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OCR for page 173
APPENDIX E
EFFECTS OF AXLE WEIGHT ENFORCEMENT
ON PAVEMENT LIFE
1.0 INTRODUCTION
.
One of the basic premises of truck weight enforcement is that there will be a net increase
in pavement life (reduction in the rate of pavement deterioration). The following discussion
summarizes two methods of determining the increase in pavement life one could expect from
reduced axle loadings accrued through enforcement activities. The methods makes use of an
AASHTO design procedure (~) providing for the traffic input to design to be in terms of
accumulated (or projected) ~ 8,000 Ib. equivalent single axle loads (ESALs).
In their approach, AASHTO uses the definition: "Load equivalency factors represent the
ratio of the number of repetitions of any axle load and axle configuration (single, tandem, tridem)
necessary to cause the same reduction in Present Serviceability Index (PSI) as one application of
an ~ 8km single axle load."(~. Thus, an axle load with an ~ 8km equivalency of 2.5 could be
considered to be 2.5 times more damaging than the ~ 8km loading.
The general approach, applied to both methods, is to determine the cumulative ESALs a
given pavement is capable of sustaining before it's serviceability is reduced to an unacceptable
level, ie, the design load capacity. Then, the traffic stream using that pavement is analyzed both
before and after enforcement efforts are implemented to determine the effects of that
enforcement on daily ESALs generated by the stream. Finally, the daily ESALs before and after
enforcement are used to determine the estimated times (before and after enforcement) required to
consume the load capacity.
The first method discussed, an approximation method, probably is the most appropriate
for We present NCHRP project as it is much easier to program and use and is in the spirit of the
study where the goal, rather than focusing on the pavement design process, is to quantify what is
accomplished by weight enforcement efforts. The method has a disadvantage in that it is unable
to recognize the fact that most traffic streams have an inherent growth rate. Not dealing with that
growth rate may result in significant errors with some traffic streams.
~ The contribution of Pavement Design Consultant, Ken McGhee, for this appendix is gratefully
acknowledged.
Appendix E
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The second method, covered in Section 5 of this appendix, is theoretically more precise,
but is much more difficult to apply as one needs a reasonably good grasp of the AASHTO
pavement design process. The second method does deal with the expected growth rate of the
Marc steam in question.
2.0 AN APPROXIMATION METHOD FOR DETERMINING THE EFFECTS OF AXLE
WEIGHT ENFORCEMENT ON PAVEMENT LIFE
2.1 Introduction
The method described here is designated as an approximation because it makes
use of a means of approximating axle equivalencies.
2.2 Assumptions
A. The analysis will be applied to a generic pavement that is defined as either a
flexible pavement or a rigid! pavement. The user will have to specify which. It
should be noted that, as shown below, for this approximation method the
pavement thickness or structural number is not a factor.
B.
2.3 Procedure
Appendix E
The fourth power rule will be used to calculate axle equivalency factors. (The rule
states that the load equivalency factor increases approximately as a function of the
ratio of any given axle load to the standard ~ 8km single axle load raised to the
fourth power.~(~)
The approximation watt be reasonably accurate, but may be in error up to about
10% in estimated changes in pavement life expectancy as compared to the more
precise method given in Section 5 of this appendix. One of the reasons the
approximation method is likely to be somewhat in error is the inability of the
method to account for growth in traffic volume throughout We life of the
pavement.
Estimate daily ESALs from axle weights measured or assumed prior to
enforcement and after enforcement for the traffic stream in question. To do this,
use the fourth power rule to calculate equivalencies. Then follow the procedure
outlined in Section 4 of this appendix to calculate ESALs. This procedure will
need to be gone through twice, once to determine the daily ESALs before
enforcement (ESALb) and once for afterward (ESALa). Examples of using the
2
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fourth power rule and of calculating daily ESALs for both rigid and flexible
pavements are given in Sections 3 and 4, respectively.
B.
