1. SESSION 6 Thickness Design
This module presents a brief overview of concrete pavement thickness design. The major emphasis is on the AASHTO 1998 Supplement and AASHTO 1986/1993 Guide methods, which some mention of the PCA method and others. We can’t present enough detail in this brief presentation to fully teach any of these design procedures, just present their highlights.

2. Objectives Identify key design parameters in concrete pavement design
Describe the principal concrete pavement design procedures
1986/1993 AASHTO Guide
1998 AASHTO Supplement
Portland Cement Association
The objectives of this session are to identify the key design parameters in any concrete pavement design procedure and to describe briefly the principal concrete pavement design procedures, namely the 1986/1993 AASHTO Guide procedure, the 1998 AASHTO Supplement procedure, and the Portland Cement Association procedure.
Some States have developed their own mechanistic design procedures, customized the AASHTO procedure to their needs, and/or developed catalogs for pavement thickness design. Instructors should familiarize themselves in advance with the concrete pavement design procedure(s) used in the State where the course is being presented.

3. Key Design Parameters Traffic Subgrade Climate Concrete properties
Base
Performance
Reliability
These are some of the key parameters found in most pavement design procedures. We will talk briefly about each of these.

4. Key Parameter: Traffic
Traffic over design period
Axle load spectrum (PCA)
numbers and weights of
axles expected over
design period
ESALs (AASHTO)
axle load spectrum
converted to number of
equivalent 18-kip [80 kN]
single-axle loads
The traffic over the design period may be expressed either by the spectrum of axle loads expected, or by an equivalent number of standard axles, such as an 18-kip [80 kN] single axle.
The PCA design procedure and mechanistic design procedures (including the AASHTO 2002 guide) use the axle load spectrum. The AASHTO design procedure uses ESALs (equivalent 18-kip [80-kN] single axle loads. The ESAL approach to traffic characterization is arguably simpler, in terms of design calculations, but it requires the same axle load spectrum data. In addition, some measure of damage must be selected to quantify the equivalency between any given axle load and type (e.g., a 36-kip [160 kN] tandem axle) and the standard axle load and type (18-kip single axle). The AASHTO load equivalency factors (LEFs) are based on loss of serviceability as the measure of relative damage.
The traffic over the design period must be estimated, taking into account current traffic demand and predicted growth in truck traffic weights and volumes.

5. Key Parameter: Subgrade
Subgrade characterization
modulus of subgrade reaction (k value)
natural soil, embankment, rigid substrate }
Embankment
The bearing capacity of the foundation (natural soil, embankment, and rigid substrate, if any) is characterized in concrete pavement design by the modulus of subgrade reaction (k value). The k value can be measured by plate bearing tests, but is usually estimated from correlations with soil type, soil strength measures such as CBR or DCP, or by backcalculation from deflection testing on existing pavements.
Subgrade
Natural soil
Rigid layer

6. Key Parameter: Climate
Environmental effects
joint opening and closing
slab curling
erosion of base and foundation
freeze-thaw weakening of soils
freeze-thaw damage to concrete
corrosion of dowels, reinforcement
Daily and seasonal variations in moisture and temperature, as well as moisture and temperature conditions during construction, influence the behavior of concrete pavements in many ways.
--Transverse joint opening and closing due to daily and seasonal variation in slab temperature.
--Upward and downward slab curling due to daily cycling of temperature gradient through the slab thickness.
--Permanent upward curling of the slab, which in some circumstances may occur during construction, as a result of the dissipation of a large temperature gradient which existed in the concrete when it hardened.
--Upward warping of the slab due to seasonal variation in the moisture gradient through the slab thickness.
--Erosion of base and foundation materials due to inadequate drainage.
--Freezing in soils may cause frost heave in some soils, and subsequent thawing may cause a significant reduction in soil bearing capacity (due to reorientation of soil particles).
--Freezing and thawing may cause damage to certain types of coarse aggregates in the concrete. Weak, porous aggregates such as limestone are vulnerable to freeze-thaw damage.
--Corrosion of dowel bars and/or steel reinforcement may be a problem particularly in coastal environments and in areas where deicing salts are used in winter.
The current concrete pavement design procedures consider only some of these climatic effects.

