aps寶典提綱版英語7土力學

課程：土力學(SoilMechanics)

提問概率：65%

德國高校對于這門課的要求

Thiscourseaimsto:

Enablestudentsto appreciatetheroleofgeotechnicsincivilengineeringprojects.

Provideknowledgeandunderstandingof thefundamentalprinciplesofsoilasanengineeringmaterial.

課程提綱（德國大學）：

SoilFormationSoilConsistencySoilCompactionSoilPermeability

Stresseswithinthesoil

APS模擬問題：（注意內容里的所有簡單計算）這門課你的分數為什么這么高？

你能說下你這門課都學了哪些關于土的知識？土可以怎么分類？

什么是風化？

什么是土的粘性？

土的流性指數如何計算？

研究土囊的壓實性有什么意義？哪些因素會影響壓實性？

土囊會受哪些應力？

Soil

ChapterOne

SoilFormationandBasic-Relationships

Isanyuncementedorweaklycementedaccumulationofmineralparticles

formedbyweatheringofrocks,thevoidbetweentheparticlescontainingwater/orair.Weakcementationcanbeduetocarbonatesoroxidesprecipitatedbetweentheparticlesorduetoorganiccarbonatesoroxidesprecipitatedbetweentheparticlesorduetoorganicmatter.

Dependingonthemethodofdeposition,soilscanbegroupedintotwocategories:

Residualsoils:

Thesoilswhichremainattheplaceofdisintegrationofparentrock.

Transportedsoils:

Thesoils,whichcarriedawayfromtheirplaceofdisintegrationtosomeotherplacebytransportingagencies.

Thetransportingagenciesmaybeclassifiedas:

i) Water ii)wind iii)gravity iv)Ice

Soingeneralsoilisformedfromdisintegrationofrocksoverlayingthe

earthcrust.

wind

rain

Weathering

Whichareusuallyresultsfromatmosphericprocessesactionontherockatorneartheearthsurface.

Mechanical(Physicalweathering):

Alltypeofactionsthatcauseadisintegrationoftheparentrocksbyphysicalmeanssuchas,gravity,windandwater.Theproductofthistypeisrounded,subroundedorgranular,itsproductscalledcoarsegrainedsoile.g.(gravelandsand)theypresentinnatureinasinglegrainstructure.

Coarsegrainedsoil

Sand&Gravel

Cohesionlesssoil

Itpropertiesarethesameasparentrock.2-Chemicalweathering

Alltypesofchemicalreactionsthatoccurbetweenthemineralsoftherockandtheenvironment(air,wateret.)andwillendupbydisintegrationofparentrockintofinegrainparticles;theseproductshavedifferentpropertiesfromtheparentrock.Theypresentinnatureasalumpsofnumberofplatelikeparticles.

Thephysicalpropertyofthisproductdoesnotreflectthesamepropertiesoftheparentrocks.

Finegrainedsoil

Siltandclay

Cohesivematerial

Itspropertiesdonotreflectthesamepropertiesoftheparentrocks.

Soil

Gravel,Dia

Sand

Silt

Clay

Dia:equivalentsdiameter(mm)

Clayminerals:Therearetwobasicstructureunitsthatformtypesofthemineralsintheclay:

TetrahedralUnit:Consistsoffouroxygenatoms(orhydroxyls,ifneededtobalancethestructure)andonesiliconatom.

Elevation Tetrahedralsheet

OctahedralUnit(consistofsixhydroxylionatapicesofanoctahedralenclosinganaluminumionatthecenter).

FormationofMinerals

Thecombinationoftwosheetsofsilicaandgibbsiteindifferentarrangementsandconditionleadtotheformationofdifferentclaymineralssuchas:

KaoliniteMineral:

Thisisthemostcommonmineralisthekaolin.Thestructureiscomposedofasingletetrahedralsheetandasinglealuminaoctahedralsheetasshowninfigurebelow:

StrongHydrogenBondSonotaffectedbywater

AnditsalsocalledChinaclay3-

Illitehasabasicstructureconsistingoftwosilicasheetswithacentralaluminasheet.

Thereisapotassiumbondbetweenthelayers.

Montmorilloniteunit:ThebasicstructuralunitissimilartothatofIllite.

