Dredging-Engineering-Part-2-soil-疏浚工程-土質(zhì)篇

DredgingEngineering-Part2soil疏浚工程土質(zhì)篇

Chapter1BasicConceptsofSoilMechanics1

1.1SoilClassification1

1.2SoilProperties1

1.2.1PhaseRelationshipsofSoil2

1.2.2Compactionand/orConsistency2

1.2.3Permeability2

1.3

ElementarySoilTests7

1.3.1PermeabilityTest7

1.3.2MohrCircle8

1.3.3CaseStudy10

1.3.4TriaxialShearTestMohrFailureEnvelop12

1.3.5DirectShearTestCoulomb’sLaw(1776)13

1.3.6StandardPenetrationTest--SPT16

1.4

PassiveandActiveFailure—Rankine’sTheoryofLateralEarthPressure17

1.4.1ActiveStressState18

1.4.2PassiveStressState20

1.5

StressesintheSubsoil20

1.5.1General20

1.5.2DeterminationofVerticalStresses22

1.5.3OverstressedorUnderstressedPoreWaterinaClayLayer24

1.6Consolidation25

Acknowledgements25

Part2

DredgingProcess

Chapter1BasicConceptsofSoilMechanics

1.1SoilClassification

Theobjectofsoilclassificationistodividethesoilintogroupssothatallthesoilsinaparticulargrouphavesimilarcharacteristicsbywhichtheymaybeidentified.Inpractice,therearemanydifferentclassificationsareusedbydifferentinstitutions,mostoftheseclassificationsystemsarebasedontheoutcomeoftheparticlesizedistributionanalysesandtheresultsoftheplotsontheplasticitychartofCasagrande.Table1-1istheinternationallymostacceptedstandardizationofparticle-size-ranges.

Table1-1Internationallymostacceptedstandardizationofparticle-size-ranges.

fine-grained

coarse-grained

Clay

Silt

sand

gravel

stone

Colloids

fine

2~6

medium

6~20

Coarse

20~60

fine

60~200

medium

200~600

coarse

600~2mm

fine

2~6

medium

6~20

coarse

20~60

cobbles

60~200

boulders

200~

μm(micron)

mm

Table1-2showstheBritishSoilClassificationSystemforEngineeringpurpose(BS5930,1981).Thenameanddescriptivelettersusedinthissystemareexplainedintable1-3.

1.2SoilProperties

1.2.1PhaseRelationshipsofSoil

Soilisamultiphasesystem,containingthreedistinctphases:solid,liquid(water)andgas(air).Inrealitytheporesinbetweenthesolidparticlesarefilledwithwaterand/orgas,figure1-1(a);however,inordertodefinethephaserelationships,anelementofsoilisschematizedinfigure1-1(b).

1.2.2Compactionand/orConsistency

Fornaturaldepositsofsoilsthecompactionoftheencounteredlayerin-situisanimportantfeature.Thecompactionofanin-situsandlayerdependsonlargelyontheparticlesizedistribution(figure1-2),themodeofsedimentationandthestresshistory.Forclaysthecompactionmoreorlessdependsonthesamefeaturesbutissomewhatmorecomplicatedbecauseforclaystheinteractionbetweenclayparticlesdependsalsoontheelectricalchargesonthesurfaceoftheparticles.Thereforeitiscommonpracticetodistinguishthenotationcompactionforgranularsoils,whichisexpressedintherelativedensityDrandthenotationconsistencyforcohesivesoils,whichisexpressedintheunstrainedshearstrengthCu.Seetable1-4.

1.2.3Permeability

Thepermeabilityofthesoildeterminestherateofingressofwaterintothesoil,eitherbygravitationalfloworbydiffusion.Sincetheindividualsandparticlesarenotbondedtogetherbyhydratedwaterandsincetheparticlesarerelativelylarge,thereisaneasyaccessofwaterintothepores.Thereforesandhasagoodpermeability(permeabilityvariesbetweenk=10-2mm/sandk=10-4mm/s).However,claysarealmostimpermeable(permeabilityvariesbetweenk=10-6mm/sandk=10-8mm/s).Thetwomainreasonsforthisverylowpermeabilityare:(1)theparticlesareverysmalli.e.ofcolloidalsize;(2)thewatersurroundingtheclayparticlesispartlyhydratedand/orelectricallybondedtotheparticleandthereforetheflowofwaterenteringtheporesisverydifficult.

