PCA

.
Publication List
;
Book Contents
u
The author of thk engineering
bulletin is Robert G.
Packard, 1? E., principal paving engineer, Paving
Transportation
Department,
Portland Cement
Association.
This publication is intended SOLELY for use by PROF!3SIONAL
PERSONNEL who we competent to evaluate the si~ificance and
limitations of the information provided herein, and who wiff accept
total responsibility
for the application of this information.
The
Portland
Cement
Association
DISCLAIMS
any and all
RESPONSIBILITY and LIABILITY for the accuracy of and the application of the information contained in this publication to the fulf
extent permitted by law.
w
0 Portland Cement Asscwiation 1984, reprinted 1$95
Publication List
Book Contents
.—-
Thickness Design for
Concrete Highway and
Street Pavements
P
CONTENTS
Chapter I. Introduction . . . . . . . . . . . .
Applications of Design Procedures.
Computer Programs Available . . . .
Basis for Design . . . . . . . . . . . . . . . . .
Metric Version . . . . . . . . . . . . . . . . . .
Chapter 2. Design Factora . . . . . . . .
Flexural Strength of Concrete . . .
Subgrade and Subbase Support .
Design Period . . . . . . . . . . . . . . . .
Traffic . . . . . . . . . . . . . . . . . . . . . . .
Projection
.................
Capacity . . . . . . . . . . . . . . . . . . .
ADTT . . . . . . . . . . . . . . . . . . . . .
Truck Dkectional Dktribution
Axle-Load Dktribution
......
Load Safety Factors . . . . . . . . . . .
Chapter 3. Design Procedure
(Axle-Load Data Available) .
Fatigue Analysis . . . . . . . . .
Erosion Analysis . . . . . . . . .
Sample Problems . . . . . . . .
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Chapter 4. Simplified Design Procedure
(Axle-Load Data Not Available) . . . . . .
Sample Problems . . . . . . . . . . . . . . . .
Comments on Simplified Procedure .
Modulus of Rupture . . . . . . . . . . . .
Design Period . . . . . . . . . . . . . . . . .
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Publication List
Aggregate Interlock or Doweled Joints . . . . . ...30
User-Developed
Design Tables . . . . . . . . . . . . . . ...30
Appendix A. Development of Design
Procedure . . . . . . . . . . . . . . . . . . . . . . . . . .
Analysis of Concrete Pavements . . . . .
Jointed Pavements
..............
Continuously
Reinforced Pavements
Truck-Load
Placement . . . . . . . . . . . . .
Variation in Concrete Strength . . . . . .
Concrete Strength Gain with Age . . . .
Warping and Curling of Concrete . . . .
Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . .
Erosion . . . . . . . . . . . . . . . . . . . . . . . . . .
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Appendix B. Daaign of Concrete Pavements
with Lean Concrete Lower Course . . . . . . . . . . . . . ...36
fsan Ccmcrete Subbase . . . . . . . . . . . . . . . . . . . . ...36
Monolithic Pavement . . . . . . . . . . . . . . . . . . . . . . ...36
Appendix
C. Analysis of Tridem Axle Loads . . . . ...39
Appendix D. Estimating Traffic Volume
by Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...42
Appendix E. References . . . . . . . . . . . . . . . . . . . . . . ...44
Daaign Worksheet for Reproduction
Book Contents
. . . . . . . . . . . ...47
Figures
1. Flexural strength, age, and design relationships,
2. Approximate interrelationships
of soil classifications
and bearing values.
3. Proportion
of tmcks in right lane of a multilane
divided highway.
4, Design 1A.
5. Fatigue analysis—allowable
load repetitions based
on stress ratio factor (with and without concrete
shoulders).
6a. Erosion analysis—allowable
load repetitions based
on erosion factor (without concrete shoulder).
6b. Erosion analysis—allowable
load repetitions based
on erosion factor (with concrete shoulder).
7. Design 1D,
8. Design 2A.
A 1. Critical axle-load positions.
A2. Equivalent edge stress factor depends on percent of
trucks at edge.
A3. Fatigue relationships.
BI. Design chart for composite concrete pavement (lean
concrete subbase),
B2. Design chart for composite
concrete
pavement
(monolithic with lean concrete lower layer).
B3. Modulus of rupture
Cl. Analysis of tridems,
versus
compressive
strength.
13b. Allowable ADT”f, Axle-Load Category 3—Pavements with Aggregate-Interlock
Joints
14a. Allowable ADTT, Axle-Load Category 4—Pavements with Doweled Joints
14b. Allowable ADl_f, Axle-Load Category 4—Pavements with Aggregate-Interlock
Joints
15. Axle-Load Dktribution
Used for Preparing Design
Tables 11 Through 14
Cl. Equivalent Stress — Tridems
C2. Erosion Factors — Tridems — Doweled Joints
C3. Erosion Factors — Tridems — Aggregate-Interlock
Joints
D 1. Design Capacities for Multilane Highways
D2. Design Capacities for Uninterrupted
Flow on TwoLane Highways
us.
3
customary
Metric
unit
unit
in.
ft
mm
m
lb
lbf
kip
lb/in.x
lb/ in.x (k value)
kg
N
kN
kPa
MPa/m
U
Conversion
coefficient
25.40
0.305
0.454
4.45
4.45
6.89
0.271
Tables
1. Effect of Untreated Subbase on k Values
2. Design k Values for Cement-Treated
Subbase
3. Yearly Rates of Traffic Growth and Corresponding
Projection Factors
4. Percentages of Four-Tke Single Units and Trucks
(ADTT) on Various Highway Systems
5. Axle-Load Data
6a. Equivalent Stress-No
Concrete Shoulder
6b. Equivalent Stress-Concrete
Shoulder
7a. Erosion Factors—Doweled
Joints, No Concrete
Shoulder
7b. Erosion Factors—Aggregate-Interlock
Joints, No
Concrete Shoulder
8a. Erosion Factom—Doweled
Joints, Concrete
Shoulder
8b. Erosion
Factors—Aggregate-Interlock
Joints,
Concrete Shoulder
9. Axle-Load Categories
10. Subgrade Soil Types and Approximate k Values
11. Allowable ADTT, Axle-Load Category 1—Pavements with Aggregate-Interlock
Joints
12a. Allowable AD’IT, Axle-Load Category 2—Pavements with Doweled Joints
12b. Allowable ADTT, Axle-Load Category 2—Pavements with Aggregate-Interlock
Joints
13a. Allowable ADTT, Axle-Load Category 3—Pavements with Doweled Joints
L-J
2
Publication List
Book Contents
CHAPTER 1
Introduction
P
P
This bulletin deals with methods of determining
slab
thicknesses adequate to carry traffic loads on concrete
streets, roads, and highways,
The design purpose is the same as for other engineered
structures—to
find the minimum thickness that will result in the lowest annual cost as shown by both first cost
and maintenance costs. If the thickness is greater than
needed, tbe pavement will give good service with low
maintenance costs, but first cost will be high. If the thickness is not adequate, premature and costly maintenance
and interruptions in traffic will more than offset the lower
first cost. Sound engineering requires thickness designs
that properly balance first cost and maintenance costs.
While this bulletin is confined to the topic of thickness
design, other design aspects are equally important to ensure the performance and long life of concrete pavements.
These include—
● Provision
for reasonably uniform support. (See Subgrades ond Subbases for Concrete Pavements,*)
● Prevention
of mud-pumping
with a relatively thin
untreated
or cement-treated
subbase on projects
where the expected truck traffic will be great enough
to cause pumping. (The need for and requirements of
subbase are also given in the booklet cited above. )
● Use of a joint
design that will afford adequate load
transfeq enable joint sealants, if required, to be effective; and prevent joint distress due to infiltration.
(See Joint Design for Concrete Highway and Street
Pavements.** )
● Use of a concrete
mix design and aggregates that will
provide quality concrete with the strength and durability needed for long fife under the actual exposure
conditions.
(See Design and Control of Concrete
Mixrf4re$.T)
The thickness design criteria suggested are based on
general pavement performance experience. If regional or
local specific performance experience becomes available
for more favorable or adverse conditions, the design criteria can be appropriately
modified. This could be the
case for particular climate, soil, or drainage conditions
and future design innovations.
Applications
The
design
of Design Procedures
procedures
given
in this text apply
to the fol-
doweled,
reinforced, and continuously
reinforced.
Plain pavements are constructed without reinforcing
steel or doweled joints. Load transfer at the joints is obtained by aggregate interlock between the cracked faces
below the joint saw cut or groove. For load transfer to be
effective, it is necessary that short joint spacings be used.
Plain-doweled pavements are built without reinforcing
steeb however, smooth steel dowel bars are installed as
load transfer devices at each contraction joint and relatively short joint spacings are used to control cracking.
Reinforced pavements contain reinforcing steel and
dowel bars for load transfer at the contraction joints. The
pavements are constructed
with longer joint spacings
than used for unreinforced pavements. Between the joints,
one or more transverse cracks will usually develop; these
are held tightly together by the reinforcing steel and good
load transfer is provided.
Commonly used joint spacings that perform well are 15
ft for plain pavements,tt
not more than 20 ft for plaindoweled pavements, and not more than about 40 ft for
reinforced pavements. Joint spacings greater than these
have been used but sometimes
greater spacing causes
pavement distress at joints and intermediate cracks between joints.
Continuously
reinforced pavements are built without
contraction joints, Due to the relatively heavy, continuous-steel reinforcement
in the longitudinal
direction,
these pavements develop transverse cracks at close intervals. A high degree of load transfer is developed at these
crack faces held tightly together by steel reinforcement.
The design procedures given here cover design conditions that have not been directly addressed before by
lowing
types
‘Portland
**portl..d
of concrete
pavements:
Cement As$o.iation
@nent Association
plain,
publication
publication
plain
1S029F’
1S059P.
tPortle.”d Cement Aswwiaticm publication EBOOIT.
TtFor very thin pavements, a 15-ft joint spacing may beexcessive–sw
the afor.sme”tioned
PCA publication . . joint desigm
3
Publication List
Book Contents
other procedures.
These include recognition of—
1, The degree of load transfer at transverse joints provided by the different pavement types described.
2. The effect of using a concrete shoulder adjacent to
the pavement; concrete shoulders reduce the flexuraI stresses and deflections caused by veh]cle loads,
3. The effect of using a lean concrete (econocrete) subbase, which reduces pavement stresses and defections, provides considerable
support when trucks
pass over joints, and provides resistance to subbase
erosion caused by repeated pavement deflections.
4. Two design criteria (a) fatigue, to keep pavement
stresses due to repeated loads with]n safe limits and
thus prevent fatigue cracking
and (b) erosion, to
limit the effects of pavement deflectionsat slab edges.
joints, and corner; and thus control the erosio~ of
foundation and shoulder matefiak. The criterion for
erosion is needed since some modes of pavement
distress such as pumping, faulting, and shoulder
distress are unrelated to fatigue,
5. Triple axles can be considered in design. While the
conventional
single-axle and tandem-axle
configurations are still tbe predominant loads cm highways,
use of triple axles (tridems) is increasing. They are
seen on some over-the-road
trucks and on special
mads used for hauling coal or other minerals. Tridems may be more damaging from an erosion criterion (deflection) than from a fatigue criterion,
Selection of an adequate thickness is dependent upon
the choice of other design features—jointing
system, t ype
of subbase if needed, and shoulder type.
Wkh these additional design conditions, the thickmss
requirements of design alternatives, which influence cost,
can lx directly compared.
Chapter 2 describes how the factors needed for solving
a design problem are determined. Chapter 3 details the
full design procedure that is used when specific axle-loaddistribution
data are known or estimated.
If detailed
axle-load data are not available, the design can be accomplished as described in Chapter 4, by the selection of one
of several categories of data that represent a range of
pavement facilities varying from residential streets up to
busy interstate highways.
Computer
Programs Available
Thickness design problems can be worked out by hand
with the tables and charts provided here or by computer
and microcomputer
with programs that are available
from Portland Cement Association.
1. Theoretical
studies of pavement slab behavior by
Westergaard,{ ‘-’)* Pickett and Ray,(G ‘land reCent]y
developed finite-element computer analyses, one of
which is used as the basis for this design procedure. [81
2. Model and full-scale tests such as Arfington Tests(9]
and several research projects conducted b? PCA and
other agencies ofl$~$bases,( ‘*’S)joints( ’d- ‘]and concrete shoulders.
3. Experimental pavements subjected to controlled test
traffic, such as the Bates Test Road,[2’] the Pktsburg Test Highway~22) the Mar$and
R6ad Test~231
the AASHO** Road Test, {24-2) and studies of inservice highway pavements made by various state
departments
of transportation.
4. The performance
of normally constructed
pavements subject to normal mixed traffic.
All these sources of knowledge are useful. However,
the knowledge gained from performance
of normally
constructed
pavements is the most important. Accordingly, it is essential to examine the relationship between
the roles that performance
and theory play in a design
procedure, Sophisticated
theoretical methods developed
in recent years permit the responses of the pavement—
stresses, deflections, pressures—to
be more accurately
modeled. This theoretical analysis is a necessary part of
a mechanistic design procedure, for it allows consideration of a full range of design-variable
combkations.
An
important second aspect of the design procedure is the
criteria applied to the theoretically computed values—
the limiting or allowable values of stress, deflection, or
presmre. Defining the criteria so that design results are
related to pavement performance experience and research
data is critical in developing a design procedure,
The theoretical parts of the design procedures given
here are based on a comprehensive
analysis of concrete
stresses and deflections by a finite-element computer prodesign
gram. co The program ~odcls the conventional
factors of concrete properties, foundation support, and
loadings, plus joint load transfer by dowels or aggregate
interlock and concrete shoulder, for axle-load placements
at slab interior, edge, joint, and corner.
The criteria for the design procedures are based on the
pavement design, performance,
and research experience
referenced above including relationships to performance
of avements at the AASHO Road Test{ z’) and to studi~~~~ 29, of the faulting of pavements.
More information on development and basis of the design procedure is given in Appendix A and Reference 30.
‘i-.’J
‘u
Metric Version
A metric version of this publication is also available from
Portland Cement Association—publication
EB209P.
Basis for Design
The thickness design methods presented here are based
on knowledge of pavement theory, performance, and research experience from the following sources:
*Supemcript numbers in parentheses denote references at the end of
thk text.
**Nw the American Association of State Hishway and Transportation Officials (AASHTO).
d
4
Publication List
Book Contents
CHAPTER 2
Design Factors
P
After selection of the type of concrete pavement (plain
pavement with or without dowels, reinforced jointed
pavement with dowels, or continuously reinforced pavement), type of subbase if needed, and type of shoulder
(with or without concrete shoulder, curb and gutter or
integral curb), thickness design is determined hased on
four design factors:
1. Flexural
strength
of the concrete
(modulus
of rupture, MR)
2. Strength of the subgrade, or subgrade and subbase
combination
(k)
3. The weights, frequencies, and types of truck axle
loads that the pavement will carry
4. D&ign period, which in this and other pavement design procedures is usually taken at 20 years, but may
be more or less
These design factors are discussed in more detail in the
following sections. Other design considerations
incorporated in the procedure are discussed in Appendix A.
Flexural Strength of Concrete
F-
Consideration
of the flexural strength of the concrete is
a,ppficable in the design procedure for the fatigue criterion, which controls cracking of the pavement under
repetitive truck loadings.
Bending of a concrete pavement under axle loads produces both compressive and flexural stresses. However,
the ratios of compressive stresses to compressive strength
are too small to influence slab thickness design. Ratios of
flexural stress to flexural strength are much higher, often
exceeding values of 0.5. As a result, flexural stresses and
flexural strength of the concrete are used in thickness design. Flexural strength is determined by modulus of rupture tests, usually made on 6x6x30-in. beams.
For specific projects, the concrete mix should be designed to give both adequate durability and flexural
strength at the lowest possible cost. Mix design procedures are described in the Portland Cement Association
publication Design and Control of Concrete A4ixt ures.
The modulus of rupture can be found by cantilever,
center-point,
or third-point
loading. An important difference in these test methods is that the third-point test
shows the minimum strength of the middle third of the
test beam, while the other two methods show strength at
only one point. The value determined by the more conservative thkd-point method (American Society for Testing and Materials, ASTM C78)isused
fordesign in this
procedure.*
Modulus of rupture tests are commonly made at 7, 14,
28, and90days.
The 7-and 14daytest
results arecompared with specification requirements for job control and
for determining when pavements can be opened to traffic.
The 28-day test results have been commonly used for
thickness design of highway sand streets and are recommended for use with this procedure; 90day results are
used forthedesign
of airfields. These values are used because there arevery fewstress repetitions during the first
28 or 90 days of pavement life as compared to the millions
of stress repetitions that occur later.
Concrete continues to gain strength with age as shown
in Fig. 1. Strength gain isshown bythesolid curve, which
represents average MR values for several series by laboratory tests, field-cured test beams, and sections of concrete taken from pavements in service.
fn this design procedure theeffects** ofvafiationsin
concrete strength from point to point in the pavement
and gains in concrete strength with age are incorporated
in the design charts and tables. The designer does not directly apply these effects but simply inputs the average
28-day strength value.
