Missing:
Journal oiResearchin EngineeringVolume 6, Number Z,Z00g T i
LA'BRED nrasrrcAN..iysrs .rtiiT;/#i; io^ti,"*"*rsoBsrcNED usrNccBR PROCEDURES tE*manu"l
O. Ekwuloand zDennisB. Eme Engineering Department, RiversStateUniversity of Science andTechnology, RiversState,Nigeria. 'Civil
tCivil
and Envi.ronmentalEngineeringDepartment University of Port Harcourt, Port Harcourt, Rivers State,Nigeria
The fatigtte and rurting deformation ,i:X,Xff, of pavements designed usingthree known CBR procedures; the Asphalt Institute, the National Crushed Stone Association and the Nigerian CBR ntethods were evaluated. The elastic praperties of the materials were determined. Structural thickness req_uirercentof the pavements were carried out using their respectived.esigncharts for a trffic volume of 622veh./day and expectedload repetition of 2.8 x I0o. Stresses,strains and deflections due to 80kN single axle load having a tyre pressure of 552kPa were computed by analyzing the e/fect due to 40kN single axle load. Strain evaluation was carried out at the underside of the asphalt concrete layer and at the top of the subgrade. The Heukelom and Klomp Model and the Asphalt Institute Model were used to evaluatepavement response. Results.showedthat the horizontal tensile strains on the underside of the asphalt concrete layer were I ISpe , 33pe and l25pe for Asphalt Institute CBR, NCSA CBR and the Nigerian CBR procedures respectively: Similarly, the vertical compressive strains at the top of the subgrade werefound to be -591pe , -5$pe and:503pe for Asphalt Institute CBR, NCSA CBR and the Nigerian CBR procedures respectively. The resulting fatigue and rutting strains were compared with the permissible values and it was found that the vertical compressive computed strains were more than permissible values. In terms of rutting criterion, the damage factors were found to be greater than a value of 1.0 for both madels. It was concluded that flexible pavements designed using the three known CBR methods are prone to rutlingfailure as a result of rutting deformation and recommended the use of mechanistic procedures in the design of flexible pavements in developing tropical countries. The study was carried out with the layered elastic analysis program EIIER,STRESS, Keywords: Layered Elsstic Analysis,' Fatigue, Rutting, Strains, Design, Flexible Pavement, CBR. INTRODUCTION Studiesin pavementengineeringhave shown that the design procedurefor highway pavementis either empirical or mechanistic.An en:pirical approachis one which is based on the resultsof experimentsor experience.This meansthat the relationshipbetweendesign inputs and pavementfailure were arrivedat through experience,experimentationor a combinationof both. The mechanisticapproachinvolves the determinationof materialparametersfor the analysis,at conditionsas close as possibleto what they are in the road structure.The mechanisticapproachis basedon the elasticor visco-elasticrepresentation of the controlof pavement well pavementstructure.In mechanisticdesign,adequate layerthicknessas as material quality are ensuredbasedon theoreticalstress,strainor deflectionanalysis.The analysisalso enablesthe pavementdesignerto predictwith some amount of certaintythe life of the pavement.Pavementfailuresin most developing tropical courtiershave been traced to any or combination of geological,geotechnical, have beencarried design,construction,and maintenanceproblems(Ajayi, 1987).While severalresearches or.rtin thesecountriesto investigatethe contributionof eachof thesefactors,the design factor has in most casesbeen overlooked.It is generallyknown that failureof asphaltpavementis due to fatiguecrackingand rufting deformation,causedby excessivehorizontaltensile strain at the bottom of the asphaltlayer.and to vertical compressivestrain on top of the subgrade.In the design of asphalt pavement,it is necessary them. While against there moves towards design have and strainsand been inl'estigatethesecritical stresses the use of the mechanisticapproachin pavementdesign in many developedcountries,the use of the empirical California Bearing Ratio (CBR) procedureis still gaining ground in some developingtropical countries even when the original owners of the procedureshave long began the applicationof the mechanisticapproachto pavementdesign.The purposeof this paper is to use the layeredelasticanalysis procedureto investigatefailure in flexible pavem 's using three known CBR procedures;the Asphalt C the National Crushed Stone AssociationCBR Institute CBR Method, the Nigerian (CBR) me'
