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

Whereas the Coulomb criterion is widely used in geotechnics, the Drucker-Prager is common in finite element method software where its circular shape allows rapid and straightforward computations of plastic strain, due to the use of the radial return closed form. Maiolino and Luong have shown that Drucker-Prager induces too greater discrepancies in the friction angle.

However, the circular shape of Drucker-Prager, even with its drawback from a physical point of view, is really a great advantage from a numerical point of view. Plastic strain computations thus go down to literal expressions, known as radial return. Radial return is both easy to implement and time saving during the computations.

Matsuoka-Nakai seems to best fit material behavior, particularly with regard to true triaxial tests. However, the closest point projection method used to compute plastic strain, is more complex to implement. Research has been directed to the improvement of this method or the use of an alternative computing method.

In this paper, the discrepancy induced by using different criteria to the Mohr-Coulomb criterion are examined in order to evaluate if the simplest and faster analysis can be performed to give a first approximation of the displacements and stress in the ballast.

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