*Fora standard 30-in. beam, c.nlcr-point-load
inEtcst val.es will be
about 75 psi higher, and cantilever-loading
1.s1 values.bout
160 psi
higher than cticrd-p.int-loa$ i.g test values. Th.x higher values are not
i“te”ded tok.sdfor
deszgnpurposts.
Iftbese other test methods are
used, adowmvard
adjustment should be made byestabtisbing acorrelationto thtrd-poi.t-load
test values.
..’IIe,e
effects are discussed in Appendix A.
5
Publication List
Book Contents
Table 1. Effect of Untreated
on kValues,
S.::;;$
pci ‘
50
100
200
300
Subbase
Subbase k value, pci
4 in,
6 in.
65
130
220
320
75
140
230
330
I
9 i“.
12 in.
65
160
270
370
110
190
320
430
“O
Table 2. Design k Values for CementTreated Subbases
Am
Fig. 1. Flexural strength, age, and design relationships.
Subgrade and Subbaae Support
The support given to concrete pavements by the subgrade,
and the subbase where used, is the second factor in thickness design. Subgrade and subbase support is defined in
terms of the Westergaard modulus of subgrade reaction
(k). It is equal to the load in pounds per square inch on a
loaded area (a 30-in. diameter
plate) divided by the deflection in inches for that load. The k values are expressed
as pounds per square inch per inch (psi/ in,) or, more
commonly, as pounds per cubic inch (pci). Equipment
and procedures for determining
k values are given in
References 31 and 32.
Since the plate-loading test is time consuming and expensive, the k value is usually estimated hy correlation to
simpler tests such as the California Bearing Ratio (CBR)
or R-value tests. The result is valid became exact determination of the k value is not required; normal variations
from an estimated value will not appreciably affect pavement thickness requirements. The relationships shown in
Fig. 2 are satisfactory for design purposes,
The AASHO Road Test{ 241gave a convincing demo”.
stration that the reduced subgrade support during thaw
periods has little or no effect on the required thickness
of concrete pavements. This is true because the brief periods when k values are low during spring thaws are more
than offset by the longer periods when tbe subgrade is
frozen and k values are much higher than assumed for
design, To avoid the tedious methods required to design
for seasonal variations in k, normal summer- or fa[/weaher
k wlues are used as reasonable
mea” values
It is not economical to me wmeated subbases for the
sole purpose of increasing k values. Where a subbase is
used,* there will be an increase in k that should be used
in the thickness design, If the subbase is an untreated
granular material, the approximate
increase in k can be
taken from Table 1.
The values shown in Table 1 are based on the Burmister[’3) analysis of two-layer systems and plate-loading
tests made to determine k values on subgrades and subbases for full-scale test slabs.( ‘4]
Cement-treated
subbases are widely used for heavyduty concrete pavements.
They are constructed
from
AASHTO Soil Classes A- 1, A-2-4, A-2-5, and A-3 gronu[ar materials. The cement content of cement-treated
subbase is based on standard ASTM laboratory freeze-thaw
and wet-dry tests(~’ 35)and PCA weight-loss criteria. [36]
Other procedures that give an equivalent qualit y of material can be used. Design kvalues forcement-treated
subbases meeting these criteria are given in Table 2.
In recent years, the use of lean concrete subbases has
been ontheincrease.
Thickness design ofconcretepavements on these very stiff subbases represents a special
case that is covered in Appendix B.
Design Period
The term design period is used in this publication rather
than pavement lije, The latter is not subject to precise
definition.
Some engineers and highway agencies consider the life of a concrete pavement ended when the first
overlay is placed. The life of concrete pavements may
vary from less than 20 ycarson some projects that have
carried more traffic than originally estimated or have had
design, material, or construction defects to more than 40
years on other projects where defects are absent,
The term design period is sometimes considered to be
synonymous with the term traffic-malysis period, Since
traffic can probably not be predicted with much accuracy
fora Iongerperiod,
a design period of 20yearsiscommonly used in pavement design procedures.
However,
there are often cases where useofashorter
orlonger design period may be economically justified, such as a special haul road that will be used foro”ly afewyears,
ora
*UW .fs.bbaseis xc. remended f.rpr.jects where conditions that
would cause nmd-p.mpi”g prevaik for diwmim
of whm subbases
sh.uldbeuwda.d
h.wthi.k they sh.uldb., se the PCAp.blicati.n,
Subgrades ond Subbasesfor Ccmc,,,e Pavemenm.
6
Publication List
~
Book Contents
.
“u’
Publication List
Book Contents
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premium facility for which a high level of performance
for a long time with little or no pavement maintenance is
desired. Some engineers feel that thedesign
period for
rural and urban highways should heinthe range of Xtto
35 years.
The design period selected affects thickness design
since it determines how many years, and thus how many
trucks, thepavement
must serve. Selection ofthcdesign
period for a specific project is based on engineering judgment and economic analysis of pavement costs and service provided throughout
the entire period.
Traffic
Tbe numbers and weights ofheavy axle loads expected
during thedesign
life are major factors in the thickness
design of concrete pavement. These are derived from estimates of
—ADT (average daily traffic in both directions, all
vehicles)
—ADTT (average daily truck traffic in both directions)
—axle loads of trucks
Information
on ADTis obtained from special traffic
counts or from state, county, or cit y traffic-volume maps.
This ADT is called the present or current ADT. The de.
sign ADT is then estimated by the commonly used meth.
ods discussed here. However, any other method that gives
a reasonable estimate of expected traffic during the design
life can be used,
Projection
One method forgetting
thetraftlc
volume data (design
ADT) needed is to use yearly rates of traffic growth and
traffic projection factors. Table 3 shows relationships between yearly rates of growth and projection factors for
both 20- and 40-year design periods.
In a design problem, the projection factor is multiplied
by the present ADT to obtain a design ADT representing
theaverage
value forthedcsign
period. Insomeprocedures, this is called AADT (average annual daily traffic).
The following fact ors influence yearly growth rates and
traffic projections:
1. Attracted or diverted traffic-the
increase over existing traffic because of improvement
of an existing
road way.
2. Normal traffic growth—the increase due to increased
numbers and usage of motor vehicles.
3. Generated traffic-the
increase due to motor vehicle
trips that wnuld not have been made if the mw facil.
ity had not been constructed.
4. Development traffic-the
increase due to changes in
land use due to construction
of the new facifity.
The combined effects will cause annual growth rates of
about 2Yoto 6%. Tbeserates correspond to20-yeartrafficprojection
factors of 1.2to 1.8asshown
in Table3,
The planning survey sections of state highway departmerits are very use fulsources ofknowledge
about traftic
grnwth and projection factors.
Table 3. Yearly Rates of Trafffc
Growth and Corresponding
Projection Factora’
Yearly
rate of
traffic
gro;th,
1~%
2
2,%
3
3,%
4
4M
5
5%
6
Prg:;ecron
1,1
1.2
1.2
1.3
1.3
1.4
1.5
1,6
1.6
1.7
1.8
40 yea~s
1.2
1.3
1.5
1.6
1.8
2,0
2.2
2.4
2.7
2.9
3.2
,Faclor. represent values at the middesig” period
that are widely used incurre”t pr.ctke, Another
mtihod of cmnp.fing these factors is based on the
averaae annual value. Differences (bothcompound
intere<t) between these two methods will ”rarely
affect design.
Where there is some question shout the rate of growth,
it may be wise to use a fairly high rate. This is true on
intercity routes andon urban projects where ahigh rate
of urban growth maycause ahlgher-than-expected
rate
oftraftic growth. However, thegrowth oftruck volumes
may be less than that for passenger cars.
High growth rates do not apply on two-lane-rural roads
and residential streets where the primary function is land
useorabutting
property service. Their growth rates may
be below 2% per year (projection factors of 1.1 “to 1.3).
Snme engineers suggest that the use of simple interest
growth rates may be appropriate,
rather than compound
interest rates, which when used with a long design period
may predict unrealistically
heavy future traffic.
“u’
Capacity
The other method of estimating design ADT is based on
capacity—the
maximum number of vehicles that can use
the pavement without unreasonable
delay. Tbis method
of estimating the volume of traffic is described in Appendix D and should be checked for specific projects where
the projected traffic volume is high; more traffic lanes
may be needed if reasonable traffic flow is desired.
ADTT
The average daily truck traffic in both directions (ADTT)
is needed in the design procedure. It may be expressed as
a percentage of ADT or as an actual value. The ADTT
value includes only trucks with six tires or more and does
not include panel and pickup trucks and other four-tire
vehicles.
The data from state, county, or city traffic-volume
maps may include, in addition to ADT, the percentage of
8
Publication List
L--’”
Book Contents
._
~
p
trucks from which ADTT can be computed.
For design of major Interstate and primary system
projects, the planning survey sections of state departments of transportation
usually make specific traffic surveys, These data are then used to determine the percentage relationship between ADT’T and ADT.
ADTT percentages and other essential traffic data can
also be obtained from surveys conducted by the highway
department at specific locations on the state highway system. These locations, called Ioadometer stations, have
been carefully selected to give reliable information
on
traffic composition,
truck weights, and axle loads. Survey results are compiled into a set of tables from which
the ADTT percentage can be determined for the highway
classes within a state. This makes it possible to compute
the ADTT percentage for each station. For example, a
highway department Ioadometer table (Table w-3) for a
Midwestern state yields the following vehicle count for a
Ioadometer station on their Interstate rural system:
All vehicles—ADT
. . . . . . . . . . . . . . . . . . . . ...9492
Trucks:
All single units and combinations
. . . . . ...1645
Panels and pickups . . . . . . . . . . . . . . . . . . . 353
Other four-tire single units . . . . . . . . . . . . 76
Therefore,
It is important to keep in mind that the ADTT percentages in Table 4 are average values computed from many
projects in all sections of the country. For this reason,
these percentages are only suitable for design of specific
projects where ADTT percentages are also about average.
For design purposes, the total number of trucks in the
design period is needed. This is obtained by multiplying
design ADT by ADTT percentage divided by 100, times
the number of days in the design period (365 X design
period in years).
For facilities of four lanes or more, the ADTT is adjusted by the use of Fig, 3.
for this station:
T* = ]645 – (353 + 76) = 1216
‘DTT
,0
1216
‘ ZY2x
’00=
‘3%
This ADTT percentage would be appropriate
for de.
sign of a project where factors influencing the growth and
composition
of traffic are similar to those at this loadometer station.
Another source of information on ADTT ercentages
!’37)
Table 4,
is the National
Truck Characteristic
Report.
which is taken from this study, shows the percentages of
four-tire single units and trucks on the major highway
systems in the United States. The current publication,
which is updated periodically, shows that two-axle, fourtire trucks comprise between 40’% to 65% of the total
number of trucks, with a national average of 49% It is
fikely that the lower values on urban routes are due to
larger volumes of passenger cars rather than fewer trucks.
PROPORTIONOF TRuCKS IN RIGHT LANE
Fig. 3. Proportion of trucks in right lane of a multilane
divided highway. (Derived from Reference 3&)
‘Tr.cks-xcludes
panels and pickups and other f. .r-ti r. vehiclcs.
Table 4. Percentage
of Four-Tire Single Units and
Trucks (ADTT) on Varioua Highway Systems
.m
I Rural average daily traffic
I Urban average daily traffic
9
Publication List
Book Contents
Truck Directional
Distribution
In most design problems, it is assumed that the weights
and volumes of trucks traveling in each direction are fairly
equ81-50-50
distribution-the
design essumes that pavement in each dirsction carries half the total ADTT. Thk
may not be true in special cases where many of the trucks
may be hauling full loads in one direction and returning
empty in the other direction. If such is the case, an appropriate adjustment is made.
Axie-Load
Oiatribufion
Data on the axle-load distribution of the truck traffic is
needed to compute the numbers of single and tandem
axles* of various weights expected during the design per.
iod. These data can be determined in one of three ways:
(1) special traffic studies to establish the loadometerdata
for the specific project; (2) data from the state highway
department’s Ioadometer weight stations (Table W4) or
weigh-in-motion
studies on routes representing
truck
weights and types that are expected to be similar to the
project under design; (3) when axle-load distribution
data are not available, methods described in Chapter 4
based on categories of representative
data for different
types of pavement facilities.
The use of axle-load data is illustrated in Table 5 in
which Table W4 data have been grouped by 2-kip and
4-kip increments for single- and tandem-axle
loads, re.
spectively. The data under the heading “Axles per 1000
Trucks” are in a convenient form for computing the axleIoad distribution, However, an adjustment must be made,
Column 2 of Table 5 gives values for all trucks, including
the unwanted values for panels, pickups, and other fourtire vehicles. To overcome this difficulty, the tabulated
values are adjusted as described in the Table 5 notes,
Column 4 of Table 5 gives the repetitions of various
single- and tandem-axle loads expected during a 20-yeardesign period for the Design 1 sample problem given in
Chapter 3.
Load Safety Factors
In the design procedure, the axle loads determined in the
previous section are multiplied by a load safety factor
(LSF). These load safety factors are recommended:
● For
Interstate and other multilane projects where
there will be uninterrupted
traffic flow and high volumes of truck traffic, LSF = 1.2.
● For highways
and arterial streets where there will be
moderate volumes of truck traffic, LSF = 1, 1.
● For roads,
residential streets, and other streets that
will carry small volumes of truck traffic, LSF = 1.0.
Aside from the load safety factors, a degree of conservatism is provided in the design procedure to compensate
Table 5. Axle-Load
Data
~
~ngle
L-J
axles
2a30
0.28
0.58
6,310
2&28
0.65
1.35
14,690
24-26
1.33
2.77
30,140
22-24
2.84
5.92
64,410
2W22
4.72
9.83
106,900
1&20
10.40
21.67
235,800
16-18
13.56
28.24
307,200
14-16
18.64
38,83
422,500
12-14
25.69
53,94
586,900
1}12
81.05
168,85
,637,000
Tandem axles
48-52
44-48
I
0.94
I
1.89
21,320
42,670
4s44
5.51
11,48
124,800
36-40
16.45
34.27
372,900
32-36
39.06
81,42
885,800
28-32
41.06
65.54
930,700
24-28
73,07
152.23
1,656,000
20-24
43.45
90.52
984,900
15-20
54,15
112.81
1,227,000
12-16
59,85
124.69
1,356,000
Columns 1 and 2derived from Ioadometer W-4 Table. This table al$oshows
13,215 tolal trucks coumed with 6,916 two-axle, four-tire trucks (52%].
Column 3 Column 2 values adjusted for two.wle,
to Column 2/[1
52/100).
four-tire trucks equal
Column 4 = Col. rnn3X [tr.cksindesig”
period ))1000. %esmnpleproblem,
Design 1, In which trucks in design period (onedirection) tolal 10,880,000,
for such things as unpredicted truck overloads and normal construction
variations in material properties and
layer thicknesses. Above that basic level of conservatism
(LSF = 1.0), the load safety factors of 1.1 or 1,2 provide
a greater allowance for the possibility of unpredicted
heavy truck loads and volumes and a higher level of pavement serviceability
appropriate
for higher type pavement facilities.
In special cases, the use of a load safet y factor as high as
1.3 may be justified to maintain a higher-than-normal
level of pavement serviceability throughout
the design
period. An example is a very busy urban freeway with no
alternate detour routes for the traffic. Here, it may be
better to provide a premium facility to circumvent for a
long time tbe need for any significant pavement maintenance that would disrupt traffic flow.
*See Appendix C if it isexpected that trucks with tridem loads will be
included i“ the traffk f.tecast.
10
Publication List
1.96
3.94
Book Contents
CHAPTER 3
Design Procedure
(Axle-Load Data Available)
P
The methods in this chapter are used when detailed axleload distribution
data have been determined or estimated
as described in Chapter 2.*
Fig. 4 is a worksheet** showing the format for corn.
pleting design problems.t
It requires as input data the
following design factors discussed in Chapter 2.
● Type of joint
and shoulder
● Concrete
flexural strength (MR) at 28 days
● k value
of the subgrade or subgrade and subbase
combination?
● Load safety factor
(LSF)
● Axle-load
distribution
(Column 1)
● Expected
number of axle-load repetitions during
the design period (Column 3)
Both a fatigue analysis (to control fatigue cracking)
and an erosion analysis (to control foundation and shoulder erosion, pumping, and faulting) are shown on the design worksheet.
The fatigue analysis will usually control the design of
light-traffic pavements (residential streets and secondary
roads regardless of whether the joints are doweled or not)
and medium traffic pavements with doweled joints.
The erosion analysis will usually control the design of
medium- and heavy-traffic pavements with undoweled
(aggregate-interlock)
joints and heavy-traffic pavements
with doweled joints.
For pavements carrying a normal mix of axle weights,
single-axle loads are usually more severe in the fatigue
analys]s, and tandem-axle loads are more severe in the
erosion analysis.
The step-by-step design procedure is as follows: The
design input data shown at the top of Fig. 4 are established and Columns 1 and 3 are tilled out. The axle loads
are multiplied by the load safety factor for Column 2.
