pavement designs based on work
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Research Report UKTRP-87-29
PAVEMENT DESIGNS BASED ON WORK
by
Herbert F. Southgate , P.E. Chief Research Engineer
and
Robert c. Deen , P .E. D irector
Kentucky Transportation Research Program College of Engineering University of Kentucky
Lexington, Kentucky 40506-0043
in cooperation with K entucky Transportation Cabinet
and
Federal Highway Administration U S Department of Transportation
T he contents of this report reflect the views of the authors who are responsible for the facts and accuracy of the data presented here in. The contents do not nec e s s ar i ly reflect the official views or policies of the University of Kentucky , of the K e n t ucky T r a n s p or t a t i on C a b i n e t , or o f t h e F e d e r a l H i g hway Adm inistration. This report does not cons t i tu t e a s t andar d , specification, or regulation. The inclusion of manufacturer names and tradenam es are for ident i f ic a t i on purposes and ar e not to considered as endorsementse
October 1987
REPORTS ISSUED
Research Study KHYPR-84-96 Development of a Composite Pavement Design Methodology
==============================================================================
UKTRP REPORT NO.
84-3
84-11
84-12
85-13
86-21
87-28
87-29
TITLE
"Thickness Design Curves for Portland Cement Concrete Pavements"
"Variations of Fatigue due to Unevenly Loaded Axles within Tridem Groups''
"Variable Serviceability Concent for Pavement Design Confirmed by AASHO
"Effects of Load Distributions and Axle and Tire Configurations on Pavement Fatigue"
"Distribution of Strain Components and Work within Flexible Pavement Structures"
"Modification to Chevron N-layer Computer Program"
"Pavement Designs Based on Work" (Final Report)
DATE
Feb 1984
Apr 1984
Apr 1984
May 1985
Sep 1986
Oct 1987
Oct 1987
Technical Report Documentation Poge 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
UKTRP-87-29
4. Title oncf Subtitle 5. Report Dote
October 1987 Pavement Designs Based on Work 6. Performing Organization Code
B. Performing Organization Report No. 7. Author's)
H. F. Southgate and R. c. De en UKTRP-87-29 .
9. Performing Orgonlzoflon Nome oncl Address 10. WorSe Unit No. (TRAIS)
Kentucky Transportation Research Program College of Engineering 11. Contract or Grant No.
University of Kentucky KYHPR-84-96 Lexington, Kentucky 40506-0043 13. Type of Report and Period Covered
12. Spcnsoring Agency Nome and Address .
Kentucky Transportation Cabinet Final State Office Building Frankfort, Kentucky 40622 u. Spons oring Agency Code
15. Supplementary Notes
Prepared in cooperation with the US Department of Transportation, Federal Highway Administration
Study Title: Development of a Composite Pavement Design Methodologv 16. Abstract
Thickness design curves presented in the report provide a· systematic methodology for the selection of equivalent pavement designs for a broad range of layered systems. This is a unified system s1noe the failure criteria are founded on the same concept of work strain an� work . The analyses of stress-strain fields in the layered systems are based on elastic layered theory. This theory is represented by the Chevron N-layered computer program.
The report also sunnnarizes the historical development and evolution of pavement design in Kentucky.
17. Key Word• 18. Distribution Statement
Pavement Design Failure Criteria Work Concepts Thickness Unlimited with approval of Kentucky Portland Cement Concrete Transportation Cabinet Asphaltic Concrete
19. Security Claul f. (af thh report) 20. Security Claulf. (of this po;e) 21. No. of Pages 22. Price
Unclassified Unclassified 50
Form DOT F 1700.7 (B-72) Reproduction of completed p11lge lluthotized
INTRODUCTION
The 1949 (1) and 1959 (2) Kentucky flexible pavement thickness design
curves were based on empirical experience. Revisions made in 1968 ( 3 ) , 1971
( 4 ) , and 1981 (5) combined elastic theory with empirical experience. The
lat ter three revisions utilized a failure criterion of tensile strain at the
bottom of the asphaltic concrete based on laboratory testing as well as a
criterion developed from theoretical analyses of ver tical compressive strains
at the top of the subgrade.
BACKGROUND
1959 KENTUCKY THICKNESS DESIGN CURVES
The 1949 Kentucky thickness design curves (1) were updated in 1959 (2 )
after a testing program consisting of pavement deflection tests and opening of
t es t p i ts on selected pavements to perform plate bearing and in situ CBR
tests, sampling of materials from each layer , and measuring surface ruts
and/or distortion of layer boundaries . Traffic analyses provided estimates of
a ccumulated f a t i gue, and the pavements were ass igned a satisfactory or
unsatisfactory performance rating. Pavements were sorted into groups having
essentially the same accumulated traffic fatigue ( equivalent 18-kip axleloads )
and a curve was drawn through the thickness-CBR plots to separate satisfactory
from unsatisfactory performances. Only two groups of "traffic fatigue" had
sufficient data to permit a complete analysis. Those designated Traffic
Curves IV and VI (3-6 million and 10-20 million EWL , respectively) represented
two levels of equivalent wheelloads ( EWLs ) . O ther traffic curves ( accumulated
fatigue) were obtained by interpolation and extrapolation. Further analyses
indicated that pavement thicknesses associated with Traffic Curve X (160-320
m illion EWL) should have been greater. The 1968 curves ( 3 ) did provide such
adjustments , making pavements for Curve X (160-320 million EWL) thicker than
before . The 1959 Traffic Curves were based on a 5-kip EWL and were converted
to an equivalent 18-kip EAL for the 1968 Kentucky design curves. Pavements
associated with a given traffic curve were thought at that time to manifest
approximately the same surface deflections.
1
ELASTIC THEORY APPLIED TO 1959 CURVES
In 196 8 , the Chevron N-1ayer computer program (based on elastic theory)
( 6 ) was obtained and used to analyze the 1959 Kentucky design curves (2 ) .
Those analyses indicated that pavements associated with the 1959 Traffic Curve
X r esulted in the same ver tical compres sive strains rather than the same
surface deflections.
ELASTIC MODULI
The elastic modulus for the asphaltic concrete pavements on the AASHO
Road Test was determined to be approximately 600 ksi (7) . This corresponded
a l s o t o a m e an annu a l t em p e r a t u r e o f 6 0 d e gr e e s F. T h e m e a n annu a l
t emperature for Kentucky is 70 degrees F , resulting in an equivalent modulus
of approximately 480 ksi ( 3 ) . Subgrades of pavements tested in 1957 had an
average CBR o f 7. Mi tchell and Shen ( 8 ) had de t ermined that the elas tic
modulus of clay could be estimated by multiplying the CBR by 1500 .
CRUSHED STONE BASE
In the 1968 analyses, a value of 25 ksi was assigned as the modulus for
crushed stone base. Subsequent analyses showed that this created a weak layer
between two stronger layers for subgrade CBRs greater than 17, leading to
unrealistic results.
Matching theory to Tr a f fic Curve X a l s o permit ted deve lopment of a
r el a tionship of moduli for the cru shed s tone layer as a function of the
modulus of the asphaltic concr e t e and the CBR of the subgrade . Analyses
indicated that the modulus of the crushed stone layer increased as the CBR of
the subgrade increased. The modulus of the crushed stone base was 2 . 8 times
the modulus of the subgrade at CBR 7. A theoretical Bousinesq solution could
be estimated as the CBR equivalent to the asphaltic modulus (480 ksi) divided
by 1500 -- a CBR of 320. These two data points were used to define
log(F) = 0 . 674797 - 0.269364 * log ( CBR) 1
i n w h i c h F = f a c t o r u s e d t o m u l t i p l y 1 5 0 0 * C B R t o o b t a i n t h e
modulus for crushed stone base, and
CBR = California Bearing Ratio.
2
FATIGUE CRITERIA
Dorman and Metcalf (9) determined from laboratory tests that fatigue of
asphaltic concrete could be described by
log(€a) = -2. 69897 - 0.163382 * log(EAL) 2
i n w h i c h e a concrete.
t e n s i 1 e s t r a i n a t t h e b o t t o m o f t h e a s p h a 1 t ic
The above relationship ( Figure 1 ) was used in the development of the 1971 (4 )
and 1981 (5) thickness design methods.
