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Authors: Salvatore, Erminio* 
Modoni, Giuseppe* 
Andò, Edward* 
Albano, Matteo* 
Viggiani, G.* 
Title: Determination of the critical state of granular materials with triaxial tests
Issue Date: 2017
Series/Report no.: /57 (2017)
DOI: 10.1016/j.sandf.2017.08.005
Abstract: While the Critical State Locus (CSL) determined from triaxial compression tests is commonly adopted for the constitutive modelling of soil, the validity of the locus for other stress paths needs to be proved. Several authors have tried to experimentally verify whether the classical CSL representation in the stress invariants - void ratio space could be considered as unique or should depend on the loading direction, but the question is still being debated and a unique conclusion has not been convincingly drawn. In order to clarify this issue, compression and extension triaxial tests are performed on granular materials with different characteristics, namely, two homogeneously distributed sands and an assembly of steel spheres prepared under different initial conditions. The procedure for identifying the CSL is reviewed and indicates the limitations arising from strain localization (shear bands and necking). All the tests show that the materials head to systematically different traces in the e-p' and p'. -q planes when sheared under triaxial compression and extension. Searching for the reasons for this phenomenon, small samples of sand are subjected to the same tests quantifying the whole strain field with X-ray tomography and a digital image correlation. This analysis reveals an inhomogeneous pattern of deformation that is strongly affected by the presence of the two rigid frictional bases and the flexible side membrane, even for the samples deforming in an apparently uniform manner. The different localization observed for the compression and extension tests justifies the dependence of the CSL on the stress path seen on the global scale. On the other hand, a unique trace of the CSL is obtained in the volumetric e-p' plane when the void ratio is measured limitedly to the zones affected by the largest distortion.
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