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Compaction banding in high-porosity limestones : Experimental observations and modelling

Abstract : The mechanical deformation of sedimentary rocks can give rise to the formation of compaction bands which can significantly affect the performance of geosystems. The objective of this thesis is to identify the formation of compaction bands in porous carbonate rocks in laboratory experiments and to propose a constitutive model based on second-gradient plasticity theory to account for the effect of local heterogeneity.Axisymmetric compression tests are combined with X-Ray Computed Tomography observations. Samples are imaged before and after several loading steps and at different confining pressure levels. Digital Volume Correlation technique is applied on consecutive images to build 3D deformation maps at a millimetric gauge length, which permit to identify strain localization zones. A simple method based on kinematic considerations is proposed to classify these zones. Compaction bands have been identified at high confining pressures, pure shear bands are obtained for low confinements whereas compactive shear bands are observed in the transitional regime. In contrast, a diffuse compaction occurs in hydrostatic loading conditions. 3D porosity maps are constructed at some intermediate meso-scale and superimposed on deformation maps. The heterogeneity of porosity is found to control the pattern of compaction bands, as they lay inside high-porosity zones and avoid denser zones. Grain crushing is identified as the main micromechanism of the deformation. Very fine particles fill the pores and induce a porosity reduction. Large pores are observed to remain intact in denser zones, as they are protected by a surrounding rigid lattice of cemented grains. When shear strain is identified in deformation bands, porosity heterogeneity is found to control the volumetric behavior. Along a compactive/pure shear band, some cracks are observed in denser zones, whereas grain crushing and pore filling are observed in the more porous zones. These mechanisms are responsible for a complex co-existence of local contractancy and dilatancy along shear bands.Standard constitutive elastic-plastic laws of homogeneous media are insufficient to model correctly compaction banding, as a zero-thickness band is obtained for rate-independent materials in a Cauchy continuum. To regularize this problem, higher-order continua (micromorphic media) can be considered, where internal lengths in relation with the microstructure are introduced in the constitutive relations. A particular issue of these models is to calibrate the higher-order parameters. In the framework of second-gradient plasticity theory, the yield surface depends on a hardening parameter, related to the plastic strain and its second gradient. The plastic porosity reduction is taken here as the hardening parameter. A calibration procedure of the additional higher-order parameters based on macroscopic mechanical data and the data provided by the X-Ray images is proposed. Once the model is calibrated, a linear stability analysis in axisymmetric triaxial loading is applied to predict the formation of compaction bands. The calibrated model is subsequently implemented in a finite element code, textit{Numerical Geolab}, to perform numerical simulations of the experiments. Numerical results are finally compared to the experimental observations
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Youssouf Abdallah. Compaction banding in high-porosity limestones : Experimental observations and modelling. Mechanics of materials [physics.class-ph]. Université Paris-Est, 2019. English. ⟨NNT : 2019PESC1024⟩. ⟨tel-02878898⟩

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