While develop ing the 1968 Kentucky thickne ss de s ign curves (3 ) , a
vertical compressive strain of 2.4 x 10-4 at the top of a CBR 7 subgrade was
determined to correspond to a fatigue of 8 x 106 18-kip EALs under the center
of one 9-kip circularly loaded area. Damage factors , sometimes called load
equivalency factors , were calculated using
DF = (1.2504 ) (P-1B)
in which P = axleload in kips and
DF = damage factor
(EAL assigned to ea caused by one 18-kip axleload)
= --------------------------------------------------
(EAL assigned to ea caused by a given axleload)
3
S everal pavement s tructures ranging from relat ively thin to thick were
subjected to a range of loads and analyzed using the Chevron N-layer program.
An arithmetic mean of the vertical compressive strains ( for different pavement
t hicknesses) was calculated for each of the various loads. Each mean strain
value was plotted versus the associated EAL calculated using Equation 2 to
produce Figure 2. This procedure resulted in a prominent downward bend of the
criterion relationship for high EALs that was not an extension ( extrapolation)
of trends for EALs less than 8 x 106 , resulting in thicker designs for large
EALs.
3
1971 KENTUCKY THICKNESS DESIGN METHOD
A series of nomographs (4 ) were developed that accurately described the
theoretical behavioral of pavements. Use of those nomographs by a group of
engineering students resulted in such a range of pavement thickness designs
that the nomographs were assessed as inappropriate for general use.
Several attributes and characteristics of the nomographs, however, became
an integral part of subsequent research efforts. Results from the 1959 test
pits ( 2 ) indicated that distortion at the top of the subgrade diminished as
the pavement thickness increased, which in turn was related to an increase in
design traffic. Thus, for designs greater than 4 million EALs, the subgrade
should be fully protected from distortion. In general, geometries of farm-to
market roads would preclude speeds necessary for hydroplaning because of water
standing in the ruts on the pavement surface. Thus, the criterion for such
ro ads would allow the subgrade to dis tort ( ru t ) provided the asphaltic
concrete is protected from fatigue cracking during the design life. Curve IA
of the 1959 Kentucky thickness design method was associated with farm-to
m arket roads subjected to the equivalent of one application of an 18-kip
axleload per day for 20 years. Criteria between 7, 300 and 4 million EALs were
established so the allowable distortion of the top of the subgrade decreased
as EALs increas ed. That was accomplished by de termining the required
thicknesses associated with both the asphaltic concrete and subgrade strain
c ri teria and adding a proportion of the difference in thicknesses to the
t hickness required by the asphaltic concrete criterion (Figure 3 ) .
A n attempt was made to assess the compatibility o f bo th a s train
controlled and stress-controlled criterion for a range of moduli of asphaltic
concrete (3 ). For a strain-control criterion, results of laboratory tests
reported in the literature indicated that strain-fatigue relationships for a
range of asphaltic concrete moduli could be expressed as parallel lines by
mos t investigators or as a series of lines converging at very low tensile
s trains and a large number of repetitions by others. Analysis of Kentucky
experience indicated that the most appropriate relationship could be expressed
as a family of strain-fatigue lines asso ciated wi th a range of mo duli of
asphaltic concrete that converge at one repetition and a large ( catastrophic)
value of tensile s train. Thus, for a given level of fa tigue, values of
t ensile s train could be determined for any desired mo dulus of asphaltic
concrete. However, the same approach was not applicable for the development
of a single stress-controlled criterion. One repetition of a catastrophic
4
load resulted in a different critical stress value and a separate stress-
fatigue relationship for each modulus of asphaltic concrete. Thu s , it was not
possible to develop a design method incorporating both stress and strain
criteriae
REVISIONS TO CHEVRON N-LAYER COMPUTER PROGRAM
The original version of the Chevron N-layer computer program ( 6 ) utilized
a single circular loaded area to obtain stresses, strains, and deflections at
radii from the center of that load. The program was revised to input multiple
loads at specified X-Y coordinates on the surface and to obtain stresse s ,
s trains , and deflections using superposition principles at any designated
location within the X-Y-Z coordinate system , the Z coordinate being the depth
below the surface . Documentat ion and example problems are conta ined in
Reference 1 1 . This development made it possible to investigate various loads ,
tire spacing s , axle spacings , number of axles/ tires within a group, uneven
loads within the same group of tires/ axles , tire contact pressure s , etc.
Another revision was the addition of an equation (10, 1 1 ) to calculate strain
energy density .
W ith the revised program , all 100 combinations of layer thicknesses used
a t the AASHO Road Te s t , of which 67 were constructed (12 ) , were analyzed . A
matrix of t ire loads ranging from 2 , 000 t o 8 , 000 p ounds on 500-pound
increments per tire were applied to each pavement for a two-tired single axle
with a spacing to represent a steering axle , a four-tired single axle , an
eight-tired tandem axle , and a twelve-tired tridem (5). Additional studies
were initia ted to quantify the effects of different axleloads within the same
g roup of axles ( tandem and tridem) ( 1 3 ) , add i t ional ax les in a group ,
additional tires per axle , and various tire pressures ( 14 ). These analyses
permitted development of load equivalency factor s , or damage factor s , for axle
and t i re arrangements u sed at the AASHO Road Te s t ( 1 5 ) a s well a s new
arrangements now seen on highways.
Results for the four-tired single axle were in ve ry close agreement with
results using the AASHTO Equation C-16 ( 1 6 ) at a level of serviceability of
2. 5 and within the range of axleloads employed at the Road Test . Howeve r , the
factors for tandem axles were different. Ad justment factors were developed to
account for uneven axleloads within a tandem or tridem group for axles weighed
o n s ta t ic weigh scales ( 1 4 ) . Ad jus tment fac tors also were developed to
account for inc reased t i re contact pressures curre n t ly being used. The
5
effects of increased tire contact pressures vary widely, depending on the
thickness of the asphaltic concrete layer ( 14 ) . Results of those analyses
were appl i ed to a traf f i c st ream on a particular inters tate pavement and
comparisons made . Accounting for tire/axle arrangements, uneven loading among
axles in the same group, and increased tire contact pressures, the Kentucky
load equivalencies resulted in an accumulated fatigue that was 1. 27 times
greater than that obtained using AASHTO factors (16, 17 ).
A compu ter program was w r i t ten to ca lcu late an average EAL for each
vehicle type based on truck traffic weighed at a particular weigh station and
r ecorded on a loadome t e r compu ter tape. The EAL was calculated for each
vehicle, summed for that truck classification, and an average value calculated
for each truck classification.
U s ing the Kentucky load equivalency relations hip s to calculate the
average load equivalency per trip for each vehicle classification results in a
c alculated 1 8-kip EAL that is approximately 7 3 p ercent of that us ing the
AASHTO load equivalency relat ionships. Combining the effects of uneven
loading and the Kentucky load equivalency relationships results in an 18-kip
EAL that i s app rox imately 88 percent of the AASHTO EAL. Combining the
Kentucky load equivalency relationships, uneven loading, and effects of tire
contact pressure results in an 18-kip EAL that is approximately 127 percent of
the AASHTO EAL. Comparing results within the Kentucky procedures only, uneven
loading between the axles within that group of axles increases the calculated
EAL by approximately 20 percent. Increased tire contact pressure resulted in
approximately an add i t ional 55 percent increase in EAL. Combining the
additional effects of uneven load distribution and increased tire contact
pressure increased the calculated EAL approximately 75 percent compared to the
EAL using only Kentucky load equivalency relationships.
1981 KENTUCKY THICKNESS DESIGN CURVES
The same matrix of pavement layer thicknesses used in the 1968 (3 ) and
1971 ( 4 ) studies was used in this revision. The modulus of the asphaltic
concrete was selected to be 480 ksi, based on results discussed previously.
The modulus of the crushed stone base was varied according to Equation 1. An
18-kip four- tired single axleload for tire spacings in use on current trucks
w a s app lied to the surface of each pavement. The 8 0-psi tire co ntact
p re s sure was used in all ca ses. Po i s s on's ratio was 0.40 for asphaltic
concrete and dense-graded aggregate bases and 0. 45 for the subgrade.
6
For a given subgrade modulus , the vertical compressive strain at the top
of the subgrade was plotted as a function of thickness of asphaltic concrete
by v isual f i t . Curves of equal thicknes s of dense-graded aggr egate were
drawn. The same me thodology was u s ed to pl o t rela t ionships of sur face
deflection and tensile strain at the bottom of the asphaltic concrete.
