教案岩土力学chapter

1、heheground.Settlements(沉降)arecausedby ysetheconditionsheheground.Settlements(沉降)arecausedby ysetheconditionswithinaderloading,weconsiderthestress-strainbehaviour.Therelationshipnastrainandstressistermedstiffness. umvalue tmaybesustainedistermed1Loadsfromfoundationsapply8.1stress(力)andnormal8.1stress

2、(力)andnormal stress(l力=Fn/=Fs/=z / = h / tcompressivestressesshearstressandstrain2vvxyxylstressandstrainzvzvvxyxylstressandstrainzvz x x2G(3 2G(3 yv z2G(3 ortriaxiales(O轴状态Stresses and strains dorectionsareequal. x = y and x = yRelevant to conditions near piles, anchors and other concentrated loads.

3、strain(平面lstressandstrainStraininonedirection=y =Relevanttoconditionsnearwalls(挡土墙)andotherlong One-al strain(平面lstressandstrainStraininonedirection=y =Relevanttoconditionsnearwalls(挡土墙)andotherlong One-al :wodirections=x=y=Relevanttoconditionsbelowwide foundations or relatively thin x compressibles

4、oil2G(3 xv 2G(3 yv4z2G(3 vMohrValues of normal stress and shear MohrValues of normal stress and shear stress must relate to a particular plane within an elementofsoil.Ingeneral,thestressesonanoth be different.laneTovisualisethestressesonsibleplanes,acalledtheMohrcircleisdrawn by plotting a (normal s

5、tress,shearstress)foraatsible5岩土中的总力初始力：在荷载作岩土中的总力初始力：在荷载作用之前，岩土中存在的力2初始力土体成分1地质历史和地Q水位有关2一般情况Q，附加力：在荷载作用之后，岩土内力发生化，改分为附加力2附加力同作用荷载1土层分布1土的分P2土体内竖向力为自重产生的竖向力土体内水平有效力为竖向有效力乘以静k土压力系数 60Whenaloadisdtosoil,itcarriedbytheWhenaloadisdtosoil,itcarriedbytheheporeswellasthesolidTheincreaseinreporewatercauses

6、drainage(flowout ofthesoil),andtheloadistransferred to the solid grains.Thetotalverticalingatabelowthegroundsurfaceistotheweightofeverythinglyingabove:soil,water,andsurfaceloading. Total stresses arecalculated from the unit weight of the soil.Unitweightrangesdry soil d: saturatedsoilg:14-2018-239.81

7、(average 17kN/m?) (average 20kN/m?) (10 kN/m?)waterwAnychangeinverticaltotalstress(v)mayalsoresultina horizontal total stress (h) at the same po.Therelationshipsbet vertical and horizontal stress are complex.n7TotalstressinhomogeneousTotalstressinhomogeneousitVerticaltotalstressatdepthv=Theunitweigh

8、t,willvarywiththe water content of the soil.= Totalstressbelowariverorlake The total stress is the sum of the weight of the soil up to the surface andtheweightofwaterabovethis: Vertical total stress at depth z,v=z+wwhere=unitweightofthesoil,w=unitweightof8Totalulti-layeredsoiltotalTotalulti-layereds

9、oiltotalThetotalstressatdepthzisthesumofthe weights of soil in each layer thickness Verticaltotalstressatdepthv=1d1+2d2+3(z-d1-where,1,2,3,etc.=unitweightsoflayers1,2,3,etc.Totalstressinunsaturatedsoiltotalstress Just above the water table the soil will remain saturated due to capillarity, bu some d

10、istance above the water table thesoilev=w.zw+sat(z-Theheightabovethewatertableupwhichthesoilwillremainsaturated depends on the grain size.9Total stress wi loadtotalstressTheadditionTotal stress wi loadtotalstressTheadditionofaurchargewill increase the total stresses below it. If the surcharge loadin

11、g is extensively wide,theincreaseinverticaltotalstress below it may be considered constantwithndequaltotheoftheVerticaltotalstressatdepthv=z+Fornarrowsurcharges,e.g.understripandpadfoundations,theverticaltotalstresseswilldecreasebothwithndhorizontalfromtheload.Insuchcases,itissarytouseasuitabledistr

12、ibutiontheory-anleisBoussinesqs集中荷载及分布荷载作用Q土中附加Z 38.3.1 Boussinesqsz z 12(2RZ)y 3p集中荷载及分布荷载作用Q土中附加Z 38.3.1 Boussinesqsz z 12(2RZ)y 3pY R(RZ(RZ) 23y312 z (2RZ)x 3p X R(RZ(RZ) 23x(R z)2R3 533p yz3p xz8.3.2 叠加原理的利8.3.2 叠加原理的利由Boussinesqs theory Oxd=B(x-a,y-aybd B(xa,yb,z, Bxa,yb,z,P(a,F矩行面均布荷载作用Q,竖向力的计

