Thickness design concrete hwy street pavements by Mebuild

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;

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The author of thk engineering bulletin is Robert G. Packard, 1? E., principal paving engineer, Paving Transportation Department, Portland Cement Association. This publication is intended SOLELY for use by PROF!3SIONAL PERSONNEL who we competent to evaluate the si~ificance and limitations of the information provided herein, and who wiff accept total responsibility for the application of this information. The Portland Cement Association DISCLAIMS any and all RESPONSIBILITY and LIABILITY for the accuracy of and the application of the information contained in this publication to the fulf extent permitted by law.

0 Portland Cement Asscwiation 1984, reprinted 1$95

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Thickness Design for Concrete Highway and Street Pavements

P CONTENTS Chapter I. Introduction . . . . . . . . . . . . Applications of Design Procedures. Computer Programs Available . . . . Basis for Design . . . . . . . . . . . . . . . . . Metric Version . . . . . . . . . . . . . . . . . . Chapter 2. Design Factora . . . . . . . . Flexural Strength of Concrete . . . Subgrade and Subbase Support . Design Period . . . . . . . . . . . . . . . . Traffic . . . . . . . . . . . . . . . . . . . . . . . Projection ................. Capacity . . . . . . . . . . . . . . . . . . . ADTT . . . . . . . . . . . . . . . . . . . . . Truck Dkectional Dktribution Axle-Load Dktribution ...... Load Safety Factors . . . . . . . . . . . Chapter 3. Design Procedure (Axle-Load Data Available) . Fatigue Analysis . . . . . . . . . Erosion Analysis . . . . . . . . . Sample Problems . . . . . . . .

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Chapter 4. Simplified Design Procedure (Axle-Load Data Not Available) . . . . . . Sample Problems . . . . . . . . . . . . . . . . Comments on Simplified Procedure . Modulus of Rupture . . . . . . . . . . . . Design Period . . . . . . . . . . . . . . . . .

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Aggregate Interlock or Doweled Joints . . . . . ...30 User-Developed Design Tables . . . . . . . . . . . . . . ...30 Appendix A. Development of Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Concrete Pavements . . . . . Jointed Pavements .............. Continuously Reinforced Pavements Truck-Load Placement . . . . . . . . . . . . . Variation in Concrete Strength . . . . . . Concrete Strength Gain with Age . . . . Warping and Curling of Concrete . . . . Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . Erosion . . . . . . . . . . . . . . . . . . . . . . . . . .

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. . . ...32 . . . ...32 . . . ...32 . . . ...33 . . . ...33 . . . ...34 . . . ...34 . . . ...34 . . . ...34 . . . ...35

Appendix B. Daaign of Concrete Pavements with Lean Concrete Lower Course . . . . . . . . . . . . . ...36 fsan Ccmcrete Subbase . . . . . . . . . . . . . . . . . . . . ...36 Monolithic Pavement . . . . . . . . . . . . . . . . . . . . . . ...36 Appendix

C. Analysis of Tridem Axle Loads . . . . ...39

Appendix D. Estimating Traffic Volume by Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...42 Appendix E. References . . . . . . . . . . . . . . . . . . . . . . ...44 Daaign Worksheet for Reproduction

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. . . . . . . . . . . ...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 based on stress ratio factor (with and without concrete shoulders). 6a. Erosion analysis—allowable load repetitions based on erosion factor (without concrete shoulder). 6b. Erosion analysis—allowable load repetitions based on 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 Cl. Analysis of tridems,

versus

compressive

strength.

13b. Allowable ADT”f, Axle-Load Category 3—Pavements with Aggregate-Interlock Joints 14a. Allowable ADTT, Axle-Load Category 4—Pavements with Doweled Joints 14b. Allowable ADl_f, Axle-Load Category 4—Pavements with Aggregate-Interlock Joints 15. Axle-Load Dktribution Used for Preparing Design Tables 11 Through 14 Cl. Equivalent Stress — Tridems C2. Erosion Factors — Tridems — Doweled Joints C3. Erosion Factors — Tridems — Aggregate-Interlock Joints D 1. Design Capacities for Multilane Highways D2. Design Capacities for Uninterrupted Flow on TwoLane Highways

us.

3 customary

Metric

unit

in. ft

mm m

lb lbf kip lb/in.x lb/ in.x (k value)

kg N kN kPa MPa/m

Conversion coefficient 25.40

0.305 0.454 4.45 4.45 6.89 0.271

Tables 1. Effect of Untreated Subbase on k Values 2. Design k Values for Cement-Treated Subbase 3. Yearly Rates of Traffic Growth and Corresponding Projection Factors 4. Percentages of Four-Tke Single Units and Trucks (ADTT) on Various Highway Systems 5. Axle-Load Data 6a. Equivalent Stress-No Concrete Shoulder 6b. Equivalent Stress-Concrete Shoulder 7a. Erosion Factors—Doweled Joints, No Concrete Shoulder 7b. Erosion Factors—Aggregate-Interlock Joints, No Concrete Shoulder 8a. Erosion Factom—Doweled Joints, Concrete Shoulder 8b. Erosion Factors—Aggregate-Interlock Joints, Concrete Shoulder 9. Axle-Load Categories 10. Subgrade Soil Types and Approximate k Values 11. Allowable ADTT, Axle-Load Category 1—Pavements with Aggregate-Interlock Joints 12a. Allowable AD’IT, Axle-Load Category 2—Pavements with Doweled Joints 12b. Allowable ADTT, Axle-Load Category 2—Pavements with Aggregate-Interlock Joints 13a. Allowable ADTT, Axle-Load Category 3—Pavements with Doweled Joints

L-J

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CHAPTER 1

Introduction

This bulletin deals with methods of determining slab thicknesses adequate to carry traffic loads on concrete streets, roads, and highways, The design purpose is the same as for other engineered structures—to find the minimum thickness that will result in the lowest annual cost as shown by both first cost and maintenance costs. If the thickness is greater than needed, tbe pavement will give good service with low maintenance costs, but first cost will be high. If the thickness is not adequate, premature and costly maintenance and interruptions in traffic will more than offset the lower first cost. Sound engineering requires thickness designs that properly balance first cost and maintenance costs. While this bulletin is confined to the topic of thickness design, other design aspects are equally important to ensure the performance and long life of concrete pavements. These include— ● Provision for reasonably uniform support. (See Subgrades ond Subbases for Concrete Pavements,*) ● Prevention of mud-pumping with a relatively thin untreated or cement-treated subbase on projects where the expected truck traffic will be great enough to cause pumping. (The need for and requirements of subbase are also given in the booklet cited above. ) ● Use of a joint design that will afford adequate load transfeq enable joint sealants, if required, to be effective; and prevent joint distress due to infiltration. (See Joint Design for Concrete Highway and Street Pavements.** ) ● Use of a concrete mix design and aggregates that will provide quality concrete with the strength and durability needed for long fife under the actual exposure conditions. (See Design and Control of Concrete Mixrf4re$.T) The thickness design criteria suggested are based on general pavement performance experience. If regional or local specific performance experience becomes available for more favorable or adverse conditions, the design criteria can be appropriately modified. This could be the case for particular climate, soil, or drainage conditions and future design innovations.

Applications The

design

of Design Procedures

procedures

given

in this text apply

to the fol-

doweled, reinforced, and continuously reinforced. Plain pavements are constructed without reinforcing steel or doweled joints. Load transfer at the joints is obtained by aggregate interlock between the cracked faces below the joint saw cut or groove. For load transfer to be effective, it is necessary that short joint spacings be used. Plain-doweled pavements are built without reinforcing steeb however, smooth steel dowel bars are installed as load transfer devices at each contraction joint and relatively short joint spacings are used to control cracking. Reinforced pavements contain reinforcing steel and dowel bars for load transfer at the contraction joints. The pavements are constructed with longer joint spacings than used for unreinforced pavements. Between the joints, one or more transverse cracks will usually develop; these are held tightly together by the reinforcing steel and good load transfer is provided. Commonly used joint spacings that perform well are 15 ft for plain pavements,tt not more than 20 ft for plaindoweled pavements, and not more than about 40 ft for reinforced pavements. Joint spacings greater than these have been used but sometimes greater spacing causes pavement distress at joints and intermediate cracks between joints. Continuously reinforced pavements are built without contraction joints, Due to the relatively heavy, continuous-steel reinforcement in the longitudinal direction, these pavements develop transverse cracks at close intervals. A high degree of load transfer is developed at these crack faces held tightly together by steel reinforcement. The design procedures given here cover design conditions that have not been directly addressed before by

lowing

types

‘Portland **portl..d

of concrete

pavements:

Cement As$o.iation @nent Association

plain,

publication publication

plain

1S029F’ 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

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other procedures. These include recognition of— 1, The degree of load transfer at transverse joints provided by the different pavement types described. 2. The effect of using a concrete shoulder adjacent to the pavement; concrete shoulders reduce the flexuraI stresses and deflections caused by veh]cle loads, 3. The effect of using a lean concrete (econocrete) subbase, which reduces pavement stresses and defections, provides considerable support when trucks pass over joints, and provides resistance to subbase erosion caused by repeated pavement deflections. 4. Two design criteria (a) fatigue, to keep pavement stresses due to repeated loads with]n safe limits and thus prevent fatigue cracking and (b) erosion, to limit the effects of pavement deflectionsat slab edges. joints, and corner; and thus control the erosio~ of foundation and shoulder matefiak. The criterion for erosion is needed since some modes of pavement distress such as pumping, faulting, and shoulder distress are unrelated to fatigue, 5. Triple axles can be considered in design. While the conventional single-axle and tandem-axle configurations are still tbe predominant loads cm highways, use of triple axles (tridems) is increasing. They are seen on some over-the-road trucks and on special mads used for hauling coal or other minerals. Tridems may be more damaging from an erosion criterion (deflection) than from a fatigue criterion, Selection of an adequate thickness is dependent upon the choice of other design features—jointing system, t ype of subbase if needed, and shoulder type. Wkh these additional design conditions, the thickmss requirements of design alternatives, which influence cost, can lx directly compared. Chapter 2 describes how the factors needed for solving a design problem are determined. Chapter 3 details the full design procedure that is used when specific axle-loaddistribution data are known or estimated. If detailed axle-load data are not available, the design can be accomplished as described in Chapter 4, by the selection of one of several categories of data that represent a range of pavement facilities varying from residential streets up to busy interstate highways.

Computer

Programs Available

Thickness design problems can be worked out by hand with the tables and charts provided here or by computer and microcomputer with programs that are available from Portland Cement Association.

1. Theoretical studies of pavement slab behavior by Westergaard,{ ‘-’)* Pickett and Ray,(G ‘land reCent]y developed finite-element computer analyses, one of which 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 other agencies ofl$~$bases,( ‘*’S)joints( ’d- ‘]and concrete shoulders. 3. Experimental pavements subjected to controlled test traffic, such as the Bates Test Road,[2’] the Pktsburg Test Highway~22) the Mar$and R6ad Test~231 the AASHO** Road Test, {24-2) and studies of inservice highway pavements made by various state departments of transportation. 4. The performance of normally constructed pavements subject to normal mixed traffic. All these sources of knowledge are useful. However, the knowledge gained from performance of normally constructed pavements is the most important. Accordingly, it is essential to examine the relationship between the roles that performance and theory play in a design procedure, Sophisticated theoretical methods developed in recent years permit the responses of the pavement— stresses, deflections, pressures—to be more accurately modeled. This theoretical analysis is a necessary part of a mechanistic design procedure, for it allows consideration of a full range of design-variable combkations. An important second aspect of the design procedure is the criteria applied to the theoretically computed values— the limiting or allowable values of stress, deflection, or presmre. Defining the criteria so that design results are related to pavement performance experience and research data is critical in developing a design procedure, The theoretical parts of the design procedures given here are based on a comprehensive analysis of concrete stresses and deflections by a finite-element computer prodesign gram. co The program ~odcls the conventional factors of concrete properties, foundation support, and loadings, plus joint load transfer by dowels or aggregate interlock and concrete shoulder, for axle-load placements at slab interior, edge, joint, and corner. The criteria for the design procedures are based on the pavement design, performance, and research experience referenced above including relationships to performance of avements at the AASHO Road Test{ z’) and to studi~~~~ 29, of the faulting of pavements. More information on development and basis of the design procedure is given in Appendix A and Reference 30.

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Metric Version A metric version of this publication is also available from Portland Cement Association—publication EB209P.

Basis for Design The thickness design methods presented here are based on knowledge of pavement theory, performance, and research experience from the following sources:

*Supemcript numbers in parentheses denote references at the end of thk text. **Nw the American Association of State Hishway and Transportation Officials (AASHTO).

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CHAPTER 2

Design Factors

After selection of the type of concrete pavement (plain pavement with or without dowels, reinforced jointed pavement with dowels, or continuously reinforced pavement), type of subbase if needed, and type of shoulder (with or without concrete shoulder, curb and gutter or integral curb), thickness design is determined hased on four design factors: 1. Flexural strength of the concrete (modulus of rupture, MR) 2. Strength of the subgrade, or subgrade and subbase combination (k) 3. The weights, frequencies, and types of truck axle loads that the pavement will carry 4. D&ign period, which in this and other pavement design procedures is usually taken at 20 years, but may be more or less These design factors are discussed in more detail in the following sections. Other design considerations incorporated in the procedure are discussed in Appendix A.

Flexural Strength of Concrete

F-

Consideration of the flexural strength of the concrete is a,ppficable in the design procedure for the fatigue criterion, which controls cracking of the pavement under repetitive truck loadings. Bending of a concrete pavement under axle loads produces both compressive and flexural stresses. However, the ratios of compressive stresses to compressive strength are too small to influence slab thickness design. Ratios of flexural stress to flexural strength are much higher, often exceeding values of 0.5. As a result, flexural stresses and flexural strength of the concrete are used in thickness design. Flexural strength is determined by modulus of rupture tests, usually made on 6x6x30-in. beams. For specific projects, the concrete mix should be designed to give both adequate durability and flexural strength at the lowest possible cost. Mix design procedures are described in the Portland Cement Association publication Design and Control of Concrete A4ixt ures.

The modulus of rupture can be found by cantilever, center-point, or third-point loading. An important difference in these test methods is that the third-point test shows the minimum strength of the middle third of the test beam, while the other two methods show strength at only one point. The value determined by the more conservative thkd-point method (American Society for Testing and Materials, ASTM C78)isused fordesign in this procedure.* Modulus of rupture tests are commonly made at 7, 14, 28, and90days. The 7-and 14daytest results arecompared with specification requirements for job control and for determining when pavements can be opened to traffic. The 28-day test results have been commonly used for thickness design of highway sand streets and are recommended for use with this procedure; 90day results are used forthedesign of airfields. These values are used because there arevery fewstress repetitions during the first 28 or 90 days of pavement life as compared to the millions of stress repetitions that occur later. Concrete continues to gain strength with age as shown in Fig. 1. Strength gain isshown bythesolid curve, which represents average MR values for several series by laboratory tests, field-cured test beams, and sections of concrete taken from pavements in service. fn this design procedure theeffects** ofvafiationsin concrete strength from point to point in the pavement and gains in concrete strength with age are incorporated in the design charts and tables. The designer does not directly apply these effects but simply inputs the average 28-day strength value.

