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VilniusVilnius GediminGedimin asas TT echniechni calcal UUniversitniversit yyDepartment of Geotechnical EngineeringDepartment of Geotechnical Engineering

RESEARCH OF SOIL SHEAR STRENGTH IN TRIAXIALRESEARCH OF SOIL SHEAR STRENGTH IN TRIAXIALTESTS AND PROBABILISTIC ASSESSMENT OF RESULTSTESTS AND PROBABILISTIC ASSESSMENT OF RESULTS

Neringa DirgelieneNeringa Dirgeliene

University of Pisa, April 2008University of Pisa, April 2008

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•• Aim of the work Aim of the work – – to improve theto improve the triaxialtriaxial compression test of soil forcompression test of soil fordetermination soildetermination soil strengthstrength parametersparameters asas preciselyprecisely asas possiblepossible andandusingusing themthem toto forecastforecast thethe soilsoil bearing resistance more reliable.bearing resistance more reliable.

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•• Literature analysis of experiments and numerical modeling showsLiterature analysis of experiments and numerical modeling shows thatthat ::üü triaxialtriaxial test is the most reliable method to model stresstest is the most reliable method to model stress --strain state of ground thanstrain state of ground than

direct shear testdirect shear test ;;üü stressstress --strain distribution are not uniform in bothstrain distribution are not uniform in both triaxialtriaxial and direct shear testsand direct shear tests

specimens;specimens;üü sandy soil strength parameters obtained fromsandy soil strength parameters obtained from triaxialtriaxial test are bigger than thetest are bigger than the ones’sones’s

obtained from the direct shear testobtained from the direct shear test ..•• The main reasons of nonThe main reasons of non --uniform stress distribution mentioned in theuniform stress distribution mentioned in the

literature are:literature are:üü notnot onlyonly normalnormal stressstress onon soilsoil samplesample surfacesurface actsacts ,, asas usualusual isis assumedassumed , also, also

tangentialtangential stressstress actsacts ;;üü influenceinfluence of of samplesample heightheight //diameterdiameter ratioratio ;;üü insufficientinsufficient drainagedrainage ;; membranemembrane effectseffects , etc., etc.

Tasks of the work is toTasks of the work is to analyseanalyse wwhathat influenceinfluence doesdoes aa nonnon --uniformityuniformity havehaveonon thethe soilsoil strengthstrength parametersparameters andand find ways to reduce orfind ways to reduce or evualateevualate it.it.

1.1. LITERATURE ANALYSISLITERATURE ANALYSIS

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55FigFig 2.2. GradingGrading curvecurve of of sandsand

2. EXPERIMENTAL ANALYSIS OF SOIL SHEAR2. EXPERIMENTAL ANALYSIS OF SOIL SHEARSTRENGTH PARAMETERS IN TRIAXIAL TESTSTRENGTH PARAMETERS IN TRIAXIAL TEST

•• ConsolidatedConsolidated --draineddrained triaxialtriaxial teststests onon poorlypoorly --gradedgraded sandsand withwith finefine(SP(SP --SM)SM) havehave beenbeen carriedcarried outout .. DenseDense andand looseloose samplessamples propertiespropertieswerewere :: densitydensity ρρ = 1,871= 1,871 grgr /cm/cm 33 ,, voidvoid ratioratio of of ee = 0= 0 ,,5151 andand ρρ ==1,6101,610 grgr /cm/cm 33 ,, ee = 0= 0 ,,74.74.

0

10

20

30

40

50

60

70

8090

100

0,01 0,1 1 10

Grain size, mm

P e r c e n t a g e p a s s i n g ,

%

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Fig 3. Device to analyse the distribution of horizontal

component of stress in soil sample:1 – metal cylinder; 2 – rubber membrane; 3 – soilsample; 4 – steel strip; 5 – fixed metal plate.

DistributionDistribution of of thethe horizontalhorizontal componentcomponent of of stressstress ininhorizontalhorizontal crosscross --sectionsection inin thethe casecase of of soilsoil axisymmetricaxisymmetric testtest

s 3τus 3

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Fig 4. Sand shear strength

• Axisymmetric circular tests findings of dense sand show that horizontalcomponent of stress inside soil sample is distributed non-uniformly.55–61 % higher horizontal component of stress was found in the sides of soil specimen cross-section and smaller was found in the centre of soilspecimen.

