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An incremental model is proposed to describe pre-failure behaviour of granular soils in plane strain conditions. The model has been derived from an approach applied in the analysis of triaxial tests. We have applied the methods of tensor algebra to transfer our triaxial results to a 2D case. The model describes the pre-failure deformations of fully drained sands and phenomena associated with undrained response such as static liquefaction. This model has a simple structure in the form of incremental equations. For some simple loading paths, these equations can be integrated analytically. For more complex loading paths a simple numerical algorithms will be sufficient. The model takes into account an initial anisotropy of soil which is ignored in most models. It also takes into account the initial state of soil, defined as rather contractive or dilative, in addition to classical geotechnical division into loose and dense sands. The proposed constitutive equations allow the study of pre-failure instabilities of sand, and some examples are presented.We have also derived analytically the equation for an instability line.

Deformations and liquefaction of granular soils in plane strain conditions