Numerical assessment of the macroscopic strength criterion of reinforced soils using semidefinite programming

Maxime Gueguin (1) , Ghazi Hassen (2) , Patrick de Buhan (2)

1 navier umr 8205 - Laboratoire Navier
2 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes

The macroscopic strength properties of reinforced soils, regarded as periodic composite materials, are investigated by means of a fem-based formulation of both the static and kinematic approaches of yield design applied to the reinforced soil's unit cell. Since the reinforced soil's individual constituents obey a 3D Mohr-Coulomb strength condition, such a numerical problem can be treated trough an optimization procedure using semidefinite programming. The whole numerical procedure is applied to the derivation of both lower bound and upper bound estimates to the macroscopic yield surface of a soil reinforced either by columnar inclusions (stone columns) or a double array of trenches (cross trench reinforcement). The so-obtained results highlight the efficiency of the proposed numerical method.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Maxime Gueguin, Ghazi Hassen, Patrick de Buhan. Numerical assessment of the macroscopic strength criterion of reinforced soils using semidefinite programming. International Journal for Numerical Methods in Engineering, 2014, 99 (7), pp.522-541. ⟨10.1002/nme.4716⟩. ⟨hal-01052946⟩