commonlywallbase

PeriodicaPolytechnicaCivilEngineering60(3),pp.
421–426,2016DOI:10.
3311/PPci.
8522CreativeCommonsAttributionRESEARCHARTICLEDesignChartsforCircular-ShapedSheetedExcavationPitsagainstSeepageFailurebyHeaveSerdarKoltuk,RagAzzamReceived25-08-2015,revised28-01-2016,accepted01-02-2016AbstractDuringtheconstructionofanexcavationpit,themainprob-lemisoftendominatedbyseepageowintotheexcavationpit.
Theporewaterpressuredevelopedbytheseepageowmaylifttheexcavationbase,andthus,mayleadtothestabilitylossoftheexcavationpit,whichisknownasseepagefailurebyheave.
Inthisstudy,basedontheresultsofthree-dimensionalsteady-stategroundwaterowanalyses,designchartsaregiventoeval-uatethesafetyagainstheaveofcircular-shapedsheetedexca-vationpitsconstructedwithinhomogeneousisotropicsoillay-ersoflimitedorunlimitedthicknesses.
Thegivendesignchartsconsiderthevariousconditionsofwaterlevelonbothup-anddownstreamsideofanexcavationpit.
Itmeansthattheycanbeusedforexcavationpitsconstructedinbothurbanareasandopenwater.
KeywordsCircular-shapedsheetedexcavationpits·seepagefailurebyheave·designchartsSerdarKoltukDepartmentofEngineeringGeologyandHydrogeologyRWTHAachenUniver-sityLochnerstr,4-20,D-52064,Aachen,Germanye-mail:koltuk@lih.
rwth-aachen.
deRagAzzamDepartmentofEngineeringGeologyandHydrogeologyRWTHAachenUniver-sityLochnerstr,4-20,D-52064,Aachen,Germanye-mail:azzam@lih.
rwth-aachen.
de1IntroductionCircular-shapedsheetedexcavationpitsareverycommonfortheconstructionsofsewers,shafts,bridgepiersandabutments.
Duetoappearingringstresses,theearthpressureactingonthewallsofacircular-shapedexcavationpitislessthanthatinasquare-orrectangular-shapedexcavationpit.
Therefore,theycanbeconstructedwithoutusingstrutsortie-backanchors,whichreducesconstructioncosts,andprovideslargeworkingarea.
Aftertheconstructionofsheetpiles,thewaterinsidetheex-cavationpitispumpedoutwhichcausesareductioninboththeporewaterpressureandthetotalstressbelowtheexcavationbase.
Additionally,afurtherreductionofthetotalstressappearsduetoexcavationprocesses.
Aseepagefailurebyheaveoccurswhentheporewaterpressuredevelopedbytheseepageowovercomesthetotalpressurebelowtheexcavationbase.
AscanbeseeninFig.
1a,theamountofsoildeformationsaroundthepartitionpanelincreaseswithincreasinghydraulicheaddier-enceH,andconsequently,thesedeformationsleadtothelossofthesoilstabilityand/orthelossofthepartitionpanel.
Forthevericationagainstseepagefailurebyheave,variousmethodshavebeendeveloped,themostwell-knownofwhicharemen-tionedbelow.
Terzaghietal.
determinedfrommodelteststhatheaveoccurswithinadistanceofaboutD/2fromthepartitionpanel(whereDistheembedmentdepthofthepartitionpanel),andthecriti-calsectionpassesthroughthebaseofthepartitionpanel[1,2].
Baumgart&Davidenkomethod,whichhasrstlypresentedinRussianlanguagein1929,considersthemaximumporewaterpressurethatdevelopsatthewalltiponthedownstreamside[3].
Harzastatedthattheexithydraulicgradientonthedownstreamsideisdecisivewithregardtoheave[4].
Marslandidentiedtwotypesofseepagefailurethroughmodeltests:pipingandheave.
Pipingoccursindensesandswhentheexithydraulicgradientadjacenttothepartitionpanelbecomesequaltocriti-calhydraulicgradientofthesoilwhereasheaveoccursinloosesandswhentheporewaterpressureatthebaseofthepartitionpanelbecomesequaltothetotalstressatthesamelevel[5].
Tanaka'sfailureconcept,whichisanextensionofTerzaghi'sDesignChartsforCircular-ShapedSheetedExcavationPitsagainstSeepageFailurebyHeave4212016603method,considersthefrictionalforcesonthesidesofvariousprismaticfailurebodiesadjacenttothesheetpile.
Theprismgivingminimumfactorofsafetyisdecisiveagainstheave[6].
Forthecasethatahorizontalstraticationexistsbetweentheexcavationbaseandthewalltip,variousvericationmethodsagainstheavecanalsobefoundintheliterature[2,7,8].
