UNIAXIAL COMPACTION OF A GRANULAR MATERIAL

SHEARING OF GRANULAR materials causes rearrangement of the granular st ructure which induces irreversible volume decrease and shear strain, i n addition to reversible strain. The model adopted describes the rever sible 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 appropri ate time-independent monotonic loading parameter increases, which inco rporate dependence on the current state, and which prescribe a directi on for the irreversible shear strain increment. The model is described by four material functions and two material constants, and has been s hown to determine valid initial response to applied shear stress. We a pply the model to the compaction of a granular material in uni-axial s train, which is described by two simultaneous differential equations f or the axial stress and compaction with the axial strain as independen t variable, together with algebraic relations for the pressure and lat eral stress. The equation forms for loading-increasing axial stress-an d unloading-decreasing axial stress-are distinct. Reformulation as dif ferential equations for the pressure and the principal stress differen ce shows that the pressure derivative depends only on two of the mater ial functions and one constant. The axial strain and lateral stress me asured during a complete load-unload cycle on a sand determine the pre ssure 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 load-unload pressure data, then the remaining two functions and const ant from the stress difference data. Solution of the resulting model d ifferential equations reproduces accurately the axial strain and later al stress variations during the experimental loading cycle. In additio n, model predictions for load-unload cycles to different maximum stres ses are illustrated, and an approximate common feature of the differen t unloading curves is determined. This is a useful property for the ap plication of the model to the propagation of a load-unload pulse where the amplitude progressively decreases due to the unloading interactio n.