Highlyaffectedbywater

HighlyaffectedbywaterwithhighshrinkageandSwellanditiscalledexpansivesoil.

ClayParticle–waterrelations:

Innatureeverysoilparticleissurroundedbywater.Sincethecentersofpositiveandnegativechargesofwatermoleculesdonotcoincide,themoleculesbehavelikedipoles.Thenegativechargeonthesurfaceofthesoilparticlethereforeattractsthepositive(hydrogen)endofthewatermolecules.Morethanonelayerofwatermoleculessticksonsurfacewithconsiderableforcedecreasewithincreaseinthedistanceofthewatermoleculefromthesurface.Theelectricallyattractedwatersurroundstheclayparticleisknownasthediffuseddouble-layerofwater.Thewaterlocatedwithinthezoneofinfluenceisknownastheadsorbedlayerasshowninfigure:

ClayParticle

Diffusedoublelayer

Adsorbedwaterlayersurroundingasoilparticle

Claystructures:

-Dispersedstructure

-flocculatedstructure

Distinguishbetweenflocculatedanddispersedstructures

Flocculated Dispersed

Morestrength Lowerstrength

Permeabilityishigher permeabilityisless

Lowcompressibility highercompressibility

BasicRelationships:

Wt=Ww+Ws

Where"#:totalweightofsoil

""∶Weightofwater"%:Weightofsolid"&∶Weightofair≈0

VolumeVt=Vv+Vs=Va+Vw

+Vs

()∶TotalVolume(*:VolumeofVoid(+:Volumeofair(,∶Volumeofwater(-:VolumeofSoild

UnitWeight–Density

"#$%

! =&#'(%*+$,-'

&#'(%.#%/0+

=*'

2'

Watercontent%

34%=55?899:; <4

56

Voidratio,e

e=v@

vA

Porosity(n%)

B%=DD?899DE

AircontentA%

F%=DG?899

DE

==5?899

=6

BulkDensity(totaldensity),HE

ρ=JK

I @K

Drydensity,

HL;M==6

DE

(N=?4=O):;(SN)

=O

Dryunitweight(TL;M)56

TL;M=DE

(SU?=O)

Specificgravity,V6

!"=%"='"?("= '"

%& %& ("?%&

!"=+"= &"?("= &" (itsvaluerangebetween2.6-2.85)

+& +& ("?+&

SolidDensity,%"

%"='"

("

, +"

=&"

("

SomeUsefulCorrelation:

1-S.e=!".-.

2-/=0

120

0=/

13/

4=/(1?")

4=03-?!"

120

120 120

%8=!"(12-)%& 9: +8=!"(12-)+&

120 120

%8=!"2"?0%& 9: +8=!"2"?0+&

%"=!"20%& 9: +"=!"20+&

120 120

%;:<=!"%& 9:+;= !"+&

120 120

10- %0==.=%?=%"?8?%&

11- +0==

=+?=!"31+

&

120

Sometypicalvaluesofvoidratio,moisturecontentinasaturatedcondition,anddryunitweightforsoilsinanaturalstatearegiveninthefollowingtable:

Table1-Voidratio,MoistureContent,andDryUnitWeightforsomeTypicalSoilsinaNaturalState.

TypeofSoil

Voidratio

Naturalmoisturecontentinasaturatedstate(%)

Dryunitweight,+;(@A?'B)

Looseuniformsand

0.8

30

14.5

Denseuniformsand

0.45

16

18

Looseangular-

grainedsiltysand

0.65

25

16

Denseangular-grainedsiltysand

0.4

15

19

Stiffclay

0.6

21

17

Softclay

0.9-1.4

30-50

11.5-14.5

Note:theweightofonekilogrammassis9.806Newton1kg=9.806N

Example-1:Initsconditionasoilsamplehasamassof2290gandavolumeof1.15*10-3m3.Afterbeingcompletelydriedinanoventhemassofthesampleis2035g.ThevalueofGsforthesoilis2.68.Determinethebulkdensity,unitweight,watercontent,voidratio,porosity,degreeofsaturationandaircontent.

