PORTLAND CEMENT
ASSOCIATION
Thickness Design for
C:r;c.-Zt Highway and
The author of this engineering bulletin is Robert G.
Packard, P. E., principal paving engineer, Paving
Transportation Department, Portland Cement
Association.
-
--
-
This publication is intended SOLELY for use by PROFESSIONAL
PERSONNEL who are competent to evaluate the significance and
limitations of the information provided herein, and who will 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 full
extent permitted by law.
O Portland Cement Association 1984, reprinted 1995
Thickness Design for
Concrete Highway and
Street Pavements
CONTENTS
.
Chapter 1 Introduction .......................... 3
Applications of Design Procedures ............... 3
Computer Programs Available . . . . . . . . . . . . . . . . . .4
Basis for Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Metric Version ................................ 4
Chapter 2. Design Factors ........................ 5
Flexural Strength of Concrete ................... 5
Subgrade and Subbase Support ................. 6
Design Period ................................ 6
Traffic ....................................... 8
Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8.
ADTT ..................................... 8
Truck Directional Distribution . . . . . . . . . . . . . . .10
Axle-Load Distribution ..................... 10
Load Safety Factors .......................... 10
Chapter 3. Design Procedure
(Axle-Load Data Available) . . . . . . . . . . . . . . . . . . . . . I 1
Fatigue Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1
Erosion Analysis ............................. I I
Sample Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Chapter 4. Simplified Design Procedure
(Axle-Load Data Not Available) .................. 23
Sample Problems ............................30
Comments on Simplified Procedure . . . . . . . . . . . . . 30
Modulus of Rupture ........................ 30
Design Period ............................. 30
Aggregate Interlock or Doweled Joints ........ 30
User-Developed Design Tables . . . . . . . . . . . . . . . . .30
Appendix A . Development of Design
Procedure ..................................... 32
Analysis of Concrete Pavements . . . . . . . . . . . . . . . . 32
Jointed Pavements ......................... 32
Continuously Reinforced Pavements .......... 33
Truck-Load Placement ........................ 33
Variation in Concrete Strength .................34
Concrete Strength Gain with Age . . . . . . . . . . . . . .34
Warping and Curling of Concrete ............... 34
Fatigue ..................................... 34
Erosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Appendix B . Design of Concrete Pavements
with Lean Concrete Lower Course ................36
Lean Concrete 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
Design Worksheet for Reproduction
.............. 47
Figures
1. Flexural strength, age, and design relationships.
2. Approximate interrelationships of soil classifications
and bearing values.
3. Proportion of trucks in right lane of a multilane
divided highway.
4. Design I A.
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 1 D.
8. Design 2A.
Al. Critical axle-load positions.
A2. Equivalent edge stress factor depends on percent of
trucks at edge.
A3. Fatigue relationships.
B1. Design chart for composite concrete pavement (lean
concrete subbase).
B2. Design chart for composite concrete pavement
(monolithic with lean concrete lower layer).
B3. Modulus of rupture versus compressive strength.
C l . Analysis of tridems.
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-Tire 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 Factors-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 ADTT, 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
13b. Allowable ADTT, Axle-Load Category 3-Pavements with Aggregate-Interlock Joints
14a. Allowable ADTT, Axle-Load Category 4-Pavements with Doweled Joints
14b. Allowable ADTT, Axle-Load Category 4-Pavements with Aggregate-Interlock Joints
15. Axle-Load Distribution Used for Preparing Design
Tables 1 1 Through 14
C l . Equivalent Stress - Tridems
C2. Erosion Factors Tridems - Doweled Joints
C3. Erosion Factors - Tridems - Aggregate-Interlock
Joints
D l . Design Capacities for Multilane Highways
D2. Design Capacities for Uninterrupted Flow on Twoan; Highways
-
customary
unit
in.
ft
Metric
unit
rnrn
m
Ib
Ibf
kg
N
kip
kN
kPa
MPal m
Ib/in.2
Ib/in.-' (k value)
Conversion
coefficient
25.40
0.305
0.454
4.45
4.45
6.89
0.27 1
CHAPTER 1
Introduction
This bulletin deals with methods of determining slab
thicknesses adequate t o 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, the 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 includeProvision for reasonably uniform support. (See Subgrades and Subbases for Concrete Pavements.*)
Prevention of mud-pumping with a relatively thin
untreated o r cement-treated subbase on projects
where the expected truck traffic will be great enough
t o 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
transfer; enable joint sealants, if required, t o beeffective; and prevent joint distress due to infiltration.
(See Joint Design for Concrete Highway and Street
Pavements.**)
Use of a concrete mix design a n d aggregates that will
provide quality concrete with the strength and durability needed for long life under the actual exposure
conditions. (See Design and Control of Concrete
Mixtures.7)
The thickness design criteria suggested are based on
general pavement performance experience. If regional o r
local specific performance experience becomes available
for more favorable o r adverse conditions, the design criteria can be appropriately modified. This could be the
case for particular climate, soil, o r drainage conditions
and future design innovations.
Applications of Design Procedures
The design procedures given in this text apply to the following types of concrete pavements: plain, plain 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 o r groove. For load transfer to be
effective, it is necessary that short joint spacings be used.
Plain-doweled pavements are built without reinforcing
steel; 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 contractionjoints. The
pavements are constructed with longer joint spacings
than used for unreinforced pavements. Between thejoints,
one o r 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
*Portland Cement Associat~onpubl~cationIS029P.
**Portland Cement Association publication IS059P.
tPortland Cement Association publ~cationEB001T.
t t For very thin pavements,a 15-ftjoint spacing may beexcessive -see
the aforementioned PCA publication on joint design.
other procedures. These include recognition of1. The degree of load transfer a t 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 flexural stresses and deflections caused by vehicle loads.
3. The effect of using a lean concrete (econocrete) subbase, which reduces pavement stresses and deflections, provides considerable support when trucks
pass over joints, and provides resistance t o subbase
erosion caused by repeated pavement deflections.
4. Two design criteria: (a) fatigue, t o keep pavement
stresses due t o repeated loads within safe limits and
thus prevent fatigue cracking; and (b) erosion, to
limit the effects of pavement deflectionsat slabedges,
joints, and corners and thus control the erosion of
foundation and shoulder materials. The criterion for
erosion is needed since some modes of pavement
distress such as pumping, faulting, and shoulder
distress are unrelated t o fatigue.
5. Triple axles can be considered in design. While the
conventional single-axle and tandem-axle configurations are still the predominant loads on highways,
use of triple axles (tridems) is increasing. They are
seen on some over-the-road trucks and on special
roads used for hauling coal o r other minerals. Tridems may be more damaging from a n erosion criterion (deflection) than from a fatigue criterion.
Selection of an adequate thickness is dependent upon
the choice of other design features-jointing system, type
of subbase if needed, and shoulder type.
With these additional design conditions, the thickness
requirements of design alternatives, which influence cost,
can be directly compared.
Chapter 2describes 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 a s 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.
I . Theoretical studies of pavement slab behavior by
~ e s t e r ~ a a r d , " - ~Pickett
'*
and ~ a ~"and
, ' recently
~
developed finite-element computer analyses, one of
which is used as the basis for this design procedure.'8'
2. Model and full-scale tests such as Arlington ~ e s t s " '
and several research projects conducted b PCA and
Y"andconother agencies on s~bbases,'~~~'~'joints"~
Crete shoulder^."^ 20'
3. Experimental pavements subjected to controlled test
traffic, such as the Bates Test ~ o a d , " " the Pittsburg Test ~ i ~ h w a the
~ , Mar
' ~ ~ land
'
Rbad ~ e s t , " "
the AASHO** Road Test, ( 2 4 - 2 4 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 t o 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 pavementstresses, 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 combinations. An
important second aspect of the design procedure is the
criteria applied t o the theoretically computed valuesthe limiting or allowable values of stress, deflection, or
pressure. Defining the criteria so that design results are
related t o 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 program.'8' The program models the conventional design
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 t o performance
of avements at the A A S H O Road ~ e s t 'and
~ ~ to
' studies''
")
of the faulting of pavements.
More information on development and basis of the design procedure is given in Appendix A and Reference 30.
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:
*Superscript numbers In parentheses denote referencesat the end of
this text.