2, Divide these by the concrete modulus of rupture and
enter as items 9 and 12.
3. FII1 in Column 4, “Allowable Repetitions;
deter.
mined from Fig. 5.
4. Compute Column 5 by dividing Column 3 by Column 4, multiplying by 100 then total the fatigue at
the bottom.
Erosion Analysis
Without concrete shoulder
● Doweled
joints or continuously
reinforced
pavements# —use Table 7a and Fig. 6a.
● Aggregate-interlock
joints—use Table 7b and Fig.
6a,
With concrete shoulder
● Doweled
joints or continuously
reinforced pavements~—use Table 8a and Fig. 6b.
● Aggregate-interlock
joints—use Table 8band Fig, 6b.
Procedure Steps:
1. Enter the erosion factors from the appropriate
as items 10 and 13 in the worksheet.
2. FIO in Column 6, “Allowable Repetitions,”
Fig. 6a or Fig. 6b.
table
from
*% Chapter 4 when axle-load distribution data are unknown.
.* A b]a”k ~0 rkshect is provided as the M page Of thk bulletin for
Fatigue Analysis
~
Without concrete shoulder, use Table &z and Fig. 5
. With concrete shoulder, use Table 6b and Fig. 5
Procedure Steps:
1. Enter as items 8 and 11 on the worksheet from the
aPPr~Priate
table the equivalent stress factors depending on trial thickness and k value.
●
Results of fatigue analysis, and thus the charts and figures
used, are the same for pavements with doweled and undoweled joints, and also for continuously
reinforced
pavements.~
p.rposes of reproduction and use in w=ific design problems.
f Computer programs for s.lving design problems are available fr.m
P.rtlmd Cement Ass.ciati.n.
ItSee Appendix B if lean concrete subbase is used.
$1. this design procedure, ccmtin”cwsly reinforced pavemems are
treated the same as dowdcd, jointed pavements—see Appendix A.
11
Publication List
Book Contents
Calculation
Project
Trial
A/
0~
thickness
Subbase-subgrade
k
/,4
&.#T-
e
/QA
Thickness
L7A?r./&/.
P&z2/’
9.5
in.
Doweled
/.70
pci
Concrete shoulder:
o
Modulus of rupture, MR
L5
Load safetv factor. LSF
/. Z?
r
of Pavement
psi
joints:
yes
K
no —
yes —no~
Design period ~
years
I
I
I
Axle
load,
hips
L
1
Single Axles
8. Equivalent stress
206
9. Stress rcatiofactor
O
10. Erosion factor
2.59
? 17
u’
11. Equivalent stress
Tandem Axles
192
13. Erosion factor
z.
T?
12. Stress ratio factor Z?Jl$K_
u
Fig. 4. Design 1A.
12
Publication List
Book Contents
3. Compute Column 7 by dividing Column 3 by Column 6, multiplying by lW, then total the erosion
damage at the bottom,
In the use of the charts, precise interpolation
of allowable repetitions is not required. If the intersection line
runs off the top of the chart, the allowable load repetitions are considered to be unlimited.
The trial thickness is not an adequate design if either of
the totals of fatigue or erosion damage are greater than
100%, A greater trial thickness should be selected for
another run, * A lesser trial thickness is selected if the
totals are much lower than 100Yo.
Sample Problems
Two sample problems are given to illustrate the steps in
the design procedure and the effects of alternate designs.
Design 1 is for a four-lane rural Interstate project; several
variations on the design—use of dowels or aggregateinterlock joints, use of concrete shoulder, granular and
cement-treated
subbases—are
shown as Designs 1A
through 1E. Design 2 is for a low-traffic secondary road,
and variations are shown as Designs 2A and 2B.
Design 1
Project and Traffic Data:
Four-lane Interstate
Rolling terrain in rural location
Design period = 20 years
Current ADT = 12,900
Projection factor = 1.5
ADTT = 19% of ADT
Traffic Calculations:
Desien ADT = 12.900 X 1.5 = 19,350 (9675 in one dire;tion)
ADTT = 19,350 X0.19= 3680 (1840 in one direction)
For 9675 one-direction
ADT, Fig. 3 shows that the
proportion of trucks in the right lane is 0.81. Therefore,
for a 20-yeardesign
period, the total number of trucks in
one direction is
1840 X 0.81 X 365 X 20 = 10,880,000 trucks
Axle-load data from Table 5 are used in this design
example and have been entered in Fig. 4 under the maximum axle load for each group.
Values Used to Calculate Thickness:**
Design 1A: doweled joints, untreated subbase, no concrete shoulder
Clay subgrade, k = 100 pci
4-in. -untreated subbase
Combined k = 130 pci (see Table 1)
LSF = 1.2 (see page 10)
Concrete MR = 650 psi
Design lB doweled joints, cement-treated
subbase, no
concrete shoulder
Same as 1A except:
4-in. cement-treated
subbaset
Combined k = 280 pci (see Table 2)
Design lC: doweled joints, untreated subbase, concrete
shoulder
Same as 1A except:
Concrete shoulder
Design ID: aggregate-interlock
joints, cement-treated
subbase, no concrete shoulder
Same as 1B except:
Aggregate-interlock
joints
Design lE: aggregate-interlock
joints, cement-treated
subbase, concrete shoulder
Same as 1D except:
Concrete shoulder
Thickness Calculations:
A trial thickness is evaluated by completing the design
worksheettt
shown in Fig. 4 for Design 1A using the
axle-load data from Table 5.
For Design 1A, Table 6a and Fig, 5 are used for the
fatigue analysis and Table 7a and Fig. 6a are used for the
erosion analysis.
Comments on Design 1
For designs 1A through 1E, a subbase of one type or another is used as a recommended practice $onfine-textured
soil subgrades for pavements carrying an appreciable
number of heavy trucks.
In Design 1A: (1) Totals of fatigue use and erosion
damage of 63% and 39%, respectively, show that the 9.5in. thickness is adequate for thedesign conditions. (2) This
design has 37% reserve capacity available for heavy-axle
loads in addition to those estimated for design purposes.
(3) Comments 1 and 2 raise the question of whethera 9.0in. thickness would be adequate for Design IA. Separate
calculations showed that 9.0 in. is not adequate because
of excessive fatigue consumption
(245Yo). (4) Design 1A
is controlled by the fatigue analysis.
A design worksheet, Fig. 7, is shown for Design 1D to
illustrate the comb]ned effect of using aggregate-interlock joints and a cement-treated
subbase. In Design 1D:
(1) Totals of fatigue use and erosion damage of l%t$ and
97%, respectively, show that IO in. is adequate. (2) Separate calculations show that 9.5 in. is not adequate because
of excessive erosion damage ( 142Yo),and (3) ~sign
1D is
controlled by the erosion analysis.
(continue
donpage21)
*Some guidance is helpful in reducing the number of trial inns. The
effect of thickness on both the fatigue and erosion damage approximately follows a geometric progression. For example, if 33% and 17870
fatigue damage are determined at trial thicknessesof 10 and 8 in., r.spectivdy, the approximate fatigue damage for t+thickness of 9 in. is
cowl to .~
= 77%
:*com&
MR. LS F. and submade k value, are tie WM. for DesiEns
1A through lE.
Weme.t-treamd subbase meeting requirements stated on page 6.
tTA blank worksheet is provided asthe last page of this bulletin for the
p.rp.ses .f =prodtiction and U= in sp=ific de$ign problems.
1S.. Subzr.de$ and Subbasesfor Concrete’ P.vetnents. Portland
Cement Aswxiatio” p“bfica.tio.
$1 For pavements with aggregate-interlock joints subjected to an appreciable num~r
design.
of truck% the fadw
,..M
will .$.aW
..1 affect
13
Publication List
Book Contents
Table 6a. Equivalent Streaa — No Concrete Shoulder
(Singla Axle/Tandam Axle)
Slab
k of Subgrade-subbase,
thickness,
In.
pci
50
100
150
200
300
500
700
4
4.5
825[679
699/586
726/585
61 6/500
6711542
57f /460
634/516
540/435
584/486
498/406
5231457
4481378
484/443
417/363
5
5.5
602/51 6
526/461
531 /436
484/367
493/399
431/353
467/376
409/331
432/349
379/305
390/321
3431278
363/307
320/264
6
6.5
485/4f 6
41 7/380
4111348
367/31 7
382/31 6
341/286
362/296
324/267
336/271
300/244
304/246
2731220
285/232
256/207
7
7.5
375[349
340/323
331 /290
300/268
307/262
279/241
292/244
265/224
2711222
246/203
246/199
224/181
231/186
210/169
8
8.5
311 /300
285/281
2741249
252)232
255/223
234/206
242/208
222/1 93
2251188
206/174
205/167
186/154
192)1 55
177/143
9
9.5
264/264
245/248
232/21 6
215/205
216/195
200/183
205/181
190/1 70
190/1 63
176/153
1741744
161 /134
163/1 33
151/124
10
10.5
226/235
21 3/222
200/1 93
187/1 83
186/1 73
174[1 64
177/160
165/151
164/144
153/1 36
150/126
140/119
141/117
132/110
11
11.5
200/21 1
133/201
175/1 74
165/165
163/155
153/1 48
154/1 43
145/1 36
144/1 29
135/122
131/113
123/1 07
123/1 04
116/96
12
12,5
177/192
1681183
155/156
147/151
144/141
136/1 35
137/130
129/124
1271116
120/111
116/1 02
109/97
109/93
103/89
13
13.5
159/1 76
152/1 68
139/144
132/136
129/1 29
122/123
122/119
116/114
113/106
107/102
103/93
98/89
97[85
92/81
14
144/162
125/133
116/116
110/109
102/98
93[85
88/78
Table 6b. Equivalent Straaa — Concrete
(Single Axle/Tandem Axle)
Slab
thic;n~,
Shoulder
“w’
k of subgrade-subbase,
pci
50
100
150
200
300
500
700
4
4.5
640/534
547/461
559/466
479/400
51 7/439
4441372
489/422
421 /356
452/403
390/336
409/388
355/322
363/384
333/31 6
5
5.5
4751404
41 6)360
41 7/349
366/309
387[323
342/285
367/308
324/271
341 /290
302/254
311/274
276/236
294/267
261/231
6
6.5
3721325
334/295
3271277
294/251
304/255
274/230
269/241
260/218
270/225
243/203
247/210
223/1 88
2341203
21 2/180
7
7,5
302/270
275/250
266/230
243/21 1
248/21 O
226)1 93
236/1 98
215/182
220/1 84
201/168
203/170
185/155
192/162
176/148
8
8,5
252/232
232/21 6
222/196
205/1 62
207/1 79
191/166
197/168
182/156
185/155
170)1 44
170/142
157/131
162/135
150/1 25
9
9.5
215/202
200/1 90
190/171
176/160
177/1 55
164/146
169/146
157/137
158/1 34
1471126
146/1 22
136/114
139/1 16
129/1 08
10
10.5
186/1 79
174/170
164/151
154/143
153/137
144/130
146/129
137/121
137/116
128/711
127/107
119/101
121)101
1>3/95
11
11.5
164/161
154/153
144/1 35
136/1 28
135/1 23
1271117
129/1 15
121/109
1201105
113/100
112/95
105/90
106/90
100/65
12
12.5
145/146
137/1 39
128/1 22
121/117
120/111
113/106
114/104
106/99
107/95
101/91
99/86
94/82
95/81
90/77
13
13,5
130/1 33
*15)112
107/101
102/95
96/86
89/78
85173
124/1
27
10S/107
102/97
97/91
91183
85174
81 /70
118/122
104/103
93/87
87179
81/71
77167
14
I
97/93
u
“’U
14
Publication List
Book Contents
60--(--’20
10,000,0001
:-
Q 15
58
2-
/
56
110
1,ocwooo8—
54
6-
52
4-
[
50
100
0.2”
2-
\
46
loo,ooo—
90
44
8+
“..3
42
6-
2
0
/-
m
a
Z
c)”
a
o
-1
w
-1
z
40
80
4-
38
.—-—
36
..
—.—
—
——
)
-——+
2-
70
i=
1=
w
a.
w
a
34
1o,ooQ—
32
t
864-
26
50
“.s”
24
22
2i
20
0.(3”
looo—
40
8-
Q ?“
18
60.80
16
30
4-
0. 9“
14
-1
I.”.
12
10
2
2“
i
/
1.s”
100 ~
Fig. 5. Fatigue analysis—allowable
toad repetitions based
on stress ratio factor (with and without concrete shoulder).
15
Publication List
Book Contents
Table 7a. Erosion Fectora — Doweled Jointa, No Concrete Shoulder
(Single Axle/Tandem Axle)
Slab
thickness,
In.
<
4
4.5
5
5.5
k of subgrade-subbase,
I
I
pci
50
100
200
300
500
700
3. 74/3.83
3.59/3. 70
3.7313.79
3.5713.65
3.7213.75
3.56/3.61 1
3.7113.73
3. 55/3,58
3. 70/3.70
3.5413.55
3.68/3.67
3.52/3.53
3.38/3.40
3. 45[3. 58
3.43/3.52
3.42/3. 48
3.41/3,45
3.40)3.42
iI
3.3313.47
3.31/3.41
3.29/3.36
3.28/3.33
3.27/3.30
3.26/3.28
6
6.5
I
3,2213.38
3,11 /3. 29
3.1 9/3, 31
3.09/3, 22
3,18/3.26
3.07/3, 16
3. 17/3.23
3,06/3. 13
3.1 5/3. 20
3.05/3. 10
3. 14/3,17
3. 03/3,07
7
7,5
I
3, 02/3.21
2. 93/3.14
2.99/3.14
2.91/3,06
2,97/3,08
2. 86/3.00
2. 96/3.05
2.6712.97
2. 95/3.01
2.86/2, 93
2. 94/2.98
2. 84/2.90
8
8.5
2. 85/3.07
2.7713.01
2, 62/2.99
2.7412.93
2.80/2.93
2. 72)2.86
2.7912.89
2.7112.82
2,7712.65
2,89/2.78
2.76/2.82
2. 68/2.75
9
9.5
2, 70/2.96
2, 63)2.90
2. 67/2.87
2. 60/2.81
2.65/2.80
2. 58/2.74
2, 63/2,76
2.56/2,70
2.6212.71
2.55/2.65
2.61/2.68
2.5412,62
10
10.5
2.5612,85
2.50/2.81
2.54/2. 76
2.47[2,71
2,51/2.68
2.4512.63
2.50/2.64
2,4412.59
2.46/2. 59
2.4212.54
2.4712,56
2.41/2.51
11
11,5
2.4412,76
2.36[2.72
2. 42/2.67
2. 36/2,62
2. 39/2.58
2.3312.54
2.38)2.54
2.32/2.49
2.36/2.49
2.30[2. 44
2,35/2,45
2.29/2.40
12
12.5
2.33/2. 68
2.2812.84
2.30/2.58
2. 25)2.54
2.28/2.49
2.2312.45
2. 26/2,44
2.2112.40
2,2512.39
2, 19/2.35
2.23/2.38
2. 18/2.31
13
13.5
2. 23[2. 61
2,1612,57
2. 20/2.50
2.t5/2 ,47
2.1812,41
2.1312.37
2.1612.36
2, 11/2.32
2. 14/2.30
2.09/2.26
2.1312.27
2. 08[2, 23
14
2. 13/2.54
2. 11/2,43
2. 06/2.34
2,07/2.29
2.05/2. 23
2.03/2. 19
Table 7b. Erosion Factors — Aggregate-Interlock
Joints,
No Concrete Shoulder (Single AxleiTandem Axle)
Slab
thickness,
in.
k of subgrade-subbme,
50
100
4
4.5
pci
200
300
500
700
3.94/4. 03
3. 79/3.91
3.91/3.95
3.7613.82
3. 68/3.89
3. 73/3.75
3. 86/3.86
3.71 [3, 72
3.62/3, 83
3.6813.68
3,77/3.80
3. 64/3.65
5
5.5
3. 86/3,81
3.54/3.72
3. 63/3,72
3,51/3,62
3, 60/3.64
3.4813,53
3,5813.80
3.46/3.49
3.55[3 ,55
3.43/3.44
3. 52/3.52
3.41 /3.40
6
6.5
3.44/3. 64
3.34/3. 56
3. 40/3.53
3.30/3.46
3. 37[3. 44
3.26/3.38
3. 35/3.40
3. 25/3.31
3.32/3.34
3.22/3. 25
3.30/3, 30
3.20/3, 21
7
7.5
3. 26/3.49
3, 16/3,43
3.21/3.39
3. 13/3.32
3. 17/3.29
3.09/3.22
3. 15/3.24
3.07/3, 17
3,1 3/3. 17
3. 04/3,1 o
3,11/3,13
3. 02/3.06
8
8,5
3.1 1/3.37
3.04/3,32
3.05/3.26
2.96/3.21
3.01/3.18
2.93/3.10
2.99/3. 10
2.81/3.04
2.96/3.03
2.S812.97
2.94/2.99
2.8712.!33
9
9.5
2. 98/3.27
2. 92/3.22
2,91/3.16
2. 65/3.11
2, 86/3,05
2. 60/3.00
2. 84/2.99
2. 77/2.94
2.81/2.92
2.7512.86
2. 79/2.87
2. 73/2.81
10
10,5
2.66/3. 18
2.81/3.14
2. 79/3.06
2. 74/3.02
2.7412.95
2. 66/2.91
2.71/2.89
2. 65/2.64
2.68/2.81
2.62/2.76
2.66/2.76
2,60/2,72
11
11.5
2.77[3. 10
2.7213,06
2.69/2.98
2. 64/2.94
2.63[2.86
2.58/2.82
2.60/2. 80
2,5512.76
2,5712.72
2.51/2,68
2.54/2.67
2.49/2.63
12
12.5
2. 68/3.03
2.64/2.99
2. 60/2,90
2,5512.87
2.5312.78
2, 48[2. 75
2,5012.72
2.4512,68
2. 46/2.64
2.41/2.60
2.44/2. 58
2.39/2.55
13
13.5
2.60/2.96
2.56/2.93
2.51/2.83
2.47/2.80
2.4412.71
2.40/2. 68
2. 40/2.65
2.36/2.61
2.36/2.56
2.32/2.53
2.34/2.51
2.30/2. 48
14
2.5312.90
2.4412.77
2.36/2.65
2.32/2.58
2, 28[2. 50
2,25[2.44
16
Publication List
Book Contents
60 T
I20
loo,cK)o,ooo8—
64-
—110
50-
— 100
–
2-
— 2.0
10,000,000
90
— 2.2
=
86-
40 – –
80
tio~
30 – –
u)
Il.