*Fora standard 30-in. beam, c.nlcr-point-load inEtcst val.es will be about 75 psi higher, and cantilever-loading 1.s1 values.bout 160 psi higher than cticrd-p.int-loa$ i.g test values. Th.x higher values are not iâ&#x20AC;&#x153;teâ&#x20AC;?ded tok.sdfor deszgnpurposts. Iftbese other test methods are used, adowmvard adjustment should be made byestabtisbing acorrelationto thtrd-poi.t-load test values. ..â&#x20AC;&#x2122;IIe,e effects are discussed in Appendix A.

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Table 1. Effect of Untreated on kValues,

S.::;;$ pci ‘ 50 100 200 300

Subbase

Subbase k value, pci 4 in,

6 in.

65 130 220 320

75 140 230 330

9 i“.

12 in.

65 160 270 370

110 190 320 430

“O

Table 2. Design k Values for CementTreated Subbases Am

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 thickness design. Subgrade and subbase support is defined in terms of the Westergaard modulus of subgrade reaction (k). It is equal to the load in pounds per square inch on a loaded area (a 30-in. diameter plate) divided by the deflection in inches for that load. The k values are expressed as pounds per square inch per inch (psi/ in,) or, more commonly, as pounds per cubic inch (pci). Equipment and procedures for determining k values are given in References 31 and 32. Since the plate-loading test is time consuming and expensive, the k value is usually estimated hy correlation to simpler tests such as the California Bearing Ratio (CBR) or R-value tests. The result is valid became exact determination of the k value is not required; normal variations from an estimated value will not appreciably affect pavement thickness requirements. The relationships shown in Fig. 2 are satisfactory for design purposes, The AASHO Road Test{ 241gave a convincing demo”. stration that the reduced subgrade support during thaw periods has little or no effect on the required thickness of concrete pavements. This is true because the brief periods when k values are low during spring thaws are more than offset by the longer periods when tbe subgrade is frozen and k values are much higher than assumed for design, To avoid the tedious methods required to design for seasonal variations in k, normal summer- or fa[/weaher k wlues are used as reasonable mea” values It is not economical to me wmeated subbases for the sole purpose of increasing k values. Where a subbase is used,* there will be an increase in k that should be used in the thickness design, If the subbase is an untreated granular material, the approximate increase in k can be taken from Table 1. The values shown in Table 1 are based on the Burmister[’3) analysis of two-layer systems and plate-loading tests made to determine k values on subgrades and subbases for full-scale test slabs.( ‘4]

Cement-treated subbases are widely used for heavyduty concrete pavements. They are constructed from AASHTO Soil Classes A- 1, A-2-4, A-2-5, and A-3 gronu[ar materials. The cement content of cement-treated subbase is based on standard ASTM laboratory freeze-thaw and wet-dry tests(~’ 35)and PCA weight-loss criteria. [36] Other procedures that give an equivalent qualit y of material can be used. Design kvalues forcement-treated subbases meeting these criteria are given in Table 2. In recent years, the use of lean concrete subbases has been ontheincrease. Thickness design ofconcretepavements on these very stiff subbases represents a special case that is covered in Appendix B.

Design Period The term design period is used in this publication rather than pavement lije, The latter is not subject to precise definition. Some engineers and highway agencies consider the life of a concrete pavement ended when the first overlay is placed. The life of concrete pavements may vary from less than 20 ycarson some projects that have carried more traffic than originally estimated or have had design, material, or construction defects to more than 40 years on other projects where defects are absent, The term design period is sometimes considered to be synonymous with the term traffic-malysis period, Since traffic can probably not be predicted with much accuracy fora Iongerperiod, a design period of 20yearsiscommonly used in pavement design procedures. However, there are often cases where useofashorter orlonger design period may be economically justified, such as a special 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 subbases sh.uldbeuwda.d h.wthi.k they sh.uldb., se the PCAp.blicati.n, Subgrades ond Subbasesfor Ccmc,,,e Pavemenm.

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premium facility for which a high level of performance for a long time with little or no pavement maintenance is desired. Some engineers feel that thedesign period for rural and urban highways should heinthe range of Xtto 35 years. The design period selected affects thickness design since it determines how many years, and thus how many trucks, thepavement must serve. Selection ofthcdesign period for a specific project is based on engineering judgment and economic analysis of pavement costs and service provided throughout the entire period.

Traffic Tbe numbers and weights ofheavy axle loads expected during thedesign life are major factors in the thickness design of concrete pavement. These are derived from estimates of —ADT (average daily traffic in both directions, all vehicles) —ADTT (average daily truck traffic in both directions) —axle loads of trucks Information on ADTis obtained from special traffic counts 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 gives a reasonable estimate of expected traffic during the design life can be used,

Projection One method forgetting thetraftlc volume data (design ADT) needed is to use yearly rates of traffic growth and traffic projection factors. Table 3 shows relationships between yearly rates of growth and projection factors for both 20- and 40-year design periods. In a design problem, the projection factor is multiplied by the present ADT to obtain a design ADT representing theaverage value forthedcsign period. Insomeprocedures, this is called AADT (average annual daily traffic). The following fact ors influence yearly growth rates and traffic projections: 1. Attracted or diverted traffic-the increase over existing traffic because of improvement of an existing road way. 2. Normal traffic growth—the increase due to increased numbers and usage of motor vehicles. 3. Generated traffic-the increase due to motor vehicle trips that wnuld not have been made if the mw facil. ity had not been constructed. 4. Development traffic-the increase due to changes in land use due to construction of the new facifity. The combined effects will cause annual growth rates of about 2Yoto 6%. Tbeserates correspond to20-yeartrafficprojection factors of 1.2to 1.8asshown in Table3, The planning survey sections of state highway departmerits are very use fulsources ofknowledge about traftic grnwth and projection factors.

Table 3. Yearly Rates of Trafffc Growth and Corresponding Projection Factora’ Yearly rate of traffic gro;th,

1~% 2 2,% 3 3,% 4 4M 5 5% 6

Prg:;ecron

1,1 1.2

1.2 1.3 1.3 1.4 1.5 1,6 1.6 1.7 1.8

40 yea~s 1.2 1.3 1.5 1.6 1.8 2,0 2.2 2.4 2.7 2.9 3.2

,Faclor. represent values at the middesig” period that are widely used incurre”t pr.ctke, Another mtihod of cmnp.fing these factors is based on the averaae annual value. Differences (bothcompound intere<t) between these two methods will ”rarely affect design.

Where there is some question shout the rate of growth, it may be wise to use a fairly high rate. This is true on intercity routes andon urban projects where ahigh rate of urban growth maycause ahlgher-than-expected rate oftraftic growth. However, thegrowth oftruck volumes 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 land useorabutting property service. Their growth rates may be below 2% per year (projection factors of 1.1 “to 1.3). Snme engineers suggest that the use of simple interest growth rates may be appropriate, rather than compound interest rates, which when used with a long design period may predict unrealistically heavy future traffic.

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Capacity The other method of estimating design ADT is based on capacity—the maximum number of vehicles that can use the pavement without unreasonable delay. Tbis method of estimating the volume of traffic is described in Appendix D and should be checked for specific projects where the projected traffic volume is high; more traffic lanes may 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 as a percentage of ADT or as an actual value. The ADTT value includes only trucks with six tires or more and does not 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

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._ ~

trucks from which ADTT can be computed. For design of major Interstate and primary system projects, the planning survey sections of state departments of transportation usually make specific traffic surveys, These data are then used to determine the percentage relationship between ADT’T and ADT. ADTT percentages and other essential traffic data can also be obtained from surveys conducted by the highway department at specific locations on the state highway system. These locations, called Ioadometer stations, have been carefully selected to give reliable information on traffic composition, truck weights, and axle loads. Survey results are compiled into a set of tables from which the ADTT percentage can be determined for the highway classes within a state. This makes it possible to compute the ADTT percentage for each station. For example, a highway department Ioadometer table (Table w-3) for a Midwestern state yields the following vehicle count for a Ioadometer station on their Interstate rural system: All vehicles—ADT . . . . . . . . . . . . . . . . . . . . ...9492 Trucks: All single units and combinations . . . . . ...1645 Panels and pickups . . . . . . . . . . . . . . . . . . . 353 Other four-tire single units . . . . . . . . . . . . 76 Therefore,

It is important to keep in mind that the ADTT percentages in Table 4 are average values computed from many projects in all sections of the country. For this reason, these percentages are only suitable for design of specific projects where ADTT percentages are also about average. For design purposes, the total number of trucks in the design period is needed. This is obtained by multiplying design ADT by ADTT percentage divided by 100, times the number of days in the design period (365 X design period in years). For facilities of four lanes or more, the ADTT is adjusted by the use of Fig, 3.

for this station: T* = ]645 – (353 + 76) = 1216

‘DTT

1216 ‘ ZY2x

’00=

‘3%

This ADTT percentage would be appropriate for de. sign of a project where factors influencing the growth and composition of traffic are similar to those at this loadometer station. Another source of information on ADTT ercentages !’37) Table 4, is the National Truck Characteristic Report. which is taken from this study, shows the percentages of four-tire single units and trucks on the major highway systems in the United States. The current publication, which is updated periodically, shows that two-axle, fourtire trucks comprise between 40’% to 65% of the total number of trucks, with a national average of 49% It is fikely that the lower values on urban routes are due to larger volumes of passenger cars rather than fewer trucks.

PROPORTIONOF TRuCKS IN RIGHT LANE

Fig. 3. Proportion of trucks in right lane of a multilane divided highway. (Derived from Reference 3&)

‘Tr.cks-xcludes

panels and pickups and other f. .r-ti r. vehiclcs.

Table 4. Percentage of Four-Tire Single Units and Trucks (ADTT) on Varioua Highway Systems

I Rural average daily traffic

I Urban average daily traffic

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Truck Directional

Distribution

In most design problems, it is assumed that the weights and volumes of trucks traveling in each direction are fairly equ81-50-50 distribution-the design essumes that pavement in each dirsction carries half the total ADTT. Thk may not be true in special cases where many of the trucks may be hauling full loads in one direction and returning empty in the other direction. If such is the case, an appropriate adjustment is made. Axie-Load

Oiatribufion

Data on the axle-load distribution of the truck traffic is needed to compute the numbers of single and tandem axles* 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 loadometerdata for the specific project; (2) data from the state highway department’s Ioadometer weight stations (Table W4) or weigh-in-motion studies on routes representing truck weights and types that are expected to be similar to the project under design; (3) when axle-load distribution data are not available, methods described in Chapter 4 based on categories of representative data for different types of pavement facilities. The use of axle-load data is illustrated in Table 5 in which Table W4 data have been grouped by 2-kip and 4-kip increments for single- and tandem-axle loads, re. spectively. The data under the heading “Axles per 1000 Trucks” are in a convenient form for computing the axleIoad distribution, However, an adjustment must be made, Column 2 of Table 5 gives values for all trucks, including the unwanted values for panels, pickups, and other fourtire vehicles. To overcome this difficulty, the tabulated values are adjusted as described in the Table 5 notes, Column 4 of Table 5 gives the repetitions of various single- and tandem-axle loads expected during a 20-yeardesign period for the Design 1 sample problem given in Chapter 3.

Load Safety Factors In the design procedure, the axle loads determined in the previous section are multiplied by a load safety factor (LSF). These load safety factors are recommended: ● For Interstate and other multilane projects where there will be uninterrupted traffic flow and high volumes of truck traffic, LSF = 1.2. ● For highways and arterial streets where there will be moderate volumes of truck traffic, LSF = 1, 1. ● For roads, residential streets, and other streets that will carry small volumes of truck traffic, LSF = 1.0. Aside from the load safety factors, a degree of conservatism is provided in the design procedure to compensate

Table 5. Axle-Load

Data

~ ~ngle

L-J

axles

2a30

0.28

0.58

6,310

2&28

0.65

1.35

14,690

24-26

1.33

2.77

30,140

22-24

2.84

5.92

64,410

2W22

4.72

9.83

106,900

1&20

10.40

21.67

235,800

16-18

13.56

28.24

307,200

14-16

18.64

38,83

422,500

12-14

25.69

53,94

586,900

1}12

81.05

168,85

,637,000

Tandem axles 48-52 44-48

0.94

1.89

21,320 42,670

4s44

5.51

11,48

124,800

36-40

16.45

34.27

372,900

32-36

39.06

81,42

885,800

28-32

41.06

65.54

930,700

24-28

73,07

152.23

1,656,000

20-24

43.45

90.52

984,900

15-20

54,15

112.81

1,227,000

12-16

59,85

124.69

1,356,000

Columns 1 and 2derived from Ioadometer W-4 Table. This table al$oshows 13,215 tolal trucks coumed with 6,916 two-axle, four-tire trucks (52%]. Column 3 Column 2 values adjusted for two.wle, to Column 2/[1 52/100).

four-tire trucks equal

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 normal construction variations in material properties and layer thicknesses. Above that basic level of conservatism (LSF = 1.0), the load safety factors of 1.1 or 1,2 provide a greater allowance for the possibility of unpredicted heavy truck loads and volumes and a higher level of pavement serviceability appropriate for higher type pavement facilities. In special cases, the use of a load safet y factor as high as 1.3 may be justified to maintain a higher-than-normal level of pavement serviceability throughout the design period. An example is a very busy urban freeway with no alternate detour routes for the traffic. Here, it may be better to provide a premium facility to circumvent for a long time tbe need for any significant pavement maintenance that would disrupt traffic flow.

*See Appendix C if it isexpected that trucks with tridem loads will be included i“ the traffk f.tecast.

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1.96 3.94

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CHAPTER 3

Design Procedure (Axle-Load Data Available)

The methods in this chapter are used when detailed axleload distribution data have been determined or estimated as described in Chapter 2.* Fig. 4 is a worksheet** showing the format for corn. pleting design problems.t It requires as input data the following 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 subbase combination? ● Load safety factor (LSF) ● Axle-load distribution (Column 1) ● Expected number of axle-load repetitions during the design period (Column 3) Both a fatigue analysis (to control fatigue cracking) and an erosion analysis (to control foundation and shoulder erosion, pumping, and faulting) are shown on the design worksheet. The fatigue analysis will usually control the design of light-traffic pavements (residential streets and secondary roads regardless of whether the joints are doweled or not) and medium traffic pavements with doweled joints. The erosion analysis will usually control the design of medium- and heavy-traffic pavements with undoweled (aggregate-interlock) joints and heavy-traffic pavements with doweled joints. For pavements carrying a normal mix of axle weights, single-axle loads are usually more severe in the fatigue analys]s, and tandem-axle loads are more severe in the erosion analysis. The step-by-step design procedure is as follows: The design input data shown at the top of Fig. 4 are established and Columns 1 and 3 are tilled out. The axle loads are multiplied by the load safety factor for Column 2.