p I
Layered ElasticAnalysisof FlexiblePavementsDesignedUring Cnn Procedures rnethod.The use of the layeredelasticanalysisconceptin this study is justified in that it is basedon tl'le elastic theory in which tlre developedstressesdue to wheel load in asphaltpavementis proportionalto strain;the stressis also recoverableafter load application(Yang, 1973). ELASTIC LAYERED SYSTE]\I The responseof pavementsystemsto wheel loadinghasbeenof interestsince 1926 rvhenWetergaardused elastic layeredtheory to predict the responseof rigid pavements(Westergaard,1926). It is generally acceptedthat pavementsare best modeled as a layeredsystem,consistingof layers of various materials (concrete,asphalt,granular base,subbaseetc.) restingon the natural subgrade.The behaviourof such a system can be analyzed using the classicaltheory of elasticity (Burmister, 1945). The Layered Elastic Analysis(LEA) is a mechanisticprocedurecapableof determiningpavementresponses(stressand strain)in asphaltpavement.The major assumptionsin the useof layeredelasticanalysis are that; i. the pavement structure be regardedas a linear elastic multilayered system in whicli the stressstrain solution of the material are characterizedby the Young's modulus of Elasticity E and poison'sratio li. ii. Each layer has a finite ihickness h exceptthe lower layer, and all are infinite in the horizontal direction. iii. The surface loading P can be representedvertically by a uniformly distributed verlical stress over a circular area. _ LAYERED ELASTIC ANALYSIS In multilayeredpavementsystem(Yoder and Witczak,1975),the locationsof the variousstressesin a threelayeredpavementsystemare as shown in Figure 1. The horizontaltensilestrainatthe bottom of the asphalt concretelayer and vertical compressivestrain at the top of the subgradeare given by equations I .0 and 2.0 respectively; o,, t - ,'r : - Et
6,, "Er
6-, U,"El
(1.0) I
eo: *(o,r.-o,r) L3
(2.0) Where, o., = verticalsffessat interfaceI (bottomof asphaltconcretelayer) or2 = verticalstressat interface2 o,, = horizontalstressat the bottomof layerI o,2 = horizontalstressat the bottomof layer2 d,.. = horizontalstressaf the top of layer3 E, and E, areModulusof elasticityof layerI and3 receptively. p = Poisson'sratio of the layer A numberof computerprogramsbasedon layeredelastictheory(Burmister,1945)havebeendevelopedfor layeredelasticanalysis.The programCFIEV (Warrenand Dieckman,1963) developedby the Chevron however,Huangand Witczak(1981)modifiedthe Companycan be appliedto linearmaterials, Research programto accountfor materialnon-linearityandnamedit DAMA. The DAMA computerprogramcan be usedto analyzea multi-layeredelasticpavementstructureundersingleor dual-wheelload,the numberof Iayerscannotexceedfive. ELSYMS developedat the Universityof Californiais a five layer linearelastic (Ahlborn, 1972).,TheKENLAYER prograrr for the determinationof stressesand strainsin pavements the solutionfor an elastic computerprogramdevelopedat the Universityof Kentuckyin 1985incorporates multiple-layered systemundera circularload.KENLAYERcanbe appliedto layeredsystemundersingle, properties beinglinearlyelastic,non-linearly elastic wheelloadswith eachlayermaterial dual,dual-tandem (Sivaneswaran layered elastic program from the et al,2001) analysis The Everstress or visco-elastic. was developedfrom WESLEA layeredelasticanalysis WashingtonStateDepartmentof Transportation elasticusingmultiplewheelloads(up to 20). The program.The pavementsystemmodelis multilayered
