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OCR for page 387
APPENDIX F
EFFECT OF LABORATORY TESTING VARIABILITY
ON PAVEMENT THICKNESS
F1
OCR for page 387
EFFECT OF LABORATORY TESTING VARIABILITY ON PAVEMENT THICKNESS
INTRODUCTION
The variability in the measured value of resilient modulus for each layer of a pavement
influences the required pavement thickness for a given level of reliability. A reliability analysis
was therefore conducted to determine the effect on pavement thickness of the observed variability
in the resilient modulus of asphalt concrete, aggregate base and subgrade materials. The 1986
AASHTO Design Guide was used in this study since it is commonly employed by design agencies.
Reliability was modeled using both the approach given in the 1986 AASHTO Design Guide and
Monte CarIo simulation.
DESIGN VARIABILITY
The coefficient of variation is a convenient way of expressing variability of material
properties and other design parameters. The coefficient of variation (CV) is defined as the
standard deviation of a variable divided by its mean value. Appendix EE of the 1986 AASHTO
Guide (Volume 2) gives the following coefficients of variation (CV) used in developing the
reliability analysis. Initial Serviceability Index: 0.067; surface strength: 0.10; surfacing thickness:
O. 10; base strength: 0.143; base thickness: 0.10; effective subgrade resilient modulus: 0.15. These
coefficients of variation are unweighted and given in decimal form.
Based on the laboratory resilient modulus studies performed as a part of the present study,
the following values of the coefficient of variation (CV) of the resilient modulus due to testing
errors is considered reasonable to use in a reliability analysis when a single specimen is tested in
a production oriented laboratory:
Material
Asphalt Concrete
Unstabilized Base
Subgrade
Coefficient of Variation (CV
0.10
0.15
0.15
Laboratory experimental errors, as defined for this study, include sample preparation, sample
alignment, and instrumentation measurement errors. As discussed subsequently, these coefficients
of variation can be readily combined with the values used in the AASHTO reliability analysis.
AASHTO Type Reliability Analysis
The 1986 AASHTO Guide provides a simple, but approximate, basis for performing a
reliability analysis which considers the likely variation of pertinent variables. The AASHTO
reliability analysis combines all the effects of variability into a single, weighted value of the
standard deviation (SO) For the present study, each variable (i) contributing variance to predicted
pavement thickness was weighted using the factors employed in the Guide developed from the
observed behavior of the AASHO Road Test. The method used to weight the variables involves
taking partial derivatives to obtain the effect on performance of each variable while holding the
other variables constant. Hence, both the value of the overall, weighted standard deviation (SO)
F2
OCR for page 387
developed in Appendix EE of the 1986 AASHTO Guide and the way variability is handled in the
design equation are intimately tied to the variability associated with the AASHO Road Test
performance.
The weighted value of standard deviation (SO) was determined in Appendix EE of the
AASHTO Guide using the equation:
o
s =~W
(F1)
where SO is the combined value of standard deviation and Si2 is the weighted value of the square
of the standard deviation for each individual variable.
An overall weighted standard deviation SO = 0.457 was used in the present study to mode!
variation excluding laboratory experimental errors. The appropriate values of So2 were summed,
given in Column K of Table EE.4 of the Guide, to obtain this value of SO. Following the approach
used in the AASHTO Guide, the variability (S2) associated with the structural number was omitted
in obtaining the combined standard deviation SO. The s2 value for the subbase was also omitted
from the sum since a subbase was not used in the present study. Also, an s2 value of 0.1938 was
used for chance variation in pavement performance for fixed traffic and s2 = 0.0429 for variation
in design period ESAL predictions. These are the values also used in the AASHTO Guide
although two values for each of these variables, obtained from different sources, are given in Table
EE.4 of the AASHTO Guide.
Experimental error in evaluating resilient moduli was considered in the same way as was
the other errors. The coefficients of variation of each layer were multiplied by the weighting
factors given in the Guide for the respective layer. The resulting values of Si2 for experimental
error were included in the Equation (Fat) summation which resulted in an overall SO = 0.564.
MONTE CARLO RELIABILITY ANALYSIS
The Monte Cario method of simulation was used, in addition to the AASHTO reliability
approach, to investigate the effect of laboratory testing variability on required pavement thickness.
The Monte CarIo method involves determining, for a given set of mean design parameters, a large
number of structural thickness designs considering the likely random variation in design
parameters. For each solution, the design variables are randomly selected from the probability
distribution of each variable. The probability distribution of each variable is defined by its mean
value and coefficient of variation (CV).
Required pavement thickness is determined using the randomly selected design parameters
and the 1986 AASHTO Guide flexible pavement design equation. If a sufficient number of designs
are used, a valid probability distribution is obtained for the unknown layer thickness (either the
asphalt concrete surfacing or aggregate base). For this study 10,000 simulations were used for
each set of mean design parameters to insure good convergence of the answers (Figure Fob. A
probability distribution for the design thickness is first obtained from the 10,000 Monte Cario
simulations. The required thickness is then selected, for a given level of reliability, from this
probability distribution using standard probability theory.
F3
OCR for page 387
0.6
 0.5' .