Estimate the effects on pavement life brought about by weight enforcement. A
given pavement will have a design load capacity of We ESAL`s and many
designers use a 30 year design life. However, real ESALs typically far exceed
those used in the design. So, the concept, assuming a zero annual growth rate in
traffic, is:
I. Calculate the life expectancy before enforcement Cubs from:
L`b = W~/(ESALb*365), . Equation (~)
2. Calculate the life expectancy after enforcement (L`a) from:
L`a = W,~/(ESAL`a*365), . Equation (2)
3. Calculate the percentage increase
~ = 1 Anti ~ ~n
.
In life (it;) from:
TV `~a  Abel fib. . Equation (3)
Note, however, that Wl8 cancels out of Equation (3) so that the percentage increase in
pavement life is also the percentage decrease in daily ESAL,s brought about by enforcement and
cart be expressed as
In = lOO*(ESALb  ESALa)/ESALb.
Because the design was does cancel out of the equations to estimate the benefit of
enforcement the only real chore when using the approximation method is in calculating We ~ 8
kip equivalencies and the average daily ESALs. It is important to recognize, however, that only
relative increases in pavement life can be determined using the approx~nation method. Absolute
values of pavement life and changes therein can be determined only through using the method
outlined In Section 5 of this appendix..
3.0 FOURTH POWER RULE OF CALCULATING AXLE EQUIVALENCIES
The formidable equations and calculations (Section 5 of this appendix) used to develop
theoretically correct 1 8 Kip axle equivalency factors have led to much interest in handy methods
of estimating those factors given a minimum of information. Fortunately, there is a generally
applicable rule of thumb: "The load equivalency factor increases approximately as a function of
Me ratio of any given axle load to the standard ~ 8km single axle load raised to the fourth
3
Appendix E
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power.". For example, calculations and AASHTO tabulations show that a 28 Lip single axle
load on a flexible pavement has ~ ~ Lip equivalency factors ranging from 3.93 to 7.54 depending
upon the structural number and terminal serviceability of the pavement being analyzed. On the
over hand, the estimated factor from the 4th power rule, independent of pavement structure and
terminal serviceability, would be
en = e~*~28/! 8~4 = ~ *5.86 = 5.86
where en is the ~ 8km equivalency for a 28kin single axle load on a flexible pavement.
and
el8 is the 18km equivalency for an 18km single axle load on a flexible pavement,
i.e. el8= 1.0.
In order to make full use of the fourth power rule in calculating equivalencies it is
necessary to establish some bases for those calculations for tandem and truism loads and to
reflect differences in ~ 8km equivalencies relating to pavement type (rigid or flexible). Table E]
below has been determined from AASHTO calculations and tabulations (~) to provide reasonable
starting points for each axle configuration and pavement type.
TABLE E  ~
BASES FOR ESTIMATION OF 1 8km EQUIVALENCY FACTORS
Flexible Rigid
Axle Basic Equivalency Equiv.
Configuration Load~kips! Factor Factor
Single ~ ~ .00 ~ .00
Tandem 34 1.09 1.95
Traded 48 1.03 2.55
Using Table E! the ~ 8km equivalency for any axle loading can be estimated through use of We
fourth power rule. For example, a 50 Lip tandem axle on a flexible pavement would have an
estimated ~ 8km equivalency of
e50 = e34*~50/3414 = 1.09*4.68  5. 10.
Appendix E
4
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AASHTO tabulations show a 50 Lip tandem axle load on a flexible pavement to have
equivalencies ranging from 3.74 to 6.15.
While most designers watt use the tabulated ~ 8km equivalencies for pavement designs, it
is well recognized that the fourth power rule may be close enough for many practical purposes
given the uncertainties in estimating traffic characteristics including axle loads.
Even when using the fourth power rule, however, pavement type (rigid or flexible) is
important. Again, as an example a 50 kip tandem axle on a ngid pavement would have an
equivalency much higher than above for a flexible pavement of approximately
e50 = e34*~50/34)A4 = ~ .95*4.68 = 9. ~ 3.
AASHTO tabulations show Mat the actual equivalency for a 50 kip tandem on a rigid pavement
ranges from 7. ~ 7 to ~ 0.73 depending upon pavement thickness and terminal serviceability.
