Chapter 5. Effect of M_R Selection on Overlay Thicknesses

Introduction

In order to design overlays for existing pavement sections using the AASHTO design guide, a M_R value must be selected to represent the characteristics of the subgrade soil, specifically, the stress conditions. When laboratory testing is completed to determine this value, a single deviator stress is often chosen to represent the design conditions. The deviator stress suggested in the literature is 41.4-kPa (6-psi). However, the actual deviator stress may be determined by using data from the field. If the actual field deviator stress is less than 41.4-kPa (6-psi), then the selected M_R value is conservative which may result in a thick overlay. On the other hand, if the field deviator stress is higher than 41.4-kPa (6-psi), then the selected M_R value is higher than the actual one which can result in a thin overlay. This chapter presents an evaluation of how three different procedures for determining resilient modulus (laboratory with a 41.4-kPa [6-psi] deviator stress, laboratory with actual deviator stress, and the AASHTO equation with field deflection measurements) affect the resulting overlay thicknesses.

Laboratory Resilient Modulus Values Based on Actual Field Stresses

The design resilient modulus values computed from the laboratory analysis in Chapter IV were based on a deviator stress of 41.4-kPa (6-psi). Since the thicknesses of each pavement section were available from the field evaluation, this information was used to compute the "actual" deviator stresses in the subgrades. The computer program, BISAR, was used in this analysis, assuming a 40-kN (9000-lbs.) wheel load, a 689-kPa (100-psi) tire pressure, and a three layer pavement structure (refer to Figure 5.1). The thicknesses of the AC and base layers along with typical Young's Modulus values used by the Wyoming DOT (refer to Table 3.3) were used in this analysis.

Figure 5.1 Assumptions Made in Calculating Actual Field Stresses

In addition, the undisturbed actuator M_R value, calculated by using a 41.4-kPa (6-psi) deviator stress, was entered into this program as the first seed moduli. Several iterations were then completed by taking the resulting deviator stress and substituting this value into the regression equation developed from the laboratory tests using undisturbed samples and the actuator LVDT's. The M_R value computed from the previous trial was inputted each time as the seed moduli until the resulting deviator stress changed by less than 3.5-kPa (0.5-psi). Tables 5.1 and 5.2 summarize the undisturbed actuator M_R values based on 41.4-kPa (6-psi) and actual field deviator stresses. M_R values for undisturbed samples, based on actuator LVDT measurements, were used in this part of the analysis simply because it was found in Chapter 4 that they best represent the characteristics of subgrade soil samples.

Comparison of Laboratory M_R Values

Because laboratory M_R values were calculated using two different stress conditions, one would want to know if there is any statistical difference between using the actual deviator stress and the assumed value of 41.4-kPa (6-psi). Therefore, the test for differences for paired data was performed. The data were placed in two groups, granular and treated, because four of the nine sites had some type of treated base, either ATB or CTB.

After completing this separation, comparisons were completed on all the sites within each group and then by each site individually. Tables 5.3 and 5.4 summarize the tests for the granular and treated sites, respectively.

Both tables show that there is not a statistical difference between the two data sets. However, by examining the variances, one would favor using the computed field deviator stresses over the assumed 41.4-kPa (6-psi) value because of the reduction in the amount of variance or variability. By determining actual deviator stresses, the resulting M_R values were more consistent within each test site.

Overlay Thickness Results

Several spreadsheets were developed to determine the overlay thicknesses for each test site. An example of this spreadsheet is shown in Appendix D. After entering the applied loads and corrected deflection measurements from the field FWD tests into the spreadsheet, several equations were solved in order to determine the SN_eff value of each test site. The first set of equations determined the M_R value based on the AASHTO equation (refer to Section 2.8.1). These M_R values were calculated by using the corrected deflection measurements taken at the following sensor locations: 305, 457, 609, 914, 1219, and 1524-mm (12, 18, 24, 36, 48, and 60-in., respectively). The underlying assumption for the AASHTO equation is that at a certain distance away from the loading plate, the measured deflection is attributable solely to the subgrade. In order to determine this distance and the resulting M_R value which will be used for design purposes, several checks must be completed. The minimum distance from the loading plate is determined with the following formula:

where:

• r = distance from center of load, inches
• a_e = radius of the stress bulb at the subgrade-pavement interface, inches

Two additional equations provide values related to this condition. First, the value of a_e is determined from the following formula:

ae =

(5.2)

where:

• a_e = radius of the stress bulb at the subgrade-pavement interface, inches
• a = NDT load plate radius (5.91-in.)
• D = total thickness of pavement layers above the subgrade, inches
• E_p = effective modulus of all pavement layers above the subgrade, psi

Second, the value of E_p is determined from the following formula:

do = 1.5pa+

(5.3)

where:

• d_o = deflection measured at the center of the load plate, inches
• p = NDT load plate pressure, psi
• a = NDT load plate radius (5.91-in.)
• D = total thickness of pavement layers above the subgrade, inches
• M_R = subgrade resilient modulus, psi
• E_p = effective modulus of all pavement layers above the subgrade, psi

These three constraints must be satisfied in order to determine the minimum distance. Once this distance is determined, the M_R value can then be adjusted with a correction factor before it is used to determine the SN_f value. In this research study, a correction factor of 0.33 was used. For each test site, nine M_R and E_p values were calculated because nine different loads were applied to each section. Final design values for both of these parameters were determined by taking a logarithmic average. Tables 5.5 and 5.6 summarize the M_R values from the three different methods: 41.4-kPa (6-psi) deviator stress, field deviator stress, and deflection measurements (referred to as LAB, FIELD, and AASHTO, respectively).

