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New Approach for the Design of High RAP HMA. Ramon Bonaquist, Ph.D., P.E. Chief Operating Officer Advanced Asphalt Technologies, LLC. Results From Recent Laboratory Efforts. Evaluate Plant Produced Mixtures RAP Contents of 25 % or More 5% Recycled Asphalt Shingles. Acknowledgements. - PowerPoint PPT Presentation

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Simple Performance TestNEAUPG MEETING OCTOBER 19, 2005

New Approach for the Design of High RAP HMA

Ramon Bonaquist, Ph.D., P.E.

NEAUPG MEETING OCTOBER 19, 2005

Results From Recent Laboratory Efforts

Evaluate Plant Produced Mixtures

5% Recycled Asphalt Shingles

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Acknowledgements

Agencies

NEAUPG MEETING OCTOBER 19, 2005

Trends

NEAUPG MEETING OCTOBER 19, 2005

AASHTO M323 Design Guidance

Gradation

Angularity

15 -25 % RAP, use one grade softer

> 25 % RAP, use blending chart

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Issues

AASHTO M323 Binder Recommendations Assume Complete Mixing of New and Recycled Binder

AASHTO M323 Does Not Address RAS Binders

Much Different Rheology than Paving Binders

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Our Approach

Degree of Mixing of New and Recycled Binder

Effective Grade of the Combined Binder

Tests

NEAUPG MEETING OCTOBER 19, 2005

Finding

Dynamic Modulus Data Can Be Used to Evaluate RAP and RAS Mixtures

Test Is Highly Sensitive to Binder Stiffness

Assess Degree of Mixing of New and Recycled Binders

Interpreted to Estimate the Effective Grade of the Combined Binder

Relatively Easy to Perform with the Simple Performance Test System

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Simple Performance Test System

Three Performance Related Tests

NEAUPG MEETING OCTOBER 19, 2005

Simple Performance Test System

Technician Friendly

NEAUPG MEETING OCTOBER 19, 2005

How?

Perform Dynamic Modulus Master Curve Testing on Plant Produced Mixture

Standard Test in Simple Performance Test System

Use Mixture Modulus Data to Estimate Effective Binder Modulus

Hirsch Model

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Examples

Compare Estimated Binder Modulus With Recovered Binder Modulus

Example 1. 9.5 mm Mixture With PG 64-22 Produced in a Batch Plant

Example 2. 9.5 mm Mixture with PG 64-22 & 5% RAS Produced in a Batch Plant

Example 3. 9.5 mm Mixture with PG 64-22 & 35 % Fractionated RAP Produced in a Double Barrel

Example 4. 19.0 mm Mixture with PG 64-22 & 45 % Fractionated RAP Produced in a Double Barrel

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

9.5 mm With PG 64-22, Batch Plant

README

Sterling, VA 20166

23.0156207583

0.0434487521

2.2727783479

187.4037806127

10

1.59

1.2113664443

-1.4127635686

0.0386577374

25.8680426663

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

27.0685340241

37.9707353926

21.4808823569

19.1611181323

34.5230411823

31.3644655547

12.2102626263

26.0540429104

35.9345051527

8.6611490295

19.9824768219

35.3888944179

This workbook is used in conjunction with the Simple Performance Test System to develop dynamic

modulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

ú

ú

ú

ú

û

ù

ê

ê

ê

ê

ë

é

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

(

)

= fitting parameters

This workbook is used in conjunction with the Simple Performance Test System to develop dynamicmodulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max = limiting maximum modulus

, , and c fitting parameters

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

)(000,435000,200,4

100

1

1

000,10

000,435

100

1000,200,4|*|

max

VFA

VMA

VMA

P

VMAxVFA

VMA

PE

c

c

(2)

where

58.0

58.0

)(000,435

650

)(000,435

20

VMA

VFA

VMA

VFA

P

c

(3)

E*

max

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

If viscosity-temperature data are not available for the binder used in the mixture, the workbook can be used

to solve a master curve equation using shift factors from the Arrhenius equation, Equation 4.

