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Micromechanical analysis of state variables for phenomenological constitutive models of soils

Subject Area Geotechnics, Hydraulic Engineering
Term from 2014 to 2021
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 254872581
 
Final Report Year 2021

Final Report Abstract

The majority of constitutive models, that are used nowadays to describe the behaviour of granular materials such as sands, are continuum models based on phenomenological approaches. In order to describe some of the phenomena occurring on the macroscopic scale, e.g., the abrupt change of stiffness due to a load reversal, constitutive models use phenomenological state variables (e.g., the inter-granular strain concept). These often lack a clear physical meaning. The mechanisms that control the macroscopic behaviour must be sought at the grain-scale with the interactions of individual particles playing the key-role. To access that scale and describe the fabric of granular assemblies, x-ray µ-computed tomography was used in this project for full-field measurements during monotonic and cyclic experiments. This non-destructive technique allows to acquire 3D images at various stages of the loading and thus, a tracking of the evolution of the fabric. The spatial resolution of such tomographies is limited as the specimen has to be mechanically representative and at the same time sufficiently small to identify individual grains in the images. Different image analysis techniques can be used to extract information on the fabric of the granular material, but they all lack a thorough metrological characterisation, especially regarding the limited spatial resolution. Therefore, it was necessary to study the different techniques and determine their uncertainties before running the experiments and evaluating the tomographies. Artificial as well as high resolution images serve as the basis of the metrological analysis which showed that the standard approaches for the analysis of contact orientations, implemented in most commercial software, strongly suffer in accuracy and often introduce huge artefacts. New techniques to refine these measures were proposed and validated on the same images. Monotonic triaxial compression tests on two different sands were studied regarding the localisation of deformation in terms of the contact fabric. The complete fabric tensor was determined inside and outside of the developing shear band throughout the experiment. Its evolution was expressed by the anisotropy and related to the macroscopic response. The specimen appears to behave homogeneously in the different zones until the onset of the localisation at which the fabric diverges. Outside of the shear band it stays relatively constant whereas it seems directly related to the stress ratio inside the shear band. The anisotropy captures the characteristic evolution of the stress response, such as peak states and softening. A series of triaxial compression tests with load reversals was conducted on specimens consisting of sand grains and glass beads. To capture the fabric response to the cycles, tomographies were acquired before and after unloading and after reloading. As opposed to numerical simulations, no large changes of the fabric during the load cycles could be observed. Qualitatively, the fabric changes similar to the numerical simulations: the anisotropy decreases upon unloading and increases upon reloading. The incremental response to each reversal was compared to the numerical simulations and the evolution of the inter-granular strain tensor for similar conditions. The latter was determined by a simplified element test with the aim of possibly relating this phenomenological variable to a truly structural one. The comparison of the evolution of the fabric and the inter-granular strain, however, showed major differences, based on which such a relation is not possible. The fabric evolves at a slower rate than the state variable and continues to evolve even throughout monotonic loading situations.

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