Permeabilityisanimportantsoilpropertythatvariesconsiderablyfordifferenttypesofsoils,asshownintable1-5.Relationsbetweensoiltypeandsoilparametersarelistedintable1-6.

Table1-2BritishSoilClassificationSystemforEngineeringPurposes

Table1-3Namesanddescriptivesymbolsforgradingandplasticitycharacteristics,usedintheBritishSoilClassificationSystemforEngineeringpurposes.

Component

Mainterm

Symbol

Qualifying

Symbol

Coarse

Gravel

Sand

G

S

Wellgraded

Poorlygraded

Poorlygraded,uniform

Poorlygapgraded

W

P

Pu

Pg

Fine

Finesoil,fines

Silt(M-soil)

Clay

F

M

C

Lowplasticity

Intermediateplasticity

Highplasticity

Veryhighplasticity

Extremelyhighplasticity

L

I

H

V

E

Organic

Peat

Pt

Organic

O

Fig.1-2Particlesizedistribution

Table1-4

Compactionofgranularsoils

Consistencyofcohesivesoils

classification

Dr

Classification

Cu[kN/m2]

Veryloose

Loose

Mediumdense

Dense

Verydense

0<15

15-35

35-65

65-85

85-100

Verysoft

Soft

Firmormedium

Stiff

Verystifforhard

<20

20-40

40-75

75-150

>150

Table1-5

Table1-6RelationbetweensoiltypeandsoilparameterstoNEN6740.

1.3

ElementarySoilTests

1.3.1PermeabilityTest

Alreadyinthemiddleofthe19thcentury(1850’s)Darcyexperimentallyfoundhisfamouslaw,whenhestudiedtheflowpropertiesofwaterthroughasand-filter-bed.Forhisexperimentsheusedaset-upsimilartothatshowninFig1-3,withwhichhecouldvarythelength(L)ofthesampleandthewaterpressuresatthetopandatthebottom.

Darcyexperimentallyfoundthatthearteofflow(Q)isproportionaltothefallofhead:

Andinverselyproportionaltothelength(L)ofthesample:

SinceQdenotesthetotaldischarge[m3/s]passingthroughthecross-sectionalarea

A[m2]ofthesamplecontainer,itwillbeclearthatthespecificrateofthefloworspecificdischarge(q)hasthedimensionofavelocity[m/s]andalsorepresentsthevelocityvofthefreewaterinthetubewherethereisnosand.

Thereal(average)velocitywithwhichthewaterpassestheporechannelsinsidethesandsampleiscalledtheseepagevelocity(Vs)andcanbedefinedbyusingtheprincipleofcontinuity.Thedischargeofwaterpassingthetotalarea(A)abovethesandsampleperunittimemustalsopassthereducedaveragearea

(Ap)oftheporechannelsinthesametime:

or

Theconstant(k)usedintheformulaaboveisthecoefficientofpermeabilitywhichhasthedimensionofavelocity[mm/s]andisanimportantsoilpropertywhichvariesconsiderablyfordifferenttypesofsoils,asshowninTable1-5.Itshouldbenotedthatkvaluesstrictlyapplytowater(200C).Allotherliquidswillhaveothervaluesforthepermeationconstant,dependingontheviscosity.

Fig.1-3Determinationofthecoefficientofpermeability

1.3.2MohrCircle

Inalmostallsoilmechanicsandfoundationengineeringproblems,whereconcentratedloadsareapplied,thehorizontalandverticalstresscomponentswillnotbeprincipalstresses:i.e.alsoshearstresseswillactonthehorizontalandverticalplanes.