The three sets of M_R values were then used to compute the effective structural number (SN_f) using the flexible pavement design equation developed by AASHTO shown below:

log10W18 = zR*So+9.36*log10(SNf+1)-0.20++2.32*log10MR-8.07

(5.4)

where:

• W₁₈ = estimated future traffic, 18-kip ESALs
• z_R = standard normal deviate (based on reliability factor)
• S_o = overall standard deviation
• SN_f = future design structural number
• ΔPSI = design present serviceability index (PSI) loss
• M_R = design resilient modulus value, psi

In this research project, the following three different estimated future levels of traffic (W₁₈) were used in the above equation: 800,000, 3,000,000, and 5,000,000 ESALs corresponding to low, medium, and high traffic levels, respectively. The following values were assumed for the rest of the variables in the above equation: 85% reliability factor, 0.45 standard deviation, and 2.5 as the change in PSI (ΔPSI).

The SN_f values were determined for all test sections based on the three calculated M_R values and three different traffic levels. This analysis resulted in a total of nine SN_f values for each test site. Tables 5.7 and 5.8 summarize all SN_f results. Next, the SN_eff values were determined using the NDT overlay procedure and the averaged M_R (based on deflection measurements) and E_p values calculated earlier for each site. Tables 5.9 and 5.10 present the SN_eff values. Recall from Chapter 2, the SN_eff for the NDT procedure is calculated with the following formula:

SNeff = 0.0045D

(5.5)

Finally, the overlay design equation was used to determine the resulting overlay thicknesses (D_ol) for each section. These values were obtained by taking the difference between the SN_f and SN_eff values (SN_ol = SN_f - SN_eff) and dividing this quantity by 0.44, the layer coefficient (a_ol) for new asphalt pavement. Tables 5.11 and 5.12 summarize the D_ol values obtained in this analysis.

Statistical Analysis

With three different methods for determining M_R (AASHTO, LAB, and FIELD), it would be of interest to know if there are any statistical differences in the calculated overlay thicknesses due to the method used. The negative thicknesses were left in the analysis in order to provide a better indication of the differences among methods. A repeated measures analysis showed no evidence of differences (null hypothesis) among the methods at low, medium, or high traffic levels (F_2,24=2.16, p-value=0.1367, F_2,24=2.18, p-value=0.1351, and F_2,24=2.18, p-value=0.1349, respectively). Huynh-Feldt epsilon values were calculated in order to account for any model violations and to make adjustments to the denominator degrees of freedom. Values were near one, indicating that violations were minor: 0.8690, 0.8725, and 0.8733 for the low, medium, and high traffic levels, respectively.

Even though there were no differences among the methods, it might also be of interest to know, at a given difference in thickness, if one could detect that the methods were not the same. Therefore, the power of the F test was performed to determine the probability of accepting the alternative hypothesis (H_a) that the methods are different. Suppose, one is interested in determining if a maximum difference of 25.4-mm (1.0-in) could be detected. At the low traffic level, there was about 92 chances in 100 that differences would be detected among the 3 different methods. At 12.7-mm (0.5-in.) differences, this detection dropped to 34 chances in 100. Overall, 19.1-mm (0.75-in.) maximal differences could be detected with 80% probability. Detecting differences of 12.7-mm (0.5-in) would not be very easy with the given data set.

Besides the above test, the Tukey procedure for pairwise comparisons was also completed. The following 95% confidence intervals were obtained (μ_.3 is the treatment mean for AASHTO, μ_.2 is the treatment mean for LAB, and μ_.1 is the treatment mean for FIELD) for the low traffic level:

These intervals suggest that AASHTO M_R values give the lowest overlay thicknesses. There is also a slight indication that field M_R values give different results than the other two procedures. However, with the current sample size, these differences are not statistically significant. Similar results were obtained at the medium and high levels of traffic as shown below by the 95% confidence intervals, respectively.

Chapter Summary

In this chapter, an analysis was presented using the 1993 AASHTO guide for overlay pavements with three different sets of M_R values calculated throughout this research. Overlay thicknesses were calculated using the non-destructive testing (NDT) method for determining the SN_eff value of a pavement section. Three different statistical analyses were then conducted to evaluate the results: a repeated measures analysis, the power of the F test, and Tukey procedure for pairwise comparisons.