0

15

30

45

60

75

0 30 60 90

s 3 , kPa

τ u , k

P a

A (beginning of displacement)C (beginning of displacement)B (beginning of displacement)A (steel strip is

pulled out)C (steel strip is

pulled out)B (steel strip is

pulled out)

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Experimental analysis of soil sampleExperimental analysis of soil sample heighheigh /diameter ratio/diameter ratioinfluence on soil shear strength parametersinfluence on soil shear strength parameters

in standardin standard triaxialtriaxial testtest

FigFig 8.8. SchemeScheme of of standardstandard triaxialtriaxial testtest apparatusapparatus ::11 – – rodrod ; 2; 2 – – cap; 3cap; 3 – – soilsoil samplesample ; 4; 4 – – latexlatex membranemembrane ;;55 – – pedestalpedestal ; 6; 6 – – porousporous stonestone ..

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FigFig 9.9. StressStress −−strainstrain obtained inobtained in triaxialtriaxial compression test on dense sand,compression test on dense sand,when height/diameter ratiowhen height/diameter ratio : a): a) H/DH/D = 2; b)= 2; b) H/DH/D = 1= 1

0

200

400

600

800

1000

1200

0 3 6 9 12 15

e1, %

s 1 - s 3 ,

k P a

50 kPa 100 kPa 200 kPa

a)a) b)b)

0

200

400

600

800

1000

1200

0 3 6 9 12 15

e1 , %

s 1

- s 3 ,

k P a

50k Pa 100 kPa 200 kPas 3= 50 kPa s 3= 100 kPa s 3= 200 kPa s 3= 200 kPas 3= 100 kPas 3= 50 kPa

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ExperimentalExperimental analysisanalysis of of influenceinfluence of of freefree horizontalhorizontalmovementmovement of of samplesample basebase onon soilsoil shearshear strengthstrength

parametersparameters duringduring triaxialtriaxial testingtesting

FigFig . 10.. 10. SchemeScheme of of improvedimproved triaxialtriaxial testtest apparatusapparatus : 1: 1 – – rodrod ;;22 – – cap; 3cap; 3 – – soilsoil samplesample ; 4; 4 – – latexlatex membranemembrane ; 5; 5 – – pedestalpedestal ;;66 – – porousporous stone; 7stone; 7 – – thrustthrust bearingbearing ; 8; 8 – – stainlessstainless steelsteel platesplates

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FigFig 11.11. StressStress --strainstrain curvecurve ss obtainedobtained inin triaxialtriaxial compressioncompression testtest onon densedense sandsand samplessamples whenwhenheight/diameter ratioheight/diameter ratio : a): a) H/DH/D = 2; b)= 2; b) H/DH/D = 1= 1

0

200

400

600

800

1000

1200

0 3 6 9 12 15

e1 , %

s 1

- s 3 ,

k P a

50 kPa 100 kPa 200 kPa

a)a) b)b)

0

200

400

600

800

1000

1200

0 3 6 9 12 15

e1, %

s 1

- s 3 ,

k P a

50 kPa 100kPa 200 kPas 3=50 kPa s 3=100 kPa s 3=200 kPa s 3=50 kPa s 3=100 kPa s 3=200 kPa

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FigFig 12.12. StressStress --strainstrain curvescurves obtainedobtained inin triaxialtriaxial compressioncompressionteststests onon densedense sandsand samplessamples ,, whenwhen σσ 33 == 100100 kPakPa

•• ComparisonComparison of of testtest resultsresults obtainedobtained inin triaxialtriaxial apparatusapparatus forfordensedense sandsand samplesample ,, whichwhich H /D = H /D = 22,, withwith freefree horizontalhorizontal movementmovementof of basebase andand forfor samplesample withwith regularregular endsends ((standardstandard triaxialtriaxialcompressioncompression testing)testing) showsshows thatthat shapeshape of of graphsgraphs ee11 == f f (s(s 11 – – ss 33)) areare

differentdifferent ..

0

100

200

300

400

500

600

0 3 6 9 12 15

e1 , %

s 1 - s 3 ,

k P a

H/D = 2, regular endsH/D = 2,free horizontal movement of baseH/D = 1, regular endsH/D = 1, free horizontal movement of base

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FigFig 14.14. DenseDense sandsand samplesample ,, whichwhich H/DH/D = 2,= 2, ininimprovedimproved triaxialtriaxial testtest apparatusapparatus

FigFig 13.13. DenseDense sandsand samplesample ,, whichwhich H/DH/D = 2,= 2, ininstandardstandard triaxialtriaxial testtest apparatusapparatus

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3.3. NUMERICAL MODELING OF STRESSNUMERICAL MODELING OF STRESS --STRAINSTRAINDISTRIBUTION IN SOIL SAMPLE DURINGDISTRIBUTION IN SOIL SAMPLE DURING

