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PORTL ND CEMENTSSOCI TIONThickness Design forC:r;c. Zt Highway and


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The author of this engineering bulletin is Robert G.Packard P E. principal paving engineer PavingTransportation Department Portland CementAssociation.This publication is intended SOLELY for use by PROFESSIONALPERSONNEL who are competent to evaluate the significance andlimitations of the information provided herein and who will accepttotal responsibility for the application of this information. ThePortland Cement Association DISCLAIMS any and allRESPONSIBILITY and LIABILITY for the accuracy of and the ap-plication of the information contained in this publication to the fullextent permitted by law.

Portland Cement Association 1984 reprinted 1995


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Thickness Design forConcrete ighway ndStreet Pavements

CONTENTShapter ntroduction 3Applications of Design Proce dures 3Compu ter Prog rams Availableasis fo r Design 4etric Version 4hapter 2 Design Factorslexural Strength of Concrete 5Subgra de a nd Subba se Suppor t 6Design Period 6Traffic 8rojection 8apacity 8D T T 8Truck Directional Distribution 0Axle Load Distribution 10Load Safety Factors 10

Chapter 3 Design ProcedureAxle-Load Data Available) 1Fatigu e AnalysisErosion Analysis I ISample Problems 13Chapter 4 Simplified Design ProcedureAxle-Load Data Not Available) 3Sample Problems 0Comm ents on Simplified Procedure 30Modu lus of Rup ture 30Design Period 30

ggregate Interlock o r Doweled Joints 30User Developed Design Tables 0Appendix A Development of Design

rocedure 32nalysis of Concrete Pavements 32Jointed Pavements 32Continuou sly Reinforced Pavements 33ruck Load Placement 33ariation in Concrete Streng th 34Concrete Strength Gain with Age 4arping and Cu rling of Concrete 34atigue 34Erosion 5Appendix B Design of Concrete Pavementswith Lean Concrete Lower Course 6Lean Concrete Sub base 6Monolithic Pavement 36

ppendix C Analysis of Tridem Axle Loads 39Appendix D Estimating Traffic Volumeby Capacity 42

ppendix E References 44Design Worksheet for Reproduction 47


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igures1 Flexural strength, age, and design relationships.2. Ap prox imate interrelationships of soil classificationsand bearing values.3. Prop ortion of truc ks in right lane of a multilanedivided highway.4. Design A.5. Fatig ue analysis-allowable load repe titions based

on stress ratio factor (with and without concreteshoulders).6a. Erosion analysis-allowable load repe titions basedon erosion factor (without concrete shoulder).6b. Erosion analysis-allowable load repe titions basedon erosion factor (with concrete shoulder).7. Design D.8. Design 2A.Al. Critical axle-load positions.A2. Equivalent edge stress factor depe nds on percent oftrucks at edge.A3. Fatigue r elationships.B1. Design chart for com posite concrete pavement (lean

concrete subbase).B2. Design cha rt f or c ompo site co ncrete pavement(monolithic with lean concrete lower layer).B3. Mod ulus of ruptu re versus compressive stre ngth .C l . Analysis of tridems.

ables1. Effect of Untreated Sub base on k Values2. Design k Values for Cement-Treated Subbase3. Yearly Ra tes of Traffic Grow th an d Correspo ndingProjection F actors4 Percentages of Four-Tire Single Units and Trucks(ADTT) on Various Highway Systems5 Axle-Load Data6a. Equivalen t Stress-No Concre te Sho ulder6b. Equivalent Stress-Concrete Sho ulder7a. Erosion Factors-Doweled Joints , No Concre teShoulder7b. Erosion Factors-Aggregate-Interlock Joints , NoConcrete Shoulder8a. Erosion Factors-Doweled Join ts, Concre teShoulder8b. Erosion Factors-Aggregate-In terlock Join ts ,Concrete Shoulder9 Axle-Load Categories10. Subgrad e Soil Types and Approx imate k Values11. Allowable A DT T, A xle-Load Category 1-Pave-ments with Aggregate-Interlock J oin ts12a. Allowable A DT T, Axle-Load Category 2-Pave-ments with Doweled Join ts12b. Allowable A DT T, Axle-Load Category 2-Pave-ments with Aggregate-Interlock Jo ints13a. Allowable A DT T, Axle-Load Category 3-Pave-ments with Doweled Joints

13b. Allowab le A DT T, Axle-Load Category 3-Pave-ments with Aggregate-Interlock Joints14a. Allowab le A DT T, A xle-Load Category 4-Pave-ments with D oweled Join ts14b. Allowab le A D TT , Axle-Load Category 4-Pave-ments with A ggregate-Interlock Joints15. Axle-Load Distribution Used for Preparing DesignTables 1 1 Thr oug h 14C l. Equivalent Stress ridemsC2. Erosion Fac tors ridems oweled JointsC3. Erosion Fac tors ridems ggregate-InterlockJoin tsD l. Design Capacit ies for M ultilane HighwaysD2. Design Capacit ies for U ninterrupted Flow on Twoan Highways

customary Metricunit unitin.f tIbIbfk ipIb/in.2Ib/in.- (k value)

r rmkNkkPaMPal m

Conversioncoefficient25 400 305

0 4544 454 456 890 27 1


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CH PTER 1ntroduction

This bullet in deals with methods of determining slabth icknesses adequa te t o car ry t ra ff ic loads on concre testreets, roads, and highways.The des ign purpose is the sa me as fo r o ther eng ineeredstructures- to f ind the minim um thickness that will re-sult in the lowest ann ua l cost as show n by both f irst costand main tenance costs . I f the th ickness is g rea te r tha nneeded, the pavement will give good service with lowmain tenance costs, but f irst cost will be high. If the thick-ness i s no t adequate , p rem ature an d cost ly main tenancean d interru ptions in traff ic will more th an offset the lowerfirst cost . Sound engineering requires thickness designsthat properly balance f irst cost and maintenance costs.While this bullet in is confined t o the top ic of thicknessdesign , o ther des ign aspec ts a re equally imp or tan t t o en-sure the per fo rmance an d lo ng l ife of concre te pavements.These include-

Prov ision fo r reasonab ly un ifo rm suppor t . See Sub-grades and Subbases for Concrete Pavem ents.*Prevention of mud-pumping with a relatively thinun trea ted o r cement- trea ted subbas e on p ro jec tswhere the expected truc k traff ic will be great enoug hto cause pumping . The need fo r and requ irements o fsubbase are also given in the booklet ci ted above.)Use of a joint design that will afford ade qua te loadtransfer ; enab le joint sealants, if required , to beeffec-t ive; and prevent joint distress due to inf i l trat ion.See Joint Design for Concrete Highway a nd StreetPavements.**Use of a conc rete m x design an d aggregates that willp rov ide qua l i ty concre te with the s t reng th and dura -b i li ty needed f o r long l i fe und er th e ac tua l exposurecondi t ions . See Design nd Control of ConcreteMixtures .7)The thickness design cr i ter ia suggested are based ongeneral pavement perform ance experience. If regional o rlocal specif ic performan ce experience becom es availablefo r more favorab le o r adverse cond i t ions , the des ign c ri -ter ia can be appropriately modif ied. This could be thecase fo r par t icu lar c l imate , so i l , o r d ra inag e cond i t ionsand future design innovations.

pplications of Design ProceduresThe design procedu res given in this text apply to the fol-lowing types of concrete pavemen ts: plain, plain doweled,reinforced, and continuously reinforced.Pla in pavements a r e const ruc ted wi thou t re in forc ingsteel or doweled joints. Loa d trans fer at th e joints is ob-tained by aggregate inter lock between the cracked facesbe low the jo in t saw cu t o r g roove . For load t ransfer to beeffective, it is necessary th at sh ort join t spa cings be used.Plain-doweled pavem ents are built without reinforcingsteel; however, smooth steel dowel bars are installed asload trans fer devices at each con trac tion joint a nd rela-t ively sh ort joint spacings are used t o cont rol cracking.Reinforced pavements contain reinforcing steel anddowel bars fo r load t ransfer a t the con t rac t ion jo in ts . Thepavem ents are constructed w ith longer joint spacingsthan used for unreinforced pavements. Between thejoints,one or mo re transverse cracks will usually develop; theseare held t ightly together by the reinforcing steel and goo dload transfer is provided.Com monly used jo in t spac ings tha t per fo rm well a re 5f t f o r p l ain p a v e m e n t s , t t n o t m o r e t h a n 2 f t fo r plain-d o wele d p a ve m e n t s , a n d n o t m o r e t h a n a b o u t 4 f t fo rreinforced pavements. J oin t spacings greater than thesehave been used but some times greater spacing causespavement distress at joints a nd in termed iate cracks be-tween joints.Contin uously reinforced pavements ar e buil t withoutcontractio n joints. Due to the relatively heavy, continu-ous-steel reinforcement in the longitudin al direction,these pave ments de velop transverse cracks at close inter-vals. A high degree of load transfer is developed at thesecrack faces held t ightly toge ther by steel reinforcement.Th e design proce dures given here cover design condi-t ions that have not been directly addressed before by

Portland Cement Associat~o npubl~cation S029P.Portland Cement Association publication IS059P.tPortland Cement Association publ~cationEB001T.t t For very thin paveme nts,a 15-ftjoint spacing may beexces sive -seethe aforementioned PCA publication on joint design .