2, Divide these by the concrete modulus of rupture and enter 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 Column 4, multiplying by 100 then total the fatigue at the bottom.

Erosion Analysis Without concrete shoulder ● Doweled joints or continuously reinforced pavements# —use Table 7a and Fig. 6a. ● Aggregate-interlock joints—use Table 7b and Fig. 6a, With concrete shoulder ● Doweled joints or continuously reinforced pavements~—use Table 8a and Fig. 6b. ● Aggregate-interlock joints—use Table 8band Fig, 6b. Procedure Steps: 1. Enter the erosion factors from the appropriate as items 10 and 13 in the worksheet. 2. FIO in Column 6, “Allowable Repetitions,” Fig. 6a or Fig. 6b.

table from

*% 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

Fatigue Analysis ~

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 depending on trial thickness and k value. ●

Results of fatigue analysis, and thus the charts and figures used, are the same for pavements with doweled and undoweled joints, and also for continuously reinforced pavements.~

p.rposes of reproduction and use in w=ific design problems. f Computer programs for s.lving design problems are available fr.m P.rtlmd Cement Ass.ciati.n. ItSee Appendix B if lean concrete subbase is used. $1. this design procedure, ccmtin”cwsly reinforced pavemems are treated the same as dowdcd, jointed pavements—see Appendix A.

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Calculation Project Trial

thickness

Subbase-subgrade

/,4

&.#T-

/QA

Thickness

L7A?r./&/.

P&z2/’

9.5

in.

Doweled

/.70

pci

Concrete shoulder:

Modulus of rupture, MR

Load safetv factor. LSF

/. Z?

of Pavement

psi

joints:

yes

no —

yes —no~

Design period ~

years

I Axle load, hips

L 1

Single Axles

8. Equivalent stress

206

9. Stress rcatiofactor

10. Erosion factor

2.59

? 17

u’

11. Equivalent stress

Tandem Axles

192

13. Erosion factor

12. Stress ratio factor Z?Jl$K_

Fig. 4. Design 1A.

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3. Compute Column 7 by dividing Column 3 by Column 6, multiplying by lW, then total the erosion damage at the bottom, In the use of the charts, precise interpolation of allowable repetitions is not required. If the intersection line runs off the top of the chart, the allowable load repetitions are considered to be unlimited. The trial thickness is not an adequate design if either of the totals of fatigue or erosion damage are greater than 100%, A greater trial thickness should be selected for another run, * A lesser trial thickness is selected if the totals are much lower than 100Yo.

Sample Problems Two sample problems are given to illustrate the steps in the design procedure and the effects of alternate designs. Design 1 is for a four-lane rural Interstate project; several variations on the design—use of dowels or aggregateinterlock joints, use of concrete shoulder, granular and cement-treated subbases—are shown as Designs 1A through 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 Interstate Rolling terrain in rural location Design period = 20 years Current ADT = 12,900 Projection factor = 1.5 ADTT = 19% of ADT Traffic Calculations: Desien ADT = 12.900 X 1.5 = 19,350 (9675 in one dire;tion) ADTT = 19,350 X0.19= 3680 (1840 in one direction) For 9675 one-direction ADT, Fig. 3 shows that the proportion of trucks in the right lane is 0.81. Therefore, for a 20-yeardesign period, the total number of trucks in one direction is 1840 X 0.81 X 365 X 20 = 10,880,000 trucks Axle-load data from Table 5 are used in this design example and have been entered in Fig. 4 under the maximum axle load for each group. Values Used to Calculate Thickness:** Design 1A: doweled joints, untreated subbase, no concrete shoulder Clay subgrade, k = 100 pci 4-in. -untreated subbase Combined k = 130 pci (see Table 1) LSF = 1.2 (see page 10) Concrete MR = 650 psi Design lB doweled joints, cement-treated subbase, no concrete shoulder Same as 1A except: 4-in. cement-treated subbaset Combined k = 280 pci (see Table 2)

Design lC: doweled joints, untreated subbase, concrete shoulder Same as 1A except: Concrete shoulder Design ID: aggregate-interlock joints, cement-treated subbase, no concrete shoulder Same as 1B except: Aggregate-interlock joints Design lE: aggregate-interlock joints, cement-treated subbase, concrete shoulder Same as 1D except: Concrete shoulder Thickness Calculations: A trial thickness is evaluated by completing the design worksheettt shown in Fig. 4 for Design 1A using the axle-load data from Table 5. For Design 1A, Table 6a and Fig, 5 are used for the fatigue analysis and Table 7a and Fig. 6a are used for the erosion analysis. Comments on Design 1 For designs 1A through 1E, a subbase of one type or another is used as a recommended practice $onfine-textured soil subgrades for pavements carrying an appreciable number of heavy trucks. In Design 1A: (1) Totals of fatigue use and erosion damage of 63% and 39%, respectively, show that the 9.5in. thickness is adequate for thedesign conditions. (2) This design has 37% reserve capacity available for heavy-axle loads in addition to those estimated for design purposes. (3) Comments 1 and 2 raise the question of whethera 9.0in. thickness would be adequate for Design IA. Separate calculations showed that 9.0 in. is not adequate because of excessive fatigue consumption (245Yo). (4) Design 1A is controlled by the fatigue analysis. A design worksheet, Fig. 7, is shown for Design 1D to illustrate the comb]ned effect of using aggregate-interlock joints and a cement-treated subbase. In Design 1D: (1) Totals of fatigue use and erosion damage of l%t$ and 97%, respectively, show that IO in. is adequate. (2) Separate calculations show that 9.5 in. is not adequate because of excessive erosion damage ( 142Yo),and (3) ~sign 1D is controlled by the erosion analysis. (continue

donpage21)

*Some guidance is helpful in reducing the number of trial inns. The effect of thickness on both the fatigue and erosion damage approximately follows a geometric progression. For example, if 33% and 17870 fatigue damage are determined at trial thicknessesof 10 and 8 in., r.spectivdy, the approximate fatigue damage for t+thickness of 9 in. is cowl to .~ = 77% :*com& MR. LS F. and submade k value, are tie WM. for DesiEns 1A through lE. Weme.t-treamd subbase meeting requirements stated on page 6. tTA blank worksheet is provided asthe last page of 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 appreciable num~r design.

of truck% the fadw

,..M

will .$.aW

..1 affect

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Table 6a. Equivalent Streaa — No Concrete Shoulder (Singla Axle/Tandam Axle) Slab

k of Subgrade-subbase,

thickness, In.

pci

100

150

200

300

500

700

4 4.5

825[679 699/586

726/585 61 6/500

6711542 57f /460

634/516 540/435

584/486 498/406

5231457 4481378

484/443 417/363

5 5.5

602/51 6 526/461

531 /436 484/367

493/399 431/353

467/376 409/331

432/349 379/305

390/321 3431278

363/307 320/264

6 6.5

485/4f 6 41 7/380

4111348 367/31 7

382/31 6 341/286

362/296 324/267

336/271 300/244

304/246 2731220

285/232 256/207

7 7.5

375[349 340/323

331 /290 300/268

307/262 279/241

292/244 265/224

2711222 246/203

246/199 224/181

231/186 210/169

8 8.5

311 /300 285/281

2741249 252)232

255/223 234/206

242/208 222/1 93

2251188 206/174

205/167 186/154

192)1 55 177/143

9 9.5

264/264 245/248

232/21 6 215/205

216/195 200/183

205/181 190/1 70

190/1 63 176/153

1741744 161 /134

163/1 33 151/124

10 10.5

226/235 21 3/222

200/1 93 187/1 83

186/1 73 174[1 64

177/160 165/151

164/144 153/1 36

150/126 140/119

141/117 132/110

11 11.5

200/21 1 133/201

175/1 74 165/165

163/155 153/1 48

154/1 43 145/1 36

144/1 29 135/122

131/113 123/1 07

123/1 04 116/96

12 12,5

177/192 1681183

155/156 147/151

144/141 136/1 35

137/130 129/124

1271116 120/111

116/1 02 109/97

109/93 103/89

13 13.5

159/1 76 152/1 68

139/144 132/136

129/1 29 122/123

122/119 116/114

113/106 107/102

103/93 98/89

97[85 92/81

144/162

125/133

116/116

110/109

102/98

93[85

88/78

Table 6b. Equivalent Straaa — Concrete (Single Axle/Tandem Axle) Slab thic;n~,

Shoulder

“w’

k of subgrade-subbase,

pci

100

150

200

300

500

700

4 4.5

640/534 547/461

559/466 479/400

51 7/439 4441372

489/422 421 /356

452/403 390/336

409/388 355/322

363/384 333/31 6

5 5.5

4751404 41 6)360

41 7/349 366/309

387[323 342/285

367/308 324/271

341 /290 302/254

311/274 276/236

294/267 261/231

6 6.5

3721325 334/295

3271277 294/251

304/255 274/230

269/241 260/218

270/225 243/203

247/210 223/1 88

2341203 21 2/180

7 7,5

302/270 275/250

266/230 243/21 1

248/21 O 226)1 93

236/1 98 215/182

220/1 84 201/168

203/170 185/155

192/162 176/148

8 8,5

252/232 232/21 6

222/196 205/1 62

207/1 79 191/166

197/168 182/156

185/155 170)1 44

170/142 157/131

162/135 150/1 25

9 9.5

215/202 200/1 90

190/171 176/160

177/1 55 164/146

169/146 157/137

158/1 34 1471126

146/1 22 136/114

139/1 16 129/1 08

10 10.5

186/1 79 174/170

164/151 154/143

153/137 144/130

146/129 137/121

137/116 128/711

127/107 119/101

121)101 1>3/95

11 11.5

164/161 154/153

144/1 35 136/1 28

135/1 23 1271117

129/1 15 121/109

1201105 113/100

112/95 105/90

106/90 100/65

12 12.5

145/146 137/1 39

128/1 22 121/117

120/111 113/106

114/104 106/99

107/95 101/91

99/86 94/82

95/81 90/77

13 13,5

130/1 33

*15)112

107/101

102/95

96/86

89/78

85173

124/1 27

10S/107

102/97

97/91

91183

85174

81 /70

118/122

104/103

93/87

87179

81/71

77167

97/93

“’U

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60--(--’20

10,000,0001 :-

Q 15

56 110

1,ocwooo8—

[

100

0.2” 2-

46 loo,ooo—

90 44

“..3

2 0

m a Z c)”

a o -1

w -1 z

.—-—

—.—

—

——

)

-——+ 2-

i= 1= w a. w

34 1o,ooQ—

32 t

864-

26 50

“.s”

24 22

0.(3” looo—

Q ?“

60.80

16 30

0. 9“

-1

I.”. 12 10

2 2“

i /

1.s”

100 ~

Fig. 5. Fatigue analysis—allowable toad repetitions based on stress ratio factor (with and without concrete shoulder).

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Table 7a. Erosion Fectora — Doweled Jointa, No Concrete Shoulder (Single Axle/Tandem Axle) Slab thickness, In. < 4 4.5 5 5.5

k of subgrade-subbase,

I I

pci

100

200

300

500

700

3. 74/3.83 3.59/3. 70

3.7313.79 3.5713.65

3.7213.75 3.56/3.61 1

3.7113.73 3. 55/3,58

3. 70/3.70 3.5413.55

3.68/3.67 3.52/3.53 3.38/3.40

3. 45[3. 58

3.43/3.52

3.42/3. 48

3.41/3,45

3.40)3.42

3.3313.47

3.31/3.41

3.29/3.36

3.28/3.33

3.27/3.30

3.26/3.28

6 6.5

3,2213.38 3,11 /3. 29

3.1 9/3, 31 3.09/3, 22

3,18/3.26 3.07/3, 16

3. 17/3.23 3,06/3. 13

3.1 5/3. 20 3.05/3. 10

3. 14/3,17 3. 03/3,07

7 7,5

3, 02/3.21 2. 93/3.14

2.99/3.14 2.91/3,06

2,97/3,08 2. 86/3.00

2. 96/3.05 2.6712.97

2. 95/3.01 2.86/2, 93

2. 94/2.98 2. 84/2.90

8 8.5

2. 85/3.07 2.7713.01

2, 62/2.99 2.7412.93

2.80/2.93 2. 72)2.86

2.7912.89 2.7112.82

2,7712.65 2,89/2.78

2.76/2.82 2. 68/2.75

9 9.5

2, 70/2.96 2, 63)2.90

2. 67/2.87 2. 60/2.81

2.65/2.80 2. 58/2.74

2, 63/2,76 2.56/2,70

2.6212.71 2.55/2.65

2.61/2.68 2.5412,62

10 10.5

2.5612,85 2.50/2.81

2.54/2. 76 2.47[2,71

2,51/2.68 2.4512.63

2.50/2.64 2,4412.59

2.46/2. 59 2.4212.54

2.4712,56 2.41/2.51

11 11,5

2.4412,76 2.36[2.72

2. 42/2.67 2. 36/2,62

2. 39/2.58 2.3312.54

2.38)2.54 2.32/2.49

2.36/2.49 2.30[2. 44

2,35/2,45 2.29/2.40

12 12.5

2.33/2. 68 2.2812.84

2.30/2.58 2. 25)2.54

2.28/2.49 2.2312.45

2. 26/2,44 2.2112.40

2,2512.39 2, 19/2.35

2.23/2.38 2. 18/2.31

13 13.5

2. 23[2. 61 2,1612,57

2. 20/2.50 2.t5/2 ,47

2.1812,41 2.1312.37

2.1612.36 2, 11/2.32

2. 14/2.30 2.09/2.26

2.1312.27 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) Slab thickness, in.