**Now the American Association of State Hlghway and Transportation Officials (AASHTO).
CHAPTER 2
Design Factors
After selection of the type of concrete pavement (plain
pavement with o r without dowels, reinforced jointed
pavement with dowels, o r continuously reinforced pavement), type of subbase if needed, and type of shoulder
(with o r without concrete shoulder, curb and gutter o r
integral curb), thickness design is determined based on
four design factors:
1. Flexural strength of the concrete (modulus of rupture, M R )
2. Strength of the subgrade, o r subgrade and subbase
combination (k)
3. The weights, frequencies, and types of truck axle
loads that the pavement will carry
4. Design period, which in this and other pavement design procedures is usually taken a t 20 years, but may
be more o r 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
Consideration of the flexural strength of the concrete is
applicable 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 6 x 6 ~ 3 0 - i n .beams.
For specific projects, the concrete mix should be designed to give both adequate durability and flexural
strength a t the lowest possible cost. Mix design procedures are described in the Portland Cement Association
publication Design and Control of Concrete Mi.utures.
The modulus of rupture can be found by cantilever,
center-point, o r 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 third-point method (American Society for Testing and Materials, ASTM C78) is used for design in this
procedure.*
Modulus of rupture tests are commonly made at 7, 14,
28, and 90 days. The 7- and 1 4 d a y test results are compared with specification requirements forjob control and
for determining when pavements can be opened to traffic.
The 28-day test results have been commonly used for
thickness design of highways and streets and are recommended for use with this procedure; 9 0 d a y results are
used for the design of airfields. These values are used because there are very few stress repetitions during the first
28 o r 90days of pavement lifeas compared to the millions
of stress repetitions that occur later.
Concrete continues t o gain strength with age as shown
in Fig. I . Strength gain is shown by the solid curve, which
represents average M R values for several series by laboratory tests, field-cured test beams, and sections of concrete taken from pavements in service.
In this design procedure the effects** of variations in
concrete strength from point t o 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.
* F o r a standard 3 0 - ~ n beam.
.
center-polnt-loading test values will be
about 75 psi higher, and cantdever-loading test values about 160 p s ~
higher than thlrd-potnt-loading test values. These higher values are not
intended t o be used for design purposes. If these other lest methods are
used, a downward adjustment should be made by establishinga correlation t o third-point-load test values.
**These effects a r e discussed In Appendix A.
Table 1. Effect of Untreated Subbase
on k Values,
S u b b a s e k value,
Subgrade
k value.
pci
12 in
100
200
300
130
220
320
140
230
330
160
270
370
190
320
430
Table 2. Design k Values for CernentTreated Subbases
Age
Subgrade
k value,
pci
Fig. 1. Flexural strength, age, and design relationships.
50
100
200
S u b b a s e k value, p c ~
4 ~ n .
6 tn
8 in
10 In
170
280
470
230
400
640
310
520
830
390
640
-
Subgrade and Subbase 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
a s pounds per square inch per inch (psilin.) or, more
commonly, as pounds per cubic inch (pci). Equipment
and procedures for determining k values are given in
References 3 1 and 32.
Since the plate-loading test is time consuming and expensive, the k value is usually estimated by correlation to
simpler tests such as the California Bearing Ratio (CBR)
or R-value tests. The result is valid because exact determination of the k value is not required; normal variations
from a n estimated value will not appreciably affect pavement thickness requirements. The relationships shown in
Fig. 2 are satisfactory for design purposes.
The A A S H O Road ~ e s t 'gave
~ ~ a' convincing demonstration 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 the subgrade is
frozen and k values are much higher than assumed for
design. T o avoid the tedious methods required to design
for seasonal variations in k , normal summer- or .fallwealher k values are used as reasonable mean values.
It is not economical to use untreated subbases for the
sole purpose of increasing k values. Where a subbase is
used,* there will be a n increase in k that should be used
in the thickness design. If the subbase is a n untreated
granular material, the approximate increase in k can be
taken from Table 1.
The values shown in Table I are based on the Burmister'j3' analysis of two-layer systems and plate-loading
tests made to determine k values on subgrades and subbases for full-scale test s ~ a b s . " ~ '
Cement-treated subbases are widely used for heavyduty concrete pavements. They are constructed from
A A S H T O Soil Classes A- I , A-2-4, A-2-5, and A-3granular materials. The cement content of cement-treated subbase is based on standard A S T M laboratory freeze-thaw
and wet-dry tests'j4 3 5 ' and PCA weight-loss riter ria.')^'
Other procedures that give a n equivalent quality of material can be used. Design k values for cement-treated subbases meeting these criteria are given in Table 2.
In recent years, the use of lean concrete subbases has
been on the increase. Thickness design of concrete pavements 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 life. 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 years on some projects that have
carried more traffic than originally estimated o r have had
design, material, o r construction defects t o 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-analysis period. Since
traffic can probably not be predicted with much accuracy
for a longer period, a design period of 20 years is commonly used in pavement design procedures. However,
there are often cases where use of a shorter o r longer design period may be economically justified, such as a special haul road that will be used for only a few years, o r a
*Use of subbase is recommended for projects where condit~onsthat
would cause mud-pump~ngprevail; for discussion of when subbases
should be used and how thick they should be, see the PCA publication.
Subgrades and Subbases for Concrete Pavements.
CALIFORNIA BEARING RATIO- CBR("
(1) For the basic Idea, see 0. J. Porter, "Foundations for Flex~blePavements," H~ghwayResearch Board Proceedfngs of the Twenty-second Annual
Meetfng, 1942, Vol 22, pages 100-136.
(2) ASTM Oes~gnatlon02487
(3) "Classif~cat~on
of H~ghwaySubgrade Mater~als."Htghway Research Board Proceedfngs 01 the Twenty-111th Annual Meetmg. 1945. Vol 25, pages
376-392.
(4) Afrport Pavfng. U.S Department of Commerce. Federal A v ~ a t ~ oAgency,
n
May 1948, pages 11-16 Est~mateduslng values gtven In FAA Desfgn
Manual for Afrport Pavements (Formerly used FAA Classif~catton.U n ~ f ~ eClassiflcatlon
d
now used )
(5) C E Warnes. "Correlation Between R Value and k Value," unpubl~shedreport. Portland Cement Assoc~at~on.
Rocky Mounta~n-Northwest
Reg~on.October 1971 (best-fit correlat~onwtth correction for saturat~on)
(6) See T. A M~ddlebrooksand G. E Bertram. "So11Tests for Design of Runway Pavements." Htghway Research Board Proceedtngs of the Twentysecond Annual Meet~ng,1942, Vol 22, page 152
(7) See Item (6). page 184.
Fig. 2. Approximate interrelationships of soil classifications and bearing values.
premium facility for which a high level of performance
for a long time with little o r no pavement maintenance is
desired. Some engineers feel that the design period for
rural and urban highways should be in the range of 30 to
35 years.
The design period selected affects thickness design
since it determines how many years, and thus how many
trucks, the pavement must serve. Selection of the design
period for a specific project is based on engineering judgment and economic analysis of pavement costs and service provided throughout the entire period.
The numbers and weights of heavy axle loads expected
during the design 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 bothdirections)
-axle loads of trucks
Information on A D T is obtained from special traffic
counts o r from state, county, o r city traffic-volume maps.
This A D T is called the present o r current ADT. The design A D T is then estimated by the commonly used methods discussed here. However, any other method that gives
a reasonable estimate of expected traffic duringthedesign
life can be used.
Projection
One method for getting the traffic 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 A D T t o obtain a design ADTrepresenting
the average value for the design period. In some procedures, this is called A A D T (average annual daily traffic).
The following factors influence yearly growth rates and
traffic projections:
I. Attracted o r diverted traffic-the increaseoverexisting traffic because of improvement of a n existing
roadway.
2. Normal traffic growth-the increasedue to increased
numbers and usage of motor vehicles.
3. Generated traffic-the increase due to motor vehicle
trips that would not have been made if the new facility had not been constructed.
4. Development traffic-the increase due to changes in
land use due to construction of the new facility.
The combined effects will cause annual growth rates of
about 2% to 6%. These rates correspond to 20-year traffic projection factors of 1.2 to 1.8 as shown in Table 3.
The planning survey sections of state highway departments are very useful sources of knowledge about traffic
growth and projection factors.
Table 3. Yearly Rates of Traffic
Growth and Corresponding
Projection Factors'
I
I
Yearly
rate of
traffic
O/O
I
I
1
1
Projection
factor.
20 years
1
I
~roiection
factor.
40 years
'Factors represent values at the middesign period
that are widely used in current practice. Another
method of computing these factors is based on the
average annual value. Differences (both compound
interest) between these two methods w ~ l lrarely
affect design.
Where there is some question about the rate ofgrowth,
it may be wise t o use a fairly high rate. This is true on
intercity routes and on urban projects where a high rate
of urban growth may cause a higher-than-expected rate
of traffic growth. However, the growth of truck volumes
may be less than that for passenger cars.
