thickness design concrete hwy street pavements
DESCRIPTION
Thickness Design forConcrete Highway andStreet PavementsTRANSCRIPT
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The author of thk engineering bulletin is Robert G.Packard, 1? E., principal paving engineer, PavingTransportation Department, Portland CementAssociation.
This publication is intended SOLELY for use by PROF!3SIONALPERSONNEL who we competent to evaluate the si~ificance andlimitations of the information provided herein, and who wiff 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 fulfextent permitted by law.
0 Portland Cement Asscwiation 1984, reprinted 1$95
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PCONTENTS
Thickness Design forConcrete Highway and
Street Pavements
Chapter I. Introduction . . . . . . . . . . . . . . . . . . . . . . . ...3Applications of Design Procedures. . . . . . . . . . . . ...3Computer Programs Available . . . . . . . . . . . . . . . ...4Basis for Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4Metric Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...4
Chapter 2. Design Factora . . . . . . . . . . . . . . . . . . . . . ...5Flexural Strength of Concrete . . . . . . . . . . . . . . . . ...5Subgrade and Subbase Support . . . . . . . . . . . . . . ...6Design Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...6Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8
Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8ADTT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...8Truck Dkectional Dktribution . . . . . . . . . . . . ...10Axle-Load Dktribution . . . . . . . . . . . . . . . . . . ...10
Load Safety Factors . . . . . . . . . . . . . . . . . . . . . . . ...10
Chapter 3. Design Procedure(Axle-Load Data Available) . . . . . . . . . . . . . . . . . . ...11
Fatigue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . ...11Erosion Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . ...11Sample Problems . . . . . . . . . . . . . . . . . . . . . . . . . ...13
Chapter 4. Simplified Design Procedure(Axle-Load Data Not Available) . . . . . . . . . . . . . . . ...23
Sample Problems . . . . . . . . . . . . . . . . . . . . . . . . . ...30Comments on Simplified Procedure . . . . . . . . . . ...30
Modulus of Rupture . . . . . . . . . . . . . . . . . . . . . ...30Design Period . . . . . . . . . . . . . . . . . . . . . . . . . . ...30
Aggregate Interlock or Doweled Joints . . . . . ...30User-Developed Design Tables . . . . . . . . . . . . . . ...30
Appendix A. Development of DesignProcedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...32
Analysis of Concrete Pavements . . . . . . . . . . . . . ...32Jointed Pavements . . . . . . . . . . . . . . . . . . . . . . ...32Continuously Reinforced Pavements . . . . . . . ...33
Truck-Load Placement . . . . . . . . . . . . . . . . . . . . . ...33Variation in Concrete Strength . . . . . . . . . . . . . . ...34Concrete Strength Gain with Age . . . . . . . . . . . . ...34Warping and Curling of Concrete . . . . . . . . . . . . ...34Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...34Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...35
Appendix B. Daaign of Concrete Pavementswith Lean Concrete Lower Course . . . . . . . . . . . . . ...36
fsan Ccmcrete Subbase . . . . . . . . . . . . . . . . . . . . ...36Monolithic Pavement . . . . . . . . . . . . . . . . . . . . . . ...36
Appendix C. Analysis of Tridem Axle Loads . . . . ...39
Appendix D. Estimating Traffic Volumeby Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...42
Appendix E. References . . . . . . . . . . . . . . . . . . . . . . ...44
Daaign Worksheet for Reproduction . . . . . . . . . . . ...47
Figures
1.Flexural strength, age, and design relationships,2. Approximate interrelationships of soil classifications
and bearing values.3. Proportion of tmcks in right lane of a multilane
divided highway.4, Design 1A.
5. Fatigue analysis—allowable load repetitions basedon stress ratio factor (with and without concreteshoulders).
6a. Erosion analysis—allowable load repetitions basedon erosion factor (without concrete shoulder).
6b. Erosion analysis—allowable load repetitions basedon erosion factor (with concrete shoulder).
7. Design 1D,8. Design 2A.
A 1. Critical axle-load positions.A2. Equivalent edge stress factor depends on percent of
trucks at edge.A3. Fatigue relationships.BI. Design chart for composite concrete pavement (lean
concrete subbase),
B2. Design chart for composite concrete pavement(monolithic with lean concrete lower layer).
B3. Modulus of rupture versus compressive strength.
Cl. Analysis of tridems,
Tables
1. Effect of Untreated Subbase on k Values2. Design k Values for Cement-Treated Subbase
3. Yearly Rates of Traffic Growth and CorrespondingProjection Factors
4. Percentages of Four-Tke Single Units and Trucks(ADTT) on Various Highway Systems
5. Axle-Load Data6a. Equivalent Stress-No Concrete Shoulder6b. Equivalent Stress-Concrete Shoulder7a. Erosion Factors—Doweled Joints, No Concrete
Shoulder7b. Erosion Factors—Aggregate-Interlock Joints, No
Concrete Shoulder8a. Erosion Factom—Doweled Joints, Concrete
Shoulder8b. Erosion Factors—Aggregate-Interlock Joints,
Concrete Shoulder
9. Axle-Load Categories10. Subgrade Soil Types and Approximate k Values11. Allowable ADTT, Axle-Load Category 1—Pave-
ments with Aggregate-Interlock Joints12a. Allowable AD’IT, Axle-Load Category 2—Pave-
ments with Doweled Joints12b. Allowable ADTT, Axle-Load Category 2—Pave-
ments with Aggregate-Interlock Joints13a. Allowable ADTT, Axle-Load Category 3—Pave-
ments with Doweled Joints
13b. Allowable ADT”f, Axle-Load Category 3—Pave-ments with Aggregate-Interlock Joints
14a. Allowable ADTT, Axle-Load Category 4—Pave-ments with Doweled Joints
14b. Allowable ADl_f, Axle-Load Category 4—Pave-ments with Aggregate-Interlock Joints
U
15. Axle-Load Dktribution Used for Preparing DesignTables 11 Through 14
Cl. Equivalent Stress — TridemsC2. Erosion Factors — Tridems — Doweled JointsC3. Erosion Factors — Tridems — Aggregate-Interlock
JointsD 1. Design Capacities for Multilane HighwaysD2. Design Capacities for Uninterrupted Flow on Two-
Lane Highways
3us.
customary Metric Conversionunit unit coefficient
in. mm 25.40
ft m 0.305lb kg 0.454lbf N 4.45kip kN 4.45lb/in.x kPa 6.89lb/ in.x (k value) MPa/m 0.271
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CHAPTER 1
IntroductionThis bulletin deals with methods of determining slabthicknesses adequate to carry traffic loads on concretestreets, roads, and highways,
The design purpose is the same as for other engineeredstructures—to find the minimum thickness that will re-sult in the lowest annual cost as shown by both first costand maintenance costs. If the thickness is greater thanneeded, tbe pavement will give good service with lowmaintenance costs, but first cost will be high. If the thick-ness is not adequate, premature and costly maintenance
P and interruptions in traffic will more than offset the lowerfirst cost. Sound engineering requires thickness designsthat properly balance first cost and maintenance costs.
While this bulletin is confined to the topic of thicknessdesign, other design aspects are equally important to en-sure the performance and long life of concrete pavements.These include—
● Provision for reasonably uniform support. (See Sub-grades ond Subbases for Concrete Pavements,*)
● Prevention of mud-pumping with a relatively thinuntreated or cement-treated subbase on projectswhere the expected truck traffic will be great enoughto cause pumping. (The need for and requirements ofsubbase are also given in the booklet cited above. )
● Use of a joint design that will afford adequate loadtransfeq enable joint sealants, if required, to be effec-tive; and prevent joint distress due to infiltration.(See Joint Design for Concrete Highway and StreetPavements.** )
● Use of a concrete mix design and aggregates that willprovide quality concrete with the strength and dura-bility needed for long fife under the actual exposureconditions. (See Design and Control of ConcreteMixrf4re$.T)
The thickness design criteria suggested are based ongeneral pavement performance experience. If regional orlocal specific performance experience becomes available
Pfor more favorable or adverse conditions, the design cri-teria can be appropriately modified. This could be thecase for particular climate, soil, or drainage conditionsand future design innovations.
Applications of Design Procedures
The design procedures given in this text apply to the fol-
lowing types of concrete pavements: plain, plain doweled,reinforced, and continuously reinforced.
Plain pavements are constructed without reinforcingsteel or doweled joints. Load transfer at the joints is ob-tained by aggregate interlock between the cracked facesbelow the joint saw cut or groove. For load transfer to beeffective, it is necessary that short joint spacings be used.
Plain-doweled pavements are built without reinforcingsteeb however, smooth steel dowel bars are installed asload transfer devices at each contraction joint and rela-tively short joint spacings are used to control cracking.
Reinforced pavements contain reinforcing steel anddowel bars for load transfer at the contraction joints. Thepavements are constructed with longer joint spacingsthan used for unreinforced pavements. Between the joints,one or more transverse cracks will usually develop; theseare held tightly together by the reinforcing steel and goodload transfer is provided.
Commonly used joint spacings that perform well are 15ft for plain pavements,tt not more than 20 ft for plain-doweled pavements, and not more than about 40 ft forreinforced pavements. Joint spacings greater than thesehave been used but sometimes greater spacing causespavement distress at joints and intermediate cracks be-tween joints.
Continuously reinforced pavements are built withoutcontraction joints, Due to the relatively heavy, continu-ous-steel reinforcement in the longitudinal direction,these pavements develop transverse cracks at close inter-vals. A high degree of load transfer is developed at thesecrack faces held tightly together by steel reinforcement.
The design procedures given here cover design condi-tions that have not been directly addressed before by
‘Portland Cement As$o.iation publication 1S029F’**portl..d @nent Association publication 1S059P.
tPortle.”d Cement Aswwiaticm publication EBOOIT.TtFor very thin pavements, a 15-ft joint spacing may beexcessive–sw
the afor.sme”tioned PCA publication . . joint desigm
3
other procedures. These include recognition of—
1, The degree of load transfer at transverse joints pro-vided by the different pavement types described.
2. The effect of using a concrete shoulder adjacent tothe pavement; concrete shoulders reduce the flex-uraI stresses and deflections caused by veh]cle loads,
3. The effect of using a lean concrete (econocrete) sub-base, which reduces pavement stresses and defect-ions, provides considerable support when truckspass over joints, and provides resistance to subbaseerosion caused by repeated pavement deflections.
4. Two design criteria (a) fatigue, to keep pavementstresses due to repeated loads with]n safe limits andthus prevent fatigue cracking and (b) erosion, tolimit the effects of pavement deflectionsat slab edges.joints, and corner; and thus control the erosio~ offoundation and shoulder matefiak. The criterion forerosion is needed since some modes of pavementdistress such as pumping, faulting, and shoulderdistress are unrelated to fatigue,
5. Triple axles can be considered in design. While theconventional single-axle and tandem-axle config-urations are still tbe predominant loads cm highways,use of triple axles (tridems) is increasing. They areseen on some over-the-road trucks and on specialmads used for hauling coal or other minerals. Tri-dems may be more damaging from an erosion crite-rion (deflection) than from a fatigue criterion,
Selection of an adequate thickness is dependent uponthe choice of other design features—jointing system, typeof subbase if needed, and shoulder type.
Wkh these additional design conditions, the thickmssrequirements of design alternatives, which influence cost,can lx directly compared.
Chapter 2 describes how the factors needed for solvinga design problem are determined. Chapter 3 details thefull design procedure that is used when specific axle-load-distribution data are known or estimated. If detailedaxle-load data are not available, the design can be accom-plished as described in Chapter 4, by the selection of oneof several categories of data that represent a range ofpavement facilities varying from residential streets up tobusy interstate highways.
Computer Programs Available
Thickness design problems can be worked out by handwith the tables and charts provided here or by computerand microcomputer with programs that are availablefrom Portland Cement Association.
Basis for Design
The thickness design methods presented here are basedon knowledge of pavement theory, performance, and re-search experience from the following sources:
1. Theoretical studies of pavement slab behavior byWestergaard,{ ‘-’)* Pickett and Ray,(G ‘land reCent]y
developed finite-element computer analyses, one ofwhich is used as the basis for this design procedure. [81
2. Model and full-scale tests such as Arfington Tests(9]and several research projects conducted b? PCA and ‘i-.’J
other agencies ofl$~$bases,( ‘*’S)joints( ’d- ‘]and con-crete shoulders.
3. Experimental pavements subjected to controlled testtraffic, such as the Bates Test Road,[2’] the Pkts-burg Test Highway~22) the Mar$and R6ad Test~231the AASHO** Road Test, {24-2) and studies of in-service highway pavements made by various statedepartments of transportation.
4. The performance of normally constructed pave-ments subject to normal mixed traffic.
All these sources of knowledge are useful. However,the knowledge gained from performance of normallyconstructed pavements is the most important. Accord-ingly, it is essential to examine the relationship betweenthe roles that performance and theory play in a designprocedure, Sophisticated theoretical methods developedin recent years permit the responses of the pavement—stresses, deflections, pressures—to be more accuratelymodeled. This theoretical analysis is a necessary part ofa mechanistic design procedure, for it allows considera-tion of a full range of design-variable combkations. Animportant second aspect of the design procedure is thecriteria applied to the theoretically computed values—the limiting or allowable values of stress, deflection, orpresmre. Defining the criteria so that design results arerelated to pavement performance experience and researchdata is critical in developing a design procedure, ‘u
The theoretical parts of the design procedures givenhere are based on a comprehensive analysis of concretestresses and deflections by a finite-element computer pro-gram. co The program ~odcls the conventional design
factors of concrete properties, foundation support, andloadings, plus joint load transfer by dowels or aggregateinterlock and concrete shoulder, for axle-load placementsat slab interior, edge, joint, and corner.
The criteria for the design procedures are based on thepavement design, performance, and research experiencereferenced above including relationships to performanceof avements at the AASHO Road Test{ z’) and to stud-i~~~~ 29, of the faulting of pavements.
More information on development and basis of the de-sign procedure is given in Appendix A and Reference 30.
Metric VersionA metric version of this publication is also available fromPortland Cement Association—publication EB209P.
*Supemcript numbers in parentheses denote references at the end ofthk text.
**Nw the American Association of State Hishway and Transporta-
tion Officials (AASHTO).
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CHAPTER 2
Design FactorsAfter selection of the type of concrete pavement (plainpavement with or without dowels, reinforced jointedpavement with dowels, or continuously reinforced pave-ment), type of subbase if needed, and type of shoulder(with or without concrete shoulder, curb and gutter orintegral curb), thickness design is determined hased onfour design factors:
1. Flexural strength of the concrete (modulus of rup-
ture, MR)
2. Strength of the subgrade, or subgrade and subbase
P combination (k)
3. The weights, frequencies, and types of truck axleloads that the pavement will carry
4. D&ign period, which in this and other pavement de-sign procedures is usually taken at 20 years, but maybe more or less
These design factors are discussed in more detail in thefollowing sections. Other design considerations incorpo-rated in the procedure are discussed in Appendix A.
Flexural Strength of Concrete
F-
Consideration of the flexural strength of the concrete isa,ppficable in the design procedure for the fatigue crite-rion, which controls cracking of the pavement underrepetitive truck loadings.
Bending of a concrete pavement under axle loads pro-duces both compressive and flexural stresses. However,the ratios of compressive stresses to compressive strengthare too small to influence slab thickness design. Ratios offlexural stress to flexural strength are much higher, oftenexceeding values of 0.5. As a result, flexural stresses andflexural strength of the concrete are used in thickness de-sign. Flexural strength is determined by modulus of rup-ture tests, usually made on 6x6x30-in. beams.
For specific projects, the concrete mix should be de-signed to give both adequate durability and flexuralstrength at the lowest possible cost. Mix design proce-dures are described in the Portland Cement Associationpublication Design and Control of Concrete A4ixt ures.
