Preface: Computational Poromechanics

This special issue of the International Journal for Multiscale Computational Engineering is dedicated to the field of computational poromechanics. We refer to the term poromechanics as a discipline that studies the coupled responses of multiphase materials that contain voids filled with one or multiple types of fluids. Materials fitting this description include many geological materials (e.g., sand, clay, and rock), live matters (e.g., bones, skins, periodontal ligament), and manufactured materials (e.g., concrete, diaper cores, and polymeric gels), among others. Inside a porous medium, the fluids in the voids may either be trapped inside the isolated pores or they may diffuse in the connected pore space. The multiple fluid constituents may also trigger chemical reactions among themselves or with the solid constituents. As a result, the deformation of the solid skeleton and the diffusion of the pore fluid are processes that strongly in- fluence each other. This coupling effect is important for many engineering applications central to our daily lives. For instance, the buildup of the pore fluid pressure may lead to the fracture of the solid constituent, which in return allows hydro-carbon to be extracted, as in the case of hydraulic fracture. If an enormous amount of fluid is injected underground, the resultant pore pressure buildup may also reactivate previously stable faults due to the reduction of effective mean pressure. Meanwhile, the hydro-mechanical coupling effect has also been used to characterize hydraulic properties that are difficult to obtain otherwise. For instance, one may indirectly estimate the effective permeability of the porous medium by examining the stress history of a given load, such as bending load applied on a beam or indentation applied on a poro-elastic half-space. The aforementioned engineering applications are just a few examples in which the knowledge of poromechanics is crucial. In recent years, the advancement of computational resource and the availability of more accurate and detailed experimental data and in situ data has made it possible to develop models with a new level of sophistication and a justifiable complexity. Meanwhile, new engineering challenges, such as geological disposal of captured carbon dioxide, nuclear waste, and the development of horizontal wellbores for hydraulic fractures, and forensic geotechnical engineering have motivated a growing interest to incorporate numerical modeling as an integral part of engineering design and analysis.This special issue provides a forum for presenting the state-of-the-art computational modeling for porous media

A unified method to predict diffuse and localized instabilities in sands

A simplified method to analyse diffuse and localized bifurcations of sand under drained and undrained conditions is presented in this paper. This method utilizes results from bifurcation analysis and critical state plasticity theory to detect the onset of pure and dilatant shear band formation, static liquefaction and drained shear failures systematically. To capture the soil collapse observed in experiments, the instability state line concept originated by Chu, Lo and Lee in 1993 is adopted. Emphasis is given to examine how the presence of pore-fluid may facilitate or delay instability after yielding occurs. The predictions of instabilities are compared with experimental data from triaxial compression tests on Toyoura and Changi sands

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 mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics

Under a pure tensile loading, cracks in brittle, isotropic, and homogeneous materials often propagate such that pure mode I kinematics are maintained at the crack tip. However, experiments performed on geo-materials, such as sedimentary rock, shale, mudstone, concrete and gypsum, often lead to the conclusion that the mode I and mode II critical fracture energies/surface energy release rates are distinctive. This distinction has great influences on the formation and propagation of wing cracks and secondary cracks from pre-existing flaws under a combination of shear and tensile or shear and compressive loadings. To capture the mixed-mode fracture propagation, a mixed-mode I/II fracture model that employs multiple critical energy release rates based on Shen and Stephansson, IJRMMS, 1993 is reformulated in a regularized phase field fracture framework. We obtain the mixed-mode driving force of the damage phase field by balancing the microforce. Meanwhile, the crack propagation direction and the corresponding kinematics modes are determined via a local fracture dissipation maximization problem. Several numerical examples that demonstrate the mode II and mixed-mode crack propagation in brittle materials are presented. Possible extensions of the model capturing degradation related to shear/compressive damage, as commonly observed in sub-surface applications and triaxial compression tests, are also discussed

Shift boundary material pointmethod: an image-to-simulation workflow for solids of complex geometries undergoing large deformation

