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Although imperceptible at the macroscale, fluctuations of physical properties are ubiquitous at the nanoscale because of thermal agitation. While fluctuations are detrimental to the accuracy of molecular simulations, their magnitude is actually a great source of information since it quantifies the elasticity of the system with respect to any evolution of the control variables. Fluctuation formulas are well known for fluids or solids but have not yet been derived for porous media. In this article, we derive fluctuation formulas for all the moduli involved in thermoporoelasticity. These fluctuation formulas are applicable even for adsorbing media and can be used for poroelasticity extended to adsorption, whereas usual poroelasticity assumes a bulk fluid in the pores. Moreover, the practical application of the fluctuation formulas in molecular simulation is straightforward, as one only needs to collect extensive quantities readily accessible and at almost no additional computational cost. The application of these fluctuation formulas is illustrated by considering a typical example of mechanosorption coupling, namely, amorphous cellulose submitted to moisture at various relative humidities. The thermoporoelastic behavior is fully characterized from the fluctuations computed during molecular simulation of amorphous cellulose. Some peculiarities of moisture-induced behavior of cellulose are discussed, such as the high Biot coefficient, the negative Biot modulus, the negative thermal expansion, and the high heat capacity. This work investigates only the case of a pure fluid in the pores with volumetric deformations but can be easily extended to fluid mixture and shearing effects. [ABSTRACT FROM AUTHOR]

The linear two-dimensional problem of flexural-gravity waves generated by an oscillating rigid plate build-in a floating poroelastic plate is studied. The problem is coupled. The plate deflections and the hydrodynamics loads are determined at the same time. The liquid under the poroelastic plate is inviscid and incompressible. Dynamics of the floating plate is described by a thin elastic plate equation. Porosity of the floating plate is taken into account only through the liquid flux into the plate. The velocity of the inflow is assumed to be governed by Darcy's law being proportional to the hydrodynamic pressure at the plate/liquid interface. Two cases of the oscillating rigid plate with and without its part in the liquid are considered. The problems are solved by the Fourier transform method for non-zero porosity and by the vertical mode method for elastic plates with zero porosity. The deflection and strain distributions are analyzed depending on the excitation frequency and the porosity. Two models of floating plate porosity, where the hydrostatic pressure is included into Darcy's law (Zavyalova's model) and excluded (Meylan's model), are compared. Plate porosity induces damping to the system. It is shown that the damping rate is non-monotonic with respect to the plate porosity. [ABSTRACT FROM AUTHOR]

This paper presents an electrochemical–thermal–hydraulic–mechanical (ETHM) coupling model by introducing the electrolyte flow field into the model of lithium-ion batteries (LIBs). First, the ETHM coupling model is established on the basis of the electrochemical–thermal–mechanical (ETM) coupling model and poroelasticity model. Then, the ETHM coupling model for the discharge of LIBs is numerically resolved and verified against the ETM coupling model using the commercial 11.5 Ah LiMn2O4 battery as an example. Subsequently, the flow and deformation characteristics (such as the Darcy's velocity, the pore pressure, the Péclet number, and the volumetric strain) are analyzed. The results suggest that the electrolyte does flow during the operation of LIBs. Furthermore, the electrolyte flow is governed by the internal pore pressure gradient induced by the poroelastic effect. The electrolyte flow behavior is also influenced by the boundary conditions. The findings in this study are of benefit to obtain in-depth understanding of the coupling mechanisms among the electrolyte flow field and the stress (strain) field, the temperature field, and the electrochemical field. [ABSTRACT FROM AUTHOR]

Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic materials, which are composites consisting of elastic frames whose pore space is filled with fluid. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip interface condition posed on the microscale. However, for certain pore fluids, the no-slip condition is known to be physically invalid. In the literature, slip boundary conditions have been considered for porous materials with rigid solid frames. For these rigid porous materials, the wave can only propagate in the pore fluid and hence the equations for the microscale are posed only in the pore space. Consequently, the slip on the interface involves only the fluid velocity and the fluid stress. In contrast, for poroelastic materials, the wave can propagate not only in the pore fluid but also in the solid frame; hence the slip conditions involve the velocities on both sides of the interface, rather than just the fluid side. With this slip condition, a variational boundary value problem governing the small vibrations of a periodic mixture of an elastic solid and a slightly viscous fluid is studied in this paper. The method of two-scale convergence is used to obtain the macroscopic behavior of the solution and to identify the role played by the slip interface condition. [ABSTRACT FROM AUTHOR]

In this work, a locking-free nonconforming virtual element method for the three-field Biot's model (the displacements, Darcy velocity and pore pressure) is developed and analyzed. We solve the model as: nonconforming VEM for the displacements, RT-like VEM for Darcy velocity and pressure. We show the well-posedness and the optimal error estimates of the discrete schemes. The numerical experiments support the convergence analysis of our method and illustrate it can be used to avoid Poisson locking and nonphysical pressure oscillations. [ABSTRACT FROM AUTHOR]

In this paper, a novel numerical approach is proposed to study the geometrically nonlinear large-amplitude vibrations of circular plates subjected to hygrothermal loading resting on an elastic foundation. It is considered that the plates are made of functionally graded (FG) porous materials whose hygro-thermo-mechanical properties are estimated based on the modified Voigt's rule of mixture. Hygroscopic stresses produced because of the nonlinear rise in moisture concentration are taken into account. Moreover, two distribution patterns for porosity (even and uneven) are considered. The Touloukian formula is also employed to assess the temperature-dependence of material properties. Based on the first-order shear deformation plate theory in conjunction with von-Kármán geometrical nonlinear relations, the variational form of the governing equations is derived using Hamilton's principle. In addition, the effect of the elastic foundation is incorporated into the formulation according to the Winkler-Pasternak model. For solving the problem of nonlinear vibrations, the generalized differential quadrature, variational differential quadrature, and Newmark-beta integration methods are utilized. The influences of important parameters such as temperature distribution, porosity volume fraction, moisture concentration, elastic foundation parameters and FG index on the geometrically nonlinear vibrations of FG porous plates with different boundary conditions induced by hygro-thermal loadings are analyzed. [ABSTRACT FROM AUTHOR]

Cement is a poroelastic material rather than elastic material. Early researchers have measured the strengths and elastic properties of oil well cement, but Biot's effective stress coefficient α remains an important unknown despite its significance to well integrity. Here, we present measurements of α for different types of oil well cement, which is calculated by the gradient of confining pressure to pore pressure under changing total stress conditions with bulk volumetric strain held constant. To 'pause' the hydration process at a specific number of days after mixing, the specimens were dried in a vacuum oven. This enabled nitrogen gas to be used for the Biot's effective stress coefficient experiments, which accelerated the equilibration times from greater than 3 h to less than 10 min for each pressure step. Results show that for all cement systems except the Pozmix cement, the typical range of α is 0.38~0.80, compressibility is 1.0~5.7 × 10 - 10 /Pa, and permeability of 0.002~0.11 mD. We also measured the effect of effective stress, curing period, and curing condition on cement's poroelastic parameters of α , compressibility, permeability, and microstructures. Finally, we applied α in a fully coupled thermoporoelastic model and found that Biot's effective stress coefficient plays a more important role in impermeable formations. This is caused by the induced/undrained pore pressure inside cement being significantly higher when the rock and cement permeability becomes lower. With a higher induced pore pressure, α will play a more significant role in maintaining well integrity. Under such circumstances, the flexible cement with lower elastic modulus and Poisson's ratio provides better performance in zonal isolation. Highlights: We conducted comprehensive measurements of oil well cement's Biot's effective stress coefficient, compressibility, and permeability. For most cement systems, Biot's effective stress coefficient is 0.38 ~ 0.80, and compressibility is 1.0 ~ 5.7 × 10 - 10 /Pa, and permeability of 0.002 ~ 0.11 mD. Biot's effective stress coefficient is significant for the relatively impermeable wellbore systems with low permeability of cement and formation. [ABSTRACT FROM AUTHOR]