13、算:L现计矩行面均布荷载作用Q,竖向力的计算:L现计算中心点和角点Q任BOxayb3pzZ dZ 5 2 (x a)2 (yb)2 z2)d(x2 y2 z2)计算中心点Q任意深度处(0,0,z)的竖向计算角点Q任意深度处(B/2,L/2,z)的竖向计算中心点Q任意深度处(0,0,z)的竖向计算角点Q任意深度处(B/2,L/2,z)的竖向p 2BLz(L 2z 2z(L2 B2 z21 (L2z2)(B2 z2)(L2 B2 z2)2 KZl 2p 8z arctg Z2z(L2B4z21 (L 4z 4z 4z KZ0 矩形基竖直均布荷载作用时角点Q的竖向附加矩形基础当面到竖直均布荷载m处指

14、均布压力作用时，基础角矩形基竖直均布荷载作用时角点Q的竖向附加矩形基础当面到竖直均布荷载m处指均布压力作用时，基础角 3p 5/zzrz1zL3p B o y2 z2zx( p ( )2 n12221m2 m1m2 矩形基竖直O角形分布荷载作用时角点以Q的竖向附加矩形基础当面到竖直均布荷载m处指均布压力作用时，基础角矩形基竖直O角形分布荷载作用时角点以Q的竖向附加矩形基础当面到竖直均布荷载m处指均布压力作用时，基础角 3p dxdy5/zzrz1xdxdy 3BL z y2 oo(mn2 (1 n21类似的，可以计算得到线均布荷载1条形均布荷载1类似的，可以计算得到线均布荷载1条形均布荷载1面

15、的矩形区域的中心点和角点Q任意处的附加力，容易解2然后，利用叠加原理计算荷载更复杂的情当层法 模量为E21泊松比为?2为 h22: E2, 2, 1: E1, 1, re(压力Underre(压力Underwaterflow)theporereatgivenu=whwisgivenbyichw=depthbelowwatertableoroverlyingwaterItisconvenienttothinkofporererepresentedbytheofwaterinanimaginarystandpipe;therejustoutsideequal tBelowthewatertable

16、,poreressaturated,porerewillbePorewaterBelowthewatertable,poreressaturated,porerewillbePorewaterandporeairnthegroundsurfaceandthetopofthesaturatedzone,thesoilTheporereinapartiallysaturatedsoilconsistsoftwo twaterpressible,butairiscompressible.Thecombined isacomplexrelationshipinvolvingpartialresandt

17、hedegreesaturationofthe?re=?pore-airre=oftenbepartiallysaturated,i.e.theporescontainamixtureofwaterandTheheightabovethewatertabletowhichthe soilissaturatediscalledthecapillary(毛细管) rise, and this depends on the grain size and type (and thus the size of pores).itive.Indrysoil,theporereisAbovethewater

18、table,whenthesoilNegativeporere(负孔隙水压力PorereinsteadyseepageInconditionsof hetherePorereinsteadyseepageInconditionsof hethereisachangeinporeConsiderseepageoccurringntwosPandThehydralicgradient(水力梯度),i,ntwosistheheaddropunitlengthntheses.ItcanbethougthofasthedrivingthewaterHydralicgradientP-Q, i=-= u/

19、(s Thusu=i.w.Butinsteady-eseepage,i=Thereforethechangeinporereduetoseepageu = i.w.Forseepageflowverticallydownward,iisForseepageflowverticallyupward,i 8.5EffectiveKarlTerzaghiwaswasto8.5EffectiveKarlTerzaghiwaswastoethefor effective stress(有效力Allmeasurableeffectsofaofstress,suchas,distortionandachan

20、geofaredueexclusivelyto changes in effective stress.Theeffectivestressisrelatedtototalstressandpore?=-reuItiseffectivetiseffectiveincausingimportantchanges:changesstrength,changesinvolume,changesin.ItdoesnotrepresentexactcontactstressnparticlesbutthedistributionofloadcarriedthesoilovertheareaMohrcir

21、clesfortotalandeffectivestress MohrcirclesMohrcirclesfortotalandeffectivestress Mohrcirclescanbedrawnforbothtotalandeffectivestress.ThesET represent the total and effective stresses on the same plane. The two circlesaredisplacedalongthenormal stress axis by the amount of porere(n=n+u),andtheirdiamet

22、ersarethesame.Thetotaleffectiveshearstressesareequal(=TheimportanceofeffectiveTheprincipleofeffectivestressisfundamentallyimportantinsoilmechanics.mustbetreatedasthebasicaxiom,oilbehaviour ernedbyChangesinwaterlevelbelowground(watertablechanges)resultinchanges in effective stresses below the water t