Fig1-4

Determinationofforcesactingonaninclinedplane

Asamatteroffactspeakingofthe〝stressstate〞inapointofthesubsoilismeaningless,withoutmentioningtheorientationoftheplaneofinterestonwhichtheforcesact.Thereforethecompletestress-stateinapointofthesubsoilcanonlybedefinedbythestress-tensor.

Ofcourseinagivensituationthestress-tensorinanypointinthesubsoilcanbedefinedinathree-dimensionalorthogonalcoordinatesystem.However,forreasonsofsymmetry,inmostcasestheresultantofforcesactingonaparticleofsoilliesinaverticalplane.Thereforeinmostsituationsitwillsufficetoconsiderthestressesinthisplaneusingatwo-dimensionalorthogonalcoordinatesystemwithahorizontal(x)axisandavertical(z)axis.

Ifthenormalstressesandshearstressesactingonasmallelementofsoilinx-andz-directionaregiven,thenthenormalstressandshearstressactingonanyotherplanewithgiveninclinationθcanbedetermined(Fig.1-4):

Incasetheprincipalplanesareorientatedparalleltothex-andz-directionthennoshearforcesactontheseprincipalplanesandthenormalstressesactingontheprincipalplanesbecomeprincipalstresses,forexample,

Thereforeinthisspecialcase,

Since,fromamathematicalpointofview,thesetwoequationsrepresentacircle,Mohrproposedtoplotthiscircle,knownasMohrcircleintheσ-τdiagram,seeFig.1-5

Fromthisfigureitcanbeobserved:

σ1=majorprincipalstress;

(2)σ3=minorprincipalstress;

Thecenter(C)oftheciecleliesontheσ-axisatadistance

OC=p=(σ1+σ3)/2

Theradiusofthecircleisq=(σ1-σ3)/2;

(σ1-σ3)iscalledthediviatorstressorthestressdifference;

Aiscalledthestresspointrepresentingtheresultingstressσr?actingontheplanewithaninclinationθ(betweenthedirectionof?σ1andthenormalonthisplane);

Thisresultingstressσrcanberesolvedinanormalstressandashearstressτθandtheangleα?betweenσrandthenormaltotheplanecanbefoundinthediagram,since

tanα=τθ/σθ=AB/OB,α=AOB;

Note,inthisspecialcase,thepole(P),alsocalledtheoriginofplanescoincideswiththepositionofσ3.ThepolePisapointontheMohrcircle,withthefollowingproperty:alinethroughthepolePandanypointAoftheMohrcirclewillbeparalleltotheplaneonwhichthestresspairgivenbypointAacts;

Themaximumshearstressτmax=q=(σ1-σ3)/2willbeobtainedinaplanewithanorientationθ=450.

Fig.1-6TheMohrcircleconstruction

1.3.3CaseStudy

Ifinapointinthesubsoilthenormalstressesandshearstressesactingontwoorthogonalplaneswithaknownorientation,forexamplerelativetothehorizontal,aregiven,Fig.1-7,thenitispossibletodeterminethemagnitudeanddirectionoftheprincipalstresseswiththeaidoftheMohrdiagram.

Thisisillustratedintheexamplebelow:

Fig.1-7Mohrcircleconstructiontofindthemagnitudeanddirectionofσ1andσ3

Graphicalsolution:

PlotthestresspointA’(25,15)andB’(65,15);

DrawtheA’B’tofindthecenterC(45,0)ofthecircle;

ErectoftheMohrcirclethroughA’andB’;

Readmagnitudeofσ1=70kN/m2andσ3=20kN/m2;

FindthepolePbydrawingalinethroughB’paralleltoBB(orthroughA’paralleltoAA);

FindthedirectionoftheprincipalplanesbydrawinglinesthroughthepoleàPσ1andPσ3;

Thedirectionoftheprincipalstressesactsperpendiculartotheprincipalplanes.Inthiscasethedirectionofσ1is450relativetothehorizontal.

