 400 600 800

Dev

iato

r stre

ss q

(kPa

)


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

0 200 400 600 800

Spec

ific v

olum

e 120592


SA1SK1SK2SK3

SK4SK5SK6SK7


130

140

150

160

170

180

1 10

Spec

ific v

olum

e 120592

SA1SK1SK2SK3

SK4SK5SK6SK7



080

090

100

0 10 20 30 40

Criti

cal s

tate

par

amet

er M

Fines ()










Soils 119872 Γ 120582



5 Conclusion







Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Soils 119872 Γ 120582



5 Conclusion







Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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