High growth rates d o not apply on two-lane-ruralroads
and residential streets where the primary function is land
use o r abutting property service. Their growth rates may
be below 2% per year (projection factors of 1.1 to 1.3).
Some 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.
Capacity
The other method of estimating design A D T is based on
capacity-the maximum number of vehicles that can use
the pavement without unreasonable delay. This 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 A D T o r as a n actual value. The ADTT
value includes only trucks with six tires o r moreand does
not include panel and pickup trucks and other four-tire
vehicles.
The data from state, county, o r city traffic-volume
maps may include, in addition to ADT, the percentage of
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 ADTT 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 loadometer 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 loadometer table (Table W-3) for a
Midwestern state yields the following vehicle count for a
loadometer 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, for this station:
ADTT
=
1216
x
9492
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 alsoabout average.
For design purposes, the total number of trucks in the
design period is needed. This is obtained by multiplying
design A D T 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
100 = 13%
This ADTT percentage would be appropriate for design 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 percentages
is the National Truck Characteristic ~ e ~ o r t . ' "Table
'
4,
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
likely that the lower values on urban routes are due to
larger volumes of passenger cars rather than fewer trucks.
Fig. 3. Proportion of trucks in right lane of a multilane
divided highway. (Derived from Reference 38.)
*Trucks-excludes
Table 4. Percentages of Four-Tire Single Units and
Trucks (ADTT) on Various Highway Systems
I Rural average daily traffic I
Hlghway
system
Interstate
Other federala~d
prlmary
Federal-a~d
secondary
Urban average daily traffrc
panels and pickups and other four-tire vehicles.
Truck Directional Distribution
In most design problems, it is assumed that the weights
and volumes of trucks traveling in each directionare fairly
equal-50-50 distribution-the design assumes that pavement in each direction carries half the total ADTT. This
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.
Table 5. Axle-Load Data
(3)
Axles per
Axles per
1000
1000
trucks
(adjusted)
Axle load.
kips
trucks
--
p
-
S ~ n g l eaxles
28-30
0.28
26-28
0.65
24-26
1.33
22-24
2.84
Axle-Load Distribution
20-22
4.72
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 period. These data can be determined in one of three ways:
(I) special traffic studies t o establish the Ioadometer data
for the specific project; (2) data from the state highway
department's loadometer weight stations (Table W-4) 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 W-4 data have been grouped by 2-kip and
4-kip increments for single- and tandem-axle loads, respectively. The data under the heading "Axles per 1000
Trucks" are in a convenient form for computing the axleload 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. T o 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 I sample problem given in
Chapter 3.
18-20
10.40
16-18
13.56
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, L S F = 1.2.
For highways and arterial streets where there will be
moderate volumes of truck traffic, L S F = 1.1.
For roads, residential streets, and other streets that
will carry small volumes of truck traffic, L S F = 1.0.
Aside from the load safety factors, a degree of conservatism is provided in the design procedure to compensate
Axles In
design
period
14-16
18 64
12-14
25 89
10-12
81 05
Tandem axles
Columns 1 and 2der1vedfrom loadometer W-4 Table Thls tablealsoshows
13 215 total trucks counted wlth 6 918 two-axle four-tlre trucks (52%)
Column 3 Column 2 values adjusted for two-axle four-t~retrucks, equal
to Column 21(1 - 521100)
~
Seesampleproblem
Column 4 = C o l u m n 3 (trucks1ndes1gnper1od)l1000
Des~gn1 In which trucks In deslgn pertod (oned~rectton)
total 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 safety 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 t o provide a premium facility to circumvent for a
long time the need for any significant pavement maintenance that would disrupt traffic flow.
*See Appendix C i f i t isexpected that trucks with tridem loads will be
~ncludedin the traffic forecast.
CHAPTER 3
Design Procedure
(Axle-Load Data Available)
The methods in this chapter are used when detailed axleloaddistribution data have been determined or estimated
as described in Chapter 2.*
Fig. 4 is a worksheet** showing the format for completing design prob1ems.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
combinationtt
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 a n 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
analysis, 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 I and 3 are filled out. The axle loads
are multiplied by the load safety factor for Column 2.
Without concrete shoulder, use Table 6a and Fig. 5
With concrete shoulder, use Table 66 and Fig. 5
Procedure Steps:
1. Enter as items 8 and I I on the worksheet from the
appropriate table the equivalent stress factors depending on trial thickness and k value.
2. Divide these by the concrete modulus of rupture and
enter as items 9 and 12.
3. Fill in Column 4, "Allowable Repetitions," determined 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$-use Table 7a and Fig. 6a.
Aggregate-interlock joints-use Table 76 and Fig.
60.
With concrete shoulder
Doweled joints o r continuously reinforced pavementsf-use Table 8a and Fig. 66.
Aggregate-interlockjoints-use Tablegband Fig. 66.
Procedure Steps:
I. Enter the erosion factors from the appropriate table
as items 10 and 13 in the worksheet.
2. Fill in Column 6, "Allowable Repetitions," from
Fig. 60 or Fig. 6b.
-
Fatigue Analysis
Results of fatigue analysis, and thus the charts and figures
used, are the same for pavements with doweled and undoweled joints, and also for continuously reinforced
pavements.$
*See Chapter 4 when axle-load distribution data are unknown.
**A blank worksheet is provided as the last page of this bulletin for
purposes of reproduction and use in specific design problems.
t Computer programs for solving design problems are available from
Port'and
t t S e e Appendix B if lean concrete subbase is used.
IIn this design procedure, continuously reinforced pavements are
treated the same as doweled, jointed pavements-see Appendix A
Calculation of Pavement Thickness
T r ~ ath~ckness
l
9.5
~n
Doweled jo~nts
yes
no
-
Subbase-subgrade k
/?fl
PC1
Concrete shoulder
yes
no
J
650
PSI
rupture. MR
M O ~ U I U S of
Load safety factor, LSF
/. 2
Fat~gueanalys~s
Axle
load,
k~ps
Mult~pl~ed
by
LSF
Expected
repet~t~ons
/. 2
1
2
Single Axles
Tandem Axles
Fig. 4. Design 1A.
12
3
Allowable
repetltlons
4
Eros~onanalys~s
Fat~gue.
percent
5
8. Equwalent stress
2 0&
9. Stress ratlo factor
0.
3 7
11. Equ~valentstress
19 2
12. Stress ratlo factor
4
5
-
Allowable
repet~t~ons
Damage
percent
6
7
10. Eros~onfactor
2.59
13. Eros~onfactor
2.74
1
3. Compute Column 7 by dividing Column 3 by Column 6, multiplying by 100; 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 100%.
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:
Design ADT = 12,900 X 1.5 = 19,350 (9675 in one direction)
ADTT = 19,350 X 0.19 = 3680 (1840 in one direction)
For 9675 one-direction ADT, Fig. 3 shows that the
proportion of trucks in the right lane is 0.81. Therefore,
for a 20-year-design period, the total number of trucks in
one direction is
1840 X 0.8 1 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 1B: 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 1C: 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 I B except:
Aggregate-interlock joints
Design 1E: aggregate-interlock joints, cement-treated
subbase, concrete shoulder
Same as I D 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 lA, 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 IE, a subbase of one type or another is used as a recommended practice1 on fine-textured
soil subgrades for pavements carrying an appreciable
number of heavy trucks.
In Design IA: (I) Totals of fatigue use and erosion
damage of 63% and 39%, respectively, show that the 9.5in. thickness is adequate for thedesignconditions. (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 whether a 9.0in. thickness would be adequate for Design IA. Separate
calculations showed that 9.0 in. is not adequate because
of excessive fatigue consumption (245%). (4) Design 1A
is controlled by the fatigue analysis.
A design worksheet, Fig. 7, is shown for Design I D to
illustrate the combined effect of using aggregate-interlock joints and a cement-treated subbase. In Design 1D:
(1) Totals of fatigue use and erosion damage of I%$f and
97%, respectively, show that 10 in. is adequate. (2) Separate calculations show that 9.5 in. is not adequate because
of excessive erosion damage (142%), and (3) Design 1D is
controlled by the erosion analysis.
(continued o n page 21)
'Some guidance is helpful in reducing the number of trial runs. The
effect of thickness on both the fatigue and erosion damage approximately follows a geometric progression. For example, if 33% and 178%
fatigue damage are determined at trial thicknesses of 10 and 8 in., respectively, the approximate fatigue damage for a thickness of 9 in. is
equal to J33X178 = 77%.