The same criteria used in the 1971 and 1981 Kentucky thickness design
methods ( 4 , 5) were used in the development of thickness design curves for
pavements where the thickne s s of the aspha l t ic conc r e t e wa s the same
percentage of the total thickness. Thickness design curves were developed for
f ou r p e r c e n t a g e s ( 3 3 , SO , 7 5 , and 1 0 0 ) o f a s p ha l t ic c o ncr e t e ( 5 ) .
Subsequently, curves were developed for pavements consisting of asphaltic
concrete on 4 inches of dense-graded aggregate base and asphalt ic concrete on
s tabilized base materials ( 1 8 ) such as pozzolanic materials , cement-treated
material s , fly-ash mixtures , etc.
RUTTING INVESTIGATIONS
With the influx of heavy trucks into the coal fields of Kentucky came
increased rutting of heavy duty pavements. Most severe rutting was located on
fairly steep upgrades and at intersections having traffic control devices. To
i nve s tiga t e this phenomenon, 4-foot wide trenches were dug to a depth of
approximately 3 feet so various layers could be observed carefully. Two of
those pavem ents consis ted of 17 and 18 inches of full-dep th asphal tic
concrete. For both those pavements , there was no distortion from the bottom
of the asphaltic concrete up to 6 inches below the surface of the pavement.
From that depth to the surface , the distortion increased. Distortion in the
top 6 inches was noted in three ways:
1 . In the wheelpaths , the cons truc t i on inter face for each
succeeding lift of pavement was displaced vertically more severely
than the interface below.
2 . The top layer o f sur face m ix was much thinner in the
wheelpaths and much thicker between wheelpaths , indicating shear
flow within the surface mix.
3 . Random orienta t i on of aggr ega te par t icles in the lower
layers changed gradually from the 6- inch depth to a parallel
orientation at the surface. Aggregate par t icles very near the
7
surface appeared to be separated by, and sliding on , a layer of
asphalt cement.
To verify shear flow was occurring , two 0.25-inch wide by 0. 25-inch deep cuts
were made in the surface of the pavement. The first cut was made at an angle
t o the centerline of the road , and the second cut was perpendicular to the
centerline. These cuts were filled with glass beads used in traffic paint to
prevent closure and to provide an identification of the cuts later. After
three weeks , the cuts in the wheelpaths were displaced downhill approximately
0 . 6 inch. No me asurements were made to de termine if the cu ts had been
displaced laterally.
FUNDAMENTAL RELATIONSHIPS
WORK
The following equation ( 1 0 , 1 1 , 19) was added to the Chevron N-layer
computer program to calculate the s t rain energy density at a given point
within
w the pavement structure:
= (1/2 ) * )..� + )l*(€21 1
2 2 + e 22 + e 33
2 2 2 + 2*€ 1 2 + 2*8 23 + 2*6 13 )
in which W = strain energy density, or energy of deformation per unit
volume , or the volume density of strain energy,
eij i , jth component of the strain tensor,
)l = E/ ( 2 (1 + � ) ) , the modulus of rigidity or the shear modulus ,
E = Young's modulus ,
(J" = Poisson's ratio
).. = E�/ ( ( 1 + rr)(l - 2�) , and
v = 81 1 + 822 + 633·
4
S train energy density takes into account all nine components of strain,
o r s t ress , four of which wi ll have no resul tant value because one shear
c omponent balances another component for two situations. Howeve r , all
c omponents are calculated and printed. Work is the three- dimensional
summation of strain energy density for the volume of material involved . Thus ,
i t was assume d tha t , for a unit volume at a given point in the pavement
8
s tructure, work also was equal to the calculated strain energy density ( Work =
in.3 x psi = in.-lb).
WORK STRAIN
"Work strain" as used in this study is not a pure strain. The equation
t o calculate s tr ain energy density contains two di f f erent terms, each
involving Poisson's ratio. Each term involves either the square of the sum of
t he principl e strains or the sum of the square of each s train component.
Dividing the s train energy density by 0 . 5 * E and taking the square root
yields a numerical value of the same order of magnitude as any individual
s train component. This value has been called work strain and is taken as the
net effect of all strain components. Similar calculations may be made using
s tress components and yielding work stress, equal to the product of Young's
modulus of elasticity and work strain.
Laboratory fatigue tes ting typically utilizes strain gages placed at the
bottom of rectangular beams of asphaltic concrete. Dimensions of the sample
beam genera l ly are such that the s train gage is func tional only in the
direction of the longest dimension. Thus, the tensile strain at the bottom of
the asphaltic concrete has been used to develop theoretical thickness design
curveso
I t should be noted that, direc tly under the center of the load, the
radial strain equals the tangential tensile strain. However, for any other
location, the tangential tensile strain is the larger of the two, but in most
cases is only slightly larger than the radial component. Wby, then, should
the radial component be ignor ed, and how should the radial component be
included? Likewise, the shear component also may be significant, particularly
at any location other than under the center of the loaded area. The 1981
Kentucky thickness design method, The Asphalt Institute design method (20 ) ,
and the Shell design method (21 ) have utilized the tensile strain component at
the bottom of the asphaltic concrete and the vertical compressive strain at
the top of the subgrade and ignored all other components. No known thickness
design procedure incorporates all strain, or stress, components into its
criteria. Work strain incorporates the effects of all strain components and
r esolves the conflict discussed above.
9
WORK VERSUS WORK STRAIN
The TOTAL amount of work done by the pavement structure due to an applied
load involves a three-dimensional summation of strain energy density that
becomes extremely expensive in terms of money and computer time. The area of
greatest range of work would be wi t hin a volume tric slice of unit width
passing through the center of the loaded areas along a given axle that is
either a single axle or one of a group of axles . Locations of greatest unit
work were identified in a previous study (22 ) , and maximum unit work was noted
t o be under the edge of the tire closest to the other dual tire. The
s tress/ strain component having the greatest variation from point to point
under the tire contact area was shear. Shear has its greatest influence at
t h e o u t e r e d ge o f the ti re c o n t a c t a r e a. The ve r t i c a l c o m p o ne n t o f
s tress/strain is greatest at the center of the tire contact area.
Theoretically, the total amount of work caused by a given axleload is the
same without regard to pavement structure . The work calculated at specific
locations within a pavement structure varies according to layer thicknesses
and subgrade moduli. This variation is relatively small, and a small change
in work requires a large change in thickness. However, work strain provides a
much wider range of values and permits easier usage in developing thickness
design curves . Thus , for convenience and ease of use , work strain has been
chosen as the variable upon which to base the thickness design curves.
LOCATION OF GREATEST REACTION
A n inves tigation was made to de te rmine the loca tion of the greatest
reaction to applied loads within two- and three-layered pavement structures.
For normally spaced dual tires , this location was beneath the edge of the tire
c loses t t o the adjacent tire ( 5 , 1 3 , 1 4 , 2 2 ) . Figure 4 i l lustrates the
relationship between work at the bottom of the asphaltic concrete with respect
t o location along the axis of the axle. The numerical value of work was
slightly larger beneath the edge of the inside tire than under the edge of the
outside tire; but the difference was negligible , particularly when compared to
the value of work under the center of the loaded area.
For two-layered pavement structures (22), the primary contributor to work
was the shear component -- stress or strain. Als o , the distribution of work
from the center to the edge of the tire varied greatly, and the variation was
predominantly due to the shear component. Maximum shear was reached at a
d ep th from the surface equal to approxim ately 35 t o 4 0 pe rcent of the
10
thickness of the asphaltic concrete layer. Thus , for an 7 . 5-inch thickness of
asphaltic concrete, the maximum shear would be at approximately 2 . 5 inches
below the surface. Considering that Kentucky often uses a l-inch surface over
a 1 . 5-inch binder course, the maximum shear is very close to a construction
i nterface -- the point of least aggregate interlock. A t an interf ace ,
compaction equipment tends to orient the longest axis of an aggregate particle
p arallel to the surface. Thus , resis tance to shearing is minima l , and
p ar ticles may move l a t erally if friction between aggregate particles is
overcome by loading forces and/or the tensile properties of the asphalt cement
is exceede d , which may occur at higher pavement temperatures. Lateral
movement of lower particles allows upper particles t o move vertically
downward , resulting in surface rutting within the wheelpath.