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 COEFFICIENT OF VARIATION

~EAN BASE ~I=NESS
DESIGN VARIABLES
4,000,000 ESALe
~ IN. A.C SURFACE
A.C. SIR · "0,~ pal
BASE SIR ~ SS,000 pal
SUBGRADE SIR ' ~ "l
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NUMBER OF SJMU"~ONS
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Figure Fat. Convergence of Monte CarIo method with increasing number of simulations
F4
OCR for page 387
The Monte CarIo simulation used in this study considered the variability of the resilient
modulus of each layer, traffic, thickness of the surfacing and also the base when present. Drainage
coefficients were not considered because the magnitude of these variables and their variation have
not been accurately quantified.
For each variable, the combined effect of resilient modulus testing variability and
variability due to other causes was determined using the following formula:
Cvi = &\1 CV i,lab + CV2 i,gen
where: CVi
CVi,lab
CVi,gen
combined coefficient of variation for variable i
variability due to MR testing error for variable i
general variability used to quantify overall error for variable i; values
were used from Appendix EE of the 1986 AASHTO Guide.
(F2)
The combined values of the coefficient of variation (CVi) associated with the resilient modulus of
the layers are as follows: surfacing = 0.1414 (0.10, 0.10~; aggregate base = 0.2072 (0.143,
0.15~; subgrade = 0.2121 (0.15, 0.15~. The two numbers given in parentheses beside each
combined value of the coefficient of variation are the coefficients of variation due to general
causes, and the variation due to resilient modulus testing error, respectively.
The coefficients of variation used in the AASHTO Guide should include variability due to
laboratory testing in evaluating the strength of the layers. The overall values of these coefficients
of variation, however, are at the lower end of the range given in the literature [F~. The
AASHTO values appear to be valid for extremely good quality control that might, for example,
be associated with zero maintenance construction. Testing variability present in the AASHTO
variability values was not considered in developing the coefficients of variations used for the
resilient modulus testing error. As a result, the Monte Cario probability simulation should give
a conservative estimate of the effect of resilient modulus testing error if the AASHTO values of
the coefficient of variation are valid. The AASHTO values are more likely, however, to be on the
unconservative side.
Uncertainty associated with both the reliability of the AASHTO design equation and the
initial serviceability were treated in the same way as in the 1986 AASHTO method. The combined
value of Si used to mode! these sources of error in the AASHTO equation was 0.3181. This value
of S was also used In the Monte CarIo analysis. Lack of equation fit to the observed AASHO Road
Test performance was by far the most important factor contributing to the combined value of SO.
All variables randomly varied in the Monte CarIo simulation had a normal probability
distribution except for the IS hip single axle loadings (ESALs). A log normal probability
distribution was used for the ESALs. A log normal distribution was found to give a reasonable
approximation to observed traffic distributions which vary from I/2 to 2 times the predicted values
[F21. A coefficient of variation of 0.03181 was used for the log of ESAL`s in the simulation.
F5
OCR for page 387
Randomly varied values of the design variables were not permitted to be less than 10% of
their mean value. Placing a lower limit on the values of these variables served to avoid
convergence problems in solving the 1986 AASHTO Guide design equation.
ANALYSIS OF PAVEMENT SECTIONS
Monte CarIo and 1986 AASHTO Guide type reliability analyses were performed on both
full depth asphalt concrete sections and sections having thick unstabilized aggregate bases. Unless
otherwise indicated, the mean value of the variables used in the analyses were as follows: (~)
ESALs = 4x106; (2) change in PSI = 2.0, and (3) asphalt concrete resilient modulus MR =
400,000 psi. The effect of subgrade resilient modulus was investigated for mean values of 2000
psi, 5000 psi, and 10,000 psi. An asphalt concrete surface thicknesses of 6 in. was used for the
sections having thick, unstabilized aggregate bases. For the aggregate base sections, the effect on
pavement behavior was investigated for resilient moduli for the base of 20,000 psi, 30,000 psi, and
40,000 psi.
After determining the probability distribution and its coefficient of variation for the
required layer thickness, a single design thickness must be determined using conventional statistical
procedures for the desired level of reliability. In this study most of the final design thicknesses
were determined using a reliability {eve! of 98 % which, for example, might be employed in the
design of an interstate pavement in an urban area. A reliability level of 85 % was also used for
selected sections.
General Summary of Results
The results of the reliability analyses are summarized in Tables F! through F4. Table
F! shows the differences in base thickness determined for the AASHTO and Monte CarIo analyses
for a reliability of 98% and a strong base (MR = 40,000 psi). Table F2 shows for a weak base
(MR = 20,000 psi) the effect on total equivalent base thickness of resilient modulus testing error
for each layer separately. Tables F3 and F4 are similar to Table F2 except they show the effect
of resilient modulus experimental error for pavement sections having a strong aggregate base and
a fills depth asphalt concrete surfacing, respectively. A more complete discussion of these results
together with illustrative figures is given in Chapter 3.
References
Rauhut, I.B., Lytton, R.~., Darter, M.I., (1984), "Pavement Damage Functions for Cost
Allocation Vol. 2 Description of Detailed Studies; Volume 2  Description of Detailed
Studies", Federal Highway Administration, FHWA/RD84/019, June.
F2. Deacon, I.A., and Lynch, R.~., (1968), "Deterioration of Traffic Parameters for the
Prediction, Projection, and Computation of EWE's", Final Report KYHPR642l, HPR
I(4), Kentucky Highway Department, Lexington.
F6
OCR for page 387
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