**Concrete M R , LSF, and subgrade k valuesare thesame for Designs
I A through I E.
tCement-treated subbase meeting requirements stated on page 6.
t t A blank worksheet is provided as the last page of this bulletin for the
purposes of reproduction and use in specific design problems.
:See Subgrades and Subbases for Concrete Pavements. Portland
Cement Association publication
f f For pavements wlth aggregate-interlock joints subjected to an appreciable number of trucks, the fatigue analysis will usually not affect
design.
Table 6a. Equivalent Stress - No Concrete Shoulder
(Single Axlenandem Axle)
Slab
thickness,
in.
50
100
150
200
300
500
700
4
4.5
825/679
699/586
726/585
616/500
671 /542
571/460
634/516
540/435
584/486
498/406
523/457
448/378
484/443
41 7/363
5
5.5
602/516
526/461
531/436
464/387
493/399
431 /353
467/376
409/331
432/349
379/305
390/321
343/278
363/307
320/264
6
6.5
465/416
417/380
411/348
367/317
382/316
341/286
362/296
324/267
336/271
300/244
304/246
273/220
285/232
256/207
7
7.5
375/349
340/323
331 /290
300/268
307/262
279/241
292/244
265/224
271 /222
246/203
246/199
224/18 1
231 /I86
2 10/169
500
700
k of subgrade-subbase, pci
Table 6b. Equivalent Stress - Concrete Shoulder
(Single AxleITandem Axle)
Slab
thickness,
~n.
k of subgrade-subbase, p c ~
.
50
100
150
200
300
I
0
0
-
"
-
o
N
I
h)
1
P
o
u
I
m
I
0
0
c o o
-
o
P
I
1
nl
I
8
I
I
o
6,
I
I
I
I
I
2I
I
CD
o
"co
8
nl
I
I
P
ALLOWABLE L O A D REPETITIONS
P
P
-
1
I
I
I
I
I
I
I
1
I
TANDEM A X L E LOAD, KlPS
I
- 2 : k g g g 8 g g
C D 0 r u 5 ; a , m
-
SINGLE A X L E LOAD, KlPS
m c o
8
'0
s
(o
0
nl
o
0
-
0
0
P ma30
8
-
0
nl
-
Pb,
8
-0
80
0,
.o
-
ru
0
Table 7a. Erosion Factors - Doweled Joints, No Concrete Shoulder
(Single Axlenandem Axle)
Slab
th~ckness.
k of subgrade-subbase, p c ~
in.
50
100
200
300
500
700
4
4.5
3.74/3.83
3.59/3.70
3.73/3.79
3.57/3.65
3.72/3.75
3.56/3.61
3.71/3.73
3.55/3.58
3 70/3.70
3 54/3.55
3 68/3 67
3 52/3.53
5
55
3.45/3.58
3.33/3.47
3.43/3.52
3.31/3.41
3.42/3.48
3.29/3 36
3 41/3.45
3 28/3.33
3.40/3.42
3.27/3.30
3.38/3.40
3 26/3.28
Table 7b. Erosion Factors - Aggregate-Interlock Joints,
No Concrete Shoulder (Single Axle/Tandem Axle)
Slab
th~ckness,
~n
50
100
200
300
500
700
4
4.5
3.94/4.03
3.79/3.91
3.91/3.95
3.76/3.82
3.88/3.89
3.73/3.75
3.8W3.86
3 71/3.72
382/3.83
3 68/3.68
3.7713.80
3.64/3.65
k of subgrade-subbase, pcl
-I
m
t
m
I
(D
a,
,
0
N
0
I
I
I
-
P
m
-
-
aD
0
10
0
IU
0
W
II
l
aiTI
A
P
0
N
0
1
1 1
o
P
0
W
1
0
0
1
1 1
W
in
P
cJ
1
1
1
W
N
1
1
o
cJ
1
1
I
I
I
I
in
r
in
l
I
N
1
I
I'
N
EROSION FACTOR
0
0,
ALL0WABL.E LOAD REPETITIONS
OD
cEl
P
0
TANDEM A X L E LOAD, KlPS
W
0
1
1
N
P
0
(I,
l
~ I ~ I ~ I i I I ~I r , r ~p lw~: , ~ l ~
h)
-
SINGLE A X L E LOAD, KlPS
1
II
0,
0
iu
1
1
o
N
' I ' I1 '
- - 0
(0
o o o g
N
1
~
0
0
Table 8a. Erosion Factors - Doweled Joints, Concrete Shoulder
(Single AxleITandem Axle)
Slab
th~ckness,
in.
50
100
200
300
500
700
4
4.5
3.28/3.30
3.13/3.19
3.24/3.20
3.09/3.08
3.21/3.13
3.06/3.00
3.19/3.10
3. 04/2. 96
315/3.09
3.01/2.93
3.12/3.08
2.98/2.91
k of subgrade-subbase, pci
Table 8b. Erosion Factors - Aggregate-Interlock Joints,
Concrete Shoulder (Single AxleITandem Axle)
Slab
th~ckness,
~n.
k of subgrade-subbase, pci
50
100
200
300
500
700
Fig. 6b. Erosion analysis-allowable load repetitions
based on erosion factor (with concrete shoulder).
Calculation of Pavement Thickness
T r ~ a th~ckness
l
-
/fl.
in
A pcl
Modulus of rupture, MR - M L PSI
Subbase-subgrade k
Load safety factor, LSF
Doweled j o ~ n t s
yes n
Concrete shoulder
yes
Mult~pl~ed
by
LSF
Expected
repet~t~ons
1-Z
1
2
3
Allowable
repetltfons
Eros~onanalys~s
Fat~gue.
percent
5
4
8. Equivalent stress-
Single Axles
9. Stress ratlo factor
m
11. Equ~valents t r e s s . / C L =
Tandem Axles
Fig. 7. Design I D .
a
Des~gnp e r ~ o d2 0 years
/. 2
Fatlgue analys~s
Axle
load.
k~ps
o v
no
12. Stress ratlo factor
Allowable
repetltlons
Damage
percent
6
7
10. Eros~onfactor
2.72
T
13. Eros~onfactor
-2.90
Worksheets for the other variations of Design 1 are not
shown here but the results are compared as follows:
Joints
Design
Subbase
1A
IB
1C
4-in. g r a n u l a r
4-in. cement-treated
ID
4-in. cement-treated
aggregate
interlock
1E
4-in. cement-treated
aggregate
interlock
4-in. g r a n u l a r
Thickness
requirement,
in.
Concrete
shoulder
doweled
doweled
doweled
Design 2B: doweled joints,** no subbase, no concrete
shoulder
Same as 2A except:
Doweled joints
Thickness Calculations:
For Design 2A, a trial thickness of 6 in. is evaluated by
completing the worksheet shown in Fig. 8, according t o
the procedure given on page 1 1. Table 6a and Fig. 5 are
used for the fatigue analysis and Table 76 and Fig. 6a are
used for the erosion analysis.
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
1 A versus I B); and concrete shoulders reduce the thickness requirement by 1.0 to 1.5 in. (Designs 1A versus 1C
and 1 D versus 1E). Use of aggregate-interlock joints instead of dowels increases the thickness requirement by
1.5 in. (Design 1 B 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 A D T
-
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 6.0-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 296, respectively. Comments: (1) The thickness 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. (3) Because of the dowels, the erosion damage is reduced from 8% t o 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'2829' showing the effects of the number oftrucks
on pavements with aggregate-interlock joints.
18
2
= - =
9
For a 40-year design period:
9 X 365 X 40 = 13 1,400 trucks
Axle-load data are shown in Table 15, Category I , and
the expected number of axle-load repetitions are shown
in Fig. 8.
Values Used t o Calculate Thickness:
Design 2A: aggregrate-interlock joints, no subbase,* no
concrete shoulder
Clay subgrade, k = 100 pci
L S F = 1.0
Concrete M R = 650 psi
*Performance experience has shown that subbases are not requ~red
when truck traffic 1s very Ilght; see the PCA publicatlon, Subgradesand
Subbases for Concrete Pavemenrs.
**Design 2B is shown for illustrative purposes only. Doweledjolnts
are not needed where truck traffic 1s very I~ght;see the PCA publication
Joinr Des~gnfor Concrete Hrghwav und Streer Pavements.
t
The type of load transfer at thejoints--dowels, or aggregate interlock-does not affect the fatigue calculations since the critical axle-load
position for stress and fatigue is where the axle loads are placed at pavement edge and midpanel, away from the joints. See Appendix A.