k of subgrade-subbme, 50

100

4 4.5

pci

200

300

500

700

3.94/4. 03 3. 79/3.91

3.91/3.95 3.7613.82

3. 68/3.89 3. 73/3.75

3. 86/3.86 3.71 [3, 72

3.62/3, 83 3.6813.68

3,77/3.80 3. 64/3.65

5 5.5

3. 86/3,81 3.54/3.72

3. 63/3,72 3,51/3,62

3, 60/3.64 3.4813,53

3,5813.80 3.46/3.49

3.55[3 ,55 3.43/3.44

3. 52/3.52 3.41 /3.40

6 6.5

3.44/3. 64 3.34/3. 56

3. 40/3.53 3.30/3.46

3. 37[3. 44 3.26/3.38

3. 35/3.40 3. 25/3.31

3.32/3.34 3.22/3. 25

3.30/3, 30 3.20/3, 21

7 7.5

3. 26/3.49 3, 16/3,43

3.21/3.39 3. 13/3.32

3. 17/3.29 3.09/3.22

3. 15/3.24 3.07/3, 17

3,1 3/3. 17 3. 04/3,1 o

3,11/3,13 3. 02/3.06

8 8,5

3.1 1/3.37 3.04/3,32

3.05/3.26 2.96/3.21

3.01/3.18 2.93/3.10

2.99/3. 10 2.81/3.04

2.96/3.03 2.S812.97

2.94/2.99 2.8712.!33

9 9.5

2. 98/3.27 2. 92/3.22

2,91/3.16 2. 65/3.11

2, 86/3,05 2. 60/3.00

2. 84/2.99 2. 77/2.94

2.81/2.92 2.7512.86

2. 79/2.87 2. 73/2.81

10 10,5

2.66/3. 18 2.81/3.14

2. 79/3.06 2. 74/3.02

2.7412.95 2. 66/2.91

2.71/2.89 2. 65/2.64

2.68/2.81 2.62/2.76

2.66/2.76 2,60/2,72

11 11.5

2.77[3. 10 2.7213,06

2.69/2.98 2. 64/2.94

2.63[2.86 2.58/2.82

2.60/2. 80 2,5512.76

2,5712.72 2.51/2,68

2.54/2.67 2.49/2.63

12 12.5

2. 68/3.03 2.64/2.99

2. 60/2,90 2,5512.87

2.5312.78 2, 48[2. 75

2,5012.72 2.4512,68

2. 46/2.64 2.41/2.60

2.44/2. 58 2.39/2.55

13 13.5

2.60/2.96 2.56/2.93

2.51/2.83 2.47/2.80

2.4412.71 2.40/2. 68

2. 40/2.65 2.36/2.61

2.36/2.56 2.32/2.53

2.34/2.51 2.30/2. 48

2.5312.90

2.4412.77

2.36/2.65

2.32/2.58

2, 28[2. 50

2,25[2.44

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Book Contents

60 T

I20

loo,cK)o,ooo8— 64-

—110 50-

— 100

–

— 2.0 10,000,000

90 — 2.2

= 86-

40 – –

tio~

30 – – u) Il. Z ~-

—

~—

g u ~

(/) a G 25-

–

; ~ (n

— 40

la- . 35

2.6 —

–

2.8

~._

–

3.0

4—3.2 2–

3.4

–

3.6

: 100,000:

w n z1-

66-

— 3.8

— 4.0 2-

14- -

– t2- -

I ,000,000: 8-

16- –

~.+

20–

2.4

~ m

~“

0 -1

u -1

a o J

; ~

—

–

IQOOO 864-

lo-

—

20 2-

9- - 18

8— 16 Fig. 6a. Erosion based

on erosion

1000 — analysis—allowable load repetitions factor (without concrete shoulder),

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Book Contents

Table &. Erosion Factors — Doweled Joints, Concrete C3inale Axle/Tandem Axle) Slab thic:ny, 4 4.5

k of s. bgrade-subbase,

Shoulder

pci

100

200

300

500

700

3.28/3.30 3.13/3.19

3. 24/3.20 3.09/3.08

3.21/3.13 3.08/3.00

3.1 9/3. 10 3.04/9 !36

3.1 5/3.09 3

3. 12/3.08

(11/793 7?),/7 Q,

5 5.5

I 3.0113.09 2.90/3. 01

2.97/2.98 2.85/2. 89

2.93/2.89 2.81/2,79

2.90/2.84 2.7912.74

2.8712.79 2.7612,68

7.35/7.77 2.7312.65

8 6.5

2,7912.93 2. 70/2.66

2.7512,82 2,6512.75

2,70/2.71 2.61/2,63

2,66/2.65 2.58[ 2.57

76S/7 . . . . SR .. 2.55/2.50

7 . 67/95A .. . . 2.52)2.45

7 7.5

2.61/2.79 2.53/2.73

2.5612.66 2.48/2.62

2.52/2.56 2.44/2.50

2.49/2.50 2.41 [2.44

2.46)2.42 2.38/2.36

2.43/2, 38 2.35/2.31

8 8.5

2.46/2. 68 2.39/2.62

2.41/2.56 2.34/2, 51

2.3612.44 2. 29/2,39

2.33)2.38 2.26/2. 32

2.30/2, 30 2,22/2,24

2.2712.24 2.20/2, 18

9 9.5

2.3212.57 2. 26/2.52

2.2712,46 2.21/2.41

2.2212,34 2,16/2.29

2.1912.27 2. 13/2.22

2, 16/2.19 2,09/2, 14

2. 13/2.13 2. 07/2.08

10 10,5

2.2012.47 2. 15/2,43

2. 15[2. 36 2. 09/2.32

2, 10/2.25 2. 04/2.20

2.07/2, 16 2.01/2.14

2.03/2.09 1.87/2.05

2.01/2.03 1.85/1.99

11 11.5

2. 10/2,39 2. 05/2.35

2.04/2.28 1.99/2.24

1.99/2. 16 1.93/2. 12

1.95/2.09 1.90/2.05

1.92/2.01 1.67/1.97

1.89/1.95 1.8411,91

12 12.5

2.00/2.31 1.95/2.27

1.94/2.20 1.69/2. 16

1,88/2.09 1.64/2.05

1.6512.02 1.81/1.98

1.82/1.93 1.77/1.89

1.7911.87 1.7411,84

13 13.5

1.91/2,23 1.66/2.20

1.85/2, 13 1,81/2.09

1.79/2.01 1.75/1.96

1.76/1.95 1.72/1.91

1,72/1.86 1.68/1.83

1.70/1.80 1.65/1.77

1.82/2, 17

1.76/2.06

1.71/1.95

1.67/1.88

1.64/1.80

1.61/1,74

‘L--J

Table 8b. Erosion Factors — Aggregate-Interlock Joints, Concrete Shoulder (~;gl; AxleiTandem Axlej slab thickness, in.

k of S“bgrade-subbase,

pci

100

200

300

500

700

4 4,5

3. 46/3,49 3. 32/3.39

3. 42/3.39 3,28/3.28

3.3813.32 3.2413.19

3. 36/3.29 3,22/3. 16

3, 32/3.26 3,1 9/3, 12

3.28/3.24 3.1 5/3. 09

5 5,5

i 3.20/3.30 3.10/3.22

3. 16/3.18 3.05/3, 10

3, 12/3.09 3,01/3,00

31 0/3.05 2.99/2,95

3.07/3.00 2. 96/2,90

3.04/?. 97 2. 93/2.66

6 6.5

3. 00/3.15 2.91/3,06

2.95/3,02 2. 86/2.96

2. 90/2,92 2,81/2,85

2.68/2.87 2.79/2.79

2,66/2.61 2,7612.73

2,6312.77 2.7412.66

7 7.5

2. 83/3.02 2.76/2,97

2,77/2.90 2,70/2.84

2.7312.78 2.65/2.72

2.7012.72 2,62/2.66

2. 68/2.66 2. 60/2.59

2. 65/2.61 2.5712.54

8 6.5

2. 69/2.92 2. 63/2.88

2.63/2.79 2. 56/2.74

2.5712.67 2.51/2.62

2.55/2.61 2.48/2. 55

2. 52/2.53 2.4512.48

2. 50/2.48 2.43/2.43

9 9.5

2. 57/2.83 2.51/2.79

2. 50/2.70 2,4412,65

2.4412,57 2. 38/2,53

2,42/2.51 2.36/2,46

2, 38/2.43 2.3312.38

2. 36/2.38 2, 30/2.33

10 10.5

2.46/2.75 2.41/2,72

2,39/2,61 2.33/2.58

2.33/2.49 2.2712.45

2.30/2,42 2,24/2.36

2.27[2 ,34 2,21/2,30

2.24/2.26 2.1 9/2.24

11 11.5

2.36/2. 66 2.32/2.65

2.26/2.54 2.2412.51

2.22/2.41 2. 17!2.36

2. 19/2.34 2.>4/2.31

2. 16/2.26 2.11/2.22

2. 14/2.20 2.09)2. 18

12 12.5

2.28/2.62 2,2412.59

2. 19/2.48 2.15/2.45

2, 13/2.34 2.09/2.31

2. 10/2.27 2. 05/2.24

2.06/2. 19 2.02/2, 15

2.04/2.13 1.99/2.10

13 13.5

2, 20/2.56 2. 16/2,5s

2. 11/2,42 2.06/2.39

2.04/2,26 2.00/2,25

2.01/2.21 1.97/2, 18

1,98[2. 12 1.93/2.09

1,95/2,06 1.91/2,03

2. 13/2.51

2,04/2.36

1.97/2.23

1.83/2. 15

1.89/2.06

1.87[2. 00

“-/’

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60-1-120

IOO,OOQOOO

‘a

—1.6

2-1

110 50

IQOOQOOO

— 1.8

I 00

—2.0 2

–2.2

I ,Ooo,ooo 8

70 a

P v 2

60 /

—2.4

4 i

– 2.6

~ (n : —2.8 w

2 g ~ 1-

100,000 —k —3.0

a 0 -1

—3.2

m 4 g

— 3.4

J 2-

— 3.6

I Qooo— 8-

1000

Fig. 6b. Erosion analysis—allowable load repetitions based on erosion factor (with concrete shoulder).

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Calculation of Pavement Thickness

Trial thickness—

/A.

Subbase-$ ubgrade h ~ Modulus of rupture, MR =~ Load safety factor, LSF

in.

Doweled joints:

yes _

no z

Pci

Concrete shoulder:

yes _

no L

psi

Design period

years

/7 %%..

C&z?#’(+&&d5.A&

Fatigue analysis Axle load, kips.

Multiplied by LSF

Expected repetitions

/. z 1

Fatigue, percent

Damage percent

10. Erosion factor ~

11. Equivalent stress.

2.57

/@7

13. Erosion factor

–~

12. Stress ratio factor ~

Total

Fig. 7. Design

Allowable repetitions

sbess~

9. Stress ratio factor

Tandem Axles

Erosion analysis

Allowable repefitio”s

6. Equivalent

Single Axles

0.6

ID.

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Total

%?/

L) —

Worksheets shown

for the other variations

Subbase

Design

of Design

here but the results are compared

Joints

Gin. gm”ular

doweled

Gin. cement-treated

hi”,

ID lE

1 are not

as follows:

Umcrete shoulder

Thickness q.i~emer. t, m.

9.5

doweled

8.5

doweled

yes

8.5

4-in. cement-treated

aggregate interlock

4+n. cement-treated

aggregate interlock

yes

granular

10.0 8.5

Design 2B: doweled joints,** shoulder Same as 2A except Doweled joints

no subbase, no concrete

TMckness Calculations: For Design 2A, a trial thickness of 6 in. is evaluated by completing the worksheet shown in F]g. 8, according to the procedure given on page 11. Table da and Fig. 5 are used for the fatigue analysis and Table 7band Fig. .5aare used for the erosion anal ysis. For Design 2B, a worksheet is not shown here but the design was worked out for comparison with Design 2A. Comments on Design 2

For Design 1 conditions, use of a cement-treated subbase reduces the thickness requirement by 1,0 in. (Design 1A versus 1B); and concrete shoulders reduce the thickness requirement by 1.0 to 1.5 in. (Designs 1A versus IC and I D versus 1E). Use of aggregate-interlock joints instead of dowels increases the thickness requirement by 1.5 in. (Design 1B versus 1D). These effects will vary in different design problems depending on the specific design conditions. Design 2

Project and Traffic Data: Two-lane-secondary road Design period = 40 years Current ADT = 600 Projection factor = 1.2 ADTT = 2.5% of ADT Traffic Calculations: Design ADT = 600 X 1.2 = 720 ADTT = 720 X 0.025 = 18 Truck traffic each way = $

For Design 2A: (1) Totals of fatigue use and erosion damage of 89% and 8%, respectively, show that the 6.O-in. thickness is adequate. (2) Separate calculations show that a 5.5-in. pavement would not be adequate because of excessive fatigue consumption. (3) The thickness design is controlled by the fatigue analysis-which is usually the case for light-truck-traffic facilities. The calculations for Design 2B, which is the same as Design 2A except the joints are doweled, show fatigue and erosion values of 89% and 21%, respectively. Comments: (1) The th]ckness requirement of 6.0 in. is the same as for Design 2A. (2) The fatigue-analysis values are exactly the same as in Design 2A. T(3) Because of the dowels, the erosion damage is reduced from 870 to 2%; however, this is immaterial since the fatigue analysis controls the design. For the Design 2 situation, it is shown that doweled joints are not required. This is borne out by pavementperformance experience on light-truck-traffic facilities such as residential streets and secondary roads and also by studies 128w ~h~~i”gtheeffects of the number of trucks on pavements with aggregate-interlock joints.

= 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, and the expected number of axle-load repetitions are shown in Fig, 8. Values Used to Calculate Thickness: Design 2A: aggregrate-interlock Joints, no subbase,* no concrete shoulder Clay subgrade, k = 100pci LSF = 1.0 Concrete MR = 650 psi

*Performance experience has show” that subbasm me not required whm truck traffic is very Iighc seethe PCA p.btication, S.bcmdesond .subbmes CO..,,(, POVWWIII,. :* Design 2B is sb,wm for illustrative purposes only. Doweled joints are not needed where truck traffic is very lighq we the PCA publication Join! Designfor Co.crele Highww and Srreel Pavemenn. T The type of load transfer at the joim40wels, or aggregate interlock4ces not affect the fatigue calculations sincethe critical axle-load position for stressand fatigue is where the axle loadsare placed at pave. ment edge and mid panel, away from the joims. See Appendix A.

f.,

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Calculation of Pavement Thickness 2A

Project &&~l-

7+9

6.0

Trial thickness Subbase-subgrade

h ~–

Modulus of rupture,

MR —-

Load safety factor, LSF

-/cm.

5PczG@z&.t/

tn.

Doweled joints:

yes _

no &

pci

Concrete shoulder:

yes _

no ~

psi /.

Lz?za+

Design period &

years

SU/6&3c

Fatigue analysis Axle load, kips

Multiplied by LSF

Erosion analysis

Expected repetitions

‘u

Allowable repetitions

Fatigue, percent

Allowable repetitions

Damage, percent

8. Equivalent

v//

stress

10. Erosio” factor

&?.

9. Stress ratio factor ~

Single Axles

11. Equivalent stress_~

Tandem Axles

Fig. 8. Design

12. Stress ratiOlactOr

13. Erosion factor U.

~—

535

2A.

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CHAPTER 4

Simplified Design Procedure (Axle-Load

Data Not Available)

The design steps described in Chapter 3 include separate calculations of fatigue consumption and erosion damage for each of several increments of single- and tandem-axle loads. This assumes that detailed axle-load data have been obtained from representative truck weigh stations, weigh-in-motion studies, or other sources. This chapter is for use when specific axle-load data are not available. Simple design tables have been generated based on composite axle-load distributions that represent different categories of road and street types. A fairly wide range of pavement facilities is covered by four categories shown in Table 9.* The designer does not directly use tbe axle-load data** because the designs have been presolved by the methods described in Chapter 3. For convenience in design use, tbe results are presented in Tables 11, 12, 13, and 14, which

Table 9.

de-Load

correspond to the four categories of traffic. Appropriate load safety factors of 1.0, 1.1, 1.2, and 1.2, respectively, have been incorporated into the desigo tables for axleIoad Categories 1, 2,3, and 4. Tbe tables show data for a design period of 20 years. (See the section “Design Period”, following.) In these tables, subgrade-subbase strength is characterized by the descriptive words Low, Medium, High, and Very High. Fig. 2 shows relationships between various subgrade-bearing values, In the event that test date are not available, Table 10 lists approximate k values for different soil types. If a subbase is to be used—see Chapter 2 *On page 30, guidelines for preparing designtables for axle-load distributions d~ffemnt fmm th.se givem here are discussed. ** Axle.load data for the four categories are given in Table 15.

