DRAFT
RESEARCH REPORT
KTC-93-1
AN ANALYTICAL INVESTIGATION
OF AASHTO LOAD EQUIVALENCIES
by
Herbert F. Southgate
Research Engineer
Kentucky Transportation Center
College of Engineering
University of Kentucky
Lexington, KY 40506-0043
in cooperation with
Transportation Cabinet
Commonwealth of Kentucky
and
Federal Highway Administration
U. 8. Department of Transportation
The contents of this report reflect the views of the author who is responsible for
the facts and accuracy of th~ data presented herein. The contents do not
necessarily reflect the official views or policies of the University of Kentucky, the
Kentucky Transportation Cabinet, nor the Federal Highway Administration. This
report does not constitute a standard, specification, or regulation. The inclusion
of manufacturer names and trade names are for identification purposes and are
not to be considered as endorsements.
January 1993
Technical Report Docummlalion Page
1. Report No.
3. Recilpllflt'e Catatog No.
2. Government Acceeeion No.
" IIJ"<1u" I
--------
-------- 1-5. Report Date
4. Title and SubUU.
Janumy 1993
An Analytical Investigation
Of AASHTO Load Equivalencies
6. Porlonnlnt 011J&niutlon Code
7. AuU.~o,
8. Perfonnino 01\lanizl.tion Report No.I
Herbert F. Southgate
KTC-93-1
10. WO<k Un~ No. (TRAIS}
9. Ptrlormint Orgeniz.lt6oll Name anct Addrete
KENTUCKY TRANSPORTATION CENTER
COLLEGE OF ENGINEERING
UNIVERSITY OF KENTUCKY
LEXINGTON, KY 40506-0043
11. Conlrflct or Grant No.
KYHPR-92-141
13. Typo of Report and Period Co-
Interim
12. Sponurint Agency Name and Addme
Kentucky Transportation Cabinet
State Office Building
Frankfort, KY 40622
14. Spon.aring Agency Code
_
15. Supp-11Jy Ho1oo
Prepared in cooperation with the US Department of Transportation, Federal Highway Administration
~ Title: FORECASTING AND BACKCASTING EQUIVALENT SINGLE AXLELOADS
,..
An ClbjeaNe ct this •uctv w•ICO d8wllop p!liCllllilftl8 Wid/or refined relal~ batw8en Keriudcy ESALs IWJd MSHTO ESALs. Kenudty load equivalency raia~ . . She reai1:
ci IIHICtllnalic ~~on elaSli: theory. AASHTO load equvaJency reiatiorlships were d8Yeioped from n!IIXIrded emprial.l data cxllledad at the MSHO Road Test. eanp.iiDn rt
Ken:Udcy and MSHTO ESALs ,., g;er:~ in-depth enat;aaaot MSHTO loadeqLJValency llqUHOI8C.16. D-19, ancllleirdMopmenlal equ10mgMm n the 1912 AASHTO lrierln Guide.
These eQueiiCN evolved fran the basic formal: used 11 analyZing AASHO Road Test dEia.
In this~ the repetrlioniJepOfted in AppenoDI.Act AASHO Road Test Space~ Report 61E weret:enlo'8rt8d 10 ESALs t.tSing EqualionC-16. For loop 3 (12-kip (53-liN) single . axleioad .m 2~ (1~ taOOem axie6oali,the ESAL.sat SBrVEal:lhtiea of 3.0, 2.5, am 2.0 exceeded the ES.'Uat taikn (P1 = 1.5). The AASHTO desicJ'I eqtaiDn, C.13, wastas:ito
calalllielhe deeign ESAL.afor eect1 otlhe MSHO Road Tesl PIM!Ml'llf1l eecmns. The ratJoci ESAI.aat a gM!n P, to ESAI.a at tailure _,the rat10ot repec•ionlalhe 111M P1m ~
at ftub.nt went Clli:Uiiad. Diracl: correilliorll ci tha 11Y8f8988 d these calculated R11101 ca::uned kH' Lane 1 ci Loops 5 and 6 and Lane 2 of Loop 6. This sa.ggesta that lie MSHTO bid
equiv~Hln:y ~ CICifRIIIIU; best for loads IJNI• ~the l8gai limb.
F1om nJCDnii!Jd Kertucilv loadcmeter data aliecledtl !iaklrB IOci*KI on lntenllie roues. aver95 percent ct aM single and taR:Iam axlelorlk*saraless than legal limits. This ~t.t
the MSHTO load eqt.uvaMn::y ftllalicu!:lhips .-e not as~· 10 actual tRiffic load&
Rai:iol cf MSHTO ESALa to Kentudcy ESAL.s may be calculated using Equmion 6 tor ftexi:lle I)IIYI!IIIIGI1l and Equation 1 for rigid pavemerta to estimate com~ cf P1 and SN, or
P, and 11iab ttic:ta-.
AASHTO load equivllllenc:iell.-e b8eed on pawmen!IIMVIC8I!Ibility and Sructldl fUfiOer tar ft!:lxible payen1l!lf'll8. or IliaD tti:knesl for rigid pavemetU. ~· Pavemllt .....
is l:lll8!:ld ~ ............. at utace rooghnHa, aadang. pelcm"IO. and rut deph. Pavernanl: flltigue • an inhefeft paramelllf. In the KertlOy aysesm, lo!:ld equio.Uncili ae b..a ~
tn-,
straiwe9J&ti:x'a•elalullllliiipa~fromlabaatoryleSIIII'Idm&c:h8dwrthlh&onllalc:ai::ulaed.,..baaedoneiaaicllecry. l~irlcludedintheKeriuckVaysentillle~
mav
thai SUifac:e rwghMII!Iwti inereMie ••h ttBfic. ~
~. patdles may be a:r&niWJd. and ruts
paranllll&ei'llll one~P;'!iwa .,. intler8rt in the dllflf aysaem and w:e Y8fR
mav c:lewJiop. The common fader betwean the two frt'SlemB il raffic. MeauaG
1a. Dlolrillutloo Slo-t
17. Key W..Uo
Kentucky Pavement Thickness Method
AASHTO Pavement Thickness Design Guide
Asphaltlc Concrete, Portland Cement Concrete
Thickness Designs, Serviceability
Equivalent Axle Loads
19. Security ClaaM. Col U.io roportj
Unclassified
Form OOT 1700.7 (8-72)
Umited with written approval of
Kentucky Transportation Cabinet
20. Security ClaaaH. Col lhlo pqo}
Unclassified
21. No. of Pagea
88
22.1'11oe
EXECUTIVE SUMMARY
An objective<J~his study was to develop procedures and/or ref~ned
relationships between Kentucky ESALs and AASHTO ESALs. An initial
investigation of the AASHTO Load Equivalencies indicated some
relationships that required more intensive investigations.
To
confirm or deny the anomalies, data from the AASHO Road Test were
analyzed using the actual loads applied to the respective Loops and
Lanes at the AASHO Road Test.
Regression equations for ESALs vs
Structural Number, SN, were obtained for each individual loop and
lane and superimposed on the same graph.
Plots of the equations
were noted to cross one another.
The plot for the equation for
Loop 3 crossed plots for equations for Loops 4-6.
Regression
equations were obtained for observed repetitions vs SN and the
equations were nearly parallel to each other and definitely in the
correct order of progression. Equations C-16 and D-19, published
in the 1972 AASHTO Interim Guide for Design of Pavement Structures
are the basis for calculating load equivalencies. One example of
the findings is the load equivalency value is nearly identical for
SNs of 1 or 6 but have different values for SNs of 3 or 4.
For
loads less than 18 kips (80 kN), the load equivalency value for SNs
3 and 4 is greater than for SNs of 1 or 6.
The reverse pattern
occurs for loads greater than 18 kips (80 kN). However, SN has no
influence upon the equivalency value for 18 kips (80-kN) (see
Figure 2).
These discrepancies gradually disappear as the
serviceability level decreases until at Pt of 1. 5, the load
equivalency values are constant without regard to SN.
A more critical investigation of the calculated AASHTO ESALs for
the pavement sections for the AASHO Road Test revealed that the
calculated ESALs increased as repetitions increased for Loops 4-6.
However, far 16 of 18 pavement sections having an AC thickness of
3 or 4 inches (76 or 102 mm, respectively) for both lanes of Loop
3, AASHTO ESALs for Pt = 3. 0, 2. 5, and 2. 0 exceeded the AASHTO
ESALs at Pt = l. 5.
Comparison of AASHO Road Test repetitions
converted to AASHTO ESALs with their AASHTO design ESALs produces
patterns similar to Figure 9 as shown in Figure 20.
Whatever
part ( s) of Equations C-16 and C-19 cause these phenomena also
affect the calculated AASHTO ESALs for the other Loops.
Investigations
suggest
that
the
AASHTO
load
equivalency
relationships were biased to the heavier loads because the pavement
structures having the greater SN values survived the testing
program while pavements having lesser SN values and lighter loads
failed (see Figure 20).
Under these circumstances, regression
analyses would be biased to the greater SN values associated with
the larger axleloads.
AASHTO load equivalencies are a function of pavement serviceability
and SN, or D, for flexible or rigid pavements, respectively.
Pavement serviceability is determined by measurements of surface
roughness, cracking, patching, and rut depth.
Inherent is
i
accumulated fatigue.
Kentucky load equivalencies are based upon
laboratory tests
resulting in strain-repetitions relationships.
These relationships
have been
correlated with theoretical
calculated strains resulting from given axleloads applied to
pavements and analyzed by elastic theory. Inherent in the Kentucky
system are the assumptions that with traffic, surface roughness of
the pavement will increase, cracking may develop, patches may be
constructed, and rutting may develop.
In summary, the common
factor between the two systems is traffic, but load equivalencies
are based on measurements of different sets of parameters with the
opposite set of one included inherently in the other.
From results of this study, the combinations of SN and Pt that
matches Kentucky ESALs lie between SN = 3 to 6 for Pt =2. 77 to
3.33, respectively, and may be estimated by
Pt
= 2.1907 + 0.194l(SN).
These values are different from the combination of SN = 5 and Pt =
2.5 used in the FHWA W-4 Loadometer Tables. Equations 6 and 7 may
be used to determine ratios of AASHTO ESALs to Kentucky ESALs for
flexible and rigid pavements, respectively.
ii
TABI.E OF CONTENTS
Executive Summary
i
Table of Contents
iii
Metric Conversion Factor Table
iv
List of Figures
v
List of Tables
vii
Introduction
l
Kentucky Methods
1
Investigation of AASHTO Methods
AASHTO Equations for Flexible Pavements
AASHTO Equations for Rigid Pavements
2
~Term
Terminal Serviceability> 1.5
Serviceability Levels
AASHTO Load Equivalency Equations
Patterns of Load Equivalencies
3
6
7
8
8
12
15
AASHO Road Test Data
Analyses of AASHO Road Test Data
Normalizing AASHO Road Test Data
Analyses Using Recorded Weight Distributions
20
20
21
22
Equality between AASHTO and Kentucky Load Equivalencies
28
Summary
32
Recommendations
33
List of References
33
Appendix A
Appendix B
Appendix C
Appendix D
iii
LIST OF FIGURES
----- - -
FIGURE 1. VARIABILITY IN AASHTO LOAD EQUIVALENCIES FOR FIXED
AXLELOADS.
FIGURE 2. VARIABILITY IN AASHTO LOAD EQUIVALENCIES FOR P, = 3.5
AND 1.5 FOR SINGLE AND TANDEM AXLES FOR FLEXIBLE
PAVEMENTS.
FIGURE 3. VARIABILITY IN AASHTO LOAD EQUIVALENCIES FOR P, = 3.5
AND 1.5 FOR SINGLE AND TANDEM AXLES FOR RIGID
PAVEMENTS.
FIGURE 4. AASHO ROAD TEST PUMPING INDEX DATA, LANE 2 (TANDEM
AXLES) VERSUS LANE 1 (SINGLE AXLES) (TABLE 54,
REFERENCE 3).
FIGURE 5.
COMPARISON OF AASHTO STRUCTURAL NUMBER TO
REPETITIONS AND AASHTO ESALS FOR AASHO ROAD TEST
SINGLE AXLE DATA AT P, = 3.5 AND 3.0.
FIGURE 6.
COMPARISON OF AASHTO STRUCTURAL NUMBER TO
REPETITIONS AND AASHTO ESALS FOR AASHO ROAD TEST
SINGLE AXLE DATA AT P, = 2.5 AND 2.0.
FIGURE 7.
COMPARISON OF AASHTO STRUCTURAL NUMBER TO
REPETITIONS AND AASHTO ESALS FOR AASHO ROAD TEST
SINGLE AND TANDEM AXLE DATA AT P, = 1.5.
FIGURE 8.
COMPARISON OF VARIOUS P,s FOR AASHTO SN AND
REPETITIONS OF SINGLE AND TANDEM LOADS FOR AASHO
ROAD TEST LOOP 4 DATA.
FIGURE 9.
RELATIONSHIP BE'IWEEN RATIO OF AASHO ROAD TEST
REPETITIONS VERSUS RATIO OF REPETITIONS CONVERTED
TO ESALS USING AASHTO EQUATION C-16.
FIGURE 10. RELATIONSHIP OF OBSERVED AASHTO SERVICEABILITY
WITH AVERAGE RATIO OF REPETITIONS OF APPLIED LOADS
AT AASHO ROAD TEST.
FIGURE 11. ACCUMULATED PERCENTAGE VS AXLELOAD FOR KENTUCKY
LOADOMETER DATA.
FIGURE 12. COMPARISON OF AASHTO SN VS AASHTO ESALS FOR
KENTUCKYLOADOMETERDATA
v
FIGURE 13. KENTUCKY LOAD EQUIVALENCY RELATIONSHIPS.
FIGURE 14. KENTUCKY LOADOMETER DATA CONVERTED TO ESALS
USING KENTUCKY LOAD EQUIVALENCY RELATIONSHIPS
AND SUPERIMPOSED ON AASHTO ESALs SHOWN IN FIGURE
12 BUT REARRANGED AS P, VS ESALS.
FIGURE 15. COMPARISON OF KENTUCKY AND AASHTO ESALS VS
SERVICEABILITY FOR PAVEMENT SECTION 121 AT AASHO
ROAD TEST.
FIGURE 16. COMPARISON OF SERVICEABILITY AND RATIO OF AASHTO
ESALS FOR UNWEIGHTED, WEIGHTED AASHO ROAD TEST
DATA, AND FORAASHTO DESIGN EQUATION CALCULATIONS
FOR SINGLE AXLELOADS AND SN USED AT AASHO ROAD
TEST.
FIGURE 17. COMPARISON OF SERVICEABILITY AND RATIO OF AASHTO
ESALS FOR UNWEIGHTED, WEIGHTED AASHO ROAD TEST
DATA, AND FORAASHTO DESIGN EQUATION CALCULATIONS
FOR TANDEM AXLELOADS AND SN USED AT AASHO ROAD
TEST.
FiGURE 18. AVERAGE RATIO OF KENTUCKY ESALS TO AVERAGE RATIO
OF REPETITIONS OF LOAD FOR AASHO ROAD TEST DATA AS
A FUNCTION OF LOOP AND SERVICEABILITY.
FIGURE 19. RATIO OF AASHO ROAD TEST ESALS TO RATIO OF ESALS
CALCULATED USING AASHTO EQUATION C-13 FOR EQUAL
SERVICEABILITY LEVEL.
FIGURE 20. COMPARISON OF RATIO OF AASHTO DESIGN ESALS TO
RATIO OF AASHO ROAD TEST REPETITIONS.
FIGURE 21. KENTUCKY WTM DATA ANALYZED USING AASHTO LOAD
EQUIVALENCY EQUATION.
FIGURE 22. PAVEMENT SERVICEABILITY VERSUS RATIO OF KENTUCKY
ESALS TO AASHTO ESALS FOR KENTUCKY TRAFFIC DATA
FOR BOTH FLEXIBLE AND RIGID PAVEMENTS.