Z
~-
—
~—
g
u
~
(/)
a
G
25-
–
50
o
i
;
~
(n
— 40
la- .
35
k
2.6 —
–
2.8
4-
~._
–
6-
3.0
4—3.2
2–
3.4
–
3.6
:
100,000:
w
n
z1-
66-
— 3.8
30
4-
— 4.0
2-
14- -
–
t2- -
I ,000,000:
8-
16- –
2-
~.+
5
w
20–
2.4
~
m
~“
0
-1
u
-1
Y
a
60
a
o
J
;
~
—
–
25
IQOOO 864-
lo-
—
20
2-
9- - 18
8— 16
Fig. 6a. Erosion
based
on erosion
1000 —
analysis—allowable
load repetitions
factor (without concrete
shoulder),
17
Publication List
Book Contents
Table &. Erosion Factors — Doweled Joints, Concrete
C3inale Axle/Tandem Axle)
Slab
thic:ny,
4
4.5
k of s. bgrade-subbase,
!
Shoulder
pci
50
100
200
300
500
700
3.28/3.30
3.13/3.19
3. 24/3.20
3.09/3.08
3.21/3.13
3.08/3.00
3.1 9/3. 10
3.04/9 !36
3.1 5/3.09
3
3. 12/3.08
(11/793
7?),/7
Q,
5
5.5
I 3.0113.09
2.90/3. 01
2.97/2.98
2.85/2. 89
2.93/2.89
2.81/2,79
2.90/2.84
2.7912.74
2.8712.79
2.7612,68
7.35/7.77
2.7312.65
8
6.5
2,7912.93
2. 70/2.66
2.7512,82
2,6512.75
2,70/2.71
2.61/2,63
2,66/2.65
2.58[ 2.57
76S/7
. . . . SR
..
2.55/2.50
7
. 67/95A
.. . .
2.52)2.45
7
7.5
2.61/2.79
2.53/2.73
2.5612.66
2.48/2.62
2.52/2.56
2.44/2.50
2.49/2.50
2.41 [2.44
2.46)2.42
2.38/2.36
2.43/2, 38
2.35/2.31
8
8.5
2.46/2. 68
2.39/2.62
2.41/2.56
2.34/2, 51
2.3612.44
2. 29/2,39
2.33)2.38
2.26/2. 32
2.30/2, 30
2,22/2,24
2.2712.24
2.20/2, 18
9
9.5
2.3212.57
2. 26/2.52
2.2712,46
2.21/2.41
2.2212,34
2,16/2.29
2.1912.27
2. 13/2.22
2, 16/2.19
2,09/2, 14
2. 13/2.13
2. 07/2.08
10
10,5
2.2012.47
2. 15/2,43
2. 15[2. 36
2. 09/2.32
2, 10/2.25
2. 04/2.20
2.07/2, 16
2.01/2.14
2.03/2.09
1.87/2.05
2.01/2.03
1.85/1.99
11
11.5
2. 10/2,39
2. 05/2.35
2.04/2.28
1.99/2.24
1.99/2. 16
1.93/2. 12
1.95/2.09
1.90/2.05
1.92/2.01
1.67/1.97
1.89/1.95
1.8411,91
12
12.5
2.00/2.31
1.95/2.27
1.94/2.20
1.69/2. 16
1,88/2.09
1.64/2.05
1.6512.02
1.81/1.98
1.82/1.93
1.77/1.89
1.7911.87
1.7411,84
13
13.5
1.91/2,23
1.66/2.20
1.85/2, 13
1,81/2.09
1.79/2.01
1.75/1.96
1.76/1.95
1.72/1.91
1,72/1.86
1.68/1.83
1.70/1.80
1.65/1.77
14
1.82/2, 17
1.76/2.06
1.71/1.95
1.67/1.88
1.64/1.80
1.61/1,74
+
‘L--J
Table 8b. Erosion Factors — Aggregate-Interlock
Joints,
Concrete Shoulder (~;gl;
AxleiTandem Axlej
slab
thickness,
in.
k of S“bgrade-subbase,
w
pci
50
100
200
300
500
700
4
4,5
3. 46/3,49
3. 32/3.39
3. 42/3.39
3,28/3.28
3.3813.32
3.2413.19
3. 36/3.29
3,22/3. 16
3, 32/3.26
3,1 9/3, 12
3.28/3.24
3.1 5/3. 09
5
5,5
i 3.20/3.30
3.10/3.22
3. 16/3.18
3.05/3, 10
3, 12/3.09
3,01/3,00
31 0/3.05
2.99/2,95
3.07/3.00
2. 96/2,90
3.04/?. 97
2. 93/2.66
6
6.5
3. 00/3.15
2.91/3,06
2.95/3,02
2. 86/2.96
2. 90/2,92
2,81/2,85
2.68/2.87
2.79/2.79
2,66/2.61
2,7612.73
2,6312.77
2.7412.66
7
7.5
2. 83/3.02
2.76/2,97
2,77/2.90
2,70/2.84
2.7312.78
2.65/2.72
2.7012.72
2,62/2.66
2. 68/2.66
2. 60/2.59
2. 65/2.61
2.5712.54
8
6.5
2. 69/2.92
2. 63/2.88
2.63/2.79
2. 56/2.74
2.5712.67
2.51/2.62
2.55/2.61
2.48/2. 55
2. 52/2.53
2.4512.48
2. 50/2.48
2.43/2.43
9
9.5
2. 57/2.83
2.51/2.79
2. 50/2.70
2,4412,65
2.4412,57
2. 38/2,53
2,42/2.51
2.36/2,46
2, 38/2.43
2.3312.38
2. 36/2.38
2, 30/2.33
10
10.5
2.46/2.75
2.41/2,72
2,39/2,61
2.33/2.58
2.33/2.49
2.2712.45
2.30/2,42
2,24/2.36
2.27[2 ,34
2,21/2,30
2.24/2.26
2.1 9/2.24
11
11.5
2.36/2. 66
2.32/2.65
2.26/2.54
2.2412.51
2.22/2.41
2. 17!2.36
2. 19/2.34
2.>4/2.31
2. 16/2.26
2.11/2.22
2. 14/2.20
2.09)2. 18
12
12.5
2.28/2.62
2,2412.59
2. 19/2.48
2.15/2.45
2, 13/2.34
2.09/2.31
2. 10/2.27
2. 05/2.24
2.06/2. 19
2.02/2, 15
2.04/2.13
1.99/2.10
13
13.5
2, 20/2.56
2. 16/2,5s
2. 11/2,42
2.06/2.39
2.04/2,26
2.00/2,25
2.01/2.21
1.97/2, 18
1,98[2. 12
1.93/2.09
1,95/2,06
1.91/2,03
14
2. 13/2.51
2,04/2.36
1.97/2.23
1.83/2. 15
1.89/2.06
1.87[2. 00
t
“-/’
18
Publication List
Book Contents
60-1-120
IOO,OOQOOO
‘a
—1.6
2-1
110
50
IQOOQOOO
— 1.8
I 00
90
1
6
—2.0
2
40
80
–2.2
I ,Ooo,ooo
8
70
a
30
P
v
2
60
/
6
—2.4
4
i
– 2.6
i
~
(n
: —2.8
w
2-
2
g
~
1-
W
100,000
—k
—3.0
8-
:
6-
a
0
-1
4-
?
—3.2
m
4
g
— 3.4
J
2-
2
16
!
— 3.6
30
14
I Qooo—
8-
25
6-
12
10
r
4
20
9
18
8
16
1
2
1000
Fig. 6b. Erosion analysis—allowable
load repetitions
based on erosion factor (with concrete
shoulder).
19
Publication List
Book Contents
Calculation of Pavement Thickness
Trial thickness—
/A.
&
Subbase-$ ubgrade h ~
Modulus of rupture, MR =~
Load safety factor, LSF
in.
Doweled joints:
yes _
no z
Pci
Concrete shoulder:
yes _
no L
psi
Design period
=L
years
/7
%%..
C&z?#’(+&&d5.A&
Fatigue analysis
Axle
load,
kips.
Multiplied
by
LSF
Expected
repetitions
/. z
1
2
Fatigue,
percent
4
5
3
Damage
percent
6
T
10. Erosion factor
~
11. Equivalent stress.
z.
72
2.57
/@7
13. Erosion factor
–~
12. Stress ratio factor ~
Total
Fig. 7. Design
Allowable
repetitions
sbess~
9. Stress ratio factor
Tandem Axles
Erosion analysis
Allowable
repefitio”s
6. Equivalent
Single Axles
u
0.6
I
ID.
20
Publication List
Book Contents
Total
%?/
L) —
Worksheets
shown
for the other variations
Subbase
Design
of Design
here but the results are compared
Joints
1A
Gin. gm”ular
doweled
lB
Gin. cement-treated
lc
hi”,
ID
lE
1 are not
as follows:
Umcrete
shoulder
Thickness
q.i~emer. t,
m.
no
9.5
doweled
no
8.5
doweled
yes
8.5
4-in. cement-treated
aggregate
interlock
no
4+n. cement-treated
aggregate
interlock
yes
granular
I
10.0
8.5
Design 2B: doweled joints,**
shoulder
Same as 2A except
Doweled joints
no subbase, no concrete
TMckness Calculations:
For Design 2A, a trial thickness of 6 in. is evaluated by
completing the worksheet shown in F]g. 8, according to
the procedure given on page 11. Table da and Fig. 5 are
used for the fatigue analysis and Table 7band Fig. .5aare
used for the erosion anal ysis.
For Design 2B, a worksheet is not shown here but the
design was worked out for comparison with Design 2A.
Comments on Design 2
For Design 1 conditions, use of a cement-treated
subbase reduces the thickness requirement by 1,0 in. (Design
1A versus 1B); and concrete shoulders reduce the thickness requirement by 1.0 to 1.5 in. (Designs 1A versus IC
and I D versus 1E). Use of aggregate-interlock
joints instead of dowels increases the thickness requirement by
1.5 in. (Design 1B versus 1D). These effects will vary in
different design problems depending on the specific design conditions.
Design 2
P
Project and Traffic Data:
Two-lane-secondary
road
Design period = 40 years
Current ADT = 600
Projection factor = 1.2
ADTT = 2.5% of ADT
Traffic Calculations:
Design ADT = 600 X 1.2 = 720
ADTT = 720 X 0.025 = 18
Truck traffic each way = $
For Design 2A: (1) Totals of fatigue use and erosion
damage of 89% and 8%, respectively, show that the 6.O-in.
thickness is adequate. (2) Separate calculations show that
a 5.5-in. pavement would not be adequate because of
excessive fatigue consumption.
(3) The thickness design
is controlled by the fatigue analysis-which
is usually the
case for light-truck-traffic
facilities.
The calculations for Design 2B, which is the same as
Design 2A except the joints are doweled, show fatigue
and erosion values of 89% and 21%, respectively. Comments: (1) The th]ckness requirement of 6.0 in. is the same
as for Design 2A. (2) The fatigue-analysis
values are exactly the same as in Design 2A. T(3) Because of the dowels, the erosion damage is reduced from 870 to 2%; however, this is immaterial since the fatigue analysis controls
the design.
For the Design 2 situation, it is shown that doweled
joints are not required. This is borne out by pavementperformance
experience on light-truck-traffic
facilities
such as residential streets and secondary roads and also
by studies 128w ~h~~i”gtheeffects of the number of trucks
on pavements with aggregate-interlock
joints.
= 9
For a 40-year design period:
9 X 365 X 40 = 131,400 trucks
Axle-load data are shown in Table 15, Category 1, and
the expected number of axle-load repetitions are shown
in Fig, 8.
Values Used to Calculate Thickness:
Design 2A: aggregrate-interlock Joints, no subbase,* no
concrete shoulder
Clay subgrade, k = 100pci
LSF = 1.0
Concrete MR = 650 psi
*Performance experience has show” that subbasm me not required
whm truck traffic is very Iighc seethe PCA p.btication, S.bcmdesond
.subbmes
CO..,,(,
POVWWIII,.
:* Design 2B is sb,wm for illustrative purposes only. Doweled joints
are not needed where truck traffic is very lighq we the PCA publication
Join! Designfor Co.crele Highww and Srreel Pavemenn.
T The type of load transfer at the joim40wels,
or aggregate interlock4ces not affect the fatigue calculations sincethe critical axle-load
position for stressand fatigue is where the axle loadsare placed at pave.
ment edge and mid panel, away from the joims. See Appendix A.
f.,
21
Publication List
Book Contents
Calculation of Pavement Thickness
2A
Project &&~l-
7+9
6.0
Trial thickness
Subbase-subgrade
h ~–
Modulus of rupture,
MR —-
Load safety factor, LSF
~
-/cm.
5PczG@z&.t/
tn.
Doweled joints:
yes _
no &
pci
Concrete shoulder:
yes _
no ~
psi
/.
Lz?za+
Design period &
o
nO
years
SU/6&3c
Fatigue analysis
Axle
load,
kips
Multiplied
by
LSF
1
2
Erosion analysis
Expected
repetitions
o
/.
‘u
Allowable
repetitions
Fatigue,
percent
Allowable
repetitions
Damage,
percent
4
5
6
7
3
8. Equivalent
v//
stress
10. Erosio” factor
&?.
*D
9. Stress ratio factor ~
Single Axles
u
11. Equivalent stress_~
Tandem Axles
Fig. 8. Design
12. Stress ratiOlactOr
13. Erosion factor
U.
~—
535
w
2A.
22
Publication List
Book Contents
P
CHAPTER 4
Simplified Design Procedure
(Axle-Load
P
Data Not Available)
The design steps described in Chapter 3 include separate
calculations of fatigue consumption and erosion damage
for each of several increments of single- and tandem-axle
loads. This assumes that detailed axle-load data have
been obtained from representative truck weigh stations,
weigh-in-motion
studies, or other sources.
This chapter is for use when specific axle-load data are
not available. Simple design tables have been generated
based on composite axle-load distributions
that represent different categories of road and street types. A fairly
wide range of pavement facilities is covered by four categories shown in Table 9.*
The designer does not directly use tbe axle-load data**
because the designs have been presolved by the methods
described in Chapter 3. For convenience in design use, tbe
results are presented in Tables 11, 12, 13, and 14, which
Table 9.
de-Load
correspond to the four categories of traffic. Appropriate
load safety factors of 1.0, 1.1, 1.2, and 1.2, respectively,
have been incorporated
into the desigo tables for axleIoad Categories 1, 2,3, and 4. Tbe tables show data for a
design period of 20 years. (See the section “Design
Period”, following.)
In these tables, subgrade-subbase
strength is characterized by the descriptive words Low, Medium, High, and
Very High. Fig. 2 shows relationships
between various
subgrade-bearing
values, In the event that test date are
not available, Table 10 lists approximate k values for different soil types. If a subbase is to be used—see Chapter 2
*On page 30, guidelines for preparing designtables for axle-load distributions d~ffemnt fmm th.se givem here are discussed.
** Axle.load data for the four categories are given in Table 15.
Cat@goriea
afti c
ADTT.+
Axle-load
category
Description
1
Residential streets
Rural and secondary roads (low to
medium’)
Collector streets
Rural and secondary roads (high,)
Arterial streets and primary roads (low,)
2
n
,.r
ADT
%
Maximum axle kinds, kips
Per dav
3ingle axles
Tandem axles
up to 25
22
38
20C-800
t -3
7oe-5ooo
5-18
40-1000
26
44
3
Arterial streets and primary roads
(medium.)
Expressways and urban and rural
interstate (low to medium.)
