LARGE DEFORMATION THEORY IN GEOMECHANICS - INFLUENCE OF KINEMATIC NONLINEARITY ON THE RESULTS OF SOME CHARACTERISTIC GEOTECHNICAL CALCULATIONS

Abstract

The geotechnical engineering calculations are usually carried out according to the small deformation and displacement theory (infinitesimal strain theory) i.e. first-order theory. A linear relationship between componental displacements and deformations is adopted. The well-known conditions for equilibrium are defined for an undeformed system i.e. undeformed structure. Therefore, the geometric and static linearity assumptions are usually valid in geotechnical engineering calculations. These linearities are collectively referred to as kinematic linearity. In other words, engineers believe that results of quite satisfactory accuracy are obtained if only material nonlinearity is taken into account in the engineering calculations, regardless of the type of geotechnical problem being analysed. Therefore, it is not necessary to apply the large (finite) deformation theory with the assumption of material nonlinearity. The main aim of this paper is to verify the previous statement in the case of some characteristic problems of Geotechnics. In the first part of this paper, the large deformation theory, which is mostly unknown to the wider professional public, is briefly presented. After that, simple numerical analyses of some characteristic problems of Geotechnics were carried out in the well-known software FLAC 2D software with the aim of comparing the results obtained for the cases of kinematic linearity and kinematic nonlinearity. The obtained results point to the fact that kinematic nonlinearity should not always be ignored in the usual geotechnical engineering calculations. Therefore, engineers are urged to be careful.