Theoretical notes

The resolution of a stability problem requires taking into account field equations and constitutive laws. The first ones are equilibrium equations, the second ones describe the behavior of the soil. These equations are particularly complex since the soil is of multiphase systems, which can be traced to single-phase systems only in dry soil conditions, or analysis in drained conditions.

In most cases we have to deal with a material that if is saturated is at least two-phase, which makes the treatment of the equilibrium equations considerably complicated. Furthermore, it is practically impossible to define a constitutive law of general validity, because the soils have a non-linear behavior already at small strains, are anisotropic, and also their behavior depends not only on the deviatoric stress but also on the normal stress. Because of the above difficulties are introduced simplifying assumptions:

•

Simplified constitutive laws are used: rigid, perfectly plastic model. It is assumed that the resistance of the material is expressed solely by the parameters cohesion (c) and angle of shearing resistance (f'), constant for the soil and characteristic of the plastic state; therefore it is assumed valid the Mohr-Coulomb failure criterion:

where:

τ = shear strength, with the size of a stress;

c' = cohesion;

u = pore-water pressure;

ϕ' = shearing resistance angle.

•	In some cases are met only in part the equations of equilibrium.