Estimated equivalencies for other single, tandem, or tridem loads on both rigid and flexible
pavements would be determined similarly using the factors given in Table E] as the bases for
those estimates.
REAPPLICATION OF THE FOURTH POWER RULE TO DETERMINATION OF DAILY
18KIP EQUIVALENCIES (ESALs) FOR A TYPICAL TRAFFIC STREAM
Table E2 provides an example of determining the average daily ESALs for a
typical traffic stream both before and after weight enforcement. In the procedure, single and
tandem (tridem if present) axle load ranges for all axles in the traffic stream are provided. The
fourth power rule is used to calculate the ~ 8km equivalency for the m~po~nt of each axle load
range. For example, the ~2,000  ~5,999 range has a midpo~nt at 14kips so the Skip
equivalency of the 14km load is needed. As given in Section 3 of this appendix, the
equivalency is calculated
en = e~14/] 8~4 = ~ *.366 = 0.366.
All other equivalencies in Table E2 are calculated using the procedures given in Section 2 which
follows and using the base values given in Table Eel.
To calculate the daily ESAL contribution of each load class the number of axles in each
class is multiplied by the ~ 8km equivalency for that class. The sum of the contributions of all
classes is the average daily ESAL`s for the traffic stream. Note in the example, that the daily
ESALs before enforcement (ESALb) was 917 while after enforcement (ESALa) the total was 653.
~,,
5
Appendix E
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Table E2
FLEXIBLE PAVEMENT, 4th Power Rule
ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM
Single
Axles
 BEFORE ENFORCEMENT  AFTER ENFORCEMENT l
Eqivalency No. Daity No. Daily
Factor Axles ESALs Axles ESALs
0.006 18 0.108 18 0.108
0.03 12 0.36 10 0 3
0.095 370 35.15 260 24.7
0.366 40 14.64 30 10.98
1 300 300 320 320
2.23 42 93.66 6 13.38
O O
0.005 18 0.09 16 0.08
0.042 24 1.008 23 0.966
0.16 50 8 40 6.4
0.76 48 36.48 36 27.36
0.976 25 24.4 123 120.048
1.38 43 59.34 52 71.76
2.11 163 343.93 27 56.97
~7 ~653.052
Axle Load Ranges
3000  6999
7000  7999
8000  1 1999
12,000 15,999
16,000 19,999
20,000  23,999
Tandem 6000  11 ,999
Axles 12,000 17,999
18,000  23,999
30,000  31,999
32,000  33,999
34,000  37,999
38,000  41,999
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As shown earlier, the percentage increase in pavement life is estimated to be
Li = lOO*(ESALb  ESALa)/ESALb = 28.8%.
Table E3 is an example of the ESAL calculations for a rigid pavement assumed to be in
the same traffic stream as above. Note the substantially higher values for both before and after
enforcement ESALs as compared to the flexible case. The estimated increase in pavement life
due to enforcement is not greatly different for the two pavement types as the rigid Li is
L`j = 100*~1283872~/1283 = 32.0%.
5.0 MORE PRECISE METHOD OF CALCULATING INCREASED PAVEMENT LIFE
DUE TO WEIGHT ENFORCEMENT
AASHTO design procedures provide for the traffic input to design to be in terms of
accumulated (or projected) 18,000 lb. equivalent single axle loads (ESALs). In their approach,
AASHTO uses the definition: "Load equivalency factors represent the ratio of the number of
repetitions of any axle load and axle configuration (single, tandem, tridem3 necessary to cause
the same reduction in Present Serviceability Index (PST) as one application of an ~ 8km single
axle load."~]). Because of that definition, many designers view the equivalency factor of a given
axle load to be a relative measure of pavement damage inflicted by that load.
The serviceability index (PS! or p) is a subjective measure of pavement condition on a O
to 5 scale with 0 defined as unusable and 5 defined as perfect. While there are many variations, a
typical new road will have an initial serviceability (pa or PS! at time 0) of about 4.4 while the
terminal or no longer acceptable serviceability (p') generally ranges from 2.0 to 3.0.