The modulus of rupture can be found by cantilever,center-point, or third-point loading. An important dif-ference in these test methods is that the third-point testshows the minimum strength of the middle third of thetest beam, while the other two methods show strength atonly one point. The value determined by the more con-servative thkd-point method (American Society for Test-ing and Materials, ASTM C78)isused fordesign in thisprocedure.*
Modulus of rupture tests are commonly made at 7, 14,28, and90days. The 7-and 14daytest results arecom-pared with specification requirements for job control andfor determining when pavements can be opened to traffic.
The 28-day test results have been commonly used forthickness design of highway sand streets and are recom-mended for use with this procedure; 90day results areused forthedesign of airfields. These values are used be-cause there arevery fewstress repetitions during the first28 or 90 days of pavement life as compared to the millionsof stress repetitions that occur later.
Concrete continues to gain strength with age as shownin Fig. 1. Strength gain isshown bythesolid curve, whichrepresents average MR values for several series by lab-oratory tests, field-cured test beams, and sections of con-crete taken from pavements in service.
fn this design procedure theeffects** ofvafiationsinconcrete strength from point to point in the pavementand gains in concrete strength with age are incorporatedin the design charts and tables. The designer does not di-rectly apply these effects but simply inputs the average28-day strength value.
*Fora standard 30-in. beam, c.nlcr-point-load inEtcst val.es will beabout 75 psi higher, and cantilever-loading 1.s1 values.bout 160 psihigher than cticrd-p.int-loa$ i.g test values. Th.x higher values are noti“te”ded tok.sdfor deszgnpurposts. Iftbese other test methods areused, adowmvard adjustment should be made byestabtisbing acorre-lationto thtrd-poi.t-load test values.
..’IIe,e effects are discussed in Appendix A.
5
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Fig. 1. Flexural strength, age, and design relationships.
Subgrade and Subbaae Support
The support given to concrete pavements by the subgrade,and the subbase where used, is the second factor in thick-ness design. Subgrade and subbase support is defined interms of the Westergaard modulus of subgrade reaction(k). It is equal to the load in pounds per square inch on aloaded area (a 30-in. diameter plate) divided by the de-flection in inches for that load. The k values are expressedas pounds per square inch per inch (psi/ in,) or, morecommonly, as pounds per cubic inch (pci). Equipmentand procedures for determining k values are given inReferences 31 and 32.
Since the plate-loading test is time consuming and ex-pensive, the k value is usually estimated hy correlation tosimpler tests such as the California Bearing Ratio (CBR)or R-value tests. The result is valid became exact deter-mination of the k value is not required; normal variationsfrom an estimated value will not appreciably affect pave-ment thickness requirements. The relationships shown inFig. 2 are satisfactory for design purposes,
The AASHO Road Test{ 241gave a convincing demo”.stration that the reduced subgrade support during thawperiods has little or no effect on the required thicknessof concrete pavements. This is true because the brief per-iods when k values are low during spring thaws are morethan offset by the longer periods when tbe subgrade isfrozen and k values are much higher than assumed fordesign, To avoid the tedious methods required to designfor seasonal variations in k, normal summer- or fa[/-
weaher k wlues are used as reasonable mea” valuesIt is not economical to me wmeated subbases for the
sole purpose of increasing k values. Where a subbase isused,* there will be an increase in k that should be usedin the thickness design, If the subbase is an untreatedgranular material, the approximate increase in k can betaken from Table 1.
The values shown in Table 1are based on the Burmis-ter[’3) analysis of two-layer systems and plate-loadingtests made to determine k values on subgrades and sub-bases for full-scale test slabs.( ‘4]
Table 1. Effect of Untreated Subbaseon kValues,
S.::;;$ Subbase k value, pci
pci ‘ 4 in, 6 in. I 9 i“. 12 in.
50 65 75 65 110100 130 140 160 190200 220 230 270 320300 320 330 370 430
Table 2. Design k Values for Cement-Treated Subbases
“O
Cement-treated subbases are widely used for heavy-duty concrete pavements. They are constructed fromAASHTO Soil Classes A- 1, A-2-4, A-2-5, and A-3 gronu-[ar materials. The cement content of cement-treated sub-base is based on standard ASTM laboratory freeze-thawand wet-dry tests(~’ 35)and PCA weight-loss criteria. [36]Other procedures that give an equivalent qualit y of mate-rial can be used. Design kvalues forcement-treated sub-bases meeting these criteria are given in Table 2.
In recent years, the use of lean concrete subbases hasbeen ontheincrease. Thickness design ofconcretepave- ~ments on these very stiff subbases represents a specialcase that is covered in Appendix B.
Design Period
The term design period is used in this publication ratherthan pavement lije, The latter is not subject to precise
definition. Some engineers and highway agencies con-sider the life of a concrete pavement ended when the firstoverlay is placed. The life of concrete pavements mayvary from less than 20 ycarson some projects that havecarried more traffic than originally estimated or have haddesign, material, or construction defects to more than 40years on other projects where defects are absent,
The term design period is sometimes considered to besynonymous with the term traffic-malysis period, Sincetraffic can probably not be predicted with much accuracyfora Iongerperiod, a design period of 20yearsiscom-monly used in pavement design procedures. However,there are often cases where useofashorter orlonger de-sign period may be economically justified, such as a spe-cial haul road that will be used foro”ly afewyears, ora
*UW .fs.bbaseis xc. remended f.rpr.jects where conditions that .would cause nmd-p.mpi”g prevaik for diwmim of whm subbasessh.uldbeuwda.d h.wthi.k they sh.uldb., se the PCAp.blicati.n, “u’Subgrades ond Subbasesfor Ccmc,,,e Pavemenm.
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premium facility for which a high level of performancefor a long time with little or no pavement maintenance isdesired. Some engineers feel that thedesign period forrural and urban highways should heinthe range of Xtto35 years.
The design period selected affects thickness designsince it determines how many years, and thus how manytrucks, thepavement must serve. Selection ofthcdesignperiod for a specific project is based on engineering judg-ment and economic analysis of pavement costs and serv-ice provided throughout the entire period.
Traffic
Tbe numbers and weights ofheavy axle loads expectedduring thedesign life are major factors in the thicknessdesign of concrete pavement. These are derived from esti-mates of
—ADT (average daily traffic in both directions, allvehicles)
—ADTT (average daily truck traffic in both directions)
—axle loads of trucks
Information on ADTis obtained from special trafficcounts or from state, county, or cit y traffic-volume maps.This ADT is called the present or current ADT. The de.sign ADT is then estimated by the commonly used meth.ods discussed here. However, any other method that givesa reasonable estimate of expected traffic during the designlife can be used,
Projection
One method forgetting thetraftlc volume data (designADT) needed is to use yearly rates of traffic growth andtraffic projection factors. Table 3 shows relationships be-tween yearly rates of growth and projection factors forboth 20- and 40-year design periods.
In a design problem, the projection factor is multipliedby the present ADT to obtain a design ADT representingtheaverage value forthedcsign period. Insomeproce-dures, this is called AADT (average annual daily traffic).
The following fact ors influence yearly growth rates andtraffic projections:
1. Attracted or diverted traffic-the increase over exist-ing traffic because of improvement of an existingroad way.
2. Normal traffic growth—the increase due to increasednumbers and usage of motor vehicles.
3. Generated traffic-the increase due to motor vehicletrips that wnuld not have been made if the mw facil.ity had not been constructed.
4. Development traffic-the increase due to changes inland use due to construction of the new facifity.
The combined effects will cause annual growth rates ofabout 2Yoto 6%. Tbeserates correspond to20-yeartraf-ficprojection factors of 1.2to 1.8asshown in Table3,
The planning survey sections of state highway depart-merits are very use fulsources ofknowledge about trafticgrnwth and projection factors.
Table 3. Yearly Rates of TrafffcGrowth and CorrespondingProjection Factora’
Yearlyrate oftraffic
gro;th,
1~%22,%33,%44M55%6
1,11.21.21.31.31.41.51,61.61.71.8
Prg:;ecron
40 yea~s
1.21.31.51.61.82,02.22.42.72.93.2
L--’”
,Faclor. represent values at the middesig” periodthat are widely used incurre”t pr.ctke, Anothermtihod of cmnp.fing these factors is basedon theaveraae annual value. Differences (bothcompoundintere<t) between these two methods will ”rarelyaffect design.
Where there is some question shout the rate of growth,it may be wise to use a fairly high rate. This is true onintercity routes andon urban projects where ahigh rateof urban growth maycause ahlgher-than-expected rateoftraftic growth. However, thegrowth oftruck volumes
“u’may be less than that for passenger cars.High growth rates do not apply on two-lane-rural roads
and residential streets where the primary function is landuseorabutting property service. Their growth rates maybe below 2% per year (projection factors of 1.1 “to 1.3).
Snme engineers suggest that the use of simple interestgrowth rates may be appropriate, rather than compoundinterest rates, which when used with a long design periodmay predict unrealistically heavy future traffic.
Capacity
The other method of estimating design ADT is based oncapacity—the maximum number of vehicles that can usethe pavement without unreasonable delay. Tbis methodof estimating the volume of traffic is described in Appen-dix D and should be checked for specific projects wherethe projected traffic volume is high; more traffic lanesmay be needed if reasonable traffic flow is desired.
ADTT
The average daily truck traffic in both directions (ADTT)is needed in the design procedure. It may be expressed asa percentage of ADT or as an actual value. The ADTTvalue includes only trucks with six tires or more and doesnot include panel and pickup trucks and other four-tire ._vehicles.
The data from state, county, or city traffic-volume ~maps may include, in addition to ADT, the percentage of
8
trucks from which ADTT can be computed.For design of major Interstate and primary system
projects, the planning survey sections of state depart-
pments of transportation usually make specific traffic sur-veys, These data are then used to determine the percent-age relationship between ADT’T and ADT.
ADTT percentages and other essential traffic data can
also be obtained from surveys conducted by the highwaydepartment at specific locations on the state highway sys-tem. These locations, called Ioadometer stations, havebeen carefully selected to give reliable information ontraffic composition, truck weights, and axle loads. Sur-vey results are compiled into a set of tables from whichthe ADTT percentage can be determined for the highwayclasses within a state. This makes it possible to computethe ADTT percentage for each station. For example, ahighway department Ioadometer table (Table w-3) for aMidwestern state yields the following vehicle count for aIoadometer station on their Interstate rural system:
All vehicles—ADT . . . . . . . . . . . . . . . . . . . . ...9492Trucks:
All single units and combinations . . . . . ...1645Panels and pickups . . . . . . . . . . . . . . . . . . . 353Other four-tire single units . . . . . . . . . . . . 76
Therefore, for this station:
T* = ]645 – (353 + 76) = 1216
1216‘DTT ‘ ZY2x ’00= ‘3%
This ADTT percentage would be appropriate for de.
,0sign of a project where factors influencing the growth andcomposition of traffic are similar to those at this load-ometer station.
Another source of information on ADTT ercentages!’37)is the National Truck Characteristic Report. Table 4,
which is taken from this study, shows the percentages offour-tire single units and trucks on the major highwaysystems in the United States. The current publication,which is updated periodically, shows that two-axle, four-tire trucks comprise between 40’% to 65% of the totalnumber of trucks, with a national average of 49% It isfikely that the lower values on urban routes are due tolarger volumes of passenger cars rather than fewer trucks.
Table 4. Percentage of Four-Tire Single Units andTrucks (ADTT) on Varioua Highway Systems
It is important to keep in mind that the ADTT percent-ages in Table 4 are average values computed from manyprojects in all sections of the country. For this reason,these percentages are only suitable for design of specificprojects where ADTT percentages are also about average.
For design purposes, the total number of trucks in thedesign period is needed. This is obtained by multiplyingdesign ADT by ADTT percentage divided by 100, timesthe number of days in the design period (365 X designperiod in years).
For facilities of four lanes or more, the ADTT is ad-
justed by the use of Fig, 3.
PROPORTIONOF TRuCKS IN RIGHT LANE
Fig. 3. Proportion of trucks in right lane of a multilanedivided highway. (Derived from Reference 3&)
‘Tr.cks-xcludes panels and pickups and other f. .r-ti r. vehiclcs.
I Rural average daily traffic I Urban average daily traffic.m9
Truck Directional Distribution
In most design problems, it is assumed that the weightsand volumes of trucks traveling in each direction are fairlyequ81-50-50 distribution-the design essumes that pave-ment in each dirsction carries half the total ADTT. Thkmay not be true in special cases where many of the trucksmay be hauling full loads in one direction and returningempty in the other direction. If such is the case, an appro-priate adjustment is made.
Axie-Load Oiatribufion
Data on the axle-load distribution of the truck traffic isneeded to compute the numbers of single and tandemaxles* of various weights expected during the design per.iod. These data can be determined in one of three ways:(1) special traffic studies to establish the loadometerdatafor the specific project; (2) data from the state highwaydepartment’s Ioadometer weight stations (Table W4) orweigh-in-motion studies on routes representing truckweights and types that are expected to be similar to theproject under design; (3) when axle-load distributiondata are not available, methods described in Chapter 4based on categories of representative data for differenttypes of pavement facilities.
The use of axle-load data is illustrated in Table 5 inwhich Table W4 data have been grouped by 2-kip and4-kip increments for single- and tandem-axle loads, re.spectively. The data under the heading “Axles per 1000Trucks” are in a convenient form for computing the axle-Ioad distribution, However, an adjustment must be made,Column 2 of Table 5 gives values for all trucks, includingthe unwanted values for panels, pickups, and other four-tire vehicles. To overcome this difficulty, the tabulatedvalues are adjusted as described in the Table 5 notes,
Column 4 of Table 5 gives the repetitions of varioussingle- and tandem-axle loads expected during a 20-year-design period for the Design 1 sample problem given inChapter 3.
Load Safety Factors
In the design procedure, the axle loads 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 uninterrupted traffic flow and high vol-umes of truck traffic, LSF = 1.2.
● For highways and arterial streets where there will bemoderate volumes of truck traffic, LSF = 1,1.
● For roads, residential streets, and other streets thatwill carry small volumes of truck traffic, LSF = 1.0.
Aside from the load safety factors, a degree of conserv-atism is provided in the design procedure to compensate
Table 5. Axle-Load Data
~
~ngle axles
2a30
2&28
24-26
22-24
2W22
1&20
16-18
14-16
12-14
1}12
0.28
0.65
1.33
2.84
4.72
10.40
13.56
18.64
25.69
81.05
0.58
1.35
2.77
5.92
9.83
21.67
28.24
38,83
53,94
168,85
Tandem axles
48-52 I 0.94 I 1.96
44-48
4s44
36-40
32-36
28-32
24-28
20-24
15-20
12-16
1.89
5.51
16.45
39.06
41.06
73,07
43.45
54,15
59,85
3.94
11,48
34.27
81,42
65.54
152.23
90.52
112.81
124.69
6,310
14,690
30,140
64,410
106,900
235,800
307,200
422,500
586,900
,637,000
21,320
42,670
124,800
372,900
885,800
930,700
1,656,000
984,900
1,227,000
1,356,000
Columns 1 and 2derived from Ioadometer W-4 Table. This table al$oshows13,215 tolal trucks coumed with 6,916 two-axle, four-tire trucks (52%].
Column 3 Column 2 values adjusted for two.wle, four-tire trucks equalto Column 2/[1 52/100).
Column 4 = Col. rnn3X [tr.cksindesig” period ))1000. %esmnpleproblem,Design 1, In which trucks in design period (onedirection) tolal 10,880,000,
for such things as unpredicted truck overloads and nor-mal construction variations in material properties andlayer thicknesses. Above that basic level of conservatism(LSF = 1.0), the load safety factors of 1.1 or 1,2 providea greater allowance for the possibility of unpredictedheavy truck loads and volumes and a higher level of pave-ment serviceability appropriate for higher type pave-ment facilities.
In special cases, the use of a load safet y factor as high as1.3 may be justified to maintain a higher-than-normallevel of pavement serviceability throughout the designperiod. An example is a very busy urban freeway with noalternate detour routes for the traffic. Here, it may bebetter to provide a premium facility to circumvent for along time tbe need for any significant pavement main-tenance that would disrupt traffic flow.
*See Appendix C if it isexpected that trucks with tridem loads will beincluded i“ the traffk f.tecast.