FIGURE 23. COMBINATION OF AASHTO STRUCTURAL NUMBERS AND
SERVICEABILITIES EQUIVALENT TO KENTUCKY ESALS.
FIGURE 24. RATIOS OF AASHTO TO KENTUCKY ESALS FOR FLEXIBLE
AND RIGID PAVEMENTS.
vi
LIST OF TABLES
TABLE 1.
KENTUCKY W-4 TABLE DATA PROPORTIONED FOR
SERVICEABILI'IY LEVEL USING AVERAGE RATIO OF
REPETITIONS OF APPLIED LOADS AT AASHO ROAD TEST.
TABLE 2.
KENTUCKY LOAD EQUIVALENCY EQUATIONS.
TABLE 3.
PROPORTIONAL DISTRIBUTION OF AXLES BY AXLELOAD
WEIGHT RANGES FOR KENTUCKY TRUCK TRAFFIC.
vii
INTRODUCTION
This report is part of a study to develop a method to estimate the accumulated
fatigue of an existing pavement. One objective of the study was to determine what
combination of AASHTO Structural Number, SN, and pavement serviceability, P,
should be used to equate calculated equivalent single axleloads, ESALs, by both
the AASHTO and Kentucky methods. This report addresses that objective by
using one set of Kentucky loadometer data to make the comparisons.
KENTUCKY METHODS
The Kentucky flexible pavement design method (1) was developed using
mechanistic analyses based on elastic theory. Load equivalency relationships were
developed as a part of that design procedure (1). A computerized procedure (2)
was developed that utlizes loadometer, average daily traffic (ADT), and vehicle
classification data (both manual and automated) to estimate design ESALs. The
automated procedure (2) incorporates the same load equivalency relationships
used in pavement design (1).
The Kentucky rigid pavement design procedure (3) was developed using
mechanistic analyses based on elastic theory and uses the same ESALs calculated
for flexible pavements. Strain-based fatigue criteria were developed and adjusted
to permit using the same ESALs calculated for flexible pavements.
Thus,
Kentucky ESALs are the result of one set of calculations for a given set of traffic
data. As a comparison, AASHTO procedures require a minimum of two sets of
1
calculations and possibly more depending upon the difference between the
resulting design thickness and the thickness used to select the set of load
equivalency relationships.
INVESTIGATION OF AASHTO METHODS
Comparison of the Kentucky and AASHTO methods required investigating the.
1986 AASHTO Design Guide.
The 1986 AASHTO Design Guide (4) provides
Traffic Equivalency Tables for terminal serviceabilities of 2.0, 2.5, and 3.0.
Inspection of these tables revealed:
1.
the numerical value varied as a function of pavement thickness for
a constant load,
2.
the value generally decreased with increasing pavement thickness,
then increased with increasing thickness, and
3.
the values changed according to level of serviceability.
Equivalency factors were computed for flexible pavements (40-kip (178-kN) single
axleload and 48-kip (214-kN) tandem axle!oad) and for rigid pavements (32-kip
(142-kN) single axleload and 52-kip (231-kN) tandem axleload) at serviceabilities
of 1.5, 2.0, 2.5, 3.0, and 3.5. Figure 1 illustrates the variations. At a terminal
serviceability of 1.5, the load equivalency value is constant without regard to
pavement type or thickness. Conversely, for a serviceability of 3.5, the variation
is greatest. Load equivalencies for the various serviceability levels tend to become
2
nearly equal for thin flexible pavements (Figures la and lb) and thick rigid
pavements (Figures lc and ld). This suggests that the basic equations required
further investigation. The equations involve pavement thickness, magnitude of
loads, and level of serviceability.
AASHTO EQUATIONS FOR FLEXIBLE PAVEMENTS
Structural Number
From the 1972 AASHTO Guide (5),
"... an SN for the entire pavement is obtained and is represented by the
general equation:
SN = a, D, + !!..! D2 + ag D 3
where SN = structural number,
layer coefficients representative of surface, base,
and subbase course, respectively.
actual thickness, in inches, of surface, base, and
subbase courses, respectively.
Layer Coefficients
... Average values of layer coefficient for materials used in the AASHO Road Test
pavements were determined from the results of the test, and were as follows:
Asphaltic concrete surface course
0.44
Crushed stone base course
0.14
3
0.14."
Sandy gravel subbase course
Derivations of the load equivalency equations are not contained in the 1986
AASHTO Guide (4), but are provided in the 1972 AASHTO Interim Guide (5) and
is quoted as follows:
"G, = ~(logW, - log p) = log((4.2-P,)/(4.2-1.5))
and
C-1
G.f~ = logW, - log p
log p = 5.93 + 9.36log(SN+1)- 4.79log(L,.+~) + 4.33log(~)
C-3
where W, = axleload applications at end of time t,
SN = structural number,
L,. = axle load in kips,
L 1 = load on one single axle or on one tandem-axle set, kips.
~ = axle code (1 for single axle and 2 for tandem axle),
p = a function of design and load variables that denotes the expected
number of axle load applications to a serviceability index of 1.5.
G, = a function (the logarithm) of the ratio of loss in serviceability at time
t to the potential loss taken to a point where P, = 1.5.
4
f3 = a function of design and load variables that influence the shape of the
p-versus-W serviceability curve.
P, =serviceability at end of timet."
When
P, = 1.5,
G, = log((4.2-1.5)/(4.2-1.5)) = log(2.7/2.7) = log(l) = 0.0,
G/ll = logW, - log p, and
logW, = log p.
Equation C-3 was developed to estimate the number of repetitions of a given
axleload that a given pavement thickness could be expected to carry at a specific
level of serviceability.
Load equivalency is the ratio of the repetitions assigned to a given level of
servicability caused by one 18-kip (80-kN) axleload to the repetitions assigned to
the same level of serviceability caused by some other axleload, L,.. The ratio of
two numbers is the same as the antilog of difference between the logarithms of the
two numbers. Thus, when P, = 1.5, G/ll has a value of 0.0 leaving:
log Wu 8 = 5.93 + 9.36log(SN+l)- 4.79log(18+1) + 4.33log(l)
1
log p = 5.93 + 9.36log(SN + 1) - 4. 79log(L,. + 1.,) + 4.33log(1.,)
2
Subtracting log(p) from log(Wu 8) leaves:
5
log(W 18 ) - log(p) = 4.79log(L, + ~)- 4.79log(l9)- 4.33log(~)
3
and log(L0 is eliminated for a single axle bec!luse log(!) is zero. Note also that all
terms involving SN have been eliminated.
AASHTO EQUATIONS FOR RIGID PAVEMENTS
Equation D-1 (5) for rigid pavements is identical to Equation C-1 for flexible
pavements. Equations D-2 and D-3 for rigid pavements are identical in format to
Equations C-2 and C-3 for flexible pavements, respectively, except for the
numerical values of the respective coefficients and exponents.
where
G, = j3ClogW,- log p) = log((4.5-P,)/(4.5-1.5))
D-1
log(p) = 5.85 + 7.35log(D + 1)- 4.62log(L 1 +~) + 3.28log(~)
D-3
L 1 = load on one single axle or on one tandem axle set, kips.
~=axle code (1 for single axle and 2 for tandem axle).
D = thickness of slab, inches.
As discussed, log(W,) = log(p) when the terminal serviceability, P., is 1.5. The ratio
6
of repetitions is the antilog of the difference between the logs of the two numbers
and the remaining terms are:
log(W,)- log(p) = 4.62log(l..,.+L 1) - 4.62log(l9) - 3.28log(4)
4
and log(4l is eliminated for a single axle because log(l) is zero. Just as Equation
3 is a general equation for flexible pavements, Equation 4 is a general equation
for rigid pavements and axle configurations when P, = 1.5. Note that pavement
thickness is not included in either Equations 3 or 4. The numerical value for the
load equivalency differs by pavement type and is a function of the different
numerical constants of 4. 79 and 4.33 shown in Equation C-3 corresponding to 4.62
and 3.28 shown in Equation D-3, respectively.
The fl term essentially is an expression of the effects of load divided by a
combination of structural number and axle configuration.
For a given load,
increasing the thickness in the denominator results in a smaller quotient, thus a
smaller value for fl results in a larger value for the term G/fl. Conversely, a
pavement structure having a lesser structural number results in a larger fl and
in turn a smaller value for G,ffl. When structural number is held constant and the
load is increased for a given axle configuration, then fl increases and the value of
Gtffl is decreased. In summary, the G/fl term is the addition of another log when
7
using the equation in a log format, or a multiplier of a non-log equation.
TERMINAL SERVICEABILITY > 1.5
The log(p) and log(W,) equations contain non-zero values for GJ~. and GJ~ 18•
When the difference is taken between the two logs, the terms 9.36log(SN+ll (for
flexible pavements), or 7.35log(D+l) (for rigid pavements), are eliminated, but the
GJp terms containing SN, or D, remain. Therefore, the GJp terms are included
when calculating load equivalencies and these terms c:;use a variation in load
equivalency value as a function of SN or D for the same axleload, W,.
SERVICEABILITY LEVELS
The instrument used for recording longitudinal profile variations was the
longitudinal profilometer and the output was referred to as the pavement slope.
From page 14 (6):
"To correlate profile variation with serviceability ratings made by the panel
the hundreds of slope measurements taken in each section were reduced to
a single statistic intended to represent the roughness of the section.
Investigation of several alternative statistics led to the choice of the
variance of the slope measurements computed from:
in which
8
• 2 -.!(I:,x,
• )2
r,x,
(1)
SV = _,ic::.·t,____ _n,.:-:.l•:..:l_.t...
n-1
SV = slope variance;
X; = the i'h slope measurement; and
n =total number of measurements."
Pavement deteriorate with time and applications of loads.
The concept of
pavement serviceability and an associated rating scale was developed while
conducting the AASHO Road Test. Initial testing resulted in the new pavements
at the AASHO Road Test being assigned a Pavement Serviceability Index, PSI, of
4.2 for flexible pavements and 4.5 for rigid pavements. The first visible signs of
deterioration corresponded to a value of 3.5. A value of 1.5 was considered as
failure.
Serviceability was not a direct function of fatigue. From page 23 (6):
"Eq. 11 was used to determine the level of serviceability of the surviving
flexible pavement sections every two weeks during the period of traffic
operation.
p = 5.03 - 1.9llog(l + SV) - O.Ol(C + Pl0 .5
in which
p = the present serviceability index;
9
-
1.38(RDl2
(11).
SV = the mean of the slope variance in the two wheel paths;
C + P = a measure of cracking and patching in the pavement surface;
and
RD = a measure of rutting in the wheelpaths."
Inspection of the recorded number of load applications published in Appendix A,
AASHO Road Test Report 61E (6), shows that a wide variation in the number of
load applications existed for the same pavement thickness and axleload. The
service life of a pavement is influenced directly by thicknesses of the various
layers, the mix design for the bound layer, quality of aggregates and asphalt
cement, construction control, stiffness of the subgrade, and environment. In this
dis1mssion, environment will not be considered since all AASHO Road Test
pavements were subjected to the same weather. Analyses (7) using elastic theory
indicated that the influential factors affecting pavement behavior in decreasing
order are stiffness of subgrade, pavement thickness, axleload, and stiffness of the
bound layer.
For rigid pavements, the following is quoted from pages 142-143 (6):
"Eq. 59 was used to determine the level of serviceability of the surviving
rigid pavement test sections every two weeks during the period of traffic
operation.
p = 5.41 - 1.80log(l + SV) - 0.09(C + P)0 ·6
10
(59).
... When it was not feasible to use the project's longitudinal profilometer to
determine the serviceability of a test section, the Bureau of Public Roads
roughometer was used.
The roughometer was equipped with a special
counter and operated at a speed of 10 mph. Through a study correlating
the output of the roughometer with that of the profilometer, a pavement
roughness expressed in inches per mile was substituted for SV with the
following result:
p = 5.41 - 1.80log(0.40R - 33) - 0.09(C + P)0 ·5
(60)
in which R is the roughometer reading in inches per mile, and the other
symbols are as previously defined. The roughometer was used only in cases
where sections were nearing failure, and it appeared that maintenance
would be required before the next regular 2-week index day period."
The definition for patching, P, is the same for flexible or rigid pavements. The
definition for cracking, C, depends on the type of pavement.
For flexible
pavements, Page 23 (6) states:
"Cracking, C, in Eq.ll is defined as the area, in square feet per 1,000 sq ft
of pavement surface, exhibiting class 2 or class 3 cracking.
Class 2
cracking is defined as that which has progressed to the stage where cracks
have connected together to form a grid-type pattern. Class 3 cracking is
11
that in which the bituminous surfacing segments have become loose."
---
---------------
--------------
For rigid pavements, Page 142 (6) states:
"Cracking, C (Eq.59), is defined as the total linear feet of Class 3 and Class
4 cracks per 1,000 sq ft of pavement area. The length of a crack is taken
as the length of its projection parallel or perpendicular to the pavement
centerline, whichever is greater. A Class 3 crack is defined as a crack
opened or spalled at the surface to a width of 1/4 in. or more over a
distance equal to at least one-half the crack length, except that any portion
of the crack opened less than 1/4 in. at the surface for a distance of 3 ft or
more is classified separately. A Class 4 crack is defined as any crack when
has been sealed."
Thus, the definition of pavement serviceability is a function of pavement type.
AASHTO LOAD EQUIVALENCY EQUATIONS
The 1986 AASHTO Guide (4) does not provide the equations used to develop the
load equivalency equations. The 1972 AASHTO Guide (5) provides the equations
and are identified herein as Equations C-13 through C-16 for flexible pavements,
and D-16 through D-19 for rigid pavements. These equations are quoted here for
the benefit of those who may not have access to them.
"The design equation for flexible pavements developed in Section C.l"
12
(Equations C-2 and C-3), "may also be written as:
log(W,) = 5.93 + 9.36 log(SN + 1) - 4. 79 log(L 1 + L.J)
+ 4.33 log(L.J) + G/13
C-13
... IfL, equals 18 kips (80 kNl, and L.J equals 1 for single axles, equation (C13) becomes:
log(Wt! 8 ) = 5.93 + 9.36 log(SN + 1)- 4.79 log (18 + 1) + G/13
C-14
For any other axle load L 1, equal to X, equation (C-13) becomes:
log(W,.) = 5. 93 + 9.36 log(SN + 1) - 4. 79 log(L,. + L.J)
+ 4.33 log(L.J) + G/13.
C-15
Subtracting Equation C-14 from Equation C-15 gives:
log(W,/Wtl 8 ) = 4. 79 log(18 + 1) - 4. 79 log(L,. + L.JJ
+ 4.33 log(L.J) + G/13. - G/13 1s
C-16."
For rigid pavements:
"The design equation for rigid pavement developed in Section D.l"
13
(Equations D-2 and D-3) "may also be written as:
log(W,) = 5.85 + 7.35 log(D + 1)- 4.62 log(L 1 + L.l
+ 3.28 log(L.) + G,/13
D-16
.. .If L 1 equals 18 kips and L. equals 1, for single axles, equation (D-16)
becomes:
log(W" 8 ) = 5.85 + 7.35 log(D + 1) - 4.62 log(18 + 1) + G,/13 18
D-17
For any other axleload L 1 equal to X, equation D-16 becomes:
log(W,,) = 5.85 + 7.35 log(D + 1) - 4.62 !og(L,. + L.l
D-18
+ 3.28 log(4) + G,/13,
Subtracting equation (D-17) from equation (D-18) gives:
log(We.!Wtisl = 4.62 log(18 + 1) - 4.62 log(L,. + 4)
+ 3.28 log<L.l + G,/13. - G,/13,s
D-19."
Note that Equation C-2 and D-2 are designated as fl. The values for coefficients
and exponents are very different resulting in quite different values for fl.
Equations C-3, C-13 through C-16 for flexible pavements, and D-3, D-16 through
14
D-19 for
contain terms involving layer thicknesses. However,
when P, = 1.5, all terms involving layer thicknesses are eliminated when
calculating load equivalencies because G, = 0.