CHEVRON N-LAYER ANALYSES
A matrix of layer thicknesses, moduli of asphaltic concrete, sub grade
moduli , and crushed stone moduli ( as a function of subgrade modulus) were
analyzed using the Chevron N-layer computer program as modified by Kentucky
( 1 1 ) . The LaGr ange interpolation method was used t o fit third degree
p o lynomial equations for various combinations within that ma trix of
t hicknesses and then used to interpolate for other required pavement
thicknesses.
COMPARISON OF WORK STRAIN AND STRAIN COMPONENTS
Figures 5 and 6 i l lustrate the relationship between wo rk strain and
t ensile s t r ain at the bot t om of the asphaltic concrete and vertical
compressive strain at the top of the subgrade, respectively. The correlation
in Figure 5 is not as good as shown in Figure 6 because the relationship
between radial strain and layer thicknesses results in a larger scatter of
data than for the relationship between tensile strain and layer thickness.
Since work strain is the net effect of all components , the correlation between
work strain and radial strain is not as good as for work strain and tensile
s train . The radial strain at the top of the subgrade is not nearly as
influential as at the b o t t om of the asphaltic concr e t e layer. Thus , the
relationship between work strain and vertical compressive strain at the top of
the subgrade has a very narrow band of data scatter .
Many laboratory fa tigue tes ts measure the tensile st rain component.
Thus , the relatively close correlation between work strain and tensile strain
1 1
of the bottom fiber has the advantage of utilizing all previous laboratory
test results and permits utilization of previous experience . Confidence in
the newer approach is increased because previous experience is utilized.
DAMAGE FACTORS
Fatigue is defined as
EAL associated with the wo rk strain caused by 18-kip
single axleload
DF = ----------------------------------------------------
EAL associated with wo rk strain caused by axleload P
5
The 1959 Kentucky design curves were based on the following fatigue equation
for single and tandem axles (2 , 3 ) :
in which DF59 A
= damage factor used in the 1959 Kentucky design system;
co n s t ant that i s the slope of the semilogari thm ic
r e l a t i o n s h i p b e t w e e n a x l e l o a d a n d r e p e t i t i o n s
a n d h a s a v a l u e o f 1 . 2 5 0 4 f o r s i n g l e a x l e s w i t h
f o u r t i r e s a n d a v a l u e o f 1 . 1 2 5 4 f o r t a n d e m
axleloads;
B = (P - 1 0 ) to correspond to the EWL sys tem used in the
1 959 Kentucky design system ,
= (P 18 ) for four-tired single axles (1968 ) , and
= (P - 3 2 ) f o r e i g h t- t i r e d t andem ax l e i n t h e 1 9 6 8
Kentucky design system; and
P axleload in kips.
6
The 1981 Kentucky thickness design curves were based on the general equation
expressed as
log(DF8 1 ) = C + D(P ) + E(P) 2 7
in which DF8 1 = damage factor used as a part of the 1 9 8 1 Kentucky design
curves and
12
C , D , E = coefficients of correlation depending upon tire and axle
configuration (see Table 1 of Reference 14) .
COMPARISON OF 1959 AND 1981 KENTUCKY THICKNESS DESIGN CURVES
Pavement thicknesses represented by the 1959 Kentucky design curves were
t o be comprised of 1/3 asphaltic concrete and 2/3 crushed stone base . A table
of layer design thicknesses had been prepared for convenience . As a result,
the 1/3 - 2/3 ratio of asphaltic concrete t o cru shed s tone base was not
maintained . For example , the thickness of crushed stone base might vary as
much as 3 to 4 inches for the same thickness of asphaltic concrete , resulting
i n per centages of asphaltic concrete thickne s ses ranging from 2 8 t o 5 2 ,
rather than the design value of 3 3 .
Thickness designs were determined for given values of CBR and 1 8-kip EALs
from both the 1959 and 1981 curve s . Values of work strain at the bottom of
the asphaltic concrete and at the top of the subgrade were determined for
those designs . Figure 7 shows the relationship between EAL and work strain at
the bottom of the asphaltic concrete . The correlation is not good . Figure 8
s hows the relationship between EAL and work strain at the top of the subgrade ,
and the correlation is much better . The larger scatter for the 1959 design
curves is a s s ociated with the range in the per centages of the asphaltic
concrete of the total thickness described above. Some of the scatter for the
1981 curves might be attributable to the use of one component of strain rather
than work strain. However , best fit curves through their respective sets of
data intersect each other as shown in Figure 8 . For relatively high values of
work strain, the 1959 curve is associated with a higher design EALs (thicker
pavement) than that for the 1981 curve . Conversely, for lower values of work
s train , the 1 9 5 9 curve is a s s ociated with a le s ser design EAL ( thinner
pavement) than for the 1981 curve .
FATIGUE RELATIONSHIPS
The 1959 Kentucky thickness design curves were empirically based; the
1981 Kentucky thickness design curves established a theoretical basis to merge
with those empirical data. However , Figure 8 displays two intersecting curves
( one for 1959 design curves and one for 1981 curves) for data that had been
assumed to be essentially the same . Kentucky W-4 tables for 1959 through 1984
were used to describe a traffic stream . Using the count and weight data, it
was possible to estimate the 20-year EAL based on each year's traffic data as
1 3
shown in Figure 9 . Thu s , a relationship was obtained that permitted adjusting
an EAL calculated using the 1959 damage factors to an equivalent value based
upon the 1981 damage factors given by
2
DF = 10( a+ b*P +c*P )
in which P = axleload in kips and
a , b , c = constants given in Table 1 for respective axle configurations .
8
These correlations show that the empirical experience matches the theoretical
work strain at the top of the subgrade while the limiting tensile capacity of
the asphaltic concrete is no t exceede d .
STRESS- OR STRAIN-CONTROLLED FATIGUE RELATIONSHIPS
Reference has been made earlier to the procedure used to proportion the
design thickness according to the difference in thicknesses required by the
t ensile st rain at the b o t tom of the asphaltic concrete and the ve rtical
compressive strain at the top of the subgrade. Final design thicknesses from
the 1981 Kentucky curves (5) for EALs less than 4 x 106 has an equivalent
vertical compressive strain that may be equated to an equivalent work strain
and/ or work stress . Therefore , one design procedure is possible for both
s tress-controlled and strain-controlled fatigue criteria as shown in Figure
1 0.
The "hooks" at either end of the 1981 Kentucky design curves (5) were the
result of averaging large variances beyond the range in axleloads normally
encountered on the highways . In the range of typical 1 8-kip design EALs , the
relationship is almost a straight line on a log-log plo t , as shown in Figure
1 1 .
A regression equation was fitted to the relationship between work strain
at the top of the subgrade and 1 8-kip EALs to determine the criterion for
positioning thickness design curves . One equation produced close agreement
with the 1981 Kentucky thickness designs for the range of low EALs. However ,
large discrepancies occurred for low CBR values in the range of high EALs.
Thu s , regression equations for criteria were obtained for three ranges of
CBRs: 3 to 5 , 5 to 7 , and 7 and greater . These three curves became the basis
for the development of all thickness design curves presented in this report .
14
The "hook" at each end of the criterion line (5 ) has been straightened
f or each of the three criterion lines in Figure 11 . The re sult is that
designs for low volume roads are slightly thicker than those required by the
1981 Kentucky design curve s . For very high 18-kip EALs (107 EAL s ) , design
thicknesses are slightly thinner than those required by the 1981 curves ( 5 ).
1987 KENTUCKY THICKNESS DESIGN CURVES
CONVENTIONAL ASPHALTIC CONCRETE/DENSE-GRADED AGGREGATE DESIGNS
Total thickness design curves have been constructed for structures where
the thicknesses of the asphaltic concrete are 33, 50, and 7 5 percent of the
total pavement thickness as shown in Figures 12-14 . Figure 15 is for pavement
s tructures having a 4-inch thickness of dense-graded aggregate below the
asphaltic concrete. These design curves were based on work strain at the top
of the subgrade as the failure criterion. Design thicknesses shown on the
vertical axes in Figures 12-15 are the total thickness of all layers above the
subgrade .
ASPHALTIC CONCRETE OVER BROKEN PORTLAND CEMENT CONCRETE
Analyses of dynamic deflections indicate the modulus of fragmented
portland cement concre te is a function of the size of broken piece s .