Solution:

!"=%= '.')* =199034?56=1.99%8

& +.+,?+*./ 9/

Unitweight,:=%8=1990?9.8=19500=?56=19.53=?56

&

%? '')*A'*6,

Watercontent,>=%@= '*6, =0.125CD12.5%

:=F@(1+>I):

" 1+K ?

19.5=2.68(1+.125)?10

1+K

e=0.538

M *.,6O

Porosity,n=+NM=+.,6O =0.3490~0.35

S.K=F@.>I

*.+',?'.TO

Degreeofsaturation,S= *.,6O = 62.267%

Aircontent,A=n(1-S)=0.35(1-.62)=0.132

ChapterTwo

PlasticityofFineGrainedSoils

Plasticityistheabilityofasoiltoundergounrecoverabledeformationatconstantvolumewithoutcrackingorcrumbling.Itisduetothepresenceofclaymineralsororganicmaterial.

Consistencylimits(Atterberglimits):

Atterberg,aSwedishscientistdevelopedamethodfordescribingthelimitconsistencyoffinegrainedsoilsonthebasisofmoisturecontent.Theselimitsareliquidlimit,plasticlimitandshrinkagelimit.

Liquidlimit(L.L):isdefinedasthemoisturecontentinpercentatwhichthesoilchangesfromliquidtoplasticstate.

PlasticLimit(P.L.):Themoisturecontentsin%atwhichthesoilchangesfromplastictosemisolidstate.

ShrinkageLimit(S.L.):Themoisturecontentsin%atwhichthesoilchangesfromsemisolidtosolidstate.

PlasticityIndex(P.I.):itistherangeinmoisturecontentwhenthesoilexhibiteditsplasticbehavior:

!.#.=%.%–!.%.

LiquidityIndex(L.I.orIL):arelationbetweenthenaturalmoisturecontents(())and(L.L.)and(P.L.)inform:

If LI>1 ThenthesoilatLiquidstateIf LI=1thenthesoilatL.L.

If%#<1thenthesoilbelowL.L.

Activity:isthedegreeofplasticityoftheclaysizefractionofthesoilandisexpressedas:

!"#$%$#&= ).+

%-."/0&1$23405#$"/31

PlasticityChart:basedonAtterberglimits,theplasticitychartwasdevelopedbyCasagrandetoclassifythefinegrainedsoil.

Someusefulnotes:

%6∶Constantatallstages

Degreeofsaturation(S%)atS.L.andupto=100%

DegreeofSaturationintheregionfromS.L.andbelow<100%

%&'()=%&,&-./.

%0'()=%0,&-./.

1'()=1-./.

RelativeDensity:istherationoftheactualdensitytothemaximumpossibledensityofthesoilitisexpressedintermsofvoidratio.

23(%)= 16,7819

16,7?16;9

?100

Or 23(%)==>?@A? =>BCD>?EB ?100

=>B =>?@A8=>?EB

16,7:Thevoidratioofthesoilinitsloosestcondition16;9:Thevoidratioofthesoilinitsdensestcondition19:ThevoidratioofthesoilinitsnaturalconditionF'6,7:Maximumdryunitweight(at16;9)

F'6;9:Minimumdryunitweight(at16,7)

F'9:Naturaldryunitweight(at19)

RD

Description

G

0 - H

loose

1? 2

3 3

medium

2? 1

3

Dense

,-

Example1:foragranularsoil,given,!"#$=17.3*+,relativedensity=82%,

3=8%and45=2.65.If8,9:=0.44.whatwouldbe8,=>?whatwouldbethedryunitweightinthelooseststate?

Solution:

!"#$= @A ?10 17.3= G.HI ?10

BCDE BCDE

∴ 8:

=0.53 KL= DMNOPDE ?100

DMNOPDMQE

0.82=DMNOPR.IS

DMNOPR.TT

∴ 8,=>=0.94

∴! (WXYZZ[8[X)= 45

! = 2.65

?10

"#$

1+8,=> ^

=13.65_`?aS

1+0.94

Example2:agranularsoiliscompactedtomoistunitweightof20.45_`?aSatmoisturecontentof18%.Whatisrelativedensityofthecompactedsoil?Given,8,=>=0.85,8,9:=0.42Wcd45=2.65?

Solution:

^

!=@A(BCef)!

