The Influence Depth of a Highway Embankment

The Influence Depth of a Highway Embankment

1Ph.D.Scholar(Geotechnical),DepartmentofCivilEngineering,BangladeshUniversityofEngineeringand Technology(BUET),Dhaka–1000,Bangladesh.

Sr.GeotechnicalEngineer,SoilInvestigationDivision,BangladeshHighwayResearchLaboratory(BRRL), Mirpur-1216,Dhaka,Bangladesh.

Email:sharif.geo.2006@gmail.com

Abstract The Axle Pressure and the Consolidation Pressure decreases with the height of highway embankmentandthedepthofsubsoil.Thisreductionof pressure depends on the height and width of the embankment.Thisdepthisthesignificantstressedzone at which the pressure reduced to 0.2 or 20%. This significantstressedzoneisdefinedastheinfluenceofa Highwayembankment.Theaxlepressureisreducedto 7% for embankment height 1-3m and to 0.7% for embankment height 4-12m at the bottom level of Highway Embankment. This observation implies that, the portion of axle pressure transferred to subsoil underlying the embankment is not significant for EquivalentStandardAxleLoad(ESAL)factorupto30.

The 70% consolidation to be occurred after the construction of the surface layer of pavement. Considering this ratio of post construction settlement, 70% consolidation pressure (Δσ70) is used in this analysis. The magnitude of influence depth or SignificantStressedZone(Ds hasbeenobtainedkeeping the range of crest width (at the top level of the embankment) from 5m to 50m and for the range of embankment height from 1.0m to 12.0m considering 70%ofconsolidationpressure(Δσ70).

Significant stressed zones (Ds) for 70% embankment pressure (Δσ70) are found as 2-6.2He for embankment topwidth5-50m.

Key Words: Consolidation pressure, Equivalent StandardAxleLoad(ESAL),HighwayEmbankment,HS 20-44,SignificantStressedZone,StressDistribution

1. INTRODUCTION

InBangladesh,itiscommonpracticetoconstruct highwayembankments on soft or very loosenatural subsoil that extends to vast depths. The assessment for bearing capacity and settlement of highway embankment is subjected to the depth of stressed zoneextendedintotheunderlyingpoorsubsoil.

The depth of subsoil (as a multiplication of embankment height) to be evaluated up to which depth the transferred stresses or pressure is significant.Toobtainthesignificantinfluencedepthor significant stressed zone a research study on stress distributiontosubsoilbelowaHighwayembankment

hasbeencarriedout.Inthisstudy,simplifiedratiosof embankment height to depth or substantial stressed zoneinsidesubsoilaredeterminedforvariousdepths andwidthsofembankment.

2. TRAFFIC LOAD ON SUBSOIL

Traffic induced stress on Highway Embankment is duetoaxleloadoftrafficvehicle.Stressesonsubsoil underlying Highway embankment are transferred portion of axle load and the self-weight of embankment.

AsperBangladeshRoadMasterPlan[1],Standard axle loads used for calculating Equivalent Standard Axle Load (ESAL) are front (steering) axle – 65 kN; rearsingleaxle–80kN;andtandemaxles–147kN. Aspertrafficsurveyindifferentnationalhighwaysin BangladeshESALfordualtyresingleaxleis33.This value is much greater than the allowable ESAL=4.8 (forheavytruck).

EquivalentStandardAxleLoad, ESAL= Wa / Wr or, Wa =ESAL(Wr) (1) where, Wa=Actual Axle Load and Wr=Reference axle load(80kN).

3. STRESS DISTRIBUTION

3.1 Distribution of Axle Load

The simplest approach of stress distribution at a depth is 2:1 (vertical to horizontal). This empirical methodisusedfortyreloadinginthisstusy(Fig-1) [2].

Duetospreadingofthesameverticalloadovera much larger area at depth, the unit stress reduced. Stressontheplanatdepthz,

∆��= ( )( ) (2)

According to Fig-1, pressure on tyre to pavement contactarea, �� = (3)

Andtheconcentratedloadonpavement,

������=(��/2)����=��/2 (4) where,Wa=AxleLoadandB,L=WidthandLengthof Tyretopavementcontactareasuccessively.

