Keywords: railway, ballast, geomaterials, criterion, Mohr-Coulomb, Drucker-Prager, Matsuoka-Nakai, numerical modelling, finite element.

While the Mohr-Coulomb criterion is widely used in geotechnics, the Drucker-Prager is common in finite element software. Its circular shape is really a great advantage from a numerical point of view, even it is a drawback from a physical point of view. In contrast, the Matsuoka-Nakai criterion seems to best fit material behaviour, particularly with regard to true triaxial tests. Moreover its smooth shape is also closer to the Mohr-Coulomb shape than that of the Drucker-Prager. However, the circular shape of Drucker-Prager allows rapid and straightforward computations of plastic strain, due to the use of the radial return closed form. In contrast, the closest point projection method used to compute plastic strain for other criteria is more complex to implement and requires more computation time. Maiolino and Luong have shown that using the Drucker-Prager criterion as a substitution for a Mohr-Coulomb criterion induces great discrepancies of the friction angle. But in previous work, the present authors have already shown that the choice of an alternative criterion should not be made without considering the particularities of the load and structure. They have also already demonstrated that acceptable results can be obtained using their models when using an appropriate Drucker-Prager Criterion. In this paper, the discrepancy induced by the use of alternative criteria to the Mohr- Coulomb, is analysed in order to choose a criterion which provides both faster analysis and a good approximation of the stress strain state in ballast.

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