Equations C-3 and D-3 were
developed to estimate the number of repetitions a given axleload may be carried
by that pavement structure by the time the pavement reached the specified level
of serviceability.
Load equivalency factors included in the 1986 AASHTO Guide (4) may be
duplicated provided that the inverse of Equations C-16 and D-19 are used. Taking
the inverse of equations involving logarithms simply requires that the algebraic
sign be reversed for each term in the equation. For tridem axles, a value of 3
must be used for i....J.
PATI'ERNS OF LOAD EQUIVALENCIES
The AASHTO load equivalency equations, C-16 and D-19, were evaluated for SN
values of 1 through 6 and D from 6 to 11 inches (150 to 279 mm, respectively) for
each of the levels of serviceability of 1.5 to 3.5 in increments of 0.5.
Single
axleloads of 10, 14, 18, 22, 26, and 28 kips (44, 62, 80, 98, 116, and 125 kN
respectively) were substituted for 1.. Tandem axleloads of 18, 28, 36, 44, and 52
kips (80, 125, 160, 196, 231 kN, respectively) were used.
Figures 2 and 3
summarize the calculations for flexible and rigid pavements, respectively. Figures
2a, 3a, 2c, and 3c correspond to a P, of 3.5 and Figures 2b, 3b, 2d, and 3d
correspond to a P, of 1.5. Appendix A contains similar figures for P, of 3.0, 2.5,
15
and 2.0.
From analyses using elastic theory, rational relationships for strain and thickness
of asphaltic concrete appear to be valid for thicknesses of 3, or more, inches (76
mm) and become irrational for thicknesses less than 3 inches (76 mm) (7). The
mean SN for AASHO Road Test pavements of 3 inches (76 mm) of asphaltic
concrete was approximately 2.8.
Comparison of single axleload equivalencies
between Figures 2a and 3a indicates quite similar patterns and values for a SN
range of 2.8 to 6 and slab thicknesses of 6 to 11 inches (36 to 279 mm,
respectively).
For tandem axleloads, the patterns are similar but the rigid
pavement values approach a factor of 2 compared to flexible pavements. Figure
4 was developed from data contained in Table 54 of Report 61E {6) and illustrates
that the volume of soil pumped from under pavement slabs subjected to tandem
axles was approximately twice that for pavements subjected to single axles. The
following is quoted from Page 2, Report 61G (8):
"Flexible pavements lost serviceability through the development of ruts and
roughness in the wheelpaths and by cracking in the asphaltic concrete
surfacing, eventually requiring patching of the surface ... Rigid pavements
lost serviceability by the development of roughness along the wheelpaths,
by slab cracking or by the necessity of patching the pavement surface due
to severe cracking and roughness. All of the failures in the rigid pavements
were preceded by pumping of material · from beneath the concrete
16
slabs... Practically all pumping occurred along the pavement edge."
From Page 38, Report 61G (8):
"At the end of test traffic, data indicated that pumping increased as load
increased (the greater the load the more the pumping, given equal slab
thickness) and decreased as slab thickness increased (the thicker the slab
the lesser the pumping, given equal load)."
It appears that the concrete slabs failed because they behaved as cantilevered
slabs over the voids caused by pumping and not due to fatigue of a supported
concret.e slab. The flexible pavements deformed to maintain contact with the base
layer. Thus, load equivalencies for the two types of pavements probably do not
reflect similar pavement behavior.
For both types of pavements, pavement structure has no influence upon load
equivalencies at P, = 1.50. As stated earlier, G, has a value of 0.0 and SN does not
appear in Equations C-16 or D-19 for either flexible or rigid pavements. For rigid
pavements, Figure 3 provided the basis for the following observations:
1. There is no influence of slab thickness on load equivalency for an 18-kip
(80 kN) single axleload. Thickness does have an influence for any other
load, but the influence is less than for flexible pavements.
17
slabs ... Practically all pumping occurred along the pavement edge."
From Page 38, Report 61G (8):
"At the end of test traffic, data indicated that pumping increased as load
increased (the greater the load the more the pumping, given equal slab
thickness) and decreased as slab thickness increased (the thicker the slab
the lesser the pumping, given equal load)."
It appears that the concrete slabs failed because they behaved as cantilevered
slabs over the voids caused by pumping and not due to fatigue of a supported
concrete slab. The flexible pavements deformed to maintain contact with the base ·
layer. Thus, load equivalencies for the two types of pavements probably do not
reflect similar pavement behavior.
For both types of pavements, pavement structure has no influence upon load
equivalencies at P, = 1.50. As stated earlier, G, has a value of 0.0 and SN does not
appear in Equations C-16 or D-19 for either flexible or rigid pavements. For rigid
pavements, Figure 3 provided the basis for the following observations:
1. There is no influence of slab thickness on load equivalency for an 18-kip
(80 kN) single axleload. Thickness does have an influence for any other
load, but the influence is less than for flexible pavements.
17
2.
For
axleloads less than 18 kips (80 kN), load equivalencies
decrease for slab thicknesses increasing from 6 inches (152 mm) to 8 inches
(203 mm) where the rate of decrease changes but continues to decrease as
slab thickness increases from 8 to 11 inches (203 mm to 279 mm,
respectively).
3. For single axleloads greater than 18 kips (80 kN), load equivalencies
decrease as slab thickness increases from 6 inches to approximately 7
inches (152 mm to 178 mm, respectively), then increases as slab thickness
increases.
4. Similar observations were noted for tandems.
Table 54 (6) lists the volume of soil pumped from under the rigid slabs at the
AASHO Road Test. Figure 4 illustrates the relationship of the volume of soil
pumped from under the rigid slab for the tandem axle vs single axle (Lane 2 vs
Lane 1) and each data point is for the same constructed slab thickness on the
same loop. The volume of soil for tandem axles is approximately twice that for
single axles. This suggests that the volume of soil pumped from under the slab
was a function of the number of impacts by individual axles and not the number
of axle groups.
Because serviceability was strongly influenced by the pavement profile (slope
variance or roughness), it appears that the volume of soil pumped from under the
rigid pavements eventually allowed the pavement slabs to crack and deform. This
18
might account for an increased roughness compared to the flexible pavement
sections. This may also explain why the load equivalencies for rigid pavements
are so much greater than for flexible pavements.
Figure 2 provided the basis for the following observations:
1. There is no influence of SN on the load equivalency for an 18-kip (80
kN) single axleload, but SN does have a prominent influence for any other
load.
2. For loads less than 18 kips (80 kN), the equivalencies increase from SNs
of 1 to 3, then decrease from SNs of 3 to 6.
3. For loads greater than 18 kips (80 kN), the equivalencies decrease from
SNs of 1 to 3, then increase from SNs of 3 to 6.
4. Similar observations were noted for tandems.
From Report 61E (6),
"The structural design of the sections in each test tangent of the traffic
loops was varied ... about a nominal design determined from designs
submitted by four highway departments ... In the traffic loops (2 through 6)
surfacing thickness varied in l-in. increments, base thickness in 3-in.
increments, and subbase thickness in 4-in. increments."
19
AASHO ROAD TEST DATA
On Page 36 of Report 61E (6), equations 13-15 are of the same format as
Equations C-1 through C-3 (5) quoted earlier in this report. Analyses of the
AASHO Road Test data provided the bases for the equations used in the AASHTO
Design Guides (4-5).
ANALYSES OF AASHO ROAD TEST DATA
Appendix A, Report 61E (6), provides the number of repetitions of load for each
pavement section by loop and lane and serviceability levels. Layer thicknesses
were converted to SN using a 1 = 0.44, a 2 = 0.14, and a 3 = 0.11 (2). The data for
repetition, SN, and serviceability were inserted into Equation C-16 to calculate 18kip (80-kN) ESALs. Regression equations relating ESALs and SNs were obtained
for each loop, lane, and level of serviceability. Figures 5c, 5d, 6c, 6d, and 7b
illustrate the
ESAL-SN
relationships between
regression equations for
serviceability levels of 3.5, 3.0, 2.5, 2.0, and 1.5 respectively. Appendix B contains
similar figures for all levels of serviceability for the tandem axle data. In Figures
5c, 5d, 6c, 6d, and 7b, logic would suggest that the positions of the regression
equation for each loop should increase in SN for increasing loop number
(increasing loads). Note that plots of regression equations for some loops cross the
plots of equations for other loops and in some cases may be in reverse positions.
Additional analyses resulted in Figures 5a, 5b, 6a, 6b, and 7a that illustrate the
relationship of regression equations through the observed repetitions of load and
20
Figures Sa and 8b are compilations of the regression equations from Figures 5-7
for Loop 4, Lanes 1 and 2, respectively. All regression equations are located in a
logical, progressive sequence.
This confirms that the observers performed
excellent work in determining the serviceability rating and recording the number
of repetitions of loadings.
NORMALIZING AASHO ROAD TEST DATA
The AASHO Road Test data provided in Appendix A of Report 61E (6) were loaded
into a personal computer spread sheet.
Equation C-16 was used to convert
observed repetitions at the AASHO Road Test to AASHTO 18-kip (80-kN)
equivalent axleloads for each pavement section and level of serviceability for both
lanes of Loops 3-6. Trends are difficult to determine when looking at the resulting
wide range in ESALs. Data were normalized by obtaining the ratio of repetitions
at any given level of serviceability to the repetitions at failure (P, = 1.5) and the
ratio ofESALs at any given level of serviceability to the ESALs at failure (P,). For
this investigation, those pavement sections not having values of observed
repetitions for each of the five levels of serviceability were eliminated, leaving 176
sections for analyses.
For each loop and each lane, the average ratio was
calculated for the ratios at each level of serviceability.
Figures 9a and 9b
illustrate the relationship between the two sets of ratios for single axle trucks and
tandem axle trucks, respectively.
21
The curves for
3 in Figures 9a and 9b indicate that the ratio of ESALs for
P,s of 3.0, 2,5, and 2.0 exceed a value of 1.0 and would indicate that the
accumulated fatigue exceeded failure during the middle of the test period and then
the accumulated fatigue was decreased to failure.
Upon reinspection of the
calculated ratios for the Lane 1, Loop 3 (12.15-kip (54-kN) single axleloads), ratios
exceeded 1.0 for 13 of 17 sections at P, = 2.5 and 15 of 17 at P, = 2.0. For Lane
2 (24-kip (107-kN) tandem axleloads) of Loop 3, the ratios for 16 of 20 sections
exceeded 1.0 for P, = 2.0 and 2.5. To verify the accuracy of these calculations,
fixed values of SN and load were substituted into appropriate locations in the
spread sheet and the repetitions were changed to a value of 1 resulting in load
equivalency factors.
These factors duplicated the values given in appropriate
serviceability and axle configuration tables of the 1986 AASHTO Design Guide (4),
This confirms that the calculations within the spread sheet were correct.
ANALYSES USING RECORDED WEIGHT DISTRIBUTIONS
An objective of this study was that Weigh-In-Motion data for 1989 and 1990 would
be used to compare ESAL calculations.
After inspecting the data, it was
determined that the data would require extensive checks prior to analyses. An
alternative source of weigh data was sought.
Prior to 1987, Kentucky Department of Highways officials utilized portable scales
or permanent loadometer stations to measure axleloads. A portion of the data
reported to FHWA included the sum of axles weighed at 11 permanent loadometer
22
stations. Stations were located on interstates, rural primary roads, and urban
--------
arterials. These data were used by FHWA to form the "W-4 Tables". To analyze
the effects of axleloads, eight years of data from Kentucky "W-4 Tables" were
recorded by appropriate weight groups for both single and tandem axle
arrangements. The numbers of recorded axleloads were summed for the eight
years for each weight range and the totals are listed in Table 1. As a simulation,
the number of axles in each weight range should be proportioned according to
some rate of accumulated trafiic, pavement deterioration, and as a function ofloss
of serviceability.
The best history of pavement deterioration, as a function ofloadings, was assumed
to be the data collected at the AASHO Road Test as shown in Figures 6-8. A
method was required to proportion the number of loadings in Table 1.
Methodology for development of the method is contained in Appendix C and
results are shown in Figure lOa. The relationship shown in Figure lOa was used
to proportion the total number of axles to simulate a loss in serviceability as
shown in Table 1. Figure lOb might be used to estimate the future volume of
trucks required to cause pavement failure based upon the number of trucks that
have travelled over the pavement and the existing level of serviceability.
· The numbers of axles shown in Table 1 were converted to accumulated
percentages as a function of increasing single and tandem axles in Figures lla
and llb, respectively. Approximately 98 percent of the single axles had loads less
than 18 kips (80 kN) (Figure lla) and 95 percent of the tandem axles had loads
less than 33 kips (148 kN) (Figure llb).
Use of AASHTO load equivalencies
should lead to specific relationships for SN and serviceability based upon results
shown in Figures 1-3 and 5-7. Figure 12 illustrates the calculated fatigue for the
distribution of axles shown in Table 1.
Figure 13 illustrates the load equivalency relationships for various tire and axle
configurations developed by Kentucky (1,11). A description of the methodology
used to develop these relationships is included in Appendix D.
Table 2 (11)
contains the general log-log polynomial equation and the appropriate values for
the constants for each tire and axle configuration. Kentucky load equivalencies
were based on theoretical mechanistic analvses using the Chevron N-layer
computer program for a wide range of loads applied to each of the theoretical 100
possible combinations of AASHO Road Test flexible pavements of which 67 were .
constructed. Kentucky load equivalency relationships include the variations of
pavement thicknesses but do not include serviceability.
The single and tandem axle Kentucky relationships were applied to the same axle
distributions shown in Table 1. Figure 14 is another presentation of Figure 12
and includes the curve based upon Kentucky load equivalencies for the same
axleload data. The curve for SN = 3 has the greatest calculated fatigue of any SN.
The Kentucky curve passes through the AASHTO curves and follows the same
general trend.
24
Equation C-16 was used to calculate the 18-kip (80-kN) ESALs for Section
Number 121 in Lane 1, Loop 3 of the AASHO Road Test.
Pavement Section
Number 121 was chosen for analyses based upon a single axleload less than 18
kips (80-kN), layer thicknesses of 3 inches (76 mm) of asphaltic concrete, 3 inches
(76 mm) of base, and 4 inches (216 mm) of subbase. The observed repetitions for
each level of serviceability (from Appendix A, ref. 6) are shown in the box on the
right side of Figure 15. The curve with the solid round points is the result of
calculations using Equation C-16 and the curve with the open round points is the
result of calculations using the Kentucky load equivalency equation for a 4-tired,
single axle.
Figure 15 suggested that similar analyses should be made by individual lanes and
loops that are surrogates for axle arrangements and loads, respectively. The same
spread sheet used to develop the curve in Figure lOa was used to obtain the 18kip (80 kN) ESALs and the mean value of ratio of those ESALs (not repetitions
as in Figure lOa) by loop, lane, and level of serviceability. Only those pavement
sections having both weighted and unweighted data for all serviceability levels
were used. The calculated mean ratios and ESALs were obtained for 16, 24, 25,
and 22 pavement sections for single axles on Loops 3-6, respectively, and 19, 25,
25, and 22 pavement sections for tandem axles on Loops 3-6, respectively. For
Loop 3, pavements having 2 inches (51 mm) of asphalt were not included. Figures
16 and 17 illustrate the relationship between serviceability and the respective
mean ESALs for the single and tandem axle arrangements, respectively. Figures
25
---------J.cl6~wunudwl:.t7-<C::!OlinUt;ruain.a-separate curve for the unweighted ESALs, weighted ESAL~
and design ESALs as calculated by Equation C-16. Figures 9a and 9b illustrate
the resulting mean ratios for the weighted ESALs for the single and tandem axles,
respectively. Because the loops are surrogates for loads, analyses for loads less
than 18 kips (80 kN) for single axles and 32 kips (142 kN) for tandems indicate
that calculated fatigue based on Equation C-16 results in calculated fatigue for the
mid range of serviceability levels greater than the final fatigue at pavement
failure for Loop 3 data. Inspection of the ratios for Loop 3 indicates that 14 of 16
sections in Lane 1 (single axles) and 15 of 19 sections in Lane 2 (tandem axles)
exceeded 1.0 at serviceability levels of 2.5 and 2.0.
