Uni-axial compaction of a granular material

Abstract

S hearing of granular materials causes rearrangement of the granular structure which induces irreversible volume decrease and shear strain, in addition to reversible strain. The model adopted describes the reversible compression and shear by hypoelastic laws, and the irreversible compaction and shear by evolutionary laws. The latter are differential relations defining the progress of irreversible strain as an appropriate time-independent monotonie loading parameter increases, which incorporate dependence on the current state, and which prescribe a direction for the irreversible shear strain increment. The model is described by four material functions and two material constants, and has been shown to determine valid initial response to applied shear stress. We apply the model to the compaction of a granular material in uni-axial strain, which is described by two simultaneous differential equations for the axial stress and compaction with the axial strain as independent variable, together with algebraic relations for the pressure and lateral stress. The equation forms for loading-increasing axial stress—and unloading—decreasing axial stress-are distinct. Reformulation as differential equations for the pressure and the principal stress difference shows that the pressure derivative depends only on two of the material functions and one constant. The axial strain and lateral stress measured during a complete load-unload cycle on a sand determine the pressure and stress difference derivatives which are correlated directly with the model differential relations. Two material functions and one constant are determined by an optimization procedure from the complete loadunload ressure data, then the remaining two functions and constant from the stress difference data. Solution of the resulting model differential equations reproduces accurately the axial strain and lateral stress variations during the experimental loading cycle. In addition, model predictions for load-unload cycles to different maximum stresses are illustrated, and an approximate common feature of the different unloading curves is determined. This is a useful property for the application of the model to the propagation of a load—unload pulse where the amplitude progressively decreases due to the unloading interaction.