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other procedures . These include recognition of-1. Th e degree of load transfer a t transverse joints pro-vided by the different pavement types described.2 . The ef fect of us ing a concrete shoulder ad jacent tothe pavem ent ; c oncrete shoulders reduce the f lex-ural s tresses and deflections caused by vehicle loads.3. The effect of using a lean concre te (econocrete) sub-base, which reduces pavement s tresses and deflec-t ions , p rovides cons iderable suppor t when t rucks

pass over jo in ts, and provides resis tance t o subbaseerosion caused by repeated pavement deflections.4. Tw o des ign cr i ter ia : (a) fa t igue, to keep pavem ents t resses due t o repeated loads wi th in safe l imi ts andthus prevent fa t igue cracking; and (b) eros ion , tolimit the effects of paveme nt def lectio nsat s labedges,jo in ts, an d corners and thus contr o l the eros ion offound at ion an d shou lder materia ls . Th e cri ter ion forerosion is needed s ince some modes of pavementd is t ress such as pumping , fau l t ing , and shoulderdis tress are unrelated to fatigue.5. Triple axles can be considered in design. While theconvent ional s ing le-ax le and tandem-axle conf ig-

ura t ions are s t i l l the pred ominan t loads on h ighways,use of tr iple axles ( tr idems) is increasing. They areseen on s om e over- the- road t rucks and on specia lroads used for haul ing coa l or o ther m inera ls. Tr i-dems may be more damag ing f rom a n e ro s ion c ri te -r ion (deflection) than from a fatigue criterion.Select ion of an adeq uate th ickness is dependent uponthe choice of other design features-jointing system, typeof subbase if needed, and shoulder type.With these additiona l design cond itions, the thicknessrequireme nts of design alternatives , which influence cost,can be directly compared.Chapter 2descr ibes how the fac tors needed for so lv ing

a des ign problem are determined . Chapter 3 deta i ls thefull design proce dure t hat is used when specif ic axle-load-d is t r ibu t ion data are known or es t imated . I f deta i ledaxle- load dat a are not avai lab le , the design can be accom-plished as described in Cha pte r 4, by the selection of oneof several categories of data that represent a range ofpavem ent facili t ies varying fro m residential s treets up tobusy inters tate highways.

Computer Programs vailableThickness design problems can be worked out by handwith the tab les and char ts provided here or by comp uterand microcomputer wi th programs that are avai lab lef rom Por t land Cement Associa t ion .

Basis for DesignThe thickness design methods presented here are basedon knowledge of pavement theory, performance, and re-search experience f ro m the fo l lowing sources :

I Theoret ica l s tud ies of pavement s lab behavior by~ e s t e r ~ a a r d , - ~ ' *ickett a n d ~ a ~ , ' ~and recentldeveloped finite-element computer analyses , one owhich is used a s the basis for this design proced ure. '82. Model an d fu l l- scale tes ts such as Ar l ing ton ~e s t san d several research projects conducted b P C A a n dothe r agencies on s ~ b b a s e s , ' ~ ~ ~ ' ~ ' j o i n t s ~n d c o nCrete shoulder^. ^ 203. Experim ental pav emen ts subjected to controlled test raf fic , such as the Bates Tes t ~ o a d , he Pi t tsbu rg Test ~ i ~ h w a ~ , ' ~ ~ 'h e M a r l an d R b ad ~ e s t ,( 2 4 - 2 4t h e A A S H O * * R o a d T e s t , and s tudies of inservice highway pavements made by various s tatdepa r tme n t s of t r an s po r t a t ion .4. Th e per form ance of norma l ly const ructed pavements subject to n orm al m ixed t raff ic.All these sources of knowledge are useful. Howeverthe knowledge gained f rom per formance of normal lyconstructed pavements is the most important. Accordingly, it is essential t o exam ine the relation ship betweenthe ro les that per formance and theory p lay in a des ignprocedure . Sophis t ica ted theoretica l m ethods developed

in recent years permit the responses of the pavement-s tresses , deflections, pressures-to be more accuratelymode led. T his theoretical analysis is a necessary par t oa mechanistic design procedure, for i t allows consideration of a full range of design-variable combinations. Animportant second aspect of the design procedure is thcr i teria appl ied to the theoret ica l ly computed values-the l imiting or allowable values of s tress , deflection, opressure. Defining the criteria so that design results arre la ted t o pavem ent per forman ce exper ience and researchdata is crit ical in developing a design procedure.The theoretical parts of the design procedures givenhere are based on a c om prehe nsive analysis of concrets tresses an d deflec tions by a finite-element c om puter program.'8 ' The program models the conventional designfactors of concrete proper t ies , fou ndat ion su ppor t , andloadings , p lus jo in t load t rans fer by dowels or aggregatin ter lock an d concrete shoulder , for ax le- load p lacementat s lab in ter ior , edge, jo in t , a nd c orner .Th e cr i teria for the des ign p rocedures are based on thpavement des ign , per formance, a nd research experiencreferenced abo ve including re la t ionships t o per formancof avem en ts a t th e A A S H O R oad ~ e s t ' ~ ~ 'nd to s tudies ) of the faulting of pavements .M ore inform at ion o n developme nt and bas is of the design procedu re is given in Appen dix A a nd Reference 30Metric VersionA metr ic vers ion of th is publ ica t ion is a lso availab le f romPort land Cem ent Association-publication EB209P.

*Superscript numbers In paren theses denote referencesat the end othis text.** No w the American Ass ociation of Stat e Hlghway and Transportation Officials AA SH TO ).


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CH PTERDesign actorsAfter selection of the type of concre te pavement plainpavement with o r without dowels, reinforced jointedpavement with dowels, or continu ously reinforced pave-ment) , type of subbase if needed, and type of shoulderwi th or wi thout concre te shoulder , curb and gut te r orin tegra l curb) , th ickness des ign is de te rmined based onfour design factors:

1 Flexura l s t r ength of the concre te mod ulus of rup-ture, M R )2. S t rength of the su bgrade , or subg rade an d subbasec ombina t i on k)3 The weights, f requencies, and types of truck axleloads that the pavement wil l carry4. Design per iod, which in this an d oth er pavement de-sign procedu res is usually taken a t 20 years, but m ay

be more or lessThese design factors are discussed in m ore detai l in thefol lowing sec t ions. Other des ign considera t ions incorpo-ra ted in the procedure a re discussed in Appendix A.

lexural Strength of oncreteConsiderat ion of the f lexural strength of the concrete isapplicable in the design procedure for the fat igue cr i te-r ion, which controls cracking of the pavement underrepeti t ive truck loadings.Bending of a concre te pavement under axle loads pro-duces both compressive and f lexural stresses. However ,the rat ios of com pressive stresses to compressive strengthare to o sm al l to inf luence s lab th ickness des ign. Ra t ios off lexural stress to f lexu ral strength a re much higher , oftenexceeding values of 0 5 As a result , f lexural stresses andflexural strength of the con crete are used in thickness de-sign. Flexural strength is determ ined by mo dulu s of rup -tu r e t es ts , u sua ll y ma de on 6x 6~ 30 - in . e a ms .For specif ic projects, the concrete mix should be de-s igned to give both a deq ua te durabi l i ty and f lexura lstrength at the lowest possible cost . Mix design proce-dures a re descr ibed in the Por t land Cem ent Assoc iat ionpublicat ion Design and Control o Concrete Mi utures

The modulus of rupture can be found by cant i lever ,cente r -point , or th i rd-point loading. An impor tant d i f -ference in these test methods is that the third-point testshows the minimum strength of the middle third of thetes t bea m, whi le the o ther two methods show s t rength a tonly one point . The va lue de te rmined by the more con-servative third-po int meth od Am erican Society for Test-ing an d Mater ials , AS TM C7 8) is used fo r design in thisprocedure .*Mod ulus of rupture tes ts a re com mo nly made a t 7 , 14,28, an d 90 days . The 7- and 14 da y tes t r esult s a re com -pared wi th spec if icat ion requi rements for jo b cont rol andfor de te rmining when pavements can be opened t o t r a ff ic.The 28-day test results have been comm on ly used forthickness des ign of h ighways and s t ree ts and a re recom-mended for use wi th th i s procedure ; 9 0 d ay result s a reused for th e design of air f ields. These values are used be-cause th ere ar e very few stress repeti tions d urin g the f irst28 or 90 day s of pavemen t l i f eas com pared t o the mi l lionsof stress repeti t ions that occur later .Concre te cont inues t o ga in s t rength wi th age as shownin Fig. I Streng th g ain is show n by the solid curve, whichrepresents average M R values for several series by lab-orat ory tests, f ie ld-cured test beams, a nd sections of con-crete taken from pavements in service.In this design proced ure the effects** of var iat ions inconcre te s t r ength f rom point to point in the pavementand ga ins in concre te s t r ength wi th age a re incorpora tedin the des ign char t s an d tables . The des igner does not d i -rect ly apply these effects but simply inputs the average28-day strength value.

*F or a s t andar d 30 - ~ n . eam. cen te r -po ln t - load ing t es t va lues wil l bea b o u t 75 psi highe r , an d cantdever loading t es t va l ue s a b o u t 1 60 p s ~h igher t han th l r d - po tn t - load ing t est va lues . T hes e h igher va lues a r e no tintende d to be used for des ign purposes . If these oth er les t method s areus ed , a dow nw ar d ad jus tm en t s hou ld be ma de by es t ab l i s h in ga co r r e -lat ion to thi rd-point- load tes t values .**T hes e e ff ec t s a r e d i s cus sed In A ppend ix A .


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AgeFig. 1. Flexural strength age and design relationships.

Table 1. Effect of Untreated Subbaseon k Values

S u b g r a d e S u b b a s e v a l u e, pciv a l u e .12 in

1 13 14 16 192 22 23 27 323 32 33 37 43

Subgrade and Subbase Support

Table 2. Design k Values for Cernent-Treated Subbases

The su ppor t g iven t o concre te pavements by the subgrade ,and the subb ase where used, i s the second fac tor in th ick-ness des ign. Subgra de and subbase s uppo r t i s def ined interms of the Westergaard modulus of subgrade reactionk) . I t i s equa l to the load in po unds per square inch on aloaded a rea (a 30- in .diam eter p la te ) d ivided by the de-f lect ion in inches for tha t load. The k values are expressed

S u b g r a d ek valuepci5

12

as pounds per square inch per inch (ps i l in . ) or , morecommonly, as pounds per cubic inch (pc i ) . Equipmentand procedures for de te rmining k values are given inReferences 3 1 an d 32.Since the pla te - loading tes t i s time consuming an d ex -pensive, the k value is usually est ima ted by correlat ion tosimpler tests such as the California Bearing R atio (C BR )or R-value tests. The result is val id because exac t deter-mina t ion of the k value is not required; normal v ar iat ionsf rom a n es t imated va lue wi ll no t app rec iably a ffect pave-ment th ickness requi rements . The re la t ionships sh own in

S u b b a s e k va lue p ~

Fig. 2 a re sa t i s fac tory for des ign purposes.T h e A A SH O R oad ~ e s t ' ~ ~ 'ave a convinc ing dem on-s t ra t ion t ha t t he r e duc ed subgr a de suppor t du r ing t ha wperiods has l i t t le or no effect on the required thicknessof concrete pavem ents. T his is t rue because the br ief per-iods when k va lues a re low dur ing spr ing thaws a re moretha n offset by the longer per iods when the su bg rade isf rozen and k va lues a re much higher than assumed fordes ign. T o avoid the tedious m ethods requi red t o designfor seasona l var ia t ions in k , normal summer or .fallwealher values are used as reasonable mean va lues .I t i s not econom ica l to use unt rea ted subb ases for thesole purpose of increasing k values. W here a sub bas e isused,* there wil l be a n increase in tha t shou ld be used