Journal of Researchin EngineeringVolume6, Number 2,2009 program can analyze hot mix asphalt (HMA) pavementstructurecontaining up to flve layers and can considerthe stresss'ensitivecharacteristics of unboundpavementmaterials. FAILURE CRITERIA IN MECHANISTIC ANALYSIS The use of mechanistic.approach requiresmodelsfor relatingthe output from elastic layeredanalysis(i:e stress,strain, or'deflections)to pavementbeaviour(e.g. performance,cracking,rutting, roughnessetc). As elastictheory can be used to computeonly the effect of traffic loads,most of the principlesin mechanistic designof highway pavementsare basedon limiting strainsih the asphaltbound layer (fatigueanalysis)and permanent deformation (rufting) in the subgrade.Fatigue cracking is a phenomenon which occurs in pavementsdue to repeatedapplicationsof traffic loads.The fatigue criterion in mechanisticdesign approach is basedon limiting the horizontaltensilestrainon the undersideof the asphaltbound layer due to repetitive loads on the pavementsurface, if this strain is excessive,cracking (fatigue failure) of the layer wili result. Various researchershave shown that the relationshipbetweenload repetitionsto failure Ni and strain for asphalt concretematerial is dependenton the horizontal tensile strain at the bottoin of the asphalt bound layer and the elasticmodulus of the asphaltconcrete. I-leukelomand Klomp (1962) suggestedrelationship betweenthe number of load repetitionsto failure and strainin asphaltconcreteas follows: Nr = 10-x
(3 . 0 ) Where,Ns X tt
E
= = = =
Numberof loadapplications to failure +2'.665logto(Ell4.Z2)+ -sloge, 0.392 Horizontaltensilestrainat thebottomof asphaltboundlayer ElasticModulusof asphaltconcrete
The allowablehorizontaltensile strain at the bottom of asphaltconcretelayer accordingto Heukelom and Klomp, (1962) is given by:
= eac l0-A = (4.0) Where,eas Allowable Strainat the bottom of the asphaltlayer : (iogleN;+2.665lo9ro(E/14.22)+0.392)/5 A : Ni Numberof actualrepetitions : E ElasticModulusof AsphaltConcrete The asphaltinstitute(AsphaltInstitute,1982)suggested thatthe relationshipbetweenfatiguefailure of asphalt concrete andtensilestrainis represented by thenumberof loadrepetitions asfollows: ?e' 854 : Ns 0.0796(e ,)-3 (E)-0
(s.0)
Where, N6 .o!
E=
=
Numberof loadapplications to failure Horizontaltensilestrainat thebottomof asphaltboundlayer ElasticModulusof asphalt concrete
Permanentdeformationor rutting is a manifestationof both densificationand permanentsheardeformation, as a mode of distressin highway pavements,pavementdesignshould be gearedtowards eliminating or reducingrutting in the pavementfor a certain period. Rufting criterion is basedon limiting the verfical compressivesubgradestrain, if the maximum verticaicompressivestrain at the surfaceof the subgradeis lessthan a critical value,then rutting will not occur for a specifienumberof traffic loadings.The magnitude of rutting has been correlatedwith the amount of traffic and the vertical compressivestrain levei at the surface of the subgrade. For permanentdeformation,Heukelom and Klomp (1962) expressedthe relationshipbetrveenthe number of repetitionsto failure and the vertical compressivestrain level at the surfaceof the subgradeas follows:
Nr= (6.0) Where
10-x
Nr: X:
Numberof loadapplications to failure + (2.408 loge.)/0.1408 Verticalcompressive strainat thesurfaceof thesubgrade
The allowableverticaltensilestrainat the top of the subgrade[Heukelom and Klomp, 1962] is given by: e suac = l0-A ! (7.0) 8
La1'eredElastic Anaiysisof FlexiblePavementsDesignedUsing CBR Procedures Where r. \'S
Allowablevenicalcompressive strainat thetopof subgrade
UBC
A O . i 4 0 8 l o g r o N2i '. f4 0 8 The relationshipbetweenrutting failure and compressive strain at the top of the subgradeis represented by the numberof load applicationsas suggestedby asphaltinstitute(Asphalt Insritute,1982) in the following forrn: = Nr 1.365xl 0-t (t,)u'"
(8..0) Where,Ng
