Poromechanics

Microcomputed tomography can be used to characterize the geometry of the pore space of a sedimentary rock, with resolu@on that is sufficiently refined for the realis@c simula@on of physical proper@es based on the 3D image. Significant advances have been made on the characteriza@on of pore size distribu@on and connec@vity, development of techniques such as laNce Boltzmann method to simulate permeability, and its upscaling. Sun, Andrade and Rudnicki (2011) recently introduced a mul@scale method that dynamically links these three aspects, which were oUen treated separately in previous computa@onal schemes. In this study, we improve the efficiency of this mul@scale method by introducing a flood--fill algorithm to determine connec@vity of the pores, followed by a mul@scale laNce Boltzmann/finite element calcula@on to obtain homogenized effec@ve anisotropic permeability. The improved mul@scale method also includes new capacity to consistently determine electrical conduc@vity and forma@on factor from CT images. Furthermore, we also introduce a level set based method that transforms poregeometry to finite element mesh and thus enables direct simula@on of pore--scale flow with finite element method. When applied to the microCT data acquired by Lindquist et al. (2000) for four Fontainebleau sandstone samples with porosi@es ranging from 7.5% to 22%, this mul@scale method has proved to be computa@onally efficient and our simula@ons has provided new insights into the rela@on among permeability, pore geometry and connec@vity. .

The loading of a granular material induces anisotropies of the particle arrangement (fabric) and of the material’s strength, incremental stiffness, and permeability. Thirteen measures of fabric anisotropy are developed, which are arranged in four categories: as preferred orientations of the particle bodies, the particle surfaces, the contact normals, and the void space. Anisotropy of the voids is described through image analysis and with Minkowski tensors. The thirteen measures of anisotropy change during loading, as determined with three-dimensional discrete element simulations of biaxial plane strain compression with constant mean stress. Assemblies with four different particle shapes were simulated. The measures of contact orientation are the most responsive to loading, and they change greatly at small strains, whereas the other measures lag the loading process and continue to change beyond the state of peak stress and even after the deviatoric stress has nearly reached a steady state. The paper implements a methodology for characterizing the incremental stiffness of a granular assembly during biaxial loading, with orthotropic loading increments that preserve the principal axes of the fabric and stiffness tensors. The linear part of the hypoplastic tangential stiffness is monitored with oedometric loading increments. This stiffness increases in the direction of the initial compressive loading but decreases in the direction of extension. Anisotropy of this stiffness is closely correlated with a particular measure of the contact fabric. Permeabilities are measured in three directions with lattice Boltzmann methods at various stages of loading and for assemblies with four particle shapes. Effective permeability is negatively correlated with the directional mean free path and is positively correlated with pore width, indicating that the anisotropy of effective permeability induced by loading is produced by changes in the directional hydraulic radius.

A finite strain multiscale hydro-mechanical model is established via an extended Hill–Mandel condition for two-phase porous media. By assuming that the effective stress principle holds at unit cell scale, we established a micro-to-macro transition that links the micromechanical responses at grain scale to the macroscopic effective stress responses, while modeling the fluid phase only at the macroscopic continuum level. We propose a dual-scale semi-implicit scheme, which treats macroscopic responses implicitly and microscopic responses explicitly. The dual-scale model is shown to have good convergence rate, and is stable and robust. By inferring effective stress measure and poro-plasticity parameters, such as porosity, Biot's coefficient and Biot's modulus from micro-scale simulations, the multiscale model is able to predict effective poro-elasto-plastic responses without introducing additional phenomenological laws. The performance of the proposed framework is demonstrated via a collection of representative numerical examples. Fabric tensors of the representative elementary volumes are computed and analyzed via the anisotropic critical state theory when strain localization occurs.

Many natural and man-made materials, such as sand, rock, concrete and bone, are multi-constituent, fluid-infiltrated porous solids. The failure of such materials is important for various engineering applications, such as CO2 sequestration, energy storage and retrieval and aquifer management as well as many other geotechnical engineering problems aimed to prevent catastrophic failures due to pore pressure build-up.