L-J
10
CHAPTER 3
Design Procedure(Axle-Load Data Available)
The methods in this chapter are used when detailed axle-load distribution data have been determined or estimatedas described in Chapter 2.*
Fig. 4 is a worksheet** showing the format for corn.pleting design problems.t It requires as input data thefollowing design factors discussed in Chapter 2.
● Type of joint and shoulder
● Concrete flexural strength (MR) at 28 days
● k value of the subgrade or subgrade and subbasecombination?
● Load safety factor (LSF)
P ● Axle-load distribution (Column 1)
● Expected number of axle-load repetitions duringthe design period (Column 3)
Both a fatigue analysis (to control fatigue cracking)and an erosion analysis (to control foundation and shoul-der erosion, pumping, and faulting) are shown on the de-sign worksheet.
The fatigue analysis will usually control the design oflight-traffic pavements (residential streets and secondaryroads regardless of whether the joints are doweled or not)and medium traffic pavements with doweled joints.
The erosion analysis will usually control the design ofmedium- and heavy-traffic pavements with undoweled(aggregate-interlock) joints and heavy-traffic pavementswith doweled joints.
For pavements carrying a normal mix of axle weights,single-axle loads are usually more severe in the fatigueanalys]s, and tandem-axle loads are more severe in theerosion analysis.
The step-by-step design procedure is as follows: Thedesign input data shown at the top of Fig. 4 are estab-lished and Columns 1 and 3 are tilled out. The axle loadsare multiplied by the load safety factor for Column 2.
● Without concrete shoulder, use Table &z and Fig. 5
. With concrete shoulder, use Table 6b and Fig. 5
Procedure Steps:1. Enter as items 8 and 11 on the worksheet from the
aPPr~Priate table the equivalent stress factors de-pending on trial thickness and k value.
2, Divide these by the concrete modulus of rupture andenter as items 9 and 12.
3. FII1 in Column 4, “Allowable Repetitions; deter.mined from Fig. 5.
4. Compute Column 5 by dividing Column 3 by Col-umn 4, multiplying by 100 then total the fatigue atthe bottom.
Erosion Analysis
Without concrete shoulder
● Doweled joints or continuously reinforced pave-ments# —use Table 7a and Fig. 6a.
● Aggregate-interlock joints—use Table 7b and Fig.6a,
With concrete shoulder
● Doweled joints or continuously reinforced pave-ments~—use Table 8a and Fig. 6b.
● Aggregate-interlock joints—use Table 8band Fig, 6b.
Procedure Steps:
1. Enter the erosion factors from the appropriate tableas items 10 and 13 in the worksheet.
2. FIO in Column 6, “Allowable Repetitions,” fromFig. 6a or Fig. 6b.
Fatigue Analysis*% Chapter 4 when axle-load distribution data are unknown.
.* A b]a”k ~0 rkshect is provided as the M page Of thk bulletin for
p.rposes of reproduction and use in w=ific design problems.Results of fatigue analysis, and thus the charts and figures
~ used, are the same for pavements with doweled and un-
f Computer programs for s.lving design problems are available fr.mP.rtlmd Cement Ass.ciati.n.
doweled joints, and also for continuously reinforcedItSee Appendix B if lean concrete subbase is used.
pavements.~$1. this design procedure, ccmtin”cwsly reinforced pavemems are
treated the same as dowdcd, jointed pavements—seeAppendix A.
11
Calculation of Pavement Thickness
Project A/ 0~ /,4 &.#T- /QA e L7A?r./&/. P&z2/’
Trial thickness 9.5 in. Doweled joints: yes K no —
Subbase-subgrade k /.70 pci Concrete shoulder: yes —no~
Modulus of rupture, MR L5 o psi
Load safetv factor. LSF /. Z?
r
LAxleload,hips
1
Design period ~ years
Single Axles
I I I
8. Equivalent stress 206 10. Erosion factor 2.59
9. Stress rcatiofactor O ? 17
u’
11. Equivalent stress 192 13. Erosion factor z. T?
Tandem Axles 12. Stress ratio factor Z?Jl$K_
uFig. 4. Design 1A.
12
3. Compute Column 7 by dividing Column 3 by Col-umn 6, multiplying by lW, 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 lineruns 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 or 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 100Yo.
Sample Problems
Two sample problems are given to illustrate the steps inthe design procedure and the effects of alternate designs.Design 1 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.
Design 1
Project and Traffic Data:
Four-lane InterstateRolling terrain in rural locationDesign period = 20 yearsCurrent ADT = 12,900Projection factor = 1.5ADTT = 19% of ADT
Traffic Calculations:
Desien ADT = 12.900 X 1.5 = 19,350 (9675 in one di-re;tion)
ADTT = 19,350 X0.19= 3680 (1840 in one direction)
For 9675 one-direction ADT, Fig. 3 shows that theproportion of trucks in the right lane is 0.81. Therefore,for a 20-yeardesign period, the total number of trucks inone direction is
1840 X 0.81 X 365 X 20 = 10,880,000 trucks
Axle-load data from Table 5 are used in this designexample and have been entered in Fig. 4 under the maxi-mum axle load for each group.
Values Used to Calculate Thickness:**
Design 1A: doweled joints, untreated subbase, no con-crete shoulder
Clay subgrade, k = 100 pci4-in. -untreated subbaseCombined k = 130 pci (see Table 1)LSF = 1.2 (see page 10)Concrete MR = 650 psi
Design lB doweled joints, cement-treated subbase, noconcrete shoulder
Same as 1A except:4-in. cement-treated subbasetCombined k = 280 pci (see Table 2)
Design lC: doweled joints, untreated subbase, concreteshoulder
Same as 1A except:Concrete shoulder
Design ID: aggregate-interlock joints, cement-treatedsubbase, no concrete shoulder
Same as 1B except:Aggregate-interlock joints
Design lE: aggregate-interlock joints, cement-treatedsubbase, concrete shoulder
Same as 1D except:Concrete shoulder
Thickness Calculations:A trial thickness is evaluated by completing the designworksheettt shown in Fig. 4 for Design 1A using theaxle-load data from Table 5.
For Design 1A, Table 6a and Fig, 5 are used for thefatigue analysis and Table 7a and Fig. 6a are used for theerosion analysis.
Comments on Design 1
For designs 1A through 1E, a subbase of one type or an-other is used as a recommended practice $onfine-texturedsoil subgrades for pavements carrying an appreciablenumber of heavy trucks.
In Design 1A: (1) Totals of fatigue use and erosiondamage of 63% and 39%, respectively, show that the 9.5-in. thickness is adequate for thedesign conditions. (2) Thisdesign has 37% reserve capacity available for heavy-axleloads in addition to those estimated for design purposes.(3) Comments 1and 2 raise the question of whethera 9.0-in. thickness would be adequate for Design IA. Separatecalculations showed that 9.0 in. is not adequate becauseof excessive fatigue consumption (245Yo). (4) Design 1Ais controlled by the fatigue analysis.
A design worksheet, Fig. 7, is shown for Design 1D toillustrate the comb]ned effect of using aggregate-inter-lock joints and a cement-treated subbase. In Design 1D:(1) Totals of fatigue use and erosion damage of l%t$ and97%, respectively, show that IO in. is adequate. (2) Sepa-rate calculations show that 9.5 in. is not adequate becauseof excessive erosion damage ( 142Yo),and (3) ~sign 1D iscontrolled by the erosion analysis.
(continue donpage21)
*Some guidance is helpful in reducing the number of trial inns. Theeffect of thickness on both the fatigue and erosion damage approxi-mately follows a geometric progression. For example, if 33% and 17870fatigue damage are determined at trial thicknessesof 10 and 8 in., r.-spectivdy, the approximate fatigue damage for t+thickness of 9 in. iscowl to .~ = 77%
:*com& MR. LS F. and submade k value, are tie WM. for DesiEns1A through lE. -
Weme.t-treamd subbase meeting requirements stated on page 6.tTA blank worksheet isprovided asthe last pageof this bulletin for the
p.rp.ses .f =prodtiction and U= in sp=ific de$ign problems.1S.. Subzr.de$ and Subbasesfor Concrete’ P.vetnents. Portland
Cement Aswxiatio” p“bfica.tio.$1 For pavements with aggregate-interlock joints subjected to an ap-
preciable num~r of truck% the fadw ,..M will .$.aW ..1 affectdesign.
13
Table 6a. Equivalent Streaa — No Concrete Shoulder(Singla Axle/Tandam Axle)
Slabthickness,
k of Subgrade-subbase, pci
In. 50 100 150 200 300 500 700
4 825[679 726/585 6711542 634/516 584/486 5231457 484/4434.5 699/586 61 6/500 57f /460 540/435 498/406 4481378 417/363
5 602/51 6 531 /436 493/399 467/376 432/349 390/321 363/3075.5 526/461 484/367 431/353 409/331 379/305 3431278 320/264
6 485/4f 6 4111348 382/31 6 362/296 336/271 304/246 285/2326.5 417/380 367/31 7 341/286 324/267 300/244 2731220 256/207
7 375[349 331 /290 307/262 292/244 2711222 246/199 231/1867.5 340/323 300/268 279/241 265/224 246/203 224/181 210/169
8 311 /300 2741249 255/223 242/208 2251188 205/167 192)1 558.5 285/281 252)232 234/206 222/1 93 206/174 186/154 177/143
9 264/264 232/21 6 216/195 205/181 190/1 63 1741744 163/1 339.5 245/248 215/205 200/183 190/1 70 176/153 161 /134 151/124
10 226/235 200/1 93 186/1 73 177/160 164/144 150/126 141/11710.5 213/222 187/1 83 174[1 64 165/151 153/1 36 140/119 132/110
11 200/21 1 175/1 74 163/155 154/1 43 144/1 29 131/113 123/1 0411.5 133/201 165/165 153/1 48 145/1 36 135/122 123/1 07 116/96
12 177/192 155/156 144/141 137/130 1271116 116/1 02 109/9312,5 1681183 147/151 136/1 35 129/124 120/111 109/97 103/89
13 159/1 76 139/144 129/1 29 122/119 113/106 103/9313.5
97[85152/1 68 132/136 122/123 116/114 107/102 98/89 92/81
14 144/162 125/133 116/116 110/109 102/98 93[85 88/78
Table 6b. Equivalent Straaa — Concrete Shoulder(Single Axle/Tandem Axle)
Slabthic;n~,
k of subgrade-subbase, pci
50 100 150 200 300 500 700
4 640/534 559/466 517/439 489/422 452/4034.5 547/461
409/388 363/384479/400 4441372 421 /356 390/336 355/322 333/31 6
5 4751404 41 7/349 387[323 367/308 341 /2905.5
311/274 294/267416)360 366/309 342/285 324/271 302/254 276/236 261/231
6 3721325 3271277 304/255 269/241 270/225 247/210 23412036.5 334/295 294/251 274/230 260/218 243/203 223/1 88 212/180
7 302/270 266/230 248/21 O 236/1 98 220/1 84 203/170 192/1627,5 275/250 243/21 1 226)1 93 215/182 201/168 185/155 176/148
8 252/232 222/196 207/1 79 197/168 185/155 170/142 162/1358,5 232/21 6 205/1 62 191/166 182/156 170)1 44 157/131 150/1 25
9 215/202 190/171 177/1 55 169/146 158/1 34 146/1 22 139/1 169.5 200/1 90 176/160 164/146 157/137 1471126 136/114 129/1 08
10 186/1 79 164/151 153/137 146/129 137/116 127/107 121)10110.5 174/170 154/143 144/130 137/121 128/711 119/101 1>3/95
11 164/161 144/1 35 135/1 23 129/1 15 1201105 112/95 106/9011.5 154/153 136/1 28 1271117 121/109 113/100 105/90 100/65
12 145/146 128/1 22 120/111 114/104 107/95 99/86 95/8112.5 137/1 39 121/117 113/106 106/99 101/91 94/82 90/77
13 130/1 33 *15)112 107/101 102/95 96/86 89/78 8517313,5 124/127 10S/107 102/97 97/91 91183 85174 81 /70
u
“w’
14 I 118/122 104/103 97/93 93/87 87179 81/71 77167
14
“’U
60--(--’20
\
58
56110
54
52
50 100
46
+
9044
t
42
40 80maZ 38
c)” 36 —ao-1 70
34w-1
32z
26
i
5024
22
i
20 40
18
1630
14
12
10 2“
/
Q 15
[
/-
0.2”
“..3
.—-—
/
“.s”
0.(3”
Q ?“
0.80
0. 9“
I.”.
1.s”
10,000,0001:-2-
1,ocwooo8—
6-
4-
2-
loo,ooo—
8-
6-
4-
.. —.— —— -——+ )
2-
1o,ooQ—
8-
6-
4-
2-
looo—
8-
6-
4-
-1
~
2
100
20i=1=wa.wa
Fig. 5. Fatigue analysis—allowable toad repetitions basedon stress ratio factor (with and without concrete shoulder).