23、able. Changes in water levelaboveground(e.g.inlakes,rivers,etc.)donotcausechangesineffectivestressesthegroundChangesineffectiveInysesitisbettertoworkinchangesofties; the effectiveChangesineffectiveInysesitisbettertoworkinchangesofties; the effective stress expresty, n ?=Ifbothtotalstressandporerecha

24、ngebythesameamount,thestressremainsconstant.Achangeineffectivestresswillcause:achangendachangeinChangesinThecriticalshearstrengthofsoilisproportionaltotheeffectivenormalstress; thus,achangeineffectivestressbringsaboutachangeinstrength.Therefore,iftheporereinstresseswillbereducedby and thecriticalstr

25、engthofthesoilwill bereducedby-sometimes leadingtofailure.Aseasidesandcastlewillactwhile,becausethepore resuctionisAseasidesandcastlewillactwhile,becausethepore resuctionislostreisnegative;asitdries,thisporeitcollapses.Note:Sometimesasandcastlewillactwhennearlydrybecauseeitedasseawaterslightlyandcem

26、entsthegrainsChangesinporeyaftertheconstructionofafoundationonafinesoil,reincreases,butybeginstodropasoccurs.Therateofchangeofeffectivenderafoundation,onceitisconstructed,willbethesameastheratechangeofporepre the soil.re,andthisiscontrolledbythepermeabilitySettlementoccursasthevolume(andthereforethi

27、ckness)ofthelayerschange.Thus,settlementoccurslyincoarsesoilshighpermeabilitiesandslowlyinfinesoilswithlowhe(岩土中竖向力的计算he(岩土中竖向力的计算Ahomogeneouslayer,ysaturatedwithThevolumetricweightofthesaturatedsoilpedtobe20TheverticalnormalhesoilnowincreaseslinearlywithAtadepthof10m,forinstance,theverticaltotalstr

28、essis200kN/m2 =kPa.Becausethegroundwaterisatrest,the hewaterwillIfthecapillaryheleis n2meter,thepolderwillremainsaturatedwhenthewatertableisloweredby2meter. Thetotalstresseswillnotchange,becausetheweightofthesoilthesame,buttheporeresthroughoutthesoilarereducedw? 2 m = 20 kN/m2. This means everywhere

29、bythesameamount.ttheeffectivestressesareWhenthesoilconsistsofverycoarsematerial,Whenthesoilconsistsofverycoarsematerial,therewillpracticallynohatcaseloweringthephreaticlevelby2metercausethetop2meterofthesoiledry.Theupper2meterofsoilelighter.Areasonablevalueforthedryvolumetricweightis16Atadepthof2mth

30、everticaleffectiveowis32kPa,andatadepth10mtheeffectivestressis112kPa.It hiscasethestressesincreaseby12kPa,comparedtothecaseofawatertablecoinciding with the ground surface.ThefigureshowssoillayersonThefigureshowssoillayersonasite. Unit weights are:dry sand: d = 16 kN/m? saturated sand: g = 20 kN/m?(a

31、)Atthetopofsaturatedsand(z=2.0Verticaltotalstressv=16.0 x2.0=32.0Porereu=Verticaleffectivestressv=v-u=32.0(b)Atthetopoftheclay(z=5.0Verticaltotalstressv=32.0+20.0 x3.0=92.0Porereu=9.81x3.0=29.4Verticaleffectivestressv=v-u =92.0-29.4=62.6EffectofchangingwaterThe EffectofchangingwaterThe figure shows

32、soil layers on a site. The unit weightofthesiltysandis18.8kN/m?(abovethe water level is presently at the surface of the silty sand, it may drop or it may rise. The following calculations show the effects of this Water table.3maboveu=9.8x6.0=58.8kPa,v=v-2mabovev=9.8x2.0+19.0 x3.0=76.6kPa,u=9.8x5.0=49

33、kPa,v=v-u=27.6kPa at the surfacev=9.8x0.0+19.0 x3.0=57kPa,u=9.8x3.0=29.4kPa,v=v-u=27.6kPa 1m below surface2mbelowu=9.8x2.0=19.6kPa,v=v-u=9.8x1.0=9.8kPa,v=v-Stresses under foundations(基础Q土的力Stresses under foundations(基础Q土的力Fromaninitials foundation aree,thestressesunderchangedbyexcavation(开挖i.e. vert

34、ical stresses are reduced. After construction(施工) the foundation loading increasesstresses.Otherchangescouldresultif the water table level changed.Thefigureshowstheelevationofafoundationtobeconstructedina homogeneoussoil.Thechangetotheclaylayeristobecalculatedandso theinitialandfinaleffectivestressesarerequiredatthemid-depthofthe Unitweights:sandaboveWT(水位)=16kN/m?,sandbelowWT(水位)= 20kN/m?,clay=18kN/m?.Calculations for final stresses8.8Short-termandlong-term 8.8Short-termandlong-term Thefigureshowshowanextensivelayerof fill(填方) will be placed on a certain sit