TRIAXIAL TESTTRIAXIAL TEST

•• DruckerDrucker --PragerPrager modelmodel waswas usedused toto simulatesimulate thethe behaviourbehaviour of of sandsand performingperforming nonlinearnonlinear analysisanalysis .. The yield criterion can beThe yield criterion can bedefined as:defined as:

wherewhere aa andand kk −− material constants which are assumedmaterial constants which are assumedunchanged during the analysis;unchanged during the analysis; σσ mm −− the mean stress;the mean stress; ss f f −− thethe

effective stress;effective stress; aa andand k k are functions of two materialare functions of two materialparameters and obtained from experiments whereparameters and obtained from experiments where f f is theis theangle of internal friction andangle of internal friction and c c is the material cohesion strength.is the material cohesion strength.

,03 =−σ+ασ= k F f m

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ValuesValues of of soilsoil shearshear strengthstrength parametersparameters

17,017,026,026,0CC ohesionohesion c c ,, kPakPa

30,030,037,937,9AngleAngle of of internalinternal frictionfriction ,, °°

ParametersParameters

forfor failurefailureplaneplane

PP arametersarametersforfor

specimenspecimenSoilSoil

shearshear

strengthstrength

parametersparameters

FigFig 15.15. Finite elements of soil sampleFinite elements of soil sample

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FigFig 16.16. Shear stressShear stress ττxyxy distribution in the sampledistribution in the sample ss::a)a) ww ithith regularregular endsends ;b);b) ww ithith freefree horizontalhorizontal movementmovement of of basebase

a)a) b)b)

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FigFig 17.17. Horizontal soil displacementsHorizontal soil displacements u u xx distribution in the sampledistribution in the sample s:s: a)a) ww ithith regularregularendsends ;b);b) ww ithith freefree horizontalhorizontal movementmovement of of basebase

a)a) b)b)

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•• AnalysisAnalysis of of stressstress – – strainstrain distributiondistribution inin samplesample usingusing finitefinite elementelementmethodmethod showsshows thatthat forfor samplesample withwith regularregular endsends tangentialtangential stressstressinin thethe contactcontact planeplane samplesample --plateplate buildsbuilds upup .. SuchSuch stressstress restrictsrestrictsdisplacementdisplacement of of samplesample endsends inin horizontalhorizontal directiondirection .. InIn thethe casecase of of freefree horizontalhorizontal movementmovement of of samplesample basebase horizontalhorizontal displacementdisplacementof of samplesample basebase occursoccurs ..

•• InIn thisthis casecase verticalvertical componentcomponent of of stressstress inin thethe bottombottom of of samplesample isisupup to 10to 10 % smaller in comparison with vertical component of stress% smaller in comparison with vertical component of stressfor sample with restricted ends.for sample with restricted ends.

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1919FigFig 20.20. Design values calculated according toDesign values calculated according to EurocodeEurocode 77: a): a) angleangle of of

internalinternal frictionfriction ; b); b) cohesioncohesion

•• DesignDesign valuesvalues of of densedense sandsand ,, whichwhich ratioratio H/DH/D = 2,= 2, shearshear strengthstrengthparametersparameters werewere calculatedcalculated byby meansmeans of of methodsmethods providedprovided ininEurocodeEurocode .. DesignDesign valuesvalues of of thethe residualresidual angleangle of of internalinternal frictionfrictionobtainedobtained forfor samplesample withwith freefree horizontalhorizontal movementmovement of of base arebase are upup toto10,810,8 % smaller than for sample with regular ends% smaller than for sample with regular ends .. DesignDesign valuesvalues of of thethe residualresidual cohesioncohesion areare lowerlower inin 43 %.43 %.

a)a) b)b)29,3 30,5

27,4 24,8

05

101520253035

regular ends free horizontal

movement of base

f d ,

°

peak ang le of internal frictionresidual angle of internal friction

23,4

16,213,8

7,9

05

10

15

20

25

regular ends free horizontalmovement of base

c d

, k P a

peak value of cohesionresidual value of cohesion

4.4. ASSESSMENT OF RELIABILITY OF SOIL STRENGTHASSESSMENT OF RELIABILITY OF SOIL STRENGTHPARAMETERS AND SOIL BEARING RESISTANCEPARAMETERS AND SOIL BEARING RESISTANCE

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Assessment of soil bearing resistance reliability byAssessment of soil bearing resistance reliability bysolving optimization problemsolving optimization problem