Numberof loadapplicationsto failure €c strainat the bottomof asphaltbound layer VerticalCompressive ln mechanisticdesign,failure criterion(transferfunction) is usedto definethe point at which failure occursin a pavementby determining the incrementaldamage.The incrementaldamageis simply the nunrber of a particular axle load expected during a given design period divided by the number of repetitions to failure. The incrementaldamageis,summedfor all axle loads to obtain the expecteddarnagefactor over the life of the pavement.The damagefactor is givenby:
tN'
D
(e.0) Where, : D DamageFactor : Ni Actual Number of Load Repetitions = N, Numberof Load Repetitionsto Failure If D is lessthan a value of one, then the pav*ement can be expectedto exceedits design life, if D is greater than one, the pavementis expectedto fail prematurely.If this value is much lessthan one, the pavementis probablydesignedtoo conservatively. CBR DESIGN PROCEDURES The CBR method of pavementdesign was first usedby the California Division of Highways as a result of extensiveinvestigationsmade on pavementfailures duringthe years 1928 and 1929 (Corps of Engineers, 1958). To predict the behaviour of pavement materials, the CBR was developed in 1929. Tests were performed on typical crushed sione representativeof base course materials and the average of these tests designatedas a CBR of 100 percent. Samplesof soil from different road conditions were tested and two design curves were produced correspondingto averageand light traffic conditions. From these curves the required thicknessof Subbase,base and surfacingwere determined.The investigationshowed that soils or pavementmaterial having the same CBR required the same thickness of overlying materials in order to prevent traffic deformation. So, once the CBR for the subgrade and those of other layers are known, the thickness of overlying materials to provide a satisfactorypavement can be determined.The US corps of Engineersadoptedthe CBR meihod (Corps of Engineers,1958) for airfield at the beginning of the Second World War Since then, severalrnodificationsof the original design curves have been made. The relationship betweenpavementthicknessand CBR (Yoder and Witczak, 1975) is as statedin equation 10.0 as follows:
wl 1-1.l pn Ls.lCBR
)
(10.0) This and other relationshipshave been usedto deriveother chartsfor flexible pavements. THE ASPHALT INSTITUTE CBR METHOD Although the Asphalt institute has developeda new thicknessdesign procedurebase on the mechanistic approach(Asphalt Institute,l98l), the original asphaltinstitutethicknessdesignprocedureis basedon the conceptof full depthasphalt,that is, usingasphaltniixturesfor all coursesabovethe subgradeor improved subgrade.Traffic analysis is in terms of 80kN equivalentsingle axle load in the form of a Design Traffic Number, DTN. The DTN is the averagedaily number of equivalent 80kN single-axle estimated for the design period. The CBR, Resistancevalue or Bearingvalue from plate loading test is used in subgrade
Journal of Researchin Engineering Volume 6, Number 2,2009 strengthevaluation.Figure Z sho*s ,n. ,n,.**ss chart for Asphalt pavementstructure.The recommended minimum total asphaltpavement(T1) is given as:
Traffic Light Medium Heavy
DTN Lessthanl0 1 0- 1 0 0 1 0 0- 1 0 0 0 Morethan1000
Minimum Ts(mm) 100 125 150 t75
The NationalCrushedStoneAssociationCBR Method TheNationalCrushesStoneAssociation(NCSA) empiricaldesignmethod(NCSA, 1972)is basedon theUS Corpsof Engineerspavementdesign.Traffic analysisis basedon the averagenumberof 80kN single-axle loadsper laneper day over a pavementlife expectancy of 20 years.The methodincorporates a factorof traffic in the designcalledDesignIndex (Dt). In the absenceof traffic surveydata,generalgroupingof vehiclescanbe obtainedfrom spotchecksof traffic andplacedin oneof thethreegroupsasfollows: Groupl: Passenger cars,papelandpickuptrucks Group2: Two-axletrucksloadedor largervehiclesemptyor carryinglight,lpads Group3: All vehicleswith morethanthreeloadedaxles Subgrade strengthevaluationis madein termsof CBR andcompactionrequirement is providedto minimize permanent deformationdueto densificatioruunder traffic.The NCSA designchartis asshownin Figure3 THE NIGERIAN