Calculation of Pavement Thickness
Trtal th~ckness
'4.0
Subbase-subgrade k
/DO
-
Modulus of rupture. MR
Load safety factor, LSF
~n
Doweled joints
yes
no r
/
pc~
Concrete shoulder
yes
no r/
ps~
Deslgn perlod
/. 0
%years
no J ~ ~ L Z S P
Fat~gueanalys~s
Axle
load,
klps
Mult~plied
by
LSF
Expected
repet~tions
1.L 7
1
2
3
Allowable
repetit~ons
Single Axles
Fatlgue.
percent
5
4
8. Equivalent stress
Eros~onanalys~s
y//
Fig. 8. Design 2A.
Damage.
percent
6
7
10. Eros~onfactor
3.F D
9. Stress ratlo factor
11. Equlvalent stress-*!?.
Tandem Axles
Allowable
repet~t~ons
12. Stress ratlo factor
0-5 3 5
13. Eroslon factor
-=-
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 the axle-load data**
because the designs have been presolved by the methods
described in Chapter 3. For convenience in design use, the
results are presented in Tables 1 1, 12, 13, and 14, which
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 design tables for axleload Categories 1, 2, 3, and 4. The 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 data are
not available, Table 10 lists approximate k values fordifferent soil types. If a subbase is to be used-see Chapter 2
*On page 30, guidelines for preparing design tables f o r axle-load distributions different f r o m those given here are discussed.
**Axle-load data f o r the f o u r categories are given i n Table 15.
Table 9. Axle-Load Cate~ories
Traffic
I
Axle-load
category
Description
I
2
3
4
ADT
Residential streets
Rural and secondary roads (low to
medium')
Collector streets
Rural and secondary roads (high')
Arterial streets and primary roads (low')
Arterial streets and primary roads
(medium')
Expressways and urban and rural
lnterstate (low to medium')
Arterial streets, primary roads.
expressways (high')
Urban and rural lnterstate (medium to
high')
3000-12,000
2 lane
3000-50.000+
4 lane or more
3000-20,000
2 lane
3000-150,000+
4 lane or more
ADTT"
1
7
1
Per day
8-30
8-30
'The descriptors high, m e d ~ u mor
, low refer to the relat~vewe~ghtsof axle loads for the type of street or road.
that IS. "low" for a rural lnterstate would represent heavier loads than "low" for a secondary road
'Trucks -two-axle, four-tire trucks excluded.
Maximum axle loads, kips
Single axles
Tandem axles
Table 10. Subgrade Soil Types and
Approximate k Values
k values
range.
Type of soil
Support
Fine-gramed soils in which silt and
clay-size particles predominate
Sands and sand-gravel mixtures with
moderate amounts of silt and clay
Sands and sand-gravel mixtures
relatively free of plastic fines
Cement-treated subbases (see page 6)
I
1
Low
75-1 20
Medium
13C-170
High
Very high
1
1
188220
25C-400
under "Subgrade and Subbase Supportw-the estimated
k value is increased according to Table I or Table 2.
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 I, 2, 3, or 4.
3. Find slab thickness requirement in the appropriate
Table I I, 12, 13, or 14. (In the use of these tables, see
discussion under "Comments on Simplified Procedure," 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 traffic. Other methods of estimating ADT and ADTT are discussed on pages 8 and 9.
The allowable ADTT values (two directions)listed 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-axle,
four-tire trucks. Therefore, the number of allowable
trucks ofall types will begreaterthanthe tabulated ADTT
(continued on page 30)
*For facilities of four lanes or more, the ADTT IS adjusted by the use
of Fig. 3.
Table 11. Allowable ADTT,* Axle-Load Categpry 1
Pavements with Aggregate-Interlock Joints (Dowels not needed)
Concrete Shoulder or Curb
No Concrete Shoulder or Curb
I
in.
'
1
Low
Medium
Slab
thickness,
~n.
Hiah
Subgrade-subbase support
Low
Medium
High
Note: Fatigue analysis controls the des~gn
Note: A fractional ADTT Indicates that the pavement can carry unlim~tedpassenger cars and two-axle, fourtire trucks, but only a few heavy trucks per week (ADTT of 0.3 x 7 days ind~catestwo heavy trucks per week.)
'ADTT excludes two-axle, f o u r - t ~ r etrucks, so total number
of
trucks allowed w ~ l be
l greater-see
text
Table 12a. Allowable ADTT,* Axle-Load Category 2
- Pavements with Doweled Joints
Concrete Shoulder or Curb
No Concrete Shoulder or Curb
Slab
thickness.
in.
Subgrade-subbase support
Low
Medium
Hlgh
Very high
I
Slab
thickness,
~n.
I
Subgrade-subbase support
Low
5
Note. Fatlgue analysis controls the deslgn.
I
Medium
Very hlgh
9
42
Concrete Shoulder or Curb
Subgrade-subbase support
Low
High
- Pavements with Aggregate-Interlock Joints
No Concrete Shoulder or Curb
~n.
3
'ADTT excludes two-axle, four-t~retrucks so total number of trucks allowed w ~ l be
l greater-see
Table 126. Allowable ADTT,* Axle-Load Category 2
thickness,
Medlum
Hlgh
Very high
Slab
th~ckness.
~n
Subgrade-subbase support
Low
Medium
Hlgh
Very high
3
42
9
120
42
450
96
650"
380
1000"
700"
1400"
970''
2100"
1100"
1900"
5
5.5
6
6.5
7
'ADTT excludes two-axle, four-tlre trucks, total number of trucks allowed w ~ l be
l greater-see
"Eros~on analys~scontrols the des~gn,otherwse fatlgue analys~scontrols
9
text
text
Table 1%. Allowable ADTT,* Axle-Load Category 3-
Pavements with Doweled Joints
No Concrete Shoulder or Curb
Slab
hickness,
in.
Concrete Shoulder or Curb
Subgrade-subbase support
Low
Medium
High
Very high
Slab
thickness,
in.
Subgrade-subbase support
I
7.5
8
8.5
9
9.5
'ADTT excludes two-axle, four-tire trucks; total number of trucks ailowed wtll be greater-see
"Erosion analysis controls the design; otherwise fat~gueanalysis controls.
text.
Low
Medium
High
Very high
Table 13b. Allowable ADTT,* Axle-Load Category 3
-
Pavements with Aggregate Interlock Joints
Concrete Shoulder or Curb
No Concrete Shoulder or Curb
thickness.
slab
~n.
I
I
Subgrade-subbase support
Low
Medium
High
Very high
I
th~ckness,
in.
'ADTT excludes two-axle, four-t~retrucks; total number of trucks allowed w ~ l be
l greater-see
"Fat~gue analysis controls the design, otherw~seeroslon analysis controls.
Subgrade-subbase support
Low
text.
Medium
High
Very high
Table 14a. Allowable ADTT,* Axle-Load Category 4 - Pavements with Doweled Joints
No Concrete Shoulder or Curb
I
I1
Slab
Ith~c:~ness,
Concrete Shoulder or Curb
Subgrade-subbase support
Low
Med~um
Hlqh
Very hlqh
II
Slab
th~ckness.
~n.
'ADTT excludes two-axle four-t~retrucks total number of trucks allowed wlll be greater-see
.Eros~onanalys~scontrols the d e s ~ g notherwise fat~gueanalys~scontrols
text
Subgrade-subbase support
Low
Medium
H~oh
Verv hiah
Table 14b. Allowable ADTT,* Axle-Load Category 4 - Pavements with Aggregate-Interlock Joints
Concrete Shoulder or Curb
No Concrete Shoulder or Curb
I
I
Slab
th~ckness.
in.
Subgrade-subbase support
Low
Medium
Hiah
Verv hiah
Subgrade-subbase support
Slab
thickness.
tn.
Low
7
7.5
8
Medium
High
Very high
240"
100"
620"
400"
910
8.5
330"
720
770
1,300
1,100
1.900
1,700
3,100
9
9.5
1,100
1.700
2.100
3.400
3.200
5.500
5.7CO
10,200
'ADTT excludes two-axle, four-t~retrucks, total number of trucks allowed w ~ l be
l greater-see
"Fat~gue analys~scontrols the des~gn,otherw~seeroslon analys~scontrols
text
values by about double for many highways on up toabout
triple or more for streets and secondary roads.
Tables 1 1 through 14 include designs for pavements
with and without concrete shoulders or curbs. Forparking lots, adjacent lanes provide edge support similar to
that of a concrete shoulder or curb so the right-hand side
of Tables 1 1 through 14 are used.
Sample Problems
Two sample problems follow to illustrate use of the simplified design procedure.
Design 3
Arterial street, two 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 13h 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.
This 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 support = low
Concrete M R = 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:
Slab Thickness. in.
1
ADTT
Therefore, a 5.5-in.-slab thickness is selected to meet
the required design ADTT value of 8.