The Sa.Jne procedure used to produce Figure 9 was duplicated except that
Kentucky load equivalencies were substituted for the AASHTO load equivalencies.
The results are shown in Figure 18a and 18b for the single and tandem axle data
(lanes 1 and 2), respectively. Because the Kentucky load equivalency relationships
do not include serviceability, the serviceability relationship is reflected in the
observed repetitions assigned to the respective serviceability value. The ratio of
repetitions and the ratio of ESALs resulting from the Kentucky load equivalency
relationships are identical because the load equivalency is the Sa.Jne regardless of
serviceability. The values for the ratios of repetitions are identical in Figures 9
and 18.
The variability in ratios for each level of serviceability is the direct
reflection of the observed repetitions for each loop and lane.
26
Figure 9 displays the relationship between ratio of observed repetitions at the
AASHO Road Test versus the ratio of the repetitions converted to ESALs using
Equation C-16. Figure 19 displays the relationship between the ratio of observed
repetitions converted to ESALs and the ratio of ESALs based on the AASHTO
Design Equation C-13 .. Inspection of Figure 19 indicates there are even greater
differences than shown in Figure 9. The ratio of repetitions at a given level of
serviceability to repetitions at failure should be the same as the ratio of design
ESALs at the same level of serviceability to ESALs at failure provided the design
equation represented observed behavior.
Figure 20 shows the relationship
between ratio of repetitions and ratio of ESALs for the AASHO Road Test data
and actual loads. The data points are averages of calculations using the same
personal computer spread sheet except that the ESALs are calculated for each
pavement section using Equation C-13.
Figure 20a indicates that the AASHTO Design Equation C-13 matches single
axleloads of 22.4 kips (100 kN) used on Loop 5 and 30 kips (133 kN) used on Loop
6. Figure 20b indicates that the best match was for a tandem axleload of 48 kips
(214 kN) used on Loop 6. The AASHTO Design Equation appears biased toward
the heavier loads. Figures lla and llb indicate that the axleload distribution for
actual traffic is for the lighter axleloads, i.e., more typical for Loops 3 and 4.
To determine whether the AASHO Road Test data (6) or the Kentucky loadometer
data were biased in some way to produce trends shown in Figures 1-3,5-7, 12, and
27
14-18, analyses were made for 599 five-axle, semi-trailer trucks weighed by WeighIn-Motion scales on a Kentucky interstate. Both AASHTO and Kentucky load
equivalency relationships were used.
For the Kentucky load equivalency
relationships, equations have been developed to account for the additional fatigue
resulting from uneven load distributions between the axles within a tandem or
tridem axle assembly. Previous analyses (11) indicate that loads are distributed
evenly between the axles of the same assembly for only 12 percent of tandems or
tridems. On the average, the additional fatigue due to uneven loading is 1.4 times
that for even loading for tandems and 2.4 for tridems. Figure 21 shows the results
of the analyses of the 599 trucks using the AASHTO load equivalencies (Equation
C-16), the Kentucky load equivalencies assuming the loads are evenly distributed
between the axles within an assembly (left vertical line), and the Kentucky fatigue
adjusted for uneven loading as recorded (the vertical line in the middle of the
Figure 21).
EQUALITY
BETWEEN
AASHTO
AND
KENTUCKY
LOAD
EQUIVALENCIES
ESALs has been the term used to describe the effects of traffic upon pavement
design and behavior. The AASHTO and Kentucky definitions of ESAL are based
on effects of traffic, but are quite different.
The Kentucky load equivalency
relationship is based on fatigue (strain versus repetitions) and developed from a
correlation of laboratory test data with theoretical analyses of static axleloads
applied to pavements and analyzed using elastic theory (see Appendix D). For
28
Kentucky, the same fatigue criterion is used as the basis for pavement thickness
--------------------designs or estimating accumulated fatigue for existing pavements.
In the
Kentucky design system, accumulated ESALs based on fatigue and inherently
assumes that pavement roughness will increase with traffic, cracking may form,
patches may be constructed, and rutting probably will develop.
The
measurements of roughness, cracking, patching, and rut depth are not a part of
Kentucky's definition of ESAL.
AASHTO ESALs are based upon pavement serviceability and structural number
for flexible pavements or slab thickness for rigid pavements.
Pavement
serviceability is based upon measurements of pavement roughness, cracking,
patching, and rut depth. Inherent in the AASHTO ESAL is accumulated fatigue.
Both systems involve the same characteristics, but the difference is in what is
measured and what is inherently included. They are not the same, but traffic is
the common item. To make a true comparison requires the application of both
definitions of load equivalencies to the same traffic stream and the resulting
calculations would be considered to be equal.
Figure 14 illustrates that the Kentucky analyses using load equivalencies intersect
the AASHTO iso-structure lines.
Because the distribution of axleloads were
common to both sets of calculations, there should exist some combination(s) of
AASHTO SN and P, equivalent to the calculated Kentucky fatigue relationship.
Figure 22a is the same as Figure 14 except that the ratio of ESALs has replaced
29.
the calculated ESALs of Figure 14. AASHTO rigid pavement load equivalency
·~---
------------------ ------ -----·----equations were applied to the same traffic distribution shown in Table 1 and the
results shown in Figure 22b.
The vertical line at a ratio of 1 (Figure 22a)
represents equality between the two systems and equality would occur in the
portion of higher serviceabilities and lower SN. Figure 22b illustrates that the
AASHTO rigid ESALs would be over twice that for Kentucky ESALs. Figure 23
illustrates that area of equality in Figure 22a. A pavement design consisting of
4 inches (102 mm) asphaltic concrete on 8 inches (204 mm) of dense graded
aggregate is equivalent to a SN of 2.88 using 0.44 for a 1 and 0.14 for a,. In Figure
23, the relationship between SN and P, is nearly a straight line having the
following equation:
P, = 2.190682 + 0.194089*SN
5
Ratios other than 1.0 may be calculated for flexible pavements by the following:
ESAL,..,;0 = [0.78155- 0.25235CP,) + 0.08253CP,) 2 +
[1.1851 - 1.2417CP,) + 0.3164CP,j")SN +
[-0.17838- + 0.18687(P,)- 0.047618CP,}"JSN 2
where ESAL,.,;0 = CAASHTO ESALS) I (KENTUCKY ESALS),
SN = AASHTO Structural Number, and
P, = pavement serviceability.
30
6
Note that the AASHTO lines for serviceability cross each other for SNs less than
4.
In Figure 23, the range of equality between the two systems for flexible
pavements appears to be a range for SN = 3.0 to 6.0 and Pt = 2.77 to 3.36.
Because results shown in Figure 21 are applicable only to five-axle semi-trailer
trucks and Figures 14 and 22 are applicable to a normal stream of truck traffic,
the more appropriate range of combinations for equality should be considered as
SN = 3 to 6 and Pt = 2. 77 to 3.36, respectively.
A range in SN of 3 to 6 is
equivalent to Kentucky 33-percent AC pavement structures of 12.5 inches (318
mm) to 25 inches (635 mm), respectively, and corresponds to a range in design
ESAL of approximately 80,000 to 11.5 million, respectively, for a CBR 7 subgrade.
Any combination in this suggested range is different from the combination of SN
= 5 and Pt = 2.5 used as a reference in the FHWA W-4 Tables.
For rigid pavements, Figure 22b shows that the ratio of AASHTO ESALs to
Kentucky ESALs ranges between approximately 2.13 and 2.33. Ratios may be
calculated for rigid pavements by Equation 7 provided the proportional
distribution of the number of axles in each weight catagory is approximately the
same as shown in Table 3:
ESAL,..,;. = (2.327 + 0.03556(P,)- 0.025201(Pil +
(-0.070155 + 0.0733(P,) - 0.01824(P,) 2)*D +
(0.0027365 - 0.00316HP,) +0.0009177(Pil*D 2
31
7
where ESALrn,;o =(AASHTO ESALSl I (KENTUCKY ESALSl,
D - rigid pavement thickness, inches, and
P, = pavement serviceability.
Figures 24a and 24b are visual displays of mathematical solutions of Equations
6 and 7, respectively. When the distribution of axles by weight category differs
from the proportion listed in Table 3, Equations 6 and 7 will not be valid and new
equations will be needed.
SUMMARY
o
AASHTO load equivalency Equations C-16 and D-19 appear to be biased
toward loads greater than the current legal load limits as shown in Figure 20.
o
Analyses of the distribution of the number of observed axleloads as a
function ofload as shown in Table 1 and Figure 11 indicate that the actual traffic
passing through loadometer stations consists of a minimum of 95 percent of the
single axles weighing less than 18 kips (80 kN) and tandem axles weighing less
than 33 kips (147 kN).
o
In comparing the AASHTO and Kentucky systems, the range of equality
between the AASHTO and Kentucky systems appears to vary over a range for SN
= 3.0 to 6.0 and Pt = 2.77 to 3.36, respectively. This combination is different from
the combination of SN = 5 and P, = 2.5 shown in the FHWA W-4 Tables. When
the proportional distribution of the number of axles is approximately the same as
shown in Table 3, Equation 6 may be used to calculate ratios for other
32
combinations of SN and P,. For rigid pavements, Equation 7 may be used.
RECOMMENDATIONS
o
When comparing AASHTO and Kentucky ESALs, a combination of
AASHTO SNs of 3 to 6 at serviceabilities of 2. 77 tO 3.36, respectively, might be
considered as shown in Figure 23.
Any combination is different from the
combination of SN = 5 and P, = 2.5 shown in the FHWA W-4 Tables. Equations
5 and 6 may be used to calculate ratios for other combinations of SN and P,
(Figure 24a). Equation 7 may be used to adjust Kentucky ESALs to AASHTO
rigid ESALs for specific pavement thicknesses (Figure 24b).
LIST OF REFERENCES
1.
J. H. Havens, R. C. Deen, and H. F. Southgate, "Design Guide for
Bituminous Concrete Pavement Structures", Research Report UKTRP-8417, Kentucky Transportation Research Program, University of Kentucky,
Lexington, KY, August 1981.
2.
H. F. Southgate, "Estimation ofEquivalentAxleloads Using Data Collected
by Automated Vehicle Classification and Weigh-In-Motion Equipment",
Research Report KTC-90-11, Kentucky Transportation Center, University
of Kentucky, Lexington, KY, June 1990.
3.
H. F. Southgate, J. H. Havens, and R. C. Deen, "Development of a
Thickness Design System for Portland Cement Concrete Pavements",
Research Report UKTRP-83-5, Kentucky Transportation Research Program,
33
University of Kentucky, Lexington, KY, February 1983.
4.
AASHTO Design Guide for Pavement Structures, the American '"'-"'"u'cmuon
of State Highway and Transportation Officials, Washington, D.C., 1986.
5.
AASHTO Interim Guide for Design of Pavement Structures, 1972 the
American Association of State Highway and Transportation Officials,
Washington, D.C., 1974 Printing.
6.
The AASHO Road Test Report 5, Special Report 61E, Highway Research
Board, Washington, D.C., 1961.
7.
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.
8.
The AASHO Road Test Report 7, Special Report 61G, Highway Research
Board, Washington, D.C., 1961.
9.
The AASHO Road Test Report 3, Special Report 61C, Highway Research
Board, Washington, D.C., 1961.
10.
T. C. Hopkins, "Relationship between Soil Support Value and Kentucky
CBR ",Division of Research, Kentucky Department of Highways, Lexington,
KY, 1970.
11.
H. F. Southgate and R. C. Deen, "Variations of Fatigue Due to Unevenly
Loaded Axles within Tridem Groups", Research Report UKTRP-84-11,
Kentucky Transportation Research Program, University of Kentucky,
Lexington, KY, April 1984.
12.
H. F. Southgate, R. C. Deen, and J. G. Mayes, "Strain Energy Analysis of
34
Pavement Designs for Heavy Trucks", Transportation Research Record 949,
Transportation Research Board, Washington, D. C., 1983.
35
AASHTO ~0 EQUf,i!>WlCES
A/lSHTO LOAD EQU\!ALEtLIES
40-i<IP ( 178--l<t,j), 4--11'<£0 SINGLE All£
:!e-l<lP (J:'i2-ld>l). 4-ffiED SIN3l£ A><l£
14
50
I
1J
40
~ r--..-.........
I~
~
'
,..._
p
1
§B
-35
7
---
2
J
4
A.'SHlO STRJCJUfW_ ltlA3ER. SN
p - .,,
5
6
•
6
6
P, "'"'2-5
I
L
/
pl"" 3..5
7
8
9
10
12
11
AGV FA.E!JfNT THIO<NESS. IN:l-ES
AA&ITO I1J!.D ECUIII)).lH~CIES
AA&ITO I1J!.D EQJIIINB~CIES
52~ (231-4#l,
8--llR£0 lilN:JEM Al<l£
.
p ""1..!-
g
p ... 2.5
PI -1.5
12
p
2.0
~ 11
P, Q: J.o
§ 10 ~
§ ~ ~ ......,
P, ,. .ls
- - ..
p
-=~
............. .......
/
.P.-3.0. /
7
0
6
4
5
6
"""'
•
7
.s
..---
.... ~ t--
'
.....
.......
..... ......... /
/
/
8
'
~
1J
p . 2D
2
14
.
14
~ 2
1.3
·!:;I
6
I
I
48-I<IP (214--kN), 8-llRED lJl.NDEM MLE
I:
I
/ ,....../
...... , / /
{:J)
5
~
.............
....... p ""'3· . , /
"""'
r-_......... r""
.......
.......... ~
11
9 ~
_l
o.
12
§~ 10 I'--
..:::.. ~ Z5
""" "' --.........-------
10
g
P -zo
r--
f'.::---.,
2!l
pl- 1.5
P, - l!i
/
I
9
10
11
AA9iTO STRJCIURI'L fU!IlEii. SN
Fa30 flll61B-IT THIDIESS. tDB
(~
i:J)
FIGURE 1. VARIABILITY IN AASHTO LOAD EQUIVALENCIES FOR FIXED
AXI..ELOADS.
12
lJ
14
AA:.."HTT SN3LE AXI£Li)ID E::JUIW'LHICES
AASKlD SINGLE Al<l£ll)AJ) EQUiv~LENCIES
6
6
<•• "")
+1419'S (82"")
1'"10 IG'S
iii
~
II!
iii
(9B l<lt)
+21119'5 (118 kiQ
..... 21119'5 {125 "")
5 +2219'S
~ .j.
~ 5
~ 4
IP, = 3.501
I
I
+
10 ~ {-45 ~NJ
(621t~
·
· ·14'5
- (9B 11'\1
+12
+26 ~ {118 lt~l
-211 14'5 (125 11'\1
~~
IOii!
--
P, = 1.!:01
3
3
~2
~< 2
I
1()-0
l<t"
10'
. 1Q-1
()-<
10'
LO'D EIJJr.PUNC!
6
m
~ 5
Ill'
@
(b)
AJlSH10 ll'NDEM AXI..fl.DI'D ECUf'.ALENCES
MSKTD TANOHt AXLfl_ffiD EOJitl'ILB'K:ES
'
1198
+!!Ill'S (00 "")
+:!!!Ill'S (125 tH)
.... J8 II'S {160 11'\1
""'*"" 4$. lofJS
1H1
.... 52 II'S 231 tH)
~ 4 P, = 3.50l
I
\
3
~2
to-•
l<t"
Ui
0! 5
II!
'
/·
I
6
I
\
I
'
\
\\\
j
I
LO'D EJ:I.JM\I..EI¥:1'
©
..... ""'
(011"')
• 2111CP.S
+.:IIIIFS
(129 JoN)
('ill i~HJ
...... 4111CF5
(1!J81d4)
[::31 liN)
+51~
~ 4 P,- 1.50
~
3
~2
I
\.
10'
10'
lo-•
1o-'
10'
LO'D EWtloi£NCl'
·fl)
FIGURE 2. VARIABILITY IN AASHTO LOAD EQUIVALENCIES FOR P, = 3.5
j.
