Numerical stability analysis of an embankment on reinforced soils

This contribution addresses the stability analysis of an embankment resting on a purely cohesive clay layer, which has been previously reinforced by a group of either columnar or cross-trench inclusions, making use of the yield design homogenisation technique and more specifically of the static approach. Lower bound estimates are first derived numerically for the reinforced soil macroscopic strength condition, from solving a non-linear optimisation problem attached to the reinforced soil's unit cell. A lower bound approximation of the criterion formulated as the sum of convex ellipsoidal sets is then derived, which allows performing a finite-element static approach on the homogenised structure as a whole, and thus produces a rigorous lower bound estimate for the stability factor, as a result of a non-linear optimisation problem solved by a dedicated software. The analysis, which is notably focused on the seldom examined situation where the native clay cannot withstand any tensile stresses (tension cut-off condition), leads to relevant conclusions as regards the relative performances of the stone column and cross-trench reinforcement techniques.