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GRAVITYRETAINING?WALL1.INTRODUCTIONRetainingwallsarestructuresusedtoprovidestabilityforearthorothermaterialwhereconditionsdisallowthemasstoassumeitsnaturalslope,andarecommonlyusedtoholdbackorsupportsoilbanks,coalororepiles,andwater.Retainingwallsareclassified,basedonthemethodofachievingstability,intosixprincipaltypes(Fig.1).Thegravity-walldependsuponitsweight,asthenameimplies,forstability.Thecantileverwallisareinforced-concretewallthatutilizescantileveractiontoretainthemassbehindthewallfromassuminganaturalslope.Stabilityofthiswallispartiallyachievedfromtheweightofsoilontheheelportionofthebaseslab.Acounterfortretainingwallissimilartoacantileverretainingwall,exceptthatitisusedwherethecantileverislongorforveryhighpressuresbehindwallandhascounterforts,whichtiethewallandbasetogether,builtatintervalsalongthewalltoreducethebendingmomentsandsheers.AsindicatedinFig.1c,thecounterfortisbehindthewallandsubjectedtotensileforces.Abuttressedretainingwallissimilartoacounterfortwall,exceptthatthebracingisinfrontofthewallandisincompressioninsteadoftension.Twoothertypesofwallsnotconsideredfurtherarecribwalls,whicharebuilt-upmembersofpiecesofprecastconcrete,metal,ortimberandaresupportedbyanchorpiecesembeddedinthesoilforstability,andsemigravitywalls,whicharewallsintermediatebetweenatruegravityandacantileverwall.Figure.1Typesofretainingwalls:(a)Gravitywallsofstonemasonry,brick,orplainconcrete.Weightprovidesoverturningandslidingstability;(b)cantileverwall;(c)counterfort,orbuttressedwall.Ifbackfillcoverscounterforts,thewallistermedacounterfort;(d)cribwall;(e)semigravitywall(smallamountofsteelreinforcementisused);(f)bridgeabutment.Bridgeabutments(Fig.1f)areoftenretainingwallswithwingwallextensionstoretaintheapproachfillandprovideprotectionagainsterosion.Theydifferintwomajorrespectsfromtheusualretainingwallin:1.Theycarryendreactionfromthebridgespan.2.Theyarerestrainedatthetopsothatanactiveearthpressureisunlikelytodevelop.Foundationwallsofbuildingsincludingresidentialconstructionareretainingwallswhosefunctionistocontaintheearthoutofbasements.Retainingwallsmustbeofadequateproportionstoresistoverturningfor(orexcessivetilting)andslidingaswellasbeingstructurallyadequate.Termsusedinretaining-walldesignareshowninFig.2.Notethatthe“toe”isboththefrontbaseprojectionandtheforwardedge;similarlyforthe“heel”.2.COMMONPROPORTIONSOFGRAVITYWALLRetaining-walldesignproceedswiththeselectionoftentativedimensions,whicharethenanalyzedforstabilityandstructuralrequirementsandarerevisedasrequired.Sincethisatrialprocess,severalsolutionstotheproblemmaybeobtained,allofwhicharesatisfactory.Acomputersolutiongreatlysimplifiestheworkinretaining-walldesignandprovidestheonlypracticalmeanstooptimizethedesign.Gravity-walldimensionsmaybemaybetakenasshowninFig.3.Gravitywalls,generally,aretrapezoidal-shapedbutalsomaybebuiltwithbrokenbacks.Thebaseotherdimensionsshouldbesuchthattheresultantfallswithinthemiddleone-thirdofthebase.Thetopwidthofthestemshouldbeontheorderof0.30m.Iftheheelprojectionisonly100to150mm,theCoulombequationmaybeusedforevaluatingthelateralearthpressure,withthesurfaceofslidingtakenalongthebackfaceofthewall.TheRankinesolutionmayalsobeusedonasectiontakenthroughtheheel.Becauseofthemassiveproportionandresultinglowconcretestresses,low-strengthconcretecangenerallyusedforthewallconstruction.Acriticalsectionforanalysisoftensileflexurestresseswilloccurthroughthejunctionofthetoeportionatthefrontfaceofwall.3.GRAVITYWALLFORCETheforcesonagravitywallareasindicatedinFig.4.TheactiveearthpressureiscomputedbyeithertheRankineorCoulombmethods.IftheCoulombmethodisused,itisassumedthatthereisincipientslidingonthebackfaceofthewall,andthepressureactsattheangleofwallfrictionδtoanormalwiththewall.TheRankinesolutionappliestoPaactingattheangleβonaverticalplanethroughtheheel.ThevectorcanthenbeaddedtotheweightvectorofthewedgeofsoilWbetweentheverticalplaneandbackofthewalltogetthedirectionandmagnitudeoftheresultantPaonthewall.TheverticalresultantRactingonthebaseisequaltothesumoftheforcesactingdownward,andwillhaveaneccentricityewithrespecttothegeometricalcenterofthebase.Takingmomentsaboutthetoe,躲sum猴ofo捏vert嗚urni馳ngm惹omen萌ts(n演et)/取R悠熊派Ift房hew養(yǎng)idth行of堆the煙base負(fù)is杰B,t就hee菌ccen哪tric灑ity杠oft勉heb貴ase斤can口then羅be毯comp盆uted想as肆濃歐附乏訴4.S如TABI午LITY虹OF懸GRAV伍ITY客WALL冒Reta擦inin棵gwa聯(lián)lls悟must慰pro他vide劉ade戲quat孔est些abil萄ity犧agai朽nst壁slid法ing,何as面show粉nin孕Fig振.5.染The霜soil顧in埋fron商tof購貸the摧wal挑lpr銷ovid桿esa洽pas蛾sive國-ear裳th-p菜ress非ure哈resi哨stan縮ce,陣as裁the是wall合ten醉dst味osl罰ide糖into小it.粘If佳the去soil允is訂exca尊vate辟dor畏ero耳ded此afte埋rth見ewa僑lli嘴sbu潔ilt,疤the瓶pas熟sive秩-pre躺ssur澤eco蠢m(xù)pon游ent移isn壯ota艦vail圖able腿and節(jié)sli戚ding蛾ins漂tabi活lity汽may視occ板ur.驚Ift產(chǎn)here謠is額cert愁aint頭yof輪no坦loss抹of寺the舒toe夾soil嶺,th還ede澇sign極erm刷ayu餃set災(zāi)hep優(yōu)assi躍vep街ress旱ure源int蛛his輩zone莫as星part樹of愈the乓slid陽ing奴resi韻stan隱ce.響Addi篩tion暴als驢lidi司ngs項(xiàng)tabi舍lity貞may充be庫deri旨ved立from灑the飲use拋of封ake贈(zèng)ybe芒neat刑hth吃eba殲se.更Unle沖sst炭hek琴eyi橋squ恰ite鴿deep歸,ho巖weve勾r,t傍hes囑lidi排ngz碧one足(Fig今.6)順may掠brid疲geo之ver伴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