4 ~ n172847

in the th ickness des ign. If the su bbase i s an unt rea tedgranu la r mate r ia l , the appro xim ate increase in k can bet a ke n f r om T a b l e 1 .The va lues shown in Table I are based o n the Burmis-ter ' j3 ' analysis of two-layer systems and plate- loadingtest s m ade to de te rmine k va lues on subgrades and sub -bases for ful l- scale tes t s~ a b s . ~ '

Cement- treated subbases are widely used for heavy-duty concre te pavements . They a re cons t ruc ted f romA A SH T O So i l C l a sse s A- I A-2-4, A-2-5, an d A 3granular mater ia l s . Th e cement conte nt of cement - t rea ted sub-base is based o n s tand ard A ST M labora tory f reeze- thawand wet-dry tests ' j4 3 5 a n d PCA wei gh t-lo ss riter ria.')^'Other procedures t ha t g ive an equiva lent qua l i ty of mate -r ial ca n be used. Design k values for cement- treated sub-bases meeting thes e cr i ter ia a re given in Table 2.In recent years, the use of lean concrete subbases hasbeen o n the increase. Thickn ess design of concrete pave-ments on these very st if f subbases represents a specialcase that is covered in Appendix B.

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Design PeriodT he t e r m design period is used in this publicat ion rathert h a n pavement life. The lat ter is not subject to precisedef ini t ion. Some engineers and highway agenc ies con-s ider the l if e of a c oncre te pavem ent ended when the f i r s toverlay is placed. The l ife of concrete pavements mayvary f rom less than 20 years on so me projects tha t havecar r ied m ore t r a f fic th an or igina lly es t imated or have haddes ign, mate r ia l , o r cons t ru c t ion defec ts to more tha n 40years on other p rojec ts where defec ts a re absent .T he t e r m design period is som etimes considered to besynonym ous w i th t he t e rm traffic analysis period. Sincetraff ic can pro bab ly no t be predicted with much accuracyfor a longer per iod, a design per iod of 20 years is com-monly used in pavement design procedures. However ,there a r e of ten cases where use of a shor te r or longer de-sign per iod ma y be eco nom ically just if ied, such as a spe-cial haul road tha t will be used fo r only a few years, o r a

in315283

Use of subbase is recommended for projects where co nd it~ on shatw ould caus e mud-pump~ngprevail; for discussion of when subbasesshould be used and how thick they should be, see the PCA publication.Subgrades and Sub bases for Concrete Pavements .

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CALIFORNIA BEARING RATIO- CBR(

(1) For the basic Idea, see 0 J. Porter, Foundations for Flex~ ble avements, H~g hwa y esearch Board Proceedfngs of the Twenty-second AnnualMeetfng, 1942, Vol 22, pages 100-136.(2) ASTM Oes~gnatlon 2487(3) Classif~cat~onf H~ gh wa y ubg rade Ma ter~ als. Htghway Research Board Proceedfngs 01 the Twenty-111th Annual Meetmg. 1945. Vol 25, pages376-392.(4) Afrport Pavfng. U.S Department of Commerce. Federal Av ~a t~ ongency, May 1948, pages 11-16 Est~mated slng values gtven In FAA DesfgnManual for Afrport Pavements (Formerly used FAA Classif~ catton. n ~ f ~ e dlassiflcatlon now used )(5) C Warnes. Correlation Between Value and k Value, unpubl~sh ed eport. Portland Cement Ass oc~ at~ on.ocky Mounta~n-NorthwestReg~on. ctober 1971 (best-fit correlat~onwtth correction for saturat~on)(6) See T. A M~ddlebrook s nd G Bertram. So11 Tests for Design of Runway Pavements. Htghway Research Board Proceedtngs of the Twenty-second Annual Meet~n g, 942, Vol 22, page 152

(7) See Item (6). page 184.

Fig 2 Approximate interrelationships of soil classifications and bearing values


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premium facil i ty for which a high level of performancefor a long time wi th l i tt le or n o pavem ent m aintenance i sdesired. Some engineers feel that the design per iod forrura l and urban highways should be in the range of 30 to35 years.The design per iod selected affects thickness designs ince it de te rmines how m any years , and thus how m anytrucks, the pavement must serve. Selection of the designperiod fo r a specific project is based o n engineer ing judg -ment an d econo mic ana lys is of pavemen t cos ts an d se rv-ice provided thro ugh out the ent i r e period.

The nu mbers an d weights of heavy axle loads expec teddur ing th e des ign l i fe a re majo r f ac tor s in the th icknessdes ign of concre te pavemen t . These a re der ived f r om es t i -mates of-AD T (average da i ly t r a ff ic in both di rec t ions , a l lvehicles)-AD TT (average da i ly t ruck t ra f f ic in bothdi rec t ions)-axle loads of trucksInformat ion o n A D T is obta ined f ro m specia l t r a ff iccoun ts or f rom s ta te , coun ty, or c i ty t r a ff ic -volume map s .This A D T is ca l led the present o r cur rent AD T. The de-s ign A D T is then es t imated by the common ly used meth-ods discussed here. However , any o ther m ethod tha t g ivesa reasonable es t imate of expec ted t r a f f ic dur ingth edes ig nlife can be used.

ProjectionOne method for ge t t ing the t r af f ic volum e da t a (designAD T) needed i s to use year ly ra tes of t ra f f ic growth andtraff ic projection factors. Table sho ws relat ionships be-tween year ly rates of growth and projection factors forboth 20- and 40-year design per iods.In a design problem , the projection factor is mult ipl iedby t he p re sen t A D T to ob t a in a de sign A D T r e pr e se n t i ngthe average va lue for the des ign per iod. In so me proce-dures , this is cal led A A D T (average an nu al daily traffic) .The fol lowing fac tor s inf luence yearly gro wth ra tes an dtraff ic projections:

I Attracte d o r diver ted traffic-the increas eove rexist-ing traffic because of improv eme nt of an exist ingroadway.2. Norm al traff ic growth-the increas edue to increasednumb ers an d usage of mo tor vehicles.3. Gen erated traff ic- the increase du e to mot or vehicletr ips th at wou ld n ot have been mad e if the new facil-i ty had not been const ruc ted.4. Dev elopm ent traffic-the increase du e to chan ges inland use due to construction of the new facil i ty.The com bined e f fec ts wi ll cause an nua l g rowth ra tes ofa bou t 2 t o 6 . These rates corresp ond to 20-year traf-f ic projection factors of 1.2 to 1.8 as sh ow n in Table 3.The plann ing survey sect ions of s ta te h ighway depar t -ments a re very useful sources of knowledge abo ut t r a f f icgrowth and projec t ion fac tor s .

Table 3. Yearly Rates of TrafficGrowth and CorrespondingProjection FactorsYearlyrate oft raf f ic Project ion ~r oi ec t i onfactor.

2 years factor.OO 4 years

Factors represent values at the middesign periodthat are widely used in current practice. Anothermethod of computing these factors is based on theaverage annual value. Differences (both compoundinterest) between these two methods w~ l l arelyaffect design.

Whe r e t he r e i s some que s t i on a bo u t t he r a t e o fg r ow th ,i t may be wise to use a fair ly high rate . This is t rue oninte rc i ty routes and on urban projec ts where a high ra teof urb an grow th m ay cause a h igher -than-expec ted ra teof t r af f ic gro wth. How ever , the grow th of truck volumesmay be less than tha t for passenger ca r s .H igh g r ow th r a t es d o no t a pp ly on tw o- l a ne - ru r a l roa dsan d res ident ia l s t r ee ts where the pr im ary func t ion i s landuse o r abu t t ing prop er ty se rvice . The i r growth ra tes maybe below 2 per yea r (projection facto rs of 1.1 to 1.3)So m e engineers sugges t tha t th e use of s imple in te resg r ow th r a te s ma y be a ppr opr i a t e , r a t he r t ha n c ompo undinterest rates, which wh en used with a long design per iodmay predict unrealist ical ly heavy future traff ic .CapacityT he o the r me thod o f e s tima t i ng des ign A D T is ba sed oncapac i ty- the ma xim um num ber of vehicles tha t can usethe pavement wi thout unreasonable de lay. This methodof est imatin g the volum e of traff ic is descr ibed in Appen-dix D an d sh ould be checked fo r spec i fic projec ts wherethe projected traff ic volume is high; more traff ic lanesmay be needed if reasonable traff ic f low is desired.ADTTThe average da i ly t ruck t r a f f ic in bo th di rec t ions (AD TT )is needed in the design proce dure. I t may be expressed asa pe rc e n ta ge o f A D T or a s a n a c tua l va lue . T he A D T Tvalue inc ludes only t rucks wi th s ix t i r es or mo rean d doesnot inc lude pane l a nd pickup t rucks and oth er four -t i revehicles.T he da t a f r om s t a t e , c oun ty , o r c i t y tr a ff ic - vo lumemap s may inc lude, in addi t ion to A DT , the percentage of


11/50

t rucks f rom which AD TT can be computed.For design of major Interstate and primary systemprojects, the planning survey sections of state depart-ments of transportation usually make specific traffic sur-veys. These da ta are then used to determ ine the percent-age re la tionship be tween A DT T and A DT .AD TT percentages and other essent ia l t ra ff ic da ta c analso be obtained fro m surveys conducted by the highwaydepartm ent at specific locations o n the state highway sys-tem. These locations, called loadometer stations, havebeen carefully selected to give reliable information ontraffic compositio n, truck weights, an d axle loads. Su r-vey results are compiled into a set of tables from whichthe A DT T percentage can be determined fo r the highwayclasses within a state. This makes it possible to computethe A DT T percentage for each s ta t ion. For exam ple , ahighway departm ent loadom eter table (Table W-3) for aMidwestern state yields the following vehicle cou nt fo r aloadometer station on their Interstate rural system:

ll vehicles-ADT .949 2Trucks: . . . . . . . .ll s ingle units and combinations 1645. . . . . . . . . . . . . . . . .ane ls and pick ups . . 353ther four-tire single units 76Therefore, for this station:

1216A DT T 100 13%9492This AD TT percentage would be appropr ia te for de-sign of a project where fact ors influencing the gro wth andcomposition of traffic are similar to those at this load-ometer station.Another source of information on A DT T percentagesis the Na tiona l T ruc k Cha ra c te ri s ti c ~ e ~ o r t . ' 'able 4,which is taken f rom this study , shows the percentages of

four-tire single units and trucks on the major highwaysystems in the United States. The current publication,which is updated periodically, show s that two-axle, fou r-tire trucks comprise between 40% to 65% of the totalnumber of trucks, with a national average of 49%. It isl ikely tha t the lower values o n urban routes a re due tolarger volum es of passenger cars rather tha n fewer trucks.