AND 1.5 FOR SINGLE AND TANDEM AXLES FOR FLEXIBLE
PAVEMENTS.
I
I
10
lCJlD EQUM'I.flCI
10'
AI>SKlD !::INGL£ AXill::l'IO ECUII;>l£HCIES
AASHKJ SN::;L£ AXLELCAD EQJMILEN:ES
11
if)
210
~
11 lr=:~==~51PT--,----r--t---ffih
+1014'S (45 k/~
.... 1414'S (82 ~
+2214'S (99kl~
'
I
""I
•ZI4'S 125 1<H
~&~~
:!!&
T
P,-3.501
9
'"
2
10
~i
+2614'S !118
::s 8
~sl
tl
t
I
I
•1~1
~
~ 7 I
tl
t
I
I
•1• I
61
61 1
'
I
I
liA I 1
~
7
\
6
16-<'
1()-' .
10'
to-e.
10'
.1Q-
lO'I) Ell.I\IUNCr
@
(t:)i
.A.ASHJC• lANOEM AXI..£L(}>.O EOOM'lENCIES
AA3-I!D TANDEM A;<Lf]_QlJJ ECU\!AI£NCIES
IP, = 3.50 I
"' 10
2
::s
9
j
::s 8
~Q 7
~
Q 7 I.
+
If
1()-'
IP,= lfol
(/)
~
8
6,
11
210
1
9
1B 14'S (!D 11'(1
... 2!1 w.; (12511'(1
..... JS 14'S (160 11'(1
...... w.; (186 ..,,
+52 w.; (231 11'(1
\
l.
10
LCW EOJI~lCI'
11
i
100
10'
It
tl
I
i
... ,. w.;
..,.zw.; 11
kH)I
"'~
I .. ,.... 35>1'5(16 kHI'
+ 44- I'FS ( 1 kt91
.... 52 >FS (
lkl~l
6
10'
10'
1()-'
10'
10'
lOO EOJI.ru£HC'r
lO'I) EQJM'J..ENC(
t:)
tJ)
FIGURE 3. VARIABILITY IN AASHTO LOAD EQUIVALENCIES FOR P, = 3.5
I
AND 1.5 FOR SINGLE AND TANDEM AXLES FOR RIGID
PAVEMENTS.
10'
AASHO ROAD TEST PUMPING DATA
'REINFORCED PAVEMENTS
..
...
..·
250
~
w
*
~ 200
* .....*
C\1~
cih!
wo:
I
:5°
50
X- J: 1,
•J
wO
c~
I
ie
+
:i 100
I
•
ii:::J
>[·.-~.
::::Ea::
:J
50
,•..•
I
'~···
-
:J
0
* ..
I
:t' ...
•
z
-~
I
.
....
..·
.·.·
.
..........
+
'
+
.
'
'
IS'ffl LANE 1
lANE 2
•
:> 1.5
:> 1.5
>1.5
- 1.5
•1.5
*
+
.'
50
+·
+'
P,
•
•
+
*
+
0
0
..
.
. . ··*
I
:z z '
a.~
..
I
:g:a:
(!)
!
.
.·..
..... ·/
........
,.
... ..
i
ZIL
..·
+
4.
.. ..
100
-1.5
'
200
'
150
250
PUMPING INDEX, lANE 1
CU IN PERl 'LINEAR'
'INCH' OF PAVEMENT
·.
' '
' : r .r
!'
ll ~
·:
•
1
t·
1
,
r
l ¥ i
FIGURE 4. AASHO ROAD TEST PUMPING INDEX DATA, LANE 2 (TANDEM
' AXLES) VERSUS ' LANE ' 1 ,(SINGLE AXLES) . (TABLE' 54,
' '· '
REFERENCE 3).
II
ll.I\SHO RQ<\0 TEST Dl.TA, R£PEll11CN3 OF lJ)I.[;·
9~GLE Al<l.flD!CS, Pt -
35
6
0
-e-LD!PJ
-e-LDIJ'4
-+-LD!P 5
5
i1i
i
Ai<>HU RLiUO TEST CATA, I'EFETilD 6 Cf I•A·
SNJLE .~A..ElJ)Affi, Pt - }3
----· -e-LDIJ' 3
... LlXF.
--r-LD<F 5
-o-Ul!P6
5
~ 4
4
1-"
,.- 1-~~ 1--- 1--........
~
r--
--
1
o.
I----
~·
f-.-<
- - _L_
-
.
---
0
200
0
400
600
f£F'ElT11aiiS Of l.ll'!l. llil.&NJS
!100
0
1.000
-lDCP3
... lDCP4
1-llXP 5
TlDCP 6
5
jilj
1.W·)
(~
Ai>SHO RQ<\0 TEST CATA, 18-KIP iftO->N)
ESULS 9NGlE A~ PI - 30
6
-I..O(p 3
4
f -
-~
.,....
:-.... ~
---
~ t;::::~_::: t:- r-:::: 1-- 1--
~·
-LD!P·
+LD!P 5
;-LD!P 6
5
IJi
400
600
AASHlO li'H<P (llO-#IJ (SilLS, THCJ..&I.('f;
@
!100
l.OOJ
--
--
i:
0
200
- f---
~ 4
..-
I
0
EI::O
600
f£PEll1Kl£ OF lD'D. lHCt.G"IIUS
At>SHO R<W:l TEST .C'AlA, 18--KIP {80-1<1'1)
£SI>,LS Sl'lGlE AA.fl..Ot>,[S, Pt - 3.5
6
400
200
€:\)
!
---v- --- -!----'
--- --- [::::: ::- --- -- :- --i:.-.:::::~ ------ --~
+LDIP6
r
----
c.-
- - ----- ---
--
-----
-
0
~
I~ ,..-
::.-
-
~~
·-·
--- ='
200
~
400
----
----
~m•
!100
600
AASHlO ii'H<P [ilO-M{> Ei'LS. TllfJ.&HflS
t---
r
•pmm
1! .101..1
~)
'
FIGURE 5. COMPARISON OF AASHTO STRUCTURAL NUMBER TO
1 L;'
REPETITIONS AND AASHTO ~SALS FOR AASHO ROAD TEST
SINGLE AXLE DATA AT P, = .5AND 3.0.
1
I
AASHO ROO ltsT ~TA, F£FETTllCN3 CF UJlD
SN3lE A:<l..£lL)Offi, PI: - 25
"
Ai\SHO ROO ltsT ~TA, FEJt ill ~.l'£ CF LO {)
SN3lE A:<l..£lL)Offi, PI: - 20
6
.... l.D(p 3
.... LLD'3
-+-LLD' 4
-.-LLO' 5
5
t:i
!---
...... LLO'~
~ 4
i: - --
1---"
.-- I-- .-
~
1---- 1.----1----
:-¢---- .,.. •
p
-----
,.,.;li
~3
1--
~
.
1----
-
ili
----p
---i: -- - - I--1---"
~
0
200
6
600
40:)
800
f-:::::: f--::
LiXf.
r-
f-"
600
40)
200
I
(I::)
AASI-0 RON) ltsT ~TA, 18---l<IP (S0---14l}
ESo>tS 9NGLE Al<lfl_o>OS, PI - 2.5
Ai\SHO H!J'.O ltsT ~TA, 18-l<JP {&_')_kN)
ESt>J.S SI'IGLE .~ PI - 20
... LLO' 3
.... LLO' •
-t-LLO' 5
5
-+-LLIF 5
..,,
-
~ 4
i: -
I w-r
~
t.i
4
z
3
I
j"..,p_6
~J
oJ
-LLO'~
~
2
I,C 0
6:x
p)
...... LLO' ~
-1
I
FUET11l:l'<S OF lD'Il, ll-ICIJ5l>NOS
6
:::
~
~
fU'E1T1lCNS OF L[)t{), 11-UJSAI£5
.... LLO'.
5
-
0
l:XXJ
+-LLIF 3
t:i
~ f.-
~LL0'5
~ 4
·J
0
I
-+-LLD'4
+LLD' 5
5
-....
~:
~·
~
_...-:
......
0
Q
200
40J
600
800
MSHlD I!H<P [llO-ld~ ES>LS, THCIEI\!<IJS
@
FIGURE 6.
l:JCQ
0
200
600
40)
MSHlD I!H<P [llO-l<l~ E9\I.S. THCIEI\!<IJS
w
COMPARISON OF AASHTO STRUCTURAL NUMBER TO
REPETITIONS AND AASHTO ESALS FOR AASHO ROAD TEST
SINGLE AXLE DATA AT P, = 2.5 AND 2.0.
00:
1.000
AASHO RQIIO TEST CATA, I'EFETTTlCt£ OF LCPD
SN3lE A,'<l..Elil"DS, Pt - 1.5
6
....-LOF!
~LDY 4
5
-
........ LD::P ~
~
-o-LDP 6
~ 4
j:
~
t-
f--
-
--- -
l--- r - -
f--
__...
~---"- ~
t-"
fL--:::1-::
t-"
f-- 1--
·~ f--
.:.--
t]lCA'_!..
f--
---
f-
_,
~~
I
o.
0
200
40J
600
BOJ
l::XXJ
F£PEliTOlS CK i..D'D, 1H:l.G'l'IC5
~I
AASI-Kl HD'D TEST lJol-11\, 18-+JP (8J-i<H)
ESl>LS 3'1GL£ A:<!..B..O'II:6 pt - 1.5
0
5
iii
.... UXF.!
-<>-LDP4
..... LOP!-
j
..,...LDF~
:::::::f-1
~ 4
z 3
i
~
::::
z~ ~
.t::::.
'r ~~
e~
~I
- ---+- +
-
-L
+ +
0
0
200
400
600
BOJ
A.Gml 18-KP (.3:l-J.N) ESI.LS. lll::J.RI'ffi
1,000
(~
FIGURE 7. COMPARISON OF AASHTO STRUCTURAL NUMBER TO
REPETITIONS AND AASHTO ESAI.S FOR AASHO ROAD TEST
SINGLE AND TANDEM AXLE DATA AT P, = 1.5.
AASHO RrnD TEST D\TA
LOCf' 4, LANE 1, 18-KIP (BJ-kN) SINGLE
·.v
I,,
~
I
V /I-<:,;;;;?)?
r:-,;~)~r
2.5
<!
2
0
3
4
REPETTTIJNS OF LOID, x 10"
7
6
5
~)
AASHO RrnD TEST D\TA
LOCf' 4, LANE 2, 32-KIP ( 142-kN) TANDEM
4.0
'l
en
~
Ui 3.0
~
0.:
0.:
•
I
I
-,
z
~
n
0.:
ffi:::; 3.5
"
n
'
/
;
;
''
/
/
.. ··
I .,;:;-... .. ~
.
~~
~
~ 2.5
;
/
~
;.::~
/
\!2
<(
.. ·· .. ·
,.·· ,.·--"
'
/
•
'
... ,. .-·
v
~
.. .. -·'
.-·· .......
/
/
:J
:<l
•
I
~·
0.:
.-·
~
2.0
0
FIGURE 8.
2
3
4
5
6
7
REPET!TIJNS OF LOID X 1<Y
8
9
10
COMPARISON OF VARIOUS P,s FOR AASHTO SN AND
REPETITIONS OF SINGLE AND TANDEM LOADS FOR AASHO
ROAD TEST LOOP 4 DATA.
AASHO RCAD TEST
31NGLE AXLE, LANE 1 [)t>.TA
~~
~-~
I
I. 1- +LOOP 3
+LOOP 4
:'i
1.0
+LOOP 5
jz1i:l
0.9
-.lla-U))> 6
9·1
-~o.
sz
o..,
---
lr
~v 0.8
.-:t::E
u..:J
02
8-l
·c! ~
0::0
.fi!rY
~ k;" l!i
_a/ ~
0.7
~
0.4- ALL F\1\VEMENT SECTIONS
0.3 o-J INDM[)JAL LOOP
0.2
0.1
0.0
0.0
/"'* /zo
~
s:CXJ 0.6
cb-u.. 0.5- RATIOS ARE AVERAGES CF
~~
.....
.------
v
•"'t"
A,
,_.....--
v./
/
v?'\ ><"
~-0·
,¥
.-"
/
l,...---"'" .30
/
-·~
w
c<<,~-.f'
.3.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
R~K) OF NUMBER OF U:W REPE'TlTKJ'.IS TO TOlAL NUtiBER OF REPEllllONS
AASHO RO\O TEST
TANDEM AXLE, LANE 2 [)6.1A
(1 '::']
F<(
::) ~
~z
1.2
1.1 - +UXJP 3
+llXf' 4
1.0 - +U))> 5
'i'l' o.9
-.lla-UXJP6
~g
__ a. 0.8
0.. 2 0.7
:zl
1 OJ 0.6
co-"- 0.5
....
_..,..\3
RATlCIS AAE A/ERAGES OF
- AlL
PAIEMENT SECTIONS
.------
~~ 0.3
c._::J
oz 0.2
lit"""'
~g 0.0
3!i
0.1
0.0
0.1
0.2
-------
0.3
0.4
.a-- ~ v
/ 'l
#/
,..,.-'.;,c /
/
iJif;?~
w 0.4 - ON NDIVDU'L LOOPS
~p
--.....
;/"
/
¥
31L
0.5
,~ \..'-
0.6
2!i
15
>!.U
.c.;ov "'
-*
0.7
0.8
0.9
1.0
~ OF TOlAL NUtiBER OF LOO REPETITKJNS 10 lOW.. NUMBER OF REPETITIONS
(~
FIGURE 9.
RELATIONSHIP BE'IWEEN RATIO OF AASHO ROAD TEST
REPETITIONS VERSUS RATIO OF REPETITIONS CONVERTED
TO ESALS USING AASHTO EQUATION C-16.
AASI--!0 F\IJAD TEST IJA.T.A. ANALYSES
RATO OF OBSEJM:D REPETillCNS FOR 176 SECfONS
..____
3.50
1---r--..
y
a + bX + eX'
X= RATIO
Y = SERVICEABILITY
c = -4. 189497
I·
0
~
~
2.00
"-....
~
b = 2.511961
K
~
a= 3.176561
R2 = 0.999927
N = 5
1.50
0.40
0.50
0.60
0.70
0.80
0.90
1.00
AIERbGE RATO OF REPETITONS
~)
SERVICEABILITY VS SERVICE LIFE
Bl>SED ON 176 F1\VEMENT SECTONS AT AASHO A.::lt\0 TEST
1.5
-!-.........--...-.--1-.,......,.-.........-~~i...---$--.~.......-.....-;-....--...
0.0
0.5
1.0
1.5
2.0
2.5
RATIO FICTOR TO PREDICT SERv'ICE LIFE
(D)
FIGURE 10. RELATIONSHIP OF OBSERVED AASHTO SERVICEABILITY
WITH AVERAGE RATIO OF REPETITIONS OF APPLIED LOADS
AT AASHO ROAD TEST.
SINGLE AXLE WEIGHT DISTRIBUTION
•vv
90
t;
~
80
__.I
70
60
~ 40 ...I
5
50
I
/
:::J
~
30
20
10
0
0
5
10
15
20
SINGLE ~. KIPS
25
30
35
~)
TANDEM AXLE WEIGHT DISTRIBUTION
100
80
t:;
70
.lJ.
60
h!
I.U
~
~
..
~
~
90
Cb
-
·_?'
~
50
4D
30
/
20
10
I
0
0
/
/
/
/
i
10
20
30
50
60
liiNDEM M ..f:!.a.D, KIPS
(~
FIGURE 11. ACCUMULATED PERCENTAGE VS AXLELOAD FOR KENTUCKY
LOADOMETER DATA.
STRUCTUR.AL f\JUMBER VS ESt.L
kENTUCI<Y LC~.DOiviETER OL\TA
6 -·
+P, = 35
z
+P, = 3.0
0:::
5 -}1-e- P, = 25
2
-,
+P, = 15
(/}
w
rn
L
___j
+P, = 2.0
4
r--
i1=:;
t5
=:;
g:
~
~~--------r-------~--------~~------~
(/1
~en 0JL____________t-----------~~IF~------lr---=~
I
L
~
1 , I I
100,000
I
I
,
...