Preliminary analyses indicated the modulus is approximately 10 ksi for totally
crushed material and increased to approximately 1,000 ksi for 30- to 3 6-inch
pieces of portland cement concrete. Overlay thickness design curves using
a sphaltic concrete are presented for three moduli of broken and seated
portland cement concrete pavements ( Figures 16-18 ) , Overlay thickness designs
s hown in Figures 16-18 may be calculated using the equation presented in
Table 2.
A SPHALTIC CONCRETE OVER PORTLAND CEMENT CONCRETE
Analyses ( 2 4 ) of temperature gradients in asphaltic and portland cement
concrete pavements indicated that at least 5 inches of asphaltic concrete
overlay is required so the temperature at the asphaltic-port land cement
concrete interface will be no higher than if the portland cement concrete were
exposed directly to the sun. The coefficient of heat transfer for the two
materials is almost identical , but the coefficient of heat absorption for
15
b lack materials i s almo s t twice that for whi t e mater i al s . Therefor e , a
s ignificant thickness of black (asphaltic) material is required to dissipate
the absorbed hea t . Without the proper thickness of asphaltic concrete, the
portland cement concrete will tend to expand with rising temperatures . If
expansion is not possible , compressive forces will increase and may result in
crushed concrete at the faces of sawed joint s , or blowups may occur .
Any overlay over a joint that has differential vertical movement will
exhib i t a reflection crack and no thickness of over lay wi l l pr event the
reflection of that joint . If there is no vertical movement , the required
overlay thickness is not a function of fatigue but is a function of the annual
r ange of temperatur e s . Thi cknes s es in excess of 5 inches ( for K entucky
conditions) will minimize horizontal (expansion/contraction) movements of the
portland cement slab .
I t does not appear that fatigue is the controlling factor for this type
of pavement structure . With heavier axle loads and increased tire contact
pressures , rutting has been observed in other states and provinces as a major
problem . This phenomenon may be a result of shear flow within the asphaltic
concrete layer .
Neither a critical magnitude of shear stress/ strain nor a fatigue-shear
relationship has been identified in literature. However, current research
involves subjecting an asphaltic concrete tubular specimen to tors ional shear
( 2 5 ) . T e s t resul t s indicate that the cr i t ical tor s ional shear s t r e s s i s
relatively low. Efforts are underway to compare torsional shear results for
hollow and solid specimens. Therefore, it is premature to develop thickness
design curves based on shear criterion .
PORTLAND CEMENT CONCRETE OVER ASPHALTIC CONCRETE
An existing asphaltic concrete pavement on a crushed stone base has a
total thickness such than even a 4-inch portland cement concrete pavement on
asphaltic concrete results in a very low value of work strain at the top of
the subgrade . Thu s , the work strain-fatigue relationship presented in Figure
8 is not appropriate. The required fatigue criterion must be appropriate to
portland cement concrete .
Development of thickness design curves for portland cement concrete over
a crushed stone base has been reported previously (26). The design criterion
depended almost entirely upon the work strain at the bottom of the portland
c em ent concr e t e s lab . The fat igue cr i t er ion was a merger of emp irical
16
cri t eria u s ed by the Po r t land Cement A s so ciation and by the American
Association of S tate Highway and Transportation Officials . The PCA design
system was based on empirical data from highways having relatively low truck
volumes and lesser gross loads in the 1940's as compared to much higher truck
traffic with larger gross loads at the AASHO Road Tes t . The concept of work
s train provided the necessary key to merge the two cri t e ria into one .
Thi cknes s d e sign curves pres ented in Figure 1 9 were developed on the
assumption that the existing asphaltic concrete pavement has deteriorated
until the modulus is 200 ksi instead of the 480 ksi of new material . The same
fatigue criteria for portland cement concrete (26 ) is used herein .
PORTLAND CEMENT CONCRETE OVER PORTLAND CEMENT CONCRETE
K entucky's thickness d e sign curves (2 6 ) should be used for port land
cement concrete overlays that are to be fully bonded to existing portland
c ement concre t e . Unhanded port land cement concrete overlays are no t
recommended at this time . Warping and curling stresses cause the unhanded
s lab to be seated or unseated, depending on the time of day and traffic . It
is conceivable that corners might break off and cracks develop at mid-slab
prematurely. Locating new sawed joints directly over old joints and cracks is
a difficult and tedious task. Some pavements overlaid with portland cement
concrete were seen in Iowa where the sawed joint was only 0 . 25 inch from a
crack reflected from the underlying slab. Reflection cracks are a severe
p roblem for ei ther bonded or unhanded concrete overlays . Joint sealing
becomes more expensive when two closely spaced joints occur because the new
s awed joint does not coincide with the old joint .
SUMMARY
A matching of empirical experience with elastic theory adequately defines
f atigue. F a tigue failure is des cribed by wo rk st rain at the top of the
subgrade.
Shear is a material problem , at least partially related to mix design.
However, the location of maximum shear is much nearer the surface than had
been thought and the maximum tolerable value of shear strain, or stress, is
much less than had been thought . Maximum shear occurs at depths that very
o f t en coincide with con s t ru c tion interfaces between layers of asphaltic
1 7
c oncrete .. Consider ation should be given t o changing the cons truction
thicknesses of layers near the surface of the pavement .
Calculated strains and stresses for multiple-tired loads usually are less
t han those due to a single loaded area .
The point of maximum work strain is located beneath the edge of the tire
closest to the adjacent tire .
Concepts of work and work strain combine all components of strain into
one net value . The work strain at the top of the subgrade appears to closely
correspond with over 40 years of empirical experience in Kentucky.
Figure 10 shows that the concept of work strain and work stress provide
the means to base a thickness design method on both strain-controlled and
s tress-controlled criteria.
The fatigue criterion for portland cement concrete pavements also applies
t o portland cement concrete overlays . Fatigue criteria for asphaltic concrete
overlays are applicable to existing asphaltic concrete pavements and for
broken and seated portland cement concrete pavements . Shear may overshadow
f atigue criteria for asphaltic concrete overlays on existing non-broken
por tland cement concrete pavements.
The following is a listing of charts appropriate for various pavement
designs:
DESCRIPTION FIGURE NO .
New pavements, 33 percent asphaltic concrete,
67 percent dense-graded crushed stone base 12
New pavements , 50 percent asphaltic concrete,
50 percent dense-graded crushed stone base 13
New pavements, 75 percent asphaltic concrete ,
2 5 percent dense-graded crushed stone base 14
New pavements , asphaltic concrete on 4-inch layer
of dense-graded crushed stone base
Asphaltic concrete over broken and seated portland
cement concrete having a modulus of 25 ksi
9-inch concrete pavement
10-inch concrete pavement
18
15
16a
16b
A sphaltic concrete over broken and seated portland
cement concrete having a modulus of 100 ksi
9-inch concrete pavement
1 0-inch concrete pavement
A sphaltic concrete over broken and seated portland
cement concrete having a modulus of 200 ksi
17a
17b
9-inch concrete pavement 18a
1 0-inch concrete pavement 18b
Portland cement concrete over asphaltic concrete
having a modulus of 200 ksi 19
FUTURE RESEARCH
The theme of the final session of the Sixth International Conference on
S tructural Design of Asphalt Pavements held on July 17 , 1987 , was "Paving the
Gap". Several speakers stated that results of research should be in a format
t h a t i s practical and easy to imp l ement and u se. Professor P e t er Pe l l ,
University of No ttingham , stated that research should be practical; yet , there
always will be a need to have fundamental research so frontiers will continue
to be advanced. Such is the case with the concepts of work and work strain.
Preliminary analyses of the observed behavior of pavements at the AASHO Road
Test using principles of work strain show promise. Additional refinement of
the analyses is needed. Combining the behavior of the AASHO Road Test with 45
years of Kentucky's empirical and theoretical designs would provide a sound
basis for the development of a mechanist ic thickness design system covering a
wide range of input values for required parameters. Such a sys tem has
potential for analyzing data collected for the Long Term Pavement Performance
port ion of the Strategic Highway Research Program.
A cursory analysis indicated that shear may be more significant than
fatigue in asphaltic concrete pavements and overlays as axleloads and tire
contact pressures increase. Also , the amount of shear and the amount of work
m ay be grea t e s t in the top 3 to 4 inches ( top 2 5 to 40 percent of the
thickness of asphaltic concrete thickness).
