國際課件2土質學與土力學soil mechanics lecture6lyh

SoilInstructor:LiuYanhua SchoolofHighway,Chang’anLectureLectureSeepage滲流andFlownet流網Effectivestress有效應力 (滲流力andSeepageDeformation滲透變形2.3SeepageandFlow ceEquation Consideringatwo-dimensionalelementofsoilofsizesdxanddzinthexandzdirections,respectively.Theerningdifferentialequationforgroundwaterflowisobtainedbyequatingtheflowratesintoandoutofthe?2h+?2h= 2.3SeepageandFlow(i ceEquation

?v+?vz?dqe=vxdz+

+?vxdx)dz+

+?vz

v+?vx =dq

?vx+?vz=

kx=?2h+?2h=vx=kx?x

vz=

kx

?z2=

ce2.3SeepageandFlow

ceEquation Itisassumedthatth soilshomogeneousandisotropicwithrespecttopermeability.thesoilandwaterare?2h+?2h= Thesolutionofanydifferentialequationrequiresknowledgeoftheboundaryconditions. problems,the ce’sequationfor2- drawingflownets.

2.3SeepageandFlowFlownet流網EquipotentialEquipotentiallines等勢線)arelinesofconstant2.3SeepageandFlow(iiFlownet流網FlowFlowlinesarepathsofwaterFlow2.3SeepageandFlowNwhereDhis drop,HisNwhereDhis drop,HistotalHDhdifferencebetweendifferencebetweenupstreamanddownstreamNDisno.ofequipotentialThelossofheadbetweentwosuccessiveequipotentialsiscalledtheequipotentialdropDh=15m h=0mh=12m

h=9m

h=6m

h=3m2.3SeepageandFlow(iiFlownet流網Aflownetconsistsoftwosetsofcurvesequipotentiallines等勢線)andflowlines流線)thatintersecteachotherat90°.llsHsl02.3SeepageandFlowFlownet流網whichtherateofflowofporefluidisThewhichtherateofflowofporefluidisThelossofheadbetweentwosuccessiveequipotentialsllsHsl02.3SeepageandFlow(iiFlownet流網)—sketchingAnequipotentiallinecannotcrossotherequipotentialTheflownetmustbeconstructedthateachelementisasquaresuchthatacirclemayinscribedwithinitthattouchesallfourofitssidesasshowninthefigureontheright.2.3SeepageandFlow(iiFlownet流網)—sketchinglineslinesofsymmetryarelines,e.g.linesEFandFGinthefigureonthetoprightareflowlines. reservoirsbehindadam,equipotentials,e.g.lineABinthefigureonthebottomrightisanequipotentialline.Impermeableboundaries2.3SeepageandFlow(iiFlownet流網TypicalFlow2.3SeepageandFlowForeachflowchannel,theForeachflowchannel,the shownontherightisgivenFlowRateb=lDq=kiA= b=klForallflowchannels(NF),thetotalflowrate =DqN =kHN =kH NF WhereNFisnumberofflowchannels,NdisnumberofequipotentialdropsandHisthetotalhead2.3SeepageandFlowk=10-andk=10-andconsiderawidthof1m,thetotalrate(qT)FlowRate =k

=10-5155=1.510-4m3s-1/DND=5DND=5ND=1ND=2ND=3ND=42.3SeepageandFlowFirst,thenumberofequipotentialdropsFirst,thenumberofequipotentialdropsfromaknownPore-waterPressureheadtothegivenpoint(A)areestimatedfromtheflownet.ThisgivesthetotalheadatthepointAas:ht=H-Hht=H-H 2.3SeepageandFlowThentheelevationheadatThentheelevationheadatthepointAwithrespectdatumisestimatedfromthegeometryoftheproblemandthepore-waterpressureatpointAisPore-waterPressuret SeepageandFlown =H-n =H-p=15-1=12d5up=hp-zp=2--59.8=Pore-waterPressure

h=15mP

h=0mh=12m

h=9m

h=6m

h=3mThetotalstress(s)carriedbyasaturatedsoilisthesumofeffectivestress(s’)carriedbythesoilparticlesandthepressurecarriedbytheporewater(u). effectivestressandnottotalstress.

4EffectiveEffectivestressisnotthecontactstressbetweentwosoilparticlesbutistheaveragestressonanethroughthesoilmassasshowninthefollowingfigure.P X

P=Ns +A-As)u P2.4EffectiveEffectiveStressunderHydrostaticConsiderasoilelementatadepth showninthefigureontheshowninthefigureonthes'=s-u=sat z- zz'2.4EffectiveEffectiveStressunderDownwardSeepageConsiderasoilelementatadepthz waterflowsdownwardsasshown thefigureonthezs'=s-u=sat zs's'='z+h2.4EffectiveEffectiveStressunderUpwardSeepageConsiderasoilelementatadepthzbelowgroundsurfacewithwatertableatthegroundsurfaceandwaterflowsupwardsasshown thefigureonthes'=s-u=sat ss'='z- 2.4Effective s’=s's'='z- hc=ichcz='g=Gs-1Gs-w1+ Δh=0Δh>0Aswaterthroughsoilitexertsadragonthesoilparticles

a 滲透力j——definethedragperunitvolumeastheseepage

0

Iftheheadlossoveraflowdistance,L,isΔh,the j= 2.5 (i gwh1F+gwLFcosa-gwh2F-TLF= ZL2.5 wh1+wZ1-wZ2-wh2-TL=gw1+Z1-Z2-h2-TL=1+Z1-2+Z2=H1-H2i=

LT=j=T=2.5 SeepageDeformation(滲透變形MainSoilboiling 2.5 (ii)SeepageDeformation—soil Boilingoccurswhentheupwardseepage sexceedsthe (effectivewei ht.2.5 (ii)SeepageDeformation—soilSiltor SandysoilW-W- i=2.5 (ii)SeepageDeformation—soilboilingCriticalHydraulicGradientj=i=g￠=

1g 1+ =(G-1)(1-n)=

-1=

1+ ='=s- SinceGsisconstant,thecriticalhydraulicgradientissolelyafunctionofthevoidratioofthesoil.2.5 (ii)SeepageDeformation—soili<icr: Stablei>icri=icr

DamageofSoilboilingCriticalstatei￡=icrFsiallowgradient(允許坡降Fs:Safetyfactor(2.5 (ii)SeepageDeformation—

sexceedthesubmergedweight,theparticlesmaybe groundsurfaceanda‘pipe’isformedinthesoilnearthePi

Internalcause——voidslargerthanfinegrainedsizebyenoughcoarsedparticlelargeseepage2.5 (ii)SeepageDeformation—2.5 (ii)SeepageDeformation—

i>Cu>icr=0.25-0.30

0

2.5 SeepageDeformation—soilboilingand

Waterflowsthroughsoilbecausethereisaintotalheadh=u+qq=hLA=ki