Numerical Analyses Of Sallow Foundations On Reinforced Soils

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[Numerical Analyses of Sallow Foundations on Reinforced Soils]



In this study we try to explore the concept of Sallow foundations in a holistic context. The main focus of the research is on the numerical analyses of sallow foundationson reinforced soils. The research also analyzes many aspects of reinforced solils and tries to gauge its effect on Sallow foundations. Finally the research describes various factors which are responsible for Reinforced soils” and tries to describe the overall effect of Implementation and verification of finite element models.

Table of Contents


Background of the Study9

Objectives of the study10

Scope of the study11


Reinforced Soil Foundations12

Embankments over Soft Soils12

Macro element modelling of shallow foundations13

Definition of generalized forces and displacements15

Structure of the macroelement model17

Modeling of the cyclic behavior of shallow foundations resting on geomesh and grid-anchor reinforced sand21


Search Tools26


Implementation and verification of finite element models28

Finite element implementation of critical state models29

Explicit stress integration with automatic sub stepping33

Load stepping scheme for displacement elements34

Time stepping scheme for mixed displacement pore pressure elements36

Finite element model37

Generic strategies to transfer material grading to the FEA38

Global node driven strategy38

Element driven strategy39

Function driven strategy41



The use of reinforcements beneath rigid shallow foundations in order to increase footing ultimate load is not a recent idea. The type of reinforcement may vary from steel beams or layers (Soni, 1992, pp. 54-78) to geogrids or geotextiles. The difficulty of highlighting and understanding the mechanical response of such complex structures is linked to the problem of performing ad hoc experimental tests. In fact, extensive experimental large scale test series are too expensive. Whereas both 1g small scale and centrifuge small scale tests, unless in a different manner, are affected by scale effect.

For this reason, in this paper, even if we are conscious that the constitutive relationships implemented into the numerical code (as far as both soils and reinforcements are concerned) are very simple (linear and pressure dependent elasticity coupled to a Mohr-Coulomb failure locus), numerical analyses have been used in order to better clarify the considered mechanical problem and not to quantitatively reproduce the experimental reality.

In fact from numerical results we derived only useful suggestions and we did not mean to substitute experimental results. The mechanical response of rigid strip shallow foundations placed on a homogeneous loose sand stratum will be analyzed by considering three global kinematic (v,u,) and three load variables (V,H,M) (Smith, 1970, pp. 357 ). Conversely to standard limit analysis results (Soni et al. 1992), the performed finite element numerical analyses will give us not only the failure locus shape in the V-H-M space, which may be also obtained experimentally, when loose sands are considered, by keeping constant the relative depth of the footing level, but also the mechanical response up to failure.

Many different factors have been analysed: the number of reinforcements, their relative depth, the relative density of sand between reinforcements, the strength and the stiffness of reinforcements, the dilatancy angle, etc (Vecchiotti, 2001, pp. 25-69).

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