•• DesignDesign valuesvalues of soil shear strength parametersof soil shear strength parameters determineddetermined usingusing ENEN19971997 andand SNiSNi PP areare notnot thethe mostmost probableprobable .. MethodMethod waswas proposedproposed totocalculatecalculate argumentsarguments designdesign valuesvalues of of thethe designdesign conditioncondition whichwhichwouldwould satisfysatisfy thethe designdesign conditioncondition z z d d = 0= 0 itself itself andand thethe probabilityprobabilityfunctionfunction of of thesethese valuesvalues wouldwould be atbe at maximummaximum ::

max),...,( 21 →n x x x f

,0),...,( 21 == nd d d id x x x g z

wherewhere f f (x(x 11 , x, x 22 ,...,,..., xxnn )) – – the probability density function of limit state the probability density function of limit statearguments;arguments; g g i i (x(x 11d d , x, x 22d d ,...,x,...,x nd nd )) – – design condition.design condition.

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FigFig 21.21. IzolinesIzolines of of thethe reliabilityreliability indexindex ββ ::(S)(S) – – design conditiondesign condition g =g = R R d d – – E E d d == 0;0;

P P – – design pointdesign point

-a Eß ß

a R ß

P

E/s E

R/s R

(S)

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Probabilistic assessment of soil bearing resistanceProbabilistic assessment of soil bearing resistancecalculated according to improvedcalculated according to improved triaxialtriaxial apparatusapparatus

resultsresults

•• Spread foundation widthSpread foundation width BB calculated according to the parameterscalculated according to the parametersof residual shearing strength, determined by usualof residual shearing strength, determined by usual triaxialtriaxial testtestapparatus is smaller by 23 % than that calculated according to tapparatus is smaller by 23 % than that calculated according to t hehedata obtained in the improveddata obtained in the improved triaxialtriaxial test apparatus.test apparatus.

1,99

1,251,20

1,53

0,00

0,25

0,50

0,75

1,00

1,25

1,50

1,752,00

regular ends free horizontalmovement of sample base

B , m

according to peak shear strength according to residual shear strength

FigFig 2222 .. ValuesValues of of foundationfoundation widthwidth B B

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FigFig 23.23. Mean, characteristic, design vMean, characteristic, design v aluesalues of soil bearing design conditionof soil bearing design conditionarguments obtained for samplearguments obtained for sample with free horizontal movement ofwith free horizontal movement of

sample basesample base using residual shear strength parametersusing residual shear strength parameters

-0,5

0,0

0,5

1,0

1,5

2,0

2,5

Xm Xk Xd Xd*

x / x m

G

Q

c

B

•• ReliabilityReliability indexindex of of soilsoil bearingbearing resistanceresistance designeddesigned accordingaccording to ENto EN19971997 andand argumentsarguments valuesvalues G G d d * * ,, Q Q d d * * ,, tantan d d *,*, c c d d * ,* , B B d d * at* at designdesign pointpointhavehave beenbeen calculatedcalculated usingusing thethe FORMFORM methodmethod . It. It waswas acceptedaccepted thatthat

permanentpermanent actionaction G G ,, variablevariable actionaction Q Q ,, soilsoil strengthstrength parametersparameters tantan ,,c c andand foundationfoundation widthwidth B B areare randomrandom valuesvalues whereaswhereas otherother argumentsargumentsareare knownknown withoutwithout deviationsdeviations ..

tan

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FigFig 24.24. R R eliabilityeliability indexindex ββ vvaluesalues of soil bearingof soil bearingresistanceresistance

•• ReliabilityReliability indexindex of of bearingbearing resistanceresistance forfor samplesample withwith regularregular endsendscalculatedcalculated byby meansmeans of of firstfirst orderorder probabilisticprobabilistic methodsmethods forfor designdesignapproachapproach 33 isis ß=4,4ß=4,4 using residual soil shear strength parametersusing residual soil shear strength parameters .. ForForsample with free horizontal movementsample with free horizontal movement – – ßß = 4,8.= 4,8.

4,44,8

4,44,0

0,0

1,0

2,0

3,0

4,0

5,0

6,0

regular ends free horizontal movementof sample base

β

according to peak shear strength according to residual shear strength

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•• TheThe calculationscalculations mademadedemonstratedemonstrate thatthat thethebiggestbiggest influenceinfluence onon thetheuncertaintyuncertainty of of marginmargin of of bearingbearing resistanceresistance isis mademadebyby thethe tangenttangent of of thethe angleangleof of internalinternal frictionfriction andandcohesioncohesion ..

