# From Complex Modulus E* to Creep Compliance D(t): Experimental and Modeling Study
## 4 Conclusions  
The objective of the work presented here was to predict creep compliance D(t) results from complex modulus E*(\(\omega\)) results. Several methods are proposed in the literature allowing to go from the frequency domain to the time domain and vice-versa such as the inverse of the transform of  
Figure 16: (**a**) Isotherms of IDT creep compliance. (**b**) IDT creep compliance vs. direct creep compliance.  
Figure 17: Master curve of creep compliance at 0 \({}^{\circ}\)C.  
Carson-Laplace and by more or less complex numerical methods. Rheological models, if properly calibrated, seem to be a very good and simple method to go from E* (cyclic test) to D(t) (static test). To achieve this objective, the proposed working method consists of two main parts: an experimental part and a modelling part. For the experimental part, two types of test were performed namely: cyclic test-E*(\(\omega\)) and creep static test-D(t). Complex modulus tests were done using direct tensile and compression tests. For creep test, a comparison was done between indirect tensile configuration (proposed by AASHTO) and direct tensile and direct compression tests.  
The results show that D(t) from direct tensile and direct compression tests are the same in the viscoelastic behavior domain and are greater than D(t) from indirect tensile test. This can be explained by the direction of the measured creep modulus. D(t) perpendicular to the direction of compaction are higher compared to the parallel one. Compared to the field, the cracks observed by lowering of temperature are in an axis perpendicular to the direction of compaction of the roads. Moreover, the compaction method proposed by AASHTO (with the gyratory compactor) is not very representative compared to compaction on site. For direct tensile and direct compression tests, the samples were compacted using MLPC wheel compactor. Additionally, it is complicated to compare creep test in IDT configuration to direct compression or tensile tests. For IDT, the results show significant difference between the strain measured in both faces. Further, it's very difficult to know if the load applied remains inside the viscoelastic behavior domain for IDT configuration. The proposed method for converting E*(\(\omega\)) to D(t) consists in using existing rheological models. 2S2P1D is very commonly used for modelling of asphalt materials but this model does not have a creep function in time domain. To change from the frequency domain to the time domain, we propose to couple the results from 2S2P1D to the approximation proposed by [PERSON]. The generalized Kelvin-Voigt model can predict the creep compliance in time domain, but it is more difficult to calibrate. A minimization method is proposed in literature to calibrate GKV model from 2S2P1D model and therefore having D(t) results directly from E* results. The two methods were compared, and the results show a very good concordance between them.  
Conceptualization, methodology and validation, A.D. ([PERSON]), D.P., A.D. ([PERSON]) and A.C.; writing--original draft preparation, A.D. ([PERSON]); writing--review and editing, D.P., A.D. ([PERSON]) and A.C. All authors have read and agree to the published version of the manuscript. This research was partially funded by Transport Quebec.  
The authors declare no conflict of interest.