��= ���� ����

Fig-1The2V:1HMethodforVerticalStressIncreaseas afunctionofsoildepthbelowtyre[2].

EmbankmentPressureatbottomlevelof embankmentis��=����whichisconsideredtobe distributedasperFig-3[3]. ConsolidationPressureatHsdepthbelowcenterof embankment[3], ����=(��+��)(��)(7) where,Hs=DepthofSubsoilunderlyingembankment, γe=BulkUnitweightofembankmentfill,Bt=Widthof embankmenttop. And,inequation(7)–thedistancebetweenstressedpointandendof embankmenttop=��/2 ��=������ +2�� �� −������ �� ��=������ �� and,��+��=������ +2�� ��

Now,forConsolidationPressureatHsdepthbelow theendofembankmenttop(replacingby0), ����=�� �� �� (8)

Fig-2

Theintersectionofpressureinterface. Pressuretransferredtoembankmentfillbelow pavement,duetoWheelLoad, ∆��=()() (5) Consideringinterface/overlapofpressurefrom twowheelinanaxle(showninFig-2), ∆��=()()=()()(6) where, ��=HeightofEmbankmentfillabovenaturalground level Theratioofstressatthosetwolevelis∆��/��.This ratioindicatesthepercentageofloadwhich transferredtoHedepth. 3.2.DistributionofEmbankmentPressure

Fig-3StressReductionduetoembankmentloading considering1V:2HSideslope[3]

AverageConsolidationPressureatHsdepthbelowthe embankment, ∆��= 1 2(∆��+∆��) (9) where,

����=ConsolidationPressureatHsdepthbelowcenter ofembankmentand����=ConsolidationPressureatHs depthbelowtheendofembankmenttop.

InBangladeshtherangeofwidthofcarriageway is3.0mto22.0m[4].Therangeofcrestwidth includingshoulder,vergeandmedianis5mto30m. For4Laneandexpresswaytherangeofcrestwidth maybe30mto40m.Inthisstudytherangeofcrest width(attoplevelofembankment)iskeptbetween 5mand50m.Therangeofembankmentheight1mto 12mandsideslopeofembankment1V:2Haretaken foranalysis.

4.SIGNIFICANTSTRESSEDZONEOFHIGHWAY EMBANKMENT

Asrecommendedby[5]thedepthof20%ofthe foundationcontactpressureissignificantstressed zoneforsettlementanalysistermedasthesignificant depthDs.Terzaghi'ssuggestionwasbasedonhis findingthatdirectstressesareregardedasnegligible iftheyaccountforlessthan20%oftheappliedstress.

4.1SignificantStressedZoneforAxlePressure

ForHS20-44TruckandTandem,thedesign contactareaoftyrefordualtyresingleaxleisasingle rectangleofwidth,B=510mmandlength,L=250mm (Fig-4).

Fordualtyretandemaxleisasinglethedesign contactareaisdoublerectangleofwidth,B=510mm andlength,L=500mm.ThesevaluesofBandLare usedincurrentanalysisofstressdistribution.

Thevaluesofthestresstransferratio∆��/��are calculatedfordifferentvalueofHeandHs.Throughthe valuesof∆��/��theamountofloadtransferredtoHs depthisassessed.

Thechangesof∆��/��withHefordifferentvalueof ESALarepresentedinChart-1fordualtyresingleaxle. Similarly,thechangesof∆��/��withHefordifferent valueofESALarepresentedinChart-2fordualtyre tandemaxle.∆isindependentofESAL.

Simplifiedmaximumratiosoftransferredloadto subsoilorthemaximumvaluesof∆��/��aretabulated inTable1.0fordifferentrangeofembankmentheight (He)accordingtoChart-1andChart-2.

Fig-4TyrecontactareaofHS20-44[6][7]

ESAL=1

ESAL=10 ESAL=30

Chart-2:HeVsσz/σ0forHe=1mto12m forDualTandemSingleAxle

AsobservedinTable1,accordingtocurrentstudy, maximum12%ofaxlepressurefortherangeof embankmentheight1-3mandmaximum1.5%ofaxle pressurefortherangeofembankmentheight4-12m istobetransferredtosubsoilunderlyingthehighway embankment.