3000-12,CO0
2 lane
3000-50,000+
4 lane or more
3-30
500-50004
30
52
4
Arterial streets, primary roads,
expressways (high’)
:~b~~ and rural Interstate (medium to
..=.. ,
3000-20,000
2 lane
3000-1 50,000+
4 lane CMnmre
a-30
150&8000+
34
60
I
‘The descript.m high, nwd. m, .r 1.$’+refer to the relative weights .1 ..1. loads for the type of street or road:
that Is, ,Tow, for a rural Interstate would represent heavier loads than low,, for a seco.d.,y mad,
‘Trucks —w-axle,
four-tire Irwks excluded,
23
Publication List
Book Contents
Tabla 10. Subarade Soil Types and
App;oximate k Values
Fine-grained soils in which silt and
clay-size pariicles predominate
Low
I
I
Sands and sand-gravel mixtures with
moderate amounts of silt and clay
subbasOS (see page 6)
7s120
Medium
13&170
High
180-220
Very high
25&400
sands and sand-gravel mixtures
relatively free of plastic fines
Cement-treated
k values
range,
pcl
SUppofl
Type of soil
discussion under “Comments
on Simplified Proccdure,” page 30.)
In the correct use of Table 9, the ADT and ADTT values are not used as the primary criteria for selecting the
axle-load category—the data are shown only to illustrate
typical values. Instead, it is correct to rely more on the
word descriptions given or to select a category based on
the expected values of maximum-axle
loads.
The ADTT design value should be obtained by a truck
classification count for the facility or for another with a
similar composition of tmffic. Other methods of estimating ADT and ADTT are discussed on pages 8 and 9,
The allowable ADTT values (two dircctions)fisted
in
the tables include only two-axle, six-tire trucks, and
single or combination
units with three axles or more.
Excluded are panel and pickup trucks and other two-exle,
four-tire trucks. Therefore,
the number of allowabIe
trucks of alI types will begrcaterthanthe
tabulated ADTT
“Subgrade
and Subbase Support’’—the estimated
value is increased according to Table 1 or Table 2.
under
k
The design steps are as follows
1. Estimate ADTT* (average daily truck traffic, two
directions, excluding two-axle, four-tire trucks)
2. Select axle-load Category 1, 2, 3, or 4.
3. Fkrd slab thickness requirement in the appropriate
Table 11, 12, 13, or 14. (In the usc of these tables, see
(continued
on page
.....
u
30)
*For facilities of four lanes or more, the ADTT is adjusted by the use
of Fig. 3.
Table 11. Allowable ADTT,* Axle-Load Cate@ry 1
Pavements with Aggregate-lntertock
Joints (Dowels not needed)
No Concrete
Slab
thickness,
in.
.:
4.5
~
z
.
(,
c
z
5.5
6
6.5
.E
5
5.5
s
6
K
z
6.5
y
Subgrade-subbase
LrJW
Medium
support
0.1
3
40
330
0.5
8
76
0.8
15
1S0
0.1
3
36
300
3
45
Low
4
4.5
2
5
5.5
30
320
0,4
9
98
760
4
4.5
5
5.5
6
5,5
:
;,5
1
13
6
60
K
z
7
7,5
110
620
403
Subgrade-subbase
Medium
support
High
0.9
25
0.2
8
130
330
430
520
0.1
Slab
thick#r+s%
High
0,)
.-
Note
Concrete Shoulder or Curb
ehoulder or Curb
1
4.5
16
160
5
5.5
0.3
6
0.2
6
73
0.1
5
1
27
2eo
75
730
610
0.2
0.6
13
130
4
57
0.6
13
150
460
Fatigue analysis controls the design.
Note: A fractional ADTT indicates that the pavement can carry unlimited passenger cars and two-axle, fourthe trucks, but only a few heavy trucks per week (ADTT of 0.3 x 7 days indicates two heavy trucks per week.)
.ADTT excludes two-axle, four-tire trucks, so total number of trucks allowed will be greater—see text.
24
Publication List
Book Contents
,..
L-J
Table 12s. Allowable
ADTT,” Axle-Load
No Concrete S’houl&r
Slab
thickness,
in.
or Curb
Subgrade-subbase
Low
Category 2 — Pavements with Doweled Joints
Medium
Concrete ahouldec or Curb
support
Hiah
Slab
thickness,
In.
Verv hioh
Low
E
5’
1,
w
Medium
s“ppmt
High
Very high
5
5.5
9
3
42
9
120
42
450
6
6.5
96
710
360
26Q0
970
3400
7
.-
Subgrade-subbase
I
5.5
4200
I
3
17
1100
6
6.5
3
29
14
120
41
320
7
7,5
210
1100
770
4000
1900
lSU
I
Note: Fatigue analysis controls the design.
.ADTT exd”des two-axle, four-tire trucks so mtel number.1 tr.cks allowed wilt be greater–see text.
Table 12b. Allowable ADTT.” Axle-Load
No Concrete
Slab
thic~~,
Subgrade-subbase
Low
Cateaorv
-.
2-
Pavements with Aggregate-Interlock
shoulder or Curb
Medium
Concrete
support
High
Very high
I
Slab
thickness,
m.
Subgrade-subbase
Low
5
5.5
9
6
6,5
e6
650. -
7
w
13W.
8
.~
I
Medium
3
42
380
1000”
1100-.
1900”
19
I&l
64
620
support
High
Very high
9
120
Jm..
42
450
1400,’
97W .
21OIY.
220
1400..
610
2100,,
19CW
6
6.5
7
6.5
7
Joints
Shoulder or Curb
11
4
19
34
150
I
1000
1900,.
WE===’
.ADTT excludes two-axle, I..,-tire trucks total ““mbw of tr.cks allowed will be greater—see text,
‘+Erosio” analysis controls the design: otherwise fatigue analysis controls.
25
Publication List
Book Contents
Table 13s. Allowable ADTT,*
No Concrete
Axle-Load
Category 3-
Pavementa with Doweled Joints
Shoulder or Curb
Concrete Shoulder or Curb
~
Slab
thickness,
in.
=
z
z.
,,
a
z
I
7.5
Subgrade-subbase
Low
9
9.5
10
Slab
thic$~,
support
High
I
Very high
250
s
8.5
Medium
lea
700
2,7CQ
““”
130
640
350
i ,600
1,300
6,200
2,700
10,800
7,000
11,500,,
9,900
Subgrade-subbase
Low
Medium
u
support
High
Very high
a===
6.5
I
67
7
7,5
8
6.5
120
I
9
370
1,600
270
8s0
1,300
5,800
3,200
14,100
440
2,300
10.s00
6,&10
.ADTT excludes two-axle, four-tire truck% total number of trucks allowed will be greater—see text.
.. Erosion analysis controls the design; otherwise fatigue analysis comrols.
‘u
v’
26
Publication List
Book Contents
Table 13b. Allowable
ADTT,*
Axle-Load
Category
3—
Pavements with Aggregate
Interlock Jointa
ConcreteShoulderor Curb
n
Slab
thic;~
Subgrade-subbase
Low
Medium
support
High
Very high
Slab
thickness,
tn.
Subgrade-subbase
Low
Medium
support
High
Very high
I
~o..
7,5
8
8,5
.%
,@y,
9
z
.
K
z
1,000
1,500
1,300
2,000
2,000
2,900
10
10.5
1,3CC
1,800
2,1C!U
2,900
2,800
4,000
4,300
6,300
10.5
5,300
11
11.5
2,500
3,300
4,000
5,500
5,700
7,900
9,200
11
8,100
12
4,400
7,500
73..
14W.
160,.
63W +
z
0
E
~
310++
1,300
640. 1,503
1,300
2,000
2,000
2,900
1,300
1,8CU
2,100
2,900
2,800
4,000
4,300
6,3oo
11
11.5
2,500
3,300
4,000
5,500
5,700
7,900
9,200
12
4,400
7,500
9.5
I
2,300
4.700
10
10.5
I
3,500
5.300
7,700
11
I
S.om
S,loo
1
8
6.5
%
380”’
10.5
1
.—
25W .
830
1,300
680
960
9
9.5
,0
~
.
,,
cc
~
350900
9.5
8
8.5,
.
a
130640,,
70..
,.
9
9.5
,0
10,5
11
11,5
12
I
I
12W+
120,,
520.,
460,,
1,600,+
56”
300>+
7
1,5
67..
130,.
62’,
460’ +
270.,
1,200.,
670..
2,700
2,301Y+
4,700
4,6oo
8,000
8,700
340.,
l,3cKl-
1,300,.
2,900
8
8,5
330”
1,9CW,
2,91Y3
2.800
4;000
4,300
6,300
9
9.5
1,400%,
2,30+1
2,900
4,700
2,500
3,300
4,000
5,500
5,700
7,9C+I
9,2oo
10
10.5
3,500
5,30U
7,700
4.400
7,500
11
8,1OQ
.ADTT excludes two-axle, four-tire trucks total number 0{ trucks allowed will be greater—see text.
,. Fatigue analysis controls the design, otherwise erosion analysis controls.
27
Publication List
Book Contents
Table 14s. Allowable ADTT,*
Axle-Load
Category 4 — Pavements with Doweled Joints
No ConcreteShoulderor Curb
I
Slab
thickness,
In.
I
Subgrade-subbase
Low
8
8.5
.
E
E
.
cc
support
Medium
High
120
340
580
2,300
9
9.5
140
570
10
10.5
2,000
6,700
8,200
24,100’.
tl
11.5
21,800
39,70W,
39,800”
+3=
z
Concrete Shoulder or Curb
I
Very high
Subgrade-subbase
Slab
thickness,
0..
270
1,300
7
7,5
1,500
5,900
5,W0
14,70W.
8
8.5
18,701%
31 ,801Y.
25,80W.
45,801Y,
9
9.5
support
w
Low
High
240
620
1,200
3,000
12,700
Very high
400
2,100
330
1,500
5,300
5,90+3
22,503
21,400
52,000’”
44,900 -
130
490
270
1,300
690
3,000
2,3oo
9,900
5,000
18,800
12,000
45,900
40,200
250
130
620
480
2,100
I
I
10
Medium
9,800
41,100’,
45,20W.
—
8.5
,-
%
z
m
cc
>
‘: I
120
120
530
340
1,400
10.5
480
1,600
1,900
6,503
5,1W
17,500
11
11.5
4,900
14,500
12
44,000
9
9.5
,0
21,400
65,000” ‘
9
9.5
12
7.5
8
S.5
340
i 9,300
45,900,,
9
9.5
t,40+3
5,2’&3
I
10
53, 8W ‘
18,41XI
1
280
8,200
300
1,300
5,200
260
1,100
40,000
8
8.5
9
9.5
280
1,100
1,000
3,900
10
10.5
3,800
12,400
13,600
48,2C0
11
40,400
2,5CW
9,300
8,200
30,700
32,800
,
‘u
.ADTT excludes two-axle fmr-tire trucks total number of Imck$ allowed will be greater—see text.
.+Erosion melysi$ c.ntrols the design; otherwise
fatigue
analysis
controls,
28
Publication List
Book Contents
Table 14b. Allowable
ADTT,*
Axle-Load
Category 4 — Pavemente with Aggregate-interlock
No ConcreteShoulderor Cub
-
I
(.
ConcreteShoulderor Curb
I
I
Subgrade-subbase
Slab
thickness,
In.
Low
Medium
supporl
High
Very high
10
=$=====
8.5
r
9
9.5
Joints
120’”
530,.
120,,
340”
1,400,,
] 2,800
5,500
9,200
11
5,900
13,600
24,200
12
12,800
2,600
5,500
9,200
11
5,900
13,600
24,200
12
] 12,800
,,,,00
I
30W+
1,30W.
2,300
10
17,900
I
I
I
1
1
8
8.5
25W ,
9
9.5
130..
620”
260,.
1,000..
2,500..
5,700
1,1OQ.,
3,4cm
5,500
10,200
17,900
a
,,
I,ow.
7,200
10,400
5,500
9,200
2,700
4,50Q
6,300
2,600
11.5
3,300
4,500
10
8
.0
12
3,600
6,100
8,800
14,900
11
5,900
13,6W
24,200
13
6,300
11,100
16,800
12
12,800
14
10.800
K
~
.ADTT excludes two-axle, four-tire trucks;
,. Fatigue
analysis
controls
!he
design;
total
otherwise
number
of trucks
allowed
erosion
analysis
controls.
w(II
be greater—see
48W ,
2,101Y.
text.
29
Publication List
Book Contents
values by about double for many highways on up to about
triple or more for streets and secondary roads.
Tables 11 through 14 include designs for pavements
with and without concrete shoulders or curbs. For parking lots, adjacent lanes provide edge support similar to
that of a concrete shoulder or curb so the right-hand side
of Tables 11 through 14 are used.
Sample Problems
Two sample problems follow to illustrate
plified design procedure.
use of the sim-
Design 3
Arterial street, twn lanes
Design ADT = 6200
Total trucks per day = 1440
ADTT = 630
Clay subgrade
4-in. untreated subbase
Subgrade-subbase
support = low
Concrete M R = 650 psi*
Doweled joints, curb and gutter
Since it is expected that axle-load magnitudes will be
about the average carried by arterial streets, not unusually heavy or light, Category 3 from Table 9 is selected,
Accordingly,
Table 13a is used for design purposes,
(Table 13a is for doweled joints, Table 13b is for aggregate-interlock joints.)
For a subgrade-subbase
support conservatively classed
as low, Table 13a, under the concrete shoulder or curb
portion, shows an allowable ADTT of 1600 for an 8-in.slab thickness and 320 for a 7.5-in. thickness.
Thk indicates that, for a concrete strength of 650 psi,
the 8-in. thickness is adequate to carry the required design ADTT of 630.
Design 4
Residential street, two lanes
ADT = 410
Total trucks per day = 21
ADTT = 8
Clay subgrade (no subbase), subgrade suppnrt = low
Concrete MR = 600 psi*
Aggregate-interlock
joints (no dowels)
Integral curb
in this problem,
Table 11 representing
axle-load
Category
1 is selected for design use. In the table
under “Concrete
Shoulder
or Curb,” the following
allowable ADTT are indicated:
Comments on Simplified Procedure
Modulus of Rupture
Cnncrete used for paving should be of high quality** and
have adequate durability, scale resistance, and flexural
strength (modulus of rupture). In reference to Tables 11
through 14, the upper pnrtions of the tables represent
concretes made with normal aggregates that usually produce good quality concretes with flexural strengths in the
area of 600 to 650 psi. Thus, the upper portions of these
tables are intended for general design use in this simplified design procedure.
The lower portions of the tables, showing a concrete
modulus of rupture of 550 psi, are intended for design use
only fm special cases. In some areas nf the country, the
aggregates are such that concretes of good quality and
durability produce strengths of only about 550 psi.
w
Design Period
The tables list the allowable ADTl% for a 20-year design
period. Fnr other design periods, multiply the estimated
ADTT by the appropriate
ratio to obtain an adjusted
value fnr use in the tables.
For example, if a 30-year design period is desired instead of 20 years, the estimated ADTT value is multiplied
by 30/20. In general, the effect of the design period on
slab thickness will be greater for pavements carrying
larger volumes of tfuck traffic and where aggregate-interlock joints are used.
Aggregate-Interlock
or Doweled
Joints
Tables 12 through 14 are divided into two parts, a and b,
to show data for doweled and aggregate-interlockj
oints,t
respectively. In Table 11, thickness requirements are the
same for pavements with doweled and aggregate-interlock
jointy doweled joints are not needed for the low truck
traffic volumes tabulated
for Category
1. Whenever
dowels are not used, joint spacings should be short—see
discussion on page 3.
User-Developed
u’
Design Tables
The purpose of this section is to describe hnw the simplified design tables were develnped so that the design engineer who wishes to can develop a separate set of design
tables based on an axle-load category different from those
given in this chapter. Some appropriate situations include
*See disc.wion under ‘Comments on Simplified Pmcedum—M.dof Rupture,- above
**See pofila”,j cenm.t Awociat i.. p.b)icat ion Design and Control
“1”S
Therefore,
the required
a 5.5-in. -slab thickness is selected to meet
design ADTT value of 8.
of Concrete Mi.wre$.
T When fatigue analysis controls the dcsiEn(see footnotes of Tables
12through 14), it will be noted that tbe ADTTvalues fmd.weled joints
and for aggregate-interlock joints are the sane (we topic ..Jointed Pavenmnts- in Appendix A). If emsi.% analysis controls, c.ncmt. modulus
of rupture will have no effect m the .dlmvable ADTT.
30
Publication List
Book Contents
d
,n
n
(1) preparation of standard sections from which a pavement thickness is selected based on amount of traffic and
other design conditions, (2) unusual axle-load distributions that may be carried on a special haul road or other
special pavement facility, and (3) an increase in legal axle
loads that would cause axle-load distribution to change.
Axle-1oad distributions for Categories 1 through 4 are
shown in Table 15. Each of these is a composite of data
averaged from several state Ioadometer (W-4) tables representing pavement facilities in the appropriate category.
Also, at the high axle-load range, loads heavier than those
listed on state department
of transportation
Wq tables
were estimated based on extrapolation.