Analyticalsolution:

1)Thesumofthenormalstressesisconstant:

(Notethisisthecoordinate(45,0)ofthecenterCofthecircle)

2)Theradiusofthecircleisdefinedby:

3)Combining1)and2):

4)Tofindthedirectionofσ1usethestresspairinwhichσθislargestàσθ=65kN/m2andτθ=+15kN/m2:

2θ=36.8700andthereforeθ=18.4350.

So,relativetothedirectionofσ1thedirectionofσθis(positive)àanti-clockwise(seesign.conventionfigure1-4).

Thedirectionofσθ

relativetothehorizontalαisgivenby,

thefigure1-7,tanα=2/1=2à

α=63.4350

Thedirectionofσθ

relativetoσ1was

θ=18.4350

Thedirectionofσ1

relativetothehorizontalis

(α-θ)=45.0000

1.3.4TriaxialShearTestMohrFailureEnvelop

Themostreliablesheartestisthetriaxialdireststresstest(Fig.1-8).Acylindricalsoilsamplewithalengthofatleasttwiceitsdiameteriswrappedinarubbermembraneandplacedinatriaxialchamber.Aspecificlateralpressure,calledchamberpressure,isappliedbymeansofwaterwithinthechamber.Thechamberpressureiskeptconstantduringeachtest.Averticalloadisthenappliedatthetopofthesampleandsteadilyandveryslowlyincreaseduntilthesamplefailsinshearalongadiagonalplane.TheMohrcirclesoffailurestressesforaseriesofsuchtestsusingdifferentvaluesofconfiningpressureareplottedasshowninFig.1-8.

Fig.1-8Triaxialsheartest,Mohrfailureenvelop(afterSower,FuHuaChen)

Thestressisuniformlydistributedonthefailureplane

Soilisfreetofailontheweakestsurface

Watercanbedrainedfromthesoilduringthetesttosimulateactualconditionsinthefield,seeFig.1-9,drainedtriaxialtestonasandsample.

Asmall-diametersamplecanbeusedandthesamplepreparationiseasy.

Triaxialsheartestapparatusiscostly.Mostconsultingengineerscannotaffordtheup-to-datecomputerizedreadout.Formostfoundationinvestigations,theuseoftriaxialsheartestsisnotjustified.Thebearingpressurevaluescanbeobtainedfromtheinterpretationoftheresultsoftheunconfinedcompressiontest.Onlyinmajorprojectssuchasearthdamconstruction,wherethevaluesofangleofinternalfrictionandcohesionarecritical,shouldthetriaxialsheartestbeconducted.Manyclientstodayconsiderthetriaxialsheartesttheapexofsoilinvestigation,andnosoilreportiscompletewithoutsuchdata.Itisbestforthenewlyestablishedconsultingfirmstospendtheirmoneyonfirldequipmentratherthanonthetriaxialshearapparatus.

Fig.1-9Drainedtriaxialsheartestonasandsample

1.3.5DirectShearTestCoulomb’sLaw(1776)

Thedirectsheartest(Fig.1-10)istheearliestmethodfortestingsoilshearingstrength.TheBoxShearapparatusconsistsofarectangularboxwithatopthatcanslideoverthebottomhalf.NormalloadisappliedverticallyatthetopoftheboxasshowninFig.1-11and1-12.

AshearingforceisappliedtothetophalfoftheboxFig.1-13,shearingthesamplealongthehorizontalsurface,andtheshearstressthatproducestheshearfailureisrecorded.Theoperationisrepeatedseveraltimesunderdifferentnormalloads.Theresultingvaluesofshearingstrengthagainstnormalloadsareplottedandtheangleofinternalfrictionandcohesionvaluedetermined.SeeFig.1-14.

Fig.1-11Directsheartest

Fig.1-12Directsheartestapparatus(afterLiu&FuHuaChen)

Fig.1-13Principleofdirectshearbox

Coulombfirstexperimentedwithsands,laterwithothertypesofsoilandusedporousstonestoallowforadrainedcondition,i.e.u=0.HeindeedfoundalinearrelationshipbetweenTandNor,sincethearea(A)oftheslidingplaneisknown,betweentheshearstressatfailureτfandthenormaleffectivestressσ’

Inwhich

φ’=angleoftheinternalfriction

c’=(apparent)cohesion

Mathematicallyseentheformularepresentsapairofstraightborderlines(thelinebelowtheσ’axisapplieswhenthedirectionofTisreversed)intheσ’-τdiagram.Allstresspairsinbetweenthesetwolinesrepresentsastressstateofequilibriuminthesoil;allstresspointsoutsidethesetwoborderlinesrepresentsastressstateoffailureinthesoil.

