Characterisation of the heterogeneity of a sand specimen in triaxial compression using x-ray CT and representative elementary volumes

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4. Characterisation of the heterogeneity of a sand specimen in triaxial compression using x-ray CT and representative elementary volumes

Triaxial tests are commonly considered to be element tests. But, when observing such a test, it becomes obvious that the soil behaviour is far from homogeneous: a single or even multiple globally visible shear bands often develop inside the specimen. To better understand the mechanisms behind such localisation phenomena, researchers began to study the micro-scale, i.e. the grain-scale, already several decades ago. The rise of x-ray computed tomography (CT) and especially micro-focus CT (CT) finally facilitated the observation of individual grain kinematics. CT also enabled the study of fabric, such as the contact fabric, i.e. the number and orientation of grain contacts, which is closely connected to the transmission of forces inside the specimen. The localisation of the contact fabric is, as opposed to the kinematics, not visible to the naked eye but can be observed when the soil fabric is analysed on a local level.

For this purpose, the size of an observation window, whose properties are representative of the investigated region of the specimen, is determined. Such a representative elementary volume (REV) is then placed in a regular grid throughout the specimen, to characterise the heterogeneity of the studied variable, in this case the contact fabric. There are several different approaches to determine the size of a REV. Here, a combination of three criteria, namely the convergence of the mean and the variance of a variable at different locations inside the specimen as well as a chi²-test, is used to reliably find a REV. The REV is determined for different loading states and variables. The variables describing the contact fabric, i.e. coordination number and contact orientation anisotropy, are compared to a traditionally analysed variable, i.e. void ratio. One final REV-size is determined for each variable.

The heterogeneity of the studied variables is identified for several loading states throughout a triaxial test and the evolution of this heterogeneity is observed. This allows for an investigation of the localisation phenomena on a spatial and temporal level. A localisation of all three variables is observed as well as a strong initial heterogeneity, especially regarding the contact orientation anisotropy, confirming the hypothesis that the soil behaves heterogeneously from very early on. The final width of the localisation zone as well as the onset of this localisation is different for the studied variables indicating a varying sensitivity to changes inside the specimen.

8th International Symposium on Deformation Characteristics of Geomaterials (ISDCG2023)

I.4) Data interpretation and geotechnical imaging