Abstract : When studying the stability of geotechnical projects on reinforced soils by columns (bearing
capacity of footings, stability of embankments and retaining structures) by the use of direct
approaches of the yield design theory some diculties are encountered especially when the
number of inclusions becomes important. This leads sometimes to overestimated strength
capacities of the reinforced soil. Another alternative, based on the homogenization method in
yield design theory, permits to overcome the mentioned diculties by solving an equivalent
homogeneous problem. By this latter, the estimation of strength capacities of the reinforced soil
becomes easier and, consequently the design methods will be more accessible for praticians.
The rst part of the present thesis is dedicated rst to the bearing capacity estimation of foundations
resting on reinforced soils by a trench. The direct kinematic approach of yield design
theory is carried out by considering the general scheme of cohesive frictional soil and constitutive
material of the trench. By exhibiting the Prandtl's mechanism failure analytical upper
bound of bearing capacity has been obtained from which some previous results in literature are
found. Then, an updated analysis is done concerning the design methods of bearing capacity of
reinforced soil by columns. In this section, it is focused on the limitation encountered by direct
approaches of yield design theory for taking account of strength anisotropy, particularly in the
case of soils reinforced by columns.
In the second part, basical concepts of the homogenization method are briey recalled. Then
the determination of macroscopic strength criteria has been carried out in the case of purely
cohesive native soil reinforced by columns made up of purely cohesive material. A closed
boundary is then established for the macroscopic strength criteria. From this result the bearing
capacity of rigid foundation resting on the homogenized reinforced soil, has been performed,
in plane strain analysis. As interesting result a better upper bound of bearing capacity is
obtained regarding the determination by using the direct kinematic approach. The stability of
an embankement built on reinforced soil made up of purely cohesive constituents has been also
studied. By performing the kinematic approach of yield design theory, an upper bound of the
stability factor has been determined.
In the third part, the reinforcement of purely cohesive soil (like soft clays) by columns made
up of a cohesive-frictional material (like stone, gravel) is investigated. The static approach (or
by inside) is rst carried out by the use of homogenization method in yield design theory to
establish a lower bound of the macroscopic strength criterion. Such a problem can be formulated
easier by making recourse to a linearized boundary of the macroscopic strength criterion hence
providing a safer estimation. Therfore lower bounds of bearing capacity of foundation resting
on homogenized reinforced soil have been established successively by performing rst elds
of stress of three zones and second of six zones. The main result recorded was a sensitive
improvement of the lower bound obtained by the stress eld of three zones, when the stress
eld of six zones is carried out.
This work is concluded by focusing on results, and advantages with respect to direct methods,
obtained by the method of homogenization in the framework of yield design theory to examine
the stability of foundations resting on reinforced soils by columns.
Key words : reinforced soils by columns, strength criterion, homogenization, periodic, associated
homogeneous problem, unit cell, macroscopic strength domain, anisotropic, factor of
stability, bearing capacity, linearization.