软土地基上分期施工的路堤沉降预测方法1

附录（英文文献及译文）SettlementpredictionofembankmentswithstageconstructiononsoftgroundLIUSong-yu（InstituteofGeotechnicalEngineering,SoutheastUniversity,Nanjing210096,China）　JINGFei（InstituteofGeotechnicalEngineering,SoutheastUniversity,Nanjing210096,China）Abstract:Themagnitudeandrateofthesettlementarethekeyelementssubjectedtodesignanalysisofembankmentsonsoftground.TheobservationalInstituteofGeotechnicalEngineering,SoutheastUniversity,Nanjing210096,Chinamethodsbasedonfieldmeasurementhaveindicatedthepromisingresultsandbecomeeffectivemethodstopredictthefinalsettlement,whiletheuncertaintiesofparametersandtheorieslimitsignificantlytheaccuracyofsettlementestimation.ThispaperpresentsanobservationalmethodtopredictthesettlementperformanceofembankmentswithstageconstructiononsoftgroundbasedonAsaokamethod.Thecasestudiesshowtheaccordanceofthepredictingresultswiththefieldmeasureddata.ItisalsogivenfromthecasestudythatthevalueofEu/Curatiorangesfrom50to100forJiangsuMarineclayanditsactualcoefficientofconsolidationisalmostoneorderofmagnitudelargerthanthelaboratorydata.Keywords:settlement,embankment,observationalmethod,stageconstruction,JiangsuMarineclay0.IntroductionSettlementandstabilityaretwoprimaryconsiderationssystematicallyrelatedtothedesignofanembankmentonsoftground.Thetoolsavailableforthestabilityevaluationseemtobesatisfactory.Thekeyelementoflongtermbehavioroftheembankmentroutinelysubjectedtodesignanalysisisthesettlement.Inotherwords,thesettlementanalysisisthemostappropriateapproachtotheembankmentanalysis.Thesettlementsofembankmentsonsoftclaysresultfromtheconsolidationandthelateralflowundertheembankments.Manyresearcheshavebeenmadeonperformanceofembankmentsonsoftground.Althoughmanyexperienceshaveshownthepracticalvalueofthetheoryforestimatingsettlementsandsettlementsrates,theyalsoillustratedsomeoftheproblemsinvolvedinmaking12 accuratepredictionofthesettlement.Duncan(1993)andOlson(1998)analyzedtheuncertaintiescausingtheshortcomingsinthecurrentstateoftheartforsettlementpredictionrespectively.Theseuncertaintiessometimesmakeitdifficultyorimpossibletoestimatethemagnitudeandrateofsettlementforembankments.Althoughthenumericalanalysismaybepossibletoimprovetheaccuracy,thesoilmodelsmayinvolvemanyparametersthatcannotbedeterminedeconomically.However,theevolutionofnumericalmethodswithcomputermayresultinsimplermodelsandcompletecodesthatareincreasinglybecomingavailable.Itisdesirablethereforetodevelopobservationalmethodsbaseduponwhichthesettlementcanbeestimatedoncesufficientdatahasbeenrecorded.Manyresearchersdevelopedthesettlementpredictionmethodsonfieldmeasurementobservation,whichhaveindicatedpromisingresultsandbecomeanacceptedmethodtoestimatefinalsettlementsandratesofsettlements.Stageconstructionisatypicalprocedureforembankmentsonthesoftground.Withacertainperiodofconsolidationateverystageconstruction,thesafetyfactoroftheembankmentcanbegenerallyraisedandthepostconstructionsettlementmaybereduced.Thesettlement-timecurveduringstageconstructionmaybemorecomplicatedthanitiswithinstantaneousloading.Theperiodforprimaryconsolidationatadefinitefinalloadwithstageconstructionmaybeincreasedsignificantly,inspiteofthefactthatthepostconstructionsettlementcanbereduced.Inordertospeeduptherateofsettlementandminimizethepostconstructionsecondarysettlementofsoftclays,surchargeisoftenusedinpractice,whichcanbetakenasatypeofstageconstructionwithtemporaryloadingandunloadingstages.Problemsrelatedtothesettlementanalysisofstageconstructionforembankmentsonsoftclaysareofthefollowingtypes:(1)Predictionofthedeformationbehaviorofstageconstructionfromtheresultsofboringsandtests.(2)Predictionofthefinalsettlementatpermanentloadfromthebehaviorofthefirststageconstruction.(3)Predictionofthepostconstructionsettlementatthepermanentloadandcorrespondingtimeofsurchargeremovedfromthebehaviorofthesurcharge.Thefirstoftheseproblemsisheavilydependentonthetheory,whichisnecessaryindesign.Theothertwopredictionsrequireempiricalratherthantheoreticalmethodsbecausetheyarebasedonobservationaldata.Inanycase,thefactthatthesecondandthirdpredictionsarederivedfromfieldobservationsmakesthemmorereliablethanthetheoreticalpredictions.Leroueiletalrevealedtheeffectivestresspathandanalyzedtherelationshipbetween12 verticalsettlementandlateraldisplacementduringstageconstruction.StamatopoulosandKotziasdevelopedamethodtodeterminethefinalsettlementatpermanentloadfromthebehaviorofsurcharge,butitisbasedontheelastictheoryanddifficulttocalculatetherateofthesettlement.Thehyperbolicmethodisbasedonthetotalload-settlementrelationshiptopredictthefinalsettlement,whichisnotsensitivetothenatureoftheinitialloadingcondition.ThispaperpresentedamethodforthepredictionofthefinalsettlementatpermanentloadfromthebehaviorofthefirststageconstructionbasedontheAsaokamethod.1.StageobservationalmethodAsaokaproposedan‘observationalprocedure’toestimatethefinalsettlementandin2situcoefficientofconsolidationfromthefieldobservationaldata.Thismethodisbecomingincreasingpopularbecauseofitssimplicityandeffectivity.ThemethodisbasedonthefactthatonedimensionalconsolidationsettlementsS0,S1,S2,…，Sjattimes0，t，2t，…，jtcanbeexpressedasafirstorderapproximationbySj=+Sj-1(1)whichrepresentsastraightlineinaSjvsSj-1plot,whereistheinterceptandistheslopeoftheline.Whentheultimatesettlementhasbeenreached:Sj=Sj-1=Sf,therefore,theultimatesettlementSfcanbegivenbySf=(2)andln=-(bothtopandbottomdrainage)(3)　