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On the one hand, solid mechanics can be modelled on the following basis. The equilibrium equation is:

дг <jjj + Pj = 0 (11.1)

Where Pj is a member of P, the vector of volume forces, ji;- is a member of j, the Cauchy stress tensor, and д represents the spatial partial derivative operator:

di = (11.2)

dXi

The stress tensor is obtained by the time integration of an (elastic, elasto-plastic or elasto-visco-plastic) constitutive equation (see Chapter 9, Section 9.4.2; Laloui, 2001; Coussy & Ulm, 2001):

Jij = fn(j, e, Z) (11.3)

where (jij is the stress rate, e is the strain rate and Z is a set of history parameters (state variables, like e. g. the preconsolidation stress). In the most classical case of elasto-plasticity, this equation reduces to:

jч = hi

where Eejkl is a member of the elasto...

When trying to replicate in-situ behaviour by computational techniques, a number

of different physical phenomena (Gens, 2001) need to be considered, including:

• The non-linear solid mechanics and especially granular unbound or bound mate­rial mechanics: we consider the relations between displacements, strains, stresses and forces within solids. The material behaviour is described by a constitutive model, which can take into account elasto-plasticity or elasto-visco-plasticity;

• The fluid flow within porous media: fluid can be a single phase of various na­tures (water, air,…) or it can be an association of two fluids, leading to unsat­
urated media (water and air,…)...

Robert Charlier[25], Lyesse Laloui, Mihael Brencic, SigurSur Erlingsson, Klas Hansson and Pierre Hornych

Abstract Different physical problems have been analysed in the preceding chapters: they relate to water transfer, to heat transfer, to pollutant transfer and to mechanical equilibrium. All these problems are governed by differential equations and boundary conditions but analytical solutions are, in general, unobtainable because of the com­plex interaction of the various aspects which are always present in real-world situ­ations. In such circumstances, numerical modelling can give a valuable alternative methodology for solving such highly coupled problems. The first part of this chapter is dedicated to a brief statement of the finite element method for highly coupled phenomena...

This Chapter presents in-situ and laboratory experimental techniques used to de­scribe mechanical behaviour of pavement materials (soils and aggregates) at dif­ferent saturation stages. Repeated triaxial load testing can be applied to obtain both stiffness characteristics and assessments of the ability of the material to with­stand accumulation of permanent deformation during cyclic loading. For unsatu­rated soils, in addition to mechanical variables, a moisture/suction control should be added, which can be imposed by several techniques as explained in the chapter. A brief presentation of the model parameters and tests needed for model calibration was introduced with particular reference to the modelling approaches described in Chapter 9...