Comments on Simplified Procedure
Modulus of Rupture
Concrete used for paving should be of high quality** and
have adequate durability, scale resistance, and flexural
strength (modulus of rupture). In reference to Tables I I
through 14, the upper portions 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 for special cases. In some areas of 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 ADTTs for a 20-year design
period. For other design periods, multiply the estimated
ADTT by the appropriate ratio to obtain an adjusted
value for use in the tables.
For example, if a 30-year design period is desired instead of 20 years, the estimated ADTTvalue is multiplied
by 30120. In general, the effect of the design period on
slab thickness will be greater for pavements carrying
larger volumes of truck 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-interlockjoints,t
respectively. In Table 11, thickness requirements are the
same for pavements withdoweled and aggregate-interlock
joints; 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 Design Tables
The purpose of this section is to describe how the simplified design tables were developed 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 discussion under "Comments on Simplified Procedure-Modulus of Rupture," above.
**See Portland Cement Association publication Design and Control
of Concrete Mixtures.
When fatigue analys~scontrols the design (see footnotes of Tables
12 through 14). it will be noted that the ADTTvalues for doweled joints
and for aggregate-interlock joints are the same (see topic "Jointed Pavements" in Appendix A). If erosion analys~scontrols, concrete modulus
of rupture will have no effect on the allowable ADTT.
(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-load distributions for Categories 1 through 4 are
shown in Table 15. Each of these is a composite of data
averaged from several state loadometer (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 W-4 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 this 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 ADTT values to be listed in design tables are
easily calculated when a constant, arbitrary ADTT is input 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 =
100 X (input ADTT)
% fatigue or erosion damage
'
Table 15. Axle-Load Distributions Used for
Preparing Design Tables 11 Through 14
load,
Axles per 1000 trucks*
Category 2
Single axles
1693.31
4
732.28
6
483.10
8
10
204.96
12
124.00
14
56.11
16
38.02
15.81
18
4.23
20
0.96
22
24
26
28
30
32
34
m
Tande axles
4
31.90
85.59
8
12
139.30
75.02
16
57.10
20
39.18
24
68.48
28
69.59
32
4.19
36
40
44
48
52
56
60
L
'Exclud~ngall two-axle, four-t~retrucks
Category 3
Category 4
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 o r 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 applied in addition to the stress-fatigue criterion.
The erosion criterion recognizes that pavements can fail
from excessive pumping, erosion 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 l wereestablished
with the following conclusions:
I . The most critical pavement stresses occur when the
truck wheels are placed a t o r near the pavement edge
and midway between the joints, Fig. A I(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
flexural stresses and fatigue yield the same values for
different joint spacings and different types of load
transfer mechanisms (dowels o r aggregate interlock)
at transverse joints. When a concrete shoulder is tied
Analysis of Concrete Pavements
The design procedure is based on a comprehensive analysis of concrete stresses and deflections at pavement
joints. corners, and edges by a finite-element computer
program.'x' It allows considerations of slabs with finite
dimensions, variable axle-load placement, and the modeling of load transfer at transverse joints Or cracks and
load transfer at the joint between pavement and concrete
shoulder. For doweled joints, dowel properties such as
diameter and modulus of elasticity are used directly. For
aggregate interlock, keyway joints, and cracks in continuously reinforced pavements, a spring stiffness value is
used to represent the load-deflection characteristics of
such joints based o n field and laboratory tests.
(01 Axle - lood p o s ~ f ~ ofor
n c r ~ t i c o lflexural stresses
-Transverse
1
Troff~c
lo"e
Free edge or
shoulder lolnf
I
I
I
2Concrete shoulder
I
( ~ used)
f
Jointed Pavements
After analysis of different axle-load positions on the slab,
~omt
Fig. A l . Critical axle-load positions.
I
I
I
on to the mainline pavement, the magnitude of the
critical stresses is considerably reduced.
2. The most critical pavement deflections occur at the
slab corner when a n axle load is placed a t the joint
with the wheels a t or near the corner, Fig. Al(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 finiteelement computer analysis, a high degree
of load transfer was assigned at the cracks of C R C P and
the crack spacing was varied. The critical load positions
established were the same as those forjointed 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 uncracked pavement to developas 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 o r 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,
doweled pavements is made. Edge stresses will sometimes
be the same and sometimes less. while corner deflections
will sometimes be less, the same, and greater at different
areas of the pavement depending on crack spacing.
The average of these pavement responses is neither
substantially better nor worse than those for jointed,
doweled pavements. As a result, in thisdesign 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 of doweled-jointed pavements.
*The greatest deflect~onsfor t r ~ d e m occur
s
when two axles are placed
at one s ~ d eof the jolnt and one axle at the other s ~ d e
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 s u b ~ t a n t i a l l ~ . " ~ '
Only a small fraction of all the trucks run with their
outside wheels placed at the edge. Most of the trucks traveling the pavement are driven with their outside wheel
placed about 2 ft from the edge. ~ a r a g i n ' s ' ~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 ~ m e r ~ ' " " s h o w e d
more trucks at edge. Other recent s t ~ d i e s ' ~showed
"
fewer
trucks at edge than Emery. For this design procedure, the
most severe condition, 6% 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 load applications increases while
the magnitudes of stress and deflection decrease. Data
on truck placement distribution and distribution 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 from 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 most
severe condition, 6% truck encroachment, has been incorporated in the design tables.
Percent trucks
of or off edge
Taragm 2 lone
04 6
Emery (paved shoulder)
600
-
-
-
--
-
-
PERCENT TRUCKS AT EDGE
Fig. A2. Equivalent edge stress factor depends on
percent of trucks at edge.
*As used here, the term "percent trucks at edge" is defined as the
percent of total trucks that are traveling with the outside of the contact
area of the outside tire at or beyond the pavement edge.
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 = 100 Cn, (C/ Ni)
where: 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
T o save a design calculation step, the effects of (C/Ni]
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 a s 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. The
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 top surface is
warmer than the bottom, tensile-restraint stressesdevelop
a t the slab bottom. During the night, the temperature distribution is reversed and tensile restraint stresses develop
a t the slab surface. Temperature distribution is usually
nonlinear and constantly changing. Also, 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 a t the bottom of the
slab exceed that a t the top more than the reverse.
The complex situation of differential conditions at a
slab's top and bottom plus the uncertainty of the zerostress position make it difficult to compute o r 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 loss of support, this is considered indirectly
in the 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%. This theoretical stress increase is
counteracted in the real case because a portion of the load
is dissipated in bringing the slab edges back in contact
with the support. Thus, the incremental load stressdue 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 is similar to that used
in the previous PCA method'j4' based conservatively on
Concrete Strength Gain With Age
The 2 8 d a y flexural strength (modulus of rupture) is used
a s the design strength. This design procedure, however,
incorporates the effect of concrete strength gain after 28
days. This modification is based on a n 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 a s the design strength.
Warping and Curling of Concrete
In addition to traffic loading, concrete slabs are also subjected to warping and curling. Warping is the upward
concavedeformation of the slab due to variationsin 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 is a long-term phenomenon, its resultant
04
lo2
lo3
I
o4
I o5
LOAD REPETITIONS
Fig. A3. Fatigue relationships.
I o6
10'
(45-49)
except that it is applied to
studies of fatigue research
edge-load stresses that are of higher magnitude. A modification in the high-load-repetition range has been made
t o 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 hypothesis'48' that fatigue resistance 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 flexural 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 a n important mode
of distress in addition t o fatigue cracking that needs t o
be addressed in the design process. This 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 materials; 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'x' with A A S H O Road ~ e s t 'perform~~'
ance data were not completely satisfactory for design
purposes. (The principal mode of failure of concrete
pavements at the A A S H O Road Test was pumping o r
erosion of the granular subbase from under the slabs.) It
was found that to be able to predict the A A S H O 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, o r rate of work, with which a n 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 (f--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 gen29' These
erally related t o studies on joint f a ~ l t i n g . " ~
studies included pavements in Wisconsin, Minnesota,
North Dakota, Georgia, and California, and included a
range of variables not found a t the A A S H O Road Test,
such as a greater number of trucks, undoweled pavements, a wide range of years of pavement service, and
stabilized subbases.
Brokaw's ~ t u d i e s ' ~ 'of
' undoweled pavements suggest
that climate o r drainage is a significant factor in pavement performance. S o far, this aspect of design has not
been i'ncluded in the design procedure, but it deserves
further studv. Investigations
of the effects of climate on
design and performance of concrete pavements have also
been reported by ~ a r t e r . ' ~ ~ '
The erosion criterion is suggested for use as a guideline.