ln=-(topdrainage)(4)TheconstanthasbeensuggestedbyMagnanandDeroytoberelatedtothecoefficientofconsolidationCvasfollows:forhorizontalradialdrainageonlyCh=(5)forverticaldrainageonlyCv=(6)12 whereDe,Harethedrainagepathlengthrespectively.AsaokamethodalsostatedthatthestraightlineinSj-Sj-1spacewouldmovedupinthecaseofmulti-stagedloading,moreover,theshiftedlinesbecomealmostparalleltotheinitialwhenthesettlementisrelativelysmallcomparedtothethicknessofclaylayer.However,itisnotdiscussedandprovidedhowtodeterminetheshiftdistancefromthelineoffirststagetothelineofthenextstage.Intheexpression(1),whenj=0thatis:t=0andS(t=0)=S0,wheretcanbetakenas0fromanytimeafterloadingworks.Iftissetas0attheexacttimeoncetheloadisexerted,then,Sj-1becomes0,therefore,S0==immediatesettlementSe.(7)　ThismeansthatAsaokamethodcanbeextendedtoobtaintheconstructionsettlement,whichequalstotheinterceptofthelinerlineinthespaceSj-Sj-1,wheret=0issetjustafterloading.Moreover,thisimmediatesettlementcontributestheshiftdistanceoftheparallellinesduringstageconstruction.Infact,fromthederivationoftheAsaokamethod,thesettlementofsoillayerscanbeexpressedasSt=(8)and(9)whereTandFaretwounknownfunctionoftime.Withtheverticaldrainageboundaryconditionsandatthegroundsurface,=T=(t,z=0).Ift=0,=(t=0,z=0)==initialelasticstrain.Therefore,S(t=0)=S0givestheimmediatesettlementSe,whichcanalsobeestimatedfromtheelasticmethodbytheequation:S0=Se=(10)ItisclearlyshownthattheAsaokamethodhasbeenextendedtopredictthesettlementofembankmentswithstageconstruction.Inotherwords,thebehaviorofnextstageconstructioncanbepredictedwiththe,fromthelaststageconstruction.Themorethepreviousstageswithsettlementmeasurement,thehighertheaccuracyofnextstageprediction.Thestageobservationalmethodincludesfollowingsteps:12 (1)Sketchobservedtimesettlementcurve.(2)Chooseatimeintervalt,whichusuallyrangesfrom10to100days,readthesettlementsSjfromthecurveattimestj(=tj,j=1,2,3,…).(3)PlotthesettlementsSj,Sj-1inacoordinatesystemwithaxisSj,Sj-1originatedfrom0.(4)Fittheplottedpointsbyastraightline,ofwhichcorrespondingslopeisreadas.TheinterceptattheSjaxisgives,whilethepointofintersectionwiththe45oline,givesthefinalconsolidationsettlementofthefirststage.(5)FromtheofthefirststageconstructiontodeterminetheundrainedmodulusEubyinverseanalysis(10).(6)DeterminethenextstageconstructionsettlementwiththeaboveknownEu(10),thusresultingintheshiftdistanceofline.(7)AssumetheCVremainsconstantduringstageconstructionandsettlementissmallcomparedwiththethicknessofsoftsoils,thismakesthelineofnextstageconstructionparalleltothefirststagewiththeslope.(8)Predictingthefinalsettlementofnextstageconstructionfromtheintersectionoftheshiftedlinewiththe45oline.