I
I
I
I
I
200,000
I
I
1.,
I
I
I
101
I
I.
I
300,000
P.ASHTO 18-KIP (80-kf\l) ESAL
FIGURE 12. COMPARISON OF AASHTO SN VS AASHTO ESALS FOR
KENTUCKY LOADOMETER DATA.
I*
I
I
II
I
,000
0
0
--
()l
o_
I
0
OJ
~I
(/)
~~
@~\~~~~1,
~'~· ~\
~
L-
0
~
_j
w
0
O'J
~~~ ~ ~~~
~\
~
0::::
~'\ 1\~
>-
u
,/
w
_j
~~\
<:f
"""-
~
y
\~
~
0
l()
r....io
0
·..Y._
<J
~~
~: 'z
n
.::::J
-,_
~
<,/
~
u
-
r\
\
/~~~
1\
f- 0
1\.
F
r-\ ~\
,.;
~
t-.. r--(06~
....
L
'./
_._
"C'
w
)'-...
0
r<J
0
.,.--
~
:::,(
ci
<[
]'\
t\.
,..._
0
C'\1
R
!-.. ~
.......:;
1-- .......
.,-(~
1:-- ~
0
'<"'""
i'
'<"'""
l_J
0
X)hJ3lV/\In03 0\()l
.=J
~
()
z
ril
~::>
()'
ril
0
..:l
~
~
(.)
C'
0
0
ril
~
-
~
~~~
:>s
1'-,~.:1'
j'::t---..
r,, ~,
f-
-7
[\
-~~
·:?)Q"
_!
-j
0
1\~
;,, .
z
0
~
~
L"
.....
UJ
(CJ
'tt
w
:""'r:
0
I'-
0
[\ \
\~~
----:=)
0
ui
0
q
0
z
~
...s
.....
~
::>
Cl
r:..
SER,JICE.ABILIT( 'VS REF'ETITIOI'·IS
f<Et,lTUCI<'r' LCADOII.'IETER DAT,L
3.50 I
I.
300
~
r:-
s
~ 2.50--1-l+ SN = 1
0
a::w
(./1
JI-&-SN=2
]+Sl''-1= 3
2.00 ~SN = 4
+SN= 5
11
...._SN= 6
1.50
100,CIOO
200.000
300,C00
AASHTO 18-KIP (80-kN) ESA.LS
FIGURE 14. KENTUCKY LOADOMETER DATA CONVERTED TO ESALS
USING KENTUCKY LOAD EQUIVALENCY RELATIONSHIPS
AND SUPERIMPOSED ON AASHTO ESALs SHOWN IN FIGURE
12 BUT REARRANGED AS P, VS ESALS.
,000
LCAD EQUI\ALE!'\JCY F:ELATIOI\-JSHIPS
.A.ASHTO A.l\10 KE~ITUCI<Y
3. 5 ---.-------.---1-.l----.--.--..---,rl
+M6HTO
_,__.
-e- f<ENfUCK'r
Q_
>_:-
~
3.0
1215-KIP (4.3.9-kN'l
SINGLE AXLELOAD
AASHO ROil.D TEST
SECTIOI\1 I'JO. 121, Si'~ = 3.06
REPORT 61 E, PAGE 245
22
w
()
>
,.., 5 +-----+---+--+--+--1-l-1
0.::: L..
w
Ul:lSERVED NO.
OF REPETITIONS
(/)
P,
1-
3.5
~
~
2.0
1
1.sl
1Q4
I
I
I I I I I I~
I
3.0
2.5
4
2.0
1.5
I I I I IIW
I
154.882
427,563
529,663
612,942
644,169
I I I I 1111
1Q5
1Q6
18-f<IP (OO-Kn) ESnLS
'
'
FIGURE 15. COMPARISON OF KENTUCKY AND AASHTO ESALS VS
SERVICEABILITY FOR PAVEMENT SECTION 121 AT AASHO
ROAD TEST.
SNGLE f'!XLES
3.5
AA9·t::J FrnD TEST CATA, LOOP 3, LAt--E 1
AA9iO R)l.[J TEST CAlA, LOOP 4, LANE 1
~ Cf"
1\~ Cf" 24 FIIIEMNT. su.:TilfS !J RJ'O TEST
~
J.O
'\
?::
~ 2.5
2.0
+ ..s.GfiO re:J;:t~ ~
I~
50
30
i"
2.0
~
100
i
,,.
(b)
AA9-IJ W.AD TEST CATA, LOOP 5, LilJ'£ 1
AA9iO R)l.[J 1EST CAlA, LOOP 6, LANE 1
I\£FIIGE Cf" 22 FIIIEMNT su.:TIJtS !J RJ'O TEST
35
..... I..Jfflff.HliD ESPlS
~
+ llEDmD ISilS
~
--- AlSffl CEn'4 fSIILS
~
~
-
1•))
200
Y.o
400
~
soo eoo
aoo
""'
100
1!1-f<P {!l)-lt9 ESI!lS " 10'
~
-
~
•""'£rnlrn pes
~
+ 1\EDiTElJ ES ~
1, "
~
30
500
I !SOlS
.,_.-ro~e
I
~
~
2.0
'"\
o
400
ty
20
--
300
200
1&-l<P (B:l-#1) EWS x 10'
25
1.5
-e-l'<fDfiiD E lS
;o.o.<>ro!Eil N E5<tS
1&-l<P (oo-#1] EWS x 10'
~
30
100
0
200
150
-.LNIIECHTEI} '51<5
\ I\_~
1.5
A-fRICE Cf" 25 FA.a.ENT su.:n:N5 .'if RY>D TEST
~5
~
"~
~ '-
. . i4WiTED ESilS
1.5
0
3.5
... ltfo.'.WiTED !51t.S
\
~
18 fliiiE}..ENT su.:rus ;;r RJ'O TEST
1.5
900
1.000
I
2
18-I<P {ro-+.H) ESI!lS • 10'
{:J)
FIGURE 16. COMPARISON OF SERVICEABILI'IY AND RATIO OF AASHTO
ESALS FOR UNWEIGHTED, WEIG TED AASHO ROAD TEST
DATA, AND FORAASHTO DESIGN !UATION CALCULATIONS
FOR SINGLE AXLELOADS AND S USED AT AASHO ROAD
TEST.
~
3
4
TANDD.,I A>:LES
!IASHO RO'ID TEST [)!ITA, LCCP 3. LANE 2
!IASHO RO'ID TEST [)!llA, LCCP 4. LANE f
M:RAGE OF 19 FIO.'EI·ENT SECTlCtS fii fO'D lEST
MF'JlGE OF 25 FM:1ENT ~ fii RlAD
.....
3.5
3.5
\ t\
3.0
~ 2.5
\\
~
2.0
1.5
.,......am
3.0
125
.
1.5
6
2(1)
100
3)')
2(1)
100
0
1!H<P (8J-ltl) ES0LS x I!Y
{:!!
(b)
..
!
!IASHO RO'ID TEST [)!llA, LCCP 5. LANE 2
!IASHO RO'ID TEST [)!llA, LCCP 6. LANU_
MF'."GE OF 2.4 fii.El.U-lf =noi'S fii RlAD TESr
MWa: OF 2.1 fii.El.U-lf =noi'S fii RlAD
~ 1'-w.
~ ~~
"'
1
'\
3.0
'"\
25
"""'
Ul
2.0
~
:!6o
JOO
-e-IIEDfl!ll ESIIS
""ff- .u&nD tE:DI ESilS
~
sco 600
~:: 3.o I
I~
I
I
I 1 .,..:--o~ES/tS~
~ 25 I
I
I ...._')l
I
I
I
i I
I
2ol
I
I
I~~~
I
II
I
1.sl
I
I
I
'Jl
""' "" """
-400
1If
....~ESilS
.... I.JfMDfl'EJ) 5ltS
l
16:!
500
4(1)
18-KP (EIHN} ESAIS x 10>
3.5
6
!SOlS
I
20
\
I !SOlS
I
V>
3.5
1.5
ESI1lS
+
OEDiTEll !SOlS
"'*" AIQf1) ~ £SillS
~
I=
....
.... LtfflECHl£D !SOlS
•
1'Ef
1ol eoo
9CO
1.100
0
I
2
'M
l!H<P ((1)-#1) ES0LS x I!Y
18-KJ> (oo-J#) ES'i$ X fO"
·l:;l
@)
FIGURE 17. COMPARISON OF SERVICEABILITY AND RATIO OF AASHTO
ESALS FOR UNWEIGHTED, WEIGHTED AASHO ROAD TEST
DATA, AND FORAASHTO DESIGN EQUATION CALCULATIONS
FOR TANDEM AXLELOADS AND SN USED AT AASHO ROAD
TEST.
I'A: I
3
I
4
AASHO Rcw:J TEST DA.TA
KENTUCKY L.Q6D ECUtvALENOES
1.0
j
a.,.
0.9-
~
::z 0.8-
~-'""""
-e-LOOP 4
8 0.7- -+-LOOP 65
0..
:;::
0.6
ch
b
I
I
I
I
I
0.3
_v-
y---
_/. 0 _.---><::
"'' \\1
'v-? . ....J\Ci ~- I
I
..1/.,
_..,.._.-----
0.4
/
/
I
.r:.
\ 'l-':/
-
I
I
I
0.5
§
L,2
-l.OOP
I
<':INGLE f. Yl c-c:
_I
'
/
/
\
/\
, ( h\-'-"
"'< f30
0.2
0.1
~
0:: 0.0
0.0
I
0.,
0.2
'
0.3
0.4
0.5
0.6
0.7
0.8
RAJIO OF REPET1110NS OF Slf'.GLE AXi..EIJ):\[)
0.9
1.0
(a)
AASHO Rcw:J TEST DA.TA
~
KENTUCKY l..OO ECUrYALENOES
1.0
f:J 0.9 - -LOOP 3
-e-LDOP 4
-=±i 0.8 _..LOOP 5
~- 0.7
-+-LOOP 6
iJ_
::z 0.6
TANDEM AXLES
'
i
.....
0.5
/_
~-·- 0.4
0.3
~
"-
1/ =-~ . . .
0.2
\
a::
0.1
0.0
\
I
y-- - .~~\
-
./
/'\
v
\
Cl
~
'
I
-,, .- \ ,,
/ . '\.·- ·t
' / -\ ·.
\
•
~---'1-"'_.---/_/ :.?_...,
"\
v-I
I
I
I
/
i
I
I
:
I
\!)
I
/
_...~\1
-· d
r,v
~
.._;, t;F-
---·
I
0.0
0. 1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
RATIJ OF REPETI110NS OF W<DEM AltiJ..OilD
0.9
1.0
(b)
FIGURE 18. AVERAGE RATIO OF KENTUCKY ESALS TO Av'ERAGE RATIO
OF REPETITIONS OF LOAD FOR AASHO ROAD TEST DATA AS
A FUNCTION OF LOOP AND SERVICEABILITY.
R.AJ(J OF A.ASHTO DESIGN ES.ALS VS A.ASHO
ROAD TESf ESAl.S FOR SINGLE AXLE D\TA
'I.L
~
~
-e-l.DOF' 3
-&-l.DOF' 4
1.1
1.0
0.9
0.8
0.7
/
-lOOP 5
/
....a..lDJP6
~ ...-
~
~ 0.6
0
rY
~
"0
0.3
0
\\_\~~'C..~
-?
0.1
0.0 ~ .,
-
----'(,\"'~
~
/""' /
/
.-::-[]\' t.'~
(·~~'
fi; 0.2
et:
/
/
0.5
0.4
·:(
,...,. ,...,./
tK
0.0
0. 1
0.2
.;r
/
/
--
~
~ /
/
/
')_.l
--~~)
/
v
/
/ V 1 .~;, V.cjS.'~-J/
4~
.
-g.,~/
/
<j
fio/:~")--
~-
~/
/
-:)~
0.3
0.4
0.5
0.6
0.7
RATO OF' AASHlD DESIGN ES.ALS
0.8
0.9
1.0
0.9
1.0
(c~
RATO OF AASHTO DESIGN ESAl.S VS AASHO
ROAD TESf ESAl.S FOR TANDEM AXLE D\TA
1.2
·~
1' 1
~
~.,
1.0
0.9
0.8
0.7
0.6
0.5
0.4
"0
0.3
~
0
~
-l.DOF' 3
/
-e-UXlP 4
-LOCf' 5
....... lDJP6
/
/
0.2
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
RtifO OF' AASHlD DESIG~l ES.ALS
(b)
FIGURE 19. RATIO OF AASHO ROAD TEST ESALS TO RATIO OF ESALS
CALCULATED USING AASHTO EQUATION C-13 FOR EQUAL
SERVICEABILITY LEVEL.
.
COMFr>.RISON BETWEEN R.AJO OF .AASHO ReAD TEST
----~RJ;'IEP~ETffOt~S AND RATIO OF Afl.SHTD-BESJGN-PESAJ:S~>:;------LO
0 LOOP 3
7~
I SINGLE AXLE I
0.9
•...< " '
~ 0.7 *
~
~
~
u...
0
0.3
~
0.2
il::
l.OOP 5
'< ~l'-
0.6
~
n
...~~' /
...
l/
1...
0.0
<:J
. ,:C
0~
&?'
/
f...--.
~
"o
;;o......
·--- ~--- it.)
-;9
'
·,
,....rv 1---.,
0.4
0.1
I n
~'<-'
A l.OOP 6
0.5
<(
,,<J.f>'
Ill l.OOP 4
0.8
[9-V
[')
11)
:7La -
,/
0.1
0.0
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
RAm OF AASHO R(W) TEST REPETITIONS
(ci)
COMPARISOt·~ BETWEEN RATO OF AASHO RCY.I.D TEST
REPET!TON'S AND RATIO OF AASHTO DESIGN ESAJ....S
1.0
•
0.9
I TANDEM AXLE I
lDOP 3
~ 0.7 *
Ill LOOP 4
0.8
Q
~
0.4
u...
0.3
0
0.2
0
ti:
Ct:
~~c:< I~'P'\,..'.J
11*1' . -;.
0.0
A
./
L...-'
0.5
0.1
':>\..
.,'<.,...-~
0.6
~
·~
,,·{.' '
l.OOP 5
A l.OOP 6
~
~
'"'
II.
....
7 l-/_
~ .
.k'
--·
v
,~
~
~
"'ffr
..
/
.
)
•!D
II!)
)
]A
"~
/
~
§P"
IF
0.0
0.1
0 .,
0.3
0.4
0.~1
0.6
0.7
RATIO OF AASHO RCWJ TEST REPETITIONS
0.8
0.9
1.0
'bi
I, '
FIGURE 20. COMPARISON OF RATIO OF AASHTO DESIGN ESALS TO
RATIO OF AASHO ROAD TEST REPETITIONS.
A. ASHTO \5 KY ESALS
59·;j ::.-.1\l-:LE SDvll-TR.D.JLER TRUCI<S
6
z
a::
w
'
1
',;-+I 'NEIGH-IN-MOTJm,J
I
I
,
I
• I
Ell I f
il
.+
II ....., Pt = 35
I
I
1111 ~
A:l
4
I "*- Pt = 2 0
1.~
(f)
c::;
J~---
I
m
2
::J
z
_j
4-r-----
&
:::>
tJ
~
~
...to.-Pt= 1.5
-B-KY EVEN
+KY u~
3-r---
z
tn
i2
-e- Pt = 3.0
-+- Pt = 2.5
~
w
2
~
1 -+-r..,...,....,...,....,.,
600
>-~
700
800
900
1,000
18-KIP (80-kN) ESALS
FIGURE 21. KENTUCKY WIM DATA ANALYZED USING AASHTO LOAD
EQUIVALENCY EQUATION.