BCDE

20.45=G.HI(BCR.Bg)?10

BCD

∴8:

=0.52 KL= DMNOPDE =

DMNOPDMQE

KL=0.85?0.52

0.85?0.42

?100=76.74%

Example3:Adrysampleofsoilhavingthefollowingproperties,L.L.=52%,

P.L.=30%,45=2.7,e=0.53. Find:Shrinkagelimit,d#$density,dryunitweight,andaircontentatdrystate.

Solution

ChapterthreeSoilCompaction

Soilcompactionisoneofthemostcriticalcomponentsintheconstructionofroads,airfield,embankmentsandfoundations.Thedurabilityandstabilityofastructurearerelatedtotheachievementofpropersoilcompaction.Structuralfailureofroads,airfieldandthedamagecausedbyfoundationsettlementcanoftenbetracedbacktothefailuretoachievepropersoilcompaction.

Compactionofsoil:

Compactionistheprocessofincreasingthedensityofasoilbypackingtheparticlesclosertogetherwithareductioninthevolumeofaironly.Compactionincreasesthedrydensityanddecreasesthevoidratio.

Purposeofcompaction:

Increaseshearstrengthofsoil

Reducevoidratiothusreducepermeability

Controllingtheswell-shrinkagemovement

Reducesettlementunderworkingload

Preventthebuildupoflargewaterpressure

Factorsaffectingcompaction:

Watercontent

Typeofsoil

Compactionenergyoreffort

Allthesefactorsareshowninthefollowingfigures:

TheeffectoftypesofsoilonthedrydensityusingthesamecompactionEnergy.

Differentincompactionenergyandtypesofsoil

Theoryofcompaction:

Compactionistheprocessofreducingtheaircontentbytheapplicationofenergytothemoistsoil.Fromcompactiontestwecanfind:

Thereisauniquerelationshipbetweenthewatercontentandthedrydensityforspecificcompactionenergy.

Thereisonewatercontent(O.M.C.)(Optimummoisturecontent)atwhichthemaxdrydensityisachieved

ThetwoabovepointscanbeclearlyshownthroughthefollowingFigure:

ChapterFive

SoilPermeabilityandFlow

SOILPERMEABILITY

Amaterialispermeableifitcontainscontinuousvoids.Allmaterialssuchasrocks,concrete,soilsetc.arepermeable.Theflowofwaterthroughallofthemobeysapproximatelythesamelaws.Hence,thedifferencebetweentheflowofwaterthroughrockorconcreteisoneofdegree.Thepermeabilityofsoilshasadecisiveeffectonthestabilityoffoundations,seepagelossthroughembankmentsofreservoirs,drainageofsubgrades,excavationofopencutsinwaterbearingsand,rateofflowofwaterintowellsandmanyothers.

HydraulicGradient

Whenwaterflowsthroughasaturatedsoilmassthereiscertainresistancefortheflowbecauseofthepresenceofsolidmatter.However,thelawsoffluidmechanicswhichareapplicablefortheflowoffluidsthroughpipesarealsoapplicabletoflowofwaterthroughsoils.AsperBernoulli's

equation,thetotalheadatanypointinwaterundersteadyflowconditionmaybeexpressedas

Totalhead=pressurehead+velocityhead+elevationhead

HydraulicGradient

Whenwaterflowsthroughasaturatedsoilmassthereiscertainresistancefortheflowbecauseofthepresenceofsolidmatter.Thelawsoffluidmechanicswhichareapplicablefortheflowoffluidthroughpipesarealsoapplicabletoflowofwaterthroughsoils.Thetotalheadatanypointinwaterundersteadyflowconditionmaybeexpressedas:

Totalhead=pressurehead+velocityhead+elevationhead

TheflowofwaterthroughasampleofsoiloflengthLandcross-sectionalareaAasshowninfigure1:

!" = %"+

!. =%.+

'"+ +

*

"

() 2-

*

/

'/+ +

() 2-

Figure

(1)flowofwaterthroughasoilsample

Forallpracticalpurposesthevelocityheadisasmallquantityandmaybeneglected.

Thewaterflowsfromthehighertotalheadtolowertotalhead.SothewaterwillflowfrompointBtoC.