(9)EstimatetheChandCVfromthevalueofwiththeequation(5)or(6).2.Casestudy2.1　SiteandprojectdescriptionSectionAofLianxuhighwayisa31kmlonghighstandardexpresswayconnectingtheportcityLianyugangtothenationalhighwaysystemofChina.ItwasbegantoconstructionfromDec.1999.Thereare104bridgesorculvertsorpasswaysinthis31kmlongsectiondesignedtoconnectembankments.Thebottomwidthoftheembankmentis40m,whiletheheightofembankmentchangesfrom3to7m.Basedonthedesigncode,thedifferentialsettlementsbetweenembankmentsandstructureshavetobecontrolledlessthan10cm.Postconstructionsettlementsofembankmentshavetobelessthan30cmduringthepostconstructionperiodof15years.Itisclearthatthemagnitudeandratesoftheembankmentsettlementsaretheextremelyimportantproblemtomaketheprojectreliableandeconomical.2.2　SubsurfaceconditionsThesectionAofLianxuhighwaypassesoverthemarinedepositplain.Thetypicalsubsoil12 profileconsistsof0to3mthinkuppercrustofstiffclayunderlainbya5.6to13mthicksoftclay,whichisnamedJiangsuMarineclay.Blowthissoftclay,liesalternatinglayersofstiffclayanddensesandextendingtobadrockwiththevariedthicknessof10to20m.2.3　SoilimprovementandembankmentconstructionDryJetMixingandstageconstructionwithsandblankethavebeendesignedtoreducethetotalsettlementandpostconstructionsettlement.TheembankmentfilledwithresidualclayfromDec.1999.Afterthefirststageconstructionof2.5～3.5mhigh,about6monthswereleftalongforsoilconsolidation.Thesettlementsareobservedregularlybysettlementplates.Duringtheperiodofthefirststageconsolidation,someobservationalsettlementsarefoundtobelargerthanthecorrespondingdesignedtotalsettlement.Itisnecessarytore-predictthebehavioroftheembankmentsbasedonthesettlementobservationalresultsofthefirststageconstruction,inordertomodifytheoriginaldesignandmakethereliabledecisionfornextstageconstruction.2.4　PredictionofthefinalsettlementThetypicalfillheightswithtimeandmeasuredgroundsurfacesettlementsatthecenterofembankmentswithsandblanketsareshown.Itcanbeseenthatthesettlementcurvedropssignificantlybetweenthefirststageandsecondstageconstruction.Thefinalsettlementsofthesecondstageconstructionarepredictedfromthefirststageobservationaldatabythestageobservationalmethod.Itindicatesthatthepredictedsettlementsarebasicallyconsistentwiththemeasuredsettlement.Table1alsoshowsthebakeanalyzedvaluesofundrainedelasticmodulusEuandcoefficientofconsolidationCvbasedonthefirststageobservationaldata,givingrangesofEu/curatioof50～100andCV(field)/CV(lab)ratioof6～12.ItseemstobeinthelowerrangeoftheEu/curatioforJiangsuMarineclaycomparedwiththeratioof70～253forBangkokclayandotherclaysexistinginthedifferentliterature.Theactualcoefficientofconsolidationappearsoneorderofmagnitudelargerthanthelaboratoryvalue,thisresultinginthefasterrateofmeasuredsettlement.3.ConclusionsOnthebasisoftheoreticalderivationofAsaokamethodandcasestudyofJiangsuMarineclay,thispaperpresentedaStageObservationalMethodforsettlementpredictionofembankmentsonsoftgroundwithstageconstruction.Thefollowingconclusionscanbegiven:(1)Consideringtheavailableobservationalmethodsforultimatesettlementprediction,theAsaokamethodmaybesuccessfullyextendedtomakethesettlementpredictionforstageconstructionembankments.12 (2)TheimmediatesettlementSeisverifiedtobeequaltotheinterceptintheSjandSj-1spaceoftheAsaokamethod,therefore,theundrainedmodulusofsoftgroundcanbeobtainedfromthefirststageconstructionmeasurements,thiscontributingtothemoreaccurateestimationofimmediatesettlementofthenextstageconstruction.(3)Assumingtheactualcoefficientofconsolidationandthethicknessofthesoftgroundremainconstantduringstageconstruction,theshiftingdistancesoftheparallellineswiththeslopeofisequaledtotheimmediatesettlements,whichcanbecalculatedwiththeinversemodulusfromthefirst(last)stageconstruction.(4)Thedistinctadvantageoftherecommendedmethodisthatthevaluesofundrainedmodulusandcoefficientofconsolidationfornextstageconstructionareinverselyanalyzedfromthefirst(last)stageconstruction.(5)Fromthecasestudy,thevalueofEu/curatiorangesfrom50to100forJiangsuMarineclay,whiletheactualcoefficientofconsolidationisalmostoneorderofmagnitudelargerthanthelaboratorydata.AcknowledgementTheresearchissponsoredbyDoctoralProgramFundsofEducationMinistryofChina.Thesupportisgratefulacknowledged.12 软土地基上分期施工的路堤沉降预测方法LIUSong-yu和JINGFei摘要：沉降量和沉降速率控制是软土地基上路堤工程设计的关键问题，由于固结理论的局限性和参数的不确定性，理论预测的精度较低，而基于现场实测数据的观测法则显示出了较高的精度。本文在Asaoka观测法的基础上,形成了一种软土路基上分期施工时路堤沉降预测的方法，结合江苏海相软土上的高速公路工程进行了沉降预测分析。关键词：沉降,路堤,观测法,分期施工,江苏海相软土0.简介对于软土地基上的路堤设计来说，沉降和稳定性是需要考虑的两个关键性因素。现有的评估路堤稳定性的方法基本上能满足设计要求。因此，沉降便成了设计分析路堤长久性的关键参数。换句话说，对沉降的分析是路堤分析的最合适的方法。软土地基上路堤的沉降主要是由于路堤的固结和侧向流动所引起的。对于软土地基上的路堤，人们做了很多这方面的研究。很多实验已经得出了对于预估沉降量和沉降率的实际值的理论，同时，实验也解释了一些涉及精确预估沉降量的问题。Duncan于1993年、Olson于1998年分别对预估沉降量在现有条件下所引起缺陷的不确定性因素进行了分析。这些不确定性因素使得估算路堤沉降量和沉降速率有时特别困难甚至是无法进行估算。尽管数值分析法能提高计算的精确性，但是土的本构模型涉及到很多不能被确定的参数。然而，随着数值分析法的计算化，这使得我们可以获得更多的土的本构模型和相应的程序代码，从而使计算得以简化得以更精确。因此，人们非常渴望发展这样一种观测方法——只要记录足够的沉降参数，通过计算机就能得到精确的沉降值。很多研究人员在现场观测的基础上发展了沉降预估法。该方法不仅能够得到精确解，还被认可为估算最终沉降量和沉降速率的方法。分期施工对于软土地基上的路堤来说是一个特殊的程序。随着每一个施工期路堤的固结，路堤的安全性会逐渐提高，竣工后的沉降量也会减少。施工时期的沉降—时间（s-t）曲线可能会比瞬时荷载的曲线更为复杂。尽管竣工后的沉降量会减少，但是施工时期路堤在稳定的最终荷载作用下的初始的固结期会明显增加。为了加快沉降速率，减小软土层的竣工后的二次沉降，实际中我们经常采用超载，也就是在竣工时期加临时荷载，然后卸载。对于软土层上路堤的施工期的沉降分析的问题有如下几种：12 (1)预估施工时期由于钻孔测试而引起的变形。(2)预估在永久荷载作用下由于第一施工期所引起的最终沉降。(3)预估在永久荷载和相应的超载下由于超载所引起的竣工后的沉降。第一个问题主要依赖于设计时的理论。其余两个问题需要以经验为根据而不是靠理论方法。因为它们是靠观测的数据而得来的。