15
Table 7a. Erosion Fectora — Doweled Jointa, No Concrete Shoulder(Single Axle/Tandem Axle)
Slabthickness,
k of subgrade-subbase, pci
In. 50 100 200 300
<
4.5 I 3.59/3. 70 3.5713.65 3.56/3.61
5 3.45[3. 58 3.43/3.52 3.42/3. 48 3.41/3,45 3.40)3.42 3.38/3.405.5 i
500 700
4 I 3. 74/3.83 3.7313.79 3.7213.75 3.7113.73 3.70/3.70 3.68/3.671 3.55/3,58 3.5413.55 3.52/3.53
I 3.3313.47 3.31/3.41 3.29/3.36 3.28/3.33 3.27/3.30 3.26/3.28
6 I 3,2213.38 3.1 9/3, 31 3,18/3.26 3. 17/3.23 3.1 5/3. 20 3.14/3,176.5 3,11 /3. 29 3.09/3, 22 3.07/3, 16 3,06/3. 13 3.05/3. 10
7
3.03/3,07
I 3,02/3.21 2.99/3.14 2,97/3,08 2.96/3.05 2.95/3.01 2.94/2.987,5 2.93/3.14 2.91/3,06 2.86/3.00 2.6712.97 2.86/2, 93 2.84/2.90
8 2.85/3.07 2,62/2.99 2.80/2.93 2.7912.89 2,7712.65 2.76/2.828.5 2.7713.01 2.7412.93 2.72)2.86 2.7112.82 2,89/2.78 2. 68/2.75
9 2,70/2.96 2.67/2.87 2.65/2.80 2,63/2,76 2.6212.71 2.61/2.689.5 2,63)2.90 2.60/2.81 2.58/2.74 2.56/2,70 2.55/2.65 2.5412,62
10 2.5612,85 2.54/2. 76 2,51/2.68 2.50/2.64 2.46/2. 59 2.4712,5610.5 2.50/2.81 2.47[2,71 2.4512.63 2,4412.59 2.4212.54 2.41/2.51
11 2.4412,76 2.42/2.67 2.39/2.58 2.38)2.54 2.36/2.49 2,35/2,4511,5 2.36[2.72 2.36/2,62 2.3312.54 2.32/2.49 2.30[2. 44 2.29/2.40
12 2.33/2. 68 2.30/2.58 2.28/2.49 2.26/2,44 2,2512.39 2.23/2.3812.5 2.2812.84 2.25)2.54 2.2312.45 2.2112.40 2, 19/2.35 2. 18/2.31
13 2.23[2. 61 2. 20/2.50 2.1812,41 2.1612.36 2. 14/2.3013.5 2,1612,57 2.t5/2 ,47
2.1312.272.1312.37 2, 11/2.32 2.09/2.26
14
2.08[2, 23
2. 13/2.54 2. 11/2,43 2.06/2.34 2,07/2.29 2.05/2. 23 2.03/2. 19
Table 7b. Erosion Factors — Aggregate-Interlock Joints,No Concrete Shoulder (Single AxleiTandem Axle)
Slabthickness,
k of subgrade-subbme, pci
in. 50 100 200 300 500 700
4 3.94/4. 03 3.91/3.95 3.68/3.89 3.86/3.86 3.62/3, 83 3,77/3.804.5 3.79/3.91 3.7613.82 3.73/3.75 3.71 [3, 72 3.6813.68 3.64/3.65
5 3. 86/3,81 3.63/3,72 3,60/3.64 3,5813.805.5 3.54/3.72
3.55[3 ,553,51/3,62 3.4813,53
3. 52/3.523.46/3.49 3.43/3.44 3.41 /3.40
6 3.44/3. 64 3.40/3.53 3. 37[3. 44 3.35/3.40 3.32/3.346.5
3.30/3, 303.34/3. 56 3.30/3.46 3.26/3.38 3. 25/3.31 3.22/3. 25 3.20/3, 21
7 3.26/3.49 3.21/3.39 3. 17/3.29 3. 15/3.24 3,1 3/3. 17 3,11/3,137.5 3, 16/3,43 3. 13/3.32 3.09/3.22 3.07/3, 17 3.04/3,1 o 3.02/3.06
8 3.1 1/3.37 3.05/3.26 3.01/3.18 2.99/3. 10 2.96/3.03 2.94/2.998,5 3.04/3,32 2.96/3.21 2.93/3.10 2.81/3.04 2.S812.97 2.8712.!33
9 2.98/3.27 2,91/3.16 2,86/3,05 2.84/2.99 2.81/2.929.5
2.79/2.872.92/3.22 2.65/3.11 2.60/3.00 2.77/2.94 2.7512.86 2.73/2.81
10 2.66/3. 18 2.79/3.06 2.7412.95 2.71/2.89 2.68/2.81 2.66/2.7610,5 2.81/3.14 2.74/3.02 2.66/2.91 2.65/2.64 2.62/2.76 2,60/2,72
11 2.77[3. 10 2.69/2.98 2.63[2.86 2.60/2. 80 2,5712.7211.5 2.7213,06 2.64/2.94
2.54/2.672.58/2.82 2,5512.76 2.51/2,68 2.49/2.63
12 2.68/3.03 2.60/2,90 2.5312.78 2,5012.72 2.46/2.6412.5
2.44/2. 582.64/2.99 2,5512.87 2,48[2. 75 2.4512,68 2.41/2.60 2.39/2.55
13 2.60/2.96 2.51/2.83 2.4412.71 2.40/2.65 2.36/2.56 2.34/2.5113.5 2.56/2.93 2.47/2.80 2.40/2. 68 2.36/2.61 2.32/2.53 2.30/2. 48
14 2.5312.90 2.4412.77 2.36/2.65 2.32/2.58 2,28[2. 50 2,25[2.44
16
60 T I20
—110
50- — 100
– 90
40 – – 80
tio~ — — ~—
30 – – 60
u) (/)Il. a
Z G
~- 25- – 50 ~“ao 0J -1
uw
-1 i
;~ 20– — 40 :
w; n~ la- .(n z
35 1-
16- -
– 30
14- -
– 25t2- -
lo- — 20
9- - 18
8— 16
Fig. 6a. Erosion analysis—allowable load repetitionsbased on erosion factor (without concrete shoulder),
— 2.0
— 2.2
– 2.4
Y k 2.6 — ~._
a – 2.8g
u~
– 3.0
~mo —3.2
5
– 3.4
– 3.6
— 3.8
— 4.0
loo,cK)o,ooo8—
6-4-
2-
10,000,000 =8-
6-
4-
2-~.+
I ,000,000:
8-
6-
4-
2-
100,000:
6-
6-
4-
2-
IQOOO -
8-
6-
4-
2-
1000 —
17
Table &. Erosion Factors — Doweled Joints, Concrete ShoulderC3inale Axle/Tandem Axle)
Slabthic:ny,
k of s. bgrade-subbase, pci
50 100 200 300 500 700
4 3.28/3.30 3.24/3.20 3.21/3.13 3.1 9/3. 10 3.1 5/3.09 3.12/3.084.5 ! 3.13/3.19 3.09/3.08 3.08/3.00 3.04/9 !36 3 (11/7937?),/7Q,5 I 3.0113.09 2.97/2.98 2.93/2.89 2.90/2.84 2.8712.79 7.35/7.775.5 2.90/3. 01 2.85/2. 89 2.81/2,79 2.7912.74 2.7612,68 2.7312.65
8 2,7912.93 2.7512,82 2,70/2.71 2,66/2.65 76S/7 SR 7 67/95A6.5 2.70/2.66 2,6512.75 2.61/2,63 2.58[ 2.57
+
7 2.61/2.797.5 2.53/2.73
8 2.46/2. 688.5 2.39/2.62
9 2.3212.57
2.5612.662.48/2.62
2.41/2.562.34/2, 51
2.2712,46
2.52/2.562.44/2.50
2.3612.442.29/2,39
2.2212,34
. . . . . . . . . . .2.55/2.50 2.52)2.45
2.49/2.50 2.46)2.42 2.43/2, 382.41 [2.44 2.38/2.36 2.35/2.31
2.33)2.38 2.30/2, 30 2.2712.242.26/2. 32 2,22/2,24 2.20/2, 18
2.1912.27 2, 16/2.19 2. 13/2.139.5 2.26/2.52 2.21/2.41 2,16/2.29 2. 13/2.22 2,09/2, 14 2.07/2.08
10 2.2012.47 2. 15[2. 36 2, 10/2.25 2.07/2, 16 2.03/2.09 2.01/2.0310,5 2. 15/2,43 2.09/2.32 2.04/2.20 2.01/2.14 1.87/2.05 1.85/1.99
11 2. 10/2,39 2.04/2.28 1.99/2. 16 1.95/2.09 1.92/2.01 1.89/1.9511.5 2.05/2.35 1.99/2.24 1.93/2. 12 1.90/2.05 1.67/1.97 1.8411,91
12 2.00/2.31 1.94/2.20 1,88/2.09 1.6512.02 1.82/1.93 1.7911.8712.5 1.95/2.27 1.69/2. 16 1.64/2.05 1.81/1.98 1.77/1.89 1.7411,84
13 1.91/2,23 1.85/2, 13 1.79/2.01 1.76/1.95 1,72/1.86 1.70/1.8013.5 1.66/2.20 1,81/2.09 1.75/1.96 1.72/1.91 1.68/1.83 1.65/1.77
14 1.82/2, 17 1.76/2.06 1.71/1.95 1.67/1.88 1.64/1.80 1.61/1,74
Table 8b. Erosion Factors — Aggregate-Interlock Joints,Concrete Shoulder (~;gl; AxleiTandem Axlej
slabthickness,
t
k of S“bgrade-subbase, pci
in. 50 100 200 300 500 700
4 3.46/3,49 3.42/3.39 3.3813.32 3.36/3.29 3,32/3.26 3.28/3.244,5 3.32/3.39 3,28/3.28 3.2413.19 3,22/3. 16 3,1 9/3, 12 3.1 5/3. 09
5 i 3.20/3.30 3. 16/3.18 3, 12/3.09 31 0/3.05 3.07/3.00 3.04/?. 975,5 3.10/3.22 3.05/3, 10 3,01/3,00 2.99/2,95 2.96/2,90 2.93/2.66
6 3.00/3.15 2.95/3,02 2.90/2,92 2.68/2.87 2,66/2.616.5 2.91/3,06 2.86/2.96
2,6312.772,81/2,85 2.79/2.79 2,7612.73 2.7412.66
7 2.83/3.02 2,77/2.90 2.7312.78 2.7012.727.5
2.68/2.66 2.65/2.612.76/2,97 2,70/2.84 2.65/2.72 2,62/2.66 2.60/2.59
8
2.5712.54
2.69/2.92 2.63/2.79 2.5712.67 2.55/2.61 2.52/2.53 2.50/2.486.5 2.63/2.88 2.56/2.74 2.51/2.62 2.48/2. 55 2.4512.48 2.43/2.43
9 2.57/2.83 2.50/2.70 2.4412,57 2,42/2.51 2,38/2.43 2.36/2.389.5 2.51/2.79 2,4412,65 2.38/2,53 2.36/2,46 2.3312.38 2,30/2.33
10 2.46/2.75 2,39/2,61 2.33/2.4910.5
2.30/2,422.41/2,72
2.27[2 ,34 2.24/2.262.33/2.58 2.2712.45 2,24/2.36 2,21/2,30 2.1 9/2.24
11 2.36/2. 66 2.26/2.54 2.22/2.41 2.19/2.34 2.16/2.26 2. 14/2.2011.5 2.32/2.65 2.2412.51 2. 17!2.36 2.>4/2.31 2.11/2.22 2.09)2. 18
12 2.28/2.62 2. 19/2.48 2, 13/2.34 2. 10/2.27 2.06/2. 19 2.04/2.1312.5 2,2412.59 2.15/2.45 2.09/2.31 2.05/2.24 2.02/2, 15 1.99/2.10
13 2,20/2.56 2. 11/2,42 2.04/2,26 2.01/2.21 1,98[2. 12 1,95/2,0613.5 2. 16/2,5s 2.06/2.39 2.00/2,25 1.97/2, 18 1.93/2.09 1.91/2,03
14 2. 13/2.51 2,04/2.36 1.97/2.23 1.83/2. 15 1.89/2.06 1.87[2. 00
‘L--J
w
“-/’
18
60-1-120
/
110
50 I 00
90
40 80
70
30 60
!16
30
14
2512
10 20
9 18
8 16
rFig. 6b. Erosion analysis—allowable load repetitionsbased on erosion factor (with concrete shoulder).
—1.6
— 1.8
—2.0
–2.2
a—2.4
Pv2 – 2.6
~(n: —2.8w
—3.0
—3.2
— 3.4
— 3.6
IOO,OOQOOO
‘a2-1
IQOOQOOO16
i
2
I ,Ooo,ooo8
6
4
i
2- 2g~1-W
100,000— k8- :
a6- 0
-1
4- ?m4g
J
2- 2
IQooo—
8-
6-
14
2
1000
19
Calculation of Pavement Thickness
Trial thickness— /A. & in. Doweled joints: yes _ no z
Subbase-$ ubgrade h ~ Pci Concrete shoulder: yes _ no L u
Modulus of rupture, MR =~ psi
Load safety factor, LSF /7Design period =L years
%%.. C&z?#’(+&&d5.A&
Fatigue analysis Erosion analysis
Axle Multiplied Expectedload, by repetitionskips. LSF Allowable Fatigue, Allowable Damage
/. zrepefitio”s percent repetitions percent
1 2 3 4 5 6 T
6. Equivalent sbess~ 10. Erosion factor z. 72
Single Axles9. Stress ratio factor ~ 2.57
11. Equivalent stress. /@7 13. Erosion factor –~
Tandem Axles 12. Stress ratio factor ~
Total0.6 I Total
%?/ L)
Fig. 7. Design ID.
—
20
Design
1A
lBlcID
lE
I
Worksheets for the other variations of Design 1 are not
shown here but the results are compared as follows:
Subbase
Gin. gm”ular
Gin. cement-treated
hi”, granular
4-in. cement-treated
4+n. cement-treated
Joints
doweled
doweled
doweled
aggregateinterlock
aggregateinterlock
Umcreteshoulder
no
no
yes
no
yes
Thicknessq.i~emer. t,
m.
9.5
8.5
8.5
10.0
8.5
For Design 1 conditions, use of a cement-treated sub-base reduces the thickness requirement by 1,0 in. (Design1A versus 1B); and concrete shoulders reduce the thick-ness requirement by 1.0 to 1.5 in. (Designs 1A versus ICand ID versus 1E). Use of aggregate-interlock joints in-stead of dowels increases the thickness requirement by1.5 in. (Design 1B versus 1D). These effects will vary indifferent design problems depending on the specific de-sign conditions.
Design 2
Project and Traffic Data:
Two-lane-secondary roadDesign period = 40 yearsCurrent ADT = 600Projection factor = 1.2
P ADTT = 2.5% of ADT
Traffic Calculations:
Design ADT = 600 X 1.2 = 720ADTT = 720 X 0.025 = 18
Truck traffic each way = $ = 9
For a 40-year design period:
9 X 365 X 40 = 131,400 trucks
Axle-load data are shown in Table 15, Category 1, andthe expected number of axle-load repetitions are shownin Fig, 8.
Values Used to Calculate Thickness:
Design 2A: aggregrate-interlock Joints, no subbase,* noconcrete shoulder
Clay subgrade, k = 100pciLSF = 1.0Concrete MR = 650 psi
Design 2B: doweled joints,** no subbase, no concreteshoulder
Same as 2A exceptDoweled joints
TMckness Calculations:
For Design 2A, a trial thickness of 6 in. is evaluated bycompleting the worksheet shown in F]g. 8, according tothe procedure given on page 11. Table da and Fig. 5 areused for the fatigue analysis and Table 7band Fig. .5aareused for the erosion anal ysis.
For Design 2B, a worksheet is not shown here but thedesign was worked out for comparison with Design 2A.
Comments on Design 2
For Design 2A: (1) Totals of fatigue use and erosiondamage of 89% and 8%, respectively, show that the 6.O-in.thickness is adequate. (2) Separate calculations show thata 5.5-in. pavement would not be adequate because ofexcessive fatigue consumption. (3) The thickness designis controlled by the fatigue analysis-which is usually thecase for light-truck-traffic facilities.
The calculations for Design 2B, which is the same asDesign 2A except the joints are doweled, show fatigueand erosion values of 89% and 21%,respectively. Com-ments: (1) The th]ckness requirement of 6.0 in. is the sameas for Design 2A. (2) The fatigue-analysis values are ex-actly the same as in Design 2A. T(3) Because of the dow-els, the erosion damage is reduced from 870 to 2%; how-ever, this is immaterial since the fatigue analysis controlsthe design.
For the Design 2 situation, it is shown that doweledjoints are not required. This is borne out by pavement-performance experience on light-truck-traffic facilitiessuch as residential streets and secondary roads and alsoby studies 128w ~h~~i”gtheeffects of the number of trucks
on pavements with aggregate-interlock joints.
*Performance experience has show” that subbasm me not requiredwhm truck traffic is very Iighc seethe PCA p.btication, S.bcmdesond.subbmesf., CO..,,(, POVWWIII,.:* Design 2B is sb,wm for illustrative purposes only. Doweled joints
are not neededwhere truck traffic isvery lighq we the PCA publicationJoin! Designfor Co.crele Highww and Srreel Pavemenn.
T The type of load transfer at the joim40wels, or aggregate inter-lock4ces not affect the fatigue calculations sincethe critical axle-loadposition for stressand fatigue is where the axle loadsare placed at pave.ment edge and midpanel, away from the joims. See Appendix A.
21
Calculation of Pavement Thickness
Project &&~l- 2A 7+9 -/cm. 5PczG@z&.t/ Lz?za+
Trial thickness 6.0 tn. Doweled joints: yes _ no &
Subbase-subgrade h ~– pci Concrete shoulder: yes _ no ~ ‘u
Modulus of rupture, MR —- ~ psi Design period & yearsLoad safety factor, LSF /. o
nO SU/6&3c
Fatigue analysis
Axle
Erosion analysis
Multipliedload,
Expectedby repetitions
kips LSF Allowable Fatigue, Allowable Damage,
/. o repetitions percent repetitions percent
1 2 3 4 5 6 7
8. Equivalent stress v// 10. Erosio” factor &?. *D
Single Axles9. Stress ratio factor ~
u
11. Equivalent stress_~ 13. Erosion factor ~—
Tandem Axles 12. Stress ratiOlactOr U. 535
Fig. 8. Design 2A.w
22
P
CHAPTER 4
Simplified 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 generated
Pbased 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 tbe axle-load data**because the designs have been presolved by the methodsdescribed in Chapter 3. For convenience in design use, tberesults are presented in Tables 11, 12, 13, and 14, which
Table 9.
Axle-loadcategory
1
2
3
4
de-Load Cat@goriea
Description
Residential streetsRural and secondary roads (low tomedium’)Collector streetsRural and secondary roads (high,)Arterial streets and primary roads (low,)
Arterial streets and primary roads(medium.)Expressways and urban and ruralinterstate (low to medium.)