Unfortunately, the analysis of traffic data from a pavement design standpoint is greatly
complicated by the fact that the relationship between axle loads and ESALs (equivalency factor)
is geometric rather than linear and the relationship is a fimction of pavement structural capacity
as well the level~fservice at which the pavement is considered to have failed (the terminal PSI).
Furler, the relationships differ for flexible and rigid pavements. ESAL equations for both types
Of pavements and for single and tandem axle loads were derived Tom the AASHO Road Test Hi.
Relationships for tridem axles have been developed through other research to extend the Road
Test results Hi.
7
Appendix E
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Table E  3
RIGID PAVEMENT, 4th Power Rule
ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM
BEFORE ENFORCEMENT T AFTER ENFORCEMENT
Eqivalency No. Daily No. Daily
Factor Axles ESALs Axles ESALs
0.006 18 0.108 18 0.108
0.03 12 0.36 10 0 3
0.095 370 35.15 260 24.7
0.366 40 14.64 30 10.98
1 300 300 320 320
2.23 42 93.66 6 13.38
O O
0.01 18 0.18 16 0.16
0.074 24 1.776 23 1.702
0.284 50 14.2 40 11.36
1.35 48 64.8 36 48.6
1.73 25 43.25 123 212.79
2.45 43 105.35 52 127.4
3.74 163 609.62 27 100.98
Total 1283.094 872.46
Axle Load Ranges
Single 3000  6999
Axles 7000  7999
8000  11999
12,000 15,999
16,000 19,999
20,000  23,999
Tandem 6000 11,999
Axles 12,000  17,999
18,000  23,999
3O,000  31,999
32,000  33,999
34,000  37,999
38,000  41,999
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The ESAL equivalency factor equations for flexible pavements are:
log~O(wX/w~) = 4.79*Iog~0~ ~+~ ~4.79*Iog~0~Ex+L,2)
Go = Tog,0~4.2 p~/2.7]
bX = 0.40 + [O O81*~Ex + L2)'`3.233/~(SN + I)^5.19*~2^3.23]
where
Go  log~0~4.5  p~/3.0]
+ 4.33*Iog~0~2 + GtIbx  Gt/b~
. Equation (4)
. Equation (5)
. Equation (6)
WX = number of loads of magnitude Ex required to reduce the PS} to pi,
wig= number of {8 kip loads required to reduce the PS] to p',
Ex =
load on one single axle or one tandem axle set (kips),
~2 = axle code (! for single axle and 2 for tandem axIe),
SN = pavement structural number (see Section 6 for examples of SN determination),
pi = terminal serviceability (on a O to 5 scale typical p' values are 2.0, 2.5, and 3.0),
and
big= value of bx when Ex = ~ ~ and ~2 = i'
For rigid pavements, the equations are:
log,O(wX/w~) = 4.62*Iog,0~+~4.62*Iog,0(L`x+~2)
+ 3.28*Iog~0~2 + G/bx  Gab
9
. Equation (7)
. Equation (~)
Appendix E
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bx = 1.00 + [3.63*(LX + L2)^5.20]/[(D + 1)^8.46*L2^3.52]
where D is the slab thickness in inches.
5.1 Flexible Pavement Examples
Equation (9)
Equations 6 and 7 above solve for the loge of the inverse of the equivalency factors. For
the flexible pavement example used in the ~ 993 AASHTO Design Guide A the SN = 5, and pi =
2.5. Assuming that on that pavement we want to determine the ~ g kip equivalency for a 22 kip
single axle load Ex = 22 hips, ~2 = l, and Equation ~ reduces to
log,O(w22/w,~) = 0.34
w22/w~ = 0.457 and the equivalency factor e22 = /0.457) = 2. ~ 8.
Similar calculations produce the tabulation of flexible pavement single axle Toad equivalency
factors for pi = 2.5 and structural numbers ~ through 6 given in Table E4.