在任何情况下，第二个和第三个从现场观测到的预估沉降量比理论算得的沉降量都可靠。Leroueiletal提出了有效应力路径，分析了施工时期竖向沉降和横向沉降之间的关系。Stamatopoulos和Kotzias发展了在永久荷载下确定最终沉降的方法，但这种方法是基于弹性理论的，而且它很难用来计算沉降率。而双曲线模型的方法又是依据总的荷载—沉降关系来预估最终沉降量，这种方法对于在初始天然荷载下的沉降很不灵敏。本文在Asaoka观测法的基础上，提出了一种软土地基上分期施工时在永久荷载作用下的预估最终沉降的方法。1.分期观测法Asaoka建议采取一个“观测过程”，利用现场观测的数据来估算最终沉降量和原位固结系数。这种方法因为其简单性和有效性而变得越来越受欢迎。该方法是基于单向固结沉降量S0,S1,S2,……，Sj在时间0，t，2t，……，jt时能被作为第一近似值，公式如下：Sj=+Sj-1(1)在时间Sj-Sj-1图里它代表了一条直线。这里是直线的截距，是直线的倾角。当达到最终沉降时：Sj=Sj-1=Sf，因此，最终沉降Sf可以由如下公式求得：Sf=(2)ln=-（两面排水时）(3)ln=-（顶部排水时）(4)常数和固结系数CV有关：Magnan和Deroy认为对于横向排水：12 Ch=(5)对于竖向排水：Cv=(6)这里De，H分别是排水路径的长度。Asaoka观测法也表明，Sj-Sj-1图中的直线在多级荷载作用下会改变位置，而且，当沉降相对较小而粘土层相对较厚时，移动的直线基本上和初始直线是平行的。但是，该方法并没有讨论给出如何确定从一个直线段到下一个直线段的移动距离。在表达式(1)中，当j=0时，t=0，S(t=0)=S0,这里t是荷载的工作时间。如果在荷载卸载的瞬间将t设置为0，那么Sj-1就变为0。因此S0==瞬时沉降Se(7)这就意味着Asaoka观测法能被扩展为求固结沉降，其值等于Sj-Sj-1图里的直线的截距，这里t=0是在荷载加上之后。此外，这种瞬时沉降也是分期施工期平行线的移动距离。事实上，根据Asaoka观测法的最初土层的沉降值能由下式求得：St=(8)(9)这里T和F是两个未知的时间系数。在竖向排水的底部和土层的顶部，=T=(t,z=0)。如果t=0，那么=(t=0,z=0)==初始弹性应变。因此，S(t=0)=S0就能得到瞬时沉降Se。Se也能由如下弹性原理的公式求解：S0=Se=(10)上式清楚地表明Asaoka观测法能够被扩展到估算施工期路堤的沉降。也就是说，下一个施工期的路堤的状况可由上一个施工期的，进行估算。上一个施工期的路堤的沉降测量值越多，下一个施工期的估算值就越精确。分期观测法包括以下几个步骤：12 (1)观察时间—沉降曲线的草图(2)选择时间间隔t，通常是10到100天之间。在tj时刻读取曲线上的沉降Sj。(3)在相应的坐标系里以Sj-Sj-1为轴，从0开始标出沉降Sj-Sj-1的点。(4)用直线将标出的点连起来，直线相应的倾角是，在Sj轴上的截距为，与45o直线的交点是第一工期的最后固结沉降量。(5)利用第一工期的通过(10)式反求不排水压缩模量。(6)通过已知的Eu来确定下一工期的路堤沉降，从而确定直线段的移动距离。(7)假设CV在分期施工时是连续的，并且假设相对于软土的厚度来说路堤沉降非常小，这可以保证下一工期的直线段平行于第一施工期的直线段。(8)从与45o斜线的交点预估下一施工期的最后沉降量。(9)利用的值通过式(5)、(6)分别估算Ch和CV。2.实例研究2.1工程地址和工程概述连云港—徐州高速公路的A段是一段长31km的高速公路，它把港口城市连云港和国家高速公路网连在一起。该工程于1999年12月开始动工。这其中包括104座桥和涵洞。该高速公路路堤的底部宽40m，高从3m到7m不等。根据设计标准，路堤和结构的沉降值必须控制在10cm以内。竣工后的路堤沉降在建成后的15年里必须小于30cm。很明显，路堤的沉降量和沉降速率对工程的可靠性和经济性是至关重要的。2.2地面下的土质条件连徐高速公路的A段要经过海相沉积平原。该平原的地基土剖面图包括0到3m厚的上层硬表层的硬粘土，其下是5.6m到13m厚的软粘土，别名江苏海相软土。软粘土下是交替间隔的硬粘土和稠粘土，厚度从10m到20m，它们一直延伸到基岩。2.3土层的改良和路堤的施工我们设计采用干射搅拌法和砂垫层分期施工法来减少总的沉降和竣工后的沉降。从1999年12月开始，路堤用残积粘土填充，在第一期施工到2.5—3.5m12 高后，让土自然固结6个月。固结沉降期间通过沉降板定期观测路堤的沉降，这一期间，一些观测到的沉降比相应的设计总沉降还大。为了修改原先的设计，使得下一施工期的方案更可靠，我们有必要再次预估基于第一施工期沉降观测结果的路堤的性状。2.4预估最终沉降从路堤填充高度和对路堤中心处砂垫层的地表沉降测试结果中，我们发现第一期和第二期的沉降曲线下降非常陡。第二施工期后的最后沉降可以由分期观测法通过第一期的观测数据来预测。这表明预估沉降量和测试沉降量基本上是相符的。曲线同时也表明基于第一期观测数据的不排水弹性模量Eu和CV的有效性。Eu/cu的比率为50—100，而CV（现场）/CV（室内）的比率为6—12。这也似乎表明江苏海相粘土Eu/cu在低范围内的比率符合。Bangkok粘土和其它已经存在的粘土的比率为70—253（也就是计算数据是有效的），而实际的固结系数值大于试验测得的值，这会导致更快速率的沉降。3.结论基于Asaoka观测法的理论来源，结合对江苏海相粘土的研究，本文发展了一种软土路基上分期施工时路堤沉降预测的方法。结论如下：(1)对比所有的最终沉降预测的观测方法，Asaoka观测法能够成功地扩展到预测分期施工路堤的沉降。(2)在根据Asaoka观测法绘制的Sj-和Sj-1图中，瞬时沉降Se被证明是等于截距的。因此，在第一期观测中，我们能够得到软土层的不排水压缩模量。它有助于我们更精确地估算下一期的瞬时沉降。(3)假定实际的固结系数和土层厚度在分期施工期仍然保持连续，倾角的平行线段的移动距离等于第一分期由公式反求的瞬时沉降值。(4)本文所介绍的这种方法的优点是下一个分期的不排水压缩模量的值和固结系数的值可由第一分期的计算分析获得。(5)实例研究表明，江苏海相软土的Eu/cu的比率从50到100不等，而实际的固结系数几乎都比实验室试验所得的数据大。12