Arterial streets, primary roads,expressways (high’):~b~~ and rural Interstate (medium to
I..=.. ,
nr
correspond to the four categories of traffic. Appropriateload safety factors of 1.0, 1.1, 1.2, and 1.2, respectively,have been incorporated into the desigo tables for axle-Ioad Categories 1, 2,3, and 4. Tbe 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 date arenot available, Table 10 lists approximate k values for dif-ferent soil types. If a subbase is to be used—see Chapter 2
*On page 30, guidelinesfor preparing designtables for axle-load dis-tributions d~ffemnt fmm th.se givemhere are discussed.
** Axle.load data for the four categories are given in Table 15.
afti c
ADTT.+
ADT
20C-800
7oe-5ooo
3000-12,CO02 lane
3000-50,000+4 lane or more
3000-20,0002 lane
3000-1 50,000+4 lane CMnmre
%
t -3
5-18
3-30
a-30
Per dav
up to 25
40-1000
500-50004
150&8000+
Maximum axle kinds, kips
3ingle axles
22
26
30
34
Tandem axles
38
44
52
60
,. ‘The descript.m high, nwd. m, .r 1.$’+refer to the relative weights .1 ..1. loads for the type of street or road:that Is, ,Tow, for a rural Interstate would represent heavier loads than low,, for a seco.d.,y mad,
‘Trucks —w-axle, four-tire Irwks excluded,
23
Tabla 10. Subarade Soil Types and discussion under “Comments on Simplified Pro-App;oximate k Values
k valuesrange,
Type of soil SUppofl pcl
Fine-grained soils in which silt andclay-size pariicles predominate I I 7s120
Low
Sands and sand-gravel mixtures with Mediummoderate amounts of silt and clay
13&170
sands and sand-gravel mixturesrelatively free of plastic fines
High 180-220
Cement-treated subbasOS (see page 6) Very high 25&400
under “Subgrade and Subbase Support’’—the estimatedk value is increased according to Table 1 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 1, 2, 3, or 4.
3. Fkrd slab thickness requirement in the appropriateTable 11, 12, 13, or 14. (In the usc of these tables, see
ccdure,” page 30.)In the correct useof Table 9, the ADT and ADTT val-
ues are not used as the primary criteria for selecting the .....axle-load category—the data are shown only to illustratetypical values. Instead, it is correct to rely more on the uword 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 asimilar composition of tmffic. Other methods of estimat-ing ADT and ADTT are discussed on pages 8 and 9,
The allowable ADTT values (two dircctions)fisted 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-exle,four-tire trucks. Therefore, the number of allowabIetrucks of alI types will begrcaterthanthe tabulated ADTT
(continued on page 30)
*For facilities of four lanesor more, the ADTT isadjusted by the useof Fig. 3.
Table 11. Allowable ADTT,* Axle-Load Cate@ry 1Pavements with Aggregate-lntertock Joints (Dowels not needed)
No Concrete ehoulder or Curb Concrete Shoulder or Curb
Slab Subgrade-subbase support Slabthickness, thick#r+s%
Subgrade-subbase support
in. LrJW Medium High Low Medium High
4 0.2 0.9
4.5.- 0,) 4.5 2 8 25
: ~ 0.1 0.8 3 5 30 130 330z. 5.5 3 15 45 5.5 320(,c 6 40 1S0 430
z 6.5 330
.- 5 0.1 0,4 4E
0.1
5.5 0.5 3 9 4.5 0.2 1 5
s 6 8 36 98 5 6 27 75
K6.5 76 300 760 5.5 73 2eo 730
z y 520 6 610
.- 5,5 0.1 0.3 1 4.5 0.2 0.6
: ;,51 6 16 5 0.6 4 13
13 60 160 5.5 13 57 150
K 7 110 403z
6 130 460
7,5 620
Note Fatigue analysis controls the design.
Note: A fractional ADTT indicates that the pavement can carry unlimited passenger cars and two-axle, four-the trucks, but only a few heavy trucks per week (ADTT of 0.3 x 7 days indicates two heavy trucks per week.)
.ADTT excludes two-axle, four-tire trucks, so total number of trucks allowed will be greater—see text.
,..
L-J
24
Table 12s. Allowable ADTT,” Axle-Load Category 2 — Pavements with Doweled Joints
No Concrete S’houl&r or Curb Concrete ahouldec or Curb
Slab Subgrade-subbase supportthickness,
in. Low Medium Hiah Verv hioh
.-E
5’1, w
Slab I Subgrade-subbase s“ppmt
thickness,In. Low Medium High Very high
5 3 9 425.5 9 42 120 450
6 96 360 970 34006.5 710 26Q0
7 4200
5.5 I 3 17
6 3 14 41 lSU6.5 29 120 320 1100
7 210 770 19007,5 1100 4000
I
Note: Fatigue analysis controls the design. .ADTT exd”des two-axle, four-tire trucks so mtel number.1 tr.cks allowed wilt be greater–see text.
Table 12b. Allowable ADTT.” Axle-Load Cateaorv 2- Pavements with Aggregate-Interlock Joints-.No Concrete shoulder or Curb Concrete Shoulder or Curb
Slab Subgrade-subbase supportthic~~,
Low Medium High Very high
I
8 13W. 19CW
w6.5 4 19
.-~ 7 I 11 34 150
WE===’
Slab Subgrade-subbase supportthickness,
m. Low Medium High Very high
5 3 9 425.5 9 42 120 450
6 e6 380Jm.. 97W .
6,5 650. - 1000” 1400,’ 21OIY.
7 1100-. 1900”
6 19 64 220 6106.5 I&l 620 1400.. 2100,,
I
7 1000 1900,.
.ADTT excludes two-axle, I..,-tire trucks total ““mbw of tr.cks allowed will be greater—see text,‘+Erosio” analysis controls the design: otherwise fatigue analysis controls.
25
Table 13s. Allowable ADTT,* Axle-Load Category 3- Pavementa with Doweled Joints
No Concrete Shoulder or Curb
Slab Subgrade-subbase supportthickness,
in. Low Medium High Very high
= I 7.5 I 250z
sz 130 350 1,300. 8.5 lea,,
640 i ,600 6,200
a 9 700 2,700 7,000 11,500,,z 9.5 2,7CQ 10,800
10 9,900
Concrete Shoulder or Curb
~ ““”
Slab Subgrade-subbase support uthic$~,
Low Medium High Very high
a===6.5 I 67
7 120 4407,5 270 8s0 2,300
8 I 370 1,300 3,200 10.s006.5 1,600 5,800 14,100
9 6,&10
.ADTT excludes two-axle, four-tire truck% total number of trucks allowed will be greater—see text... Erosionanalysis controls the design; otherwise fatigue analysis comrols. ‘u
26
v’
Table 13b. Allowable ADTT,* Axle-Load Category 3 — Pavements with Aggregate Interlock Jointa
n Slabthic;~
Subgrade-subbase support
Low Medium High Very highI
7,5 ~o.. 25W .
8 130- 350- 8308,5 ,@y, 640,, 900.- 1,300
% 9 680 1,000 1,300 2,000z 9.5 960.
1,500 2,000 2,900
10 1,3CC 2,1C!U 2,800K
4,300
z 10.5 1,800 2,900 4,000 6,300
11 2,500 4,000 5,700 9,20011.5 3,300 5,500 7,900
12 4,400 7,500
8 73.. 310++8.5, 14W. 380”’ 1,300
. 9 160,. 640. - 1,300a
2,0009.5 63W + 1,503 2,000 2,900
~ ,0. 1,300 2,100 2,800,,
4,300
cc10.5 1,8CU 2,900 4,000 6,3oo
~ 11 2,500 4,000 5,700 9,20011.5 3,300 5,500 7,900
12 4,400 7,5001 1
8 56”6.5 70.. 300>+,.
.— 9 120,, 340., 1,300,.% 9.5 12W+ 520., l,3cKl- 2,900z ,00 460,, 1,9CW, 2.800 4,300
E10,5 1,600,+ 2,91Y3 4;000 6,300
~ 11 I 2,500 4,000 5,700 9,2oo11,5 3,300 5,500 7,9C+I
12 I 4.400 7,500
ConcreteShoulderor Curb
Slabthickness,
Subgrade-subbase support
tn. Low Medium High Very high
10.5 5,300
11 8,100
9.5 I 2,300 4.700 S.om
10 I 3,500 7,70010.5 I 5.300
11 S,loo
7 62’,1,5 130,. 460’ +
8 67.. 270., 670.. 2,301Y+8,5 330” 1,200., 2,700 4,700
9 1,400%, 2,900 4,6oo 8,7009.5 2,30+1 4,700 8,000
10 3,500 7,70010.5 5,30U
11 8,1OQ
.ADTT excludes two-axle, four-tire trucks total number 0{ trucks allowed will be greater—see text.,. Fatigue analysis controls the design, otherwise erosion analysiscontrols.
27
Table 14s. Allowable ADTT,* Axle-Load Category 4 — Pavements with Doweled Joints
No ConcreteShoulderor CurbI I
Slab Subgrade-subbase supportthickness,
In. Low Medium High Very high
8 2708.5 120 340 1,300
. 9 140 580 1,500 5,W0E
9.5 570 2,300 5,900 14,70W.E. 10 2,000 8,200 18,701% 25,80W.
+3=cc 10.5 6,700 24,100’. 31 ,801Y. 45,801Y,
z tl 21,800 39,800”11.5 39,70W,
—
8.5 300
,- 9 120 340 1,300% 9.5 120 530 1,400 5,200
z ,0m 480 1,900 5,1W i 9,300
10.5 1,600 6,503 17,500 45,900,,cc> 11 4,900 21,400 53, 8W ‘
11.5 14,500 65,000” ‘
12 44,000
9 2609.5 280
‘: I1,100
12 8,200 40,000
Concrete Shoulder or Curb
I
Slab Subgrade-subbase supportthickness, w
0.. Low Medium High Very high
7 4007,5 240 620 2,100
8 I 330 1,200 3,000 9,8008.5 I 1,500 5,300 12,700 41,100’,
9 5,90+3 21,400 44,900 -9.5 22,503 52,000’”
10 45,20W.
7.5 130 490
8 270 690 2,3ooS.5 340 1,300 3,000 9,900
9 t,40+3 5,000 12,000 40,2009.5 I 5,2’&3 18,800 45,900
10 18,41XI
1
8 130 4808.5 250 620 2,100
9 280 1,000 2,5CW 8,2009.5 1,100 3,900 9,300 30,700
10 3,800 13,600 32,80010.5 12,400 48,2C0 ,
11 40,400‘u
.ADTT excludes two-axle fmr-tire trucks total number of Imck$ allowed will be greater—see text..+Erosion melysi$ c.ntrols the design; otherwise fatigue analysis controls,
28
Table 14b. Allowable ADTT,* Axle-Load Category 4 — Pavemente with Aggregate-interlock Joints
No ConcreteShoulderor Cub- I I
(.Slab Subgrade-subbase supporl
thickness,In. Low Medium High Very high
=$=====8.5 30W+
9 120’” 340” 1,30W.9.5 120,, 530,. 1,400,, 2,300
r
1 1
a ,, I,ow. 3,300 4,50Q 7,2008.0 11.5 2,700 4,500 6,300 10,400
K12 3,600 6,100 8,800 14,900
~ 13 6,300 11,100 16,800
14 10.800
ConcreteShoulderor CurbI
10 ] 2,800 5,500 9,200 ,,,,00
11 5,900 13,600 24,200
12 12,800
I
10I
2,600 5,500 9,200 17,900
I11 5,900 13,600 24,200
12 ] 12,800
I
8 130.. 48W ,8.5 25W , 620” 2,101Y.
9 260,. 1,000.. 2,500.. 5,700
9.5 1,1OQ., 3,4cm 5,500 10,200
10 2,600 5,500 9,200 17,900
11 5,900 13,6W 24,200
12 12,800
.ADTT excludes two-axle, four-tire trucks; total number of trucks allowed w(II be greater—see text.
,. Fatigue analysis controls !he design; otherwise erosion analysis controls.
29
values by about double for many highways on up to abouttriple or more for streets and secondary roads.
Tables 11 through 14 include designs for pavementswith and without concrete shoulders or curbs. For park-ing lots, adjacent lanes provide edge support similar tothat of a concrete shoulder or curb so the right-hand sideof Tables 11 through 14 are used.
Sample Problems
Two sample problems follow to illustrate use of the sim-plified design procedure.
Design 3
Arterial street, twn lanesDesign ADT = 6200Total trucks per day = 1440ADTT = 630Clay subgrade4-in. untreated subbaseSubgrade-subbase support = lowConcrete M R = 650 psi*Doweled joints, curb and gutter
Since it 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 13b 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.
Thk 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 4
Residential street, two lanesADT = 410Total trucks per day = 21ADTT = 8Clay subgrade (no subbase), subgrade suppnrt = lowConcrete MR = 600 psi*Aggregate-interlock joints (no dowels)Integral curb
in this problem, Table 11 representingCategory 1 is selected for design use. Inunder “Concrete Shoulder or Curb,” theallowable ADTT are indicated:
axle-loadthe tablefollowing
Comments on Simplified Procedure
Modulus of Rupture
Cnncrete used for paving should be of high quality** andhave adequate durability, scale resistance, and flexural wstrength (modulus of rupture). In reference to Tables 11through 14, the upper pnrtions 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 fm special cases. In some areas nf the country, theaggregates are such that concretes of good quality anddurability produce strengths of only about 550 psi.
Design Period
The tables list the allowable ADTl% for a 20-year designperiod. Fnr other design periods, multiply the estimatedADTT by the appropriate ratio to obtain an adjustedvalue fnr use in the tables.
For example, if a 30-year design period is desired in-stead of 20 years, the estimated ADTT value is multipliedby 30/20. In general, the effect of the design period onslab thickness will be greater for pavements carryinglarger volumes of tfuck traffic and where aggregate-inter-lock joints are used.
Aggregate-Interlock or Doweled Joints
Tables 12 through 14 are divided into two parts, a and b, u’
to show data for doweled and aggregate-interlockj oints,trespectively. In Table 11, thickness requirements are thesame for pavements with doweled and aggregate-interlockjointy 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 Tables
The purpose of this section is to describe hnw the simpli-fied design tables were develnped 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
Therefore, a 5.5-in. -slab thickness is selected to meetthe required design ADTT value of 8.
30
*See disc.wion under ‘Comments on Simplified Pmcedum—M.d-“1”S of Rupture,- above**See pofila”,j cenm.t Awociat i.. p.b)icat ion Design and Control
of Concrete Mi.wre$.T When fatigue analysis controls the dcsiEn(see footnotes of Tables
12through 14), it will be noted that tbe ADTTvalues fmd.weled jointsand for aggregate-interlock joints are the sane (we topic ..Jointed Pave-
dnmnts- in Appendix A). If emsi.% analysis controls, c.ncmt. modulusof rupture will have no effect m the .dlmvable ADTT.
(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-
,n 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-1oad distributions for Categories 1 through 4 areshown in Table 15. Each of these is a composite of dataaveraged from several state Ioadometer (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 Wq 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 thk 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 are solvedwith the given axle-load distribution by computer withthe desired load safety factor at different thicknesses andsubbase-subgrade k values,
Allowable ADTTvalues to be listed in design tables areeasily calculated when a constant, arbkrary 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
n Allowable ADTT =100 X (input ADTT)
% fatigue or erosion damage
100(1000) _ 2193—
45.6
Table 15. Axle-Load Distributions Used forPreparing Design Tablss 11 Through 14
Axleload,
Axles per 1000 trucks,
kips Category 1 :ategory 2
3ingle :Ies4—~68
10121416182022242628303234
m48
12162024283236404448525660
732.26483,10204,96124.0056.1138.0215.814.230.96
axles31,9085.59
139,3075.0257.1039.1868.4869.59
4.19
233.6o142.70116,7647,7623,8816.61
6.632,601.600.07
47.0191,1559.2545,0030.7444.4354.7638.79
7.761.16
Category 3
182.0247.7331.8225.1516.337.855,211.780.850,45
99.3465.9472.54
121.22103,63
56.2521.31
8.012.911.18
Category 4
57.0768.2741,82
9.694,163.521.780.630.540.19
71,1695.78
109.5478,1820,31
3.523.031.791,070.57
.Excludng all two-axle, Iour-tire trucks.