These two steps
were desired for obtaining a more representative general
distribution
and smoothing irregularities that occur in
individual W-4 tables. The steps are considered appropriate for the design use of these particular categories described earlier in thk chapter.
As described in Chapter 2, the data is adjusted to exclude two-axle, four-tire trucks, and then the data are
partitioned into 2000- and 4000-lb axle-load. increments.
To prepare design tables, design problems are solved
with the given axle-load distribution by computer with
the desired load safety factor at different thicknesses and
subbase-subgrade
k values,
Allowable ADTTvalues to be listed in design tables are
easily calculated when a constant, arbkrary ADTT is in.
put in the design problems as follows: assume input
ADTT is 1000 and that 45.6% fatigue consumption
is
calculated in a particular design problem, then
Allowable
ADTT
=
—
100 X (input ADTT)
% fatigue or erosion damage
100(1000)
45.6
_
2193
Table 15. Axle-Load Distributions Used for
Preparing Design Tablss 11 Through
Axle
load,
kips
Axles per 1000 trucks,
Category
3ingle
—~ 4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
:Ies
m
axles
31,90
85.59
139,30
75.02
57.10
39.18
68.48
69.59
4.19
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
14
732.26
483,10
204,96
124.00
56.11
38.02
15.81
4.23
0.96
1
:ategory
2
233.6o
142.70
116,76
47,76
23,88
16.61
6.63
2,60
1.60
0.07
47.01
91,15
59.25
45,00
30.74
44.43
54.76
38.79
7.76
1.16
Category 3
182.02
47.73
31.82
25.15
16.33
7.85
5,21
1.78
0.85
0,45
Category 4
57.07
68.27
41,82
9.69
4,16
3.52
1.78
0.63
0.54
0.19
99.34
65.94
72.54
121.22
103,63
56.25
21.31
8.01
2.91
1.18
71,16
95.78
109.54
78,18
20,31
3.52
3.03
1.79
1,07
0.57
.Excludng all two-axle, Iour-tire trucks.
31
Publication List
Book Contents
,.
‘u
APPENDIX A
Development of Design Procedure
The thickness design procedure presented here was prepared to recognize current practices in concrete pavement
construction ‘and performance experience with concrete
pavements that previous design procedures have not addressed. These include:
● Pavements
with different types of load transfer at
transverse joints or cracks
● Lean concrete
subbases under concrete pavements
● Concrete
shoulders
● Modes of distress,
primarily due to erosion of pavement foundations,
that are unrelated to the traditional criteria used in previous design procedures
A new aspect of the procedure is the erosion criterion
that is amlied in addition to the stress-fatieue criterion.
The ero~~n criterion recognizes that pave~ents can fail
from excessive pumping, e%sion of foundation, and joint
faulting. The stress criterion recognizes that pavements
can crack in fatigue from excessive load repetitions.
This appendix explains the basis for these criteria and
the development of the design procedure. References 30
and 57 give a more detailed account of the topic.
the critical placements shown in Fig. A I were established
with the following conclusions:
1 The most critical Davement stresses occur when the
truck wheels are placed at or near the pavement edge
and midway between the joints, Fig. A l(a). Since the
joints are at some distance from this location, transverse joint spacing and type of load transfer have
very little effect on the magnitude of stress. In the
design procedure, therefore, the analysis based on
fk”ral
stresses and fatigue yield the same values fOr
different joint spacings and different types of load
transfer mechanisms (dowels or aggregate interlock)
at transverse joints. When a concrete shoulder is tied
The design procedure is based on a comprehensive anaiysis of concrete stresses and deflections at pavement
joints, corners, and edges by a finite-element computer
of slabs with finite
program. IN ,t ~I]ow~ ~o”~iderations
dimensions, variable axle-load placement, and the modeling of load transfer at transverse joints 6r cracks and
load transfer at the joint between pavement and concrete
shoulder. For doweled joints, dowel properties such as
diameter and modulus of elastic it y are used direct] y. For
aggregate, interlock, keyway joints, and cracks in comim
uously reinforced pavements, a spring stiffness value is
used to represent the load-deflection
characteristics
of
such joints based on field and laboratory tests.
analysis
of different
U“
I
L–––––––L–––––_J
(.) Axle. I.od p.sil ion for criticolf lexw.1 stresses
Freeedgem
shoulder
joint
m
i
Troffic
lone
i
>
,
Concrete
(,F medl
shoulder
L–––____J__——––––
(b)
Jointed Pavements
After
I
I
Analysis of Concrete Pavements
_.
.
Axle load pmitio. for critic.! deflections
d
axle-load
positions
on the slab,
Fig.
Al. Critical axle-load positions.
32
Publication List
Book Contents
on to the mainline pavement, the magnitude
critical stresses is considerably reduced.
of the
2. The most critical pavement deflections occur at the
slab corner when an axle load is placed at the joint
with the wheels at or near the corner, Fig. A I(b). *
In this situation, transverse joint spacing has no effect on the magnitude of corner deflections but the
type of load transfer mechanism has a substantial
effect. This means that design results based on the
erosion criteria (deflections) may be substantially
affected by the type of load transfer selected, especially when large numbers of trucks are being designed for. A concrete shoulder reduces corner deflections considerably.
Continuously
P
Reinforced
Pavements
A continuously
reinforced
concrete
pavement
(CRCP)
is one with no transverse joints and, due to the heavy,
continuous steel reinforcement in the longitudinal direction, the pavement develops cracks at close intervals.
These crack spacings on a given project are variable, running generally from 3 to 10 ft with averages of 4 to 5 ft.
In the finite-element computer analysis, a high degree
of load transfer was assigned at the cracks of CRCP and
the crack spacing was varied. The critical load positions
established were the same as those for jointed pavements.
For the longer crack spacings, edge stresses for loads
placed midway between cracks are of about the same
magnitude as those for jointed pavements. For the average and shorter crack spacings, the edge stresses are less
than those for jointed pavements, because there is not
enough length of untracked pavement to develop as much
bending moment.
For the longer crack spacings, corner deflections are
somewhat less than those for jointed pavements with
doweled transverse joints. For average to long crack
spacings, corner deflections are about the same as those
for jointed, doweled pavements. For short crack spacings
of 3 or 4 ft, corner deflections are somewhat greater than
those for jointed, doweled pavements, especially for tandem-axle loads.
Considering natural variations in crack spacing that
occur in one stretch of pavement, the following comparison of continuously
reinforced pavements with jointed,
dnweled pavements is made. Edge stresses will sometimes
be the same and sometimes
will sometimes
less, while
corner
Truck Load Placement
Truck wheel loads placed at the outside pavement edge
create more severe conditions than any other load position. As the truck placement moves inward a few inches
from the edge, the effects decrease substantially.(”)
Only a small fraction of all the trucks run with their
nutside wheels placed at the edge. Most of the trucks traveling the pavement are driven with their outside wheel
placed abnut 2 ft from the edge, Taragin’s(40] studies reported in 1958, showed very little truck encroachment at
pavement edge for 12-ft lanes for pavements with unpaved shoulders. More recent studies by Emery(”) shnwed
more trucks at edge, Other recent studies”’] showed fewer
trucks at edge than Emery. Fnr this design prncedure, the
most severe conditinn, 6c%of trucks at edge, * is assumed
so as to be on the safe side and to take account of recent
changes in United States law permitting wider trucks.
At increasing distances inward from the pavement
edge, the frequency of lnad applications increases while
the magnitudes of stress and deflecting decrease. Data
on truck placement distribution and distributing of stress
and deflection due to loads placed at and near the pavement edge are difficult to use directly in a design procedure. As a result, the distributions
were analyzed and
more easily applied techniques were prepared for design
purposes.
For stress-fatigue analysis, fatigue was computed incrementally at fractions of inches inward fmm the slab
edge for different truck-placement
distributions;
this
gave the equivalent edge-stress factors shown in Fig. A2.
(This factor, when multiplied by edge-load stress, gives
the same degree of fatigue consumption that would result
from a given truck placement distribution,)
The mnst
severe condition, 6T0 truck encroachment,
has been incorporated in the design tables.
deflections
be less, the same, andgreater
at different
of the pavement
depending
on crack spacing.
The average of these pavement responses is neither
substantially
better nor worse than those for jointed,
doweled pavements. As a result, in this design procedure,
the same pavement responses and criteria are applied to
continuously
reinforced pavements as those used with
jointed, doweled pavements. This recommendation
is
consistent with pavement performance experience. Most
design agencies suggest that the thickness of continuously
reinforced pavements should be about the same as the
thickness nfdoweled-jointed
pavements.
areas
P
*The greatest deflections
at one
for tridwm
occur
when
two
axles
are placed
side of the ioint and me axle at the other side.
0:ME2!&ia
cc
0123
4567a
PERCENT
TRuCKS
AT
EDGE
Fig. A2. Equivalent edge stress factor depends
percent of trucks at edge.
on
*As used hm, the term ‘<percenttrucks at edge,, is defined as the
percent of totat tmcks that a= travetiw with the outside of the con~ct
area of the outside tire at or beyond the pavement edge.
33
Publication List
Book Contents
For erosion analysis, which involves deflection at the
slab corner, the most severe case (6% of trucks at edge) is
again assumed. Where there is no concrete shoulder, corner loadings (6% of trucks) are critical; and where there
is a concrete shoulder, the greater number of loadings
inward from the pavement corner (94’% of trucks) are
critical. These factors are incorporated
into the design
charts as follows:
Percent erosion damage
where
= 100 Xn (C/ Ni)
n, = expected number of axle-load
repetitions for axle-group i
Ni = allowable number of repetitions for axle-group i
C = 0.06 for pavements without
shoulder, and
0.94 for pavements with
shoulder
To save a design calculation step, the effects of (C/NiI
are incorporated
in Figs. 6a and 6b of Chapter 3 and
Tables 11 through 14 of Chapter 4.
Variation in Concrete Strength
Recognition of the variations in concrete strength is considered a realistic addition to the design procedure. Expected ranges of variations in the concrete’s modulus of
rupture have far greater effect than the usual variations
in the properties of other materials, such as subgrade and
subbase strength, and layer thicknesses. Variation in concrete strength is introduced by reducing the modulus of
rupture by one coefficient of variation.
For design purposes, a coefficient of variation of 15%
is assumed and is incorporated
into the design charts and
tables. The user does not directly apply this effect, fie
value of 15% represents fair-to-good quality control, and,
combined with other effects discussed elsewhere in this
appendix, was selected as being realistic and giving reasonable design results.
effect is influenced greatly by creep.
Curling refers to slab behavior due to variations of
temperature.
During the day, when the tnp surface is
warmer thanthe bottom, tensile-restraint stresses develop
at the slab bottom. During the night, the temperature distribution isreversed andtensile restraint stresses develop
at the slab surhce. Temperature
distribution
is usually
nonlinear and constantly changing, Alsn, maximum daytime and nighttime temperature
differentials exist for
short durations,
Usually the combined effect of curling and warping
stresses are subtractive from load stresses because the
moisture content and temperature
at the bottom of the
slab exceed that at the top more than the reverse.
The complex situation ofdifferential
conditions ata
slab’s top and bottom plus the uncertainty of the zerostress position make it difficult tocompute
or measure
the restraint stresses with any degree of confidence or
verification.
At present, the information
available on
actual magnitudes of restraint stresses does not warrant
incorporation
of the items in this design procedure.
As for the lnss of support, this is considered indirectly
in tbe erodibility criterion, which is derived from actual
field performance and therefore incorporates normal loss
of support conditions,
Calculated stress increase due to loss of support varies
from about 5%to 15%Thisth eoreticalst ressincreaseis
counteracted
in the real case because a portion of the load
is dissipated in bringing the dab edges back in contact
with the support. Thus, the incremental load stress due to
a warping-type loss of support is not incorporated
in this
design procedure,
~
.
Fatigue
The flexural fatigue criterion used in the procedure presented here is shown in Fig, A3. It issimilar to that used
in the previous PCAmethndi4’]
based conservativelyon
Concrete Strength Gain With Age
0,9
The 28day flexural strength (modulus of rupture) is used
as the design strength. This design procedure, however,
incorporates the effect of concrete strength gain after 28
days. This modification is based on an analysis that incremented strength gain and load repetitions
month by
month for 20-year and 40-year design periods. The effect
is included in the design charts and tables so the user
simply inputs the 28-day value as the design strength.
0.8
Curve
by Hil,do,f
And Kesler
Constant Pmb,tdl;ty
0.05
Q
$
Wh
a7
m
Pc&
curve
:
:
m
0.6
Warping and Curling of Concrete
0.5
In addition to traffic Ioadi”g, concrete slabs am also ~~b.
jetted to warping and curling. Warping is the upward
concave deformation of the slab due to variations in moisture content with slab depth. The effect of warping is twofold: It results in loss of support along the slab edges and
also in compressive restraint stresses in the slab bottom,
Since warping isalong-term
phenomenon,
itsres”ltam
Extended
0,4,.2
,.3
LOAD
>._
,@
, ~,
REPETITIONS
u--”
Fig. A3. Fatigue relationships.
34
Publication List
, ,y
104
C.,,,
Book Contents
studies of fatigue research[4s-”9) except that it is applied to
edge-load stresses that are of higher magnitude. A modification in the high-load-repetition
range has been made
to eliminate the discontinuity in the previous curve that
sometimes causes unrealistic effects,
The allowable number of load repetitions for a given
axle load is determined based on the stress ratio (flexural
stress divided
by the 28-day modulus
of rupture).
The
fatigue curve is incorporated
into the design charts for
use by the designer.
Use of the fatigue criterion is made on the Miner hypothes]s 140that fatigue ~e~istance not consumed by rePetitions of one load is available for repetitions of other
loads. In a design problem, the total fatigue consumed
should not exceed 100%.
Combined with the effect of reducing the design modulus of rupture by one coefficient of variation, the fatigue
criterion is considered to be conservative for thickness
design purposes.
Erosion
,P
~
Previous mechanistic
design procedures
for concrete
pavements are based on the principle of limiting the ffexural stresses in a slab to safe values. This is done to avoid
flexural fatigue cracks due to load repetitions.
It has been apparent that there is an important mode
of distress in addition to fatigue cracking that needs to
be addressed in the design process. T& is the erosion of
material beneath and beside the slab.
Many repetitions of heavy axle loads at slab corners
and edges cause pumping; erosion of subgrade, subbase,
and shoulder materialy voids under and adjacent to the
slab; and faulting of pavement joints, especially in pavements with undoweled joints.
These particular pavement distresses are considered to
be more closely related to pavement deflections than to
flexural stresses.
Correlations
of deflections computed from the finiteelement analysis(a] with AASHO Road Test{ 24]performance data were not completely satisfactory for design
purposes.
(The principal mode of failure of concrete
pavements at the AASHO Road Test was pumping or
erosion of the granular subbase from under the slabs.) It
was found that to be able to predict the AASHO Road
Test performance,
different values of deflection criteria
would have to be applied to different slab thicknesses,
and to a small extent, different foundation
moduli (k
values),
More useful correlation was obtained by multiplying
the computed corner deflection values (w) by computed
pressure values (.P) at the slab-foundation
interface, Power, or rate of work, with which an axle load deflects the
slab is the parameter used for the erosion criterion—for a
unit area, the product of pressure and deflection divided
by a measure of the length of the deflection basin (l—
radius of relative stiffness, in inches). The concept is that
a thin pavement with its shorter deflection basin receives
a faster load punch than a thicker slab. That is, at equal
pw’s and equal truck speed, the thinner slab is subjected
to a faster rate of work or power (inch-pound per second).
A successful correlation with road test performance was
obtained with this parameter,
The development of the erosion criterion was also generally related to studies on joint faulting. [2* 29) These
studies included pavements in Wisconsin, Minnesota,
North Dakota, Georgia, and California, and included a
range of variables not found at the AASHO Road Test,
such as a greater number of trucks, undoweled pavements, a wide range of years of pavement service, and
stabilized subbases.
Brokaw’s studies (2o of ““doweled pavements suggest
that climate or drainage is a significant factor in pavement performance.
So far, this aspect of design has not
been included in the design procedure. but it deserves
further study. Investigations of the effects of climate on
design and performance of concrete pavements have also
been reported by Darter. [”]
The erosion criterion is suggested for use as a guideline.
It can be modified according to local experience since
cfimate, drainage, local factors, and design innovations
may have an influence. Accordingly, the 100% erosiondamage criterion, an index number correlated with general performance
experience, can be increased or decreased based on specific performance data gathered in
the future for more favorable or more adverse conditions.
35
Publication List
Book Contents
b’
APPENDIX B
Design of Concrete Pavements with Lean
Concrete Lower Course
Following is the thickness design procedure for composite concrete pavements incorporating
a lower layer of
lean concrete, either as a suhhase constructed separately
or as a lower layer in monolithic construction.
Design
considerations
and construction practices for such pavements are discussed in References 50 through 52.
Lean concrete is stronger than conventional
subbase
materials and is considered to be nonerodable,
Recognition of its superior structural properties can be taken by
a reduction in thickness design requirements.
Analysis of composite concrete pavements is a special
case where the conventional two-layer theory (single slab
on a foundation)
is not strictly applicable.