25.295

11

14714.19

)log(

1

*)log(

T

E

t

a

e

Max

E

(4)

Where:

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

2. A data entry spreadsheet (DATA)

3. A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4. A summary report spreadsheet of the 2002 Design Guide fit (VTSMASTERREPORT)

5. A spreadsheet to perform the Arrhenius fit (ARRHENIUSFIT)

6. A summary report spreadsheet for the Arrhenius fit (ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift factors, the reference temperature, and the measured dynamic modulus data. If only two specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the 2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow highlighted cell (Cell J25) to minimize the sum of the squared errors between the measured and predicted values. Initial estimates for the optimization should be input in Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25, the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT spreadsheet. It includes the measured data, the optimized master curve parameters, and plots of the dynamic modulus master curve, the shift factors, and the phase angle master curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a master curve using Arrhenius temperature shift factors, Equation 4. Use the solver function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared errors between the measured and predicted values. Initial estimates for the optimization should be input in Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell I25, the final values of the master curve parameters are given in Cells B4 to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve parameters, and plots of the dynamic modulus master curve, the shift factors, and the phase angle master curve.

MBD015A195B.doc

(

)

[

]

{

}

)

Max = limiting maximum modulus

(, (, ( and c fitting parameters

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

ú

ú

ú

ú

û

ù

ê

ê

ê

ê

ë

é

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

(

)

NEAUPG MEETING OCTOBER 19, 2005

9.5 mm With PG 64-22 + 5% RAS, Batch Plant

README

Sterling, VA 20166

26.4606785844

0.0377919257

2.265000259

184.0773099451

10

1.59

1.258303614

-1.4597007383

0.0346975861

28.8204487219

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

454041.671350786

31670

296680.878734479

6630

165365.812229873

1114

78146.3557597868

175.7

31410.7922892483

34.14

10679.3499977627

6.607

3013.85083403

693.0731695212

127.8060835939

13.3998449109

This workbook is used in conjunction with the Simple Performance Test System to develop dynamic

modulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

ú

ú

ú

ú

û

ù

ê

ê

ê

ê

ë

é

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

(

)

= fitting parameters

This workbook is used in conjunction with the Simple Performance Test System to develop dynamicmodulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max = limiting maximum modulus

, , and c fitting parameters

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

)(000,435000,200,4

100

1

1

000,10

000,435

100

1000,200,4|*|

max

VFA

VMA

VMA

P

VMAxVFA

VMA

PE

c

c

(2)

where

58.0

58.0

)(000,435

650

)(000,435

20

VMA

VFA

VMA

VFA

P

c

(3)

E*

max

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

If viscosity-temperature data are not available for the binder used in the mixture, the workbook can be used

to solve a master curve equation using shift factors from the Arrhenius equation, Equation 4.

25.295

11

14714.19

)log(

1

*)log(

T

E

t

a

e

Max

E

(4)

Where:

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

2. A data entry spreadsheet (DATA)

3. A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4. A summary report spreadsheet of the 2002 Design Guide fit (VTSMASTERREPORT)

5. A spreadsheet to perform the Arrhenius fit (ARRHENIUSFIT)

6. A summary report spreadsheet for the Arrhenius fit (ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift factors, the reference temperature, and the measured dynamic modulus data. If only two specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the 2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow highlighted cell (Cell J25) to minimize the sum of the squared errors between the measured and predicted values. Initial estimates for the optimization should be input in Cells B4 to B7. Suggested initial estimates are given.…

New Approach for the Design of High RAP HMA

Ramon Bonaquist, Ph.D., P.E.

NEAUPG MEETING OCTOBER 19, 2005

Results From Recent Laboratory Efforts

Evaluate Plant Produced Mixtures

5% Recycled Asphalt Shingles

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Acknowledgements

Agencies

NEAUPG MEETING OCTOBER 19, 2005

Trends

NEAUPG MEETING OCTOBER 19, 2005

AASHTO M323 Design Guidance

Gradation

Angularity

15 -25 % RAP, use one grade softer

> 25 % RAP, use blending chart

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Issues

AASHTO M323 Binder Recommendations Assume Complete Mixing of New and Recycled Binder

AASHTO M323 Does Not Address RAS Binders

Much Different Rheology than Paving Binders

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Our Approach

Degree of Mixing of New and Recycled Binder

Effective Grade of the Combined Binder

Tests

NEAUPG MEETING OCTOBER 19, 2005

Finding

Dynamic Modulus Data Can Be Used to Evaluate RAP and RAS Mixtures

Test Is Highly Sensitive to Binder Stiffness

Assess Degree of Mixing of New and Recycled Binders

Interpreted to Estimate the Effective Grade of the Combined Binder

Relatively Easy to Perform with the Simple Performance Test System

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Simple Performance Test System

Three Performance Related Tests

NEAUPG MEETING OCTOBER 19, 2005

Simple Performance Test System

Technician Friendly

NEAUPG MEETING OCTOBER 19, 2005

How?