31
,.
‘u
APPENDIX A
Development of Design ProcedureThe thickness design procedure presented here was pre- the critical placements shown in Fig. A I were establishedpared to recognize current practices in concrete pavement with the following conclusions:construction ‘and performance experience with concretepavements that previous design procedures have not ad- 1dressed. These include:
● Pavements with different types of load transfer attransverse joints or cracks
● Lean concrete subbases under concrete pavements
● Concrete shoulders
● Modes of distress, primarily due to erosion of pave-ment foundations, that are unrelated to the tradi-tional criteria used in previous design procedures
A new aspect of the procedure is the erosion criterionthat is amlied in addition to the stress-fatieue criterion.The ero~~n criterion recognizes that pave~ents can failfrom excessive pumping, e%sion of foundation, and jointfaulting. The stress criterion recognizes that pavementscan crack in fatigue from excessive load repetitions.
This appendix explains the basis for these criteria andthe development of the design procedure. References 30and 57 give a more detailed account of the topic.
Analysis of Concrete Pavements
The design procedure is based on a comprehensive anai-ysis of concrete stresses and deflections at pavementjoints, corners, and edges by a finite-element computerprogram. IN ,t ~I]ow~ ~o”~iderations of slabs with finite
dimensions, variable axle-load placement, and the mod-eling of load transfer at transverse joints 6r cracks andload transfer at the joint between pavement and concreteshoulder. For doweled joints, dowel properties such asdiameter and modulus of elastic ity are used direct] y. For
The most critical Davement stresses occur when thetruck wheels are placed at or near the pavement edgeand midway between the joints, Fig. A l(a). Since thejoints are at some distance from this location, trans-verse joint spacing and type of load transfer havevery little effect on the magnitude of stress. In thedesign procedure, therefore, the analysis based onfk”ral stresses and fatigue yield the same values fOr _.
different joint spacings and different types of loadtransfer mechanisms (dowels or aggregate interlock)at transverse joints. When a concrete shoulder is tied
U“
I I I
L–––––––L–––––_J(.)Axle. I.od p.sil ion for criticolf lexw.1 stresses
maggregate, interlock, keyway joints, and cracks in comim Freeedgem i iuously reinforced pavements, a spring stiffness value is shoulder joint
used to represent the load-deflection characteristics of > Concrete shoulder, (,F medl
such joints based on field and laboratory tests.L–––____J__——––––
Jointed Pavements (b) Axle load pmitio. for critic.! deflections
After analysis of different axle-load positions on the slab, Fig. Al. Critical axle-load positions.
32
Trofficlone
.
d
on to the mainline pavement, the magnitude of thecritical stresses is considerably reduced.
2. The most critical pavement deflections occur at theslab corner when an axle load is placed at the jointwith the wheels at or near the corner, Fig. A I(b). *In this situation, transverse joint spacing has no ef-fect on the magnitude of corner deflections but thetype of load transfer mechanism has a substantialeffect. This means that design results based on theerosion criteria (deflections) may be substantiallyaffected by the type of load transfer selected, espe-cially when large numbers of trucks are being de-signed for. A concrete shoulder reduces corner de-flections considerably.
Continuously Reinforced Pavements
A continuously reinforced concrete pavement (CRCP)is one with no transverse joints and, due to the heavy,continuous steel reinforcement in the longitudinal direc-tion, the pavement develops cracks at close intervals.These crack spacings on a given project are variable, run-ning generally from 3 to 10 ft with averages of 4 to 5 ft.
In the finite-element computer analysis, a high degreeof load transfer was assigned at the cracks of CRCP andthe crack spacing was varied. The critical load positionsestablished were the same as those for jointed pavements.
For the longer crack spacings, edge stresses for loadsplaced midway between cracks are of about the samemagnitude as those for jointed pavements. For the aver-age and shorter crack spacings, the edge stresses are lessthan those for jointed pavements, because there is not
P enough length of untracked pavement to develop as muchbending moment.
For the longer crack spacings, corner deflections aresomewhat less than those for jointed pavements withdoweled transverse joints. For average to long crackspacings, corner deflections are about the same as thosefor jointed, doweled pavements. For short crack spacingsof 3 or 4 ft, corner deflections are somewhat greater thanthose for jointed, doweled pavements, especially for tan-dem-axle loads.
Considering natural variations in crack spacing thatoccur in one stretch of pavement, the following compari-son of continuously reinforced pavements with jointed,dnweled pavements is made. Edge stresses will sometimes
be the same and sometimes less, while corner deflections
will sometimes be less, the same, andgreater at different
areas of the pavement depending on crack spacing.The average of these pavement responses is neither
substantially better nor worse than those for jointed,doweled pavements. As a result, in this design procedure,the same pavement responses and criteria are applied tocontinuously reinforced pavements as those used withjointed, doweled pavements. This recommendation isconsistent with pavement performance experience. Mostdesign agencies suggest that the thickness of continuouslyreinforced pavements should be about the same as thethickness nfdoweled-jointed pavements.
P*The greatest deflections for tridwm occur when two axles are placed
at one side of the ioint and me axle at the other side.
Truck Load Placement
Truck wheel loads placed at the outside pavement edgecreate more severe conditions than any other load posi-tion. As the truck placement moves inward a few inchesfrom the edge, the effects decrease substantially.(”)
Only a small fraction of all the trucks run with theirnutside wheels placed at the edge. Most of the trucks trav-eling the pavement are driven with their outside wheelplaced abnut 2 ft from the edge, Taragin’s(40] studies re-ported in 1958, showed very little truck encroachment atpavement edge for 12-ft lanes for pavements with un-paved shoulders. More recent studies by Emery(”) shnwedmore trucks at edge, Other recent studies”’] showed fewertrucks at edge than Emery. Fnr this design prncedure, themost severe conditinn, 6c%of trucks at edge, * is assumedso as to be on the safe side and to take account of recentchanges in United States law permitting wider trucks.
At increasing distances inward from the pavementedge, the frequency of lnad applications increases whilethe magnitudes of stress and deflecting decrease. Dataon truck placement distribution and distributing of stressand deflection due to loads placed at and near the pave-ment edge are difficult to use directly in a design proce-dure. As a result, the distributions were analyzed andmore easily applied techniques were prepared for designpurposes.
For stress-fatigue analysis, fatigue was computed in-crementally at fractions of inches inward fmm the slabedge for different truck-placement distributions; thisgave the equivalent edge-stress factors shown in Fig. A2.(This factor, when multiplied by edge-load stress, givesthe same degree of fatigue consumption that would resultfrom a given truck placement distribution,) The mnstsevere condition, 6T0 truck encroachment, has been in-corporated in the design tables.
0:ME2!&iacc 0123 4567a
PERCENT TRuCKS AT EDGE
Fig. A2. Equivalent edge stress factor depends onpercent of trucks at edge.
*As used hm, the term ‘<percent trucks at edge,, is defined as thepercent of totat tmcks that a= travetiw with the outside of the con~ctarea of the outside tire at or beyond the pavement edge.
33
For erosion analysis, which involves deflection at theslab corner, the most severe case (6% of trucks at edge) isagain assumed. Where there is no concrete shoulder, cor-ner loadings (6% of trucks) are critical; and where thereis a concrete shoulder, the greater number of loadingsinward from the pavement corner (94’% of trucks) arecritical. These factors are incorporated into the designcharts as follows:
Percent erosion damage = 100 Xn (C/ Ni)
where n, = expected number of axle-loadrepetitions for axle-group i
Ni = allowable number of repeti-tions for axle-group i
C = 0.06 for pavements withoutshoulder, and0.94 for pavements withshoulder
To save a design calculation step, the effects of (C/NiIare incorporated in Figs. 6a and 6b of Chapter 3 andTables 11 through 14 of Chapter 4.
Variation in Concrete Strength
Recognition of the variations in concrete strength is con-sidered a realistic addition to the design procedure. Ex-pected ranges of variations in the concrete’s modulus ofrupture have far greater effect than the usual variationsin the properties of other materials, such as subgrade andsubbase strength, and layer thicknesses. Variation in con-crete strength is introduced by reducing the modulus ofrupture by one coefficient of variation.
For design purposes, a coefficient of variation of 15%is assumed and is incorporated into the design charts andtables. The user does not directly apply this effect, fievalue of 15% represents fair-to-good quality control, and,combined with other effects discussed elsewhere in thisappendix, was selected as being realistic and giving rea-sonable design results.
Concrete Strength Gain With Age
The 28day flexural strength (modulus of rupture) is usedas the design strength. This design procedure, however,incorporates the effect of concrete strength gain after 28days. This modification is based on an analysis that incre-mented strength gain and load repetitions month bymonth for 20-year and 40-year design periods. The effectis included in the design charts and tables so the usersimply inputs the 28-day value as the design strength.
Warping and Curling of Concrete
In addition to traffic Ioadi”g, concrete slabs am also ~~b.jetted to warping and curling. Warping is the upwardconcave deformation of the slab due to variations in mois-ture content with slab depth. The effect of warping is two-fold: It results in loss of support along the slab edges andalso in compressive restraint stresses in the slab bottom,Since warping isalong-term phenomenon, itsres”ltam
effect is influenced greatly by creep.Curling refers to slab behavior due to variations of
temperature. During the day, when the tnp surface iswarmer thanthe bottom, tensile-restraint stresses developat the slab bottom. During the night, the temperature dis-tribution isreversed andtensile restraint stresses develop ~at the slab surhce. Temperature distribution is usuallynonlinear and constantly changing, Alsn, maximum day-time and nighttime temperature differentials exist forshort durations,
Usually the combined effect of curling and warpingstresses are subtractive from load stresses because themoisture content and temperature at the bottom of theslab exceed that at the top more than the reverse.
The complex situation ofdifferential conditions ataslab’s top and bottom plus the uncertainty of the zero-stress position make it difficult tocompute or measurethe restraint stresses with any degree of confidence orverification. At present, the information available onactual magnitudes of restraint stresses does not warrantincorporation of the items in this design procedure.
As for the lnss of support, this is considered indirectlyin tbe erodibility criterion, which is derived from actualfield performance and therefore incorporates normal lossof support conditions,
Calculated stress increase due to loss of support variesfrom about 5%to 15%Thisth eoreticalst ressincreaseiscounteracted in the real case because a portion of the loadis dissipated in bringing the dab edges back in contactwith the support. Thus, the incremental load stress due toa warping-type loss of support is not incorporated in thisdesign procedure, .
Fatigue
The flexural fatigue criterion used in the procedure pre-sented here is shown in Fig, A3. It issimilar to that usedin the previous PCAmethndi4’] based conservativelyon
0,9
0.8Curveby Hil,do,f And Kesler Wh
Constant Pmb,tdl;ty 0.05
Q$ a7
m Pc& curve
:
: 0.6m
0.5
Extended C.,,, >._
0,4-,.2 ,.3 104 ,,y ,@ ,~,
LOAD REPETITIONS
Fig. A3. Fatigue relationships.u--”
34
studies of fatigue research[4s-”9) except that it is applied toedge-load stresses that are of higher magnitude. A modi-fication in the high-load-repetition range has been madeto eliminate the discontinuity in the previous curve thatsometimes causes unrealistic effects,
The allowable number of load repetitions for a givenaxle load is determined based on the stress ratio (flexural
stress divided by the 28-day modulus of rupture). Thefatigue curve is incorporated into the design charts foruse by the designer.
Use of the fatigue criterion is made on the Miner hy-140that fatigue ~e~istance not consumed by rePe-pothes]s
titions of one load is available for repetitions of otherloads. In a design problem, the total fatigue consumedshould not exceed 100%.
Combined with the effect of reducing the design mod-ulus of rupture by one coefficient of variation, the fatiguecriterion is considered to be conservative for thicknessdesign purposes.
Erosion
Previous mechanistic design procedures for concretepavements are based on the principle of limiting the ffex-ural stresses in a slab to safe values. This is done to avoidflexural fatigue cracks due to load repetitions.
It has been apparent that there is an important modeof distress in addition to fatigue cracking that needs tobe addressed in the design process. T& is the erosion of
,Pmaterial beneath and beside the slab.
Many repetitions of heavy axle loads at slab cornersand edges cause pumping; erosion of subgrade, subbase,and shoulder materialy voids under and adjacent to theslab; and faulting of pavement joints, especially in pave-ments with undoweled joints.
These particular pavement distresses are considered tobe more closely related to pavement deflections than toflexural stresses.
Correlations of deflections computed from the finite-element analysis(a] with AASHO Road Test{ 24]perform-ance data were not completely satisfactory for designpurposes. (The principal mode of failure of concretepavements at the AASHO Road Test was pumping orerosion of the granular subbase from under the slabs.) Itwas found that to be able to predict the AASHO RoadTest performance, different values of deflection criteriawould have to be applied to different slab thicknesses,and to a small extent, different foundation moduli (kvalues),
More useful correlation was obtained by multiplyingthe computed corner deflection values (w) by computedpressure values (.P) at the slab-foundation interface, Pow-er, or rate of work, with which an axle load deflects theslab is the parameter used for the erosion criterion—for aunit area, the product of pressure and deflection dividedby a measure of the length of the deflection basin (l—radius of relative stiffness, in inches). The concept is thata thin pavement with its shorter deflection basin receives
~ a faster load punch than a thicker slab. That is, at equalpw’s and equal truck speed, the thinner slab is subjectedto a faster rate of work or power (inch-pound per second).
A successful correlation with road test performance wasobtained with this parameter,
The development of the erosion criterion was also gen-erally related to studies on joint faulting. [2* 29)Thesestudies included pavements in Wisconsin, Minnesota,North Dakota, Georgia, and California, and included arange of variables not found at the AASHO Road Test,such as a greater number of trucks, undoweled pave-ments, a wide range of years of pavement service, andstabilized subbases.
Brokaw’s studies (2o of ““doweled pavements suggest
that climate or drainage is a significant factor in pave-ment performance. So far, this aspect of design has notbeen included in the design procedure. but it deservesfurther study. Investigations of the effects of climate ondesign and performance of concrete pavements have alsobeen reported by Darter. [”]
The erosion criterion is suggested for use as a guideline.It can be modified according to local experience sincecfimate, drainage, local factors, and design innovationsmay have an influence. Accordingly, the 100% erosion-damage criterion, an index number correlated with gen-eral performance experience, can be increased or de-creased based on specific performance data gathered inthe future for more favorable or more adverse conditions.
35
APPENDIX B
b’
Design of Concrete Pavements with LeanConcrete Lower CourseFollowing is the thickness design procedure for compos-ite concrete pavements incorporating a lower layer oflean concrete, either as a suhhase constructed separatelyor as a lower layer in monolithic construction. Designconsiderations and construction practices for such pave-ments are discussed in References 50 through 52.
Lean concrete is stronger than conventional subbasematerials and is considered to be nonerodable, Recogni-tion of its superior structural properties can be taken bya reduction in thickness design requirements.
Analysis of composite concrete pavements is a specialcase where the conventional two-layer theory (single slabon a foundation) is not strictly applicable.
The design procedure indicates a thickness for a two-layer concrete pavement equivalent to a given thicknessof normal concrete. The latter is determined by the pro-cedures described in Chapters 3 and 4. The equivalenceis based on providing thickness for a two-layer concretepavement that will have the same margin of safety* forfatigue and erosion as a single-layer normal concretepavement.
In the design charts, Fig. B] and Fig, B2, the requiredlayer thicknesses depend on the flexural strengths of thetwo concrete materials as determined by ASTM C78.Since the quality of lean concrete is often specified on thebasis of compressive strength, Fig. B3 can be used to con-vert this to an estimated flexural strength (modulus ofrupture) for usc in preliminary design calculations.