Hence,accordingtoTerzaghi'srecommendation [5]transferofaxleloadtosubsoilisnotsignificantfor thefoundationdeignofhighwayembankment.

4.2SignificantStressedZoneforEmbankment Pressure

Consolidationsettlementofthesubsoilunderlying thehighwayembankmentwilltakeplacefor embankmentpressureorself-weightproduced pressure.ConsolidationPressure(Δσ)isderivedfrom onlyEmbankmentPressure(qe).

Chart-3:Settlement-timecurve[8]

Thetransferofembankmentpressureissignificantfor assessmentofconsolidationsettlement.

Theresidualportionofconsolidationsettlementis tobeconsideringinassessmentofsettlementrisk. Accordingtoobservedtime-settlementcurvesunder surchargeloadispresentedinChart-3andinTable2 [8].

Table2'stime-settlementdataindicatesthat, followingthecompletionofembankmentfilling,at least30%ofthetotalconsolidationwilloccurduring thenexttwoyearsofconstruction.

Sothat,afterconstruction70%consolidationtobe consideredasresidualsettlement.Forthosetwo

references,significantstressedzonesforHighway Embankmentareanalyzedaccounting70% ConsolidationPressure(����)atHsdepthdueselfweightinducedpressureofembankment.

Now,70%ConsolidationPressureatHsdepth (kN/m2), ����=0.7× 1 2(∆��+∆��)=0.35(∆��+∆��)(10)

Thevaluesofthestresstransferratio����/qeare calculatedfordifferentvalueofHe,BtandHs.Changeof ����/qefordifferentDepthRatio(Hs/He)are presentedinChart-4toChart-9forrangeofBt=5mto 50mandrangeofHe=1mto12m.DepthRatio(Hs/He) at����/qe=0.20istermedasforwidthof EmbankmentTop,Bt=5mto50mandheightof embankment,He=1mto12mispresentedinTable3 andinChart-10.

DepthRatio(Hs/He)at����/qe=0.20forwidthof EmbankmentTop,Bt=5mto50mandheightof embankment,He=1mto12mispresentedalternately inChart-11.

AccordingtopowertrendlineofChart-11,Depth Ratio(Hs/He)forΔσ50/qe=0.20istermedas maybeexpressedbyequation(11.1)to(11.6)–=3.32(��)forBt=5m(11.1)

=4.52(��)forBt=10m(11.2) =6.11(��)forBt=20m(11.3) =7.20(��)forBt=30m(11.4) =8.00(��)forBt=40m(11.5) =8.44(��)forBt=50m(11.6)

Significantstressedzone, Ds=�� (12)

Table3:ValuesofforwidthofBt=5mto50m andHe=1mto12m Bt(m)51020304050He(m) 3.64.76.27.27.881 2.73.64.75.56.26.82 2.43.13.94.75.35.83 2.22.73.64.24.75.14 2.12.33.13.53.94.36 1.92.22.73.13.63.88 1.92.12.52.93.23.610 1.82.02.42.73.03.312

He=1mHe=2m

He=1mHe=2m He=3mHe=4m He=6mHe=8m He=10mHe=12m

Δ σ 70 /q e

Δ σ 70 /q e

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

0.09

0.29 123456789

0.07

Hs/He

Chart-6:Hs/HeVsΔσ70/qeforBt=20m

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

0.09

Δ σ 70 /q e

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

He=1mHe=2m He=3mHe=4m He=6mHe=8m He=10mHe=12m 0.07

0.29 123456789

0.09

Hs/He Chart-7:Hs/HeVsΔσ70/qeforBt=30m

He=1mHe=2m He=3mHe=4m He=6mHe=8m He=10mHe=12m

0.29 123456789

Hs/He

Chart-8:Hs/HeVsΔσ70/qeforBt=40m

Hence,theSignificantstressedzone,Dsfor70% consolidationpressuremaybeexpressedbyequation (13.1)to(13.6)–

