Using Multi-Objective Optimization to Enhance Calibration of Performance Models in the Mechanistic-Empirical Pavement Design Guide

APPENDIX A. DETAILS OF CALIBRATION INPUT DATA

ASPHALT CONCRETE DYNAMIC MODULUS

Computed AC dynamic modulus is available in the LTPP database for the surface layers. However, for asphalt stabilized layers, dynamic modulus values are not included in the LTPP. In those cases, the ANNACAP software was run to obtain the dynamic modulus at five temperatures (–10, 4.4, 21.1, 37.8, and 54.4 ºC) and for four frequencies (0.1, 1, 10, and 25).⁽⁶⁴⁾ This software calculates the dynamic modulus based on an ANN algorithm. The input data are the resilient modulus at 5, 25, and 40 ºC and the shift factors. The details of the software and the ANN model are reported by Kim et al.⁽¹²⁾ Table 38 shows the resulting estimated dynamic modulus values for SPS-1 and SPS-5 test sections.

Table 38. Dynamic modulus for the Florida SPS-1 and SPS-5 experiment test sections.

ASPHALT CONCRETE CREEP COMPLIANCE

MEPDG at input level 1 requires the AC creep compliance modulus at three temperatures (–20, –10, and 10 ºC) and seven loading frequencies (1, 2, 5, 10, 20, 50, and 100 s). The LTPP creep compliance test was done under a different set of temperatures (–10, 5, and 25 ºC) but similar loading frequencies to the MEPD input values. Therefore, a conversion process that is suggested in the literature is applied to generate the master curve and then fit a generalized viscoelastic model.⁽⁶⁵⁾ The log time–temperature shift factor is considered linearly correlated with the temperature. The sections included in the analysis are located in areas where the yearly lowest temperature is above 0 ºC. Therefore, the creep compliance conversion was not performed, and input level 3 was considered for the MEPDG analysis. However, for some other locations, where the temperature falls below 0 ºC, the conversion process needs to be applied.

The conversion process begins with the calculation of the reduced time that can be calculated using equation 48:

     (48)

Where:

t_T = time to obtain the creep compliance at temperature T.
t_T0 = time to obtain the creep compliance at temperature T₀ (1, 2, 5, 10, 20, 50, and 100 s).
β = slope of the straight line of the relationship between the time–temperature shift factor and the temperature, which is calculated using equation 49:

     (49)

Where:

T = temperature.
T₀ = reference temperature.

The generalized model can be composed by a number of connected Kelvin models. The creep compliance model for a constant stress condition is expressed as in equation 50:

     (50)

Where:

D(t) = creep compliance at time t.
G_i = creep compliance coefficients.
n = number of Kelvin models.
T_i = time durations to cover the range of interest.

Creep compliance coefficients are calculated solving the simultaneous equations as in equation 51:

     (51)

Where:

{G_i} = vector of creep compliance coefficients.
{D_i} = vector of creep compliance.
[E] = creep compliance matrix as in equation 52:

     (52)

RESILIENT MODULUS FOR UNBOUND AND SUBGRADE LAYERS

Table 39 shows the available resilient modulus values for unbound materials in the LTPP database.

Table 39. Calculated resilient modulus of unbound materials.

RUTTING DATA

SPS-1

Table 40, table 41, and table 42 list the average rut depth values measured through the monitoring period for every test section on the Florida SPS-1 site.

Table 40. Average measured rut depth for Florida SPS-1 test sections 120107 to 120111.

Table 41. Average measured rut depth for Florida SPS-1 test sections 120112 to 120105.

Table 42. Average measured rut depth for Florida SPS-1 test sections 120101 to 120161.

SPS-5

Table 43, table 44, and table 45 list the average rut depth values measured through the monitoring period for every test section on the Florida SPS-5 site.

Table 43. Average measured rut depth for Florida SPS-5 test sections 120502 to 120565.

Table 44. Average measured rut depth for Florida SPS-5 test sections 120509 to 120504.

Table 45. Average measured rut depth for Florida SPS-5 test sections 120562 to 120564.

APT ARB

Table 46 shows the measured rut depth on the APT ARB experiment sections with HVS passes.

Table 46. Average measured rut depth (mm) for FDOT ARB experiment sections.

APT DASR

Table 47 shows the measured rut depth on the APT DASR experiment sections with HVS passes.

Table 47. Average measured rut depth (mm) for FDOT DASR experiment sections.