Cat@goriea afti c ADTT.+

Axle-load category

Description

Residential streets Rural and secondary roads (low to medium’) Collector streets Rural and secondary roads (high,) Arterial streets and primary roads (low,)

,.r

ADT

Maximum axle kinds, kips

Per dav

3ingle axles

Tandem axles

up to 25

20C-800

t -3

7oe-5ooo

5-18

40-1000

Arterial streets and primary roads (medium.) Expressways and urban and rural interstate (low to medium.)

3000-12,CO0 2 lane 3000-50,000+ 4 lane or more

3-30

500-50004

Arterial streets, primary roads, expressways (high’) :~b~~ and rural Interstate (medium to ..=.. ,

3000-20,000 2 lane 3000-1 50,000+ 4 lane CMnmre

a-30

150&8000+

‘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,

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Tabla 10. Subarade Soil Types and App;oximate k Values

Fine-grained soils in which silt and clay-size pariicles predominate

Low I

Sands and sand-gravel mixtures with moderate amounts of silt and clay

subbasOS (see page 6)

7s120

Medium

13&170

High

180-220

Very high

25&400

sands and sand-gravel mixtures relatively free of plastic fines Cement-treated

k values range, pcl

SUppofl

Type of soil

discussion under “Comments on Simplified Proccdure,” page 30.) In the correct use of Table 9, the ADT and ADTT values are not used as the primary criteria for selecting the axle-load category—the data are shown only to illustrate typical values. Instead, it is correct to rely more on the word descriptions given or to select a category based on the expected values of maximum-axle loads. The ADTT design value should be obtained by a truck classification count for the facility or for another with a similar composition of tmffic. Other methods of estimating ADT and ADTT are discussed on pages 8 and 9, The allowable ADTT values (two dircctions)fisted in the tables include only two-axle, six-tire trucks, and single 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 allowabIe trucks of alI types will begrcaterthanthe tabulated ADTT

“Subgrade and Subbase Support’’—the estimated value is increased according to Table 1 or Table 2.

under

The design steps are as follows 1. Estimate ADTT* (average daily truck traffic, two directions, excluding two-axle, four-tire trucks) 2. Select axle-load Category 1, 2, 3, or 4. 3. Fkrd slab thickness requirement in the appropriate Table 11, 12, 13, or 14. (In the usc of these tables, see

(continued

on page

..... u

30)

*For facilities of four lanes or more, the ADTT is adjusted by the use of Fig. 3.

Table 11. Allowable ADTT,* Axle-Load Cate@ry 1 Pavements with Aggregate-lntertock Joints (Dowels not needed) No Concrete Slab thickness, in.

4.5 ~

z . (, c z

5.5 6 6.5

5 5.5

K z

6.5 y

Subgrade-subbase LrJW

Medium

support

0.1 3 40 330

0.5 8 76

0.8 15 1S0

0.1 3 36 300

3 45

Low 4 4.5

5 5.5

30 320

0,4 9 98 760

4 4.5 5 5.5 6

5,5

;,5

1 13

6 60

K z

7 7,5

110 620

403

Subgrade-subbase Medium

support High 0.9 25

0.2 8 130

330

430

520

0.1

Slab thick#r+s%

High 0,)

Note

Concrete Shoulder or Curb

ehoulder or Curb

4.5

16 160

5 5.5

0.3

0.2 6 73

0.1 5

1 27 2eo

75 730

610

0.2 0.6 13 130

4 57

0.6 13 150

460

Fatigue analysis controls the design.

Note: A fractional ADTT indicates that the pavement can carry unlimited passenger cars and two-axle, fourthe 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.

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,..

L-J

Table 12s. Allowable

ADTT,” Axle-Load

No Concrete S’houl&r Slab thickness, in.

or Curb

Subgrade-subbase Low

Category 2 — Pavements with Doweled Joints

Medium

Concrete ahouldec or Curb support

Hiah

Slab thickness, In.

Verv hioh

Low

5’ 1,

Medium

s“ppmt

High

Very high

5 5.5

3 42

9 120

42 450

6 6.5

96 710

360 26Q0

970

3400

Subgrade-subbase

5.5

4200

17 1100

6 6.5

3 29

14 120

41 320

7 7,5

210 1100

770 4000

1900

lSU

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 No Concrete Slab thic~~,

Subgrade-subbase Low

Cateaorv -.

Pavements with Aggregate-Interlock

shoulder or Curb

Medium

Concrete

support

High

Very high

Slab thickness, m.

Subgrade-subbase Low

5 5.5

6 6,5

e6 650. -

13W.

Medium 3 42 380 1000”

1100-.

1900”

19 I&l

64 620

support

High

Very high

9 120 Jm..

42 450

1400,’

97W . 21OIY.

220 1400..

610 2100,,

19CW

6 6.5 7

6.5

Joints

Shoulder or Curb

150

1000

1900,.

WE===’

.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.

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Table 13s. Allowable ADTT,* No Concrete

Axle-Load

Category 3-

Pavementa with Doweled Joints

Shoulder or Curb

Concrete Shoulder or Curb ~

Slab thickness, in. =

z. ,, a

7.5

Subgrade-subbase Low

9 9.5 10

Slab thic$~,

support

High

Very high 250

s 8.5

Medium

lea 700 2,7CQ

““”

130 640

350 i ,600

1,300 6,200

2,700 10,800

7,000

11,500,,

9,900

Subgrade-subbase Low

Medium

support

High

Very high

a=== 6.5

7 7,5

8 6.5

120

370 1,600

270

8s0

1,300 5,800

3,200 14,100

440 2,300

10.s00

6,&10

.ADTT excludes two-axle, four-tire truck% total number of trucks allowed will be greater—see text. .. Erosion analysis controls the design; otherwise fatigue analysis comrols.

‘u

v’ 26

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Table 13b. Allowable

ADTT,*

Axle-Load

Category

3—

Pavements with Aggregate

Interlock Jointa

ConcreteShoulderor Curb

Slab thic;~

Subgrade-subbase Low

Medium

support High

Very high

Slab thickness, tn.

Subgrade-subbase Low

Medium

support

High

Very high

I ~o..

7,5 8 8,5

,@y,

z . K z

1,000 1,500

1,300 2,000

2,000 2,900

10 10.5

1,3CC 1,800

2,1C!U 2,900

2,800 4,000

4,300 6,300

10.5

5,300

11 11.5

2,500 3,300

4,000 5,500

5,700 7,900

9,200

8,100

4,400

7,500 73.. 14W.

160,. 63W +

z 0 E ~

310++ 1,300

640. 1,503

1,300 2,000

2,000 2,900

1,300 1,8CU

2,100 2,900

2,800 4,000

4,300 6,3oo

11 11.5

2,500 3,300

4,000 5,500

5,700 7,900

9,200

4,400

7,500

9.5

2,300

4.700

10 10.5

3,500 5.300

7,700

S.om

S,loo

1 8 6.5

380”’

10.5

.—

25W . 830 1,300

680 960

9 9.5 ,0

~ . ,, cc ~

350900

9.5

8 8.5, . a

130640,,

70.. ,.

9 9.5 ,0 10,5 11 11,5 12

12W+

120,, 520.,

460,, 1,600,+

56” 300>+

7 1,5 67..

130,.

62’, 460’ +

270., 1,200.,

670.. 2,700

2,301Y+ 4,700

4,6oo 8,000

8,700

340., l,3cKl-

1,300,. 2,900

8 8,5

330”

1,9CW, 2,91Y3

2.800 4;000

4,300 6,300

9 9.5

1,400%, 2,30+1

2,900 4,700

2,500 3,300

4,000 5,500

5,700 7,9C+I

9,2oo

10 10.5

3,500 5,30U

7,700

4.400

7,500

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 analysis controls.

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Table 14s. Allowable ADTT,*

Axle-Load

Category 4 — Pavements with Doweled Joints

No ConcreteShoulderor Curb I Slab thickness, In.

I Subgrade-subbase Low

8 8.5 . E E .

support

Medium

High

120

340

580 2,300

9 9.5

140 570

10 10.5

2,000 6,700

8,200 24,100’.

tl 11.5

21,800 39,70W,

39,800”

+3= z

Concrete Shoulder or Curb

I Very high

Subgrade-subbase

Slab thickness, 0..

270 1,300

7 7,5

1,500 5,900

5,W0 14,70W.

8 8.5

18,701% 31 ,801Y.

25,80W. 45,801Y,

9 9.5

support w

Low

High

240

620

1,200

3,000 12,700

Very high 400 2,100

330 1,500

5,300

5,90+3 22,503

21,400 52,000’”

44,900 -

130

490

270 1,300

690 3,000

2,3oo 9,900

5,000 18,800

12,000 45,900

40,200

250

130 620

480 2,100

I I

Medium

9,800 41,100’,

45,20W.

—

8.5

z m

cc >

‘: I

120

120 530

340 1,400

10.5

480 1,600

1,900 6,503

5,1W 17,500

11 11.5

4,900 14,500

44,000

9 9.5

21,400 65,000” ‘

9 9.5

7.5 8 S.5

340

i 9,300 45,900,,

9 9.5

t,40+3 5,2’&3

53, 8W ‘

18,41XI 1

280

8,200

300 1,300 5,200

260 1,100

40,000

8 8.5 9 9.5

280 1,100

1,000 3,900

10 10.5

3,800 12,400

13,600 48,2C0

40,400

2,5CW 9,300

8,200 30,700

32,800 , ‘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,

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Table 14b. Allowable

ADTT,*

Axle-Load

Category 4 — Pavemente with Aggregate-interlock

No ConcreteShoulderor Cub -

ConcreteShoulderor Curb

I Subgrade-subbase

Slab thickness, In.

Low

Medium

supporl High

Very high

=$===== 8.5

9 9.5

Joints

120’” 530,.

120,,

340” 1,400,,

] 2,800

5,500

9,200

5,900

13,600

24,200

12,800

2,600

5,500

9,200

5,900

13,600

24,200

] 12,800

,,,,00

30W+

1,30W. 2,300

17,900

I I

8 8.5

25W ,

9 9.5

130.. 620”

260,.

1,000..

2,500..

5,700

1,1OQ.,

3,4cm

5,500

10,200 17,900

I,ow.

7,200 10,400

5,500

9,200

2,700

4,50Q 6,300

2,600

11.5

3,300 4,500

8 .0

3,600

6,100

8,800

14,900

5,900

13,6W

24,200

6,300

11,100

16,800

12,800

10.800

K ~

.ADTT excludes two-axle, four-tire trucks; ,. Fatigue

analysis

controls

!he

design;

total

otherwise

number

of trucks

allowed

erosion

analysis

controls.

w(II

be greater—see

48W , 2,101Y.

text.

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values by about double for many highways on up to about triple or more for streets and secondary roads. Tables 11 through 14 include designs for pavements with and without concrete shoulders or curbs. For parking lots, adjacent lanes provide edge support similar to that of a concrete shoulder or curb so the right-hand side of Tables 11 through 14 are used.

Sample Problems Two sample problems follow to illustrate plified design procedure.

use of the sim-

Design 3 Arterial street, twn lanes Design ADT = 6200 Total trucks per day = 1440 ADTT = 630 Clay subgrade 4-in. untreated subbase Subgrade-subbase support = low Concrete M R = 650 psi* Doweled joints, curb and gutter Since it is expected that axle-load magnitudes will be about the average carried by arterial streets, not unusually 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 aggregate-interlock joints.) For a subgrade-subbase support conservatively classed as low, Table 13a, under the concrete shoulder or curb portion, 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 design ADTT of 630. Design 4 Residential street, two lanes ADT = 410 Total trucks per day = 21 ADTT = 8 Clay subgrade (no subbase), subgrade suppnrt = low Concrete MR = 600 psi* Aggregate-interlock joints (no dowels) Integral curb in this problem, Table 11 representing axle-load Category 1 is selected for design use. In the table under “Concrete Shoulder or Curb,” the following allowable ADTT are indicated:

Comments on Simplified Procedure Modulus of Rupture Cnncrete used for paving should be of high quality** and have adequate durability, scale resistance, and flexural strength (modulus of rupture). In reference to Tables 11 through 14, the upper pnrtions of the tables represent concretes made with normal aggregates that usually produce good quality concretes with flexural strengths in the area of 600 to 650 psi. Thus, the upper portions of these tables are intended for general design use in this simplified design procedure. The lower portions of the tables, showing a concrete modulus of rupture of 550 psi, are intended for design use only fm special cases. In some areas nf the country, the aggregates are such that concretes of good quality and durability produce strengths of only about 550 psi.

Design Period The tables list the allowable ADTl% for a 20-year design period. Fnr other design periods, multiply the estimated ADTT by the appropriate ratio to obtain an adjusted value fnr use in the tables. For example, if a 30-year design period is desired instead of 20 years, the estimated ADTT value is multiplied by 30/20. In general, the effect of the design period on slab thickness will be greater for pavements carrying larger volumes of tfuck traffic and where aggregate-interlock joints are used. Aggregate-Interlock

or Doweled

Joints

Tables 12 through 14 are divided into two parts, a and b, to show data for doweled and aggregate-interlockj oints,t respectively. In Table 11, thickness requirements are the same for pavements with doweled and aggregate-interlock jointy doweled joints are not needed for the low truck traffic volumes tabulated for Category 1. Whenever dowels are not used, joint spacings should be short—see discussion on page 3.

User-Developed

u’

Design Tables

The purpose of this section is to describe hnw the simplified design tables were develnped so that the design engineer who wishes to can develop a separate set of design tables based on an axle-load category different from those given in this chapter. Some appropriate situations include

*See disc.wion under ‘Comments on Simplified Pmcedum—M.dof Rupture,- above **See pofila”,j cenm.t Awociat i.. p.b)icat ion Design and Control

“1”S

Therefore, the required

a 5.5-in. -slab thickness is selected to meet design ADTT value of 8.

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 joints and for aggregate-interlock joints are the sane (we topic ..Jointed Pavenmnts- in Appendix A). If emsi.% analysis controls, c.ncmt. modulus of rupture will have no effect m the .dlmvable ADTT.

