Multiscale thermo-hydro-mechanical-chemical coupling effects for fluid-infiltrating crystalline solids and geomaterials: theory, implementation, and validation

Extreme climate change and demanding energy resources have led to new geotechnical engineering challenges critical for sustainable development and resilient infrastructure of our society. Applications such as geological disposal of nuclear waste and carbon dioxide, artificial ground freezing, and hydraulic fractures all require an in-depth understanding of the thermo-hydro-mechanical coupling mechanisms of geomaterials subjected to various environmental impact. This dissertation presents a multiphysical computational framework dedicated to address the issues related to those unconventional applications. Our objective is not only incorporating multiphysical coupling effects at the constitutive laws, but also taking into account the nonlocal effects originated from the flow of pore-fluid, thermal convection and diffusion among solid and fluid constituents, and crystallization and recrystallization of crystals in the pore space across length scales. By considering these coupling mechanisms, we introduce a single unified model capable of predicting complex thermo-hydro-mechanical responses of geological and porous media across wide spectra of temperature, confining pressure and loading rate. This modeling framework applies to two applications, i.e., the freezing and thawing of frozen soil and the modeling of anisotropic crystal plasticity/fracture response of rock salt. Highlights of the key ingredients of the models cover the stabilization procedure used for the multi-field finite element, the return mapping algorithm for crystal plasticity, the micromorphic regularization of the Modified Cam-Clay model, and the strategy for enhancing computational efficiency of solvers, such as pre-conditioner, adaptive meshing, and internal variable mapping. By introducing the multiphysical coupling mechanisms explicitly, our computational geomechanics model is able to deliver more accurate and consistent results without introducing a significant amount of additional material parameters. In a parallel effort, we analyze the impact of thermo-hydro-mechanical (THM) coupling effects on the dynamic wave propagation and strain localization in a fully saturated softening porous medium. The investigation starts with deriving the characteristic polynomial corresponding to the governing equations of the THM system. The theoretical analysis based on the Abel–Ruffini theorem reveals that the roots of the characteristic polynomial for the THM problem cannot be expressed algebraically. Our analysis concludes that the rate-dependence introduced by multiphysical coupling may not regularize the THM governing equations when softening occurs

Computational thermo-hydro-mechanics for multiphase freezing and thawing porous media in the finite deformation range

A stabilized thermo-hydro-mechanical (THM) finite element model is introduced to investigate the freeze–thaw action of frozen porous media in the finite deformation range. By applying the mixture theory, frozen soil is idealized as a composite consisting of three phases, i.e., solid grain, unfrozen water and ice crystal. A generalized hardening rule at finite strain is adopted to replicate how the elasto-plastic responses and critical state evolve under the influence of phase transitions and heat transfer. The enhanced particle interlocking and ice strengthening during the freezing processes and the thawing-induced consolidation at the geometrical nonlinear regimes are both replicated in numerical examples. The numerical issues due to lack of two-fold inf–sup condition and ill-conditioning of the system of equations are addressed. Numerical examples for engineering applications at cold region are analyzed via the proposed model to predict the impacts of changing climate on infrastructure at cold regions

Wave propagation and strain localization in a fully saturated softening porous medium under the non-isothermal conditions

The (THM) coupling effects on the dynamic wave propagation and strain localization in a fully saturated softening porous medium are analyzed. The characteristic polynomial corresponding to the governing equations of the THM system is derived, and the stability analysis is conducted to determine the necessary conditions for stability in both non-isothermal and adiabatic cases. The result from the dispersion analysis based on the Abel–Ruffini theorem reveals that the roots of the characteristic polynomial for the THM problem cannot be expressed algebraically. Meanwhile, the dispersion analysis on the adiabatic case leads to a new analytical expression of the internal length scale. Our limit analysis on the phase velocity for the non-isothermal case indicates that the internal length scale for the non-isothermal THM system may vanish at the short wavelength limit. This result leads to the conclusion that the rate-dependence introduced by multiphysical coupling may not regularize the THM governing equations when softening occurs. Numerical experiments are used to verify the results from the stability and dispersion analyses

Computational thermomechanics of crystalline rock, Part I: A combined multi-phase-field/crystal plasticity approach for single crystal simulations

Rock salt is one of the major materials used for nuclear waste geological disposal. The desired characteristics of rock salt, i.e., high thermal conductivity, low permeability, and self-healing are highly related to its crystalline microstructure. Conventionally, this microstructural effect is often incorporated phenomenologically in macroscopic damage models. Nevertheless, the thermo-mechanical behavior of a crystalline material is dictated by the nature of crystal lattice and micromechanics (i.e., the slip-system). This paper presents a model proposed to examine these fundamental mechanisms at the grain scale level. We employ a crystal plasticity framework in which single-crystal halite is modeled as a face-centered cubic (FCC) structure with the secondary atoms in its octahedral holes, where a pair of Na and Cl ions forms the bond basis. Utilizing the crystal plasticity framework, we capture the existence of an elastic region in the stress space and the sequence of slip system activation of single-crystal halite under different temperature ranges. To capture the anisotropic nature of the intragranular fracture, we couple a crystal plasticity model with a multi-phase-field formulation that does not require high-order terms for the phase field. Numerical examples demonstrate that the proposed model is able to capture the anisotropy of inelastic and damage behavior under various loading rates and temperature conditions