Thepresentstudyfocusesontheseepagefailurebyheaveinho-mogeneoussoillayersinwhichnohorizontalstraticationispresentbetweentheexcavationbaseandthewalltip.
Fig.
1.
Seepagefailurebyheave:a)developmentofheaveintwo-dimensionalmodeltests,b)vericationagainstheaveThemostcommonlyusedmethodtoevaluatethesafetyagainstheavewasintroducedbyTerzaghietal.
[2].
Inhismethod,limitstateconditionisobtainedbyequatingtheaver-ageporewaterpressureatthebottomoftheheavezonewiththeconstruction-relatedtotalstressatthesamelevel(seeFig.
1b):h·γw+D·γsat=(hav+h+D)·γw(1)Substituting(γsat=γ'+γw)intoEq.
(1)givesD·γ=hav·γw(2)γγw=havD(3)icr=iav(4)whereγsatandγarethesaturatedandsubmergedunitweightsofthesoilrespectively,γwistheunitweightofthewater,havistheaveragehydraulicheadatthebottomoftheheavezone,histheheightofthewaterlevelontheexcavationbase,Distheembedmentlengthofthewallbelowthewaterlevel,asshowninFig.
1b.
Theratiosofhav/Dandγ/γwarecalledtheaveragehydraulicgradientiavandthecriticalhydraulicgradientofthesoilicr,respectively.
Thesafetyagainstheaveisassuredwhenicrisgreaterthaniav.
However,theactualeldconditions,namelythesoilandtheowconditions,maydierfromtheassumedtheoreticalmodel.
Therefore,thestabilitycomputationsareonlyapproximateandshouldbecompensatedusingasafetyfactor(FS=icr/iav).
Asafetyfactorof1.
5isrecommendedagainstseepagefailurebyheave[9].
Butitisoftenuncertainwhetherthepartsofem-beddedwallsbelowtheexcavationbaseare100%waterproofornot.
Insuchcases,ahighersafetyfactorshouldbeusedsinceadefectonthewallendangersthesafetyagainstseepagefailure[10].
Todeterminetheaveragehydraulicgradientiavintheheavezone,thedistributionofporewaterpressurewithinthesoilshouldbeknown.
ThetheoryofseepageowthroughsaturatedsoilsisbasedonLaplace'sequation,whichisobtainedbyin-troducingDarcy'slawintothecontinuityequation.
Commonly,two-dimensionalLaplace'spartialdierentialequationisusedtodeterminethedistributionofporewaterpressurewithinthesoil:kx·2hx2+kz·2hz2=0(5)wherekxandkzarethehydraulicconductivitiesofsoil,h/xandh/zarethehydraulicgradientsinanypointwithinthesoilinhorizontal(x)andvertical(z)directions,respectively.
ThesolutionofEq.
(5)iscommonlyobtainedusingagraphreferredtoasownet.
However,itisnoteasytodrawaownetincomplexowconditions(e.
g.
instratiedsoils),whichismostlythecaseinpracticalseepageproblems.
Furthermore,theexperimentalandnumericalstudiesdemonstratedthattheporewaterpressuresobtainedfromthree-dimensionalmodelscanbetoolargerthanthoseobtainedfromtwo-dimensionalmodels[6,11–13].
Inthepresentstudy,three-dimensionalLaplace'spartialdif-ferentialequationissolvedbyusingtheniteelementsoftwareABAQUS6.
12[14].
Basedontheresultsofthree-dimensionalsteady-stategroundwaterowanalyses,whichalsocorrespondtoaxisymmetricanalyses,designchartsaregiven.
Thechartsenableuserstoevaluatethestabilityagainstheaveofcircular-shapedsheetedexcavationpitsconstructedinhomogeneousisotropicsoillayersoflimitedorunlimitedthicknesses.
2NumericalAnalysesThenumericalmodelsusedinthisstudyconsideronlyaquar-terofcircular-shapedsheetedexcavationpitstakingadvantageofsymmetry.
ThehorizontaldistancefromthewalltotheouterboundariesofthesoilmodelRischosensuchthatitseectontheresultsisnegligiblysmallwhereastheverticaldistancefromthewallbasetothetopsurfaceofthelowersoillayerTisvar-iedbetween0.
0625·Dand8D(seeFig.
2a).
Thethicknessofthelowersoillayerischosensuchthatitseectonthehy-draulicgradientisnegligiblysmall.
Thewaterlevelsontheup-anddownstreamsides,whichareshownwiththeblue-coloredsurfaces,lieonthetopsurfaceoftheuppersoillayerandontheexcavationbase,respectively.
ThesymbolHinFig.