The design procedure indicates a thickness for a twolayer concrete pavement equivalent to a given thickness
of normal concrete. The latter is determined by the procedures described in Chapters 3 and 4. The equivalence
is based on providing thickness for a two-layer concrete
pavement that will have the same margin of safety* for
fatigue and erosion as a single-layer normal concrete
pavement.
In the design charts, Fig. B] and Fig, B2, the required
layer thicknesses depend on the flexural strengths of the
two concrete materials as determined by ASTM C78.
Since the quality of lean concrete is often specified on the
basis of compressive strength, Fig. B3 can be used to convert this to an estimated flexural strength (modulus of
rupture) for usc in preliminary design calculations.
Lean Concrete Subbase
The largest paving use of lean concrete has been as a subbase under a conventional
concrete pavement, This is
nonmonolithic
construction
where the surface course of
normal concrete is placed on a hardened lean concrete
subbase. Usually, the lean concrete subbase is built at
least 2 ft wider than the pavement on each side to support
the tracks of the sfipform paver. This extra width is structurally beneficial for wheel loads applied at pavement
edge.
The normal practice has been to select a surface thick-
ness about twice the subbase thickness; for example, 9 in.
of concrete on a 4- or 5-in. subbase.
Fig. B 1 shows the surface and subbase thickness requirements set to be equivalent to a given thickness of
normal concrete without a lean concrete subbase.
A sample problem is given to illustrate the design procedure. From laboratory tests, concrete mix designs have
been selected that give moduli of rupture of 650 and 200
psi~*respectively,
for the surface concrete and the lean
concrete subbase. Assume that a I&In.-thickness requirement has been determined for a pavement without lean
concrete subbase as set forth in Chapter 3 or 4.
As shown by the dashed example line in Fig. BI, designs equivalent to the 10-in. pavement are (1) 7.7-in.
concrete on a 5-in. lean concrete subbase, and (2) 8. l-in.
concfcte on a &]n. lean concrete subbase.
Monolithic
W’
Pavement
In some areas, a relatively thin concrete surface course is
constructed
monolithically
with a lean concrete lower
layer. Local or recycled aggregates can be used for the
lean concrete, resulting in cost savings and conservation
of bighqualit y aggregates.
●ll.
criteria are that (1) stressratios in either of the two concrete
layers not exceed that of the reference pavement and (2)erosion values
at the s.bbase-s.bgrade interface not exceed those of the reference pavement. Rational. for the criteria is give. in Reference 50 plus two ad&ltimal considerations: (1) erosion criteria is included in addition to the
fatigue approach given in the referencq and (2) for nonmonolithic con-
struction, some structural benefit C141is added because the subbase is
constructed wider than the pavement.
. . F1.xural wemgth of !..” comxete m be used as a subbase is usually
selected to be between i50 to 250 psi (compressive Wength, 750 to 1200
psih these relatively low strengths are used to minimize reflective cracking from tbe unjointed subbase (.s..1 practice is to leave the s.hhm.
.“jointed) through the concrete surface. lf, c.ntmry toc.rrem practic.,
joints are placed in the subbase, the stcmgth of the 1..” comrete would
“.1 have to b. restricted m the lower m “ge.
36
Publication List
,..
Book Contents
,,.
u
Modulus
of
of Leon
Rupture
350
Concrete,
450
I50
psi
250
350
450
250.
<
14
/
450
I 50
350
14
<
13
250 .. / ‘
,0
_
.< “%
/ ‘
/
12
I50
;
/ ‘
6).
/ ‘
II
/ /
/
d
/
)
0
I 0(.++
~
–;
4
9
r
9
are thicknesses
surface
course
of concrete
Fig. B1. Design chart for composite concrete pavement (lean concrete subbase),
37
Publication List
Book Contents
Modulus
of Rupture
of Lean Concrete, psi
450
150
250
350
450
14
350
/,
13 -
12
“l-
t+htl+’tft
‘0+--wH--tf7b%4
3“ Surface
4“ Surface
Fig. B2, Design chart for composite concrete pavement (monolithic
with lean concrde
Iowef layer).
Unlike the lean concrete subbases discussed in the previous section, the lower layer of lean concrete is placed
at the same width as the surface course, and joints are
sawed deep enough to induce fulldepth cracking through
both layers at the joint locations.
Fig. B2 is the design chart for monolithic pavements.
To illustrate its use, assume that the design strengths of
the two concretes are 650 and 350 psi, and that the design
procedures of Chapter 3 or 4 indicate a thickness requirement of 10 in. for fulldepth
normal concrete.
As shown by the dashed example fine in Fig. B2, monolithic designs equivalent to the IO-in. pavement are (1)4in. concrete surface on 8.3-in. lean concrete, or (2) 3-in.
surface on 9.3-in. lean concrete.
COMPRESSIVE
Fig.
38
Publication List
STRENGTH,
PSI
B3. Modulus of rupture versus compressive strength
(from Reference 50).
Book Contents
APPENDIX C
Analysis of Tridem Axle Loads
loads* can be included
along with single- and
tandem-axle loads in the design analysis by use of data
given in this appendix.
The same design steps and format outlined in Chapter
3 are followed except that Tables C I through C3 are used.
From these tables for tridems, equivalent stress and erosion factors are entered in an extra design worksheet.
Then Fig. 5 and Fig. ti or 6b are used to determine allowable numbers of load repetitions. Fatigue and erosion
damage totals for tridems are added to those for singleand tandem-axle loads,
An extension of the sample problem, Design 1A given
in Chapter 3, is used here to illustrate the procedure for
tridem loads. Assume that, in addition to the single- and
tandem-axle loads, a section of the highway is to carry a
fleet of special coal-hauling trucks equipped with tridems
at the rate of about 100 per working day for an estimated
period of 10 year> so:
100 trucks X 250 days X 10 years = 250,000 total trucks
Tridem
P
The trucks in one direction are normally all loaded to
their capacity of 54,000-lb tridem load plus 7000-lb steering-axle (single-axle) load. (When it is examined, the
steering axles are not heavy enough to affect the design
results.)
Fig. C 1 represents a portion of tbe extra design worksheet needed to evaluate tbe effects of these tridems. Since
Design 1A (9:5-in. pavement, combined k of 130 pci) is a
pavement with doweled joints and no concrete shoulder,
Tables Cl and C2 are used to determine the equivalent
stress and erosion factors, Items 1 I and 13 on the worksheet.
For this example, Fig. 5 is used to determine allowable
load repetitions for the fatigue analvsis and l%. 6a is used
for tbe”erosion analysis.
The tridem loads of 54,000 lb are multiplied by t he load
safety factor for Design 1A of 1.2, giving a design axle
load of 64,800 lb. Before using the charts for allowable
load
repetitions,
three
(64,800/3
the tridem
= 21,600
load
(3 axles)
lb) so that
is divided
the load
by
scale for
axles can be used, **
As show” in Fig, Cl, the tridem causes only 9.3% erosion damage and 0% fatigue damage. These results, added
to the effects of the single and tandem axles shown in Fig.
4 are not sufficient to require a design thickness increase.
single
*A trid.m or triple axle isa set of three axles each sp.ced at 48 to 54in.
apart. These am used on special heavy-duty haul trucks.
..Thl$ is not to say th.tatridcm hasthe~meeff=t asthrec singieaxles.
The damaging effects of tridem, tandem, and single axles are incorporated into their rqmtive equivalent stress and emsicm factor tables,
which i“ the sequeme of the design steps is taken into accmmt before
the charm for allowable-load repetitions arc entered. This divisicm by
three for tridetm is made just to avoid the complexity of adding a third
scale on the charts for allowable-load qxtitio.s,
39
Publication List
Book Contents
Calculation
of Pavement Thickness
7f
Trial
thickness
S.bbase-sub.arade
Modulus
k
.1 nmt”re,
Load safely
factor,
5?5-
(n:
Doweled
L.?o
.,i
concrete
MR ~
LSF
psi
1
C9sig”
M“!tiPlied
Z??,(L
joints
sh.w ldw
Period
D
yes’+.0
yes
~
-.
—
_
no X
L-J
yea,,
z
Fatigue
Axle
load,
I@
/
T.
analysis
Erosion
analysis
ExPect&
repetition,
~gYF
Allowable
repetition,
/7
Fatigue,
percent
Allowable
repetitions
Damage,
percent
1516
111213/4
1
1
1
[
171
I
I
I
1
I
1
I
I
I
Total
74 be
I
Total
o
ZzdJ&
X6
4224
SAw’7
7.3
/>
6++
Fig. Cl. Analysis of tridems.
,.-
u’
Tabla Cl. Equivalent Stress-Tridems
(Without Concrete Shouldar/With
Slab
k of
thickness,
Concrete Shoulder)
subgrsde.subbase,
pcl
50
100
150
200
300
500
700
4
4,5
51W431
439/365
456/392
380/328
4371377
359/31 3
428/369
349/305
419/362
339/297
41 4/360
331/392
41 2/359
32S/291
5
5.5
367/317
347[279
328/281
290/246
305/266
266/231
293/258
253/223
282/250
240/214
272[244
230/206
269/242
226/206
8
6.5
315[249
289/225
261/218
238/1 96
237/204
214/163
223/1 96
201/175
209/187
186/1 66
198/1 80
173/159
193/1 78
168/1 56
7
7.5
267/304
247/1 87
219/178
203/1 62
196/1 65
181/151
183/1 58
166/1 43
167/1 49
153/135
154/142
139/1 27
148/1 38
132(124
6
6.5
230/172
215/159
189/1 49
177[1 36
168/1 36
1561126
156/131
145/121
141/123
131/113
126/116
116/106
120/112
109/102
9
9.5
2W147
1871137
166/ 128
157/120
148/119
140/111
136/112
129/1 05
122/105
115/98
108/98
101/91
101/94
93/87
in.
10
1741127
10.5
183/119
148/112
140/105
133/104
125/97
122/98
115/92
106/91
103/86
95/64
89/79
87/61
82/78
11
11.5
153/111
142/104
133/89
125/93
119/92
113/86
110/87
104/82
98/81
93{76
S5174
80/70
78177
74/67
12
12.5
133/97
123/91
119/83
113/33
106/82
103/78
100[78
95/74
89/72
85/66
77/66
73[63
70/63
67/847
13
13.5
114/85
105/80
107/79
101/75
98/74
93/70
91/70
87/67
81/65
78[62
70/80
67[57
64/57
61/54
97175
98/71
89/67
83/63
75/59
65/54
59/51
14
40
Publication List
Book Contents
,..
L/”
Table CZ. Eroalon Factors-Tridema-Doweled
(Without Concrete Shoulder/With
p
Slab
thickness,
,.,
Joints
Concrete !Woulder)
k of subgrade-subbase,
50
100
200
300
pci
500
700
4
4,5
3.8913.33
3.7813.24
3.82/3.20
3.69/3,10
3.7513.13
3.62./2.99
3.70/3.10
3.57/2.95
3,61,13.05
3.50,(2.91
3.53/3.00
3.4412.87
5
5.5
3,68/3.16
3.59/3.09
3.56/3,01
3.49/2.94
3.50/2.89
3.40/2.80
3.4612.83
3,36/2.74
3.4012.79
3.3012.67
3.3412.75
3.2512.84
6
6.5
3.51/3.03
3,44/2,97
3,40/2.87
3.33/2.82
3.3112.73
3.23/2.67
3.28/2.66
3.18/2.59
3.2112.58
3.12(2,50
3.16/2.54
3.08/2.45
7
7.5
3,37[2,92
3.31/2,87
3.26/2.76
3.20/2.72
3,18/2.61
3,09/2.56
3.10/2.53
3.03/2.47
3.04!2.43
2.97/2.37
3.00/2.37
2.93/2.31
6
8,5
3.26/2,83
3.20/2.79
3.14/2.67
3.09/2.63
3,03/2.51
2.9712.47
2.97/2.42
2.91/2,38
2.80/2.32
2.84,(2.27
2.86/2,25
2.79/2,20
9
9.5
3.15/2.75
3.11/2.71
3.04/2.59
2.99/2.55
2.92/2.43
2.67/2,39
2.66/2,34
2.81/2.30
2.7612,23
2.73/2.18
2.73t2.15
2,68/2. 11
10
10.5
3.08/2.67
3.02/2.64
2.94/2.51
2.90/2.48
2.83/2.35
2,78/2.32
2.76/2,26
2.7.2/2.23
2.68,/2.15
2.64/2.1 1
2,63/2,07
2.58/2.04
11
11.5
2.98/2.60
2.94/2.57
2.86/2.45
2.82/2.42
2.74/2.29
2.70/2.26
2.68/2,20
2.64/2.16
2,59/2.08
2.55,,2.05
2.54/2.00
2.50/1.97
12
12.5
2.91/2.54
2.6712.53
2.79/2.39
2.75/2,36
2.67/2.23
2.63/2.20
2.60/2.13
2.56/2.11
2.51/2.02
2.48,{1 .99
2.48/1.94
2.42/1.91
13
13,5
2,8412.48
2,61/2,46
2.72/2.33
2,68/2.30
2.6012.17
2.56/2.14
2.53/2.06
2.49/2.05
2.44,{1.96
2,41,(1 .93
2.39/1.88
2.35/1.86
14
2.78/2.43
2.6512.28
2.53/2.12
2.46/2.03
2.38,(1 .91
2.32/1 .83
P
Table C3. Erosion Fectors—Tridems-Aggregate-interlock
(Without Concrete Shoulder/With Concrete
Slab
thic;.,
k of subgrade-subbase,
4
4.5
Joints
:~oulder)
pci
50
100
200
300
5130
700
4.06/3.50
3.9513.40
3.97[3.36
3.8513.26
3.68/3.30
3,78/3.16
3.62/3.25
3.70/3.13
3.7413.21
3.63/3.08
3.6713.16
3.58/3.04
5
5.5
I
3,85[3,32
3,76/3,26
3.75/3.19
3,66/3.11
3.66/3.06
3.56/3.00
3.60/3.03
3.51[2.94
3.52/2.97
3.4312.67
3.46/2.93
3.37[2 .83
6
6.5
I
3,68/3,20
3.61/3.14
3.58/3.05
3.50/2.99
3.4LV2.92
3.40/2.86
3,42/2.66
3.34/2.79
3.35,/2.79
3.27,/2.72
3.29/2.74
3.21/2.67
7
7.5
3.54/3.09
3.48/3.05
3.43/2.94
3.3712.89
3.33/2.80
3.2612.75
3.27/2.73
3.20/2.67
3.20/2,65
3.13/2.59
3,14/2.60
3.06/2.54
8
8.5
3.42/3.01
3.3712.97
3.31/2,84
3.25/2.80
3,20/2.70
3.15/2.65
3.14/2.62
3.09/2.58
3.07/2.54
3.01/2,49
3.01/2.46
2.96/2.43
9
9.5
3.32/2.94
3.2712.91
3.20/2.77
3.15/2.73
3.09/2.61
3.0412.56
3.03/2.53
2.98/2.49
2,95/2,44
2.90/2.40
2.90/2.38
2.85/2.34
10.5
3.22/2.88
3.f 8/2.85
3.11/2,70
3.06/2.67
3.00/2.54
2.95/2.51
2.93/2.46
2.89/2.42
2.85/2.36
2.8112.32
2.60/2,29
2.76[2 .26
11
11.5
3.14/2.83
3.10/2.80
3.02/2.85
2,98/2.62
2.91/2.48
2.8712.45
2.8412.39
2.80/2.36
2.7712.29
2.72/2.26
2.71/2.22
2.67/2.19
10
41
Publication List
Book Contents
APPENDIX D
Estimating Traffic Volume by Capacity
At the time of preparing this bulletin, information
on highway capacity is under extensive revision and computational
methods and results may be substantially
changed. New publications of AASHTO and theFHWA
“Highway Capacity Manual,” expected to be published
in 1984 and 1985, should be used when available and they
will replace the methods and references presented in this
appendix.)
In Chapter 2, the traffic volume (ADTI is estimated by
a method based cm the projected rates of traffic growth.
When the projected traffic volume is relatively high for a
specifk project, this method should be checked by the
capacity method described here.
The practical capacity of a pavement facility is defined
as the maximum number of vehicles per lane per hour
that can pass a given point under prevailing road and
traffic conditions without unreasonable delay or restricted freedom to maneuver. Prevailing conditions include
composition
of traffic, vehicle speeds, weather, alignment, proffle, number and width of lanes, and area.
The termproctical
capacity is commonly used in reference to existing highways, and the term design capaciry
is used. for design purposes. Where traffic flow is uninterrupted-or
nearly so—practical
capacity and design
capacity are numerically equel and have essentially the
same meaning. In accordance with AAS HTO usage1s3 ’41
the term design capacity is used in this text. Design capacities for various kinds of multilane highways are summarized in Table DI.
(Note:
AD T Capacity of Multilane Highways
For thickness design it is necessary to convert the pasaenger cars per hour in Table D1 to average daily traffic
in both directions, ADT, For multilane highways with
uninterrupted
flow tbe following formula is used:
ADT =
100P
100+ Tpd-
1) x
Table D1. Design Capacities for
Multilane Highways
Design capacity:
passenger cars
pe;;r2ftJne
Type of highway
rreew.ys vm. w access comm
‘Suburt )an freeways with full access control
,.. . .