19
IMPLEMENTATION
Thickness design curves have been prepared for new asphaltic concrete
pavements and asphaltic concrete overlays on broken and seated portland cement
concrete pavement . All sets of curves are based upon the principal of work,
provide equivalent designs , and may be implemented as presented in the report.
20
REFERENCES
1. R. F. Baker and w. B. Drake , "Investigation of Field and Laboratory Methods for Evaluating Subgrade Support in the Design of Highway F l exible Pavements ," Bulletin No. 1 , Vol 4 , Engineering Experiment S t ation, University of Kentucky, Lexington, KY, September 1949.
2. w. B. Drake and J. H. Havens , "Kentucky Flexible Pavement Design S tudies ," Bulletin No. 4 , Vol 1 3 , Engineering Experiment Station, University of Kentucky, Lexington, KY , June 1959.
3. H. F. Southgate, R. c. Deen, and J. H. Havens , "Rational Analysis of K entucky Flexible Pavement Design Criterion," Research Report 270, Division of Research, Kentucky Department of Highways , Lexington, K Y , November 1968.
4. R. c. Deen, H. F. Southgate , and J. H. Havens , "Structural Analysis of Bituminous Concrete Pavements , " Research Report 305 , Division of Research, Kentucky Department of Highways , Lexington, KY, May 1971.
5. J. 11. Havens , R. c. Deen, and II, F. Southgat e , "Design Guide for Bituminous Concrete Pavement Structures ," Research Report UKTRP-81-1 7 , K e n t u c ky Tr a n s p o r t a t i on Re s e a r c h P r o g r am , C o l l e g e o f Engineering , University of Kentucky, Lexington, KY, August 1981.
6. J. Michelow, "Analysis of Stresses and Displacements in an rr-Layered Elastic System under a Load Uniformily Distributed on a Circular Area," unpublished, California Research Corporation, Chevron Oil Company, Richmond, CA, September 2 4 , 1963.
7. AASIIO Road Test: S t. Louis Conference P roceeding s , D.C. , Special Report 7 3 , Highway Research Board , 1962.
Washington,
8. J. K. Mitchell and c. K. Shen, "Soil-Cement Properties Determined by Repeated Loading in Relat ion to Bases for Flexible Pavement s , " P roceedings , Second International Conference, Structural Design of A sphalt Pavements , University of Michigan, Ann Arbor, MI, 1968.
9. G. M. Dormon , and c. T. Metcalf , "De s i gn Curves for Flexible Pavements Based on Layered Systems Theory," Record No. 71, Highway Research Board, Washington, D. C. , 1965.
10. R. c. Deen, H. F. Southgate, and J. G. Mayes , "The Effect of Truck D e s i g n on P a v e m e n t P e r f o rm a nc e , " P r o c e e d ings , V o l 4 9 , T h e A s sociation of Asphalt Paving Technologist s , St. Pau l , MN, 1980.
11. H. F . S o u t hg a t e , R. c. D e e n , D . 11. C a i n , and J. G. M a y e s , "Modification to Chevron N-Layer Computer Program ," Research Report UKTRP-87-28 , Kentucky Transportation Research Program , College of Engineering , University of Kentucky , Lexington, KY, October 1987.
12. AASIIO Road Test: Report 2 Materials and Construction, Highway Research Board, Washington, D. c., 1962.
2 1
13. H . F. Sou thgate , R . c. Deen , and J, G . Maye s , "S train Energy Analysis of Pavement De s i gns for Heavy Trucks , " Re cord 9 4 9 , Transportation Research Board, Washington, D . c., 1982 .
1 4 . H . F . Southgate and R. c. Deen, "Effects of Load Distributions and Axle and Tire Configurations on Pavement Fatigue ," Proceeding s , S ix t h In ternat ional Conference , S t ructural De s ign of Asphalt P a vemen t s , Unive r s i ty of Michig a n , Ann Arb o r , MI , 1 9 8 7 ; also Proceeding s , Second National Weigh- in-Motion Conference , Vo l One , A t lanta, GA , 1985 .
1 5 . AASHO Road Test: Repo r t 5--P avement Research, H ighway Re search Board , Washington, D . c., 1962 .
1 6 . 1 9 7 2 AASHTO I nterim Guide for D e s ign of P avement S tructure s , American Association of State Highway and Transportation Official s , Washington, D . C . , 1972 (1982 Printing) .
1 7 . Guide for Design of P avement S tructure s , American Association of S tate Highway and Transportation Official s , Washington, D . c. , 1986 .
1 8 . H . F . Southgate , "Thickness Design Curves for Asphaltic Concrete on a 4-inch Layer of Dense-Graded Aggregate , or on 6 , 9 , or 12 Inches o f S t a b ilized So i l , or for Maximum U t i lization of Dense-Graded Aggregate ," Research Report UKTRP-86-14 , Kentucky Transportation Research Program , College of Engineering , University of Kentucky, Lexington, KY, May 1986 .
1 9 . I . S . Soko lnikoff , Mathematical T heory of E la s t icity , Second Edition, McGraw-Hill Book Company, New York, 1956 .
2 0 . Thickness De sign Manual Series No . September 198 1 .
Asphalt Pavements for Highways and Stree t s , 1 (MS-1 ) , The Asphalt Institute, College Park, MD,
2 1 . Shell 1963 Design Charts for Flexible Pavements , Shell International Pe troleum Company Limited, London, UK , 1963; also , Addendum to the Shell Pavement Design Manual, London, UK , 1985 .
2 2 . H . F. Southgate and R. c. Deen, "Distributions of Strain Components a nd Wo rk within Flexible Pavement S t ru c ture s , " Re search Report UKTRP-86-21 , Kentucky Transportation Research Program , College of Engineering, University of Kentucky, Lexington, KY, September 1986.
2 3 . K . Atkinson, Elementary Numerical Analy s i s , John Wiley & Sons , New York, NY, 1985 .
2 4 . H . F. Southgate , D . c. Newberry, Jr . , R. c. Deen , and J, H . Havens , " Re surfac ing , Re stora t io n , and Reha b i l i t a t ion of Interstate H ighways: Criteria and Logic Used to Determine January 3, 1977 Needs and E s t imates of Cos t s , " Re search Report 4 7 5 , Divis ion of Research, Kentucky Department of Highways , Lexington , KY, July 1977,
22
2 5. J. M . B. de Sou s a , "Dynam ic Proper t ies of Pavement Mat erials , " Dissertation Series UCB-ITS-DS-86-3 , Institute of Transportation S tudies , University of California, Berkeley, December 1986 .
2 6. H . F. Southgate and R. c. Deen, "Thickness D e s i gn Curves for Portland Cement Concrete Pavements , " Research Report UKTRP-84-3, Kentucky Transportation Research Program , College of Engineering , University of Kentucky, Lexington , KY, February 1984 .
23
F igure l.
F igure 2.
LIST OF FIGURES
Relationship between A sphaltic Concrete Single Axleload.
Tensile Strain at Bottom of and Rep e t i t ions of 18-kip
Relationship between Vertical Compressive Strain a t Top of Subgrade and Rep e t i t ions of 18-kip Single Axleload.
Figure 3. Adjustment of Design Thickness for Rut ting as a Function of Repetitions of 18-kip EAL .
F igure 4. Work at the Bottom of Asphaltic Concrete versus Location along Axis of Axle.
F igure 5. Re lationship b e tween Work S t rain and Tens ile S train at Bottom of Asphaltic Concrete.
F igure 6. Relationship between Work Strain and Vertical Compressive Strain at Top of Subgrade .
F igure 7. Relationship between Work S train at Bottom of Asphaltic Concrete and Repetitions of 18-kip EAL .
F igure 8. Re l a t i on s hip b e twe e n W o rk S t r a i n a t Top of Subgrade and Repetitions of 18-kip EAL.
F igure 9 . Estimated Annual 18-kip EAL versus Calendar Year.
F igure 10. Pavement Des ign Pro cedure for Either S t r e s s Control or Strain Control .
F igure 11. Work S train at Top of Subgrade vs 18-kip EAL Criterion for Three Ranges of CBRs .