2brep-resentstheverticaldistancebetweenthelevelontheupstreamside,wherethewaterbeginstoowthroughthesoil,andthelevelonthedownstreamside,wherethewaterowsoutofthePeriod.
Polytech.
CivilEng.
422SerdarKoltuk,RagAzzamsoil.
ThesymbolsDandbrepresenttheembedmentlengthofthewallbelowthewaterlevel,andtheradiusoftheexcavationpitrespectively.
Fig.
2.
Numericalmodel:(a)entiremodel;(b)zoomoftheexcavationpitThesheetpilesaremodelledusingagapwithanignorablethickness.
Thesurfacesofthesheetpilesareimpermeablebydefault.
Theverticalboundariesandthebottomboundaryofthesoilmodelsarealsoimpermeable.
Thedeformationsofthemod-elsthatresultfromthegroundwaterow,inotherwordsfromthechangeofeectivestresses,areprevented.
Thesoillay-ersaremodelledwith8-nodebricktrilineardisplacement/porepressureelements(C3D8P).
Themeshisrenednearthewallwheretheowgradientsareconcentrated.
Thenumberofele-mentsinthemodelsischosensuchthatitseectontheresultsisnegligiblysmall.
Accordingly,thenumberofelementsvariesbetweenabout20,000and100,000dependingonthemodelsize.
Thewaterlevelonthedownstreamside,namelytheleveloftheexcavationbaseisconsideredasreferencelevel.
Accordingly,theporepressureboundaryconditionontheupstreamsideissetequaltothepotentialheadH,andonthedownstreamsideissetequaltozero.
3ResultsandDiscussionsInthegivendesigncharts,itisdistinguishedbetweentwoba-siccases:Intherstcase,theuppersoillayerisassumedtobemorepermeablethanthelowersoillayerkupper/klower>1whilethelowerlayerisassumedtobemorepermeablethantheupperlayerkupper/klower1Fig.
4.
Baseoftheassumedthree-dimensionalfailurebodyFig.
3showstheequipotentiallines(surfaces)forcircular-shapedsheetedexcavationpitsconstructedwithinhomogeneoussoillayersoflimited(kupper/klower1)andunlimitedthick-nesses(kupper/klower=1).
Inthecaseofkupper/klower1(seeFig.
3c).
Athree-dimensionalbodywiththewidthsuggestedbyTerza-ghifortwo-dimensionalcasesisconsideredasfailurebody.
Thewhite-coloreddashedlinewithadistanceofD/4fromthewallinFig.
4indicatesthelocationoftheaverageporewaterpressureatthebottomofthefailurebody.
DesignChartsforCircular-ShapedSheetedExcavationPitsagainstSeepageFailurebyHeave4232016603(a)(b)(c)Fig.
5.
Designchartsagainstseepagefailurebyheaveinthecaseofkupper/klower:a)100/1,b)10/1,c)2.
5/1(a)(b)(c)Fig.
6.
Designchartsagainstseepagefailurebyheaveinthecaseofkupper/klower:a)1/2.
5,b)1/10,c)1/100Period.
Polytech.
CivilEng.
424SerdarKoltuk,RagAzzamInFig.
5andFig.
6,thedesignchartsaregiventoevaluatethesafetyagainstheaveofcircular-shapedsheetedexcavationpits.
Inthecharts,theaveragehydraulicgradientsweredeterminedforsixvariousratiosofb/D=0.
25,0.
5,1,2,4,8andeightvariousratiosofT/D=0.
625,0.
125,0.
25,0.
5,1,2,4,8.
Forotherratiosofb/DandT/Dthatlyingbetweenthevaluesgivenabove,iavcanbedeterminedusingalinearinterpolation.
AscanbeseeninFigs.
5and6,thelowersoillayerlosesitseectontheaveragehydraulicgradientdevelopedinthefail-urebodyfortheratiosofT/Daboveacertainvaluedepend-ingontheratioofb/D.
Inthiscase,theuppersoillayercanbeassumedasahomogeneousisotropicsoillayerofunlimitedthickness.
Accordingly,allchartsgivethesamevalueofiavforasameratioofb/D.
Itshouldbementionedthat:1thegivendesignchartsarevalidforH/D=1.
Inordertode-terminetheaveragehydraulicgradientiavfortheotherratiosofH/D,thevaluesofiavobtainedfromthechartsmustbemultipliedbyH/D.
InthecasethatHisequaltozero,thevaluesofiavobtainedfromthechartsmustbemultipliedbytheratioofpotentialdierencetoembedmentdepthH/D.
Anaveragehydraulicgradientthatisobtainedinthiswaycontainsamaximumerrorof±5%;2thegivendesignchartsarevalidforexcavationpits,whichcorrespondtothecaseinFig.
7a.