Perform Dynamic Modulus Master Curve Testing on Plant Produced Mixture

Standard Test in Simple Performance Test System

Use Mixture Modulus Data to Estimate Effective Binder Modulus

Hirsch Model

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

Examples

Compare Estimated Binder Modulus With Recovered Binder Modulus

Example 1. 9.5 mm Mixture With PG 64-22 Produced in a Batch Plant

Example 2. 9.5 mm Mixture with PG 64-22 & 5% RAS Produced in a Batch Plant

Example 3. 9.5 mm Mixture with PG 64-22 & 35 % Fractionated RAP Produced in a Double Barrel

Example 4. 19.0 mm Mixture with PG 64-22 & 45 % Fractionated RAP Produced in a Double Barrel

Advanced Asphalt Technologies, LLC

NEAUPG MEETING OCTOBER 19, 2005

9.5 mm With PG 64-22, Batch Plant

README

Sterling, VA 20166

23.0156207583

0.0434487521

2.2727783479

187.4037806127

10

1.59

1.2113664443

-1.4127635686

0.0386577374

25.8680426663

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

27.0685340241

37.9707353926

21.4808823569

19.1611181323

34.5230411823

31.3644655547

12.2102626263

26.0540429104

35.9345051527

8.6611490295

19.9824768219

35.3888944179

This workbook is used in conjunction with the Simple Performance Test System to develop dynamic

modulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

ú

ú

ú

ú

û

ù

ê

ê

ê

ê

ë

é

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

(

)

= fitting parameters

This workbook is used in conjunction with the Simple Performance Test System to develop dynamicmodulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max = limiting maximum modulus

, , and c fitting parameters

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

)(000,435000,200,4

100

1

1

000,10

000,435

100

1000,200,4|*|

max

VFA

VMA

VMA

P

VMAxVFA

VMA

PE

c

c

(2)

where

58.0

58.0

)(000,435

650

)(000,435

20

VMA

VFA

VMA

VFA

P

c

(3)

E*

max

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

If viscosity-temperature data are not available for the binder used in the mixture, the workbook can be used

to solve a master curve equation using shift factors from the Arrhenius equation, Equation 4.

25.295

11

14714.19

)log(

1

*)log(

T

E

t

a

e

Max

E

(4)

Where:

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

2. A data entry spreadsheet (DATA)

3. A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4. A summary report spreadsheet of the 2002 Design Guide fit (VTSMASTERREPORT)

5. A spreadsheet to perform the Arrhenius fit (ARRHENIUSFIT)

6. A summary report spreadsheet for the Arrhenius fit (ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift factors, the reference temperature, and the measured dynamic modulus data. If only two specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the 2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow highlighted cell (Cell J25) to minimize the sum of the squared errors between the measured and predicted values. Initial estimates for the optimization should be input in Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25, the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT spreadsheet. It includes the measured data, the optimized master curve parameters, and plots of the dynamic modulus master curve, the shift factors, and the phase angle master curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a master curve using Arrhenius temperature shift factors, Equation 4. Use the solver function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared errors between the measured and predicted values. Initial estimates for the optimization should be input in Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell I25, the final values of the master curve parameters are given in Cells B4 to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve parameters, and plots of the dynamic modulus master curve, the shift factors, and the phase angle master curve.

MBD015A195B.doc

(

)

[

]

{

}

)

Max = limiting maximum modulus

(, (, ( and c fitting parameters

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

ú

ú

ú

ú

û

ù

ê

ê

ê

ê

ë

é

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

(

)

NEAUPG MEETING OCTOBER 19, 2005

9.5 mm With PG 64-22 + 5% RAS, Batch Plant

README

Sterling, VA 20166

26.4606785844

0.0377919257

2.265000259

184.0773099451

10

1.59

1.258303614

-1.4597007383

0.0346975861

28.8204487219

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

Master Curve Model:

log10 (E*) = Delta + (Max - Delta) / (1+EXP (Beta + Gamma* log10 (tr)))