Table 4 Percentages of Four-Tire Single Units andTrucks ADTT) on Various Highway Systems

It is impo rtant t o keep in mind that the A DT T percent-ages in Table 4 are average values computed fro m manyprojects in all sections of the country. For this reason,these perc entages are on ly suitable for design of specificprojects where A D TT p ercentages are alsoa bou t average.Fo r design purposes, the t otal num ber of trucks in thedesign period is needed. This is obtained by multiplyingdesign A D T by A D T T percentage divided by 100, timesthe number of days in the design period (365 X designperiod in years).Fo r facilities of fou r lanes or more, the A DT T is ad-justed by the use of Fig. 3

Fig. 3 Proportion of trucks in right lane of a multilanedivided highway. Derived from Reference 38.)

Trucks-excludes panels and pickups and other fou r-tire vehicles.

H l g h w a ysystemInterstateOther federa l -a ~ d r lm aryF e d e r a l - a ~ dsecondary

Rura l average dai ly t ra f f ic Urban average dai ly t ra ff rc


12/50

Truck Directional DistributionIn most design problems, it is assumed that the weightsan d volumes of truck s traveling in each directionare fairlyequal-50-50 distribution-the design assumes tha t pave-ment in each direction carries half the total ADTT Thismay n ot be true in special cases where m any of the trucksmay be hauling full loads in on e direction and r eturningempty in the o ther direction. f such is the case, an appr o-priate adjustment is made.Axle Load DistributionDat a on the axle-load distributio n of the truck traffic isneeded to compute the numbers of single and tandemaxles* of various weights expected d urin g the design per-iod. These data can be determined in one of three ways:(I ) special traffic studies to establish the Ioadometer dat afor the specific project; (2) dat a fr om th e state highwaydepartment's lo adome ter weight stations (Table W-4) o rweigh-in-motion studies on routes representing truckweights and types th at ar e expected to be similar to theproject under design; (3) when axle-load distributiondata are not available, methods described in Chapterbased on categories of representative data fo r differenttypes of pavement facilities.The use of axle-load da ta is illustrated in Tab le inwhich Table W-4 data have been grouped by 2-kip and4-kip increments for single- and tandem-axle loads, re-spectively. The da ta unde r the heading Axles per 1000Trucks are in a convenient form for comp uting the axle-load distribution. However, an adjustmen t must be made.Colu mn 2 of Table gives values for all trucks, includingthe unwanted values for panels, pickups, and other fo ur-tire vehicles. To overcome this difficulty, the tabulatedvalues are adjusted as described in the Table notes.Colu mn of Table gives the repetitions of varioussingle- and tandem -axle loads expected during a 20-year-design period for the Design sample problem given inChapter 3.

Load Safety FactorsIn the design procedure, the axle load s determined in theprevious section are multiplied by a load safety factor(LSF). These load safety factors are recommended:

For Interstate and other multilane projects wherethere will be uninterru pted traffic flow an d high vol-umes of truck traffic , L S F 1.2.For highways an d arterial streets where there will bemoderate volumes of truck traffic , LSF 1.1.For roads, residential streets, and o ther streets thatwill carry small volumes of truck traffic , LS F 1.0.

Aside fr om the lo ad safety factors, a degree of conserv-atism is provided in the design procedure to compensate

Table 5. Axle Load Data(3)Axles per1000t rucks

(adjusted)Axle load.k ipsAxles Indesignperiod

Axles per1000t rucks

Tandem axles

pS~n g le x les

Columns 1and 2der1ved rom oadometer W 4 Table Thls tablealsoshows13 215 total trucks counted w lth 6 918 two-axle four- tlre trucks (52 )Column 3 Column 2 values adjusted for two-axle fou r-t~ rerucks, equalto Column 21(1 - 521100)Column =Column3~trucks1ndes1gnper1od)l1000eesampleproblemDes~ gn In which trucks In deslgn pertod (oned~rec tton)otal 10,880.000

28-3026-2824-2622-2420-2218-2016-1814-1612-1410-12

for such things as unpredicted truck overloads and nor-mal construction variations in material properties andlayer thicknesses. A bov e tha t basic level of conserva tism(L SF 1.0), the load safety factors of 1.1 or 1.2 providea greater allowance for the possibility of unpredictedheavy truck loads an d volum es and a higher level of pave-ment serviceability appropriate for higher type pave-ment facilities.In special cases, the use of a load safety factor as high as1.3 may be justified to maintain a higher-than-normallevel of pavement serviceability throughout the designperiod. A n exam ple is a very busy urb an freeway with noalternate detour routes for the traffic . Here, it may bebetter to provide a premiu m facility to circumvent for along time the need for any significant pavement main-tenance that would disrupt traffic flow.

0.280.651.332.844.72

10.4013.5618 6425 8981 05

*See Appendix C if t sexpected that trucks with tridem loads will be~nclu ded n the traffic forecast.


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CH PTERDesign ProcedureAxle-Load Data Available)

The m ethod s in this cha pte r are used when detailed axle-loaddi s t r ibut ion data have been determined o r es t imatedas described in Chapter 2.*Fig. 4 i s a worksheet** showing the form at for com-pleting design prob1ems.t I t requires as input dat a thefollowing design factors discussed in Ch apte r 2.Type of jo in t and shoulderConcrete f lexural s t rength (M R) a t 28 daysk value of the subgrade or subgrade and subbasec o m b i n a t i o n t tLoad safe ty fac tor (LSF)Axle-load dis tr ib ution (Column 1)Expected nu mb er of axle-load repetit ions duringthe design period (Column 3)

Both a fatigue analysis ( to control fatigue cracking)and a n e ro s ion analy si s ( to con t ro l f ounda t ion and s hou l -der eros ion, pum ping, an d faul t ing) are shown on the de-sign w orksheet.Th e fatigue analysis will usually co ntro l the design oflight-traff ic pavements (residential s treets and se conda ryroa ds regardless of w hether the joints ar e doweled o r not)an d medium traffic pavemen ts with doweled joints .Th e erosion analysis will usually con trol the design ofmedium- and heavy-traff ic pavements with undoweled(aggregate-interlock) joints and heavy-traffic pavementswith doweled joints .For pavements car ry ing a normal mix of ax le weights ,s ingle-axle loads a re u sually mo re severe in the fatigueanalysis , and tandem-axle loads are more severe in theerosion analysis.The s tep-by-step design procedure is as follows: Thedesign input da ta show n at the top of F ig. 4 are es tab-l ished and Columns and 3 are f i lled ou t . T he axle loadsare multiplied by the load safety factor for Column 2.

Without concre te shoulder , use Table 6a and Fig. 5With concrete shoulder, use Table 66 and Fig. 5

Procedure S teps :1. Enter as i tems 8 and on the worksheet f rom theappropriate table the equivalent s tress factors de-pending on t r ial th ickness and k value.2. Divide these by the concrete mod ulus of rupture andenter as i tems 9 and 12.3. Fill in Co lum n 4 Allowable Repetitions, deter-mined from Fig. 5.4. C o m p u t e C o l u m n 5 by d iv id ing Colum n 3 by Col-u m n 4 multiplying by 100; then t ota l the fatigue atthe bot tom.

Erosion nalysisWithout conc re te shoulder

Doweled joints or continuously reinforced pave-ments$-use Table 7a and Fig. 6aAggregate-interlock joints-use Table 76 an d Fig.60

With concre te shoulderDoweled joints o r continuou sly reinforced pave-mentsf-use Table 8a and Fig. 66.Aggregate-interlockjoints-use Table gban d F ig. 66 .

Procedure S teps :I . Enter the eros ion fac tors f rom the appropr ia te tab le

as i tems 10 an d 13 in the worksheet.2. Fill in Column 6 Allowable Repetitions, fromFig. 6 or F ig . 6b.

See Chapter when axle-load distribution data are unknown.Fatigue nalysis **A blank worksheet is provided as the last page of this bulletin forpurposes of reproduction and use in specific design problems.Results of fatigue analysis , an d th us the c harts an d f igures t Computer programs for solving design problems are available fromused , are the same for pavements wi th doweled and un- Port andt tS e e A p p en d ix B if lean concrete subbase is used.doweled joints , and also for continuously reinforced IIn this design procedure, continuously reinforced pavements arepavements.$ treated the same as doweled , jointed pavements-see Appendix A


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Calculation of Pavement Thickness

Tr~a lh~ckness 9 5 ~n Doweled o~n ts yes noubbase-subgrade k ?f l PC1 Concrete shoulder yes no

M O ~ U I U Sof rupture. R 65 PSLoad safety facto r LSF / 2

8 Equwalent stress 0 10 Eros~onactor 2 599 Stress ratlo fac tor 0 7

Axleloadk ~ p s

1

Single Axles

Tandem Axles

Mul t~p l~edbyLSF

/.2

11. Equ~ vale nt tress 9 2 13. Eros~onactor 2 7 412 Stress ratlo facto r4 5

Fig 4 Design 1A

12

Expectedrepet~t~onsFat~gue nalys~s

Allowablerepetltlons

4

Eros~on nalys~s

Fat~gue.percent

5

Allowablerepet~t~ons

6

Damagepercent

7


15/50

3. Compute Column 7 by dividing Column 3 by Col-umn 6, multiplying by 100; then total the erosiondamage at the bottom.In the use of the charts, precise interpolation of allow-able repetitions is not required. If the intersection line

runs off the top of the chart, the allowable load repeti-tions are considered to be unlimited.The trial thickness is not an adequate design if either ofthe totals of fatigue o r erosion damage are greater than100%. A greater trial thickness should be selected foranother run.* A lesser trial thickness is selected if thetotals are much lower than 100%.