F igure 12. Thickness Design Curves for Pavement Structures Comprised of 33 Percent Asphaltic Concrete and 67 Percent Crushed Stone Aggregate Bas e .
F igure 13. Thickness Design Curves for Pavement Structures Comprised of 50 Percent Asphaltic Concrete and 50 Percent Crushed Stone Aggregate Base .
F igure 14. Thickness Design Curves for Pavement Structures Comprised of 75 Percent Asphaltic Concrete and 25 Percent Crushed S tone Aggregate Base.
Figure 15 . Thickness Design Curves for Pavement Structures Compr i sed of Asphaltic Concrete on 4 Inches of Crushed Stone Aggregate Base.
24
Figure 16. Thickness Design Curves for Asphaltic Concrete on Broken and Seated Po r tland Cement Concrete Having a Young's Modulus of 25 ksi .
Figure 17. Thickness Design Curves for Asphaltic Concrete on Broken and S e a t e d Po r t land Cement Concrete Having a Young's Modulus of 100 ksi .
Figure 18. Thickness Design Curves for Asphaltic Concrete on Broken and Seated Po r t l and Cement Concrete Having a Young's Modulus of 200 ksi .
Figure 19. Thickness Design Curves for Port land Cement Concrete on Asphaltic Concrete Having a Young's Modulus of Elasticity of 200 ksi.
25
TABLE 1 . REGRESSION COEFFICIENTS TO CALCULATE DAMAGE FACTORS FOR VARIOUS AXLE CONFIGURATIONS
log(Damage Factor) = a + b( log(Load ) ) + c ( log( load) ) 2
================================================================
AXLE CONFIGURATION
Two-Tired Single Front Axle
F our-Tired Single Rear Axle
E ight-Tired Tandem Axle
Twelve-Tired Tridem Axle
S ixteen-Tired Quad Axle
a
-3.540112
-3 .439501
-2.979479
-2 . 740987
-2. 589482
COEFFICIENTS
b c
2 . 728860 o. 289 133
0.423747 1. 846657
-1 . 265144 2. 007989
-1. 873428 1. 964442
-2. 224981 1. 923512
2 6
TABLE 2 . VALUES FOR COEFFICIENTS TO CALCULATE OVERLAY THICICNESS OF ASPHALTIC CONCRETE ON BROKEN PCC
==========================--=====--===========---===-======
OLT = a + b*log(EAL) + c*(log(EAL))2
where OLT = overlay thickness and
a , b, and c = regression coefficients = f(CBR)
= d + e*log(CBR) + f*(log(CBR))2
MODULUS OF THICKNESS OF COEFFICIENT BROKEN PCC BROKEN PCC
(ksi) ( inches) COEFFICIENT d e f
25 9 a -39 . 55341825 7 . 559521621 -o. 181394144 b 12 . 27682107 -2 . 774707235 0.0884178858 c -{) . 612631087 0.210962531 -o.0077519796
10 a -70.28424248 21 . 272191482 -1 . 578324527 b 20. 54802239 -6. 5107715697 0.46901845188 c -1 . 169270477 0.4633902917 -o.o335234984
100 9 a -51 . 97 485309 10. 138201032 -{).494600481 b 15 . 181766663 -3 . 5133660621 0. 1729875084 c -{) .819240853 0.2696910591 -{).0137252471
10 a -72 .03822884 15. 174210016 -o.837114874 b 20.439819522 -4 .8767616024 0.2654316355 c -1 . 171268401 0. 3613069921 -{).0199286739
200 9 a -58.32810531 11 .980305722 -o.661994556 b 16 . 282821001 -3.9776753781 0. 2156855133 c -o.898751519 0.3016042334 -o. 0165359824
10 a 13 . 616843885 -{) .538274742 0. 0051893437 b -5 . 016295968 -o. 3930013094 0.0298301792 c 0 .6511910044 0.0458919219 -{).0036225523
2 7
·3 10
-5 10 3 10
21 6( � 18 pc
..... ......
4 10
... ...
r-.. ... ... r-.. ...
.......... -..... .......... -1-- -...
-... ..... ..._ ....
-...
5 6 10 10 1 8-KIP EAL
-�-o -...
.......... �
7 10
-
-
...
:"""
8 10
F i gure 1 . Re l a t i onsh i p between Tens i l e Stra i n a t Bottom of Aspha l t i c Concrete and Repet i t i o ns of 1 8-k i p S i ng l e A x l e l oad .
28
g � 10 -4
3 10
4 10
.... ....
� ....
"
5 6 10 10
18-KIP EAL
....
'\
7 10
'!\
8 10
F i gure 2 . R e l a t i onsh i p between Ver t i c a l Compressive Str a i n a t Top o f Subgrade and Repet i t i ons of 1 8-k i p S i ng l e Ax l e l oad .
29
I
1 00
80
60
40
20
0 3
1 0
I 4
1 0
v /
I
I I
5 6 10 10
18 KIP EAL
II /
7 10
8 10
F i gure 3 . Ad j ustment o f Des ign Th i c: l:ness for Rutt i.ng as il Func: t i on of Repet i t i ons of 18-k i p EAL .
30
I .c. u .5
F i gure 4 .
4!100 LB 4!100 LB
c:L c:L
20 30 40
l AXLE
SUM OF WORK
THROUGH 8 INCHES
---- OF ASPHALT I C
CONCRETE AND 8 INCHES OF SUBGRADE
...._ ___ 8 1NCHES OF
50
ASPHALTIC CONCRET -- ONLY
8 INCHES OF SUBGRADE ONLY
60 70 80 Y D i stanc e , Inches
Work at the Bo t tom of Aspha l t i c Concrete versus Locat ion a l ong Ax i s of A x l e .
3 1
'!l' _,
I V
/ / /
/
10"4 TENSILE STRAIN AT BOTTOM OF ASPHALT
-3 10
Fi gure 5 . Re l a t i on•h i p between Wor k S tr a i n and Tens i l e Str a i n a t Bo t tom of A5pha l t i c Concrete .
32
1 0-2 w 0 <( a: (!) m :::> C/) 1 0-3 LL 0 a..
� lei: z 1 0-4 < �
/ � a: 0
�
-5 1 0 -5
1 0
v
/ ..
� 1/
1 4 Jlliflr
v
1 0-4 VERTICAL STRAIN AT TOP OF SUBGRADE
Fi gure 6 . R e l a t i onsh i p between Work Str a i n and Ver t i c a l Compres s i ve Str a i n a t Top o f Subgrade .
33
""' I
19
4 1 0
�1 IKtf
,195
..... '
IGNS
5 1 0
9
I
()
I 7
NS
H
6 1 0
-
1 8-KIP EAL
r- b
7 1 0
�
8 1 0
F i gure 7 . Re l a t i onsh i p between Work Str a i n at Bottom of Aspha l t i c Concrete and Repet i t i ons of 1 8-k i p EAL .
34
N. � t. �
\
� r
� 19 �
�m1 , . ,
5 1 0
5�
K'l
t DE Sl l.j I"
m; -II IG� s
6 1 0
18-KIP EAL
...,
,_ I
7 1 0
1"":00
8 1 0
Fi gure B . Rel a t i onsh i p be tween Wor k Str a i n at Top of Subgrade and Repe t i t i ons of 1 8- k i p EAL.
35
:.-
---
..... ,... -,.,.. ,.,..
loo""' � �
� ,. _, l.-' /. ' ' � ;...--
1 03 60 62 64 66 68 70 72 7 4 76 78 80 82 84 86
CALENDAR YEAR F i gure 9 . Est i mated Annua l 1 8-k i p EAL versus Cal endar Year .
36
-
.
2 3 4 5 6 0 10 10 10 10
18-KIP EAL WOR K STRESS VS WORK STRAIN
FATIGUE AT BOTTOM OF ASPHALTIC CONCRETE
At:, MODUWS • 480 KSI
7 10
/ - /
8 10 \ 7 10
6 � 10 \ � 10
5
\ cb 4 ... 10 \ 3
10 \ 2 10 -4 ·3 ·2
10 10 10 WORK STRAIN
F i gure 1 0 . Pavement Des i g n Proc edure for E i ther S t r ess Con t r o l
or Str a i n Cont r o l .
37
� (!)
1 0 -2
� LL 0
.....
