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APPENDIX F EFFECT OF LABORATORY TESTING VARIABILITY ON PAVEMENT THICKNESS F-1
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) F-2
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 (F-1) 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. F-3
0.6 - 0.5' . At o ~0.4 a: it, 0.3 o z ~0.2 Cal OIL l1J 0.1 o C' 21 (A ~__ _ l ~ - 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 APSI . AS _ . . O O _ __ ~ . -15 0 2000 4000 6000 8000 10000 12000 NUMBER OF SJMU"~ONS 20 .z - 18 On 17 ~t at lull 16 Figure Fat. Convergence of Monte CarIo method with increasing number of simulations F-4
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. (F-2) 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 [F-21. A coefficient of variation of 0.03181 was used for the log of ESAL`s in the simulation. F-5
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 F-2 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 F-3 and F4 are similar to Table F-2 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/RD-84/019, June. F-2. Deacon, I.A., and Lynch, R.~., (1968), "Deterioration of Traffic Parameters for the Prediction, Projection, and Computation of EWE's", Final Report KYHPR-64-2l, HPR- I(4), Kentucky Highway Department, Lexington. F-6
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