7. Key Parameter: Concrete
Concrete strength
28-day modulus of
rupture (flexural
strength) used in
thickness design
Concrete flexural strength is usually characterized by the 28-day modulus of rupture (MR) from beam loading tests (either midpoint or third-point loading). The flexural strength may also be estimated from compressive strength (e.g., from cylinder tests).
The corresponding elastic modulus (E) can be measured but is usually estimated from strength data. The elastic modulus is a measure of the relative stiffness of the concrete and influences the way that the concrete distributes loads.
Concrete stiffness
28-day modulus of elasticity

8. Key Parameter: Base Base characteristics type thickness stiffness
erodibility
drainability
slab/base friction
PCC Slab
The base properties which influence concrete pavement performance are the material type, thickness, stiffness, erodibility, drainability, and slab/base friction. Some of these factors are considered explicitly in the AASHTO and PCA design procedures.
Base

9. Key Parameter: Performance
Performance criteria
One or more performance criteria used to define the end of the performance life of the pavement
AASHTO: loss of serviceability
PCA: fatigue cracking, erosion
All pavement thickness design procedures incorporate performance criteria that define the end of the performance life of the pavement. In the AASHTO methodology, the performance criterion is the loss of serviceability (riding comfort) which occurs as a result of accumulated damage by traffic load applications. The PCA procedure uses both fatigue cracking and erosion criteria.

10. Key Parameter: Reliability
Design reliability
margin of safety against premature failure
higher functional classes and traffic volumes warrant higher reliability
AASHTO: adjustment to ESALs
PCA: adjustment to strength
Design reliability is the margin of safety for which a pavement is designed. It is the probability that the pavement will perform satisfactorily over the traffic and environmental conditions for the design period. The selection of the level of reliability reflects the degree of risk of premature failure that the designer is willing to accept. Facilities of higher functional classes and higher traffic volumes warrant higher safety factors in design.
A margin of safety is needed in design because of the uncertainty inherent in several aspects of the design process:
--estimation of inputs (traffic, subgrade k, concrete strength, initial serviceability, etc.)
--predictive capability of the performance model (quality of fit to data on which it is based)
--replication error (differences in performance of seemingly identical pavement sections under identical conditions – arguably due to factors not considered in the performance model)
In the AASHTO methodology, the desired level of design reliability is achieved by an adjustment to the traffic (ESAL) input. In the PCA procedure, a safety factor is applied to the concrete flexural strength input. This was also the approach used in the AASHTO methodology prior to the 1986 AASHTO Guide.
To avoid undue conservatism in design, no safety factors should be applied to any other inputs in the AASHTO design procedure.

11. Evolution of the AASHTO Method
Original AASHO Road Test model (1961)
applicable to Road Test conditions only
1962 extended AASHO model
strength, elastic modulus, k value, ESALs
1972 extended AASHO model
J factor
1981 modification
modulus of rupture safety factor
The original AASHO model (as published in 1961) was applicable only to the AASHO Road Test slabs, materials, soils, climate, and loads. The original model was extended in a 1962 “interim guide” publication to incorporate a performance model which related the log of allowable load applications for a given serviceability loss to the ratio of concrete flexural strength to Spangler’s corner stress. The use of load equivalency factors to compute ESALs was also incorporated in the 1962 extension.
The rigid pavement model was again extended in 1972, by the replacement of the constant 3.2 in Spangler’s corner equation with the variable J, allowing characterization of different corner support conditions (load transfer and shoulder type). In 1981, the design procedure was modified to incorporate a safety factor applied to the concrete modulus of rupture.

12. Evolution of the AASHTO Method (continued)
1986 AASHTO Guide
drainage factors, revised J, reliability
1993 AASHTO Guide
overlay chapters revised
1998 AASHTO Supplement
revised model, improved k guidelines,
curling/warping, structural effects of base
The AASHTO rigid pavement design procedure was modified in many respects in the 1986 revision, including:
--addition of a drainage adjustment factor (Cd ),
--determination of the design k value as a function of subgrade resilient modulus, base thickness, base elastic modulus, base erodibility, depth to rigid substrate, and seasonal variation;
--revised J factor values,
--reliability adjustment applied to ESAL input instead of to modulus of rupture
No changes were made to the rigid pavement design procedure in The only change to the Guide was the revision of Part III, Chapter 5, on overlay thickness design.
The 1998 AASHTO supplement procedure was developed under NCHRP 1-30 and incorporates many changes, including:
--new slab stress model, based on midslab load, curling, and warping stresses
--new guidelines for determining the design k value
--consideration of base thickness, modulus, and interface friction in slab stress calculation
--consideration of joint spacing on slab stress
--corner stress check for undoweled pavements, faulting checks for doweled and undoweled pavements