This dissertation investigates two mechanical aspects of fluid infiltrated porous media, i.e., the predictions of diffuse and localized failures of porous media and the heterogeneous microstructures developed after failures. We define failures as material conditions in which homogeneous deformation becomes unattainable.

To detect instabilities, a critical state plasticity model for sand is implemented. By seeking bifurcation points of the incremental, linearized constitutive responses, we establish local criteria that detect onsets of drained soil collapse, static liquefaction and formation of deformation bands under locally drained and undrained conditions. Fully undrained and drained triaxial compression simulations are conducted and the stability of the numerical specimens are assessed via a perturbation method.

To characterize deformation modes after failures, a multi-scale framework is designed to determine microstructural attributes from pore space extracted from X-ray tomographic images and improve the accuracy and speed of a multi-scale lattice Boltzmann/finite element hierarchical flow simulation algorithm. By comparing the microstructural attributes and macroscopic permeabilities inside and outside a compaction band formed in Aztec Sandstone, our numerical study reveals that elimination of connected pore space and increased tortuosity are the main causes that compaction bands are flow barriers.

A simplified method to analyze 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 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 et al 2003 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.

This chapter offers a comprehensive derivation of the constitutive equations of linear poroelasticity. A main purpose of this survey is to assist with the formulation of experimental strategies for the measurement of poroelastic constants. The complete set of linearized constitutive relations is phrased alternatively in terms of undrained bulk parameters or drained skeleton parameters. Displayed in the form of a mnemonic diagram, this can provide a rapid overview of the theory. The principal relationships between alternative sets of material parameters are tabulated, among them the well-known Gassmann or Brown-Korringa fluid substitution relations that are rederived here without any pore-scale considerations.

A fluid infiltrating porous solid is a multiphase material whose mechanical behavior is significantly influenced by the pore fluid. In particular, the diffusion, advection, capillarity, heating, cooling and freezing of pore fluid, the build-up of pore pressure and the mass exchanges among the solid and fluid constituents may all influence the stability and integrity of the solid skeleton, cause shrinkage, swelling, fracture or liquefaction. These coupling phenomena are important for numerous disciplines, including but not limited to geophysics, biomechanics, and material sciences. The objective of this course is to present the fundamental principles of poromechanics that are essential for engineering practice and to prepare students for more advanced study on porous media.

Governing equations of poroelastodynamics in time and frequency domain are derived. The continuity equation complements the momentum balance equations. After reduction for spherical symmetry (geometry and loading), the governing equations in frequency domain are solved by introducing wave potentials. The wave propagation velocities are obtained as the real parts of the characteristic equation of the coupled ODE system. Time domain solution for Dirac type boundary pressure is obtained through numerical inversion of transformed solutions. The results are compared to the solution in classical elasticity theory found in the literature.

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 non-isothermal porous media. Projection-based stabilization procedure is derived to eliminate spurious pore pressure and temperature modes due to the lack of the two-fold inf-sup condition of the equal-order finite element. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for non-isothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this thermo-hydro-mechanical model. Copyright © 2015 John Wiley & Sons, Ltd.

A stabilized enhanced strain finite element procedure for poromechanics is fully integrated with an elasto-plastic cap model to simulate the hydro-mechanical interactions of fluid-infiltrating porous rocks with associative and non-associative plastic flow. We present a quantitative analysis on how macroscopic plastic volumetric response caused by pore collapse and grain rearrangement affects the seepage of pore fluid, and vice versa. Results of finite element simulations imply that the dissipation of excess pore pressure may significantly affect the stress path, and thus alter the volumetric plastic responses.