It can be modified according t o local experience since
climate, drainage, local factors, and design innovations
may have a n influence. Accordingly, the 100% erosiondamage criterion, a n index number correlated with general performance experience, can be increased or decreased based o n specific performance data gathered in
the future for more favorable o r more adverse conditions.
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 subbase 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. B1 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 t o a n estimated flexural strength (modulus of
rupture) for use 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 slipform paver. Thisextra width is structurally beneficial for wheel loads applied a t 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- o r 5-in. subbase.
Fig. Bl shows the surface and subbase thickness requirements set t o be equivalent to a given thickness of
normal concrete without a lean concrete subbase.
A sample problem is given t o 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 10-in.-thickness requirement has been determined for a pavement without lean
concrete subbase a s set forth in Chapter 3 or 4.
As shown by the dashed example line in Fig. B1, designs equivalent t o the 10-in. pavement are (1) 7.7-in.
concrete on a 5-in. lean concrete subbase, and (2) 8.1-in.
concrete o n a 4-in. lean concrete subbase.
Monolithic Pavement
In some areas, a relatively thin concrete surface course is
constructed monolithically with a lean concrete lower
layer. Local o r recycled aggregates can be used for the
lean concrete, resulting in cost savings and conservation
of high-quality aggregates.
*The criterla are that (I) stress ratios in either of the two concrete
layers not exceed that of the reference pavement; and (2)erosionvalues
at the subbase-subgrade interface not exceed those ofthereferencepavernent. Rationale for the criteria is given in Reference 50 plus two additional considerations: (I) erosion criteria is included in addition to the
fatigue approach given in the reference; and (2) for nonmonolithicconstruction, some structural benefit (I4) is added because the subbase is
constructed wider than the pavement.
Flexural strength of lean concrete to be used as a subbase is usually
selected to be between 150 to 250 p s ~
(compressive strength, 750 to 1200
PSI);these relatively low strengths are used to rn~nlmizereflectlvecrackIng from the unjolnted subbase (usual practice is to leave the subbase
unjolnted) through the concrete surface. If, contrary tocurrent practice.
jolnts are placed in the subbase, the strength of the lean concrete would
not have to be restricted to the lower range.
**
Modulus of Rupture of L e a n Concrete, p s i
350 450
I
250
../
150 250 350 450
/
14
-
13
--
12
-
-
II
10
5" Sub base
4" Subbase
Dimensions shown on curves
are thicknesses of concrete
surface course
Fig. B1. Design chart for composite concrete pavement (lean concrete subbase).
9
Modulus of Rupture of Lean Concrete, psi
450
150 250 3 5 0 4 5 0
I
3" Surface
4" Surface
Fig. 82. Design chart for composite concrete pavement (monolithic with lean concrete lower 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 full-depth cracking through
both layers at the joint locations.
Fig. B2 is the design chart for monolithic pavements.
T o 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 line in Fig. B2, monolithic designs equivalent to the 10-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 STRENGTH. PSI
Fig. 83. Modulus of rupture versus compressive strength
(from Reference 50).
APPENDIX C
Analysis of Tridem Axle Loads
Tridem 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 C 3 are used.
From these tables for tridems, equivalent stress and erosion factors are entered in an extra design worksheet.
Then Fig. 5 and Fig. 6a o r 66 are used to determine allowable numbers of load repetitions. Fatigue and erosion
damage totals for tridems are added t o those for singleand tandem-axle loads.
An extension of the sample problem, Design I A 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 a n estimated
period of 10 years; so:
100 trucks X 250 days X 10 years = 250,000 total trucks
The trucks in one direction are normally all loaded t o
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 I represents a portion of the extra design worksheet needed to evaluate the effects of these tridems. Since
Design I A (9:5-in. pavement, combined k of 130 pci) is a
pavement with doweled joints and no concrete shoulder,
Tables C1 and C2 are used t o determine the equivalent
stress and erosion factors, Items I I and 13 on the worksheet.
For this example, Fig. 5 is used to determine allowable
load repetitions for the fatigue analysis and Fig. 6a is used
for the erosion analysis.
The tridem loads of 54,000 Ib are multiplied by the load
safety factor for Design 1A of 1.2, giving a design axle
load of 64,800 Ib. Before using the charts for allowable
load repetitions, the tridem load (3 axles) is divided by
three (64,800/3 = 2 1,600 Ib) so that the load scale for
single axles can be used. **
As shown in Fig. C I , the tridem causes only 9.3% erosion damage and 0% fatigue damage. These results, added
t o the effects of the singleand tandem axles shown in Fig.
4 are not sufficient to require a design thickness increase.
*A tridem or triple axle is a set of three axles each spaced at 48 to 54in.
apart. These are used on special heavy-duty haul trucks.
**This is not to say that atridem hasthesameeffectasthreesingleaxles.
The damaging effects of tridem, tandem, and single axles are incorporated into their respective equivalent stress and erosion factor tables,
which in the sequence of the design steps is taken into account before
the charts for allowable-load repetitions are entered. This division by
three for tridems is made just to avoid the complexity of adding a third
scale on the charts for allowable-load repetitions.
Calculation of Pavement Thickness
--
project
/~/AT
Ax / e ~
T r ~ ath~ckness
l
1-70
Modulus of rupture, MR
Load safety factor LSF
:
load.
yes/^ n o
Doweled j o ~ n t s
Subbase-subgrade k
Mult~pl~ed
by
Concrete shoulder
ps~
Des~gnp e r ~ o dA years
/. 7
Expected
repetltlons
Allowable
repetlt~ons
LSF
L2
3
2
yes
Fat~gue,
percent
-Axles
x
/12
Damage.
percent
6
11. Equwalent stress-
5-9
Allowable
repet~t~ons
5
4
-
no r
/
pc~
7
13. E r o s ~ o nfactor
7,
,
12. stress ratlo factor A!GLZ~
3
Total
Total
0
ii A= adJd
rb &A&
skdruh
Fig. C1. Analysis of tridems.
Table C1. Equivalent Stress-Tridems
(Without Concrete ShoulderIWith Concrete Shoulder)
Slab
thickness,
5'. 3
k of subgrade-subbase, pcl
~ n .
50
100
150
200
300
500
700
4
4.5
51W431
439/365
456/392
380/328
437/377
359/313
428/369
349/305
419/362
339/297
414/360
331/292
41 2/359
328/291
/> fi++
Table C2. Erosion Factors-Trldems-Doweled
Joints
(Without Concrete ShoulderIWith Concrete Shoulder)
Slab
thickness,
~n.
k of subgrade-subbase, p c ~
50
100
200
300
500
700
Joints
Table C3. Erosion Factors-Tridems-Aggregate-Interlock
(Without Concrete ShoulderIWith Concrete Shoulder)
Slab
thickness,
~n.
4
4.5
k of subgrade-subbase, pci
50
100
200
300
500
700
4.06/3.50
3.95/3.40
3.97/3.38
3.85/3.28
3.88/3.30
3.76/3.18
3.82/3.25
3.70E.13
3.7413.21
3.6313.08
3.67/3.16
3.5613.04
APPENDIX D
Estimating Traffic Volume by Capacity
(Note: 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 theFH WA
"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 (ADT) is estimated by
a method based on the projected rates of traffic growth.
When the projected traffic volume is relatively high for a
specific project, this method should be checked by the
capacitymethod 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, profile, number and width of lanes, and area.
The term practical capacity is commonly used in reference to existing highways, and the term design capacity
is used for design purposes. Where traffic flow is uninterrupted-or nearly so-practical capacity and design
capacity are numerically equal and have essentially the
same meaning. In accordance with AASHTO usage'" 5 4 '
the term design capacity is used in this text. Design capacities for various kinds of multilane highways are summarized in Table Dl.
A D T Capacity of Multilane High ways
For thickness design it is necessary to convert the passenger cars per hour in Table D l to average daily traffic
in both directions, ADT. For multilane highways with
uninterrupted flow the following formula is used:
ADT
=
Table D l . Design Capacities for
Multilane Highways
Design capacity.
passenger cars'
per 12-ft lane
per hour
Type of hlghway
Urban freeways wlth full access control
(30 to 35 mph)
Suburban freeways with full access control
(35 to 40 mph)
Rural freeways wlth full or partlal access
control
- -
-
--
Rural major hlghways w ~ t hmoderate
cross trafflc and roadslde interference
Rural major h~ghwaysw ~ t hconsiderable
cross traffic and roadslde Interference
'Also Includes panels p ~ c k u p sand other four-tlre commerc~alvehlcles
that functlon as passenger cars In terms of trafflc capacity Values are
taken from References 53 and 54
j = number of passenger cars equivalent to one
truck
K
= 4 in rolling terrain
= 2 in level terrain
= design hour volume,
DHV, expressed as a
percentage of ADT
= 15% for rural freeways in this text
= 12% for urban freeways in this text**
D = traffic, percent, in direction of heaviest travel
during peak hours-about 50% to 75%
= 67% for rural freeways in this text
= 60% for urban freeways in this text
IOOP
x - 5000N
100 + T,hO- 1)
KD
where P = passenger cars* per lane per hour (from
Table D l )
N = number of lanes-total both directions
Tph = trucks, percent, during peak hours
= 213 ADTT in this booklet
*See footnote a t b o t t o m o f Table D l .