!"?!.=(%"+23)-(%.+27)

45 45

Where,%"and%.=89:*;<=>??:;A,'"and'.=PressureHead.Thelossofheadperunitlengthofflowmaybeexpressesas:

==?

C

Whereiisthehydraulicgradient.

Hydraulicgradient:

Thepotentialdropbetweentwoadjacentequipotentialsdividedbythedistancebetweenthemisknownasthehydraulicgradient.

DARCY'SLAW

Darcyin1856derivedanempiricalformulaforthebehaviorofflowthroughsaturatedsoils.Hefoundthatthequantityofwaterqpersecflowingthroughacross-sectionalareaofsoilunderhydraulicgradient/canbeexpressedbytheformula

q=kiA

orthevelocityofflowcanbewrittenas

!=#

$

Wherekistermedthehydraulicconductivity(orcoefficientofpermeability)withunitsofvelocity.Thecoefficientofpermeabilityisinverselyproportionaltotheviscosityofwaterwhichdecreaseswithincreasingtemperature;therefore,permeabilitymeasurementatlaboratorytemperaturesshouldbecorrectedtothevaluesatstandardtemperatureof200Cusingthefollowingequation.

Where%&':Coefficientofpermeabilityat200C

%(:CofficientofpermeabilityatLab.Temperture0C

)(Viscosityofwateratlab.Temperature

)&'Viscosityofwaterat200C

Table(1):Theof!"

!#$

atdifferenttemperature.

DISCHARGEANDSEEPAGEVELOCITIES:

FigurebelowshowsasoilsampleoflengthLandcross-sectionalareaA.Thesampleisplacedinacylindricalhorizontaltubebetweenscreens.ThetubeisconnectedtotworeservoirsR1andR2inwhichthewaterlevelsaremaintainedconstant.ThedifferenceinheadbetweenR1andR2ish.Thisdifferenceinheadisresponsiblefortheflowofwater.SinceDarcy'slawassumesnochangeinthevolumeofvoidsandthesoilissaturated,thequantityofflowpastsectionsAA,BBandCCshouldremainthesameforsteadyflowconditions.Wemayexpresstheequationofcontinuityasfollows

qaa=qbb=qcc

Ifthesoilberepresentedasdividedintosolidmatterandvoidspace,thentheareaavailableforthepassageofwaterisonlyAv.Ifvs.isthevelocityofflowinthevoids,andv,theaveragevelocityacrossthesectionthen,wehave

Where!"istheareaofthevoid,#$istheseepagevelocity,#istheapproachvelocity

A:isthecrosssectionalareaofthesample

#= !?(

$ !"?(

Wheren:istheporosityofthesoil

#=#)

#"

#=#

*

METHODSOFDETERMINATIONOFHYDRAULIC

CONDUCTIVITYOFSOILS(Coefficientofpermeability).

Stresseswithinthesoil

Stresseswithinthesoil:Typesofstresses:

Geostaticstress:SubSurfaceStressescausebymassofsoil

Verticalstress !"=∑#?

HorizontalStress!"='(!"

Note:Geostaticstressesincreasedlineralywithdepth.2-Stressesduetosurfaceloading:

Infintlyloadedarea(filling)

Pointload(concentratedload)

Circularloadedarea.

Rectangularloadedarea.

Introduction:

Atapointwithinasoilmass,stresseswillbedevelopedasaresultofthesoillyingabovethepoint(Geostaticstress)andbyanystructureorotherloadingimposedintothatsoilmass.

1-

stressesdueGeostaticsoilmass

!"= #?(Geostaticstress)

!)=*(!" , where*(:isthecoefficientofearthpressureatrest.

EFFECTIVESTRESSCONCEPT:Insaturatedsoils,thenormalstress(σ)atanypointwithinthesoilmassissharedbythesoilgrainsandthewaterheldwithinthepores.Thecomponentofthenormalstressactingonthesoilgrains,iscalledeffectivestressorintergranularstress,andisgenerallydenotedbyσ'.Theremainder,thenormalstressactingontheporewater,isknowsasporewaterpressureorneutralstress,andisdenotedbyu.Thus,thetotalstressatanypointwithinthesoilmasscanbewrittenas:

!="#?+u

This