CBR METHOD The Nigerian(CBR) designprocedureis an empiricaiprocedurewhich usesthe CaliforniaBearingRatio and traffic volume as the sole designinputs.The m.ethodusesa set of designcuryesfor determining structuralthicknessrequirement.The curveswere first developedby the US Corps of Engineersand modifiedby the British Transportation and Road ResearchLaboratory(TRRL, i970), it was adoptedby Nigeriaas containedin the FederalHighwayManual(HighwayManuel,1973).TheNigerian(CBR)design methodis a CBR-Trafficvolume method,the thicknessof the pavementstructureis dependenton the anticipatedtraffic, the strengthcf the foundationmaterial,the quality of pavementmaterialusedand the constructionprocedure.This methodconsiderstraffic in the form of numberof commercialvehicles/day exceeding 29.89kN(3 tons).Subgradestrenglhevaluationis madein termsof CBR. The selectionof pavementstructureis madefrom designcurvesshownin Figure4. The thicknessof the pavementlayersis dependent on the expectedtraffic loading.Recommended minimumasphaltpavementsurfacethicknessis considered in termsof light,mediumandheavytraffic asfollows: Light trafiic 50mm Medium 75mm Heavy l00mm MBTHODOLOGY The designchartsshown in Figures2-4 were used in the structuralthicknessdesignof the pavement.The pavementmaterial propertiesused for design and analysisare presentedin Table 4. The traffic data used for thicknessdesignusingthe threeCBR proceduresas shown below: 4-lanehighway Faciliry: 4% Traffic growth rate:
Designperiod: 20yrs Axle Configurations: - Buses 200vehiday - 2-axleunits I 5Oveh/day - Z-axlelorry units I 00veh/day - 3-axlelorryunits 9Tvehlday - 3-axletractorunits 75vehlday perday: 622vehlday TotalNo.of vehicles (ESAL):2.8x 10" Expected Repetitions The Federal Highway Administration Washington(FHWA, 2001) procedure was adopted irr the determinationof the expected repetitions in the form of 80kN Equivalent Single Axle Load The et al,200l) layeredelasticahalysisprogramu'asemployedin the the analysisof Everstress(Sivaneswaran the d pavernents.Stresses,strainsand deflectiondue to 80kN single axle load having a tvre pressureof
10
Layered ElasticAnalysisof FtexiblePavementsDesignedUsing CBR procedures 5!2kPa was corttputedby analyzingthe effect due to 40kN single load on a circular plate of radius l5l'9mrn. Evaluationof fatigueand ruttingstrainswerecarriedout on the underside of the asphaltconcrele layerand at the top ofthe subgrade. RESULT AND DISCUSSION The resultof structuralthicknessdesigncarriedout for the three CBR proceduresare presentedin Table l, while the result of the layeredelastic analysisby Everstressare presentedin Tabies Z. Tlte pavernent responseusingHeukelomand Klop(1962) andAsphaltInstitute(l982)modelsare presentedin Tables3 and 4 respectively. Resultsshow that the computedmaximum horizontaltensilestrainat undersideof the asplralt concretelayer for the AsphaltInstitute,NCSA and Nigerian CBR proceduresare I l8pe,33pe and l25pe respectively'Using the Heukelomand Klomp model,the permissibletensilestrainas presentedin Table 3.0 for the expectedtraffic is2726p,e,and the numberof load repetitionsto failure are 1.9 xl0r3, I x l016and l . 4 x l 0 r 3 r e s u l t i n g i n d a m a g e f a c t o r s o1f. 5 x 1 0 ' , 2 . 7 x l 0 - r 0 a n d 2 . 0 x 1 0 ' ? f o rt h e A s p h a l t l n s t i t u t e , N C S A and Nigerian CBR proceduresrespectively.With respectto the Asphalt Institute model, the number of load repetitionsto failure for the computedstrainsare.8..4x108, 5.6 x l0r0 and 7.0 x 108resulting in damage , factors of 3.20 x l0-3, 5.01 x ld'5 and 8.59 xl0-a for the Asphalt Institute,NCSA and Nfterian CBR proceduresrespectively.This implies that fatigue failure due to fatigue cracking will not occur in the pavementssince the computedstrainsare less than the permissiblevalue and the damagefactors are less than l. Similarly,the computedvertical compressivestrain at the top of the subgradeu.i -S9tpe, -543pe and -503pe for the Asphaltlnstitute, NCSA and Nigerian CBR proceduresrespectively-Using ihe Heukelomand Klomp model,the permissiblecompressivestrain as presentedin Table 3.0 foi the expected t r a f f i c i s 4 S 3 p r e , a n d t h e n u m b e rloofa d r e p e t i t i o n s t o f a i l u raer e 6 . 