A Multi-Phase-Field Anisotropic Damage-Plasticity Model for Crystalline Rocks

Many engineering applications, such as geological disposal of nuclear waste, require reliable predictions on the thermo-hydro-mechanical responses of porous media exposed to extreme environments. This presentation will discuss the relevant modeling techniques designed specifically for such environmental conditions. In particular, we will provide an overview of the coupling method of crystal plasticity and multi-phase-field model designed to replicate the thermal- and rate-dependent damage-plasticity of crystalline rock. Special emphasis is placed on capturing the intrinsic anisotropy of salt grain in 3D with respect to damage behavior and plastic flow by incorporating the crystallographic information of salt

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

We introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain

Identifying Material Parameters for a Micro-Polar Plasticity Model Via X-Ray Micro-Computed Tomographic (Ct) Images: Lessons Learned from the Curve-Fitting Exercises

Abstract: Unlike a conventional first-order continuum model, the material parameters of which can be identified via an inverse problem conducted at material point that exhibits homogeneous deformation, a higher-order continuum model requires information from the derivative of the deformation gradient. This study concerns an integrated experimental-numerical procedure designed to identify material parameters for higher-order continuum models. Using a combination of microCT images and macroscopic stress–strain curves as the database, we construct a new finite element inverse problem which identifies the optimal value of material parameters that matches both the macroscopic constitutive responses and the meso-scale micropolar kinematics. Our results indicate that the optimal characteristic length predicted by the constrained optimization procedure is highly sensitive to the types and weights of constraints used to define the objective function of the inverse problems. This sensitivity may in return affect the resultant failure modes (localized vs. diffuse), and the coupled stress responses. This result signals that using the mean grain diameter alone to calibrate the characteristic length may not be sufficient to yield reliable forward predictions. Key words: micro-CT imaging, micro-polar plasticity, critical state, higher-order continuum, Hostun San

Effects of spatial heterogeneity and material anisotropy on the fracture pattern and macroscopic effective toughness of Mancos Shale in Brazilian tests

For assessing energy-related activities in the subsurface, it is important to investigate the impact of the spatial variability and anisotropy on the geomechanical behavior of shale. The Brazilian test, an indirect tensile-splitting method, is performed in this work, and the evolution of strain field is obtained using digital image correlation. Experimental results show the significant impact of local heterogeneity and lamination on the crack pattern characteristics. For numerical simulations, a phase field method is used to simulate the brittle fracture behavior under various Brazilian test conditions. In this study, shale is assumed to consist of two constituents including the stiff and soft layers to which the same toughness but different elastic moduli are assigned. Microstructural heterogeneity is simplified to represent mesoscale (e.g., millimeter scale) features such as layer orientation, thickness, volume fraction, and defects. The effect of these structural attributes on the onset, propagation, and coalescence of cracks is explored. The simulation results show that spatial heterogeneity and material anisotropy highly affect crack patterns and effective fracture toughness, and the elastic contrast of two constituents significantly alters the effective toughness. However, the complex crack patterns observed in the experiments cannot completely be accounted for by either an isotropic or transversely isotropic effective medium approach. This implies that cracks developed in the layered system may coalesce in complicated ways depending on the local heterogeneity, and the interaction mechanisms between the cracks using two-constituent systems may explain the wide range of effective toughness of shale reported in the literature

A Multifeatured Data-Driven Homogenization for Heterogeneous Elastic Solids

A computational homogenization of heterogeneous solids is presented based on the data-driven approach for both linear and nonlinear elastic responses. Within the Double-Scale Finite Element Method (FE2) framework, a data-driven model is proposed to substitute the micro-level Finite Element (FE) simulations to reduce computational costs in multiscale simulations. The heterogeneity of porous solids at the micro-level is considered in various material properties and geometrical attributes. For material properties, elastic constants, which are Lame’s coefficients, are subjected to be heterogeneous in the linear elastic responses. For geometrical features, different numbers, sizes, and locations of voids are considered to reflect the heterogeneity of porous solids. A database for homogenized microstructural responses is constructed from a series of micro-level FE simulations, and machine learning is used to train and test our proposed model. In particular, four geometrical descriptors are designed, based on N-probability and lineal-path functions, to clearly reflect the geometrical heterogeneity of various microstructures. This study indicates that a simple deep neural networks model can capture diverse microstructural heterogeneous responses well when given proper input sources, including the geometrical descriptors, are considered to establish a computational data-driven homogenization scheme