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A Simple Method to Determine the Tertiary Flow in Repeated Load Test: Step-Wise Method
By:Shu Wei GohZhanping You, P.E.
Overview
Introduction of Flow Number Problem Statement Existing Methods Proposed Method Comparison Results Conclusions
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
Flow Number Test
Typically called flow number test, dynamic creep test, and repeated load test
0.1s loading
Time (Second)
Stre
ss (
kPa)
0.9s dwell
Flow Number: Traditional Method
0
0 Cycle Number
Stra
in R
ate
Flow Number: Minimum point of strain rate
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Fitting Method Moving Average Periods (MAPs) Regression Technique Jason Bausano and R. Christopher Williams Method (Unpublished)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.
Three Deformation Methods by Zhou et al.
Tertiary
Perm
anen
t Str
ain
Cycle Number
Flow Number
Primary Curve
,b
p aN 100% 3% 1 / 2 _ .ep
D st nd ptMeasured
Secondary Curve:
' 'p cN d
100% 1% _'dp
dR Flow Numer
Polynomial Fitting Method (Bausano and Williams, Unpublished)
y = -4E-17x6 + 6E-13x5 - 4E-09x4 + 2E-05x3 - 0.0375x2 + 65.804x + 8787.6
R2 = 0.9994
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
0 1000 2000 3000 4000 5000 6000
Cycle Numbers
Cre
ep S
tiff
nes
s x
Cyc
le N
um
ber
0
10000
20000
30000
40000
50000
60000
Mic
ro-S
trai
n
Flow Number
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
Non-uniform discontinuity data point
8600
8800
9000
3500 3550 3600 3650 3700 3750 3800Cycle Number
Micro-Strain
Shifting the discontinuity data points forward along the x-axis
8550
8600
8650
8700
8750
8800
3490 3540 Cycle Number
Micro-Strain
3
45 6
8
9 10
Shifted data point after using the Step-Wise method
8550
8600
8650
8700
8750
8800
3490 3540 Cycle Number
Micro-Strain
3
45 6
8
9 10
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
Comparison Results
Flow Number from Three-Stage Deformation MethodFlo
w N
um
ber
fro
m S
tep
-Wis
e M
eth
od
Comparison Results
Flow Number from Polynomial Fitting Method
Flo
w N
um
ber
fro
m S
tep
-Wis
e M
eth
od
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.