�
1 0 6 18-KIP . EAL
(
/
>7 v r--im
F i gure 1 1 . Wor k Str a i n at Top o f Subgrade vs 1 8-k i p EAL Cr i ter i on for Three Ranges of CBRs .
38
f3 25 z
40
38
36
34
. , ""' � B 1"\\ [J I
/ / 1-L- 2 � ... -,, ,-,..n/-;,r"J[ IV/0 3 -7" "" / / ,
- 32 m 30
· -� - ·
'· . .. , _ ,,, �0\ 1\.•P / -7 /
_/ 5 17 _ii / r,r _/ / 1 6 'I' .... '7, v .. z
5 �
28
26
24
22
20
18
1 6
1 4 � .L;
12 4 1 0
i= I �l
"' v / 1/ r7 �
:.. 17 r::;
� � .... 7 �
/ � ... ... 7 7
_/ ... Iii' 1./ � ..... � � '".:.;;
r.,...o" e:; �
7 � '" _/ li"'
_/ _.. v 7 17' _/' 1/ .... _/' v .... ""' ...................... �
""' � �s:
1 06 1 8-KIP EAL
.... _/ 1/ IV "" _/ _/ ""' _/' _.. .. I; /.-- "/ � � _/� [h 1'-""' :....-"'./. K 1'-
" 1.-- :;..-"'_/' "\.. "' '""
� 1:0-....
Fi gure 1 2 . Th i c kness Des i gn Curves for Pavement Structures Comp r i sed of 33 Percent Aspha l t i c Concrete and 67 Percent Crushed S_tone Aggregate Base .
3 9
ffi :::c 0 �
� z � Q F z � ffi 0
36
34
32
30
28
26
24
22
20
1 8
1 6
14
12
10 -8
4 10
I · "" Ml'J
•
h-I I
�
� '"''"'
./ / / /
5 1 0
'--.
,.
.,. ....
I
v
""' ...... �
I� lfJ
./ .;'
/
/ /
6 1 0
.;'
""'
-:;..
1 8-KIP EAL
GO'
!:;;;
v li' �
� /
.;' � /
/ V :/
._, ":;..
�
7 1 0
,..,. ""'
....
....
I;' I;' I;' I;' ""- !:"
CBR
8 1 0
2
3
5 7 1 1
F i gure 1 3 . T h i c k ness Des i g n Curves fc•r Pavement Struc tures Compr i sed of 50 F'er c:ent Aspha l t i c: Concrete and 50 F'er c:ent Crushed St one Aggregate Base .
40
f3 :I: 0 � en f3 z � Q FE z � f3 c
26
24 PL
22 �I
20
18
16
14
12
10
8 4
1 0
l HI
1-
I;' /
�ss I = ]!"
nut Jl ��
..........
"'
/ / . / /
V"/ � I' l'_h
/ l/ v v l/ / I/:
//� � 5
1 0 6
10
18-KIP EAL
I/ I;' I;'
l/� ....::
/ /
V/ /"h
7 1 0
v / /
::....-:
/ � � �
�
CBR
-2
8 1 0
_"l -
. J:: 7
1 1
F i gure 1 4 . T h i c kness Des i g n Cul-ves for Pavement S t r uc tures Compr i sed c•f 75 Percent Aspha 1 t i c Cc•ncr ete and 25 Pel-cent Crushed Stone Aggregate Base .
41
24 4-�"": ..
8
Rl
--
4 10
'A -
:,....:
�· ·� "''" lEI 1 1 Jr �E liAnr II
c� R
v v .... � �
'I
·�
v / IL / �
I/ � �..;I-' �
106
18-KIP EAL
•
:J I\ �� - 2 CBR
-3 � r - 5
/ 1-".,. l-7 ./ / -1 1
� �h � � I'
��
F i gure 1 5 . Th i c: kness Des i g n Curves for Pavement StrLic: tures Compr i sed o f Aspha l t i c: Conc:rete o n 4 Inc:hes of
Crushed Stone Aggregate Base .
42
18 � 16 I 14 � 12 � 10
i : Si
4
9 -
PCC su
/ //
NC 1-1 MC o• II
1 � � lx
1...-....
v !/ ....
v ,. .......... iii' �
18 10 - N " UJ � 16
14 12
4 5 10
PC su
.#.
c BG M
• Hi I
1/ 1.-lh r., 1--� )...-
N Pi � 25 Ki Sl ..us
� ,. / �
/ � v � / v :...-/� / � v/ :..... �
� �
18-KIP EAL
bKEfl 1I1C.I � 25
u� �BR
/ /
"/ v v ...... � 8 10
p be KS
I/ 1::7 v v 1.; 1./ ... 1/ "" 1/' !.; I.-"" ...... � y� � !::"
18-KIP EAl..
/ ...... .., v ., v., v.., V/ � VA v
""" v v / / /
V/ � !::?'
7 10
"""
...... v v ...... _, v. � ....
...... v 1/ v v � � �
,. ,. I/ I/ � I; ...... 1.-' � � ... �
� � ....
1.-' 1.-'
� .... l.-' ...... � �
CBR 2
-3
5 7
-9 -1 1
CBR 2 3
-5 -7
9 -1 1
8 10
F i gure 1 6 . Th i c kness Des i g n Curves f o r Aspha l t i c Concrete on Broken and Seated Pc•r t l and Cement Concrete Having a Young ' s Mod u l us o f E5 k s i .
43
16 9 - I" c4 PCC M 'r SUB 3R I[) =
- 5�( .
�
4 / /.I
16
6 10
1 0· PCC su_
IN< M<
•• u
��-- � D �L�l r ••
�
II'"' � �
KEN
100 ws !3R
/ v/ v/ V_/ // 6 10
p be KSI
/
/ "' �..-/ v�.--/ 17�.--
j I/.;;-� v, � ��
18-KIP EAL
�EN �c p 00 Kl l liS - 150 b Cl
v v I/ ,; ""
�
� � 1/ ..... , 1/ J..-�.-
� � '/ � !/ �v �::; p 7 ' K:;BR
18-KIP EAL
/ / / V/ V.h � w
7 10
v v v 0 v.: � f9
./
� �
"' �
/ / I'� " �/ .I �� � v
/ v ./
� / � "/
� % % � � v
�
CBR
2 3 5 7
- 9 -1 1
8 10
��--I/!.-�� '...-�-' �� �;;
F i g u r e 1 7 . T h i c kness Des i gn Curves for Asph a l t i c Concrete o n Bro ken and Seated Por t l and Cement Cc•ncrete Hav i ng a
Young ' s Modu l us of 1 00 k s i .
44
9 -
PC� ��
4 6 10
18 w � 16
� 14 � 12
� 10
i e
� 6 4
1 0
PCC �l '"
-
6 10
1M I
u hr . Ill� -� ln "
- 11� 0
•• ·� I f
Ul 1n II' l
��� �
EN F
200 ln 1 L� �R
./ V/ V/ 6 10
c:c
,KSI
v "� I-" ......
/ v ......
/ v ""
18-KIP EAL
200 In 1 1�
6 10
/ ./
PO
<SI
� /
:;
""' _...... � / �"" ..... .......
18-KIP EAL
.
./ V' "" / / L,... �
""'/ � v ...... ,..... h � � �� //. t:'l � :::: � � � 7 10
/ "'/ /..,-
v../.:: � � 7 10
� v
.... � / � ...... / /. /� ,.......,..... / /'/ % � �� � � ,. 0
ICBR -2
r ....
8 10
7 9 1
CBR
-� -5 -7 l-9 .:....1 1
6 10
Fi gure 1 8 . Th i c kness Des i g n Curves fc•r Asph a l t i c: Cone: rete c•n Brc• k en and Seated Por t l and Cement Concrete Hav i ng a
Young ' s Mod u l us o f 200 k s i .
45
5-INCI � 14
ov
v
1--
4 • 10
18 6.5-INC H IC •
18 �� IC
� � �
1/ .... v
/ v /
f 10
111-KP EAI.
CRETE � Sl
I-' 1/
/ / /
V/ v
It;. ll
/ 1.;' /
/ / :,....-'
,_., ft
101
CBR
-6
CBR
-6 8 -
101
F i gure 1 9 . T h i c kness Des i gn CLirves for Po r t l and Cement Concrete
on Aspha l t i c Concrete Havi ng a Young ' s Mod u l us of E l ast i c i ty o f 200 k s i .
46