Fig.1-14Coulomb’sfailurelinesintheσ’-τdiagram

WhenCoulomb’sfailurelineisconsideredagain,itisevidentthattheultimatestateofstressforanystresspoint(S)onthefailurelinecanberepresentedbyaMohrcircletouchingthatpointon

thefailureline,seeFig.1-15.However,thedirectsheartesthasthedisadvantagethattheactualstressstateisnotknownandthattheslidingplaneisinfactdeterminedinadvance.

Fig.1-15ultimatestressstaterepresentedbyaMohrcircletouchingCoulomb’sfailureline

Tensilefailure

InFig.1-15theCoulomb’sfailureintersectstheσ’axiswithσ’=σt=-c’cotanφ’,theintersectingpointTrepresentsatensilefailureinthesoil.

1.3.6StandardPenetrationTest--SPT

Probablytheoldestmethodoftestingsoilisthe〝PenetrationResistanceTest.〞InperformingthePenetrationResistanceTest,thesplitspoonsampleusedtotakesoilsamplesisutilized.Thesplitspoonisdrivenintothegroundbymeansof1140-lbhammerfallingafreeheightof30in.ThenumberofblowsNnecessarytoproduceapenetrationof12in.isregardedasthepenetrationresistance.Toavoidseatingerrors,theblowsforthefirst6in.ofpenetrationarenottakenintoaccount;thoserequiredtoincreasethepenetrationfor12in.constitutetheNvalue,alsocommonlyknownasthe〝blowcount〞.Thefollowingshouldbeconsideredinperformingthepenetrationtest:

DepthFactor—ThevalueofNincohesionlesssoilsisinfluencedtosomeextentbythedepthatwhichthetestismade.Thisisbecauseofthegreaterconfinementcausedbytheincreasingoverburdenpressure.Inthedesignofspreadfootingsonsand,acorrectionofpenetrationresistancevalueisnotexplicitlyrequired.Inotherproblems,particularlythoseconcernedwiththeliquefactionofsand,however,acorrectionisnecessary.

WaterTableWhenpenetrationiscarriedoutbelowthewatertableinfinesandsorsiltysands,theporepressuretendstobereducedinthevicinityofthesampler,resultinginatransientdecreaseinNvalue.

DrivingConditionsThemostsignificantfactoraffectingthepenetrationresistancevalueisthedrivingcondition.Itisessentialthatthedrivingconditionshouldnotbeabused.Thestandardpenetrationbarrelshouldnotbepackedbyoverdrivingsince,atthisforce,thesoilactsagainstthesidesofthebarrelandcausesincorrectreadings.Anincreaseinblowcountbyasmuchas50%cansometimesbecausedbyapackedbarrel.

CobbleEffectThebarrelwillbouncewhendrivingoncobbles;hence,nousefulvaluecanbeobtained.Sometimes,asmallpieceofgravelwilljamthebarrel,therebypreventingtheentranceofsoilintothebarrel,thussubstantiallyincreasingtheblowcount.

CaliforniaSamplerConsiderableeconomycanbeachievedbycombiningthepenetrationtestwithsamplingasdescribedunder〝undisturbedsample〞.FieldtestshavebeenconductedcomparingtheresultsofthepenetrationresistanceoftheCaliforniasamplerwiththoseofstandardpenetrationtests.Thetestsindicatethattheresultsarecommensurable,withtheexceptionofverysoftsoil(N<4)andverystiffordensesoil(N>30).Bycombiningthepenetrationresistancetestwithsampling,moretestscanbemadeandundisturbedsamplescanbeobtainedwithoutresortingtheuseofShelbytubes.