Reference Temperature:

454041.671350786

31670

296680.878734479

6630

165365.812229873

1114

78146.3557597868

175.7

31410.7922892483

34.14

10679.3499977627

6.607

3013.85083403

693.0731695212

127.8060835939

13.3998449109

This workbook is used in conjunction with the Simple Performance Test System to develop dynamic

modulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

ú

ú

ú

ú

û

ù

ê

ê

ê

ê

ë

é

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

(

)

= fitting parameters

This workbook is used in conjunction with the Simple Performance Test System to develop dynamicmodulus master curves. It has the capability to solve a modified version of the 2002 Design Guide master

curve equation, Equation 1.

Max = limiting maximum modulus

, , and c fitting parameters

The maximum limiting modulus is estimated from mixture volumetric properties using the Hirsch model

and a limiting binder modulus of 1 GPa (145,000 psi), Equations 2 and 3.

)(000,435000,200,4

100

1

1

000,10

000,435

100

1000,200,4|*|

max

VFA

VMA

VMA

P

VMAxVFA

VMA

PE

c

c

(2)

where

58.0

58.0

)(000,435

650

)(000,435

20

VMA

VFA

VMA

VFA

P

c

(3)

E*

max

= limiting maximum mixture dynamic modulus

VMA = Voids in mineral aggregates, %

VFA = Voids filled with asphalt, %

If viscosity-temperature data are not available for the binder used in the mixture, the workbook can be used

to solve a master curve equation using shift factors from the Arrhenius equation, Equation 4.

25.295

11

14714.19

)log(

1

*)log(

T

E

t

a

e

Max

E

(4)

Where:

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

1.

3.

A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4.

A summary report spreadsheet of the 2002 Design Guide fit

(VTSMASTERREPORT)

5.

6.

(ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the

DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum

modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift

factors, the reference temperature, and the measured dynamic modulus data. If only two

specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS

parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the

2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow

highlighted cell (Cell J25) to minimize the sum of the squared errors between the

measured and predicted values. Initial estimates for the optimization should be input in

Cells B4 to B7. Suggested initial estimates are given. After solver optimizes Cell J25,

the final values of the master curve parameters are given in Cells B4 to B7.

VTSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the VTSFIT

spreadsheet. It includes the measured data, the optimized master curve parameters, and

plots of the dynamic modulus master curve, the shift factors, and the phase angle master

curve.

ARRHENIUSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to a

master curve using Arrhenius temperature shift factors, Equation 4. Use the solver

function tool on the yellow highlighted cell (Cell I25) to minimize the sum of the squared

errors between the measured and predicted values. Initial estimates for the optimization

should be input in Cells B4 to B7. Suggested initial estimates are given. After solver

optimizes Cell I25, the final values of the master curve parameters are given in Cells B4

to B7.

ARRHENIUSMASTERREPORT Spreadsheet

This spreadsheet provides an output of the optimized master curve from the

ARRHENIUSFIT spreadsheet. It includes the measured data, the optimized master curve

parameters, and plots of the dynamic modulus master curve, the shift factors, and the

phase angle master curve.

2. A data entry spreadsheet (DATA)

3. A spreadsheet to perform the 2002 Design Guide fit (VTSFIT)

4. A summary report spreadsheet of the 2002 Design Guide fit (VTSMASTERREPORT)

5. A spreadsheet to perform the Arrhenius fit (ARRHENIUSFIT)

6. A summary report spreadsheet for the Arrhenius fit (ARRHENIUSMASTERREPORT)

DATA Spreadsheet

All data needed to develop a master curve is input in the highlighted cells in the DATA spreadsheet. This includes VMA and VFA for computing the limiting maximum modulus, A and VTS parameters for the binder for use in the 2002 Design Guide shift factors, the reference temperature, and the measured dynamic modulus data. If only two specimens were tested, leave the data cells for Specimen 3 blank. Note: A and VTS parameters are only needed for the 2002 Design Guide master curve (VTSFIT)

VTSFIT Spreadsheet

This spreadsheet is set up for using the solver function to fit the measured data to the 2002 Design Guide master curve, Equation 1. Use the solver function tool on the yellow highlighted cell (Cell J25) to minimize the sum of the squared errors between the measured and predicted values. Initial estimates for the optimization should be input in Cells B4 to B7. Suggested initial estimates are given.…

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