Abstract
The description of the mechanical behavior of bitumen on the basis of its microstructure allows its improvement and moreover the development of equivalent or even more sustainable materials with similar properties. For this reasons, a micromechanical model for bitumen is proposed, allowing the description of the viscoelastic bitumen behavior depending on characteristics of different material phases. The definition and demarcation, respectively, of material phases is based on SARA fractions, and polarity considerations that support the assumption of asphaltene micelle structures within a contiguous matrix and the assumed interactions between them. A sufficient number of static creep tests on artificially composed bitumen samples with asphaltene contents from 0 to 30 wt% served both as identification as well as validation experiments for the developed micromechanical model. An excellent agreement between experimental results and model predictions indicates that the model is able to reproduce significant microstructural effects, such as interactions between asphaltenes, which strongly influence the bitumen behavior. This model is therefore expected to contribute to a better understanding of the influence of the bitumen microstructure on the macroscopic mechanical behavior and subsequently be able to describe the mechanical consequences of microstructural effects like aging.
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Acknowledgments
The authors gratefully acknowledge financial support from the Austrian Research Promotion Agency (FFG) and the sponsors Pittel+Brausewetter, Swietelsky and Nievelt through project “OEKOPHALT—Physical–chemical fundamentals on bitumen aging”. They further appreciate the support of Daniel Großegger and Thomas Riedmayer with sample preparation and execution of CR tests.
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Appendices
Appendix 1: Stroud’s integration formula
The scalar weights \(\omega (\vartheta _j,\varphi _j)\) in Eq. 11 and the orientations \(\vartheta _j\) and \(\varphi _j\) are defined in Table 5.
Appendix 2: Transformation of local Hill’s shape tensors into global frame
To sum up the tensors in Stroud’s integration formula [32, 40] in Eq. 11, the tensors \({\mathbf{P}}^{*,{\rm arom}}_{\rm cyl}(\vartheta _j,\varphi _j,{\rm p})\) have to be given in the same base frame. While analytical expressions for \({\mathbf{P}}_{\rm cyl}\) are available in a local base frame [9, 13] coinciding with the principal axis of the ellipsoid (see Fig. 15), the corresponding components of \({\mathbf{P}}\) in \([6\times 6]\) “Kelvin–Mandel” matrix notation, reading as [7, 17, 29]
can be transformed very efficiently from local frames to one global frame through [29]
with \({\mathbf{Q}}^t(\varphi ,\vartheta )\) as the transpose of \({\mathbf{Q}}(\varphi ,\vartheta )\), and
The components \(q_{ij}\) are the elements of the matrix \({\mathbf{q}}\) in \({\mathbf{Q}}\), reading as
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Eberhardsteiner, L., Füssl, J., Hofko, B. et al. Influence of asphaltene content on mechanical bitumen behavior: experimental investigation and micromechanical modeling. Mater Struct 48, 3099–3112 (2015). https://doi.org/10.1617/s11527-014-0383-7
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DOI: https://doi.org/10.1617/s11527-014-0383-7