Withtheexceptionoftheareaofstandardfineloosesands,thedepthfactorandthewatertableelevationfactorcanbedisregarded.

Theresultsofthestandardpenetrationtestcanusuallybeusedforthedirectcorrelationwiththepertinentphysicalpropertiesofsoil,asshowninTable1-7.

Thecorrelationforclayasindicatedcanberegardedasnomorethanacrudeapproximation,butthatforsandsisreliableenoughtopermittheuseofN-valueinfoundationdesign.TheuseofNvaluebelow4andover50fordesignpurposesisnotdesirable,unlesssupplementedbyothertests.Someelaboratepile-drivingformulaearebasedonfieldpenetrationresistancevalue.Theyshouldbeusedwithcaution,astheerrorinvolvedinNvaluecanbemorethananyoftheothervariables.

Whendrivingonhardbedrockorsemi-hardbedrocksuchasshale,iftheamountofpenetrationisonlyafewinchesinsteadoffull12in.,itiscustomarytomultiplythevaluebyafactortoobtaintherequired12in..Forinstance,ifafter30blowsthepenetrationisonlytwoinches,itisassumedthattheNvalueis120.Suchanassumedvaluewhenusedforthedesignofthebearingcapacityofbedrockmightbeinerror.Analternativeisthepressuremetertestasdescribedbelow,whichmayofferabetteranswer.

Somecontractscallforapenetrationtestforevery5ftandsamplingatthesameintervaloreverychangeofsoilstratum.Thismaynotbenecessary.Thefieldengineershouldusehisorherjudgmenttoguidethefrequencyofsamplingandavoidunnecessarysamplingsothatthecostofinvestigationcanbeheldtoaminimum.Samplesintheupper10to15ftareimportant,asthisisgenerallythebearingstratumofshallowfootings.Soilcharacteristicsatthislevelalsogoverntheslab-on-gradeconstructionandearth-retainingstructures.Samplingandpenetrationtestsatlowerdepthsbecomecriticalwhenadeepfoundationsystemisrequired.

Table1-7PenetrationresistanceandsoilpropertiesoftheStandardPenetrationTest

Sands(fairlyreliable)

Clays(ratherreliable)

Numberofblows

Perft,N

Relativedensity

Numberofblows

Perft,N

consistency

0-4

4-10

10-30

30-50

over50

Veryloose

Loose

Medium

Dense

Verydense

Below2

2-4

4-8

5-15

15-30

over30

Verysoft

Soft

Medium

Stiff

Verystiff

hard

(afterPeck&FuHuaChen)

1.4

PassiveandActiveFailure—Rankine’sTheoryofLateralEarthPressure

Consideranoutstretchedterrainwithhorizontalsurface.Thesubsoilconsistsofhomogeneoussoilwithanangleofinternalfrictionφ’andc’.

Fig1-16Excavationwithinfiniterigidwallsembracedwiththrustswithhydraulicjacks

AssumethattheverticalsteelwallsoftheexcavationshowninFig.1-16areinfiniterigidandthewallfrictionbetweensteelandsoiliszero.

Wealreadyhavethefeelingthatthejackforcenecessarytopreventthewallsfrommovingtowardseachotherisconsiderablylessthanthejackforcenecessarytomovethewallsapartfromeachother.Whenthewallstendtomoveawayfromthemassofsoilbythelateralearthpressure,wespeakofactiveearthpressure;whenthelateralearthpressureresistsamovementagainstit,wespeakofapassiveearthpressure.

Letusconsideranelementofsoil,Fig.1-16.Sincethereisnofrictionbetweenwallandsoil,thehorizontalstressandverticalstressactingonthesoilelementareprincipalstressesandtheelementofsoilwillbehaveinexactlythesamewaylikeaspecimentestedintriaxialtest.Consideringthefactthattheverticalprincipalstressσ’vdoesnotalter,thequestiontoansweristodetermineσ’handtheinclination(tothevertical)ofthefailureplanefor:

theactivestressstate;

thepassivestressstate.