Recent technology advancements on X-ray computed tomography (X-ray CT) offer a nondestructive approach to extract complex three-dimensional geometries with details as small as a few microns in size. This new technology opens the door to study the interplay between microscopic properties (e.g., porosity) and macroscopic fluid transport properties (e.g., permeability). To take full advantage of X-ray CT, we introduce a multiscale framework that relates macroscopic fluid transport behavior not only to porosity but also to other important microstructural attributes, such as occluded/connected porosity and geometrical tortuosity, which are extracted using new computational techniques from digital images of porous materials. In particular, we introduce level set methods, and concepts from graph theory, to determine the geometrical tortuosity and connected porosity, while using a Lattice Boltzmann/Finite Element scheme to obtain homogenized effective permeability at specimen-scale. We showcase the applicability and efficiency of this multiscale framework by two examples, one using a synthetic array and another using a sample of natural sandstone with complex pore structure.

The objective of this research is to use grain-scale numerical simulations to analyze the evolution of stress anisotropy exhibited in wetted granular matters. Multiphysical particulate simulations of unsaturated granular materials were conducted to analyze how the interactions of contact force chains and liquid bridges influence the macroscopic responses under various suction pressure and loading history. To study how formation and rupture of liquid bridges affect the mechanical responses of wetted granular materials, a series of suction-controlled triaxial tests were simulated with two grain assemblies, one composed of large particles of similar sizes, another one composed of a mixture of large particles with significant amount of fines. Our results indicate that capillary stress are anisotropic in both sets of specimens, and that the stress anisotropy is more significant in granular assemblies filled with fine particles. A generalized tensorial Bishop's coefficient is introduced to analyze the connections between microstructrual attributes and macroscopic responses. Numerical simulations presented in this paper indicate that the principal values and directions of this Bishop's coefficient tensor are path dependent.

The problem of predicting the land subsidence caused by the depletion of underground hydrocarbon reservoirs is of considerable concern to the petroleum industry in many parts of the world and has been dealt with in numerous studies over the last 40 years. When treated as a poroelastic inclusion problem, an integral representation, known as Maysel’s formula from formally analogous thermoelastic problems can provide an attractive method of solution. Maysel’s method suggests an economic approach to solving general, nonhomogeneous problems of compaction-induced stressing and surface subsidence numerically. We illustrate its use for a disk-shaped reservoir in a horizontally stratified half-space.

Poroelasticity Viscoelasticity Indentation Vocal folds a b s t r a c t It is hypothesized that the bulk viscoelasticity of soft tissues is determined by two lengthscale-dependent mechanisms: the time-dependent response of the extracellular matrix (ECM) proteins at the nanometer scale and the biophysical interactions between the ECM solid structure and interstitial fluid at the micrometer scale. The latter is governed by poroelasticity theory assuming free motion of the interstitial fluid within the porous ECM structure. In a recent study (Heris, H.K., Miri, A.K., Tripathy, U., Barthelat, F., Mongeau, L., 2013. J. Mech. Behav. Biomed. Mater.), atomic force microscopy was used to measure the response of porcine vocal folds to a creep loading and a 50-nm sinusoidal oscillation. A constitutive model was calibrated and verified using a finite element model to accurately predict the nanoscale viscoelastic moduli of ECM. A generally good correlation was obtained between the predicted variation of the viscoelastic moduli with depth and that of hyaluronic acids in vocal fold tissue. We conclude that hyaluronic acids may regulate vocal fold viscoelasticity. The proposed methodology offers a characterization tool for biomaterials used in vocal fold augmentations.

This paper presents a multi-scale analysis of a dilatant shear band using a three dimensional discrete element method and a lattice Boltzmann/finite element hybrid scheme. In particular, three dimensional simple shear tests are conducted via the discrete element method. A spatial homogenization is performed to recover the macroscopic stress from the micro-mechanical force chains. The pore geometries of the shear band and host matrix are quantitatively evaluated through morphology analyses and lattice Boltzmann/finite element flow simulations. Results from the discrete element simulations imply that grain sliding and rotation occur predominately with the shear band. These granular motions lead to dilation of pore space inside the shear band and increases in local permeability. While considerable anisotropy in the contact fabric is observed within the shear band, anisotropy of the permeability is, at most, modest in the assemblies composed of spherical grains.