Again, for the flexible pavement example one can calculate equivalency factors for
+~_1~~ ret 1~1.~ l_~r art;_;_ ~
1   at, __ _ _
~llklt;lIl Wilt; lUdLlb fly ~18111118 ~ 42 = 2 in Equations 4 and 5. went using a 34 kip tandem axle
load Equation 4 reduces to
log~O(wX/w,') = 0.03 7
wow = 0.918 and the equivalency factor e34 = I/~0.918) = 1.09.
The last calculation shows that for a flexible pavement a 34 hip tandem load is approximately
equivalent to an ~ ~ kip single axle load. Similar calculations produce the tabulation of flexible
pavement tandem axle load equivalency factors for pi = 2.5 and structural numbers ~ through 6
given In Table D.5 of Me ~ 986 AASHTO Guide for the Design o/Pavement Structures.
Studies by Treybig, et.al.~ have extended the AASHO Road Test results to trident axles.
While He analysis of tndem axle equivalencies is well beyond the scope of the present study,
Table D.6 of the 1986 AASHTO Guide for the Design of Pavement Structures is a tabulation of
flexible pavement trident equivalency factors for structural numbers 1 through 6 and pi = 2.5. It
should be noted in that Table that a 48 kip trident load has an ~ g kip equivalency of
approximately one.
Appendix E
10
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5.2 Rigid Pavement Examples
For the rigid pavement example used in the ~ 993 AASHTO Design Guide (~) the slab
thickness D = 1 0, and pi = 2.5. Assuming that on that pavement we want to determine the ~ ~ kip
equivalency for a 22 kip single axle load Ex = 22 Lips, ~2 = it, and Equation 7 reduces to
log,O(w22/w~) = 0.3 76
w22/w~ = 0.421 and the equivalency factor e22 = I/~0.421) = 2.38.
Similar calculations produce the tabulation of rigid pavement single axle load equivalency
factors for pi = 2.5 and slab thicknesses of 6 through ~ 4 given in Table D. ~ 3 of the ~ 986
AASHTO Guide for the Design of Pavement Structures.
Again, for the rigid pavement example one can calculate equivalency factors for tandem
axle loads by assigning ~2 = 2 in Equations 7 and 9. Then, using a 34 kip tandem axle load
Equation 7 reduces to
log,O(w34/w~) 0.289
W34/W,8 = 0.514 and the equivalency factor e34 = I/~0.514) = 1.95.
The last calculation shows that for a rigid pavement a 34 hip tandem load has an
equivalency nearly double that for an ~ ~ kip single axle load. Similar calculations produce the
tabulation of rigid pavement tandem axle load equivalency factors for pi = 2.5 and slab
thicknesses of 6 through 14 inches given in Table D.14 in the 1986 AASHTO Guide for the
Design of Pavement Structures.
Again, while the analysis of tridem axle equivalencies is well beyond the scope of the
present study, Table D.15 in the 1986 AASHTO Guide for the Design of Pavement Structures is
a tabulation of rigid pavement tandem equivalency factors for slab thicknesses of 6 Trough 14
inches and p' = 2.5.
5.3 Calculating ESAL Applications for Mixecl Traffic
Table E4 is an example of total daily ESAL calculation for trucks (in most such analyses
buses are included with trucks while passenger cars and pickup trucks are ignored as the ESAL
contributions of those classes are insignificant) in a traffic stream for a flexible pavement where
SN = 5 and Pt = 2.5. Note that the table summarizes single and tandem axles separately as the
equivalency factors are quite different.
