Simulating spatial heterogeneity through a CT-FE mapping scheme discloses boundary effects on emerging compaction bands

Deformation experiments on porous rocks conducted at sufficiently high confining pressure may result into localized compaction. While strain localization is expected to be triggered by material heterogeneities, evidence of compaction zones propagating from the specimen boundaries is often observed, thus indicating that sample-platen friction plays a relevant role on the compaction banding patterns.

This paper aims to examine this hypothesis and quantify the relative role played by field heterogeneities and boundary effects by using a numerical replica of specimens for which compaction localization was tracked through x-ray micro-tomography. For this purpose, finite element simulations are performed, where spatially-distributed  heterogeneities of the porosity field are replicated through a computerized-tomography to finite-element (CT-FE) mapping scheme. The concept of representative elementary volume is used to extract material state variables directly from the CT scans, eventually associating each integration point to a corresponding volume in the digital image.

Full-field numerical analyses conducted on the virtual replicas show that frictionless specimens promote the onset of compaction localization in zones characterized by higher porosity (i.e., lower strength). By contrast, the presence of platen-specimen friction nearly eliminates the impact of material heterogeneities, such that compaction localization is forced to occur at the specimen boundaries. Furthermore, the analyses reveals the existence of an intermediate range of platen-specimen friction coefficient which favors the emergence of a transitional regime of strain localization at which material heterogeneity and boundary effects concurrently control the compaction banding patterns. Numerical simulations based on quasi-synthetic spatial fields have also revealed a marked dependence of the three zones on the degree of heterogeneity, showing that increasing values of boundary friction are necessary to offset the effect of material weaknesses in strongly heterogeneous samples.

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