Whenthewaterlevelonthedownstreamsideliesabovetheexcavationbaseand/orthewaterlevelontheupstreamsideliesabovethegroundsur-face,theaveragehydraulicgradientiavobtainedfromFig.
5orFig.
6mustbemultipliedbyH/H.
ThesymbolsH,HareshowninFig.
7forthevariousconditionsofthewaterlevel;Fig.
7.
Useofthegivenchartsforvariouswaterlevelconditions3Equation(3),icr=γ'/γw,isvalidwhenthegroundwaterlevelonthedownstreamsideliesonorabovetheexcavationbase.
Ifthegroundwaterleveliskeptbelowtheexcavationbaseforsafetyreasons,thecriticalhydraulicgradienticrisgivenas:icr=d·γ+D(γsatγw)D·γw(6)whereγisthemoistureunitweightofsoil,disthedistancebetweentheexcavationbaseandthepumpedgroundwaterlevelonthedownstreamside,andDistheembedmentlengthofthewallbelowthepumpedgroundwaterlevel(seeFigures7aand7c).
Inthefollowing,theuseofthegivendesignchartsisex-plainedthroughtwoexamples.
Forthispurpose,acircular-shapedsheetedexcavationpitwiththedimensionsgiveninFig.
8isexaminedrst.
Theexcavationpitisconstructedwithinasiltynesand,whichisunderlainbyagravellysandwithapermeabilitycoe-cientof4.
5x104m/s,inanurbanarea.
Thesiltynesandhasapermeabilitycoecientof5x106m/s.
Themoistureandsatu-ratedunitweightsofthesiltynesandare19and19.
5kN/m3re-spectively.
Theunitweightofwaterisassumedtobe10kN/m3.
FromFig.
8,theratiosofH/D,b/DandT/Daredeter-minedas8/4=2,4/4=1,2/4=0.
5respectively.
Theratioofkupper/klowerisequalto1/90,sothattheaveragehydraulicgra-dientiavisdeterminedas0.
74fromFig.
6c.
ButthisvalueisvalidforH/D=1,sothatitmustbemultipliedbyH/D=2.
Finally,iaviscalculatedas0.
74x2=1.
48.
ThecriticalhydraulicgradientiscalculatedbyEq.
(6):icr=0.
5*19+4*(19.
510)4*10=1.
19Thenthesafetyfactoriscalculatedas:FS=icriav=1.
191.
48=0.
8Fig.
8.
Amodelexampletouseofthegivendesignchartsforcircular-shapedexcavationpitsinurbanareasDesignChartsforCircular-ShapedSheetedExcavationPitsagainstSeepageFailurebyHeave4252016603Inthesecondexample,acircular-shapedsheetedexcavationpitwiththedimensionsgiveninFig.
9isstudied.
Theexca-vationpitisconstructedwithinagravelysand,whichisun-derlainbyacohesivesoilwithapermeabilitycoecientof1.
25x108m/s,inopenwater.
Thegravelysandhasaperme-abilitycoecientof2x106m/sandasaturatedunitweightof20kN/m3.
Theunitweightofwaterisassumedtobe10kN/m3.
Fig.
9.
Amodelexampletouseofthegivendesignchartsforcircular-shapedexcavationpitsinopenwaterFromFig.
9,theratiosofH/D,b/DandT/Daredeter-minedas2/4=0.
5,12/4=3,8/4=2,respectively.
Theratioofkupper/klowerisequalto160,sothattheaveragehydraulicgradientiavisdeterminedas0.
45fromFig.
5a.
ButthisvalueisvalidforH/D=1,sothatitmustbemultipliedbyH/D=0.
5.
Furthermore,thevaluesobtainedfromthegivendesignchartsarevalidforexcavationpits,whichcorrespondtothecaseinFig.
7a.
However,thewaterlevelconditionsinthisexamplecorrespondtothecaseinFig.
7d,sothatthedeterminedvaluemustalsobemultipliedbyH/H=4.
2/2=2.
1.
Finally,iaviscalculatedas0.
45x0.
5x2.
1=0.
47.
ThecriticalhydraulicgradientiscalculatedbyEq.
(3):icr=γsatγwγw=201010=1Thenthesafetyfactoriscalculatedas:FS=icriav=10.
47=2.
14ConclusionsTheaveragehydraulicgradientsonthedownstreamsidesofcircular-shapedsheetedexcavationpitswithvariousdimen-sionsaredetermined,andtheresultsarepresentedintheformofcharts.
Utilizingthegivencharts,thesafetyfactoragainstheaveofcircular-shapedsheetedexcavationpits,whicharecon-structedwithinhomogeneousisotropicsoillayersoflimitedorunlimitedthicknessesinopenwaterorurbanareas,canbeeasilyandquicklyevaluated.
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