The development of reliable experimental techniques for characterization of chemoporomechancial shale-fluid interactions is important for the design of drilling fluids that maximize shale stability. In this context, testing of millimeter-scale specimens is promising because small specimens require shorter test durations and are more readily available from offcuts of preserved core or potentially from drill cuttings or wellbore cave-in material than larger core plugs that are required for more conventional experimentation. Here we present experiments wherein we measure the axial displacement of 4 mm long by 4 mm diameter cylindrical shale specimens that are subjected firstly to a mechanical axial loading and then to an osmotic loading associated with a sudden increase in the salinity of the surrounding fluid. The response to both stages of loading is consistent with theoretical, chemoporoelastic predictions. In particular, the model predicts two types of behavior depending on the ratio between the reflection coefficient and the so-called chemomechanical coupling coefficient that quantifies the volumetric strain as a result of a change in ion content. Consistent with predictions, both monotonic shrinkage and initial shrinkage followed by partial recovery are observed in our testing campaign which includes 20 shales from a variety of geological settings. Quantitative characterization is also carried out by selecting chemoporoelastic parameter values that minimize the mismatch between the data and the model. The results show that the reflection coefficient and the chemomechanical coupling parameter are correlated with each other and with both the Cation Exchange Capacity (CEC) and the Specific Surface Area (SSA). Based on the consistency of the data from test to test and with the model, together with the fact that the key chemoporoelastic coefficients are sensibly correlated with CEC and SSA, we conclude that these millimeter-scale experiments are able to provide useful characterization for better understanding and predicting shale-fluid interactions.

As observed in reconstructed 3D images of the field compaction bands (Lenoir et al 2010), their formation may cause a significant reduction in porosity and permeability. This paper describes essential a lattice Boltzmann/finite element model that may be advantageous for calculating effective permeability of compaction bands from obscured structure in a cost-efficient way. The pressing issues include the homogenization technique and the scale effect of the effective permeability.

Fine-migration-induced permeability damage in geological reservoirs is a critical problem in several environmental and energy operations. This study presents a novel numerical model aimed at predicting the hydro-mechanical response of a saturated porous formation containing fines to injection-induced fluid flow. The proposed model contains two novel components: incorporation of spatiotemporal fluid flow in the porous formation, and integration of the coupled interactions between the poroelastic response of the saturated porous formation and fine mobilization, migration, and straining. The modified particle detachment model has been adopted, using the maximum retention function for a monolayer of size-distributed fines. The results from the proposed model reveal that incorporation of the fines migration, mobilization, and straining has a substantial impact on in situ pore pressures (~ 65% higher pore pressures were predicted at wellbore vicinity after 1 h injection when incorporating particle straining). The findings also depict a lower fine-migration-induced permeability damage when incorporating the poroelastic response of the porous layer to injection flow. Coupled interactions between geomechanical response of porous media and migration of in situ fines under injection. Higher injection-induced pore pressures when incorporating particle mobilization and straining. Reduction in fine-migration-induced permeability damage due to poroelastic response of injection layer. Coupled interactions between geomechanical response of porous media and migration of in situ fines under injection. Higher injection-induced pore pressures when incorporating particle mobilization and straining. Reduction in fine-migration-induced permeability damage due to poroelastic response of injection layer.

An adaptively stabilized finite element scheme is proposed for a strongly coupled hydro-mechanical problem in fluid-infiltrating porous solids at finite strain. We first present the derivation of the poromechanics model via mixture theory in large deformation. By exploiting assumed deformation gradient techniques, we develop a numerical procedure capable of simultaneously curing the multiple locking phenomena related to shear failure, incompressibility imposed by pore-fluid and/or incompressible solid skeleton, and yet produce solutions that satisfy the inf-sup condition. The template based generic programming and automatic differentiation techniques used to implement the stabilized model are also highlighted. Finally, numerical examples are given to show the versatility and efficiency of this model.

