Geomechanical Modeling of Inception and Propagation of Compaction Bands in Porous Rocks

SHAHIN, Ghassan

doi:https://doi.org/10.21985/n2-2rz0-ta87

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Geomechanical Modeling of Inception and Propagation of Compaction Bands in Porous Rocks

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The term compaction band identifies a rich variety of structural features of the Earth's crust that affect formations of sedimentary rocks. The most common definition for compaction band often found in the literature describes them as narrow planar zones of concentrated porosity reduction, which may involve limited to none shear offset between adjacent rock volumes. These structures occur through Spatio-temporal processes in media characterized by intrinsic heterogeneity which have so far eluded complete understanding. Examples include their emergence in geological settings characterized by very different tectonic regimes, and thus characterized by different subsurface stress fields and background tectonic strain. The outcomes of such variability are concentrated compaction zones with different thickness, length, and spacing. This thesis investigated compaction banding in porous rocks by means of analytical and computational geomechanics. In this context, constitutive laws based on a standard strain-hardening plasticity and involving tunable hardening and softening variables were used to reproduce the phenomenology of selected porous rocks. The model is augmented by incorporating rate effects to capture the inherent viscosity of these materials and their long-term inelastic deformability. This work led to the calibration and the assessment of the performance against data for two porous rocks, a siliciclastic sandstone and a carbonate rock, displaying a distinct hardening behavior and very different compaction band patterns. Compaction banding is simulated as a form of material instability of porous viscoplastic solids. For this purpose, the controllability theory and the mathematical tools for nonlinear differential systems are employed to develop criteria for identifying the time of incipient instability. The importance of material heterogeneity in the context of compaction localization analysis was examined on the bases of synthesized and real porosity maps connected from computerized tomography images to finite element models through a novel mapping scheme based on the concept of representative elementary volume. The analysis focused on the role played by the spatial heterogeneity in generating delayed compaction bands, determining the zones where the localized compaction nucleates, and controlling the extent of its propagation. This role is further quantified in the presence of interfering factors, specifically frictional boundaries, that could induce heterogeneous stress fields, and the bias that they could generate in the context of assessing the compaction banding characteristics. This thesis also involves numerical analyses of field-scale problems, where theoretical models are used to elucidate the interactions taking place between layers of sandstone prone to compaction localization and bounding elastic layers in multi-strata systems. Various scenarios and combinations of geological processes and tectonic settings are tested to understand the conditions promoting the coexistence of various modes of compaction banding in natural formations. The analyses of delayed compaction bands based on viscoplastic idealization revealed that pulses of overstress correspond to stages of inception and propagation of new compaction bands. Intimate relations between the spatial patterns of deformation bands and the temporal dynamics of deformation are demonstrated. While homogeneous compaction develops with decaying rates of accumulation, localized compaction occurs through stages of accelerating deformation. Spatial variations in the local yielding resistance provide hotspots for inelastic deformation, eventually generating delayed compaction bands under moderated levels of loading. Furthermore, the spatial heterogeneity is shown to play a predominant role in determining the location at which compaction banding nucleates and the extent of its propagation. In frictionless specimens, the onset of compaction localization is promoted in zones characterized by higher porosity (i.e., lower strength). Yet, this role is critically affected by the existence of interfering conditions, such as frictional boundaries in laboratory testings which were found to nearly eliminate the impact of material heterogeneities, such that compaction localization is forced to occur at the specimen boundaries. Furthermore, the analyses revealed 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. The analyses show 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. Furthermore, it was found that the effects of boundary friction can be strong enough to bias the identification of compaction banding characteristics. Field-scale simulations show that the nucleation and propagation of compaction bands in sandstone formation in multi-strata systems are influenced by the contrast elasticity of the bounding layers. As a result of Poisson effects, stiffer bounding layers promote higher mean stress and lower deviatoric stresses, eventually shifting the point of intersection of the stress path with the yield surface, and hence the angle of compaction localization. It is also shown that the sequential growth of compaction bands induces deviations in the field of local stress responses leading to varying types of compaction band along rock formations. The coexistence of various types of band, however, is generated by a rich loading history, suggesting that, contrary to some hypotheses, the sequencing of compaction band formation may not be contemporaneous. These findings feature the importance of geomechanical modeling when performed in conjunction with strain localization analyses in providing a useful guidance to explain the origin of natural formations and reduce the uncertainty involved in the geological reconstruction of field observations.

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