Sample roblemsTwo sample problems are given to illustrate the steps inthe design procedure and the effects of alternate designs.Design is for a four-lane rural Interstate project; severalvariations on the design-use of dowels or aggregate-interlock joints, use of concrete shoulder, granular andcement-treated subbases-are shown as Designs 1Athrough 1E. Design 2 is for a low-traffic secondary road,and variations are shown as Designs 2A and 2B.

DesignProject and Traffic Data:

Four-lane InterstateRolling terrain in rural locationDesign period 20 yearsCurrent ADT 12,900Projection factor 1.5ADTT 19% of ADT

Traffic Calculations:Design ADT 12,900X 1.5 19,350 (9675 in one di-rection)ADTT 19,350X 0.19 3680 (1840 in one direction)For 9675 one-direction ADT, Fig. 3 shows that the

proportion of trucks in the right lane is 0.81. Therefore,for a 20-year-design period, the total number of trucks inone direction is

1840 X 0.8 X 365 X 20 10,880,000 trucksAxle-load data from Table 5 are used in this design

example and have been entered in Fig. 4 under the maxi-mum axle load for each group.Values Used to Calculate Thickness:**Design A: doweled joints, untreated subbase, no con-crete shoulder

Clay subgrade, k 100 pci4-in.-untreated subbaseCombined k 130 pci (see Table 1LSF 1.2 (see page 10)Concrete MR 650 psiDesign 1B: doweled joints, cement-treated subbase, noconcrete shoulderSame as 1A except:4-in. cement-treated subbasetCombined k 280 pci (see Table 2)

Design C: doweled joints, untreated subbase, concreteshoulderSame as 1A except:Concrete shoulderDesign ID: aggregate-interlock joints, cement-treatedsubbase, no concrete shoulderSame as B except:Aggregate-interlock jointsDesign E: aggregate-interlock joints, cement-treatedsubbase, concrete shoulder

Same as ID except:Concrete shoulderThickness Calculations:trial thickness is evaluated by completing the designworksheettt shown in Fig. 4 for Design 1A using theaxle-load data from Table 5.For Design lA, Table 6a and Fig. 5 are used for thefatigue analysis and Table 7a and Fig. 6a are used for theerosion analysis.Comments on Design 1For designs 1A through IE, a subbase of one type or an-other is used as a recommended practice1on fine-texturedsoil subgrades for pavements carrying an appreciablenumber of heavy trucks.

In Design IA: (I) Totals of fatigue use and erosiondamage of 63% and 39%, respectively, show that the 9.5in. thickness is adequate for thedesignconditions. 2) Thisdesign has 37% reserve capacity available for heavy-axleloads in addition to those estimated for design purposes.3) Comments and 2 raise the question of whether a 9.0-

in. thickness would be adequate for Design IA. Separatecalculations showed that 9.0 in. is not adequate becauseof excessive fatigue consumption (245%). (4) Design 1Ais controlled by the fatigue analysis.A design worksheet, Fig. 7, is shown for Design ID toillustrate the combined effect of using aggregate-inter-lock joints and a cement-treated subbase. In Design 1D:(1) Totals of fatigue use and erosion damage of I% f and97%, respectively, show that 10 in. is adequate. 2) Sepa-rate calculations show that 9.5 in. is not adequate becauseof excessive erosion damage (142%), and 3) Design D iscontrolled by the erosion analysis.

continued on page 21

'Some guidance is helpful in reducing the number of trial runs. Theeffect of thickness on both the fatigue and erosion damage approxi-mately follows a geometric progression. For example, if 33 and 178fatigue damage are determined at trial thicknesses of 10 and 8 in., re-spectively, the approx imate fatigue damage for a thickness of 9 in. isequal to J33X 78 77 .**Concrete MR , LSF, and subgrade k valuesare thesame for DesignsI A through I E.tCement-tr eated subbase meeting requirements stated on page 6.t t A blank worksheet is provided a s the last page of this bulletin for thepurposes of reproduction and use in specific design problems.

:See Subgrades and Subbases for Concrete Pavements PortlandCement Association publicationf For pavements wlth aggregate-interlock joints subjected to an ap-preciable number of trucks, the fatigue analysis will usually not affectdesign.


16/50

Table 6a. Equivalent Stress No Concrete ShoulderSingle Axlenandem Axle)

Table 6b. Equivalent Stress Concrete ShoulderSingle AxleITandem Axle)

Slabthicknessin.44 555 566 577 5

k of subgrade-subbase pci50 100 150 200 300 500 700

825/679 726/585 671 /542 634/516 584/486 523/457 484/443699/586 61 6/500 571 460 540/435 498/406 448/378 41 7/363602/516 531 436 493/399 467/376 432/349 390/321 363/307526/461 464/387 431 /353 409/331 379/305 343/278 320/264465/416 411/348 382/316 362/296 336/271 304/246 285/232417/380 367/317 341/286 324/267 300/244 273/220 256/207375/349 331 /290 307/262 292/244 271 /222 246/199 231 /I 86340/323 300/268 279/241 265/224 246/203 224/18 1 2 10/169

Slabthickness~ n .

k of subgrade-subbase p c ~50 100 150 200 300 500 700


17/50

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18/50

Table 7b. Erosion Factors Aggregate-Interlock Joints,o Concrete Shoulder Single Axle/Tandem Axle)

Table 7a. Erosion Factors Doweled Joints, No Concrete ShoulderSingle Axlenandem Axle)

Slabth~ckness.in44 555 5

k o subgrade-subbase p c ~50 100 200 300 500 700

3 74/3 83 3 73/3 79 3 72/3 75 3 71/3 73 3 70/3 70 3 68/3 673 59/3 70 3 57/3 65 3 56/3 61 3 55/3 58 3 54/3 55 3 52/3 533 45/3 58 3 43/3 52 3 42/3 48 3 41 3 45 3 40/3 42 3 38/3 403 33/3 47 3 31/3 41 3 29/3 36 3 28/3 33 3 27/3 30 3 26/3 28

Slabth~ckness~n44 5

k of subgrade-subbase pcl50 100 200 300 500 700

3 94/4 03 3 91/3 95 3 88/3 89 3 8W3 86 382 /3 83 3 7713 803 79/3 91 3 76/3 82 3 73/3 75 3 71 3 72 3 68/3 68 3 64/3 65


19/50

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20/50

Table 8a Erosion Factors Doweled Joints, Concrete ShoulderSingle AxleITandem Axle)Slabth~cknessin.

44.5

k of subgrade-subbase pci50 100 200 300 500 700

3.28/3.30 3.24/3.20 3.21/3.13 3.19/3.10 315/3.09 3.12/3.083.13/3.19 3.09/3.08 3.06/3.00 3. 04/2. 96 3.01/2.93 2.98/2.91

Table 8b. Erosion Factors Aggregate-Interlock Joints,Concrete Shoulder Single AxleITandem Axle)Slabth~ckness~ n .

k of subgrade-subbase pci50 100 200 300 500 700


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Fig. 6b. Erosion analysis-allowable load repetitionsbased on erosion factor with concrete shoulder).


22/50


Tr~a lh~ckness f l in Doweled o~nts yes n oSubbase-subgrade k cl Concrete shoulder yes noModulus of rupture MR M L S Des~gn er~od2 earsLoad safety facto r LSF /

Single Axles

Axleload.k ~ p s

1

8 Equivalent stress- 10 Eros~onactor 29 Stress ratlo factorm

11 Equ~valen t t re ss. /CL= 13 Eros~onactor 2.90

Mu l t~p l~edbyLS12

Tandem Axles 12 Stress ratlo factor

Expectedrepet~t~ons

Fig 7 Design ID

Fatlgue analys~s

Allowablerepetltfons

4

Eros~ on nalys~s

Fat~gue.percent

5

Allowablerepetltlons

6

Damagepercent


23/50

Workshee ts for the other var ia t ions of Des ign 1 are notshown here but the results are compared as follows:

Design1AI B1CI DE

Subbase4-in. granular4-in. cement-treated4-in. granular4-in. cement-treated4-in. cement-treated

Joints Concreteshoulderdoweleddoweleddoweledaggregateinterlockaggregateinterlock

Thicknessrequirement,in.

For Design 1 conditions, use of a cement-treated sub-base reduces the thickness requirem ent by 1.0 in. (Design1A versus I B); and concrete shou lders reduce the thick-ness requirem ent by 1.0 to 1.5 in. (Designs 1A versus 1Ca nd 1D versus 1E). Use of aggreg ate-inte rlock joints in-stead of dowels increases the thickness requirement by1.5 in. (Design 1 B versus 1D). These effects will vary indifferent design problems depen ding o n the specific de-sign conditions.esign

Project and Traffic Data:Two-lane-secondary roadDesign period 40 yearsCur re n t AD T 600Projection factor 1.2A D T T 2 .5 o f A D T

Traffic C alculations:Design A D T 600 1.2 720ADTT 720 0.025 18 18Truck traffic each way 92For a 40-year design period:

9 365 40 13 1,400 tru cksAxle-load d ata are show n in Table 15, Category I andthe expected number of axle-load repetitions are shownin Fig. 8.

Values Used to Calculate Thickness:Design 2A: aggregrate-interlock joints, n o subbase,* noconcrete sho ulderClay subgrade, k 100 pciL S F 1 . 0Concre te M R 650 ps i

Design 2B: doweled joints ,** no subbase , no concre teshoulderSam e as 2A except :Doweled jointsThickness Calculations:Fo r Design 2A, a trial thickness of in. is evaluated bycompleting th e worksheet show n in Fig. 8, according tothe p rocedure given on page 1 1 Table 6a and Fig. 5 a reused for the fa t igue ana lys is and Table 76 a n d Fig. 6a a reused for the erosion analysis.Fo r Design 2B, a worksheet is not sho wn here but thedesign was worked ou t fo r comp arison with Design 2AComments on Design 2For Design 2A: (1) Totals of fatigue use and erosiondam age of 89 and 8 , respectively, show that the 6.0-inthickness is adequ ate. (2) Sepa rate calculations show thaa 5.5-in. pavement would no t be adequ ate because oexcessive fatigue consum ption . (3) Th e thickness designis contr olled by the fatigu e analysis-which is usually thecase fo r light-truck-traffic facilities.Th e calculations for Design 2B, which is the same asDesign 2A except the joints are doweled, show fatiguean d ero sio n values of 89 an d 296, respectively. Co m-ments: (1) The thickness require men t of 6.0 in. is the sameas fo r D esign 2A. (2) The fatigue-analysis values ar e exactly the same as in Design 2A. (3) Because of the dowels, the erosion dam age is reduced fro m 8 to 2 ; however, this is immaterial since the fatigue analysis contro lthe design.For the Design 2 situation, it is shown that doweledjoints are not required. This is borne out by pavementperformance experience on light-truck-traffic facilitiesuch as residential streets and s econd ary roads an d alsoby studies '28 9 showing the effects of the num ber oftruckson pavements with aggregate-interlock joints.