7x 1 0 5 ,l . 2 x l 0 6 a n d 2 . l x l 0 6 r e s u l t i n g in damagefactorsof 4.18, 42.28and 1.33 for the Asphalt Institute,NCSA and Nigerian CBR procedures respectively.Using the Asphalt Institute mode-I,the number of load repetitionsto failure for the-computed strainsare 3.9 x 105,5.7 x 105and 8.0 x L05resulting.in damagefactors of 7.22,4.94 and 3.51 for the Asphalt Institute,NCSA and Nigerian CBR proceduresrespectively.The result indicatesthat rutting failure will occur in the pavementas a result of rutting deformationsince the computedstrains are greaterihan the permissible value and the damagefactors are greater than l. ln general, the above result shows that the pavements designed using the three CBR-based procedures will not serve its intended traffic as the pavementwill fail as a result of rutting deformation.The controlling criterion is rutting criterion. CONCLUSION This study presentsa layeredelastic analysis of flexible pavementsdesignedby the Asphalt Institute CBR method, the National Crushed Stone Association CBR method and the Nigerian CBR method. From the resultsobtained,the following conclusionsare herebymade: i. The rufting sfrains of flexible pavementsdesignedusing the three known CBR methods are greater than permissiblevalues. ii. Flexible pavementsdesignedusing the three known CBR proceduresare prone to early failure due to rutting deformation. The "design factors" is one of the causesof road failures in some developingtropical countries. iii. iv. There is need forthe use of mechanisticapproachin the design of flexible pavementsin developing tropical countries. a Table l: Pavemen t Material lropen resand Thickness Layer Material CBR Resilient No. (%) Modulus,E
Poison's Ratio
(Mpa)
1
Surface(Asphalt Concrete)
2 3
Base(granularmaterial)
80
Subbase(stabilized)
A .+
Suberade
Thickness of Pavement Layer (mm)
Asphalt NCSA Institute CBR CBR
Nigeria CBR
3450
0.3s
r00
50
IJ
837 4t7
290
62
5
52
0.40 0.45 0.45
206
30
11
288
Journalof Research tr ""*tl::rfne
vofumeu,.n'-1". 7,2009
Everstress able 2: Result of Layered Elastic AnalysisUsine E CBRPROCEDURE LayerNo. HorizontalTensileStrainat Depth: Z Position the bottom of the Asphalt (cm) Laver
(x io{)
9.999 30.601
I
INSTITUTE ASPFLA,LT CBR
+
NCSA CBR
1
I I
NIGERIANCBR
4
4.999 34.001 7.499 42.541
E**
E""
ll8
ll8
VerticalCompressive Strainat theTop of Subgrade (X 10'6) tr uzz
591 JJ
J)
125
t25
543
503
able 3; Fatisue and Rutting Failure Analysis Basedon Heukelom and Klg!!p ResponseModel(l
Procedure
RuttinsCriterion FatieueCriterion Damage No. of Damage Actual Allowabl No. of Actual Allowabl e Repetitions Factor Strain Repetitions Factor Strain D_ to Failure Strain to Failure D: Ni/Nr ct Strain Ni/Nr (10'6) N, e" (10*) Nr e, (l 0n) (10") CC
ASPI-IALT INSTITUTE CBR NCSACBR
NIGERIAN CBR
118
2726
JJ
2726
t25
2726
1 . 9x l d r l
I x 1016
1 . 4x l 0 r l
1 . 5x l 0 - 7
591
483
6 . 7x 1 0 5
4.18
2.? x l0-ro
543
483
1 . 2x 1 0 6
2.28
2.0 xl0-7
503
483
2 . 1x 1 0 6
I.JJ
a b l e 4 : F a t i s u e a n d R u t t i n s F a i l u r e A n a l v s i sB a s e do n A s p h a l tl n s ti t u t e K e s D o n s eM
FatisueCriterion Procedure
Actual Straine,
(10") ASPHALT INSTITUTE CBR N C S AC B R
NIGERIAN CBR
118
JJ
t25
962
RuttinsCriterion No. of Repetitions to Failure N,
Damage Factor D = Ni/Ni
591
3 . 9x 1 0 5
7.22
5 . 0 ix l 0 - 5
543
5 . 7x l 0 '
4.94
8 . 5 9x l 0 ' a
503
8 . 0x 1 0 5
3.51
No. of Repetitionsto Failure Nr
Damage Factor D = NiA,[i
Actual Straine"
8 . 4x l 0 8
3 . 2 0x l 0 - l
5 . 6x 1 0 r o
7 . 0x 1 0 8
t2
(10")
Lal'eredElasticAnall'sisof FlexiblePat,enrents DesignedUsing CBII Procedures
h r ,E r Interface I
(J22
(Jr2
Interface 2 Pt = 0.5, hr, Ez
Figure 1: Three-Layer PavementSystemShox'ing Location of Stresses
(ln)
(qt\)
t!r
'J
17{
,'"l.o
;:l'. "J
t1
faob Chryf b fihnFflod
b...d
m
,0
I
Frt
12 {to
B ''J 3
10
126
t^ 'l'f-
I1
ll
ii ,1
Fa+,.