100
<)JMPARISON OF KENTUCK1' .AND AASHTO FLE:<JBLE
PAVEM&IT UJAD E<JUIVA.LENCIES FiJR KENTlXKY TRA..FFlC
0:
>-
5
\2
,3.0
fj
;:::
8JV1 2.5 4---~~~--~---------4----------~--~~~=1
-9-SN= 2
t:;:
GJ
"5
GJ
~
+SN-3
J.-----+------+------+---1+~
2.0
=4
1.5
0.5
10
1.5
2.0
RAW = (A.ASHTO ESAL.Sl/(I<ENTUCKY E"'....ALS)
2.5
(o)
OJMPARISON OF KENTUCKY M-JD A.ASHTO RIGID PAVEMENT
LOID EQUIVALENCIES FOR KENTUCKY TRAFFlC
0'' =
78
0:
g
i3
V1
~
If
3.0
?~
-·-'
2.0
2.0
2.1
2.2
2.3
2.4
RATIO = (AASHTO ESAL.S)!(I<ENTUCKY ESALS)
2.5
(b)
FIGURE 22. PAVEMENT SERVICEABILITY VERSUS RATIO OF KENTUCKY
ESALS TO AASHTO ESALS FOR KENTUCKY TRAFFIC DATA
FOR BOTH FLEXIBLE AND RIGID PAVEMENTS.
COiv1BII\lt'ITIClf\IS OF SN .b.I'-JD Pt VVITH At.SHTO
ESALS EOUAL liJ f<EhiTIJO(( ESALS
3.5
CALCULJ'!JEO ESALS BASED Ot'-1 OISTRIBUTim.l
OF A><LELClADS SH>:)VvN IN TABLE 1
il.
- ,..
~
,.
_j
............
~~
...,*-'
0 ~ \. ,i
~
tJ
~ 30 I
"~
I
-~~/.r ·
I ab ~= 20.1940f9
190082
C'l
1-
zw
::::;;:
w
~
u::
2.5~----~---+----~----~---T----~----~---+----~~~
1
"
L
4
3
.uASHTO STRUCTURAL ~JUMBER, Sl·-1
5
FIGURE 23. COMBINATION OF AASHTO STRUCTURAL NUMBERS AND
SERVICEABILITIES EQUIVALENT TO KENTUCKY ESALS.
6
'
1
-n
-
..... SN
-·"
::d
~SN= 2
~ .S
'7
•.:::;=-· i.6
·71
1..5
~
w 1.4
•:J
~
~
II
Q
~
:t:
!
-+-'>N = 3
cJ
··""f'·
I
:
;
-t-O::N=4
I
-SN=5
I
I
I
•.1.8
rJ.7
I
I
1!.6
"""
2.0
rJ.5
1.5
ff / /
#'//
#'//
#'//
/
///
/
V../ ,./ /
I
I
0.9
ff
///
:
J.-SN = 6
1.3
1.2
1.1
1.0
'
.
I
A
I
f'/ 7
7.//'"' V /
~ _../
~-------i
__..
""'
i
I
I
'
2.5
HVEMENT SERv1CEA.BIUTY. P,
3.0
3.5
(0)
AASHTO AND KENTUCKY RIGID ESALS
2.4 . . . . - - - - - - . . . . . - - - - - - , - - - - - - . . , . . - - - - - - - . . ,
..... o = 6 ~--i------+-----+~,..:::....--....::....:,-­
II
Q
~
..... o=l:l
2.1
~0=10~--+----------+---------4---~~~~
-t-0=12~--+----------+----------4-------~~
+0 = 14
2.0 .:j.!::=;==;:=/.__,-!-,-----~-+--.....-------+-----,--,....-.,-1.5
2.0
3.0
3.5
2.5
~ENT SERv1CEABIU1Y, P,
(~
FIGURE 24. RATIOS OF AASHTO TO KENTUCKY ESALS FOR FLEXIBLE
AND RIGID PAVEMENTS.
TABLE 1. KENTUCKY W-4 TABLE DATA PROPORTIONED FOR SERVICEABILITY
LEVEL USING AVERAGE RATIO OF REPETITIONS OF APPLIED LOADS
A. T AASHO ROAD TEST
..
SERVICEABILITY. Pt
I
'
2
I
1.5
3
2.5
3.5
I
TOTAL
I
PROPORTIONAL NUMBER OF AXLES
NO. OF
DISTRIBUTION COEFFICIENTS
AXLELOAD AXLES I
1
KIPS
I SIN<.i[E I 0.413418 0.661171 0.803602 0.9074181
215687.9 344945.5 419254.4 473417.11
521719
b<!l/18
2
313514 129612.3 207286.4 251940.5 284488.21
313514
5
23410.2 37439.47 45504.76 51383.43
56626
56626
7.5
406723
10
406723 168146.5 268913.5 326843.4 369067.6
38932.1
43961.67
48447 20028.85 32031.75
48447
14
6674.63 10674.61
12974.15 14650.26
16145
16145
17
2342
2342 968.2245 1548.463 1882.036 2125.172
18.25
3839.61
1975.31
3159.075
4335.642
4778
4778
19.25
2658
2658 1098.865 1757.393 2135.974 2411.916
21
1306
1306 539.9236 863.4894 1049.504 1185.088
23
460 190.1722 304.1387 369.6569 417.4121
460
25
.
605
28
605 250.1178 400.0085 486.1792 548.9877
32
350 144.69621 231.4099 281.2607 317.5962
350
TOTAL
1248310
1105493
1375673
SINGLES I 1375673 568727.71 909555.1
;
I
I
I
b
9
15
21
27
31
32.25
33.25
35
37
39
41
43
45
48
52
TOTAL
TANDEMS
I ANI li-M.
bJbU
Z:!ll ./tlb
JbJ/.<!tib
4<!l:ll:l.<! f
4tlb4. titlb
b:.:lbU
139466
160246
108006
158133
763661
149391
34428
28820
11310
4406
2131
922
697
607
2184
57657.73
66248.55
44651.6
65375
31571.06
6176.049
14233.15
11914.7
4675.755
1821.519
880.9933
381.1712
288.1522
250.9446
902.9045
92210.88
105950
71410.44
104553
50490.99
9877.234
22762.8
19054.95
7477.844
2913.12
1408.955
609.5997
460.8362
401.3308
1443.998
112075.1
128774
86793.83
127076
61367.86
12005.01
27666.41
23159.81
9088.738
3540.67
1712.476
740.921
560.1105
487.7864
1755.067
126553.9
145410.1
98006.56
143492.7
69295.86
13555.91
31240.58
26151.78
10262.89
3998.082
1933.707
836.6391
632.4701
550.8025
1981.8
139466
160246
108006
158133
76366
14939
34428
28820
11310
4406
2131
922
697
607
2184
748011
309241.1
494563.2
601103.1
678758.4
748011
I
TABLE 2. KENTUCKY LO,I\D EQUIVALENCY EQUATIONS
KENTUCKY LOAD EQUIVALENCY FACTORS (LEF) BASED ON ELASTIC
THEORY AND MSHO ROAD TEST PAVEMENT THICKNESSES
I
LOG(DAMAGE FACTOR)= A+ B'kLOG(LOAD) + C"(LOG(LOAD) ... 2)
NOTE: (LOAD EXPRESSED IN KIPS)
COEFFICIENTS
B
A
DESCRIPTION I
TWO-TIRED
2.72886
-3.540112
STEERING
0.289133
FOUR-TIRED
I SINGLE REAR
c
I
I
-3.439501
0.423747
1.846657
-7.47681392
7.31958101
-1.5377459
I
-7.042515531
5.64606809
-0.51945722
EIGHT-TIRED
I
TANDEMAXLES I
-2.979479
-1.265144
2.007989
8.115983411
- 1.650684632
5.94259543
-0.56377024
I FOUR- TIRED
I
TANDEM
i
SIX-TIRED
TANDEM
SIX-TIRED
TRIDEM
I
I
I
I
I
-8.98760945
lEN-TIRED
TRIDEM
-8.3649958
I
TWELVE- TIRED
TRIDEM AXLES
-2.740987
-1.873428
1.964442
SIXTEEN TIRE
QUAD AXLES
-2.589482
-2.224981
1.923512
0.0018635439
-0.198429071
0.0242188935
1.20191282
-9.069960E-05
-0.1 746353238
MULTIPLYING
FACTORS, MF:
UNEVEN LOAD
TANDEM
TRIDEM
I
I
NOlE: TOTAL LEF = (LEF)x(MF)
I
PROPORTIOf'JfiJ_ DISTRIBUTION
OF KENTUCKY W-4 DATA
Tfl.BLE 3.
·I SINGLE ·1
TOTfiJ_ I
51
7 51
1oI
141
17i
I
PROPORTIOI'JfiJ_ I
DISTRIBUTION ;
5217191 0.379246
3135141 0.227899
566261 0.041162
406723 0.295654
48447 0.035217
16145 0.011736
2342 0.001702
47781 0.003473
2658 0.001932
1306 0.000949
460 0.000334
0.00044
605
350 0.000254
. AXLELOAD! NO. OF
I, KIPS . AXLES
I.
18.251
19.25 i
21 I
231
25
28
i
32
I TOTfiJ_
SINGLES I 13756731
1
I
I
TANDEM
AXLELOAD
KIPS I
5350 0.007152
139466 0.186449
15
160246 0.214229
108006 0.144391
21
158133 0.211405
271
31
76366 0.102092
14939 0.019972
32.251
33.25
34428 0.046026
35
28820 0.038529
37
11310
0.01512
39
4406
0.00589
41
0.002849
2131
431
922 0.001233
45
697 0.000932
607 0.000811
48
2184
52
0.00292
TOTfiJ_
TANDEMS
748011
1
!
I
I
I
~~
i
I
I
I
APPENDIX A
,'\,USHl 0 Sit CLE AXLELQ!lD EQUI\ALEI UE'
AASHTO SltK:;LE MEL£AD EQUI\l!JEt-ICIES
6
-<11-lOIG'S
!
. . t41CFS
iii
+Zl!G'S
+2lit<PS
..... !28 tcFS
5
~ 4
~
f\.
tt16 ..3
(62 ~~
(98 141)
1:2:5 t4-.1
P, = 3.50
\
3
§z
v
1 .
10""
6
r;
(.f5 "")
!
ii'i
l£;i
~i!
\
1/
-
·--
~
\r\
!\
""'6r- 2B KFS
( 125 ld(t
I
3
1\
'
- - - - I- -
~ 2 ---
-
-
-<II-1DIG'S
v
m
!
P,
~
I
--
10'
10'
(q,
I
I
USHTO SINGLE AXLELJ:»D EC::Uii,f;l£NUE ;
!
ii'i
~-z
2~
\!!~
(""' ltl)
... l41<FS (6211'1]
+ 22 I<F5 (98 ltl)
...... :;:s tP.i (116 J4-J'
5
~
1...
. . 29 I<FS ( 1:25 J4-~
. 10'
1(11
)~
-·-.
--
1-
>- .
--
I0- 1
J.J:Wl EQI.Ml£1-ICT'
t;)
!:!)
FIGURE Al.
-- .
.
---
---10'
1..1}10 EOJI\I>l.B'ICr
-
--
--
---
Jo-e
;~
3
~ z -- -
I
-
K'i'
I I
~ 4 P = 2.00
1
2
10""
--
... lJ I<F5
2.50
I II
3
--
6
*
5
~ 4
..
I..DAD EUII~lfH:Y
(45a
{62
(98 14
+22~
26 I<I'S ( 110 14-1)
..... "" ~ (12514-1)
... 14 t<FS
:-
--
r
lQ-1
J~
10'
~
AllS-ITO SttU£ A)<J_£L()IJ) EQU\i'LE~CIES
6
;53
J
lf.»D EOJI\I>l.B'ICt
-···--
-
1£~
+->-
JO'
m~
5
(98 141)
+ 26 KFS ( 116 kt~~'
~ 4 P, = 3.00
'
J.
(<51<N)
(62 ~·J
... >OKFS
-e- 14 KFS
+Z2KFS
RELATIONSHIP BETWEEN LOAD EQUIVALENCIES FOR SINGLE
AXLELOADS OF 10, 14, 18, 22, 26, AND 28 KIPS (45,
62, 98, 116, AND 125 kN, RESPECTIVELY) AND AASHTO
STRUCTURAL NUMBER FOR Pt = 3.5, 3.0, 2.5, AND 2.0.
--
1(1
AASI-ITO T/lNDEM AXI..ELOAD EQJfWll.lNCIES
AJISHTO TANIX11 AXLEIJ)OD
6
!
+18 I<P.i
. . 2111<P.i
ii'i
--- J5 I<P.i
..... 44 I<P.i
... S! I<P.i
5
(80~
(125 o.N)
r60
o.N)
196 :::g
231
P,__ = 3.50
fI
6
v
~~
1/
t-
-
\
(BO ~¢<)
+2111<FS (125 ~I
+JSI<FS (100 ~I
+441<FS (196 ...
... S! I<FS (231 ~
5
~ 4 P,
'\
~
-·
-
1o-'
+ 18 1<P.i
ii'i
\
I\
2
!
I
j
1\.
,\,.
3.00
3
--
2
--
-
-
1 1-
v
-
-
-
h
-
-
-
-
-f--
- - --· - m~
10'
-
-
\
t·- --
1\
l!J'
EQUI\~EI UEt
-- --
L.--
lQ-1
lLl'D EOOIW£NC1'
f
l[J'
10'
lC(
~)
IIASHTO TPNITM AXl..ELOC>D EQUf.KENOES
) EQUI'REI K:l S
6
!
6
ii'i
~
~
I
!
ii'i
5
... 18 I<FS (00 ~
+ 2S lofi { 12.5 loN)
+
I<FS (
~¢<)
..... 441<FS {196 loN)
...... 52 I<FS (231 o.N)
36
4
J
160
~
~
P, = 2.50
-
-
5
4
J
. 1---·
... 18 KFS (80 I<'~
. . 2!! I<FS ( 125 "''
+ 36 I<FS ( 160 "''
-
+ 44 ta::s ~ 196 W'l
--
~
I I
I
lo-'
.
.....,.52 KFS 231 W'-1
~ 2 P, I 2.00I
2
r- -
10"-'
l!J'
lLl'D EOOII'l.fl-1...1'
e
FIGURE A2.
10'
J.')-11
ro~
l!J'
L.:W:· ECIJII'l.fH::.·
w
RELATIONSHIP BETWEEN LOAD EQUIVALENCIES FOR TANDEM
AXLELOADS OF 18, 28, 36, 44, AND 52 KIPS (80, 125,
160, 196, AND 231 kN, RESPECTIVELY) AND AASHTO
STRUCTURAL NUMBER FOR P< = 3.5, 3.0, 2.5, AND 2.0.
10'
AI'SHKl SNGL£ A:>l.EI...CAD EQII\I'<LH·CIES
11
1/)
2
10
~
.... 1l14'S
... 14 I4'S
... 22 I4'S
+liS I4'S
..... :!1314'S
(45 1<>0
(62 1<>0
(98 1<>0
11~ ~
125
:5 6
i
Q
10
·--
7
6
16-t
-
---1-
~
12
I
-r-
P_.- 3.50
:s
8 ----
Q
1
~
~-
J
IOo
1--
-
-~
···I.
---"
---- ---
·:J-'
1{}-'
(ti•
AAS-IlD SN8L£ A>3£LCl'D EQIJI"•LENCES
AiiSH10 ~lNGL£ AXL£10\0 ECU\?l£NCIES
11
. . 10 tP.i \45 lt"J
... 14 I4'S (62 ~
"' 10 ... 2214'S (98
2
.... 10 IP.i
... 14 IP.i
22 If'S
If)
-lr- 26 I4'S (116 1<>0
.... ""I4'S (125 kl
210 +
I
~~
I I
!!lil
9
P,- 2.50
:s 6
I I
~
~ 7
:s 8i
~
Q
1
ft
6
10'
lf.mEWMUNC\'
"3
(98
- +26~ ~:16kll
..... 2S tPS 125 ldt
i'
12
1()-'
(45 kl~
(62 kl9
P, = 2.00
-~-
-
-
-- ·--
-
!C~
-::;lil
-fL-'---
Q
1()->
1V
10'
La.!> EOMHliCl'
f!)
