By W.S. Venturini

Numerical recommendations for fixing many difficulties in continuum mechanics have skilled a big development within the final two decades as a result of improvement of enormous excessive pace desktops. particularly, geomechanical pressure research can now be modelled inside of a extra life like context. besides the fact that many functions in geomechanics are nonetheless being performed making use of linear theories, soil and rock fabrics were proven experimentally to be bodily nonlinear. Soils don't get well their preliminary country after removing of transitority a lot and rock doesn't deform in share to the hundreds utilized. the hunt for a unified conception to version the genuine reaction of those fabrics is most unlikely as a result complexities excited by each one case. sensible options in geomechanical research has to be supplied through due to the fact that fabric homes range from element to indicate, as well as different major gains equivalent to non-homogeneous media, in situ rigidity , kind of loading, time results and discontinuities. a potential replacement to take on one of these challenge is to inttoduce a few simplified assumptions which a minimum of delivers an approximate answer in every one case. The validity or accuracy of the ultimate answer received is usually based upon the method followed. for this reason, the alternative of a competent idea for every specific challenge is one other tricky choice which can be 2 taken by means of the analyst in geomechanical pressure analysis.

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When plane stress condition is assumed for the two-dimensional analysis, equivalent values have to be defined to maintain the same formulation for both plane strain and plane stress cases. 5) = v/(l+v) Considering an elastic body defined by a domain boundary r, G and a its partial equilibrium is established by analysing a system of forces and momenta for a generic point. J ,J + b. 1. 6) 30 where 0 .. ~J are the components of the stress tensor and b. ~ stands for body force values which are defined as forces acting on elements of volume or mass inside the body.

Telles and Brebbia (38), based on the appropriate concept for the derivative of the singular integral of the inelastic term, suggested approaches using initial strain and stress processes to model plastic behaviour with the boundary element method. Their first approach follows the Mendelson's process (41) in which an "initial strain" form of the inelastic term is considered. This formulation is only capable of handling incompressible plastic strain using the isotropic von Mises yield criterion.

Many researches have already been carried out trying to find realistic time-dependent behaviours for such materials. In particular, Lama and Vutukuri (14) have given extensive overviews of many time-dependent theories formulated to model rheological behaviour of rocks. Viscoelastic responses which can be associated with Maxwell or Kelvin models (fig. 1) have been adopted several times to study long-time deformations in geomechanical problems using numerical techniques. One of the first applications of such an approach in rock material design was carried out by Zienkiewicz, Watson and King (85) using a finite element formulation.

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