11
Appendix E
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Table E  4
FLEXIBLE PAVEMENT SN =5, psubt = 2.5
ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM
BEFORE ENFORCEMENT AFTER ENFORCEMENT
Eqivalency No. Daily No. Daily
Factor Axles ESALs Axles ESALs
0.005 18 0.09 18 0.09
0.032 12 0.384 10 0.32
0.088 370 32.56 260 22.88
0.36 40 14.4 30 10.8
1 300 300 320 320
2.18 42 91.56 6 13.08
O O
0.005 18 0.09 16 0.08
0.037 24 0.888 23 0.851
0.151 50 7.55 40 6.04
0.758 48 36.384 36 27.288
0.974 25 24.35 123 119.802
1.38 43 59.34 52 71.76
2.08 163 339.04 27 56.16
Total 906.636 649.151
Axle Load Ranges
Single 3000  6999
Axles 7000  7999
8000  11999
12,000 15,999
16,000 19,999
20,000  23,999
Tandem
Axles
6000  11,999
12,000  17,999
18,000  23,999
30,000  31,999
32,000  33,999
34,000  37,999
38,000  41,999
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In the tabulation, axle loadings are grouped as convenient. Then, the equivalency factors
are determined from Equations 4 through 9. Alternatively, the equivalencies could be
interpolated from the appropriate tables (Tables D.4, D.5, D.6, D.13, D.14, or D.15 ofthe 1986
AASHTO Guide for the Design of Pavement Structures as appropnate) in order to estimate the
ESAL contribution from each axle grouping. For example, note that the heaviest single axle
class in the stream is 26,000  29,999. The equivalency factor applied to that group is 5.39 as
given in Table D.4 of the 1 986 AASHTO Guide for the Design of Pavement Structures for a 28
hip single axle load. There was only one axle in that group so the total ESAL contribution from
the group is 1*5.39 = 5.39 ESALs. Similarly, the total ESAL contribution from all groups is the
estimated ESALs for the traffic stream. For the example, daily ESALs are determined for both
the before arid after enforcement conditions. The total daily ESALs before enforcement (ESALb)
is 907 while the total after enforcement RESALE is 649.
The estimated increase in pavement life is then
L`j = lOO*(ESAL`b  ESAL`a)/ESALb = 100*~907  6491/907 = 28.4%.
Note that this value is very close to that determined in Section 4 through the fourth power rule
for the same traffic stream on a generic flexible pavement.
A similar analysis has been applied to the above traffic stream assuming the pavement in
question is rigid with a slab thickness (D) of ~ O in. and a terminal serviceability index Spit of 2.5.
This analysis is summarized in Table E5 where it may be noted that the major difference is in
the equivalency factors for tandem axles which are much higher than for the flexible pavement
case. For the rigid case, the total dally ESALs before enforcement (ESALb) is 1303 while the
total after enforcement RESALE is 871.
The estimated increase in pavement life for this case is then
Li = 100*~1301871~/1301 = 33.~%.
Again, the estimated increase in pavement life for this method is very close to that determined in
Section 4 through Me fourth power rule for We same traffic stream on a generic ngid pavement.
If, instead of estimating the increase in pavement life, it is desired to determine an
estimate of absolute pavement life before and after enforcement activities it is necessary to apply
the AASHTO design equations as given in Section 6 of this appendix.
13
Appendix E
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Table E  5
RIGID PAVEMENT, D = 10, psubt = 2.5
ESAL ESTIMATES FOR TYPICAL TRAFFIC STREAM
BEFORE ENFORCEMENT  AFTER ENFORCEMENT
Eqivalency No. Daily No. Daily
Factor Axles ESALs Axles ESALs
0.006 18 0.108 1 18 0.108
0.03 12 0.36 10 0.3
0.081 370 29.97 260 21.06
0.338 40 13.52 30 10.14
1 300 300 320 320
2.38 42 99.96 6 14.28
O O
0.085 18 1.53 16 1.36.
0.064 24 1.536 23 1.472
0.254 50 12.7 40 10.16
1.32 48 63.36 36 47.52
1.72 25 43 123 211.56
2.48 43 106.64 52 128.96
3.87 163 630.81 27 104.49
Total 1303.494 871.41
Axle Load Ranges
Single
Axles
3000  6999
7000  7999
8000  11999
12,000  15,999
16,000 19,999
20,000  23,999
Tandem 6000 11,999
Axles 12,000  17,999
18,000  23,999
30,000  31,999
32,000  33,999
34,000  37,999
38,000  41,999
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6.0 DETERMINATION OF FLEXIBLE PAVEMENT STRUCTURAL NUMBER AND
ESTIMATED PAVEMENT LIFE FROM AASHTO EQUATIONS
6.1 DETERMINATION OF FLEXIBLE PAVEMENT STRUCTURAL NUMBER
The structural number (SN) is a measure of relative pavement strength and is defined as:
SN = a,h, + a2h2 +     + aj\ Equation (10)
where:
from the top down, h, is the thickness of layer one which has a layer coefficient of a,, h2
is the thickness of layer two which has a layer coefficient of al, etc. Table E6 is a
tabulation of layer coefficients for materials typically used in flexible pavement
construction.