UT-Austin's Devine Fracture Pilot Site, 50 miles southwest of San Antonio, Texas, has been targeted for a comprehensive, multidisciplinary development of fracture diagnostic techniques that are cross-validated by ground-truth data acquisition near a recently created, 175-ft-deep, horizontal hydraulic fracture (Ahmadian et al. 2018 Demonstration of proof of concept of electromagnetic geophysical methods for high resolution illumination of induced fracture networks. In Proceedings of the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, Texas, USA, 23–25 January 2018. SPE-189858-MS.). To evaluate the fracture diagnostic methods at this site, we conducted injection tests with a predefined volumetric flow-rate profile, resembling a diagnostic fracture injection test on September 2020. Subsequently, we developed hydrogeological and geomechanical models based on flow-rate and bottomhole-pressure measurements. History-matching efforts using a simplified layer-cake hydrogeological model resulted in the field-scale formation permeability of 9.87 × 10–15 m2 (10 mD) and Darcy-scale fracture permeability. The analysis of the bottomhole pressure and injection-rate history showed that (1) the newly created horizontal fracture was closed adjacent to the injection well pre-injection and (2) the initial pump-pressure increase at a nominal volumetric injection rate led to near-well fracture reopening, fluid conductivity increase, and abrupt injection-rate increase. To overcome hydrogeological-model limitations of predicting fracture reopening throughout injection, we extended the modeling to a finite-element, poroelastic analysis of horizontal-fracture growth using a cohesive-zone model. Using this fracture-reopening model, we improved the history match of the transient-pressure response during the experiment by adjusting the hydromechanical properties. Post-injection pressure transient analyses helped reduce uncertainty in the overburden-stress gradient, and the initial hydraulic-fracturing simulation verified the plausibility of achieving the surveyed propped fracture area. Highlights: We proposed a procedure for developing a hydrogeological model to improve the history matching of the bottomhole pressure during a hydraulic-fracture reopening. We compared the outcomes of this hydrogeological model with a calibrated poroelastic model, showing the advantage of the later model for fracture reopening and re-closure. We suggest using a spatiotemporally variable fracture permeability obtained from a poroelastic model in a hydrogeological model to simulate fracture reopening. We estimated an almost similar overburden-stress gradient using G-function pressure transient analysis of post-shut-in bottomhole pressure data from two short and long injection tests. [ABSTRACT FROM AUTHOR]

Various applications in science and engineering involve porous materials where the fluid erodes the solid either chemically or mechanically and transports the finer particles through the larger pore spaces of the residual solid. In soil mechanics, the process is called suffusion. In rocks, erosion is mainly due to chemical dissolution. Irrespective of the manner in which the solid erodes, the much finer particles mix with the pure fluid to form a thick fluid whose mass density is greater than that of the pure fluid but less than that of the intact solid. As the solid loses mass, its porosity increases and its mechanical properties degrade, thus impacting the deformation and fluid flow responses of the system. This paper formulates the complex kinematics and conservation equations governing the solid–fluid interaction with internal erosion. We use the classic u / p formulation in which u is the displacement of the residual solid and p is the pressure in the thick fluid. We focus on the case of chemical erosion in rocks where the eroded particles are so small that the interface between them and the pure fluid may be neglected. We then present numerical examples demonstrating the flow and deformation processes in porous materials subjected to internal erosion. [ABSTRACT FROM AUTHOR]

The structure of soils is often heterogeneous with layered strata having distinct permeabilities. An advanced mathematical and numerical coupled model of elastic wave propagation in poroelastic multi-layered soils subjected to subsoil water infiltration is proposed in this study. The coupled model was based on the introduction of an inhomogeneous functionally graded fluid-saturation of the considered soil depending on the infiltration time, which was evaluated employing Richards' equation. The time-harmonic solution was formulated in terms of the Fourier transform of Green's matrix and the surface load that excites the vibration. The convergence and efficiency of the proposed approach are demonstrated. An example of dispersion curves for partially saturated porous strata made of loam, sand, and rock at different infiltration times is provided, and it is shown that the characteristics of the surface acoustic waves change with time, which can be further used for inverse problems' solution. [ABSTRACT FROM AUTHOR]