~
!!§1
- - 1-
€
10'
u:ro EO.I\IUH::r
11
~~r
I
ft
1()-'
---
.... 10 IP.i (45 1<>0
... 14 IP.i (62 1<>0
T 22 IP.i (S6 ""l)
:o; If'S i 116 kl~
+ 28 If'S ( I 25 ""l)
2"' +
~ ~ r&lq2
~~
!!~
9
~--"SHlO SINGLE .A)<LEL{l'ID EOlJII,;>IJ:JICil':i
11
--
I
-
-
----
o
10'
g
FIGURE A3.
--
RELATIONSHIP BETWEEN LOAD
AXLELOADS OF 10, 14, 18,
62, 98, 116, AND 125 kN, RESPECTIVELY) AND AASHTO
RIGID PAVEMENT THICKNESSES FOR Pt = 3.5, 3.0, 2.5,
AND 2.0.
1(11
AASHlO TANC£M AXLELO'IO EQUIINHICIES
11
~
P.~SHTO lN.£:EM A)(lilJJ'<D EQUIW.I HICILS
-
11
liP,= 3.~
2
10
i
7--
Q
~
9
• -
~
:5 8
i
~ ~--
f--- 1--
9
liP,=
$00
--r--TTTT
"' 10 -1_.-~--
:56·---·--·-
--
i1l
if;
c
-i0"18- (llll<ll)
.... :EtPS (125 1-Jt)
-
-
6
1()-'
1cP
+ :Ja - ( 160 "')
; - # tFS (196 ktl)
+ 5 2 - (231 "~
10 1
fit
10'
7-11-----4
1111-----li +-
_.,_........__._
sl ~~ 11111~1
1()-1
~
I
A,<.SHlD TANC£1.1 A>lELCAD EQ_II\I"LEI U::.S I
11
,IP, = 250
i
~
8
~
~52...-..s
€
10'
lim WJflifl 1C1
©
FIGURE A4.
l£'. ----
10
&
0
-- - -
-
-- - - -
-c... 1!1 01'5 ("' i<N)
f-
Q
+ 2!! II'S ( I ;s '-"9
-+- J6 tFS (EO i<N)
-
"* 44 tFS
~
(231 "'9
10'
_co
---
c- -
>-- -
~ 7 - - --
... 18 to:FS \8l IN)
• 3!14'5 (125 "'9
-+- :Ja tO'S (160 kl9
+4414'5 (196 "'9
Q
'
2 f-·>---
9
~ 7
--r--
tn
10
10'
1('
I
\b)
--
1(}-'
1()1
l!)IJ) EIHJI< IN::.
AASHKJ ~NDEM 1\;<lfl_[)ll{) ECUt•.N.Et ICES
i
1<11)
!12- (1 1 "~
-~-
1C•
(:Y
"'
2
tE kll}
:28 ws <
- +~ toFS (I 0 kl~
Ill----1- --1----llt I++
-t-44 f':F'S (1
Lm> ErJ IIJ>I.HICl'
11
~
~-';;r.; kit)
\1~ ._H)
.... 52 ti'S ( ~1 "~
€
ltJ-1
-,
ltJ'
10'
LJ)IJ) EIHilill::.·
~
RELATIONSHIP BETWEEN LOAD EQUIVALENCIES FOR TANDEM
AXLELOADS OF 18, 28, 36, 44, AND 52 KIPS (80, 125,
160, 196, AND 231 kN, RESPECTIVELY) AND AASHTO
RIGID PAVEMENT THICKNESSES FOR Pt = 3.5, 3.0, 2.5,
AND 2.0.
'
1~·
APPENDIX B
MSHO ROO TEST D'ITA, JtF£11TICNS OF LOlO
ll>J-C8A A)<l.flii\ffi, Pt - 35
1'11-ro.t A)<llli)o\£6, Pt - 3.0
STR,>JGHT LI'JE LOG-LDG ~GRfSSICI'J EQUATICNS
6
Ullf •
...-UJCP,
-t-IDCP6
r
~
0_
--
~~
4
1-~
6
1-'"
~
~
~
•~cum
600
400
tii
~
000
=
i
-+-LCXP 5
4
5
~ 4
~ -;:::::.
i: ::::-:;::::::.
'
r-
~
0
1.(YJO
21JO
0
AI\SHO ROO TEST D'ITA, 18---+<IP (&:HN)
E9'LS 11>NC8A A'lilEl.l:l'[S, Pt - 3.0
6
i:
--
in
5
+LCXP J
+LCXP 4
...-LCXP 5 -o-LDIF6
i: v'uiOP5
.-.:;
0
@
FIGURE Bl.
1.000
--··
0' = m •
0
200
~~
,_-
-
I""
Trnrn-N
400
600
BJO
18--1<1' (BJ-I<N) .v&flD ES.'I.5. lHCJ.£AJ·Ui
:....- f--
1-
::---
-
::;::::7
.:JJP
-
~>-"'
F-
--
~ 4
'""' 6
1,{):I ·II
800
Af>SH:l ROO TEST, 18-WP (80-1¢(\
ESI>J.S W«M A'>UJ.CIIffi, Pt - 35
-f--.:::
,.....- r;::::::: ::::~ 4 ~
200
600
400
(~
p-
---
---- - - - -
V"
FEP£1110£ IF Lf}l[( 110..5'1 D>
1-'"
----
--·-- -
ij
+UJCP5
f-o-IDCP 6
0
-;::::; :::--- t--
jl!l!!>
~
+UJCPJ
ili
-
.....-:: ;:::::::;-
-t-LDIF 6
~OF lO'D, nn&llli
1t-IDCP4
~---
+IDCP4
5
~
--- --- - >
zoo
0
6
---
+IDCP3
..~!""
+UJCP4
-::::
i
__. t---:::: l-- ~
~
S'TRAIGHT UtiE LOG-LOG REGRESSIOtl EQU>.liDIIc;
6
+UJCPJ
5
I
Ai'SI U RCJiiD TEST D'ITA, ltF£110016 OF L(J\Ct
~
600
400
·=~=L=
800
1.0 _I)
113--1<1' (6H<!~ .v&flD ES.'I.5. THOJSAI.JJS
ifJ)
RELATIONSHIP BETWEEN AASHTO STRUCTURAL NUMBER AND
REPETITIONS OF TANDE M AXLELOADS OR 18-KIP (80-kN)
ESALs FOR AASHO ROAD TEST DATA AT Pt VALUES OF 3.5
AND 3.0.
I
II
I
AI'SHO RQilD TEST D\TA, ltF£llTI::NS Cf liJlD
WCEM M..El1YICS, Pt - 25
AASH) RQIID TEST !AlA, JtF£TmJI6 Cf l.•::AU
WU11 A.'tlli:AI:S, Pt - 2.0
STR.~IGHT UNE LOG-LOG REGRESSON EQU~HJNS
6
..,..LCXP3
ili
I
.... UlCP3
-9-I!XP4
5
+LCXP5
+taPS
-
4
r
0
.....~· ~
I-
....- ~
~
6
STRAt3HT LIIIE LOG-LOG REGRESSION EQl>\U::•IIS
6
~
~
--
------ - I
1-
600
400
600
-+-UlCP 6 -
4
,..,.
.-,- --=
~
...-:..---..~
.. =
~~~
20)
0
l'tP£ Ill UIS OF LD>Q 11-U.&NC&
5
Vi
I
..,_LCXP3
-e-Ul!P4
+taPS
...... Ul!P.
<mTnn
tTT..-.Tn 1
,,-,-,......,,
800
6(1)
400
--·----
1,00.J
AASHO RQilD 1E5T D\l.l\, 18-KIP (f:D-W I)
E5'ILS W££M Al<l£lfllffi, Pt - 20
- - ----
6
+lDIF 3
--
Vi
p
i:W'.
z
~
~·
.....
--
~
~
40J
600
600
18-I<P (I:IJ-l¢j) .veJlO ES>'iS THCIJSAia
@
FIGURE B2.
1.0CO
----
+lDIF 5 -
5
·----
+LQ(J' 6
3
2
~
0
TTT....-n-YT
200
-e-liXF.
I.
4
r
.-r>
"~
~---·
(I:}
AASI-D R~ TEST !AlA, 18--l<lP (00-+t~)
E5'ILS Tl>l'llEM Mllili>C:S. Pt - 2.5
..-
- - c----
~
IUETIOCNS OF lil'D. THCI.£AH:·.s
I~
6
.¢
-
0
l,O:xJ
--
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ifJ)
RELATIONSHIP BETWEEN AASHTO STRUCTURAL NUMBER AND
REPETITIONS OF TANDE M AXLELOADS OR 18-KIP (80-kN)
ESALs FOR AASHO ROAD TEST DATA AT Pt VALUES OF 2.5
AND 2.0.
AASI-D RQIIJ) TEST D'llA, REFE Ill Klt-13 CF I CM
llii'I:EM A'I.BJ)I£6, PI - I .5
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FIGURE B3.
RELATIONSHIP BETWEEN AASHTO STRUCTURAL NUMBER AND
REPETITIONS OF TANDEM AXLELOADS OR 18-KIP (80-kN)
ESALs FOR AASHO ROAD TEST DATA AT A Pt VALUE OF 1. 5.
APPENDIX C
DEVELOPMENT OF FIGURE 10
Under the section "Normalizing AASHO R'oad Test Data", the ratio of ESALs at each P,
to ESALs at failure (P, = 1.5) was calculated for each of the 176 pavement sections
having values of observed repetitions for all five levels of P,.
Use of Equation C-16
produced irrational results for Loop 3 and the ratio of ESALs was abandoned.
Ratios of repetitions were calculated for each P, to repetitions at failure (P, = 1.5) for all
176 pavement sections. The average of all 176 pavement sections (Lanes 1 and 2) was
obtained for each of the five levels of P,. Figure lOa displays the results and includes a
polynomial regression equation fitted to the averages.
APPENDIX D
DEVELOPMENT OF KENTUCKY LOAD EQUIVALENCY RELATIONSHIPS
Between 1972 and 1976, large 3-axle and 4-axle single frame dump
trucks
(vehicle class
Kentucky to haul coal.
an 8-inch
(203-rnm)
steering
respectively).
7)
were
introduced
into eastern
Tires on the steering axle increased from
width to
respectively) widths.
recorded
6 and
14- to 16-inch
(356- to 406- mm,
In-pavement, Weigh-In-Motion (WIM) scales
axleloads
of
8
to
22
kips
(36
to
98
kN,
It was decided that load equivalency factors (LEF)
should be developed for
2-tired axles
and for other tire-axle
configurations using the same methodology to obtain LEF for the
steering
axle
relationships.
in
order
WIM
to
data
assure
compatibility
indicated
loads
were
between
not
LEF
equally
distributed on the dual-tire assemblies of tandems and tridems and
adjustment factors were required to account for additional fatigue
caused by uneven loading.
If
factors
compared
are
to
to AASHTO
be
developed,
load
the
equivalency
relationships
factors
and
the
should
be
pavement
structures tested at the AASHO Road Test should be analyzed to
obtain the new LEF.
The following conditions and criteria were
used to develop the Kentucky LEF.
o
The original Chevron n-Layer computer program was modified to
include superposition principles and to include the equation
necessary to calculate strain energy density, SED.
o
AASHO Road Test Pavement Sections constructed on Loops 3-6:
AC:
2 to 6 inches on l-inch increments (51 to 152 mm on
Base:
0 to 9 inches on 3-inch increments (0 to 229 mm on
76-mm increments)
Subbase:
0 to 16 inches on 4-inch increments (0 to 406
mm on 102-mm increments).
These combinations resulted in the construction and testing of
120 sections of which 12 were duplicates.
The 120 sections
consisted of 100 possible combinations of layer thicknesses
but
not
Earlier
all
combinations
Kentucky
structures
using
analyses
the
were
constructed
on
each
Loop.
of
typical
Kentucky
pavement
Chevron
n-Layer
computer
program
indicated that peculiar and unreliable results were obtained
for asphaltic concrete thicknesses less than 3 inches (76 mm).
For development of KY LEF, the 2-inch (51-mm) AC sections at
the AASHO Road Test were eliminated from the matrix leaving 80
possible combinations of layer thicknesses.
o
AASHO Road Test soil samples were sent to a number of research
and testing laboratories and one of these was the Division of
Research, Kentucky Department of Highways.
using the Kentucky CBR test procedure.
Soils were tested
Test results indicated
that the soil corresponded to a Kentucky CBR of 5.3,
or a
modulus of 7,950 psi (55 kPa).
o
Results of Kentucky research indicated that the mean annual
temperature for Kentucky was approximately 70 degrees F ( 21 c)
corresponding to a modulus of elasticity of 480 ksi (3.3 kPa).
Similarly,
average temperature at the AASHO Road Test was
approximately 60 degrees F (16 C) corresponding to a modulus
of elasticity of 600 ksi (4.1 kPa).
o
Each tire within a fixed tire-axle configuration was loaded
equally for the range of 2,000 pounds to 8,000 pounds (0.9 to
3.6 kg, respectively) in increments of 500 pounds (0.23 kg).
o
Strains,
stresses,
and strain energy densities
(SED)
were
computed at the bottom of the asphaltic concrete and at the
top of the subgrade.
o
Tensile
strains
computed
at
concrete were converted to
the
bottom of
"work strain"
the
asphaltic
by the procedure
given in reference 12 in the main body of this report.
o
With these computed strains,
ESALs were computed using a
strain-ESAL relationship appropriate to 600 ksi (4.1 kPa) and
based upon laboratory fatigue test results (reference 4 in the
main portion of this report).
o
LEF
were
computed
for
each
load
on
each
tire-axle
configuration and for each pavement structure by:
LEF = N, / NL
where
N18 = ESALs due to the calculated strain for an
18-kip (80-kN), 4-tired single axle, and
NL
= ESALs
load,
L
due to the calculated strain for
in
kips,
for
the
tire-axle
configuration.
o
After the LEF values were calculated for the complete matrix
of load and pavement structures, a regression analysis was
performed for all LEF values for all pavement structures for
a particular tire-axle configuration.
The best regression
equation was determined to be:
log(LEF) =a+ blog(L) + c(log(L))'
where a, b, and c are constants given in Table 2 of main
text.
o
Considering the diversified pavement structure thicknesses and
combinations of layer thicknesses, the scatter of tandem loads
= 1 was approximately +/-
at an LEF
1 kip
(4.45-kN).
For
tridems, the scatter at LEF = 1 was approximately+/- 1.5 kips
(6.7kN).
o
Rationale
for
Kentucky
method
detrimental
pavement
is
thickness
to
effects
design
protect
beyond
the
normal
assumed
for
the
from
any
consolidation
for
subgrade.
thicknesses appropriate to Interstate traffic to letting the
subgrade rut or shear but the asphaltic concrete to remain
intact for
farm-to-market
Farm-to-market roads
roads.
in
Kentucky traverse generally hilly, and/or curvy terrain that
should prevent speeds approaching hydroplaning conditions.
Thus, rutting is not considered a dangerous attribute for low
volume, low speed roads.
Subgrades deform but do not have any
significant fatigue characteristics.
However, true fatigue of
asphaltic concrete is a bending phenomenon.
Thus, strains at
the
should
bottom
relationship
of
the
with
asphaltic
repetitions
concrete
of
determined by laboratory testing.
while
have
has
a
loading
as
been
Analyses
indicate that
the magnitude of tensile strain and the associated
number of repetitions differs significantly with structure
thickness and subgrade support, the ratio of repetitions for
other loads on the same pavement and subgrade varies very
little.
For thin ~avements, the strains are relatively high
for thin pavements, and relatively low for thick pavements but
the ratio of the associated ESALs from the fatigue criterion
line
are
nearly
the
same.
Therefore,
Kentucky
LEF
relationships inherently include structure but the equations
are not affected specifically by structure.