Performance experience has shown that subbases are not r equ~ rewhen truck traffic 1s very Ilght; see the PCA publicatlon, SubgradesanSubbases or Concrete PavemenrsDesign 2B is shown for illustrative purposes only. Doweledjolntsare not needed where truck traffic 1s very I~ gh t;ee the PCA publicationJoinr Des~gnor Concrete Hrghwav und Streer Pavementst The type of load transfer at thejoints--dowels, or aggregate interlock-does not affect the fatigue calculations since the critical axle-loadposition f or stress and fa tigue is where the axle loads are placed at pavement edge and midpanel, away from the joints. See Appendix A.


24/50


Trtal th~ckness 4.0 ~n Doweled oints yes norSubbase-subgrade k D O p c ~ Concrete shoulder yes norModulus of rupture. MR p s ~ Deslgn perlo d earsLoad safety factor, LS /.

o ~ ~ L Z S P

8 Equivalent stress y 10 Eros~onactor 3 F D9 Stress ratlo factor

Axleload,klps

1

Single Axles

11 Equlvalent stress -* ? . 13 Eroslon factor =

Mult~pliedbyLSF1.

2

Tandem Axles 12 Stress ratlo factor 0 3 5

Expectedrepet~tions

3

Fig 8 Design 2A

Fat~gue nalys~s

Allowablerepetit~ons

4

Eros~on nalys~s

Fatlgue.percent Allowablerepet~t~ons

6

Damage.percent


25/50

CHAPTER 4Simplified Design Procedure

Axle-Load Data Not Available)The design steps described in Chapter 3 include separatecalculations of fatigue consumption and erosion damagefor each of several increments of single- and tandem-axleloads. This assumes that detailed axle-load data havebeen obtained from representative truck weigh stations,weigh-in-motion studies, or other sources.This chapter is for use when specific axle-load data arenot available. Simple design tables have been generatedbased on composite axle-load distributions that repre-sent different categories of road and street types. A fairlywide range of pavement facilities is covered by four cate-gories shown in Table 9.The designer does not directly use the axle-load data**because the designs have been presolved by the methodsdescribed in Chapter 3 For convenience in design use, theresults are presented in Tables 1, 12 13, and 14, which

Table 9. Axle Load Cate~ories

Axle-loadcategory DescriptionResidential streetsRural and secondary roads (low tomedium')Collector streetsRural and secondary roads (high')Arterial streets and primary roads (low')

3

correspond to the four categories of traffic. Appropriateload safety factors of 1.0, 1.1, 1.2, and 1.2, respectivelyhave been incorporated into the design tables for axle-load Categories 1, 2 3, and 4. The tables show data for adesign period of 20 years. (See the section DesignPeriod , following.)In these tables, subgrade-subbase strength is charac-terized by the descriptive words Low Medium High andVery High. Fig. 2 shows relationships between varioussubgrade-bearing values. In the event that test data arenot available, Table 10 lists approximate k values fordif-ferent soil types. If a subbase is to be used-see Chapter 2

Arterial streets and primary roads(medium')Expressways and urban and rurallnterstate (low to medium')

4

*On page 30, guidelines for p repa ring design tables for axle-load distributions different from those given here are discussed.

**Axle- load data for the four categories are given in Table 15.

Arterial streets, primary roads.expressways (high')Urban and rural lnterstate (medium tohigh')

TrafficI ADTTADT 7

3000-1 2,000 8-302 lane3000-50.000lane or more3000-20,000 8-302 ane3000-1 0,000lane or more

Per dayMaximum axle loads, kips

Single axles Tandem axles

'The descriptors high, med ~u m, r low refer to the relat~ ve e~ ghts f axle loads for the type of street or road.that IS low for a rural lnter state woul d represent heavier loads than low for a secondary road

'Trucks wo-axle, four-tire trucks excluded.


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Table 10. Subgrade Soil Types andApproximate k Valuesk valuesrange.Type of soil Support

Fine-gramed soils in which silt and Lowclay-size particles predominate 75 1 20Sands and sand-gravel m ixtures w ithmoderate amounts of silt and clay Medium 13C 170Sands and sand-gravel mixturesrelatively free of plastic fines High 188220Cement-treated subbases (see page 6) Very high 25C 400

under Subgrade and Subbase Supportw-the estimatedk value is increased according to Table or Table 2.The design steps are as follows:

1. Estimate ADTT* (average daily truck traffic, twodirections, excluding two-axle, four-tire trucks)2. Select axle-load Category I, 2, 3, or 4.3. Find slab thickness requirement in the appropriateTable I, 12, 13, or 14. (In the use of these tables, see

discussion under Comments on Simplified Pro-cedure, page 30.)In the correct use of Table 9 the ADT and ADTT val-ues are not used as the primary criteria for selecting theaxle-load category-the data are shown only to illustratetypical values. Instead, it is correct to rely more on theword descriptions given or to select a category based onthe expected values of maximum-axle loads.The ADTT design value should be obtained by a truckclassification count for the facility or for another with a

similar composition of traffic. Other methods of estimat-ing ADT and ADTT are discussed on pages 8 and 9.The allowable ADTT values (two directions)listed inthe tables include only two-axle, six-tire trucks, andsingle or combination units with three axles or more.Excluded are panel and pickup trucks and other two-axle,four-tire trucks. Therefore, the number of allowabletrucks ofall types will begreaterthanthe tabulated ADTTcontinued on page 30

Fo r faci li ties of four lanes or m ore, the ADTT IS adjusted by the useof Fig. 3.

Table 11. Allowable ADTT,* Axle-Load CategpryPavements with Aggregate-Interlock Joints Dowels not needed)No Concrete Shoulder or Cu rb

in. Low Medium Hiah

Note: Fatigue analysis controls the d es~ gn

Concrete Shoulder or CurbSlab Subgrade-subbase supportthickness,~ n . Low Medium High

Note: A fractional ADTT Indicates that the pavement can carry un li m~ ted assenger cars and two-axle, four-tire trucks, but only a few heavy trucks per week (ADTT of 0.3 7 days ind~cateswo heavy trucks per week.)ADTT excludes two-axle, four -t~r e rucks, so total number of trucks allowed w ~ l l e greater-see text


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Table 12a. Allowable ADTT, Axle-Load Category 2 avements with Doweled JointsNo Concrete Shoulder or Curb Concrete Shoulder or Curb

Slablabthickness.in.

Subgrade-subbase suppor tubgrade-subbase suppor tLow Medium Hlgh Very high

Note. Fatlgue analysis controls the deslgn. 'ADTT excludes two-axle, f our- t~rerucks so total number of trucks allowed w~ l l e greater-see

thickness,~ n .5

Table 126. Allowable ADTT, Axle-Load Category 2 Pavements with Aggregate-Interlock Joints

Low Medlum High Very hlgh3 9 42

No Concrete Shoulder or Curb Concrete Shoulder or CurbSubgrade-subbase supportthickness,~ n . Low Medium Hlgh Very high

'ADTT excludes two-axle, four-tlre trucks, total number of trucks allowed w ~ l l e greater-see textEros~on analys~ s ontrols the de s~gn , therwse fatlgue analys~s ontrols

Slabth~ckness.~n

55.566.57

Subgrade-subbase supportLow Medium Hlgh Very high

3 9 429 42 120 450

96 380 700 970''650 1000 1400 2100

1100 1900


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Table 1 . Allowable ADTT, Axle-Load Category 3- Pavements with Doweled JointsNo Concrete Shoulder or Curb Concrete Shoulder or Curb

Slabhickness,in.7.588.599.5

Subgrade-subbase supportLow Medium High Very high

Slabthickness, Subgrade-subbase supportin. Low Medium High Very high

ADTT excludes two-axle, four-tire trucks; total number of trucks ailowed wtll be greater-see text.Erosion analysis controls the design; otherwise fat ~g ue nalysis controls.


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Table 13b. Allowable ADTT, Axle-Load Category 3 Pavements with Aggregate Interlock JointsNo oncrete Shoulder or urb

Subgrade-subbase supportthickness.slabn . Low Medium High Very high

oncrete Shoulder or urb

Subgrade-subbase supportth~cknessin. Low Medium High Very high

'ADTT excludes two-axle, four- t~re rucks; total number of trucks allowed w ~ l l e greater-see text.Fat~gue analysis controls the design, ot herw~ se roslon analysis controls.


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Table 14a. Allowable ADTT, Axle-Load Category 4 Pavements with Doweled JointsNo Concrete Shoulder or Curb Concrete Shoulder or Curb

Slab Subgrade-subbase suppor tIth~c:~ness Low Me d~ um Hlqh Very hlqhSlab Subgrade-subbase suppor tth~ckness. Low~ n . Med ium H~ oh Verv h iah

ADTT excludes two-axle four -t~r erucks total number of trucks allowed wlll be greater-see text.Eros~onanalys~s ontrols the d es~g notherwise fat~gue nalys~s ontrols


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Table 14b. Allowable ADTT, Axle-Load Category 4 Pavements with Aggregate-Interlock JointsNo oncrete Shoulder or urb

Slab Subgrade-subbase supportth~ckness.in. Low Medium Hiah Verv hiah

'ADTT excludes two-axle, four-t~ re rucks, total number of trucks allowed w~ l l e greater-see textFat~gue analys~s ontrols the d es~gn , the rw~se roslon analys~s ontrols

oncrete Shoulder or urb

Slabthickness.tn.

7.588.599.5

Subgrade-subbase supportLow Medium High Very high

100 400240 620 91 0

330 770 1,100 1,700720 1,300 1.900 3,100

1,100 2.100 3.200 5.7CO1.700 3.400 5.500 10,200


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values by about double for many highways on up toabouttriple or more for streets and secondary roads.Tables through 14 include designs for pavementswith and without concrete shoulders or curbs. Fo rpar k-in lots adjacent lanes provide edge support similar tothat of a concrete shoulder or curb so the right-hand sideof Tables 1 through 14 are used.

