Title: Computational microporomechanics for phase-changing geological materials
Description: Global challenges associated with extreme climate events and increasing energy demand require significant advances in our understanding and predictive capability of coupled multi- physical processes across spatial and temporal scales. While classical approaches based on the mixture theory may shed light on the macroscopic poromechanics simulations, accurate forward predictions of the complex behavior of phase-changing geomaterials cannot be made without understanding the underlying coupling mechanisms among constituents at the microstructural scale. To precisely predict the multi-physical behaviors originated by smaller scales, fundamental understandings of the micromechanical interactions among phase constituents are crucial. Hence, this dissertation discusses mathematical and computational frameworks designed to capture coupled thermo-hydro-mechanical-fracture processes in phase-changing porous media that incorporate necessary microscopic details. To achieve this goal, this dissertation aims to introduce a practical way to investigate how phase transition and evolving microstructural attributes at small scales affect the applicability of meso- or macroscopic finite element simulations, by leveraging the phase field method to represent the regularized interfaces of phase constituents.

Firstly, a multi-phase-field microporomechanics model is presented to model the growth and thaw of ice lenses. In specific, we extend the field theory for ice lens that is not restricted to one-dimensional space. The key idea is to represent the state of the pore fluid and the evolution of freezing-induced fracture via two distinct phase field variables coupled with balance laws, which leads to an immersed approach where both the homogeneous freezing and ice lensing are distinctively captured. Secondly, a thermo-hydro-mechanical theory for geological media with thermally non-equilibrated constituents is presented, where we develop an operator-split framework that updates the temperature of each constituent in an asynchronous manner. Here, the existence of an effective medium is hypothesized, in which the constituents exhibit different temperatures while heat exchange among the phases is captured via Newton’s law of cooling. Thirdly, an immersed phase field model is introduced to predict fluid flow in fracturing vuggy porous media, where crack growth may connect previously isolated voids and form flow conduits.

In this approach, we present a framework where the phase field is not only used as a damage parameter for the solid skeleton but also as an indicator of the pore space, which enables us to analyze how crack growth in vuggy porous matrix affects the flow mechanism differently compared to the homogenized effective medium while bypassing the needs of partitioning the domain and tracking the moving interface. Finally, we present a new phase field fracture theory for higher-order continuum that can capture physically justified size effects for both the path-independent elastic responses and the path-dependent fracture. Specifically, we adopt quasi-quadratic degradation function and linear local dissipation function such that the physical size dependence are insensitive to the fictitious length scale for the regularized interface, which addresses the numerical needs to employ sufficiently large phase field length scale parameter without comprising the correct physical size effect.