# From Complex Modulus E* to Creep Compliance D(t): Experimental and Modeling Study
## 3 Results and Discussion
### Indirect Tensile Creep Test Results  
IDT creep tests were carried out by applying a static load on a diametral axis on cylindrical specimens. The deformations were measured on both sides of the specimens. The applied loads as well as the deformations on both faces are presented in Figure 14.  
Figure 12: EXP shift factor vs. the inverse of Williams–Landel–Ferry (WLF) equation.  
Figure 13: Master curve of creep compliance at 0 \({}^{\circ}\)C.  
The difference in strain measured on both sides increased by increasing test temperature. At \(-20\)\({}^{\circ}\)C the variation of horizontal strain between face 1 and face 2 was 2% \(\pm\) 5% and for vertical strain the difference was 30% \(\pm\) 10%. At \(-10\)\({}^{\circ}\)C the gap for horizontal strain was 4% \(\pm\) 3% and vertical strain it was 5% \(\pm\) 1%. Finally, for \(0\)\({}^{\circ}\)C the difference was very significant for horizontal strain 37% \(\pm\) 3% and 16% \(\pm\) 1% for vertical strain. Additionally, it can be noted that the maximal vertical strain at \(0\)\({}^{\circ}\)C was greater than the limit of viscoelastic domain found in the literature. However, because of the shape of the specimen, it was not possible to test the complex modulus before and after the static load. The gap between strains measured on both faces can be an indicator that the viscoelastic limit was exceeded; for that reason, the test was stopped after 100 s and not carried out at \(10\)\({}^{\circ}\)C.  
The ratio between the mean horizontal strain (X) and the mean vertical strain (Y) was measured, the results are presented in Figure 15. The points follow a polynomial law of order two in the range of temperature tested.  
IDT creep results were calculated using the equation proposed by AASHTO. The results (isotherms) are presented in Figure 16. The values appear lower than direct tensile (DT) and direct compression (DC) tests except for the test points at \(0\)\({}^{\circ}\)C, which may confirm that the linear viscoelastic limit was exceeded. At \(-20\)\({}^{\circ}\)C, creep compliance from IDT test was lower than direct tensile and direct compression creeps with factor ranging between 15.0 to 1.05. At \(-10\)\({}^{\circ}\)C there is a factor of 3.0 to 1.05 with two points at 0.85. At \(0\)\({}^{\circ}\)C, the factor ranges from 0.75 to 0.35.  
The master curves of IDT creep compliance test are presented at \(0\)\({}^{\circ}\)C in Figure 17 where the creep compliance from GKV model and the creep compliance from the 2S2P1D model coupled to Kopelman approximation and from direct tensile and compression creep test are compared. To build the master curve for IDT, test shift factors were determined graphically and seem to be ten times bigger the inverse of WLF law using the same C1 and C2 from complex modulus test. It is difficult to know the reason of that, C1 and C2 are empirical constants depending on the material. However, this may be related to the correction factor proposed by the AASHTO.  
Figure 14: Creep loading for indirect tensile test at (**a**) \(-20\)\({}^{\circ}\)C, (**b**) \(-10\)\({}^{\circ}\)C, (**c**) \(0\)\({}^{\circ}\)C, (**d**) IDT configuration  
The results show that creep compliance determined from IDT (corrected) test appears lower than the creep predicted from GKV model and 2S2P1D model coupled to Kopelman approximation except for the points determined at 0 \({}^{\circ}\)C. This could be explained by the fact that the viscoelastic domain was exceeded and therefore the creep was much more pronounced in this case. Additionally, Figure 17 shows the non-corrected IDT creep compliance (without applying C\({}_{\text{cmpl}}\)). In this case, to build the master curve, the shift factors were determined using the inverse of WLF law.  
Figure 16: _Cont._  
Figure 15: X/Y vs. test temperature.