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

The macroscopic strength properties of reinforced soils, regarded as periodic composite materials, are investigated by means of a FEM-based formulation of both static and kinematic approaches of yield design applied to the reinforced soil's unit cell. Because the reinforced soil's individual constituents obey a 3D Mohr-Coulomb strength condition, such a numerical problem can be treated through 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.