Sample ProblemsTwo sample problems follow to illustrate use of the sim-plified design procedure.Design 3Arterial street, two lanesDesign ADT 6200Total trucks per day 1440ADTT 630Clay subgrade4-in. untreated subbaseSubgrade-subbase support low

Concrete MR 650 psi*Doweled joints, curb and gutterSince i t is expected that axle-load magnitudes will beabout the average carried by arterial streets, not unusual-ly heavy or light, Category 3 from Table 9 is selected.Accordingly, Table 13a is used for design purposes.(Table 13a is for doweled joints, Table 13h is for aggre-gate-interlock joints.)For a subgrade-subbase support conservatively classedas low, Table 13a, under the concrete shoulder or curbportion, shows an allowable ADTT of 1600 for an 8-in.-slab thickness and 320 for a 7.5-in. thickness.This indicates that, for a concrete strength of 650 psi,

the 8-in. thickness is adequate to carry the required de-sign ADTT of 630.Design 4Residential street, two lanesADT 410Total trucks per day 21ADTT 8Clay subgrade (no subbase), subgrade support lowConcrete MR 600 psi*Aggregate-interlock joints (no dowels)Integral curb

In this problem, Table 11 representing axle-loadCategory 1 is selected for design use. In the tableunder Concrete Shoulder or Curb, the followingallowable ADTT are indicated:

Slab Thickness. in. ADTT

Therefore, a 5.5-in.-slab thickness is selected to meetthe required design ADTT value of 8

Comments on Simplified ProcedureModulus of RuptureConcrete used for paving should be of high quality** andhave adequate durability, scale resistance, and flexuralstrength (modulus of rupture). In reference to Tables I Ithrough 14, the upper portions of the tables representconcretes made with normal aggregates that usually pro-duce good quality concretes with flexural strengths in thearea of 600 to 650 psi. Thus, the upper portions of thesetables are intended for general design use in this simpli-fied design procedure.The lower portions of the tables, showing a concretemodulus of rupture of 550 psi, are intended for design useonly for special cases. In some areas of the country, theaggregates are such that concretes of good quality anddurability produce strengths of only about 550 psi.Design PeriodThe tables list the allowable ADTTs for a 20-year designperiod. For other design periods, multiply the estimatedADTT by the appropriate ratio to obtain an adjustedvalue for use in the tables.For example, if a 30-year design period is desired in-stead of 20 years, the estimated ADTTvalue is multipliedby 30120. In general, the effect of the design period onslab thickness will be greater for pavements carryinglarger volumes of truck traffic and where aggregate-inter-lock joints are used.Aggregate Interlock or Doweled JointsTables 12 through 14 are divided into two parts, a and bto show data for doweled and aggregate-interlockjoints trespectively. In Table 11, thickness requirements are thesame for pavements withdoweled and aggregate-interlockjoints; doweled joints are not needed for the low trucktraffic volumes tabulated for Category 1. Wheneverdowels are not used, joint spacings should be short-seediscussion on page 3.

User Developed Design TablesThe purpose of this section is to describe how the simpli-fied design tables were developed so that the design engi-neer who wishes to can develop a separate set of designtables based on an axle-load category different from thosegiven in this chapter. Some appropriate situations include

*See discussion under Com ments on Simplified Procedure-Mod-ulus of Rupture, above.**See Portland Cement Association publication Design and Controlof Concrete MixturesWhen fatigue an aly s~s ontrols the design (see footnotes of Tables12 through 14). it will be noted that the AD TT val ue s for dowele d jointsand for aggregate-interlock joints are the same (see topic Jointed Pave-ments in Appendix A ). If erosion ana lys ~s ontrols, concrete modulusof rupture will have no effect on the allowable AD TT .


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(1) preparation of standard sections from which a pave-ment thickness is selected based on amount of traffic andother design conditions, 2) unusual axle-load distribu-tions that may be carried on a special haul road or otherspecial pavement facility, and (3) an increase in legal axleloads that would cause axle-load distribution to change.

Axle-load distributions for Categories through 4 areshown in Table 15. Each of these is a composite of dataaveraged from several state loadometer (W-4) tables rep-resenting pavement facilities in the appropriate category.Also, at the high axle-load range, loads heavier than thoselisted on state department of transportation W-4 tableswere estimated based on extrapolation. These two stepswere desired for obtaining a more representative generaldistribution and smoothing irregularities that occur inindividual W-4 tables. The steps are considered appropri-ate for the design use of these particular categories de-scribed earlier in this chapter.

As described in Chapter 2, the data is adjusted to ex-clude two-axle, four-tire trucks, and then the data arepartitioned into 2000- and 4000-lb axle-load increments.

To prepare design tables, design problems a re solvedwith the given axle-load distribution by computer withthe desired load safety factor at different thicknesses andsubbase-subgrade k values.Allowable ADTT values to be listed in design tables areeasily calculated when a constant, arbitrary ADTT is in-put in the design problems as follows: assume inputADTT is 1000 and that 45.6 fatigue consumption iscalculated in a particular design problem, then

Allowable ADTT 100 X (input ADTT)fatigue or erosion damage

Table 15. Axle Load Distributions Used forPreparing Design Tables Through 14load,

468

10121416182022242628303234

Tande48

12162024283236404448525660

Single axles1693.31732.28483.10204.96124.0056.1138.0215.814.230.96

axles31.9085.59

139.3075.0257.1039.1868.4869.59

4.19

Axles per 1000 trucks*Category 2 Category 3 Category 4

Exclud~ng l l two-axle, four-t~rerucks


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APPENDIX ADevelopment of Design ProcedureThe thickness design pro cedure presented here was pre-pared to recognize current practices in concrete pavem entconst ruc t ion and per formance exper ience wi th con cre tepavements tha t previous des ign procedures have not ad -dressed. These include:

Pavements with different types of load transfer att r ansverse jo ints o r c racksLean concre te subbases under concre te pavementsConcre te shouldersModes of distress, pr imari ly due t o erosion of pave-ment found a t ions , tha t a re unre la ted t o the t r adi -t ional cr i ter ia used in previous design procedures

A new aspect of the procedu re is the erosio n cr i ter ionthat is applied in addit ion to the stress-fat igue cr i ter ion.The erosion cr i ter ion recognizes that pavements c an fai lf rom excessive pumping, e ros ion of found a t ion, and jo intfault ing. The stress cr i ter ion recognizes that pavementscan crack in fat igue from excessive load repeti t ions.

This appen dix expla ins the bas is for these c r ite r ia a ndthe development of the design procedure. References 30a nd 57 give a mo re detai led accou nt of the topic.nalysis of Concrete Pavements

The design proc edure is based o n a comprehensive ana l -ysis of concrete stresses and def lect ions at pavementjoints. corners, and edges by a f ini te-element computerpro gram . x I t a l lows considerat io ns of slabs with f ini tedimensions , var iable axle - load placement , an d the m od-eling of load transfer at t ransverse joints Or cracks andload transfer at the joint between pavement an d concreteshoulder . F or doweled jo ints , dowel proper t ies such asdiam eter and mod ulus of elastici ty are used d irect ly. Fo raggregate inter lock, keyway joints, an d cracks in contin-uously reinforced pave men ts, a spring stiffness value isused to represent the load-def lect ion character ist ics ofsuch joints based o n f ield and laboratory tests.Jointed PavementsAfter analysis of different axle- load posit ions o n the slab,

the c r i tica l p lacements shown in F ig . A l wereestabl ishedwith the fol lowing conclusions:I The most cr i t ical pavement stresses occur when thet ruck whee ls a re placed a t or near the pavement edgeand midway be tween the jo ints , F ig. A I (a ) . S ince thejoints a re a t som e dis tance f rom this loca t ion, tr ans-verse joint spacin g and type of load transfer havevery little effect on the magnitude of stress. In thedesign procedure. therefore, the analysis based onflexural stresses an d fat ig ue yield th e same values fordifferent joint spacings and different types of loadt ransfe r m echanisms (dowels or aggrega te in te r lock)at t ransverse joints. When a concrete shou lder is t ied

(01 Axle - l oo d p o s ~ f ~ o nor c r~ t ico l lexura l s t resses

oncrete shoulderI I ( ~ fsed) I

Free edge orshoulder lolnf

Fig. A l Critical axle load positions.

- Tr ansv er se ~ o m tT r o f f ~ co e


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on t o the m ainline pavement , the magni tude of thecr i t ical stresses is considerab ly reduc ed.2. The most cr i t ical pavement def lect ions occur at thes lab corner when a n axle load i s p laced a t th e jo intwi th th e wheels a t or near the co rner , F ig . Al (b) .*In this si tuation, t ransverse joint spacin g has no ef-fect on th e mag nitude of corn er def lect ions but thetype of load t r ansfe r mechanism has a subs tant ia leffect . This means that design results based on theerosion cr i ter ia (def lect ions) may be substantial ly

affected by th e type of lo ad transfer selected, espe-cial ly when large numbers of trucks are being de-s igned for . A concre te shou lder r educes corner de-f lect ions considerably.Continuously Reinforced PavementsA cont inuously re inforced concre te pavement (CRCP)is one wi th no t r ansverse jo ints a nd , due to the heavy,con tinu ou s steel reinforcement in the longitud inal direc-t ion, the pavement develops cracks at c lose intervals.These crack spacings o n a given project are var iable, run-ning genera l ly f ro m to 10 ft with averag es of 4 t o 5 f t .In the f in i tee lemen t com puter ana lysis , a h igh degreeof load t r ansfe r was ass igned a t the c racks of C R C P an dthe crack spacing was var ied. Th e cr i t ical load posit ionses tabl i shed were the same a s those for jointed pavements .For the longer crack spacings, edge stresses for loadsplaced midway be tween c racks a re of about the samemagni tude a s those for jo inted pavements. Fo r the aver -age and sho rter crack sp acings, the edge stresses are lessthan those for jo inted pavements , because there is notenou gh length of uncracked pavement to deve lo pas muchbending moment .For the longer c rack spac ings , corner def lec t ions a resomewh at less than those for jo inted pavements wi thdoweled t r ansverse jo ints . Fo r average to lon g c rackspac ings , corner def lec t ions a re ab ou t the sam e as thosefor o inted, doweled pavements . F or shor t c rack spac ingsof or 4 f t , corner deflec tions a re som ewhat grea te r thanthose for jo inted, doweled p avements , especia lly for tan-dem-axle loads.Consider ing na tura l var ia t ions in c rack spac ing tha toccur in one stretch of pavemen t, the fol lowing com pari -son of continuou sly reinforced pavements w ith jointed ,doweled pavem ents is ma de. Edge stresses will som etimesbe the sam e and som etimes less. while corner def lect ionswill sometimes be less, the sam e, and greater at dif ferenta reas of the pavement depending on c rack spac ing.The average of these pavement responses is neithersubs tant ial ly b e t te r no r w orse tha n those for jo inted,doweled pavements. As a result, in thisdes ign proced ure,the same pavement responses and c r ite r ia a re appl ied tocont inuously re inforced pavements as those used wi thjointed, doweled pavements . This r ecommendat ion i sconsistent with pavement performance experience. Mostdesign agencies suggest that the thickness of continu ouslyre inforced pavements should be about the same as thethickness of doweled-jointed pavements.

