1. A Simple Method to Determine
the Tertiary Flow in Repeated
Load Test: Step-Wise Method
By:
Shu Wei Goh
Zhanping You, P.E.
2. Overview
Introduction of Flow Number
Problem Statement
Existing Methods
Proposed Method
Comparison Results
Conclusions
3. Introduction
What is Flow Number?
The point where the asphalt mixture begin
to deform significantly and the individual
aggregates that make up the skeleton of
the matrix start to “flow” –aggregate slide
through each other
4. Flow Number Test
Typically called flow number test, dynamic creep
test, and repeated load test
0.1s loading
Time (Second)
Stress(kPa)
0.9s dwell
5. Typical Flow Number Result
Primary
Secondary
Tertiary
PermanentStrain
Cycle Number
Flow Number
6. Flow Number: Traditional Method
0
0 Cycle Number
StrainRate
Flow Number: Minimum point of strain rate
8. Existing Methods
Traditional Method (NCHRP 9-19)
Polynomial Fitting Method
Moving Average Periods (MAPs)
Regression Technique
Jason Bausano and R. Christopher Williams Method (Unpublished)
Examined the flow number by plotting creep stiffness times cycles
versus cycle
Three Stage Deformation Method (By Zhou et al.)
Using power law model to describe the primary curve and using simple
linear method to describe secondary curve.
Archilla et al. (2007) Method
Model the deformation curve by calculating the differential of strain rate
divide by twice the sampling interval, and then smoothed the curve by
running a five-point moving average for each cycle.
9. Three Deformation Methods by Zhou et al.
Tertiary
PermanentStr
Cycle Number
Flow Number
Primary Curve
,
b
p aNε = 100% 3% 1 / 2 _ .e
p
D st nd pt
Measuredε
∆
= × < =
Secondary Curve:
' 'p cN dε = +
100% 1% _
'
d
p
d
R Flow Numer
ε
= × < =
11. Proposed Methods – Step-Wise
Method
Assumption:
Permanent Strain will only increase during flow
number test
Method using:
Smoothing the discontinuity data point to provide
step-wise increasing.
Plot strain rate versus cycle number and defined the
flow number at minimum point of strain rate.
If the lower strain slope locate at N max, there is no
flow number
13. Shifting the discontinuity data
points forward along the x-axis
8550
8600
8650
8700
8750
8800
3490 3540 Cycle Number
Micro-Strain
3
4
5 6
8
9
10
14. Shifted data point after using the
Step-Wise method
8550
8600
8650
8700
8750
8800
3490 3540 Cycle Number
Micro-Strain
3
4
5 6
8
9
10
15. Step-Wise Method
Step 1: Smoothing the measured
permanent deformation by re-allocating
the measured results using the Excel
function call “Sort Ascending.”
Step 2: Calculate the strain rate using the
modified permanent deformation result.
Step 3: Determine the flow number by
locating the minimum point of strain rate
18. Conclusions
The proposed approach provides a practical and
consistent method to determine the initiation of tertiary
flow.
The entire non-uniform discontinuity data point can be
easily smoothed using the excel function called “Sort
Ascending.”
The R-square value of 0.971 and 0.992 respectively
were found from the comparison and this indicated that
these methods have showed a good correlation with the
proposed Step-Wise method.