,/])(

[ 222 z X

i X ii X

A z σσ

∆∆

=α

0,348

0,023

0,614

0,0090,0050

0,1

0,2

0,3

0,4

0,5

0,6

0,7

G Q c B

α x

i

tan

•• In order to determine which design condition argument makes theIn order to determine which design condition argument makes thehighest influence on the uncertainty of margin of resistance, thhighest influence on the uncertainty of margin of resistance, th eeimportance factor of argument should be calculated:importance factor of argument should be calculated:

i=1,2,…,n.

FigFig 25.25. Influence of design condition arguments on theInfluence of design condition arguments on theuncertainty of the margin of soil bearing resistanceuncertainty of the margin of soil bearing resistance

using test results of improved apparatususing test results of improved apparatus

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5.5. GENERAL CONCLUSIONSGENERAL CONCLUSIONS

1.1. AxisymmetricAxisymmetric circularcircular teststests findingsfindings of of densedense sandsand showshow thatthathorizontalhorizontal componentcomponent of of stressstress insideinside soilsoil samplesample isis distributeddistributednonnon --uniformly.uniformly. 5555 – – 6161 % high% high erer horizontalhorizontal componentcomponent of of stressstress waswasfoundfound inin thethe sidessides of of soilsoil specimenspecimen crosscross --sectionsection andand smallersmaller waswasfoundfound inin thethe centrecentre of of soilsoil specimenspecimen ..

2.2. It was suggested method for reducing restraint effects of sampleIt was suggested method for reducing restraint effects of sampleends on soil shear strength testing by improvingends on soil shear strength testing by improving triaxialtriaxial testtestapparatus with free horizontal movement of sample base. Analysisapparatus with free horizontal movement of sample base. Analysisof of stressstress --strainstrain distributiondistribution inin samplesample usingusing finitefinite elementelement methodmethodshowsshows thatthat forfor samplesample withwith regularregular endsends tangentialtangential stressstress inin thethecontactcontact planeplane samplesample --plateplate buildsbuilds upup . It are not. It are not evualatedevualated forforcalculationcalculation of of shearshear strengthstrength designdesign parametersparameters ..

3.3. ComparisonComparison of of testtest resultsresults obtainedobtained inin triaxialtriaxial apparatusapparatus forfor densedense

sandsand samplesample withwith freefree horizontalhorizontal movementmovement of of basebase andand forfor samplesamplewithwith regularregular endsends ((standardstandard triaxialtriaxial compressioncompression testtest )) showsshows thatthatshapeshape of of graphsgraphs areare differentdifferent ..

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4.4. DesignDesign valuesvalues of of densedense sandsand ,, whichwhich ratioratio H/DH/D = 2,= 2, shearshear strengthstrengthparametersparameters werewere calculatedcalculated byby meansmeans of of methodsmethods providedprovided ininEurocodeEurocode .. DesignDesign valuesvalues of of thethe residualresidual angleangle of of internalinternal frictionfriction

obtainedobtained forfor samplesample withwith freefree horizontalhorizontal movementmovement of of base arebase are upupto 10,8to 10,8 % smaller than for sample with regular ends% smaller than for sample with regular ends .. DesignDesign valuesvaluesof of thethe residualresidual cohesioncohesion areare lowerlower inin 43 %.43 %. It explains propositionIt explains propositiongiven in literature that sandy soil strength parameters obtainedgiven in literature that sandy soil strength parameters obtainedfromfrom triaxialtriaxial test are higher than parameters, obtained from thetest are higher than parameters, obtained from thedirect shear test.direct shear test.

5.5. Spread foundation width was calculated using results obtainedSpread foundation width was calculated using results obtained

from standardfrom standard triaxialtriaxial test according the residual values of soiltest according the residual values of soilshear strength parameters are 23 % smaller than foundation widthshear strength parameters are 23 % smaller than foundation widthcalculated using improved apparatus results.calculated using improved apparatus results.

6.6. ApplyingApplying probabilisticprobabilistic methodsmethods itit waswas determineddetermined thatthat uncertaintyuncertaintyof of groundground ultimateultimate limitlimit statestate designdesign conditioncondition isis thethe mostmostsignificantlysignificantly influencedinfluenced byby thethe angleangle of of internalinternal frictionfriction andandcohesioncohesion .. Therefore, soil strength parameters determinationTherefore, soil strength parameters determination

methods should be improved intending to correct soil groundmethods should be improved intending to correct soil groundcalculation methods.calculation methods.

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Thanks for your attention!Thanks for your attention!

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RESEARCH OF SOIL SHEAR STRENGTH IN TRIAXIAL TESTSRESEARCH OF SOIL SHEAR STRENGTH IN TRIAXIAL TESTSAND PROBABILISTIC ASSESSMENT OF RESULTSAND PROBABILISTIC ASSESSMENT OF RESULTS

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