‘Rural freeways with Wll or p
~
control
Rural major highway!
cross traffic and road.,..
Rural major highways with c
cross traffic and roadside Inwrmrerwe
I
,AIso includes panels, pickups, and other four-tire oxnrnerci.1 vehicles
that function a. passenger cars in terms of traffic capacity. Values are
taken from References 53 and 54,
j = ~“mber Of passenger cars equivalent tO One
truck
= 4 in rolling terrain
= 2 in level terrain
K = design hour volume, DHV, expressed as a
percentage of ADT
= 15% for rural freeways in this text
= 12% for urban freeways in thk text**
D = traffic, percent, in direction of heaviest travel
during peak hours—about
5070 to 75%
= 67% for rural freeways in this text
= 6090 for urban freeways in this text
5000N
KD
where P
= passenger cars* per lane per hour (from
Table D 1)
N = number of lanes—total both directions
T,, = trucks, percent, during peak hours
= 2/3 ADT_f in this booklet
‘See f..tn.te at bottom of Table D!.
**s,, Reference 54, pa.~e$96 m 98, and Reference 56.
42
Publication List
Book Contents
p
Detailed discussions of this formula will be found in
References 53, 54, and 55. As presented here, the symbol
for one term, T, of the formula, T,~, differs from the symbol for this term in the references. In this text:
T = trucks—includes
only single units with more
than four tires and all combinations.
(Does
not include panels, pickups, and other single
units with only four tires.)
ADTT = average daily truck traffic in both directions—may be expressed as a percentage of
ADT or as an actual value.
Capacity of Two-Lane Highways
Important factors in the design capacit y of two-lane highways are (1) the percent of total project length where sight
distance is less than 1500 ft, and (2) lane widths of less
than 12 ft.* The design capacity in vehicles per hour (vph)
for unintermpted
flow on two-lane highways is shown
in Table D2.
It is good practice to use both traffic projection factors and design capacity for thickness design of specific
projects. For example, if an existing two-lane route is carrying 4000 ADT and the projection factor is 2.7, the projected ADT would be 10,800. This is more than 4000
vehicles per day (vpd) greater than the design capacity of
virtually all two-kme highways.** On the other hand,
10,800 ADT is below the design capacity of most fourlane highways.t
Hence, the design should be made for
10,800 ADT on a four-lane roadway, Design capacity
should not be used where it shows a greater ADT than
shown by traffic projection.
p
*Lane widths of lessthan 12ft are rarely used in current pract i.., except for very lightly traveled two-lam roads where land serviceis a primary function.
**SW Table D2.
?S.. Refermct 53, Table 11-14.
Table D2. De$ign Capacities for Uninterrupted
Flow on Two-Lsne Highways’
Design Capacity, both directions, in vph,-
==
I
Rolling
40
800
o
I 900
40
80
80
800
720
620
7Cnl
620
640
570
510
440
500
k:~
‘KHx!uui
Source: Reference 53, Table 11-10,P.39e88.
‘. T.b.lar ..1..s apply where lateral clearance is not mstri.led. Where clearance is less th.” 6 H
apply factors In Reference 53, Table IIF 7, page 89.
VTr.cks, does not include four-tire vehicle..
43
Publication List
Book Contents
w’
APPENDIX E
References
1. Westergaard,
H. M., “Computation
of Stresses in
Concrete
Roads,” High way Research Board pro.
ceedings, Fifth Annual Meeting, 1925, Part 1, pages
90 to 112.
2. Westergaard, H. M., “Stresses in Concrete Pavements
Computed by Theoretical Analysis,” Public Roads,
Vol. 7, No. 2, April 1926, pages 25 to 35.
3. Westergaard,
H. M., “Analysis of Stresses in Concrete Roads Caused by Variations in Temperature,”
Public Roads, Vol. 8, No. 3, May 1927, pages 201 to
215.
4. Westergaard,
H. M., “Theory of Concrete Pavement
Design;
High way Research Board Proceedings,
Seventh Annual Meeting, 1927, Part 1, pages 175 to
181.
5. Westergaard,
H. M., “Analytical Tools for Judging
Results of Structural Tests of Concrete Pavements?
Public Roads, Vol. 14, No. 10, December 1933, pages
185 to 188.
6. P1ckett, Gerald; Ravine, Milton E.; Jones, WMam C.;
and McCormick,
Frank J., “Deflections,
Moments
and Reactive Pressures for Concrete pavements,”
Kansas State College Bulletin No. 65, October 1951.
7. Pickett, Gerald, and Ray, Gordon K., “Influence
Charts for Concrete Pavements?
American Society
of Civil Engineers Transactions, Paper No. 2425, Vol.
116, 1951, pages 49 to 73.
8. Tayabji, S. D., and Coney, B. E., “Analysis of Jointed
Concrete Pavements,” report prepared by the Construction Technology Laboratories
of the Portland
Cement Association for the Federal Highway Administration,
October 1981.
9. Teller, L. W., and Sutherland, E. C., “The Structural
Design of Concrete Pavements,” Public Roads, Vol.
16, Nos. 8, 9, and 10 (1935) Vol. 17, Nos. 7 and 8
(1936); Vol. 23, No. 8 (1943).
10. Childs, L. D., Coney, B. E., and Kapernick, J. W.,
“Tests to Evaluate Concrete Pavement Subbases,”
Proceedings of American Society of Civil Engineers,
Paper No. 1297, Vol. 83 (H W-3), July 1957, pages 1 to
41;, also PCA Development
Department
Bulletin
DXOI1.
11. Childs., L. D., and Kapernick, J. W., “Tests of Concrete Pavement Slabs on Gravel Subbases,” Proceedings of American Society of Civil Engineers, Vol. 84
(HW-3), October 195fi also PCA Development
Department Bulletin DX021.
12. Childs. ,, L. D.. and Kanernick.
.
. J. W... “Tests of Concrete Pavements on Crushed Stone Subbases,” Proceedings of American Society of Civil Engineers,
Proc. Paper No. 3497, Vol. 89 (H W- 1), April 1963,
pages 57 to 8@ also PCA Development Department
Bulletin DX065.
13. Childs, L. D., “Tests of Concrete Pavement Slabs on
Cement-Treated
Subbases,” Highway Research Record 60, Highway Research Board, 1963, pages 39 to
58; also PCA Development
Department
Bulletin
DX086.
14. Childs, L. D., “Cement-Treated
Subbases for Concrete Pavements,”
Highway Research Record 189,
Highway Research Board, 1967, pages 19 to 43; also
PCA Development
Department
Bulletin DX125.
15. Childs, L. D., and Nussbaum, P. J,, “Repetitive Load
Tests of Concrete Slabs on Cement-Treated
Subbases,” RD025P, Portland Cement Association, 1975.
16. Tayabji, S. D., and Coney, B. E,, “Improved Rigid
Pavement Joints,” paper presented at Annual Meeting
of Transportation
Research Board, January 1983 (to
be published in 1984).
17. Childs, L. D., and Ball, C. G., “Tests of Joints for
Concrete Pavements,”
RD026P, Portland Cement
Association,
1975.
18. Coney, B. E., and Humphrey, H. A., “Aggregate interlock at Joints in Concrete Pavements,” Highway
Research Board Record No. 189, Transportation
Research Board, 1967, pages I to 18.
19. Coney, B. E., Ball, C. G., and Arriyavat, P., “EvaluatiOn Of Concrete Pavements with Tied Shoulders or
Widened Lanes,” Transportation
Research Record
666, Transportation
Research Board, 1978; also Pmt-
44
Publication List
Book Contents
z “’
‘~
....
‘
‘~
p
P
land Cement Association,
Research and Development Bulletin RD065P, 1980.
20. Sawan, J. S., Darter, M. L, and Dempsey, B. J.,
“Structural Analysis and Design of PCC Shoulders,”
Report No. FH WA-RD-8 1-122, Federal Highway
Administration,
April 1982.
21. Older, Clifford, “Highway
Research in Illinois,”
Proceedings of American Society of Civil Engineers,
February 1924, pages 175 to 217.
22. Aldrich, Lloyd, and Leonard, Ino B., “Report of
Highway Research at Pittsb”rg,
California,
19zI1922,” California State Pri”ti”g office,
23. Road Test One-MD, Highway Research Board Special Report No. 4, 1952.
24. The AASHO Road Test, Highway Research Board
Special Report No. 6 I E, 1962.
25. The AASHO Road Test, Highway Research Board
Special Report No. 73, 1962.
26. AA SHTO Inlerim Guide for Design of Pavement
Structures, /972, Chapter 111 Revised, 1981, American Association of State Highway and Transportation Officials, 1981,
27. Fordyce, Phil, and Teske, W. E,, “Some Relationships of tbe AASHO Road Test to Concrete Pavement Design,” High way Research Board Record No,
44, 1963, pages 35 to 70.
28. Brokaw, M. P., “Effect of Serviceability and Roughness at Transverse Joints on Performance
and Design of Plain Concrete Pavement,” Highway Research
Board Record 471, Transportation
Research Board,
1973.
29. Packard, R. G., “Design Considerations
For Control
of Joint Faulting of Undoweled Pavements,”
F70ceedings of International Conference on Concrete
Pavement Design, Purdue University, February 1977.
30. Packard, R. G., and Tayabji, S. D., “Mechanistic Design of Concrete Pavements to Control Joint Faulting
and Subbase Erosion,” International
Seminar on
Drainage and Erodability at the Concrete Slab-Subbase-Shoulder
Interfaces, Paris, France, March 1983.
31. Standard Method for Nonrepetitive Static Plate Load
Tests of Soils and Flexible Pavement Components,
for Use in Evaluation and Design of Airport and
Highway Pavements, American Society for Testing
and Materials, Designation D 1196.
32. “Rigid Airfield Pavements,” Corps of Engineers, U.S.
Army Manual, EM 1110-45-303, Feb. 3, 1958,
33. Burmister, D. M., “The Theory of Stresses and Dis.
placements in Layered Systems and Applications to
Design of Airport Runway s,” Highway Research
Board Proceedings, Vol. 23, 1943, pages 126 to 148.
34. Standard Methods for Freezing-and-Thawing
Tests
of Compacted Soil-Cement Mixtures, American Society for Testing and Materials, Designation D560.
35. Standard Methods for Wetting-and-Drying
Tests of
Compacted Soil-Cement Mixtures, American Society
for Testing and Materials, Designation D559.
36. Soil- Cement Laboratory
Handbook,
Portland Cement Association publication EB052S, 1971.
37. “National Truck Characteristic
Report, 1975- 1979,”
U.S. Department
of Transportation,
Federal Highway Administration,
Washington,
D. C,, June 1981.
38. Becker, J. M., Darter, M. I., Snyder, M. B., and
Smith, R. E., “COPES Data Collection Procedure—
Appendix A,” June 1983, Appendix to final report of
National Cooperative
Highway Research Program,
Project 1-19, Concrete Pavement Evaluation System,
draft submitted to Transportation
Research Board.
39. Load Stress at Pavement Edge, Portland Cement
Association publication IS030P, 1969.
40. Taragin, Asriel, “Lateral Placement of Trucks on
Two-Lane and Four-Lane D]vided Highways,” Pub/it Roads, Vol. 30, No. 3, August 1958, pages71 to 75,
41. Emery, D. K., Jr,, “Paved Shoulder Encroachment
and Transverse Lane Displacement for Design Trucks
on Rural Freeway s,” a report presented to the Committee on Shoulder Design, Transportation
Research
Board, January 13, 1975.
42, “Vehicle Shoulder Encroachment
and Lateral Placement Study,” Federal Highway Administration
Report No. FH WA/ MN-80/6, Minnesota Department
of Transportation,
Research and Development
Office, July 1980.
43. Darter, M, 1,, “Structural
Design for Heavily Trafficked Plain-Jointed
Comrete
Pavement Based o“
Serviceability
Performance,”
TRR 671, Analysis of
Pavement Systems, Transportation
Research Board,
1978, pages 1 to 8.
44. Thickness Design for Concrete Pavemenls, Portland
Cement Association publication 1S0 IOP, 1974.
45, Kesler, Clyde E., “Fatigue and Fracture of Concrete,”
Stanton Wolker Lecture Series of the Malerials Sciences, National Sand and Gravel Association and National Ready Mixed Concrete Association,
1970,
46. Fordyce, Phil, and Yrjanson, W. A,, “Modern Design
of Concrete Pavements;
American Society of Civil
Engineers, Transportation Engineering Journal, Vol.
95, No. TE3, Proceedings Paper 6726, August 1969,
pages 407 to 438.
47. Ballinger, Craig A., “The Cumulative Fatigue Damage Characteristics
of Plain Concrete,” Highway Research Record 370, Highway Research Board, 1971,
pages 48 to 60.
48. Miner, M. A., “Cumulative
Damage in Fatigue,”
American Society of Mechanical
Engineers Transactions, Vol. 67, 1945, page A 159.
49. Klaiber, F. W., Thomas, T. L., and Lee, D. Y., “Fatigue Behavior of Air-Entrained
Concrete: Phase 11,”
Engineering Research Institute, Iowa State University, February 1979.
50. Packard, R. G., “Structural Design of Concrete Pavements with Lean Concrete Lower Course,” Proceedings of Second International Conference on Concrete
Pavement Design, Purdue University, April 1981.
51. Yrjanson, W. A., and Packard, R. G., “Econocrete
Pavements—Current
Practices,” Transportation
Research Record 741, Performance of Pavements Designed with Low-Cost Materials, Transportation
Research Board, 1980, pages 6 to 13.
45
Publication List
Book Contents
52. Ruth, B. E., and Larsen, T. J., “Save Money with
Econocrete
Pavement
Systems,”
Concrete Inrer.
national, American Concrete Institute, May 1983.
53. A Policy on Geometric Design of Rural Highways,
American Association
of State Highway Officials,
Washington,
D. C., 1954.
54. A Policy on Arterial Highways in Urban Areas,
American Association
of State Highway Officials,
Washington,
D. C., 1957.
55. Highway Capacity Manual, Bureau of Public Roads,
U.S. Department
of Commerce, Washington,
D. C.,
1966.
56. Schuster, J. J., and Michael, H. L., “Vehicular Trip
Estimation in Urban Areas; Engineering Bulletin of
Purdue University, Vol. XLWII, No. 4, July 1964,
pages 67 to 92.
57. Packard,
R. G., and Tayabji, S. D., “New PCA
T’lickness Design Procedure for Concrete Highway
and Street Pavements,” Proceedings of Third International Conference on Concrete Pavement Design
and Rehabilitation,
Purdue University, April 1985.
‘u’
7..
“u
46
Publication List
Book Contents
Calculation of Pavement Thickness
p
Project
Trial thickness
Subbase-subgrade
k
Modulus of rupture, MR
m.
Doweled joints:
yes _
no _
pci
Concrete shoulder:
yes _
no _
psi
Di!sign period _
years
Load safety factor, LSF
Axle
load,
hips
1
8. Equivalent stress
Single Axles
10. Erosion factor
9. Stress ratio factor
,p
11. Equivalent stress
Tandem Axles
13. Erosion factor
12. Stress ratio factor
1
P’
Total
Publication List
Book Contents
Total
/-.. ,,
‘u
Microcomputer Program for Thickness Design of
Concrete Highways, Streets, and Parking Lots
PCAPA V—the low-cost software for concrete pavement design
PCAPA V’s easy-to-use,
●
High-speed
solutions
●
Pavement
“
Comprehensive
theory
●
Realistic
criteria
The
fatigue
design
computer
performance,
routine
to pavement
thickness
and subbase
program
consider
or undoweled),
menu-driven
design
erosion
concrete
design
based
at transverse
shoulders,
problems
calculations
procedures,
!oad transfer
u
offers
curbs
on this manual
and
and gutters,
longitudinal
and
and verified
joints
adjacent
by
(doweled
parking-lot
Ianee.
Traffic
traffic
The
load considerations
load
software
or later),
design
category
runs
on IBM
and the package
Processing
personal
includes
Any designer
Or available
computers
a floppy
traffic
can choose
load data
a stored
can
and compatibles(128K,
diskette,
the user’s
manual,
be input.
DOS
2.0
and this
Thickness Design for Concrete Highway and Street Pavements.
manual,
To order
are simplified.
to fit the situation.
PCAPA~(MCO03),
Department,
contact
5420
the Portland
Old Orchard
Road,
Cement
Skokie,
Association,
IL
Order
60077-1083,
(800)888-6733
PORTLAND
An .rganizati.m.(
.em..t
ma..
facl.r.m
t. improve
.nd
CEMENT
ml
I
exte+a the uses d po,tla.d
mme.t
5420 Old Orchard
Road, Skokie,
,7-~..
‘u
I ASSOCIATION
and concrete through
Illinois
rn.cket development,
engineert.g,
reyea.ch, education,
md Public.(faim
work.
60077-1083
Printed in U.S.A.
Eel 09.01 P
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