Appendix B
Progress in Tasks A3, A5 and B6
Task A3 – Experimental Design (Prepared by: A. Abu Abdo, F. Bayomy)
MnRoad Mixes
To verify results from the Idaho mix designs, MnRoad mix designs were acquired from
selected test sections at MnRoad. Seven sections were identified and selected -- four from
mainline test sections (Cells 16, 17, 19 and 20) and three from the low volume road test sections
(Cells 33, 34 and 35). Those sections are identified in Figure 33. In addition, field performance
data related to these sections were obtained from published MnRoad results. Laboratory tests
have been completed on these MnRoad mixes. These tests included: dynamic modulus (E*),
binder dynamic shear modulus (G*), Flow Number (FN), and Gyratory Stability (GS). Analyses
of test data are in progress.
QR6_Appendix B: Progress in Tasks A3, A5 and B6 - Page 1
Figure 3 Typical Selected Test Sections from MnRoad
QR6_Appendix B: Progress in Tasks A3, A5 and B6 - Page 2
Task A5 – Data Analysis (prepared by A. Abu Abdo, and F. Bayomy)
E*-Proposed Model
𝐺∗
𝜌𝑤 .𝐺𝑆.𝐺𝑚𝑏
),
(1−𝑃𝑏 )
Using dimensional analysis, |E*| was found to be a function of (𝑃 ) and (
𝑏
where the binder effects are measured by |G*|, Gmb, and Pb, aggregates effects are measured by
GS, Gmb, and Ps (1-Pb), and finally air voids are measured by Gmb is a at Further analysis led to a
relationship in the form:
|𝐺 ∗ | 𝜌𝑤 . 𝐺𝑆. 𝐺𝑚𝑏 𝑏
|𝐸 ∗ | = 𝑎 (
.
)
(1 − 𝑃𝑏 )
𝑃𝑏
(1)
The experimental program included seventeen laboratory preparations of Idaho mixes
from which 408 Data points of E* were collected. A regression analysis was used to determine
the coefficients a and b. Results from the 408 data points indicated that the coefficients a and b
should be equal to 1.08 and 0.5583, respectively. Thus the final model can be expressed as:
|𝐸 ∗ | = 1.08 (
|𝐺 ∗ | 𝜌𝑤 . 𝐺𝑆. 𝐺𝑚𝑏 0.5583
.
)
(1 − 𝑃𝑏 )
𝑃𝑏
(2)
where,
|E*|: dynamic modulus for asphalt mix, MPa,
|G*|: dynamic shear modulus for RTFO aged binder, MPa,
Pb: binder content,
GS: gyratory stability, kN.m,
Gmb: bulk specific gravity of mix, Gmb = Gmm (1-AV%).
Gmm: maximum specific gravity of mix,
ρw : unit weight of water (1000 kg/m3), and
AV%: air voids.
The results from the MnRoad mixes (Task A3) may change the coefficients a and b slightly.
E*- Calculation Software
To facilitate the calculation/prediction of E* of hot mix asphalt (HMA), a Visual
Basic.Net software was developed as shown in Figure 4. The software can also be used to
determine the Gyratory Stability (GS). The software determines E* using the proposed model
and exports the results in a format that can be imported by MEPDG software.
QR6_Appendix B: Progress in Tasks A3, A5 and B6 - Page 3
Figure 4 E* Software
Several inputs are required to determine E* for a given sample. These data can be found in
the Job Mix Formula, compaction data, and air voids calculations. The required data is
summarized as follows:
1. Binder data: Binder grade or the binder dynamic shear modulus (G*) at required
temperatures and frequencies.
2. Mix data:
a. Maximum theoretical specific gravity (Gmm).
b. Percent of binder content (Pb).
c. Air voids (AV%).
d. Gyratory Stability (GS). To determine GS, the following inputs are required,
i. Mix data: Maximum theoretical specific gravity, final bulk specific gravity
(Gmb), and final weight of compacted sample (dry weight).
ii. Compactor data: Vertical stress (default value is 600 kPa), gyration angle
(default value is 1.25°), mold diameter (150 or 100 mm), output file for
either Servopac or Pine compactors (For other compactors change of
height and vertical forces versus number of gyrations data are required),
and N-design.
QR6_Appendix B: Progress in Tasks A3, A5 and B6 - Page 4
Task B6 – Reliability Analysis (prepared by A. Abu Abdo and R. Nielsen)
The Quarter 5 report described the development of a regression analysis which predicts
the visco-elastic parameter A, as function of test temperature and frequency. As a part of Task
B2, researchers are developing a 2D visco-elastic finite element model of the APA rutting test,
which includes an improved load-vs.-time, model – e.g., a half-wave sine function. The finite
element model will be used in a numerical (Monte Carlo) simulation of the rut
development. The APA rutting test will be simulated with the values of E* and A treated as
random variables. The probability distribution and parameters for E* will come from the
laboratory E* tests. The visco-elastic parameter A is expected to be normally distributed. The
mean and standard deviation for A will be determined from the regression analysis. The Monte
Carlo simulation will estimate the mean and standard deviation of the rutting predicted by the
APA test. The standard deviation of the predicted rutting will then be compared at least
indirectly to the standard deviation for the rutting in the MEPDG.
QR6_Appendix B: Progress in Tasks A3, A5 and B6 - Page 5