1.4.1ActiveStressState

FromtheMohrdiagram(Fig.1-17)itcanberead:

Let

whichiscalledthecoefficientofactivestress,thenwehave:

Forcohesivesoil:

Forcohesionlesssoil(c’=0):

Fig.1-17

Fromthefigureitcanbereadthat2αa=90+φ’àαa=450+φ’/2,whereαaistheinclinationbetweentheactivefailureplaneandthehorizontal.Hencetheanglebetweentheactivefailureplaneandtheverticalis±(450-φ’/2).

Note:ofcoursewhenanelementofsoilneartheleft-hand-wallinthefigureisconsidered,theslidingplanesindicatedbydashedlines()willoccur(τnegative).

1.4.2PassiveStressState

SimilarlyitcanbereadfromtheMohrdiagram:

Which,whenworkedoutsimilarly,resultsin:

Let

whichiscalledthecoefficientofpassivestress,thenwehave:

Forcohesivesoil:

Forcohesionlesssoil(c’=0):

Inexactlythesamewayitcanbederivedfromthefigurethattheinclinationofthepassivefailureplanesrelativetotheverticalis

±(450+φ’/2).

1.5

StressesintheSubsoil

1.5.1General

Thetransmissionofforcesinamassofdrygranularsoiliseffectuatedbynormalforces(N)andfrictionorshearforces(S)actingonthecontactareasbetweenindividualgrains.Sincetheeffectivecontactareabetweenindividualgrainsgenerallyisverysmall,thenormalstressesandshearstressesmayamounttoincrediblyhighvalues.Forexample,whenidealizedsphericalparticlesofequalsizeareconsidered(Fig.1-18),thenitwillbeclearthatthetheoreticalcontactareabetweentheparticlesdrawneartozeroandhencethetransmittedstressinthecontactpointdrawneartoaninfinitevalue.Howeverinreality,seenthroughthemicroscope,someelasticdeformationofthematerialwilloccuratthelocationofthecontactpointandhencetheactualcontactareaincreaseintoaflatfiniteareaofcircularshape,Fig1-18(b).Ifthematerialoftheparticlesisveryhardandbrittleitmayoccurthatsuchanelasticdeformationisinsufficienttocreatealargeenoughcontactarea,resultinginaplasticdeformationoreveninruptureofthecrystallinestructureàcrushedparticles.

Ofcourse,insoilmechanicsengineering,itwillbeunpracticaltoconsiderforcesandstressesbetweenindividualparticles.Therefore,basedontheassumptionthatinamassofdrysoilalltheforcesactingonbetweenindividualparticlesareinequilibrium,alsotheresultingforcesatanyarbitrarychosenplanemustbeinequilibrium,seeFig.1-19.

Fig.1-18Stresstransmissionbetweensphericalparticles

Fig.1-19Anarbitrarychosenplanethroughamassofdrysoil

EachofthebalancingresultantsR1,R2,R3,R4,………,actingontheplanecanberesolvedintoanormal(N)andtangential(T)component.Nowthen,consideringthetotalarea(A)oftheplanethestressesinsoilmechanicsaredefined:

Normaltotheplane:

effectivestress

In-plane:

shearstress

Thesymbolσ’andτ’(with‘)indicatethatthestressesareeffectivei.e.thatstressesactupongrainsinthesubsoilmass.Sometimesinliteraturethesymbolσeandτeareused.Insoilmechanicscompressivestressesarepositive(+).

Inthedefinitionabove,amassofdrysoilhasbeenconsidered.Whenthemassofthesoiliscompletelysaturated,thentheporesarefilledwithwaterunderpressure:u=porewaterpressure,whichineverypointactsperpendiculartothesurfaceofeachgrain.Therefore,whenanarbitrarychosenplaneisconsideredtheporewaterpressureuactsperpendiculartothetotalsurfaceareaofthisplane.Inthesectionthroughtheporesthereiswaterunderpressure;inthesectionthroughthegrainsthereisalsou,transmittedviathesolidgrains.So,combiningthecontactstressesbetweenparticlesandtheporewaterpressure,thetotalnormal