Molecular simulation of adsorption of water molecules in nanoporous amorphous biopolymers, e.g., cellulose, reveals nonlinear swelling and nonlinear mechanical response with the increase in fluid content. These nonlinearities result from hydrogen bond breakage by water molecules. Classical poroelastic models, employing porosity and pore pressure as basic variables for describing the "pore fluid," are not adequate for the description of these systems. There is neither a static geometric structure to which porosity can sensibly be assigned nor arrangements of water molecules that are adequately described by giving them a pressure. We employ molar concentration of water and chemical potential to describe the state of the "pore fluid" and stress-strain as mechanical variables. A thermodynamic description is developed using a model energy function having mechanical, fluid, and fluid-mechanical coupling contributions. The parameters in this model energy are fixed by th...

Bone is a complex material showing a hierarchical and porous structure but also a natural ability to remodel thanks to cells sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to represent the bone response under mechanical solicitation. It relies on the homogenization technique, simulating bone as a homogeneous structure having a porous microstructure saturated with bone fluid. The numerical modeling of the loading of a finite volume of bone enables the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the study of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is kept inside the structure) and quantified through this model. The presented poroelastic numerical model is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling.

Subsidence in Yunlin County, Taiwan, is serious and continuous. The Taiwan High Speed Rail (THSR) route crosses the subsidence area and might be affected by differential settlements. It is important to evaluate the pumping quantity for water resource management and to predict the subsidence for land resource management to mitigate the subsidence problem in Taiwan. This study combines first-order second-moment (FOSM) stochastic poroelastic theory with nonlinear parameters to develop a FOSM nonlinear stochastic poroelastic model and applies it to quantify groundwater pumping and future subsidence with uncertainty. The additional loading and discharge are evaluated by fitting the subsidence historical data to the numerical model. The results show that the proposed model well describes the subsidence behavior and quantifies groundwater pumping. However, the numerical results are larger than the monitoring data at various depths, which might be due to the different compaction situations in individual formations of the aquifer system. The predicted subsidence at the Yuanchang monitoring well is the largest (0.32 ± 0.52 m in 2020) with consideration of the climate change effects, achieved by adding an additional discharge of 31.7 %. The large uncertainty is caused by the large variation of hydraulic conductivity caused by the heterogeneity of the aquifer system, which could be improved by doing more experiments or using a conditioned model. The information provided in this study is useful for the safety of THSR and for land and groundwater resource management in Yunlin County, Taiwan.

The combined study of effects of poroelasticity and couple stresses on the performance of lubrication aspects of porelastic bearings in general and that of synovial joints in particular are analyzed. The modified form of Reynolds equation which incorporates the elastic nature of cartilage and Stokes couple-stress fluid as lubricant is derived and solved using a recently developed wavelet multigrid method. This method has greatest advantage of minimizing the errors using wavelet transforms in obtaining accurate solution as grid size tends to zero. It is found that, 6-7 cycles are required to obtain a reasonably accurate solution in the multigrid scheme, whereas, only one cycle is required to obtain the solution in the wavelet-multigrid method. Also, matrix of discrete wavelet-transform acts as a natural preconditioner producing rapid convergence. It is observed that, the poroelastic bearings with couple-stress fluid as lubricant provide enhancement in pressure and ensure the increased load carrying capacity compared with viscous fluids. This may be one of the reasons in the efficient lubrication and proper functioning of synovial joints.

Many problems in subsurface rocks which are naturally filled with saturated cracks and pores (with one or more fluid phases) are better understood in a poroelastic framework. Displacement discontinuity method (DDM) is particularly ideal for problems involving fractures and discontinuities. However, the DDM in its original form is limited to elastic problems. The paper derives fundamental solutions of a poroelastic DDM. Then introduces a numerical formulation and implementation for the poroelastic DDM in a code named constant element poroelastic DDM (CEP-DDM). The accuracy and validity of the proposed solution and the newly developed code is verified by an analytical solution at short-time and long-time. Numerical results showed good agreement with analytical results at short time (undrained response) and long time (t = 8000 s) (drained response). A crack propagation scheme for crack propagation problems is introduced and demonstrated in an example which enables the code to follow crack propagation in time and space.