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(1) preparation of standard sections from which a pavement thickness is selected based on amount of traffic and other design conditions, (2) unusual axle-load distributions that may be carried on a special haul road or other special pavement facility, and (3) an increase in legal axle loads that would cause axle-load distribution to change. Axle-1oad distributions for Categories 1 through 4 are shown in Table 15. Each of these is a composite of data averaged from several state Ioadometer (W-4) tables representing pavement facilities in the appropriate category. Also, at the high axle-load range, loads heavier than those listed on state department of transportation Wq tables were estimated based on extrapolation. These two steps were desired for obtaining a more representative general distribution and smoothing irregularities that occur in individual W-4 tables. The steps are considered appropriate for the design use of these particular categories described earlier in thk chapter. As described in Chapter 2, the data is adjusted to exclude two-axle, four-tire trucks, and then the data are partitioned into 2000- and 4000-lb axle-load. increments. To prepare design tables, design problems are solved with the given axle-load distribution by computer with the desired load safety factor at different thicknesses and subbase-subgrade k values, Allowable ADTTvalues to be listed in design tables are easily calculated when a constant, arbkrary ADTT is in. put in the design problems as follows: assume input ADTT is 1000 and that 45.6% fatigue consumption is calculated in a particular design problem, then Allowable

ADTT

= â&#x20AC;&#x201D;

100 X (input ADTT) % fatigue or erosion damage 100(1000) 45.6

2193

Table 15. Axle-Load Distributions Used for Preparing Design Tablss 11 Through Axle load, kips

Axles per 1000 trucks, Category

3ingle â&#x20AC;&#x201D;~ 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34

:Ies

axles 31,90 85.59 139,30 75.02 57.10 39.18 68.48 69.59 4.19

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60

732.26 483,10 204,96 124.00 56.11 38.02 15.81 4.23 0.96

:ategory

233.6o 142.70 116,76 47,76 23,88 16.61 6.63 2,60 1.60 0.07

47.01 91,15 59.25 45,00 30.74 44.43 54.76 38.79 7.76 1.16

Category 3

182.02 47.73 31.82 25.15 16.33 7.85 5,21 1.78 0.85 0,45

Category 4

57.07 68.27 41,82 9.69 4,16 3.52 1.78 0.63 0.54 0.19

99.34 65.94 72.54 121.22 103,63 56.25 21.31 8.01 2.91 1.18

71,16 95.78 109.54 78,18 20,31 3.52 3.03 1.79 1,07 0.57

.Excludng all two-axle, Iour-tire trucks.

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‘u

APPENDIX A

Development of Design Procedure The thickness design procedure presented here was prepared to recognize current practices in concrete pavement construction ‘and performance experience with concrete pavements that previous design procedures have not addressed. These include: ● Pavements with different types of load transfer at transverse joints or cracks ● Lean concrete subbases under concrete pavements ● Concrete shoulders ● Modes of distress, primarily due to erosion of pavement foundations, that are unrelated to the traditional criteria used in previous design procedures A new aspect of the procedure is the erosion criterion that is amlied in addition to the stress-fatieue criterion. The ero~~n criterion recognizes that pave~ents can fail from excessive pumping, e%sion of foundation, and joint faulting. The stress criterion recognizes that pavements can crack in fatigue from excessive load repetitions. This appendix explains the basis for these criteria and the development of the design procedure. References 30 and 57 give a more detailed account of the topic.

the critical placements shown in Fig. A I were established with the following conclusions: 1 The most critical Davement stresses occur when the truck wheels are placed at or near the pavement edge and midway between the joints, Fig. A l(a). Since the joints are at some distance from this location, transverse joint spacing and type of load transfer have very little effect on the magnitude of stress. In the design procedure, therefore, the analysis based on fk”ral stresses and fatigue yield the same values fOr different joint spacings and different types of load transfer mechanisms (dowels or aggregate interlock) at transverse joints. When a concrete shoulder is tied

The design procedure is based on a comprehensive anaiysis of concrete stresses and deflections at pavement joints, corners, and edges by a finite-element computer of slabs with finite program. IN ,t ~I]ow~ ~o”~iderations dimensions, variable axle-load placement, and the modeling of load transfer at transverse joints 6r cracks and load transfer at the joint between pavement and concrete shoulder. For doweled joints, dowel properties such as diameter and modulus of elastic it y are used direct] y. For aggregate, interlock, keyway joints, and cracks in comim uously reinforced pavements, a spring stiffness value is used to represent the load-deflection characteristics of such joints based on field and laboratory tests.

analysis

of different

U“

L–––––––L–––––_J (.) Axle. I.od p.sil ion for criticolf lexw.1 stresses

Freeedgem shoulder

joint

m i

Troffic lone

> ,

Concrete (,F medl

shoulder

L–––____J__——–––– (b)

Jointed Pavements After

Analysis of Concrete Pavements

Axle load pmitio. for critic.! deflections

d axle-load

positions

on the slab,

Fig.

Al. Critical axle-load positions.

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on to the mainline pavement, the magnitude critical stresses is considerably reduced.

of the

2. The most critical pavement deflections occur at the slab corner when an axle load is placed at the joint with the wheels at or near the corner, Fig. A I(b). * In this situation, transverse joint spacing has no effect on the magnitude of corner deflections but the type of load transfer mechanism has a substantial effect. This means that design results based on the erosion criteria (deflections) may be substantially affected by the type of load transfer selected, especially when large numbers of trucks are being designed for. A concrete shoulder reduces corner deflections 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 direction, the pavement develops cracks at close intervals. These crack spacings on a given project are variable, running generally from 3 to 10 ft with averages of 4 to 5 ft. In the finite-element computer analysis, a high degree of load transfer was assigned at the cracks of CRCP and the crack spacing was varied. The critical load positions established were the same as those for jointed pavements. For the longer crack spacings, edge stresses for loads placed midway between cracks are of about the same magnitude as those for jointed pavements. For the average and shorter crack spacings, the edge stresses are less than those for jointed pavements, because there is not enough length of untracked pavement to develop as much bending moment. For the longer crack spacings, corner deflections are somewhat less than those for jointed pavements with doweled transverse joints. For average to long crack spacings, corner deflections are about the same as those for jointed, doweled pavements. For short crack spacings of 3 or 4 ft, corner deflections are somewhat greater than those for jointed, doweled pavements, especially for tandem-axle loads. Considering natural variations in crack spacing that occur in one stretch of pavement, the following comparison of continuously reinforced pavements with jointed, dnweled pavements is made. Edge stresses will sometimes be the same and sometimes will sometimes

less, while

corner

Truck Load Placement Truck wheel loads placed at the outside pavement edge create more severe conditions than any other load position. As the truck placement moves inward a few inches from the edge, the effects decrease substantially.(”) Only a small fraction of all the trucks run with their nutside wheels placed at the edge. Most of the trucks traveling the pavement are driven with their outside wheel placed abnut 2 ft from the edge, Taragin’s(40] studies reported in 1958, showed very little truck encroachment at pavement edge for 12-ft lanes for pavements with unpaved shoulders. More recent studies by Emery(”) shnwed more trucks at edge, Other recent studies”’] showed fewer trucks at edge than Emery. Fnr this design prncedure, the most severe conditinn, 6c%of trucks at edge, * is assumed so as to be on the safe side and to take account of recent changes in United States law permitting wider trucks. At increasing distances inward from the pavement edge, the frequency of lnad applications increases while the magnitudes of stress and deflecting decrease. Data on truck placement distribution and distributing of stress and deflection due to loads placed at and near the pavement edge are difficult to use directly in a design procedure. As a result, the distributions were analyzed and more easily applied techniques were prepared for design purposes. For stress-fatigue analysis, fatigue was computed incrementally at fractions of inches inward fmm the slab edge for different truck-placement distributions; this gave the equivalent edge-stress factors shown in Fig. A2. (This factor, when multiplied by edge-load stress, gives the same degree of fatigue consumption that would result from a given truck placement distribution,) The mnst severe condition, 6T0 truck encroachment, has been incorporated in the design tables.

deflections

be less, the same, andgreater

at different

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 to continuously reinforced pavements as those used with jointed, doweled pavements. This recommendation is consistent with pavement performance experience. Most design agencies suggest that the thickness of continuously reinforced pavements should be about the same as the thickness nfdoweled-jointed pavements. areas

P *The greatest deflections at one

for tridwm

occur

when

two

axles

are placed

side of the ioint and me axle at the other side.

0:ME2!&ia cc

0123

4567a

PERCENT

TRuCKS

EDGE

Fig. A2. Equivalent edge stress factor depends percent of trucks at edge.

*As used hm, the term ‘<percenttrucks at edge,, is defined as the percent of totat tmcks that a= travetiw with the outside of the con~ct area of the outside tire at or beyond the pavement edge.

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For erosion analysis, which involves deflection at the slab corner, the most severe case (6% of trucks at edge) is again assumed. Where there is no concrete shoulder, corner loadings (6% of trucks) are critical; and where there is a concrete shoulder, the greater number of loadings inward from the pavement corner (94’% of trucks) are critical. These factors are incorporated into the design charts as follows: Percent erosion damage where

= 100 Xn (C/ Ni)

n, = expected number of axle-load repetitions for axle-group i Ni = allowable number of repetitions for axle-group i C = 0.06 for pavements without shoulder, and 0.94 for pavements with shoulder

To save a design calculation step, the effects of (C/NiI are incorporated in Figs. 6a and 6b of Chapter 3 and Tables 11 through 14 of Chapter 4.

Variation in Concrete Strength Recognition of the variations in concrete strength is considered a realistic addition to the design procedure. Expected ranges of variations in the concrete’s modulus of rupture have far greater effect than the usual variations in the properties of other materials, such as subgrade and subbase strength, and layer thicknesses. Variation in concrete strength is introduced by reducing the modulus of rupture by one coefficient of variation. For design purposes, a coefficient of variation of 15% is assumed and is incorporated into the design charts and tables. The user does not directly apply this effect, fie value of 15% represents fair-to-good quality control, and, combined with other effects discussed elsewhere in this appendix, was selected as being realistic and giving reasonable design results.

effect is influenced greatly by creep. Curling refers to slab behavior due to variations of temperature. During the day, when the tnp surface is warmer thanthe bottom, tensile-restraint stresses develop at the slab bottom. During the night, the temperature distribution isreversed andtensile restraint stresses develop at the slab surhce. Temperature distribution is usually nonlinear and constantly changing, Alsn, maximum daytime and nighttime temperature differentials exist for short durations, Usually the combined effect of curling and warping stresses are subtractive from load stresses because the moisture content and temperature at the bottom of the slab exceed that at the top more than the reverse. The complex situation ofdifferential conditions ata slab’s top and bottom plus the uncertainty of the zerostress position make it difficult tocompute or measure the restraint stresses with any degree of confidence or verification. At present, the information available on actual magnitudes of restraint stresses does not warrant incorporation of the items in this design procedure. As for the lnss of support, this is considered indirectly in tbe erodibility criterion, which is derived from actual field performance and therefore incorporates normal loss of support conditions, Calculated stress increase due to loss of support varies from about 5%to 15%Thisth eoreticalst ressincreaseis counteracted in the real case because a portion of the load is dissipated in bringing the dab edges back in contact with the support. Thus, the incremental load stress due to a warping-type loss of support is not incorporated in this design procedure,

Fatigue The flexural fatigue criterion used in the procedure presented here is shown in Fig, A3. It issimilar to that used in the previous PCAmethndi4’] based conservativelyon

Concrete Strength Gain With Age 0,9 The 28day flexural strength (modulus of rupture) is used as the design strength. This design procedure, however, incorporates the effect of concrete strength gain after 28 days. This modification is based on an analysis that incremented strength gain and load repetitions month by month for 20-year and 40-year design periods. The effect is included in the design charts and tables so the user simply inputs the 28-day value as the design strength.

0.8 Curve

by Hil,do,f And Kesler Constant Pmb,tdl;ty 0.05 Q $

Pc&

curve

: : m

0.6

Warping and Curling of Concrete 0.5

In addition to traffic Ioadi”g, concrete slabs am also ~~b. jetted to warping and curling. Warping is the upward concave deformation of the slab due to variations in moisture content with slab depth. The effect of warping is twofold: It results in loss of support along the slab edges and also in compressive restraint stresses in the slab bottom, Since warping isalong-term phenomenon, itsres”ltam

Extended

0,4,.2

,.3

LOAD

>._

, ~,

REPETITIONS

u--” Fig. A3. Fatigue relationships.

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104

C.,,,

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studies of fatigue research[4s-”9) except that it is applied to edge-load stresses that are of higher magnitude. A modification in the high-load-repetition range has been made to eliminate the discontinuity in the previous curve that sometimes causes unrealistic effects, The allowable number of load repetitions for a given axle load is determined based on the stress ratio (flexural stress divided by the 28-day modulus of rupture). The fatigue curve is incorporated into the design charts for use by the designer. Use of the fatigue criterion is made on the Miner hypothes]s 140that fatigue ~e~istance not consumed by rePetitions of one load is available for repetitions of other loads. In a design problem, the total fatigue consumed should not exceed 100%. Combined with the effect of reducing the design modulus of rupture by one coefficient of variation, the fatigue criterion is considered to be conservative for thickness design purposes.

Erosion

Previous mechanistic design procedures for concrete pavements are based on the principle of limiting the ffexural stresses in a slab to safe values. This is done to avoid flexural fatigue cracks due to load repetitions. It has been apparent that there is an important mode of distress in addition to fatigue cracking that needs to be addressed in the design process. T& is the erosion of material beneath and beside the slab. Many repetitions of heavy axle loads at slab corners and edges cause pumping; erosion of subgrade, subbase, and shoulder materialy voids under and adjacent to the slab; and faulting of pavement joints, especially in pavements with undoweled joints. These particular pavement distresses are considered to be more closely related to pavement deflections than to flexural stresses. Correlations of deflections computed from the finiteelement analysis(a] with AASHO Road Test{ 24]performance data were not completely satisfactory for design purposes. (The principal mode of failure of concrete pavements at the AASHO Road Test was pumping or erosion of the granular subbase from under the slabs.) It was found that to be able to predict the AASHO Road Test performance, different values of deflection criteria would have to be applied to different slab thicknesses, and to a small extent, different foundation moduli (k values), More useful correlation was obtained by multiplying the computed corner deflection values (w) by computed pressure values (.P) at the slab-foundation interface, Power, or rate of work, with which an axle load deflects the slab is the parameter used for the erosion criterion—for a unit area, the product of pressure and deflection divided by a measure of the length of the deflection basin (l— radius of relative stiffness, in inches). The concept is that a thin pavement with its shorter deflection basin receives a faster load punch than a thicker slab. That is, at equal pw’s and equal truck speed, the thinner slab is subjected to a faster rate of work or power (inch-pound per second).

A successful correlation with road test performance was obtained with this parameter, The development of the erosion criterion was also generally related to studies on joint faulting. [2* 29) These studies included pavements in Wisconsin, Minnesota, North Dakota, Georgia, and California, and included a range of variables not found at the AASHO Road Test, such as a greater number of trucks, undoweled pavements, a wide range of years of pavement service, and stabilized subbases. Brokaw’s studies (2o of ““doweled pavements suggest that climate or drainage is a significant factor in pavement performance. So far, this aspect of design has not been included in the design procedure. but it deserves further study. Investigations of the effects of climate on design and performance of concrete pavements have also been reported by Darter. [”] The erosion criterion is suggested for use as a guideline. It can be modified according to local experience since cfimate, drainage, local factors, and design innovations may have an influence. Accordingly, the 100% erosiondamage criterion, an index number correlated with general performance experience, can be increased or decreased based on specific performance data gathered in the future for more favorable or more adverse conditions.