Lean Concrete Subbase
The largest paving use of lean concrete has been as a sub-base under a conventional concrete pavement, This isnonmonolithic construction where the surface course ofnormal concrete is placed on a hardened lean concretesubbase. Usually, the lean concrete subbase is built atleast 2 ft wider than the pavement on each side to supportthe tracks of the sfipform paver. This extra width is struc-turally beneficial for wheel loads applied at pavementedge.
The normal practice has been to select a surface thick-
ness about twice the subbase thickness; for example, 9 in.of concrete on a 4- or 5-in. subbase.
Fig. B 1 shows the surface and subbase thickness re-quirements set to be equivalent to a given thickness ofnormal concrete without a lean concrete subbase.
A sample problem is given to illustrate the design pro-cedure. From laboratory tests, concrete mix designs havebeen selected that give moduli of rupture of 650 and 200psi~*respectively, for the surface concrete and the leanconcrete subbase. Assume that a I&In.-thickness require-ment has been determined for a pavement without lean ,..concrete subbase as set forth in Chapter 3 or 4.
As shown by the dashed example line in Fig. BI, de- W’signs equivalent to the 10-in. pavement are (1) 7.7-in.concrete on a 5-in. lean concrete subbase, and (2) 8. l-in.concfcte on a &]n. lean concrete subbase.
Monolithic Pavement
In some areas, a relatively thin concrete surface course isconstructed monolithically with a lean concrete lowerlayer. Local or recycled aggregates can be used for thelean concrete, resulting in cost savings and conservationof bighqualit y aggregates.
●ll. criteria are that (1) stressratios in either of the two concretelayers not exceed that of the reference pavement and (2)erosion valuesat the s.bbase-s.bgrade interface not exceed those of the reference pave-ment. Rational. for the criteria is give. in Reference 50 plus two ad&l-timal considerations: (1) erosion criteria is included in addition to thefatigue approach given in the referencq and (2) for nonmonolithic con-struction, some structural benefit C141is added because the subbase isconstructed wider than the pavement.. . F1.xural wemgth of !..” comxete m be used as a subbase is usuallyselected to be between i50 to 250 psi (compressive Wength, 750 to 1200psih these relatively low strengths are used to minimize reflective crack-ing from tbe unjointed subbase (.s..1 practice is to leave the s.hhm.
,,.
.“jointed) through the concrete surface. lf, c.ntmry toc.rrem practic.,joints are placed in the subbase, the stcmgth of the 1..” comrete would u“.1 have to b. restricted m the lower m “ge.
36
Modulus of Rupture of Leon Concrete, psi
350 450 I50 250 350 450
250.
14 <
450 /
350I50
13<
250 .. / ‘,0
// ‘
12I50 ;
6)./ ‘
/ /
II / ‘ / d
0/ )
I0(.++ ~ –;
4
9 r
are thicknesses of concrete
surface course
14 _
.< “%
9
Fig. B1. Design chart for composite concrete pavement (lean concrete subbase),
37
Modulus of Rupture of Lean Concrete, psi
450 150 250 350 450
14
350
13 -/,
12
“l- t+htl+’tft‘0+--wH--tf7b%4
Fig. B2,
3“ Surface 4“ Surface
Design chart for composite concrete pavement (monolithic with lean concrde Iowef
Unlike the lean concrete subbases discussed in the pre-vious section, the lower layer of lean concrete is placedat the same width as the surface course, and joints aresawed deep enough to induce fulldepth cracking throughboth layers at the joint locations.
Fig. B2 is the design chart for monolithic pavements.To illustrate its use, assume that the design strengths ofthe two concretes are 650 and 350 psi, and that the designprocedures of Chapter 3 or 4 indicate a thickness require-ment of 10 in. for fulldepth normal concrete.
As shown by the dashed example fine in Fig. B2, mono-lithic designs equivalent to the IO-in. pavement are (1)4-in. concrete surface on 8.3-in. lean concrete, or (2) 3-in.surface on 9.3-in. lean concrete.
layer).
COMPRESSIVE STRENGTH, PSI
Fig. B3. Modulus of rupture versus compressive strength(from Reference 50).
38
APPENDIX C
Analysis of Tridem Axle LoadsTridem loads* can be included along with single- andtandem-axle loads in the design analysis by use of datagiven in this appendix.
The same design steps and format outlined in Chapter3 are followed except that Tables C I through C3 are used.From these tables for tridems, equivalent stress and ero-sion factors are entered in an extra design worksheet.Then Fig. 5 and Fig. ti or 6b are used to determine al-lowable numbers of load repetitions. Fatigue and erosiondamage totals for tridems are added to those for single-
P and tandem-axle loads,An extension of the sample problem, Design 1A given
in Chapter 3, is used here to illustrate the procedure fortridem loads. Assume that, in addition to the single- andtandem-axle loads, a section of the highway is to carry afleet of special coal-hauling trucks equipped with tridemsat the rate of about 100 per working day for an estimatedperiod of 10 year> so:
100 trucks X 250 days X 10 years = 250,000 total trucks
The trucks in one direction are normally all loaded totheir capacity of 54,000-lb tridem load plus 7000-lb steer-ing-axle (single-axle) load. (When it is examined, thesteering axles are not heavy enough to affect the designresults.)
Fig. C 1 represents a portion of tbe extra design work-sheet needed to evaluate tbe effects of these tridems. Since
Design 1A (9:5-in. pavement, combined k of 130 pci) is apavement with doweled joints and no concrete shoulder,Tables Cl and C2 are used to determine the equivalentstress and erosion factors, Items 1 I and 13 on the work-
sheet.For this example, Fig. 5 is used to determine allowable
load repetitions for the fatigue analvsis and l%. 6a is usedfor tbe”erosion analysis. - - -
The tridem loads of 54,000 lb are multiplied by t he loadsafety factor for Design 1A of 1.2, giving a design axleload of 64,800 lb. Before using the charts for allowable
load repetitions, the tridem load (3 axles) is divided by
three (64,800/3 = 21,600 lb) so that the load scale for
single axles can be used, **As show” in Fig, Cl, the tridem causes only 9.3% ero-
sion damage and 0% fatigue damage. These results, addedto the effects of the single and tandem axles shown in Fig.4 are not sufficient to require a design thickness increase.
*A trid.m or triple axle isa set of three axles each sp.ced at 48 to 54in.apart. These am used on special heavy-duty haul trucks.
..Thl$ is not to say th.tatridcm hasthe~meeff=t asthrec singieaxles.The damaging effects of tridem, tandem, and single axles are incorpo-rated into their rqmtive equivalent stress and emsicm factor tables,which i“ the sequeme of the design stepsis taken into accmmt beforethe charm for allowable-load repetitions arc entered. This divisicm bythree for tridetm is made just to avoid the complexity of adding a thirdscale on the charts for allowable-load qxtitio.s,
39
Calculation of Pavement Thickness
7f T. Z??,(L D/
Trial thickness 5?5- (n: Doweled joints yes’+.0 —
S.bbase-sub.arade k L.?o .,i concrete sh.w ldw yes _ no X
Modulus .1 nmt”re, MR ~ psi
Load safely factor, LSF 1 zC9sig” Period ~ yea,,
Fatigue analysis Erosion analysis
Axle M“!tiPliedload,
ExPect&~gYF repetition,
I@ Allowable Fatigue, Allowable Damage,
/7repetition, percent repetitions percent
111213/4 1516 171
1 1 1 [ I II
-.
L-J
I 1 1 I I I I
Totalo
Total7.3
74 be ZzdJ& X6 4224 SAw’7 /> 6++Fig. Cl. Analysis of tridems.
,.-
u’Tabla Cl. Equivalent Stress-Tridems
(Without Concrete Shouldar/With Concrete Shoulder)
Slabthickness,
k of subgrsde.subbase, pcl
in. 50 100 150 200 300 500 700
4 51W431 456/392 4371377 428/369 419/362 414/360 412/3594,5 439/365 380/328 359/31 3 349/305 339/297 331/392 32S/291
5 367/317 328/281 305/266 293/258 282/250 272[244 269/2425.5 347[279 290/246 266/231 253/223 240/214 230/206 226/206
8 315[249 261/218 237/204 223/1 96 209/187 198/1 80 193/1 786.5 289/225 238/1 96 214/163 201/175 186/1 66 173/159 168/1 56
7 267/304 219/178 196/1 65 183/1 58 167/1 49 154/142 148/1 387.5 247/1 87 203/1 62 181/151 166/1 43 153/135 139/1 27 132(124
6 230/172 189/1 49 168/1 36 156/131 141/123 126/116 120/1126.5 215/159 177[1 36 1561126 145/121 131/113 116/106 109/102
9 2W147 166/ 128 148/119 136/112 122/105 108/98 101/949.5 1871137 157/120 140/111 129/1 05 115/98 101/91 93/87
10 1741127 148/112 133/104 122/98 106/91 95/64 87/6110.5 183/119 140/105 125/97 115/92 103/86 89/79 82/78
11 153/111 133/89 119/92 110/87 98/81 S5174 7817711.5 142/104 125/93 113/86 104/82 93{76 80/70 74/67
12 133/97 119/83 106/82 100[78 89/72 77/66 70/6312.5 123/91 113/33 103/78 95/74 85/66 73[63 67/847
13 114/85 107/79 98/74 91/70 81/65 70/80 64/5713.5 105/80 101/75 93/70 87/67 78[62 67[57 61/54
14 97175 98/71 89/67 83/63 75/59 65/54 59/51
,..
L/”
40
Table CZ. Eroalon Factors-Tridema-Doweled Joints(Without Concrete Shoulder/With Concrete !Woulder)
Slabthickness,
k of subgrade-subbase, pci
p ,., 50 100 200 300 500 700
4 3.8913.33 3.82/3.20 3.7513.13 3.70/3.10 3,61,13.05 3.53/3.004,5 3.7813.24 3.69/3,10 3.62./2.99 3.57/2.95 3.50,(2.91 3.4412.87
5 3,68/3.16 3.56/3,01 3.50/2.89 3.4612.835.5
3.4012.79 3.3412.753.59/3.09 3.49/2.94 3.40/2.80 3,36/2.74 3.3012.67 3.2512.84
6 3.51/3.03 3,40/2.87 3.3112.73 3.28/2.666.5
3.2112.58 3.16/2.543,44/2,97 3.33/2.82 3.23/2.67 3.18/2.59 3.12(2,50 3.08/2.45
7 3,37[2,92 3.26/2.76 3,18/2.61 3.10/2.537.5 3.31/2,87
3.04!2.43 3.00/2.373.20/2.72 3,09/2.56 3.03/2.47 2.97/2.37 2.93/2.31
6 3.26/2,83 3.14/2.67 3,03/2.51 2.97/2.428,5
2.80/2.32 2.86/2,253.20/2.79 3.09/2.63 2.9712.47 2.91/2,38 2.84,(2.27 2.79/2,20
9 3.15/2.75 3.04/2.59 2.92/2.43 2.66/2,34 2.7612,23 2.73t2.159.5 3.11/2.71 2.99/2.55 2.67/2,39 2.81/2.30 2.73/2.18 2,68/2. 11
10 3.08/2.67 2.94/2.51 2.83/2.35 2.76/2,26 2.68,/2.15 2,63/2,0710.5 3.02/2.64 2.90/2.48 2,78/2.32 2.7.2/2.23 2.64/2.1 1 2.58/2.04
11 2.98/2.60 2.86/2.45 2.74/2.29 2.68/2,20 2,59/2.08 2.54/2.0011.5 2.94/2.57 2.82/2.42 2.70/2.26 2.64/2.16 2.55,,2.05 2.50/1.97
12 2.91/2.54 2.79/2.39 2.67/2.23 2.60/2.13 2.51/2.02 2.48/1.9412.5 2.6712.53 2.75/2,36 2.63/2.20 2.56/2.11 2.48,{1 .99 2.42/1.91
13 2,8412.48 2.72/2.33 2.6012.17 2.53/2.06 2.44,{1.96 2.39/1.8813,5 2,61/2,46 2,68/2.30 2.56/2.14 2.49/2.05 2,41,(1 .93 2.35/1.86
14 2.78/2.43 2.6512.28 2.53/2.12 2.46/2.03 2.38,(1 .91 2.32/1 .83
PTable C3. Erosion Fectors—Tridems-Aggregate-interlock Joints
(Without Concrete Shoulder/With Concrete :~oulder)
Slabthic;.,
k of subgrade-subbase, pci
50 100 200 300 5130 700
4 4.06/3.50 3.97[3.36 3.68/3.30 3.62/3.25 3.7413.21 3.6713.164.5 3.9513.40 3.8513.26 3,78/3.16 3.70/3.13 3.63/3.08 3.58/3.04
5 I 3,85[3,32 3.75/3.19 3.66/3.06 3.60/3.03 3.52/2.97 3.46/2.935.5 3,76/3,26 3,66/3.11 3.56/3.00 3.51[2.94 3.4312.67 3.37[2 .83
6 I 3,68/3,20 3.58/3.05 3.4LV2.92 3,42/2.66 3.35,/2.79 3.29/2.746.5 3.61/3.14 3.50/2.99 3.40/2.86 3.34/2.79 3.27,/2.72 3.21/2.67
7 3.54/3.09 3.43/2.94 3.33/2.80 3.27/2.73 3.20/2,657.5
3,14/2.603.48/3.05 3.3712.89 3.2612.75 3.20/2.67 3.13/2.59 3.06/2.54
8 3.42/3.01 3.31/2,84 3,20/2.70 3.14/2.62 3.07/2.54 3.01/2.468.5 3.3712.97 3.25/2.80 3.15/2.65 3.09/2.58 3.01/2,49 2.96/2.43
9 3.32/2.94 3.20/2.77 3.09/2.61 3.03/2.53 2,95/2,449.5
2.90/2.383.2712.91 3.15/2.73 3.0412.56 2.98/2.49 2.90/2.40 2.85/2.34
10 3.22/2.88 3.11/2,70 3.00/2.54 2.93/2.46 2.85/2.36 2.60/2,2910.5 3.f 8/2.85 3.06/2.67 2.95/2.51 2.89/2.42 2.8112.32 2.76[2 .26
11 3.14/2.83 3.02/2.85 2.91/2.48 2.8412.39 2.7712.29 2.71/2.2211.5 3.10/2.80 2,98/2.62 2.8712.45 2.80/2.36 2.72/2.26 2.67/2.19
41
APPENDIX D
Estimating Traffic Volume by Capacity(Note: At the time of preparing this bulletin, informationon highway capacity is under extensive revision and com-putational methods and results may be substantiallychanged. New publications of AASHTO and theFHWA“Highway Capacity Manual,” expected to be publishedin 1984 and 1985, should be used when available and theywill replace the methods and references presented in thisappendix.)
In Chapter 2, the traffic volume (ADTI is estimated bya method based cm the projected rates of traffic growth.When the projected traffic volume is relatively high for aspecifk project, this method should be checked by thecapacity method described here.
The practical capacity of a pavement facility is definedas the maximum number of vehicles per lane per hourthat can pass a given point under prevailing road andtraffic conditions without unreasonable delay or restrict-ed freedom to maneuver. Prevailing conditions includecomposition of traffic, vehicle speeds, weather, align-ment, proffle, number and width of lanes, and area.
The termproctical capacity is commonly used in refer-ence to existing highways, and the term design capaciryis used. for design purposes. Where traffic flow is uninter-rupted-or nearly so—practical capacity and designcapacity are numerically equel and have essentially thesame meaning. In accordance with AAS HTO usage1s3 ’41the term design capacity is used in this text. Design capac-ities for various kinds of multilane highways are sum-marized in Table DI.
AD T Capacity of Multilane HighwaysFor thickness design it is necessary to convert the pas-aenger cars per hour in Table D1 to average daily trafficin both directions, ADT, For multilane highways withuninterrupted flow tbe following formula is used:
ADT =100P 5000N
100+ Tpd- 1) x KD
where P = passenger cars* per lane per hour (fromTable D 1)
N = number of lanes—total both directionsT,, = trucks, percent, during peak hours
= 2/3 ADT_f in this booklet
Table D1. Design Capacities forMultilane Highways
Design capacity:
Type of highwaypassenger cars
pe;;r2ftJne
‘Suburt,.. . .