* Th e g rea te s t d e f le c t~o n s o r t r~ d e ms ccu r wh en two ax le s a re p laceda t on e s ~ d e f th e jo ln t a n d o n e ax le a t th e o th e r s~ d e

Truck Load PlacementTruck wheel loads placed at the outside pavement edgecrea te mo re severe condi t ions tha n an y othe r load pos i-t ion. As the truck placement moves inward a few inchesf r om the e dge, t he ef fe ct s de c re a se su b ~ t a n t i a l l~ . ~ 'Only a small f ract ion of al l the trucks run with theiroutside wheels placed a t the edge. Mo st of the trucks trav-el ing the pavement are dr iven with their outside wheelplaced about 2 f t f r om the e dge. ~a r a g in ' s ' ~ t ud i es re -ported in 1958, showed very l i t tle t ruck encro achm ent atpavement edge for 12-f t lanes for pavements with un-pave d shou lde rs . M or e r ec en t s t ud i es by ~ m e r ~ ' sh ow emor e t ruc ks at edge . O the r re ce nt s t ~ d i e s ' ~ how ed fewert rucks a t edge th an Emery. Fo r th is design procedure , themost severe condit ion, 6 of trucks a t edge,* is assumedso as t o be on the sa fe s ide and to take accou nt of r ecentchang es in United Sta tes law perm itt ing wider trucks.At increasing distances inward from the pavementedge, the f requency of load ap plicat ion s increases whilethe magnitudes of stress and def lect ion decrease. Dataon t ruck placement d is t r ibut ion a nd dis t r ibut ion of s t ressand def lec t ion du e to loads placed a t and near the pave-ment edge a re difficult to use direct ly in a design proce-dure. As a result , the distr ibutions were analyzed andmo re easily applied techniques were prepared for designpurposes.For stress-fat igue analysis, fat igue was computed in-cremental ly at f ract ions of inches inward from the slabedge for different t ruck-placement distr ibutions: thisgave th e equivalent edge-stress factors sh own in Fig. A2.(This factor, when multiplied by edge-load stress, givesthe sam e degree of fat igue con sum ptio n that would resultf rom a given truck placement distr ibution.) The mostsevere condit ion, 6 t ruck encroachment, has been in-corporated in the design tables.

Percent trucksof or o f f edge

Taragm 2 lone 0 4 6Emery paved shoulder) 6 0 0

PERCENT TRUCKS T EDGE

Fig A2 Equivalent edge stress factor depends onpercent of trucks at edge

*As used here , the term percent t rucks a t edge is defined as thepercent of to ta l t rucks tha t are traveling with the outs ide of the contactarea of the outs ide t i re a t or beyond the pavem ent edge.


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Fo r erosion analysis, which involves def lect ion at theslab corner , the most severe case (6 of trucks at edge) isagain assumed . W here there is no concrete shoulde r , cor-ner loadings (6 of trucks) are cr i tical ; and w here thereis a concrete shoulder , the greater number of loadingsinward f rom the pavement corner (94 of t rucks) a recr i t ical . These factors are incorporated into the designcharts as fol lows:Percent erosion dam age 100 Cn, ( C / Ni

where: n expec ted num ber of axle -loadrepe t it ions for ax le -groupNi allowable number of repeti-t ions for axle -groupC 0.06 for pavements wi thoutshoulder , and0.94 for pavements withshoulder

T o save a design calculat ion step , the effects of C / N i ]are incorporated in Figs. 6a a n d b of Cha p t e r a ndTables 11 throu gh 14 of C hapte r 4 .

Variation in Concrete StrengthRecogn it ion of the var iat ions in concrete stren gth is con-sidered a real ist ic add it ion t o the design proced ure. Ex-pected ranges of variations in the concrete's modulus ofrupture have far greater effect than the usual var iat ionsin the proper t ies of o th er mate r ia l s, such as subgrade andsubbase stre ngth , and layer thicknesses. Variat ion in con-crete strength is introduced by reducing the modulus ofrupture by one coeff icient of var iat ion.For design purp oses, a coeff icient of var iat ion of 15is assumed and is incorpora ted in to the des ign char t s andtables. The user does not direct ly apply this effect . Thevalue of 15 represents fair - to-good quali ty con trol , an d,combined with other effects discussed elsewhere in thisapp end ix, w as selected as being real ist ic a nd giving rea-sonable design results .

Concrete Strength Gain With AgeThe 28 da y f lexural s t r ength (mo dulus of rupture ) is usedas the design strength. This design procedure, however ,incorporates th e effect of concrete strength gain af te r 28days. This m odif icat ion is based o n an analysis that incre-mented s t rength ga in and load repe t i t ions month bym on th fo r 20-year an d 40-year design per iods. Th e effecti s inc luded in the des ign char t s and tables so the users imply inputs the 28-day va lue a s the des ign s t rength .

Warping and Curling of ConcreteIn addi t ion to t r af fic loading, concre te s labs a re a l so sub-jec ted to warping an d cur l ing. W arping is the upwardconcavede format ion of the s lab due to var ia t ions in mois-ture co ntent with slab depth. The effect of warpin g is two-fold: I t r esult s in loss of sup por t a long the s lab edges andalso in compressive restraint stresses in the slab bot tom .Since warping is a long-term phenomenon, i ts resultant

effect is influenced greatly by creep.Cur l ing re fe r s to s lab behavior due to var ia t ions oftempera ture . Dur ing the day, when the top sur face i swarmer t han the bo t tom , tens i le - res t raint s t r essesdeve lopa t the s lab bot tom . D ur ing the night, the tempera ture dis -tr ibutio n is reversed and tensi le restraint stresses developa t the s lab sur face . Tempera ture dis t r ibut ion i s usual lynon l i ne a r a nd c ons t a n tl y c ha ng ing . A l so , ma x imu m da y-t ime an d night t ime tempera ture di f ferent ia l s exist forshor t du r a t i ons .Usually the combined effect of cur l ing and warpingstresses are subtractive from load stresses because themois ture content and tem pera ture a t the bot tom of thes lab exceed tha t a t the top more than the reverse .The comp lex s i tua t ion of d i f fe rent ia l condi t ions a t aslab's top and bottom plus the uncertainty of the zero-s t ress pos i t ion make i t d i ff icul t to compu te o r measurethe restraint stresses with any degree of confidence orver i f ica t ion. At present , the informat ion ava i lable onac tua l magn i tudes of r es t ra int s t r esses does no t war rantinco rpora t io n of the i tems in th i s des ign procedure .As for th e loss of su ppo r t , th i s is cons idered indi rec tlyin the erod ibil i ty cr i ter ion, which is der ived from actu al

f ie ld per formanc e an d there fore incorpora tes normal lossof suppor t condi t ions .Calculated stress increase du e to loss of sup port var iesfrom ab ou t 5 to 15 . This theoretical stress increase iscoun teracted in the real case because a port ion of the loadis dissipated in br inging the slab edges back in contactwi th the sup por t . Th us , the incrementa l load s t ressdue toa warping-typ e loss of sup po rt is not incorporated in thisdes ign p rocedure .

FatigueTh e f lexural fat igue cr i ter ion used in the pro cedure pre-sented here is shown in Fig. A3 It is similar to t hat usedin the previous PC A m ethod ' j4 ' based conservat ive ly on

lo l o 3 Io4 Io Io6 10LOAD REPETIT IONS

Fig A3 Fatigue relationships


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4 5 - 4 9 )studies of fat igue research except th at i t is applied toedge-load stresses that ar e of higher magnitude. A modi-fication in the high-load-repetition range has been madeto eliminate the discontinu ity in the previous curve thatsometimes causes unrealistic effects.The allowable num ber of load repeti t ions for a givenaxle load is determined based on the stress rat io (f lexuralstress divided by the 28-day modulus of rupture) . Thefatigue curve is incorporated into the design charts foruse by the designer.Use of the fatigue cr i ter ion is made on the Miner hy-pothesis'48' tha t fatigu e resistance no t consu med by repe-ti t ions of one load is available for repeti t ions of otherloads. In a design problem, the total fat igue consumedshould not exceed 100%.Com bined with th e effect of reducing the design mod-ulus of r uptu re by o ne coeff icient of variation, the fatiguecriter ion is considered t o be conservative for thicknessdesign purposes.

ErosionPrevious mechanist ic design procedures for concretepavements a re based on th e principle of l imiting the f lex-ural stresses in a slab t o safe values. This is done to avoidflexural fat igue cracks due to load repeti t ions.I t has been appare n t tha t there is a n impor tan t modeof d is tress in add i t ion to fa t igue c rack ing tha t needs tobe addressed in the design proc ess. This is the erosion ofmaterial beneath and beside the slab.Ma ny repeti t ions of heavy axle loads at sla b cornersan d edges cause pum ping; erosion of subgrade, subbase,and shou lder mater ia ls ; vo ids under and ad jacen t to theslab; and fault ing of paveme nt joints, especially in pave-ments with undoweled joints.

These part icular pavem ent distresses ar e considered tobe more closely related to pavement deflections than toflexural stresses.Correlations of deflections computed from the f inite-element analysis 'x 'with A AS H O R oad ~ e s t ' ~ ~ 'e r fo rm-ance data were not completely satisfactory for d

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