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b’

APPENDIX B

Design of Concrete Pavements with Lean Concrete Lower Course Following is the thickness design procedure for composite concrete pavements incorporating a lower layer of lean concrete, either as a suhhase constructed separately or as a lower layer in monolithic construction. Design considerations and construction practices for such pavements are discussed in References 50 through 52. Lean concrete is stronger than conventional subbase materials and is considered to be nonerodable, Recognition of its superior structural properties can be taken by a reduction in thickness design requirements. Analysis of composite concrete pavements is a special case where the conventional two-layer theory (single slab on a foundation) is not strictly applicable. The design procedure indicates a thickness for a twolayer concrete pavement equivalent to a given thickness of normal concrete. The latter is determined by the procedures described in Chapters 3 and 4. The equivalence is based on providing thickness for a two-layer concrete pavement that will have the same margin of safety* for fatigue and erosion as a single-layer normal concrete pavement. In the design charts, Fig. B] and Fig, B2, the required layer thicknesses depend on the flexural strengths of the two concrete materials as determined by ASTM C78. Since the quality of lean concrete is often specified on the basis of compressive strength, Fig. B3 can be used to convert this to an estimated flexural strength (modulus of rupture) for usc in preliminary design calculations.

Lean Concrete Subbase The largest paving use of lean concrete has been as a subbase under a conventional concrete pavement, This is nonmonolithic construction where the surface course of normal concrete is placed on a hardened lean concrete subbase. Usually, the lean concrete subbase is built at least 2 ft wider than the pavement on each side to support the tracks of the sfipform paver. This extra width is structurally beneficial for wheel loads applied at pavement edge. 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 requirements set to be equivalent to a given thickness of normal concrete without a lean concrete subbase. A sample problem is given to illustrate the design procedure. From laboratory tests, concrete mix designs have been selected that give moduli of rupture of 650 and 200 psi~*respectively, for the surface concrete and the lean concrete subbase. Assume that a I&In.-thickness requirement 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, designs 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

W’

Pavement

In some areas, a relatively thin concrete surface course is constructed monolithically with a lean concrete lower layer. Local or recycled aggregates can be used for the lean concrete, resulting in cost savings and conservation of bighqualit y aggregates.

●ll. criteria are that (1) stressratios in either of the two concrete layers not exceed that of the reference pavement and (2)erosion values

at the s.bbase-s.bgrade interface not exceed those of the reference pavement. Rational. for the criteria is give. in Reference 50 plus two ad&ltimal considerations: (1) erosion criteria is included in addition to the fatigue approach given in the referencq and (2) for nonmonolithic con-

struction, some structural benefit C141is added because the subbase is constructed wider than the pavement. . . F1.xural wemgth of !..” comxete m be used as a subbase is usually selected to be between i50 to 250 psi (compressive Wength, 750 to 1200 psih these relatively low strengths are used to minimize reflective cracking 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 “.1 have to b. restricted m the lower m “ge.

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,,. u

Modulus

of Leon

Rupture

350

Concrete,

450

I50

psi

250

350

450

250. <

14 /

450 I 50

350

14 <

250 .. / ‘ ,0

_ .< “%

/ ‘

/ 12

I50

; / ‘ 6). / ‘

/ / /

)

0 I 0(.++

–; 4

r 9 are thicknesses surface course

of concrete

Fig. B1. Design chart for composite concrete pavement (lean concrete subbase),

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Modulus

of Rupture

of Lean Concrete, psi 450

150

250

350

450

14 350 /,

13 -

“l-

t+htl+’tft

‘0+--wH--tf7b%4

3“ Surface

4“ Surface

Fig. B2, Design chart for composite concrete pavement (monolithic

with lean concrde

Iowef layer).

Unlike the lean concrete subbases discussed in the previous section, the lower layer of lean concrete is placed at the same width as the surface course, and joints are sawed deep enough to induce fulldepth cracking through both layers at the joint locations. Fig. B2 is the design chart for monolithic pavements. To illustrate its use, assume that the design strengths of the two concretes are 650 and 350 psi, and that the design procedures of Chapter 3 or 4 indicate a thickness requirement of 10 in. for fulldepth normal concrete. As shown by the dashed example fine in Fig. B2, monolithic designs equivalent to the IO-in. pavement are (1)4in. concrete surface on 8.3-in. lean concrete, or (2) 3-in. surface on 9.3-in. lean concrete.

COMPRESSIVE Fig.

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STRENGTH,

PSI

B3. Modulus of rupture versus compressive strength (from Reference 50).

Book Contents

APPENDIX C

Analysis of Tridem Axle Loads loads* can be included along with single- and tandem-axle loads in the design analysis by use of data given in this appendix. The same design steps and format outlined in Chapter 3 are followed except that Tables C I through C3 are used. From these tables for tridems, equivalent stress and erosion factors are entered in an extra design worksheet. Then Fig. 5 and Fig. ti or 6b are used to determine allowable numbers of load repetitions. Fatigue and erosion damage totals for tridems are added to those for singleand tandem-axle loads, An extension of the sample problem, Design 1A given in Chapter 3, is used here to illustrate the procedure for tridem loads. Assume that, in addition to the single- and tandem-axle loads, a section of the highway is to carry a fleet of special coal-hauling trucks equipped with tridems at the rate of about 100 per working day for an estimated period of 10 year> so: 100 trucks X 250 days X 10 years = 250,000 total trucks Tridem

The trucks in one direction are normally all loaded to their capacity of 54,000-lb tridem load plus 7000-lb steering-axle (single-axle) load. (When it is examined, the steering axles are not heavy enough to affect the design results.) Fig. C 1 represents a portion of tbe extra design worksheet needed to evaluate tbe effects of these tridems. Since

Design 1A (9:5-in. pavement, combined k of 130 pci) is a pavement with doweled joints and no concrete shoulder, Tables Cl and C2 are used to determine the equivalent stress and erosion factors, Items 1 I and 13 on the worksheet. For this example, Fig. 5 is used to determine allowable load repetitions for the fatigue analvsis and l%. 6a is used for tbe”erosion analysis. The tridem loads of 54,000 lb are multiplied by t he load safety factor for Design 1A of 1.2, giving a design axle load of 64,800 lb. Before using the charts for allowable load

repetitions,

three

(64,800/3

the tridem = 21,600

load

(3 axles)

lb) so that

is divided

the load

scale for

axles can be used, ** As show” in Fig, Cl, the tridem causes only 9.3% erosion damage and 0% fatigue damage. These results, added to the effects of the single and tandem axles shown in Fig. 4 are not sufficient to require a design thickness increase. single

*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 incorporated into their rqmtive equivalent stress and emsicm factor tables, which i“ the sequeme of the design steps is taken into accmmt before the charm for allowable-load repetitions arc entered. This divisicm by three for tridetm is made just to avoid the complexity of adding a third scale on the charts for allowable-load qxtitio.s,

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Calculation

of Pavement Thickness

7f Trial

thickness

S.bbase-sub.arade Modulus

.1 nmt”re,

Load safely

factor,

5?5-

(n:

Doweled

L.?o

.,i

concrete

MR ~ LSF

psi 1

C9sig”

M“!tiPlied

Z??,(L

joints sh.w ldw Period

yes’+.0 yes

—

no X

L-J

yea,,

Fatigue Axle load, I@

analysis

Erosion

analysis

ExPect& repetition,

~gYF

Allowable repetition,

Fatigue, percent

Allowable repetitions

Damage, percent

1516

111213/4

[

171

I I

Total

74 be

I Total

ZzdJ&

4224

SAw’7

7.3

6++

Fig. Cl. Analysis of tridems. ,.-

u’ Tabla Cl. Equivalent Stress-Tridems (Without Concrete Shouldar/With Slab

k of

thickness,

Concrete Shoulder)

subgrsde.subbase,

pcl

100

150

200

300

500

700

4 4,5

51W431 439/365

456/392 380/328

4371377 359/31 3

428/369 349/305

419/362 339/297

41 4/360 331/392

41 2/359 32S/291

5 5.5

367/317 347[279

328/281 290/246

305/266 266/231

293/258 253/223

282/250 240/214

272[244 230/206

269/242 226/206

8 6.5

315[249 289/225

261/218 238/1 96

237/204 214/163

223/1 96 201/175

209/187 186/1 66

198/1 80 173/159

193/1 78 168/1 56

7 7.5

267/304 247/1 87

219/178 203/1 62

196/1 65 181/151

183/1 58 166/1 43

167/1 49 153/135

154/142 139/1 27

148/1 38 132(124

6 6.5

230/172 215/159

189/1 49 177[1 36

168/1 36 1561126

156/131 145/121

141/123 131/113

126/116 116/106

120/112 109/102

9 9.5

2W147 1871137

166/ 128 157/120

148/119 140/111

136/112 129/1 05

122/105 115/98

108/98 101/91

101/94 93/87

in.

1741127

10.5

183/119

148/112 140/105

133/104 125/97

122/98 115/92

106/91 103/86

95/64 89/79

87/61 82/78

11 11.5

153/111 142/104

133/89 125/93

119/92 113/86

110/87 104/82

98/81 93{76

S5174 80/70

78177 74/67

12 12.5

133/97 123/91

119/83 113/33

106/82 103/78

100[78 95/74

89/72 85/66

77/66 73[63

70/63 67/847

13 13.5

114/85 105/80

107/79 101/75

98/74 93/70

91/70 87/67

81/65 78[62

70/80 67[57

64/57 61/54

97175

98/71

89/67

83/63

75/59

65/54

59/51

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,..

L/”

Table CZ. Eroalon Factors-Tridema-Doweled (Without Concrete Shoulder/With p

Slab thickness, ,.,

Joints Concrete !Woulder)

k of subgrade-subbase, 50

100

200

300

pci 500

700

4 4,5

3.8913.33 3.7813.24

3.82/3.20 3.69/3,10

3.7513.13 3.62./2.99

3.70/3.10 3.57/2.95

3,61,13.05 3.50,(2.91

3.53/3.00 3.4412.87

5 5.5

3,68/3.16 3.59/3.09

3.56/3,01 3.49/2.94

3.50/2.89 3.40/2.80

3.4612.83 3,36/2.74

3.4012.79 3.3012.67

3.3412.75 3.2512.84

6 6.5

3.51/3.03 3,44/2,97

3,40/2.87 3.33/2.82

3.3112.73 3.23/2.67

3.28/2.66 3.18/2.59

3.2112.58 3.12(2,50

3.16/2.54 3.08/2.45

7 7.5

3,37[2,92 3.31/2,87

3.26/2.76 3.20/2.72

3,18/2.61 3,09/2.56

3.10/2.53 3.03/2.47

3.04!2.43 2.97/2.37

3.00/2.37 2.93/2.31

6 8,5

3.26/2,83 3.20/2.79

3.14/2.67 3.09/2.63

3,03/2.51 2.9712.47

2.97/2.42 2.91/2,38

2.80/2.32 2.84,(2.27

2.86/2,25 2.79/2,20

9 9.5

3.15/2.75 3.11/2.71

3.04/2.59 2.99/2.55

2.92/2.43 2.67/2,39

2.66/2,34 2.81/2.30

2.7612,23 2.73/2.18

2.73t2.15 2,68/2. 11

10 10.5

3.08/2.67 3.02/2.64

2.94/2.51 2.90/2.48

2.83/2.35 2,78/2.32

2.76/2,26 2.7.2/2.23

2.68,/2.15 2.64/2.1 1

2,63/2,07 2.58/2.04

11 11.5

2.98/2.60 2.94/2.57

2.86/2.45 2.82/2.42

2.74/2.29 2.70/2.26

2.68/2,20 2.64/2.16

2,59/2.08 2.55,,2.05

2.54/2.00 2.50/1.97

12 12.5

2.91/2.54 2.6712.53

2.79/2.39 2.75/2,36

2.67/2.23 2.63/2.20

2.60/2.13 2.56/2.11

2.51/2.02 2.48,{1 .99

2.48/1.94 2.42/1.91

13 13,5

2,8412.48 2,61/2,46

2.72/2.33 2,68/2.30

2.6012.17 2.56/2.14

2.53/2.06 2.49/2.05

2.44,{1.96 2,41,(1 .93

2.39/1.88 2.35/1.86

2.78/2.43

2.6512.28

2.53/2.12

2.46/2.03

2.38,(1 .91

2.32/1 .83

P Table C3. Erosion Fectorsâ&#x20AC;&#x201D;Tridems-Aggregate-interlock (Without Concrete Shoulder/With Concrete Slab thic;.,

k of subgrade-subbase,

4 4.5

Joints :~oulder)

pci

100

200

300

5130

700

4.06/3.50 3.9513.40

3.97[3.36 3.8513.26

3.68/3.30 3,78/3.16

3.62/3.25 3.70/3.13

3.7413.21 3.63/3.08

3.6713.16 3.58/3.04

5 5.5

3,85[3,32 3,76/3,26

3.75/3.19 3,66/3.11

3.66/3.06 3.56/3.00

3.60/3.03 3.51[2.94

3.52/2.97 3.4312.67

3.46/2.93 3.37[2 .83

6 6.5

3,68/3,20 3.61/3.14

3.58/3.05 3.50/2.99

3.4LV2.92 3.40/2.86

3,42/2.66 3.34/2.79

3.35,/2.79 3.27,/2.72

3.29/2.74 3.21/2.67

7 7.5

3.54/3.09 3.48/3.05

3.43/2.94 3.3712.89

3.33/2.80 3.2612.75

3.27/2.73 3.20/2.67

3.20/2,65 3.13/2.59

3,14/2.60 3.06/2.54

8 8.5

3.42/3.01 3.3712.97

3.31/2,84 3.25/2.80

3,20/2.70 3.15/2.65

3.14/2.62 3.09/2.58

3.07/2.54 3.01/2,49

3.01/2.46 2.96/2.43

9 9.5

3.32/2.94 3.2712.91

3.20/2.77 3.15/2.73

3.09/2.61 3.0412.56

3.03/2.53 2.98/2.49

2,95/2,44 2.90/2.40

2.90/2.38 2.85/2.34

10.5

3.22/2.88 3.f 8/2.85

3.11/2,70 3.06/2.67

3.00/2.54 2.95/2.51

2.93/2.46 2.89/2.42

2.85/2.36 2.8112.32

2.60/2,29 2.76[2 .26

11 11.5

3.14/2.83 3.10/2.80

3.02/2.85 2,98/2.62

2.91/2.48 2.8712.45

2.8412.39 2.80/2.36

2.7712.29 2.72/2.26

2.71/2.22 2.67/2.19

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Book Contents

APPENDIX D

Estimating Traffic Volume by Capacity At the time of preparing this bulletin, information on highway capacity is under extensive revision and computational methods and results may be substantially changed. New publications of AASHTO and theFHWA “Highway Capacity Manual,” expected to be published in 1984 and 1985, should be used when available and they will replace the methods and references presented in this appendix.) In Chapter 2, the traffic volume (ADTI is estimated by a method based cm the projected rates of traffic growth. When the projected traffic volume is relatively high for a specifk project, this method should be checked by the capacity method described here. The practical capacity of a pavement facility is defined as the maximum number of vehicles per lane per hour that can pass a given point under prevailing road and traffic conditions without unreasonable delay or restricted freedom to maneuver. Prevailing conditions include composition of traffic, vehicle speeds, weather, alignment, proffle, number and width of lanes, and area. The termproctical capacity is commonly used in reference to existing highways, and the term design capaciry is used. for design purposes. Where traffic flow is uninterrupted-or nearly so—practical capacity and design capacity are numerically equel and have essentially the same meaning. In accordance with AAS HTO usage1s3 ’41 the term design capacity is used in this text. Design capacities for various kinds of multilane highways are summarized in Table DI. (Note:

AD T Capacity of Multilane Highways For thickness design it is necessary to convert the pasaenger cars per hour in Table D1 to average daily traffic in both directions, ADT, For multilane highways with uninterrupted flow tbe following formula is used: ADT =

100P 100+ Tpd-

1) x

Table D1. Design Capacities for Multilane Highways Design capacity: passenger cars pe;;r2ftJne

Type of highway

rreew.ys vm. w access comm ‘Suburt )an freeways with full access control ,.. . . ‘Rural freeways with Wll or p ~ control Rural major highway! cross traffic and road.,.. Rural major highways with c cross traffic and roadside Inwrmrerwe

,AIso includes panels, pickups, and other four-tire oxnrnerci.1 vehicles that function a. passenger cars in terms of traffic capacity. Values are taken 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 a percentage of ADT = 15% for rural freeways in this text = 12% for urban freeways in thk text** D = traffic, percent, in direction of heaviest travel during peak hours—about 5070 to 75% = 67% for rural freeways in this text = 6090 for urban freeways in this text

5000N KD

where P

= passenger cars* per lane per hour (from Table D 1) N = number of lanes—total both directions T,, = trucks, percent, during peak hours = 2/3 ADT_f in this booklet

‘See f..tn.te at bottom of Table D!. **s,, Reference 54, pa.~e$96 m 98, and Reference 56.

