A homogenization approach for assessing the yield strength properties of stone column reinforced soils

Abstract

International audienceThe macroscopic strength properties of a purely cohesive soil reinforced by a periodic distribution of "stone columns" made of a highly frictional granular material are investigated in a rigorous way on the basis of the yield design homogenization approach. Starting from a first crude lower bound approximation to the macroscopic strength criterion of the stone column reinforced soil, a much more accurate failure surface is then drawn in the space of stresses as a result of a series of numerical elastoplastic simulations performed on the reinforced soil unit cell subject to radial strain controlled loading paths. The anisotropic characteristics of the so obtained original criterion are then highlighted by means of its representation in the Mohr plane attached to any oriented facet. The paper concludes with a first illustrative implementation of the method on the derivation of an upper bound estimate for the ultimate bearing capacity of a stone column reinforced foundation

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

“…Even though it allows to have more information than the method presented here (namely along the stress path during the loading increase), this procedure may quickly become slow and tedious, because many increments are necessary to capture the limit load. Authors have made such calculations with a similar computer and commercial finite element code, with von Mises and Drucker-Prager materials, which have taken several days with the same discretization of the stress space [22]. With a dedicated homemade finite element code, which permits to treat Tresca and MohrCoulomb materials in an elastoplastic procedure, the so-obtained macroscopic strength domain is in quite good agreement with the present results.…”

Ultimate bearing capacity of a foundation reinforced by columns or cross trenches under inclined loads: a homogenization approach

“…This intuitive idea is fully and rigorously confirmed by the homogenization method developed in the context of the yield design theory for reinforced soils in general and column‐reinforced soils in particular . It has thus been shown that a purely cohesive soil reinforced by purely cohesive inclusions (‘lime columns’ technique) may be perceived as a homogenous but anisotropic purely cohesive medium.…”

Stability analysis of homogenized stone column reinforced foundations using a numerical yield design approach

“…The recent improvement of numerical methods has allowed to get an accurate knowledge of the macroscopic failure behaviour of stone column reinforced soils [20,34]. But the implementation of such a macroscopic strength domain in order to analyze the stability of homogenized equivalent structures remains so far quite inexistent for such reinforced soils [35].…”

“…where the first four equations refer to the static admissibility in the context of periodicity (see [20] for more details). The respect of the local strength criterion is expressed by the last condition.…”

“…The analysis of stone column reinforced soils based on this particular class of failure mechanisms reveals a fundamental drawback from the yield design point of view [19,20]. Indeed, a key ingredient to implementing this approach is the possibility of calculating the maximum resisting work, which in the present case takes the form:…”