13. Effect of Subgrade k and Base Stiffness
400
Lean concrete base (E = 1 Mpsi, friction = 35)
Asphalt-treated base (E = 500 ksi, friction = 6)
Granular base (E = 25 ksi, friction = 1.5)
Subgrade k-value (psi/in)
200
The interaction between subgrade k value and base stiffness which is reflected in the AASHTO Supplement model is illustrated in this chart. For this example, when the subgrade is weak, an increase in base stiffness increases the allowable ESALs considerably. However, when the subgrade is stiffer, increasing the base stiffness achieves relatively smaller increases in the allowable ESALs. This chart also illustrates that, for this example, when the base is granular, the allowable ESALs are fairly insensitive to the subgrade stiffness, but when the base is treated, an increase in subgrade stiffness decreases the allowable ESALs.
100 5 10 15 20 25 30 35 40 45 50
Allowable ESALs (millions)

14. Effect of Climate on Slab Thickness
Required Slab Thickness (in)
8.0
8.5
9.0
9.5
10.0
10.5
11.0
Miami, FL
Las Vegas, NV
Raleigh, NC
The effect of climate on required slab thickness which is reflected in the 1998 AASHTO Supplement model is illustrated in this chart. For a given design ESAL level, a given joint spacing, and other given design inputs, the chart shows the variation in required slab thickness as a function of the design temperature differential, for seven locations across the United States.
Baltimore, MD
Chicago, IL
Albany, NY

15. Effect of Climate on Joint Spacing
Allowable Joint Spacing (ft) 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Miami, FL
12 ft min
20 ft max
recommended
recommended
Las Vegas, NV
Raleigh, NC
The effect of climate on allowable joint spacing which is reflected in the 1998 AASHTO Supplement model is illustrated in this chart. This chart is similar to the chart in the preceding slide, except that in this chart, the slab thickness has been held constant and the allowable joint spacing computed. The recommended lower and upper limits on joint spacing are 12 and 20 ft [3.65 and 6.1 m]. For this example, the calculated allowable joint spacing for Miami is less than 12 ft [3.65 m]; an increase in slab thickness would be required to accommodate a 12-ft [3.65 m] joint spacing. The calculated allowable joint spacings for Chicago and Albany exceed the recommended maximum of 20 ft [6.1 m], suggesting that a slight reduction in slab thickness could be made if used with a 20 ft [6.1 m] joint spacing.
Baltimore, MD
Chicago, IL
Albany, NY

16. PCA Method Axle load spectrum Total damage due to fatigue and erosion
Joint, edge, and corner loading stresses
Dowels or aggregate interlock
Some of the key features of the Portland Cement Association method of concrete slab thickness design are listed in this slide and the next. Traffic is characterized by the truck axle load spectrum, and 6 percent of truck passes are assumed to be edge loadings.
The PCA method incorporates a fatigue model which relates allowable load repetitions to a stress-to-strength ratio. The stresses at slab joints, edges, and corners are determined from charts derived from JSLAB finite element analyses. Damage due to erosion of support at slab corners is also considered in the prediction of the allowable loads.
A composite k value (foundation and base) is used for design. The primary safety factor is a reduction applied to the concrete strength. In the most recent revision of the procedure, an option is included to permit the application of a safety factor to the axle loads as well, for high traffic conditions.

17. PCA Method (continued)
Asphalt or tied concrete shoulder
Composite k
Safety factor on concrete strength
Safety factor on axle loads for high traffic conditions
More key features of the Portland Cement Association method of concrete slab thickness design.

18. Other Methods
Customized AASHTO methods: empirical adaptations, calibration to local conditions
Mechanistic-empirical methods: mechanistic stress calculation + empirical cracking model
Zero-Maintenance, NCHRP 1-26
Design catalogs: guidelines on thickness and other design details, formatted for ease of use
NCHRP 1-32, other countries
This session has focused on three concrete pavement design methods: the 1986/1993 and 1998 AASHTO methods and the PCA methods. Among the other approaches to concrete pavement design used in the United States are the following:
--customized version of the AASHTO method,
--mechanistic-empirical methods, and
--design catalogs.

19. Summary
Modern concrete pavement design procedures consider not only slab thickness and traffic loading, but also:
multilayer foundations
structural contribution of base
interaction between thickness and joint spacing
Concrete pavement design, by the most modern and widely used methods, consider (to varying degrees) not just the relationship between slab thickness, concrete strength, and traffic loadings, but also other important factors, such as:
--appropriate characterization of multilayered foundations,
--the structural contribution of the base,
--the relationship between required slab thickness and allowable joint spacing

20. Summary (continued) climatic effects (curling, warping, joint opening)
load transfer and edge support
cracking, faulting, corner break distresses
--the effects of daily and seasonal temperature and moisture variation, as well as weather conditions during construction;
--the effects of transverse joint load transfer and longitudinal edge support on slab stresses and deflections, and
--multiple distress modes, e.g., transverse cracking, corner breaks, and joint faulting.