Modeling and quantification of anisotropy and heterogeneity in geomaterials

Geomaterials such as soils and rocks are inherently anisotropic, heterogeneous, sensitive to changes in temperature, and prone to strain localization, a common manifestation of material instability that has been linked traditionally to failure of materials. Accurate prediction of strength in geomaterials with distinct bedding planes requires knowledge of the bedding plane orientation relative to that of the load. In addition, thermal softening is known to have significant influence on the strength and strain localization properties of geomaterials. In this work, a thermoplastic framework is developed for modeling the coupled thermo-mechanical response and predicting the inception of shear band in transversely isotropic materials using the general framework of critical state plasticity. The formulation incorporates anisotropy in both elastic and plastic responses under the assumption of infinitesimal deformation. The model is first calibrated using experimental data from triaxial tests to demonstrate its capability in capturing anisotropy in the mechanical response. Simulations of strain localization are carried out under two different conditions, namely, isothermal localization and adiabatic localization. The adiabatic formulation investigates the effect of temperature on localization via thermo-mechanical coupling. Numerical simulations are presented to demonstrate the important role of anisotropy, hardening, and thermal softening on strain localization inception and orientation. Subsequently, simulations of the strength of two rocks, namely, Tournemire shale and a simulated transversely isotropic rock, suggest that the mechanical model can reproduce the general U-shaped variation of rock strength with bedding plane orientation quite well. It is shown that strength and shear band formation depend on many factors, including the stress loading condition, anisotropy parameters, and thermal effects. Geomaterials are also highly heterogeneous and consist of various phases that form complex structures persisting at multiple scales. Another portion of this work focuses on multi-scale quantification of heterogeneity in nanoporous geomaterials using high-resolution imaging techniques. For this purpose, Transmission X-ray microscopy and X-ray micro-tomography were used to image samples of Woodford shale, a nanoporous rock, at the length scales ranging from nano-meters to millimeters. While high-resolution imaging is crucial for characterizing the microstructure of this rock, it is generally not feasible to image a large sample at a high resolution over a large field of view (FOV), thus limiting characterization of the microstructure of this material. In this work, a stochastic framework is developed based on multiple-point statistics that uses high-resolution training images to enhance low-resolution images obtained over a large FOV. Comparison of the simulation results with true high-resolution images shows that the method can offer a solution to the trade-off between imaging resolution and FOV associated with imaging of heterogeneous materials. The described multi-scale imaging approach has vast applications to computational modeling such as computational homogenization, mesh sensitivity studies and multi-scale modeling methods.

Advisor: Borja Ronaldo I. (Ronaldo Israel)
Deierlein Gregory G. (Gregory Gerard)
Linder Christian (Engineering professor)