In the first part of this thesis, a three-dimensional rheological model was constructed to represent the deformation behavior of a granular material. The constitutive relations for a granular material were subsequently derived. The rheological model was conceivedfrom the observed behavior of granular material from laboratory experiments and from theoretical considerations. The constitutive relations were expressed in incremental forms to account for thestress history and loading path dependency of a granular material's behavior, such as non-linearity, initial or induced anisotropy, history and path dependency, and shear dilatance.
The qualitative and quantitative behavior of a granular material such as sand under shear stress from experimental results and from the proposed constitutive relations was examined and compared. Itwas found that the experimental data and the proposed constitutiverelations were in close agreement.
Due to the number of parameters involved, and the non-symmetrical resulting stiffness matrix in a general stress-strain formulation,it is difficult to apply the proposed constitutive in a finite element computer formulation at the present state of the art. Consequently the application of finite element methods to non-linear problems was examined in more detail as a preliminary step. The effect, or theresults of the material properties, the finite element mesh size and the computational procedure was examined in detail in Part II of this thesis.