E
''l
f,J 3l
'J
E"i r1 $*J
ar
E'l !{ I t1
E:i Irl
Etj E'.1
f,."J
:o{ rsJ
;
j;J
" J'o
Figure2: ThicknessRequircmentfor AsphaltPavementStructure
13
o
Journal of Researchin EngineeringVolume 6, Number 2,2009
CBR% 5 678e10 1!-19 1J^t=)).
Thicknegs deslgn chart
Figure3: NCSADesignChart PlvSrtrt o
a
to
CI aatottatcQaF-aoa
!
-
c
a
= otlaa rlvSItFr
to
ttz
- trcHla
CBRDesignchart Figure4: The Nigerian t4
Layered ElasticAnalysisof FlexililePavemelrtsDcsignedUsing CBII Proccdurcs
\r .* ?
REFEI{ENCES Alrlborn, Q., 1912. ELSI'M| fcon]puter Prograrnfbr DeternriningStressesand Stlains in Irive Larcr Syslerl].Universityof California,Berkelev. Ajai,i,L. A.. 1987.Tlroughtson RoadFailuresin Nigeria.TlteNigerianEngineer,Vol. 22. r.r-o. 1 pp. 10-i7 A s p l n l t l n s t i t u l e1. 9 8 1 .T h i c k n e s s D e s i g n - A s p h a l t P a v e m e n t s f o r H i g h u ' a y s a n d S t r e e t sS. M n suN a lo e rai e l. AsphaltInstitute,l982.Research anclDevelopnrerit of Asphaltlustitute'sThicknessDesignl\4anual. 9'r'Ed,. 'Ihe Research Repon82-2, AsphaltInstitute. Brlnnister,D. N4.,i945. The Celeral Tlieory of Stresses and Displacerrrerrt in LayeredSystenrs. Journal of Applied Plrysics. Vol. 15,pp. 89-94,126-127,296-302. Corps of Engineer.s, 1958.Engineeriiigand l)esign-FlexiblePavements.EM-1 I 10-45-302 l{eukelornS/., and l(lomp A.J.G.,.1962. DynarriiiTestingas a Meansof ControllingPavenients Duringand After Construction.Proceeiings of the Intcrnational Conference on the Stru,cturalDesign of Asphalt Pattetnenl, Ann Arbor, Micli;gan,U.S.A. Highway l\4anuei-Part I Design, 1973. F'ederallriinistry r-,fltrlorks,Lago,s. Httang,D., artd Witczack,lvl. \tI. 1981. PrograrnDAtrM (Chevron),User's llfanual. Dcparlnrentof Civil Engineering,Universityof i\iaryland. NationalCruslredStoneAssociatian,l9J2.Flexiblc PavementDesignCuide for Highrvays.ACST P ubI icati orts,WashingtonD.C. Sivanesrvaran, N., Piecce,L. M. and Mahoney.J- P.,2001. Everstress(Version 5.0) [LayeredElastic Analysis Progranr]tr\rashingtonStateDepartmentof Transportation. TransportarrdRoad Researclz Laboratory,1g70.A Guide to the StructuralDesignof Pavenrents for Nerv Roads.RoadNote 29,3'oEd. Departmentof Eirvironment,HMSO, London. Yang, H. H., 1973.AsphaltPavementDesign-'fhe ShellMethod" Proceedings,1't'International Conferencean Struclural Designo-{AsphaltPavernents. Warren, H. and Dieckman, W. L. 1963. Numerical ComputationalStressesand Strains in Multi-La1,er AsphaltPavementSystenl.InternalReport,ChevronResearchCctrporation,Richrnond.CA. Weslergaard, Computedby TheoreticalAnalysis.Public Roads, H. M., 1926.Stressesin ConcretePar,'ement Vol, 7, No. 2, pp. 25-35. Yoder, E. J., and Witczak,M. W., 1975.Principlesof PavementDesigrt. 2ndEdition,John Wilcy and Sons, lnc. New York.
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