19 20 Seismic waves have been observed to increase the permeability in fractured 21 aquifers. A detailed, predictive understanding of the process has been hampered by 22 a lack of constraint on the primary physical controls. What aspect of the oscillatory 23 forcing is most important in determining the magnitude of the permeability 24 enhancement? Here we present laboratory results showing that flow rate is the 25 primary control on permeability increases in the laboratory. We fractured Berea 26 sandstone samples under triaxial stresses of tens of megapascals, and applied 27 dynamic fluid-stresses via pore pressure oscillations. In each experiment, we varied 28 either the amplitude or the frequency of the pressure changes. Amplitude and 29 frequency each separately correlated with the resultant permeability increase. More 30 importantly, the permeability changes correlate with the flow rate in each 31 configuration, regardless of whether flow rate variations were driven by varying 32 amplitude or frequency. We also track the permeability evolution during a single set 33 of oscillations by measuring the phase lags (time delays) of successive oscillations. 34 Interpreting the responses with a poroelastic model shows that 80% of the 35 permeability enhancement is reached during the first oscillation and the final 36 permeability enhancement scales exponentially with the imposed change in flow 37 rate integrated over the rock volume. The establishment of flow rate as the primary 38 control on permeability enhancement from seismic waves opens the door to 39 quantitative studies of earthquake-hydrogeological coupling. The result also 40 3 suggests that reservoir permeability could be engineered by imposing dynamic 41 stresses and changes in flow rate. 42 43 I. Introduction 44 45 Transient permeability enhancement produced by dynamic stresses is now a well-46 documented observation in fractured aquifers (Elkhoury et al., 2006; Xue et al., 47 2013; Lai et al., 2014). These studies show that shaking of the shallow crust during 48 the passage of seismic waves generates transient permeability enhancement. A 49 better understanding of this complex coupling between the fractured aquifer 50 properties and the dynamic stresses is important for both fundamental and applied 51 sciences. The fluid and pressure redistributions associated with the change in 52 permeability may destabilize critically stressed faults (

An extension of a mathematical model for non-isothermal multiphase materials to consider the dissolution of air in liquid water and air mass sources during its desorption at lower water pressure is presented. The solid skeleton is assumed elasto-plastic; heat, water and air flows and water phase changes are taken into account. Physics of air dissolution and water cavitation in porous media is discussed. A numerical example where cavitation develops during strain localization in undrained water saturated dense sands is solved with the developed model as discretized in space and time with the Finite Element Method.

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 influence 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 hydrocarbon 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. In the paper " Poromechanical cohesive surface element with elastoplasticity for modeling cracks and interfaces in fluid-saturated geomaterials, " written by Regueiro, Wang, Sweetser, and Jensen, a multiphysical cohesive element is introduced to capture the multiphysical responses of fluid-saturated geomaterials. While the solid constitutive response of the cohesive surface element is governed by a traction-separation law, the effective hydraulic conductivity of the embedded strong discontinuity depends on the mechanical aperture, the distance between the upper and lower surfaces of the fracture. The numerical examples have shown that such a numerical treatment is useful for capturing the hydro-mechanical responses of existing cracks as well as interface between soil and foundation. In the cases where cracks or shear slip may propagate and the evolving crack geometry is not known a priori, a proper algorithm to predict the onset, propagation direction, and branching of the cracks without injecting mesh bias is essential. In the paper " Simulating fragmentation and fluid-induced fracture in disordered media using random finite-element meshes, " by Bishop, Martinez, and Newell, a computational approach based on random close-packed Voronoi tessellations is introduced to simulate fracture initiation, propagation and coalescence. By using meshes discretized by polygon finite elements to minimize mesh bias, the authors have demonstrated that the proposed algorithm is able to replicate complex fluid patterns. Their results indicate that the simulations based on this new approach may achieve mesh convergence in a weak or distributed sense. At the reservoir or field scale, explicitly modeling each individual crack over a large volume becomes unfeasible due to high computational cost. The authors of the paper " Multiscale model for damage-fluid flow in fractured porous media, " Wan and Eghbalian, attempt to provide closed-form solutions to predict the homogenized responses of fractured porous media distributed with strong discontinuities. By incorporating shape and orientation of the distributed cracks into the up-scaling process, macroscopic mechanical and hydraulic properties of the effective medium are obtained solely from those of the micro-constituents.