We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries in the geometrically nonlinear regime. While the material point method is used to circumvent the mesh distortion issues commonly exhibited in Lagrangian meshes, a shifted domain technique originated fromMain and Scovazzi (J Comput Phys 372:972–995, 2018) is used to represent the boundary conditions implicitly via a level set or signed distance function. Consequently, this method completely bypasses the need to generate high-quality conformal mesh to represent complex geometries and therefore allows modelers to select the space of the interpolation function without the constraints due to the geometric need. This important simplification enables us to simulate deformation of complex geometries inferred from voxel images. Verification examples on deformable body subjected to finite rotation have shown that the new shifted domain material point method is able to generate frame-indifferent results. Meanwhile, simulations using micro-CT images of a Hostun sand have demonstrated that this method is able to reproduce the quasi-brittle damage mechanisms of single grain without the excessively concentrated nodes commonly displayed in conformal meshes that represent 3D objects with local fine details

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

Modeling deformation bands in thermal softening and fluid infiltrating porous solids at finite strain

Onset and modes of deformation bands are often influenced by nonmechanical loading triggered by seepage of pore fluid and thermal effects. Experimental evidence has established that temperature changes can alter the shape and size of the yield surface and cause shear band to form in geomaterials that are otherwise stable. Understanding this thermo-hydro-mechanical responses are important for many engineering applications, such as carbon dioxide storage and extraction of hydrocarbon in which hot or cool fluid are often injected into deep porous rock formations. The purpose of this research is to simulate this coupled process using a thermoporoplasticity model with extended hardening rules. A key feature of this model is that evolution of internal variables is governed by both the plastic dissipation and the change of temperature. An adaptively stabilized monolithic finite element model is proposed to simulate the fully coupled thermo-hydro-mechanical behavior of porous media undergoing large deformation. We first formulate a finite-deformation thermo-hydro-mechanics field theory for nonisothermal porous media. The corresponding (monolithic) discrete problem is then derived adopting low-order elements with equal order of interpolation for the three coupled fields. A projection based stabilization procedure is designed to eliminate spurious pore pressure and temperature modes due to the lack of the two-fold inf–sup condition of the equal-order finite elements. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for nonisothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this model

A unified variational eigen-erosion framework for interacting brittle fractures and compaction bands in fluid-infiltrating porous media

The onset and propagation of the cracks and compaction bands, and the interactions between them in the host matrix, are important for numerous engineering applications, such as hydraulic fracture and CO2 storage. While crack may become flow conduit that leads to leakage, formation of compaction band often accompanies significant porosity reduction that prevents fluid to flow through. The objective of this paper is to present a new unified framework that predicts both the onset, propagation and interactions among cracks and compaction bands via an eigen-deformation approach. By extending the generalized Griffith’s theory, we formulate a unified nonlocal scheme that is capable to predict the fluid-driven fracture and compression-driven anti-crack growth while incorporating the cubic law to replicate the induced anisotropic permeability changes triggered by crack and anti-crack growth. A set of numerical experiments are used to demonstrate the robustness and efficiency of the proposed model

A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking

This manuscript introduces a unified mathematical framework to replicate both desiccation-induced and hydraulic fracturing in low-permeable unsaturated porous materials observed in experiments. The unsaturated porous medium is considered as a three-phase solid–liquid–gas effective medium of which each constituent occupies a fraction of the representative elementary volume. As such, an energy-minimization-based phase-field model (PFM) is formulated along with the Biot’s poroelasticity theory to replicate the sub-critical crack growth in the brittle regime. Unlike hydraulic fracturing where the excess pore liquid pressure plays an important role at the onset and propagation of cracks, desiccation cracks are mainly driven by deformation induced by water retention. Therefore, the wettability of the solid skeleton may affect the evolution of the capillary pressure (suction) and change the path-dependent responses of the porous media. This air–water–solid interaction may either hinder or enhance the cracking occurrence. This difference of capillary effect on crack growth during wetting and drying is replicated by introducing retention-sensitive degradation mechanisms in our phase field fracture approach. To replicate the hydraulic behaviors of the pore space inside the host matrix and that of the cracks, the path-dependent changes of the intrinsic permeability due to crack growth and porosity changes are introduced to model the flow conduit in open and closed cracks. Numerical examples of drying-induced and hydraulic fracturing demonstrate the capability of the proposed model to capture different fracture patterns, which qualitatively agrees with the fracture mechanisms of related experiments documented in the literature