**See Reference 54, pages 96 t o 98, and Reference 56
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, Tph,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 capacity of two-lane highways are ( I ) 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 uninterrupted flow on two-lane highways is shown
in Table D2.
It is good practice t o use both traffic projection factors and design capacity for thickness design of specific
projects. For example, if a n existing two-lane route is carrying 4000 A D T and the projection factor is 2.7, the projected A D T would be 10,800. This is more than 4000
vehicles per day (vpd) greater than the design capacity of
virtually all two-lane highways.** On the other hand,
10,800 A D T is below the design capacity of most fourlane highways.7 Hence, the design should be made for
10,800 A D T on a four-lane roadway. Design capacity
should not be used where it shows a greater A D T than
shown by traffic projection.
*Lane widths of less than 12 ft are rarely used in current practice, except for very lightly traveled two-lane roads where Land service is a primary function.
**See Table D2.
tSee Reference 53, Table 11-14,
Table D2. Design Capacities for Uninterrupted Flow on Two-Lane Highways*
Terrain
Level
Design capac~ty,both directions. In vph"
where: L = lane w ~ d t hin feet
Tph =trucks, %. ~npeak h o u r t
Al~gnment,
percent of total
project length with
s ~ g h td~stance
of less than
1500 ft
0
10
20
0
10
20
0
10
20
0
20
40
900
860
800
780
750
700
690
660
620
770
740
690
670
640
600
600
570
530
690
660
620
600
580
540
530
510
480
L = 11
L = 12
Tph '
L
Tph '
= 10
Tph
'Source Reference 53. Table 1 1 10 page 88
"Tabular values apply where lateral clearance 1s not restr~cted Where clearance
apply factors In Reference 53 Table 11-11 page 89
t Trucks does not ~ n c l u d ef c u r - t ~ r eveh~cles
IS
less than 6 ft
'
APPENDIX E
References
I. Westergaard, H. M., "Computation of Stresses in
Concrete Roads," Highway Research Board Proceedings, Fifth Annual Meeting. 1925, Part I, 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," Highway Research Board Proceedings,
Seventh Annual Meeting, 1927, Part I, 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. Pickett, Gerald; Raville, Milion E.; Jones, WilliamC.;
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 Colley, 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., Colley, B. E., and Kapernick, J. W.,
"Tests to Evaluate Concrete Pavement Subbases,"
Proceedings of American Society of Civil Engineers,
Paper No. 1297, Vol. 83 (HW-3), July 1957, pages I to
41;. also PCA Development Department Bulletin
DXOI I.
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 1958; also PCA Development Department Bulletin DX021.
12. Childs, L. D., and Kapernick, J. W., "Tests of Concrete Pavements on Crushed Stone Subbases," Proceedings of American Society of Civil Engineers,
Proc. Paper No. 3497, Vol. 89 (HW-I), April 1963,
pages 57 to 80; 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 DX 125.
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 Colley, 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. Colley, B. E., and Humphrey, H. A., "Aggregate Interlock at Joints in Concrete Pavements," Highway
Research Board Record No. 189, Transportation Research Board, 1967, pages 1 to 18.
19. Colley, B. E., Ball, C. G., and Arriyavat, P., "Evaluation of Concrete Pavements with Tied Shoulders or
Widened Lanes," Transportalion Research Record
666, Transportation Research Board, 1978; also Port-
land Cement Association, Research and Development Bulletin RD065P, 1980.
20. Sawan, J. S., Darter, M. I., and Dempsey, B. J.,
"Structural Analysis and Design of PCC Shoulders,"
Report No. FHWA-RD-81-122, 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 Pittsburg, California, 19211922," California State Printing 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 1 E, 1962.
25. The AASHO Road Test, Highway Research Board
Special Report No. 73, 1962.
26. AASHTO Interim Guide for Design of Pavement
Structures, 1972, Chapter 111 Revised, 1981, American Association of State Highway and Transportation Officials, 1981.
27. Fordyce, Phil, and Teske, W. E., "Some Relationships of the AASHO Road Test to Concrete Pavement Design," Highway 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," Proceedings 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.
3 1. 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 1 196.
32. "Rigid Airfield Pavements," Corps of Engineers, U.S.
Army Manual, EM 1 1 10-45-303, Feb. 3, 1958.
33. Burmister, D. M., "The Theory of Stresses and Displacements in Layered Systems and Applications to
Design of Airport Runways," 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 ProceduresAppendix 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 Divided Highways," Public Roads, Vol. 30, No. 3, August 1958, pages 7 1 to 75.
41. Emery, D. K., Jr., "Paved Shoulder Encroachment
and Transverse Lane Displacement for Design Trucks
on Rural Freeways," 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-8016, Minnesota Department
of Transportation, Research and Development Office, July 1980.
43. Darter, M. I., "Structural Design for Heavily Trafficked Plain-Jointed Concrete Pavement Based on
Serviceability Performance," T R R 671, Analysis of
Pavement Systems, Transportation Research Board,
1978, pages 1 to 8.
44. Thickness Design for Concrete Pavements, Portland
Cement Association publication ISOIOP, 1974.
45. Kesler, Clyde E., "Fatigue and Fracture of Concrete,"
Stanton Walker Lecture Series of the Materials 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, 197 1,
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 198 1.
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.
52. Ruth, B. E., and Larsen, T. J., "Save Money with
Econocrete Pavement Systems," Concrete International, 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. XLVIII, No. 4, July 1964,
pages 67 to 92.
57. Packard, R. G., and Tayabji, S. D., "New PCA
Thickness Design Procedure for Concrete Highway
and Street Pavements," Proceedings of Third International Conference on Concrete Pavement Design
and Rehabilitation, Purdue University, April 1985.
Calculation of Pavement Thickness
Project
T r ~ ath~ckness
l
~n.
Doweled jo~nts:
yes
no
Subbase-subgrade k
PC1
Concrete shoulder. yes
no
Modulus of rupture. MR
PSI
Design penod
years
Load safety factor. LSF
Fat~gueanalys~s
Axle
load,
klps
Mult~pl~ed
by
LSF
1
2
Expected
repetitlons
Allowable
repetitions
4
3
Eros~onanalys~s
Fat~gue.
percent
5
8. Equ~valentstress
Allowable
repetlt~ons
Damage.
percent
6
7
10. Eros~onfactor
9. Stress ratlo factor
Single Axles
11. Equwalent stress
13. Eros~onfactor
12. Stress ratlo factor
Tandem Axles
I
Total
I
Total
I
\
I
Microcomputer Program for Thickness Design of
Concrete Highways, Streets, and Parking Lots
PCAPAV-the
low-cost software for concrete pavement design
PCAPAVs easy-to-use, menu-driven routine offers
High-speed solutions to pavement thickness design problems
Pavement fatigue and subbase erosion calculations
Comprehensive theory
Realistic design criteria
The computer program design procedures, based on this manual and verified by
performance, consider !oad transfer at transverse and longitudinal joints (doweled
or undoweled), concrete shoulders, curbs and gutters, and adjacent parking-lot
lanes.
Traffic load considerations are simplified. Any designer can choose a stored
traffic load category to fit the situation. Or available traffic load data can be input.
The software runs on IBM personal computers and compatibles (128K, DOS 2.0
or later), and the package includes a floppy diskette, the user's manual, and this
design manual, Thickness Design for Concrete Highway and Street Pavements.
To order PCAPAV (MCOO3),contact the Portland Cement Association, Order
Processing Department, 5420 Old Orchard Road, Skokie, IL 60077-1083,
(800)868-6733
PORTLAND CEMENT
ASSOCIATION
An organmation of cement manufadurento improve and extend the user of portland cement and concrete through market development, eng~neerlng,research. education, and
public aifdlrs work.
/
5420 Old Orchard Road, Skok~e,lll~no~s
60077-1083
Printed in U.S.A.
EB109.01P