Approximations of the macroscopic strength criterion of reinforced soils, with application to structural stability analyses

International audienceThe macroscopic strength properties of a stone column reinforced soil are investigated numerically. Using the kinematic approach of the yield design theory applied to the reinforced soil's unit cell, a numerical upper bound estimate of its strength domain is provided. Since this domain cannot be used directly for a structural stability analysis, an approximation method is performed, using a sum of ellipsoidal sets. The result is a rigorous upper bound estimate for the macroscopic strength criterion depending on few parameters. The relative error of this method is quantified not exceeding a few percents. Then, this approximation is used in order to treat the problem of an embankment resting upon a stone column reinforced soil. Again, performing the kinematic approach on this structure, a rigorous upper bound estimate of the ultimate stability factor is obtained numerically. The gain in terms of ultimate capacity improvement is observed, as compared to the non reinforced configuration. This result is compared to a simplified analysis, based on a rule of mixture formula, where strong disparities are highlighted