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Detailed discussions of this formula will be found in References 53, 54, and 55. As presented here, the symbol for one term, T, of the formula, T,~, differs from the symbol for this term in the references. In this text: T = trucks—includes only single units with more than four tires and all combinations. (Does not include panels, pickups, and other single units with only four tires.) ADTT = average daily truck traffic in both directions—may be expressed as a percentage of ADT or as an actual value. Capacity of Two-Lane Highways Important factors in the design capacit y of two-lane highways are (1) the percent of total project length where sight distance is less than 1500 ft, and (2) lane widths of less than 12 ft.* The design capacity in vehicles per hour (vph) for unintermpted flow on two-lane highways is shown in Table D2. It is good practice to use both traffic projection factors and design capacity for thickness design of specific projects. For example, if an existing two-lane route is carrying 4000 ADT and the projection factor is 2.7, the projected ADT would be 10,800. This is more than 4000 vehicles per day (vpd) greater than the design capacity of virtually all two-kme highways.** On the other hand, 10,800 ADT is below the design capacity of most fourlane highways.t Hence, the design should be made for 10,800 ADT on a four-lane roadway, Design capacity should not be used where it shows a greater ADT than shown by traffic projection.

p *Lane widths of lessthan 12ft are rarely used in current pract i.., except for very lightly traveled two-lam roads where land serviceis a primary 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,-

== I Rolling

800

I 900

40 80 80

800 720 620

7Cnl

620

640 570 510 440

500

k:~

‘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..

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w’

APPENDIX E

References 1. Westergaard, H. M., “Computation of Stresses in Concrete Roads,” High way Research Board pro. ceedings, Fifth Annual Meeting, 1925, Part 1, pages 90 to 112. 2. Westergaard, H. M., “Stresses in Concrete Pavements Computed by Theoretical Analysis,” Public Roads, Vol. 7, No. 2, April 1926, pages 25 to 35. 3. Westergaard, H. M., “Analysis of Stresses in Concrete Roads Caused by Variations in Temperature,” Public Roads, Vol. 8, No. 3, May 1927, pages 201 to 215. 4. Westergaard, H. M., “Theory of Concrete Pavement Design; High way Research Board Proceedings, Seventh Annual Meeting, 1927, Part 1, pages 175 to 181. 5. Westergaard, H. M., “Analytical Tools for Judging Results of Structural Tests of Concrete Pavements? Public Roads, Vol. 14, No. 10, December 1933, pages 185 to 188. 6. P1ckett, Gerald; Ravine, Milton E.; Jones, WMam C.; and McCormick, Frank J., “Deflections, Moments and Reactive Pressures for Concrete pavements,” Kansas State College Bulletin No. 65, October 1951. 7. Pickett, Gerald, and Ray, Gordon K., “Influence Charts for Concrete Pavements? American Society of Civil Engineers Transactions, Paper No. 2425, Vol. 116, 1951, pages 49 to 73. 8. Tayabji, S. D., and Coney, B. E., “Analysis of Jointed Concrete Pavements,” report prepared by the Construction Technology Laboratories of the Portland Cement Association for the Federal Highway Administration, October 1981. 9. Teller, L. W., and Sutherland, E. C., “The Structural Design 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

41;, also PCA Development Department Bulletin DXOI1. 11. Childs., L. D., and Kapernick, J. W., “Tests of Concrete Pavement Slabs on Gravel Subbases,” Proceedings of American Society of Civil Engineers, Vol. 84 (HW-3), October 195fi also PCA Development Department Bulletin DX021. 12. Childs. ,, L. D.. and Kanernick. . . J. W... “Tests of Concrete Pavements on Crushed Stone Subbases,” Proceedings of American Society of Civil Engineers, Proc. Paper No. 3497, Vol. 89 (H W- 1), April 1963, pages 57 to 8@ also PCA Development Department Bulletin DX065. 13. Childs, L. D., “Tests of Concrete Pavement Slabs on Cement-Treated Subbases,” Highway Research Record 60, Highway Research Board, 1963, pages 39 to 58; also PCA Development Department Bulletin DX086. 14. Childs, L. D., “Cement-Treated Subbases for Concrete Pavements,” Highway Research Record 189, Highway Research Board, 1967, pages 19 to 43; also PCA Development Department Bulletin DX125. 15. Childs, L. D., and Nussbaum, P. J,, “Repetitive Load Tests of Concrete Slabs on Cement-Treated Subbases,” RD025P, Portland Cement Association, 1975. 16. Tayabji, S. D., and Coney, B. E,, “Improved Rigid Pavement Joints,” paper presented at Annual Meeting of Transportation Research Board, January 1983 (to be published in 1984). 17. Childs, L. D., and Ball, C. G., “Tests of Joints for Concrete Pavements,” RD026P, Portland Cement Association, 1975. 18. Coney, B. E., and Humphrey, H. A., “Aggregate interlock at Joints in Concrete Pavements,” Highway Research Board Record No. 189, Transportation Research Board, 1967, pages I to 18. 19. Coney, B. E., Ball, C. G., and Arriyavat, P., “EvaluatiOn Of Concrete Pavements with Tied Shoulders or Widened Lanes,” Transportation Research Record 666, Transportation Research Board, 1978; also Pmt-

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Book Contents

z “’ ‘~

.... ‘ ‘~

land Cement Association, Research and Development 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 Highway Administration, 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 of Highway Research at Pittsb”rg, California, 19zI1922,” California State Pri”ti”g office, 23. Road Test One-MD, Highway Research Board Special Report No. 4, 1952. 24. The AASHO Road Test, Highway Research Board Special Report No. 6 I E, 1962. 25. The AASHO Road Test, Highway Research Board Special Report No. 73, 1962. 26. AA SHTO Inlerim Guide for Design of Pavement Structures, /972, Chapter 111 Revised, 1981, American Association of State Highway and Transportation Officials, 1981, 27. Fordyce, Phil, and Teske, W. E,, “Some Relationships of tbe AASHO Road Test to Concrete Pavement Design,” High way Research Board Record No, 44, 1963, pages 35 to 70. 28. Brokaw, M. P., “Effect of Serviceability and Roughness at Transverse Joints on Performance and Design of Plain Concrete Pavement,” Highway Research Board Record 471, Transportation Research Board, 1973. 29. Packard, R. G., “Design Considerations For Control of Joint Faulting of Undoweled Pavements,” F70ceedings of International Conference on Concrete Pavement Design, Purdue University, February 1977. 30. Packard, R. G., and Tayabji, S. D., “Mechanistic Design of Concrete Pavements to Control Joint Faulting and Subbase Erosion,” International Seminar on Drainage and Erodability at the Concrete Slab-Subbase-Shoulder Interfaces, Paris, France, March 1983. 31. Standard Method for Nonrepetitive Static Plate Load Tests of Soils and Flexible Pavement Components, for Use in Evaluation and Design of Airport and Highway Pavements, American Society for Testing and 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 to Design of Airport Runway s,” Highway Research Board Proceedings, Vol. 23, 1943, pages 126 to 148. 34. Standard Methods for Freezing-and-Thawing Tests of Compacted Soil-Cement Mixtures, American Society for Testing and Materials, Designation D560. 35. Standard Methods for Wetting-and-Drying Tests of Compacted Soil-Cement Mixtures, American Society for Testing and Materials, Designation D559. 36. Soil- Cement Laboratory Handbook, Portland Cement Association publication EB052S, 1971.

37. “National Truck Characteristic Report, 1975- 1979,” U.S. Department of Transportation, Federal Highway Administration, Washington, D. C,, June 1981. 38. Becker, J. M., Darter, M. I., Snyder, M. B., and Smith, R. E., “COPES Data Collection Procedure— Appendix A,” June 1983, Appendix to final report of National Cooperative Highway Research Program, Project 1-19, Concrete Pavement Evaluation System, draft submitted to Transportation Research Board. 39. Load Stress at Pavement Edge, Portland Cement Association publication IS030P, 1969. 40. Taragin, Asriel, “Lateral Placement of Trucks on Two-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 Encroachment and Transverse Lane Displacement for Design Trucks on Rural Freeway s,” a report presented to the Committee on Shoulder Design, Transportation Research Board, January 13, 1975. 42, “Vehicle Shoulder Encroachment and Lateral Placement Study,” Federal Highway Administration Report No. FH WA/ MN-80/6, Minnesota Department of Transportation, Research and Development Office, July 1980. 43. Darter, M, 1,, “Structural Design for Heavily Trafficked Plain-Jointed Comrete Pavement Based o“ Serviceability Performance,” TRR 671, Analysis of Pavement Systems, Transportation Research Board, 1978, pages 1 to 8. 44. Thickness Design for Concrete Pavemenls, Portland Cement Association publication 1S0 IOP, 1974. 45, Kesler, Clyde E., “Fatigue and Fracture of Concrete,” Stanton Wolker Lecture Series of the Malerials Sciences, National Sand and Gravel Association and National Ready Mixed Concrete Association, 1970, 46. Fordyce, Phil, and Yrjanson, W. A,, “Modern Design of Concrete Pavements; American Society of Civil Engineers, Transportation Engineering Journal, Vol. 95, No. TE3, Proceedings Paper 6726, August 1969, pages 407 to 438. 47. Ballinger, Craig A., “The Cumulative Fatigue Damage Characteristics of Plain Concrete,” Highway Research Record 370, Highway Research Board, 1971, pages 48 to 60. 48. Miner, M. A., “Cumulative Damage in Fatigue,” American Society of Mechanical Engineers Transactions, Vol. 67, 1945, page A 159. 49. Klaiber, F. W., Thomas, T. L., and Lee, D. Y., “Fatigue Behavior of Air-Entrained Concrete: Phase 11,” Engineering Research Institute, Iowa State University, February 1979. 50. Packard, R. G., “Structural Design of Concrete Pavements with Lean Concrete Lower Course,” Proceedings of Second International Conference on Concrete Pavement Design, Purdue University, April 1981. 51. Yrjanson, W. A., and Packard, R. G., “Econocrete Pavements—Current Practices,” Transportation Research Record 741, Performance of Pavements Designed with Low-Cost Materials, Transportation Research Board, 1980, pages 6 to 13.

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52. Ruth, B. E., and Larsen, T. J., “Save Money with Econocrete 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 Trip Estimation in Urban Areas; Engineering Bulletin of Purdue University, Vol. XLWII, No. 4, July 1964, pages 67 to 92. 57. Packard, R. G., and Tayabji, S. D., “New PCA T’lickness Design Procedure for Concrete Highway and Street Pavements,” Proceedings of Third International Conference on Concrete Pavement Design and Rehabilitation, Purdue University, April 1985.

‘u’

7..

“u

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Calculation of Pavement Thickness

p Project Trial thickness Subbase-subgrade

Modulus of rupture, MR

Doweled joints:

yes _

no _

pci

Concrete shoulder:

yes _

no _

psi

Di!sign period _

years

Load safety factor, LSF

Axle load, hips

8. Equivalent stress Single Axles

10. Erosion factor

9. Stress ratio factor

11. Equivalent stress

Tandem Axles

13. Erosion factor

12. Stress ratio factor

1 Pâ&#x20AC;&#x2122;

Total

Publication List

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/-.. ,,

‘u

Microcomputer Program for Thickness Design of Concrete Highways, Streets, and Parking Lots PCAPA V—the low-cost software for concrete pavement design PCAPA V’s easy-to-use, ●

High-speed

solutions

●

Pavement

“

Comprehensive

theory

●

Realistic

criteria

The

fatigue design

computer

performance,

routine

to pavement

thickness

and subbase

program

consider

or undoweled),

menu-driven

design

erosion

concrete

design

based

at transverse

shoulders,

problems

calculations

procedures,

!oad transfer

offers

curbs

on this manual

and

and gutters,

longitudinal and

and verified joints

adjacent

(doweled

parking-lot

Ianee. Traffic traffic The

load considerations

load

software

or later), design

category runs

on IBM

and the package

Processing

personal

includes

Any designer

Or available computers

a floppy

traffic

can choose load data

a stored

can

and compatibles(128K,

diskette,

the user’s

manual,

be input. DOS

2.0

and this

Thickness Design for Concrete Highway and Street Pavements.

manual,

To order

are simplified.

to fit the situation.

PCAPA~(MCO03), Department,

contact

5420

the Portland

Old Orchard

Road,

Cement Skokie,

Association, IL

Order

60077-1083,

(800)888-6733

PORTLAND An .rganizati.m.(

.em..t

ma..

facl.r.m

t. improve

.nd

CEMENT

ml I

exte+a the uses d po,tla.d

mme.t

5420 Old Orchard

Road, Skokie,

,7-~.. ‘u

I ASSOCIATION

and concrete through

Illinois

rn.cket development,

engineert.g,

reyea.ch, education,

md Public.(faim

work.

60077-1083

Printed in U.S.A.

Eel 09.01 P

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