~
rreew.ys vm. w access comm
)an freeways with full access control
‘Rural freeways with Wll or pcontrol
Rural major highway!cross traffic and road.,..
Rural major highways with ccross traffic and roadside Inwrmrerwe
I
,AIso includes panels, pickups, and other four-tire oxnrnerci.1 vehiclesthat function a. passengercars in terms of traffic capacity. Values aretaken from References 53 and 54,
j = ~“mber Of passenger cars equivalent tO One
truck= 4 in rolling terrain= 2 in level terrain
K = design hour volume, DHV, expressed as apercentage of ADT
= 15% for rural freeways in this text= 12% for urban freeways in thk text**
D = traffic, percent, in direction of heaviest travelduring peak hours—about 5070 to 75%
= 67% for rural freeways in this text= 6090 for urban freeways in this text
‘See f..tn.te at bottom of Table D!.**s,, Reference 54, pa.~e$96 m 98, and Reference 56.
42
Detailed discussions of this formula will be found inReferences 53, 54, and 55. As presented here, the symbolfor one term, T, of the formula, T,~, differs from the sym-
pbol for this term in the references. In this text:
T = trucks—includes only single units with morethan four tires and all combinations. (Doesnot include panels, pickups, and other singleunits with only four tires.)
ADTT = average daily truck traffic in both direc-tions—may be expressed as a percentage ofADT or as an actual value.
Capacity of Two-Lane HighwaysImportant factors in the design capacit y of two-lane high-ways are (1) the percent of total project length where sightdistance is less than 1500 ft, and (2) lane widths of lessthan 12 ft.* The design capacity in vehicles per hour (vph)for unintermpted flow on two-lane highways is shownin Table D2.
It is good practice to use both traffic projection fac-tors and design capacity for thickness design of specificprojects. For example, if an existing two-lane route is car-rying 4000 ADT and the projection factor is 2.7, the pro-jected ADT would be 10,800. This is more than 4000vehicles per day (vpd) greater than the design capacity ofvirtually all two-kme highways.** On the other hand,10,800 ADT is below the design capacity of most four-lane highways.t Hence, the design should be made for10,800 ADT on a four-lane roadway, Design capacityshould not be used where it shows a greater ADT thanshown by traffic projection.
p
*Lane widths of lessthan 12ft are rarely used in current practi.., ex-cept for very lightly traveled two-lam roads where land serviceis a pri-mary function.
**SW Table D2.?S.. Refermct 53, Table 11-14.
Table D2. De$ign Capacities for Uninterrupted Flow on Two-Lsne Highways’
==
Design Capacity, both directions, in vph,-
40 800 7Cnl 620
I o I 900 640 500 k:~
Rolling40 800 570
80 720 51080 620 440
‘KHx!uui
Source: Reference 53, Table 11-10,P.39e88.‘. T.b.lar ..1..s apply where lateral clearance is not mstri.led. Where clearance is less th.” 6 H
apply factors In Reference 53, Table IIF 7, page 89.VTr.cks, does not include four-tire vehicle..
43
w’
APPENDIX E
References1. Westergaard, H. M., “Computation of Stresses in
Concrete Roads,” High way Research Board pro.ceedings, Fifth Annual Meeting, 1925, Part 1, pages90 to 112.
2. Westergaard, H. M., “Stresses in Concrete PavementsComputed by Theoretical Analysis,” Public Roads,Vol. 7, No. 2, April 1926, pages 25 to 35.
3. Westergaard, H. M., “Analysis of Stresses in Con-crete Roads Caused by Variations in Temperature,”Public Roads, Vol. 8, No. 3, May 1927, pages 201 to215.
4. Westergaard, H. M., “Theory of Concrete PavementDesign; High way Research Board Proceedings,Seventh Annual Meeting, 1927, Part 1, pages 175 to181.
5. Westergaard, H. M., “Analytical Tools for JudgingResults of Structural Tests of Concrete Pavements?Public Roads, Vol. 14, No. 10, December 1933, pages185 to 188.
6. P1ckett, Gerald; Ravine, Milton E.; Jones, WMam C.;and McCormick, Frank J., “Deflections, Momentsand Reactive Pressures for Concrete pavements,”Kansas State College Bulletin No. 65, October 1951.
7. Pickett, Gerald, and Ray, Gordon K., “InfluenceCharts for Concrete Pavements? American Societyof Civil Engineers Transactions, Paper No. 2425, Vol.116, 1951, pages 49 to 73.
8. Tayabji, S. D., and Coney, B. E., “Analysis of JointedConcrete Pavements,” report prepared by the Con-struction Technology Laboratories of the PortlandCement Association for the Federal Highway Ad-ministration, October 1981.
9. Teller, L. W., and Sutherland, E. C., “The StructuralDesign of Concrete Pavements,” Public Roads, Vol.16, Nos. 8, 9, and 10 (1935) Vol. 17, Nos. 7 and 8(1936); Vol. 23, No. 8 (1943).
10. Childs, L. D., Coney, B. E., and Kapernick, J. W.,“Tests to Evaluate Concrete Pavement Subbases,”Proceedings of American Society of Civil Engineers,Paper No. 1297, Vol. 83 (H W-3), July 1957, pages 1 to
11.
12.
41;, also PCA Development Department BulletinDXOI1.
Childs., L. D., and Kapernick, J. W., “Tests of Con-crete Pavement Slabs on Gravel Subbases,” Proceed-ings of American Society of Civil Engineers, Vol. 84(HW-3), October 195fi also PCA Development De-partment Bulletin DX021.
Childs. L. D.. and Kanernick. J. W.. “Tests of Con-,, . . .crete Pavements on Crushed Stone Subbases,” Pro-ceedings of American Society of Civil Engineers,Proc. Paper No. 3497, Vol. 89 (H W- 1), April 1963, z “’pages 57 to 8@ also PCA Development Department ‘~Bulletin DX065.
13. Childs, L. D., “Tests of Concrete Pavement Slabs onCement-Treated Subbases,” Highway Research Rec-ord 60, Highway Research Board, 1963, pages 39 to58; also PCA Development Department BulletinDX086.
14. Childs, L. D., “Cement-Treated Subbases for Con-crete Pavements,” Highway Research Record 189,Highway Research Board, 1967, pages 19 to 43; alsoPCA Development Department Bulletin DX125.
15. Childs, L. D., and Nussbaum, P. J,, “Repetitive LoadTests of Concrete Slabs on Cement-Treated Sub-bases,” RD025P, Portland Cement Association, 1975.
16. Tayabji, S. D., and Coney, B. E,, “Improved RigidPavement Joints,” paper presented at Annual Meetingof Transportation Research Board, January 1983 (tobe published in 1984).
17. Childs, L. D., and Ball, C. G., “Tests of Joints forConcrete Pavements,” RD026P, Portland CementAssociation, 1975.
18. Coney, B. E., and Humphrey, H. A., “Aggregate in-terlock at Joints in Concrete Pavements,” HighwayResearch Board Record No. 189, Transportation Re-search Board, 1967, pages I to 18.
19. Coney, B. E., Ball, C. G., and Arriyavat, P., “Evalua- ....tiOn Of Concrete Pavements with Tied Shoulders or ‘Widened Lanes,” Transportation Research Record ‘~666, Transportation Research Board, 1978; also Pmt-
44
p
P
land Cement Association, Research and Develop-ment Bulletin RD065P, 1980.
20. Sawan, J. S., Darter, M. L, and Dempsey, B. J.,“Structural Analysis and Design of PCC Shoulders,”Report No. FH WA-RD-8 1-122, Federal HighwayAdministration, April 1982.
21. Older, Clifford, “Highway Research in Illinois,”Proceedings of American Society of Civil Engineers,February 1924, pages 175 to 217.
22. Aldrich, Lloyd, and Leonard, Ino B., “Report ofHighway Research at Pittsb”rg, California, 19zI-1922,” California State Pri”ti”g office,
23. Road Test One-MD, Highway Research Board Spe-cial Report No. 4, 1952.
24. The AASHO Road Test, Highway Research BoardSpecial Report No. 6 I E, 1962.
25. The AASHO Road Test, Highway Research BoardSpecial Report No. 73, 1962.
26. AA SHTO Inlerim Guide for Design of PavementStructures, /972, Chapter 111 Revised, 1981, Ameri-can Association of State Highway and Transporta-tion Officials, 1981,
27. Fordyce, Phil, and Teske, W. E,, “Some Relation-ships of tbe AASHO Road Test to Concrete Pave-ment Design,” High way Research Board Record No,44, 1963, pages 35 to 70.
28. Brokaw, M. P., “Effect of Serviceability and Rough-ness at Transverse Joints on Performance and De-sign of Plain Concrete Pavement,” Highway ResearchBoard Record 471, Transportation Research Board,1973.
29. Packard, R. G., “Design Considerations For Controlof Joint Faulting of Undoweled Pavements,” F70-ceedings of International Conference on ConcretePavement Design, Purdue University, February 1977.
30. Packard, R. G., and Tayabji, S. D., “Mechanistic De-sign of Concrete Pavements to Control Joint Faultingand Subbase Erosion,” International Seminar onDrainage and Erodability at the Concrete Slab-Sub-base-Shoulder Interfaces, Paris, France, March 1983.
31. Standard Method for Nonrepetitive Static Plate LoadTests of Soils and Flexible Pavement Components,for Use in Evaluation and Design of Airport andHighway Pavements, American Society for Testingand Materials, Designation D 1196.
32. “Rigid Airfield Pavements,” Corps of Engineers, U.S.Army Manual, EM 1110-45-303, Feb. 3, 1958,
33. Burmister, D. M., “The Theory of Stresses and Dis.placements in Layered Systems and Applications toDesign of Airport Runway s,” Highway ResearchBoard Proceedings, Vol. 23, 1943, pages 126 to 148.
34. Standard Methods for Freezing-and-Thawing Testsof Compacted Soil-Cement Mixtures, American So-ciety for Testing and Materials, Designation D560.
35. Standard Methods for Wetting-and-Drying Tests ofCompacted Soil-Cement Mixtures, American Societyfor Testing and Materials, Designation D559.
36. Soil- Cement Laboratory Handbook, Portland Ce-ment Association publication EB052S, 1971.
37. “National Truck Characteristic Report, 1975- 1979,”U.S. Department of Transportation, Federal High-way Administration, Washington, D. C,, June 1981.
38. Becker, J. M., Darter, M. I., Snyder, M. B., andSmith, R. E., “COPES Data Collection Procedure—Appendix A,” June 1983, Appendix to final report ofNational Cooperative Highway Research Program,Project 1-19, Concrete Pavement Evaluation System,draft submitted to Transportation Research Board.
39. Load Stress at Pavement Edge, Portland CementAssociation publication IS030P, 1969.
40. Taragin, Asriel, “Lateral Placement of Trucks onTwo-Lane and Four-Lane D]vided Highways,” Pub-/it Roads, Vol. 30, No. 3, August 1958, pages71 to 75,
41. Emery, D. K., Jr,, “Paved Shoulder Encroachmentand Transverse Lane Displacement for Design Truckson Rural Freeway s,” a report presented to the Com-mittee on Shoulder Design, Transportation ResearchBoard, January 13, 1975.
42, “Vehicle Shoulder Encroachment and Lateral Place-ment Study,” Federal Highway Administration Re-port No. FH WA/ MN-80/6, Minnesota Departmentof Transportation, Research and Development Of-fice, July 1980.
43. Darter, M, 1,, “Structural Design for Heavily Traf-ficked Plain-Jointed Comrete Pavement Based o“Serviceability Performance,” TRR 671, Analysis ofPavement Systems, Transportation Research Board,1978, pages 1 to 8.
44. Thickness Design for Concrete Pavemenls, PortlandCement Association publication 1S0 IOP, 1974.
45, Kesler, Clyde E., “Fatigue and Fracture of Concrete,”Stanton Wolker Lecture Series of the Malerials Sci-ences, National Sand and Gravel Association and Na-tional Ready Mixed Concrete Association, 1970,
46. Fordyce, Phil, and Yrjanson, W. A,, “Modern Designof Concrete Pavements; American Society of CivilEngineers, Transportation Engineering Journal, Vol.95, No. TE3, Proceedings Paper 6726, August 1969,pages 407 to 438.
47. Ballinger, Craig A., “The Cumulative Fatigue Dam-age Characteristics of Plain Concrete,” Highway Re-search Record 370, Highway Research Board, 1971,pages 48 to 60.
48. Miner, M. A., “Cumulative Damage in Fatigue,”American Society of Mechanical Engineers Trans-actions, Vol. 67, 1945, page A 159.
49. Klaiber, F. W., Thomas, T. L., and Lee, D. Y., “Fa-tigue Behavior of Air-Entrained Concrete: Phase 11,”Engineering Research Institute, Iowa State Univer-sity, February 1979.
50. Packard, R. G., “Structural Design of Concrete Pave-ments with Lean Concrete Lower Course,” Proceed-ings of Second International Conference on ConcretePavement Design, Purdue University, April 1981.
51. Yrjanson, W. A., and Packard, R. G., “EconocretePavements—Current Practices,” Transportation Re-search Record 741, Performance of Pavements De-signed with Low-Cost Materials, Transportation Re-search Board, 1980, pages 6 to 13.
45
52. Ruth, B. E., and Larsen, T. J., “Save Money withEconocrete Pavement Systems,” Concrete Inrer.national, American Concrete Institute, May 1983.
53. A Policy on Geometric Design of Rural Highways,American Association of State Highway Officials,Washington, D. C., 1954.
54. A Policy on Arterial Highways in Urban Areas,American Association of State Highway Officials,Washington, D. C., 1957.
55. Highway Capacity Manual, Bureau of Public Roads,U.S. Department of Commerce, Washington, D. C.,1966.
56. Schuster, J. J., and Michael, H. L., “Vehicular TripEstimation in Urban Areas; Engineering Bulletin ofPurdue University, Vol. XLWII, No. 4, July 1964,pages 67 to 92.
57. Packard, R. G., and Tayabji, S. D., “New PCAT’lickness Design Procedure for Concrete Highwayand Street Pavements,” Proceedings of Third Inter-national Conference on Concrete Pavement Designand Rehabilitation, Purdue University, April 1985.
46
‘u’
7..
“u
pCalculation of Pavement Thickness
Project
Trial thickness m. Doweled joints: yes _ no _
Subbase-subgrade k pci Concrete shoulder: yes _ no _
Modulus of rupture, MR psiDi!sign period _
Load safety factor, LSFyears
Axleload,hips
1
8. Equivalent stress 10. Erosion factor
Single Axles9. Stress ratio factor
,p
11. Equivalent stress 13. Erosion factor
Tandem Axles12. Stress ratio factor
1
P’
Total Total
/-.. ,,
‘u
Microcomputer Program for Thickness Design ofConcrete Highways, Streets, and Parking Lots
PCAPA V—the low-cost software for concrete pavement design
PCAPA V’s easy-to-use, menu-driven routine offers
● High-speed solutions to pavement thickness design problems
● Pavement fatigue and subbase erosion calculations
“ Comprehensive theory
● Realistic design criteria
The computer program design procedures, based on this manual and verified by
performance, consider !oad transfer at transverse and longitudinal joints (doweled
or undoweled), concrete shoulders, curbs and gutters, and adjacent parking-lot
Ianee.
Traffic load considerations are simplified. Any designer can choose a stored
traffic load category to fit the situation. Or available traffic load data can be input.
The software runs on IBM personal computers and compatibles(128K, DOS 2.0
or later), and the package includes a floppy diskette, the user’s manual, and this
design manual, Thickness Design for Concrete Highway and Street Pavements.To order PCAPA~(MCO03), contact the Portland Cement Association, Order
Processing Department, 5420 Old Orchard Road, Skokie, IL 60077-1083,
(800)888-6733
u
mlPORTLAND CEMENT I I ASSOCIATION,7-~..
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