As an example of SN determination, if a pavement is comprised of 6in. of crushed stone
base (a2 = 0. 14) and 4in. of asphalt concrete (a, = 0.44) the pavement has a SN = 0.44*4 +
0.14*6 = 2.6.
6.2 DETERMINATION OF ESTIMATED PAVEMENT LIFE FROM AASHTO
EQUATIONS
6.21 FLEXIBLE PAVEMENTS
6.211 AASHTO Design Equation
The AASHTO Design equation for flexible pavements is:
tog,OW~ = ZR*SO + 9.36*Iog~0(SN + 1)  0.20
+ (Iog~O(DPSI/2.711/~0.40 + 1094/(SN+115'9)
+ 2.32*Iog~0MR 8.07
where:
Wig
Equation ~ ~
The predicted accumulated traffic on the design lane during the design
period (typically 30 years) in equivalent ESALs,
15
Appendix E
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Appendix E
ZR = the starboard normal deviate corresponding to the desired design reliability (for
50% reliability ZR = 0 and I/2 of the pavement wart fail before the end of
the design period, etc.) (a typical reliability for major highways is 95%
with ZR =  ~ .64),
SO = the overall standard deviation associated with pavement performance prediction (a
typical value for flexible pavements is 0.35),
SN = the pavement structural number defined earlier,
DPSI= the change in pavement serviceability during the design period (a typical value is
1.9), and
MR = the effective roadbed soil resilient modulus (AASHTO T 274) in psi.
6.212 Example of Design Equation Use
For purposes of demonstrating the effects of chances in cumulative ESALs it may be best
to simplify Equation ~ ~ above by using typical values for all variables except ESALs and SN.
The 1993 AASHTO Design Guide (~) offers a convenient example where the following values
are assigned:
ZR= ~64 (reliability = 95°/O)
SO = 0.35
DPSI= I.9
MR = 5000 psi.
Then, the AASHTO flexible design equation reduces to:
log~OW~ = 0.26 + 9.36*Iog,0(SN + I)

c~
0.15.3/~0.40 + 1094/(SN+~5 ~9) Equation ~12)
It should be emphasized that Equation 12 is a gross simplification of the AASHTO
flexible pavement design equation and should never be used for the design of specific
pavements. The sole purpose of the simplified equation is to permit analysis of the ESAL vs.
thickness relationship as a part of the study to assess the effects of weight enforcement on
pavement performance.
To examine the effects of various cumulative ESALs on pavement life it is convenient to
assume a known existing pavement of say SN = 5. Equation ~ 2 then solves
16
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TABLE E 6
PAVING MATERIALS USED IN MSHTO DESIGNS
RIGID PAVEMENTS
Modulus of
Material Typical Thicla~ (in.) Modulus of Rupture (psi) Subgrade Reaction (pci)
(4 cl~aract'3rs) (3 characters) (3 characters)
PCC (poplars! 615 in.
carry Default = 650 Default = 200
As)
FLEXIBLE PAVEMENTS
Typical
Material Thickness (h) (in.)
(4 characters)
Surface: high stab.
asphalt 1  4 in.
concrete
four stability
asphalt 1  4 in.
concrete
Base: high slate. 2 16in.

asphalt
coracle
Shed 2 12in.
Strength
Coethcient (a)
(4 characters)
Default = 0.44
DefauH = 0.20
Default =0.40 (1)
Default = 0.14
sandy 2  12in. DefauH = 0.07
~1
cerr~e'*
by 4  8 in. Default = 0.20
sane
aspect
hid 4  Sin. Default= 0.34
sane
lime
bmabrent 4  8 in.
