Competitive and Sustainable Growth (GROWTH) Programme
SAMARIS
Sustainable and Advanced MAterials for Road InfraStructure
Work Package 5
Annex K
Determination of Parameters for Huet-Sayegh Model
Document number:
SAM-05-DE28Annex A
Version: Draft
Date: 27/10/2005
Name and signature
Drafted: Ronald Blab, Roman Lackner, Lisa Aigner
Reviewed:
Verified:
Validated:
Approved by SAMARIS Management Group:
Date
27/10/2005
SAMARIS DE-28-Annex-K
TABLE OF CONTENTS
1.
DESCRIPTION OF PARAMETER DETERMINATION FOR HUETSAYEGH MODEL WITHIN MS EXCEL .................................................................... 2
1.1
Open and prepare file ....................................................................................................... 2
1.2
Model description .............................................................................................................. 2
1.3
Input of measurement data .............................................................................................. 2
1.4
Determination of model parameters ................................................................................ 3
1.4.1 Determination of temperature-independent parameters ......................................................... 3
1.4.2 Specification of temperature dependence of parameter τ ....................................................... 4
1.5
Results ................................................................................................................................. 4
I
Description of parameter determination for Huet-Sayegh Model within MS Excel
1. DESCRIPTION OF PARAMETER DETERMINATION FOR
HUET-SAYEGH MODEL WITHIN MS EXCEL
Based on the values for the complex modulus E* [MPa] and phase angle  [◦] extracted from
oscillatory uniaxial tests performed for different temperatures and frequencies, the model
parameters for the Huet-Sayegh model can be determined according to the following
procedure:
1.1 Open and prepare file



Open file ”Huet Sayegh.xls“ with Microsoft EXCEL
Save file using a user-specified name
Open sheet ”analysis“
1.2 Model description

The upper box contains a brief model description (for detailed information, see Annex
J)
1.3 Input of measurement data

• For the different experimental conditions, provide temperature T [◦C], frequency f
[Hz], and the extracted values from the experimental data, such as the complex modulus
E∗ [MPa] and the phase angle ϕ [◦] (see Figure 1)
Figure 1:
2
Screen-shot of input of experimentally-obtained data
SAMARIS DE-28-Annex-K
1.4 Determination of model parameters
1.4.1 Determination of temperature-independent parameters
Change parameters E0 , E∞ , Ja , Jb , k, and h until best fit in the Cole-Cole and the Black
diagram is found. The quality of the approximation of the experimental data by the model
response corresponding to the selected values for the parameters is given by the ”sum of
squares” (see Figure 2). Hereby, the model response is obtained from Equations (26) and (27)
for the real part E’ and the imaginary part E’’ of E* by setting τ = 1 (see Annex J). For the
specification of the temperature-independent parameters, the following procedure is
recommended:
 Specify E0 and E∞:
E0 is the value of E’ = Real(E*) at the left intersection point of the model-response
curve and the ordinate of the Cole-Cole diagram.
E∞ is the value of E’ = Real(E*) at the right intersection point of the model-response
curve and the ordinate of the Cole-Cole diagram.
 Specify k and h, with 0 < k < h < 1:
The value of k affects the right slope of the model-response curve in the Cole-Cole
diagram.
The value of h affects the left slope of the model-response curve in the Cole-Cole
diagram.
 Specify Ja and Jb:
The values of Ja and Jb affect the height of the model-response curve in the Cole-Cole
diagram (i.e., the values for E’’ = Imaginary(E*)).
Figure 2:
D:\533563176.doc
Screen-shot showing specification of Huet-Sayegh parameters for τ = 1 s
3
Description of parameter determination for Huet-Sayegh Model within MS Excel
1.4.2 Specification of temperature dependence of parameter τ



Adapt values for characteristic time τ corresponding to the different temperatures
considered in the experimental program until the best fit in the diagram shown in Figure
3 (complex modulus E* vs. frequency f) is found. Again, the quality of the fit is given by
the sum of squares, representing the deviation between model response and
experimental results (see Figure 3).
Select a reference temperature T0 for determination of the activation energy Ea.
Adapt value for activation energy Ea until the best fit in the characteristic time–
temperature diagram (τ − T diagram) is found.
Figure 3:
Screen-shot showing specification of values for characteristic time τ for
different temperatures
1.5 Results
The results, i.e., the temperature-independent parameters E0 ,E∞ , Ja , Jb , k, h, and the
temperature-dependent parameter τ (T), given by the reference temperature T0 and the
activation energy Ea, are listed in the table at the bottom of the sheet ”analysis”.
4
SAMARIS DE-28-Annex-K
References
HUSA, MS Excel sheet adapted from HUSARoad, Lausanne
Figures
Figure 1: Screen-shot of input of experimentally-obtained data ............................................... 2
Figure 2: Screen-shot showing specification of Huet-Sayegh parameters for τ = 1 s ............... 3
Figure 3: Screen-shot showing specification of values for characteristic time τ for
different temperatures ................................................................................................ 4
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