Objective: To investigate the relevance of the human vertebral endplate poromechanics on the fluid and metabolic transport from and to the intervertebral disc (IVD) based on educated estimations of the poromechanical parameter values of the bony endplate (BEP).

A stabilized enhanced strain finite element procedure for poromechanics is fully integrated with an elasto-plastic cap model to simulate the hydro-mechanical interactions of fluid-infiltrating porous rocks with associative and non-associative plastic flow. We present a quantitative analysis on how macroscopic plastic volumetric response caused by pore collapse and grain rearrangement affects the seepage of pore fluid, and vice versa. Results of finite element simulations imply that the dissipation of excess pore pressure may significantly affect the stress path and thus alter the volumetric plastic responses.

Intervertebral disc metabolic transport is essential to the functional spine and provides the cells with the nutrients necessary to tissue maintenance. Disc degenerative changes alter the tissue mechanics, but interactions between mechanical loading and disc transport are still an open issue. A poromechanical finite element model of the human disc was coupled with oxygen and lactate transport models. Deformations and fluid flow were linked to transport predictions by including strain-dependent diffusion and advection. The two solute transport models were also coupled to account for cell metabolism. With this approach, the relevance of metabolic and mechano-transport couplings were assessed in the healthy disc under loading-recovery daily compression. Disc height, cell density and material degenerative changes were parametrically simulated to study their influence on the calculated solute concentrations. The effects of load frequency and amplitude were also studied in the healthy disc by considering short periods of cyclic compression. Results indicate that external loads influence the oxygen and lactate regional distributions within the disc when large volume changes modify diffusion distances and diffusivities, especially when healthy disc properties are simulated. Advection was negligible under both sustained and cyclic compression. Simulating degeneration, mechanical changes inhibited the mechanical effect on transport while disc height, fluid content, nucleus pressure and overall cell density reductions affected significantly transport predictions. For the healthy disc, nutrient concentration patterns depended mostly on the time of sustained compression and recovery. The relevant effect of cell density on the metabolic transport indicates the disturbance of cell number as a possible onset for disc degeneration via alteration of the metabolic balance. Results also suggest that healthy disc properties have a positive effect of loading on metabolic transport. Such relation, relevant to the maintenance of the tissue functional composition, would therefore link disc function with disc nutrition.

Bending an elastic beam leads to a complicated 3D stress distribution, but the shear and transverse stresses are so small in a slender beam that a good approximation is obtained by assuming purely uniaxial stress. In this paper, we demonstrate that the same is true for a saturated poroelastic beam. Previous studies of poroelastic beams have shown that, to satisfy the Beltrami-Michell compatibility conditions, it is necessary to introduce either a normal transverse stress or shear stresses in addition to the bending stress. The problem is further complicated if lateral diffusion is permitted. In this study, a fully coupled finite element analysis (FEA) incorporating the lateral diffusion effect is presented. Results predicted by the "exact" numerical solution, including load relaxation, pore pressure, stresses and strains, are compared to an approximate analytical solution that incorporates the assumptions of simple beam theory. The applicability of the approximate beam-bending solution is investigated by comparing it to FEA simulations of beams with various aspect ratios. For "beams" with large width-to-height ratios, the Poisson effect causes vertical deflections that cannot be neglected. It is suggested that a theory of plate bending is needed in the case of poroelastic media with large width-to-height ratios. Nevertheless, use of the approximate solution yields very small errors over the range of width-to-height ratios (viz, 1-4) explored with FEA.