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

Typical Flow Number Result

Primary

Secondary

Tertiary

Perm

anen

t Str

ain

Cycle Number

Flow Number

Flow Number: Traditional Method

0

0 Cycle Number

Stra

in R

ate

Flow Number: Minimum point of strain rate

Problem Statement

Measured Flow Number

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Fitting Method Moving Average Periods (MAPs) Regression Technique Jason Bausano and R. Christopher Williams Method (Unpublished)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Polynomial Fitting Method (Bausano and Williams, Unpublished)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.

Question?