D^uR = 0.=
Subbase: sandy
gravel 2  18in. Default = 0.11
sand or
sandy clay 2 18in.
Default = 0.~)8
Except as noted, default values are from the 1972 MSHTO Interim Guide
for Design of Pavement Structures.
(a) Recommendation of Me Project 2~34 research beam.
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1ogl0Wl8 = 6.72
and Wl8 = 5.2 x 106.
If the traffic stream analyzed above for a flexible pavement with SN = 5 arid pi = 2.5 is
used the before (ESALb) and after DESALT enforcement daily ESALs are 907 and 649,
respectively.
It can be shown that a pavement undergoing an annual growth rate in traffic volume will
accumulate the design Was according to Me equation
n = Bog* + r*W~/365*ESAL)~/Iog~O(! + r)....Equation (13)
where n = the estimated pavement life in years,
r = the annual growth rate expressed as a decimal,
ESAL = the average daily ESALs at the beginning of the analysis period.
Assuming a 5% annual rate of growth in traffic for the above example the pavement
would have been predicted to last
no = Fog* + 0.05*5.2 x 106/365*907~/Iog~0~.05) = 12.0 yrs.
With the same growth rate after enforcement the pavement would be predicted to last
A= [Iog~O*~] + 0.05*5.2 x 106/365*649~/Iog~0~.05) = 15.3 yrs.
Then, We increase in expected pavement life due to enforcement is 15.3  12.0 = 3.3 years or
27.5%. Note that the percentage increase in pavement life compares well with that determined
from Me approximation method used earlier.
6.22 RIGID PAVEMENTS
6.221 AASHTO Design Equation
The AASHTO Design equation for ngid pavements is:
log~OW~ = ZR*SO + 7.35*Iog~0(D + 1)  0.06
+ [Iog~O(DPSI/3.0~/~1 + (1.624*107~/(D+11846]
~ (4 22  0.32p~*Iog~o{tst*c~(Do.75

Appendix E
1.132~/~215.63*~(D°75  18 42/(EJk)°25~] E ti (14)
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where, in addition to that defined above:
D=
1 _
s
J=
E
c
the slab thickness (in.)
estimated mean PCC modulus of rupture (AASHTO T97) in psi,
a factor used to account for the ability of rigid slab to transfer loads across
discontinuities such as cracks and joints (typical values range from 2.5 to
4.0, see AASHTO),
PCC elastic modulus in psi (typically 4 to 5 * lob), and
the modulus of subgrade reaction, the load in pounds per square inch on a
loaded area of the roadbed soil or subbase divided by the deflection in
inches of the soil or subbase (psi/in), (typical values are 50 to 3001.
In addition, for rigid pavements the initial serviceability (PSIO or PS} at time O) is about 4.2 while
the terminal or no longer acceptable serviceability (PSI') is about 2.5. Therefore, a typical DPST
is about I.7.
Now, it is possible to solve Equation 14 for local conditions and, and making the
appropriate substitutions in EquationI3, go through the analysis of before and after enforcement
traffic streams to assess the impact of that enforcement on pavement life.
7.0 CONCLUSION
The foregoing discussion of pavement design pnociples has addressed the major issues
underlying methods of determining Me increase In pavement life one could expect from reduced
axle loadings accrued through enforcement activities. The application of these principles is seen
In the software product of NCHRP 2034, the Truck Weight Enforcement Evaluation Tool.
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Appendix E
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Appendix E
8.0 REFERENCES
American Association of State Highway and Transportation Officials, "AASHTO Guide
for Design of Pavement Structures", Washington, DC, ~ 993.
American Association of State Highway and Transportation Officials, "AASHTO Interim
Guide for Design of Pavement Structures ~ 972", (Chapter Ill Revised, ~ 98 ~ ),
Washington, DC, ~ 972, ~ 98 i.
Treybig, H. J. and H. L. Von Quintus, "Equivalency Factor Analysis and Prediction for
Triple Axles", Report No. BR2/l, Austin Research Engineers for Texas Research and
Development Foundation, Austin, TX, 1976.
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