��=3.32(��)forBt=5m(13.1) ��=4.52(��)forBt=10m(13.2) ��=6.11(��)forBt=20m(13.3) ��=7.20(��)forBt=30m(13.4)

Δ σ 70 /q d

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

He=1mHe=2m He=3mHe=4m He=6mHe=8m He=10mHe=12m 0.07

He=1mHe=2m He=3mHe=4m He=6mHe=8m He=10mHe=12m

0.09

0.07

0.29 123456789

Hs/He

Chart-9:Hs/HeVsΔσ70/qeforBt=50m

��=8.00(��)forBt=40m(13.5) ��=8.44(��)forBt=50m(11.6)

ApproximatelysimplifiedvaluesofDsisgivenin Table4.

Table4:SimplifiedvaluesofDsfor70% consolidationpressure Withof Embankment Top,Bt 5-1020-3040-50He (m)

Ds

3He5He6.2He14 2He2.8He3.5He6-12

SimplifiedformofDsfor70%consolidation pressuremaybeexpressedbyequation(14.1)and (14.2)–��=4.7(��)forBt=5-20m(14.1) ��=7.9(��)forBt=30-50m(14.2)

5.CONCLUSION

Maximum12%ofaxlepressureforembankment height1-3mandmaximum1.5%ofaxlepressurefor

embankmentheight4-12mistobetransferredto subsoilunderlyingthehighwayembankment. AccordingtoTerzaghi'srecommendationfor significantstressedzone,transferredportionofaxle loadtosubsoilisnotsignificantregardlessofESAL.

Thetransferredportionofconsolidationismuch moresignificantthantransferredaxlepressure. Considering70%consolidationtobeoccurredafter constructionofsurfacelayerofpavement,70% consolidationpressureisusedinthisanalysis.The depthwasidentifiedatwhichthepressureisreduced to20%ofΔσ70andthisdepthistermedassignificant stressedzone(Ds).

Significantstressedzonesforembankment pressurearefound2-3Heforembankmenttopwidth 5-10m,2.8-5Heforembankmenttopwidth20-30m and3.5-6.2Heforembankmenttopwidth40-50m.

Bt=5mBt=10mBt=20m Bt=30mBt=40mBt=50m

He Chart-11:Hs/HeVsHefor(Δσ70)/qe=0.20

ACKNOWLEDGEMENTS

Theauthoracknowledgedthesupportoftheauthority ofBangladeshHighwayResearchLaboratory(BRRL), Mirpur,Dhaka,Bangladesh.

DECLARATION

Thisismyownresearchwork.Thisisnotcopyofany research.

REFERENCES

[1]RoadMasterPlan(2009),HighwaysandHighways Division(RHD),Bangladesh.

[2]Holtz,R.D.,andKovacs,W.D.(1981),“An IntroductiontoGeotechnicalEngineering,PrenticeHall,Inc,EaglewoodCliffs,NewJersey.

[3]Das,B.M.(2011),“FoundationEngineering”, Chapter-5,7thEdition,GlobalEngineering.

[4]GeometricDesignStandardsManual(2005), HighwaysandHighwaysDivision(RHD),Bangladesh, P.116.

[5]Terzaghi,K.(1936),“OpeningDiscussionon SettlementofStructure”,FirstInternational ConferenceonSoilMechanicsandFoundation Engineering,HarvardUniversity,USA.

[6]FHWA-IF-12-027(2012),“ManualForDesign, Construction,andMaintenanceofOrthotropicSteel DeckBridges”,USDepartmentofTransportation, FederalHighwayAdministration,PublicationNo. FHWA-IF-12-027,February2012,P.76.

[7]AASHTO(2016),“HL-93VehicularLiveLoading, Truck,TandemandDesignLaneLoad”,Civil EngineeringTutor,August,2016.

[8]Kim,H.J.andMission,J.L.(2011),“Numerical AnalysisofOne-DimensionalConsolidationinLayered ClayUsingInterfaceBoundaryRelationsinTermsof InfinitesimalStrain”,InternationalJournalof Geomechanics©ASCE,2011.11:72-77.