We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic–parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of physical interest for this problem are proposed. Computations performed by space–time finite element approximations with continuous and discontinuous discretizations of the time variable are summarized. By this work, we intend to stimulate comparative studies by other research groups for the evaluation of dynamic poroelasticity solver regarding the accuracy of discretization techniques, the efficiency and robustness of iterative methods for the linear systems, and the arrangement of the model equations in terms of their variables (two‐field or multifield formulations). [ABSTRACT FROM AUTHOR]

Hydromechanical models have typically assumed constant stress-independent elastic moduli to estimate, forecast, and history-match earth surface uplift. The effect of stressdependent elastic moduli and poroelastic constant (i.e., Biot coefficient) on Earth surface uplift during injection is investigated in this study. Experimental data gathered for different rock types shows that Biot coefficient and bulk modulus vary in response to Terzaghi effective stress. Stress-dependent elastic modulus was imported to the numerical model representing Berea sandstone. Hydromechanical simulations were performed to model CO2 injection into the Berea reservoir by incorporating elastic moduli stress dependency. Hydromechanical modeling results show that using stress-independent elastic moduli causes under-estimation of Earth surface uplift due to injection. A decrease in Young’s modulus and an increase in Biot coefficient because of injection can contribute to a higher estimated uplift. Neglecting the stress dependency effect could cause an erroneous estimate of potential surface uplift due to injection. The impact of geological properties of Berea and injecting brine instead of CO2 on surface uplift trend were also investigated. [ABSTRACT FROM AUTHOR]

Performing geometry-resolved simulations of flows over rough and porous walls is highly expensive due to their multiscale characteristics. Effective models that circumvent this difficulty are often used to investigate the interaction between the free-fluid and such complex walls. These models, by construction, employ an intrinsic averaging process and capture only macroscopic physical processes. However, physical experiments or direct simulations yield micro- and macroscale information, and isolating the macroscopic effect from them is crucial for rigorously validating the accuracy of effective models. Despite the increasing use of effective models, this aspect received the least attention in the literature. This paper presents an efficient averaging technique to extract macroscopic interface data from the flow field obtained via direct simulations or physical experiments. The proposed methodology employs a combination of signal processing and polynomial interpolation techniques to capture the macroscopic information. Results from the ensemble averaging are used as the reference to quantify the accuracy of the proposed method. Compared to the ensemble averaging, the proposed method, while retaining accuracy, is cost-effective for rough and porous walls. To the best of our knowledge, this is the only averaging method that works for poroelastic walls, for which the ensemble averaging fails. Moreover, it applies equally to viscous- and inertia-dominated flows over irregular surfaces. [ABSTRACT FROM AUTHOR]

An analytical solution of unsaturated poroelastic transversely isotropic (TI) half‐space under surface time‐harmonic load with consideration of compressibility, viscous and inertial coupling of soil skeleton, pore‐water and pore‐air, as well as the capillary pressure is investigated in this paper. Firstly, the governing equations of unsaturated TI soil are established in cylindrical coordinate system. Then, the displacement function and operator theory are introduced to decouple the general solution. Secondly, Fourier expansion and Hankel transform are applied to the circumferential and radial coordinates, and the integral general solutions of soil skeleton displacement, pore‐water displacement and pressure, pore‐air displacement and pressure, and the total stress components are derived in the transformed domain. Combined with boundary conditions and continuity conditions, the fundamental solution of unsaturated TI half‐space is obtained. Finally, the proposed solution is verified by benchmarking with two existing solutions. The influence of the TI parameters, vibration frequency and the degree of saturation on the dynamic response of unsaturated poroelastic half‐space is investigated. [ABSTRACT FROM AUTHOR]

The assessment of seismic risk and the prevention of earthquake occurrences during reservoir operation present significant challenges in terms of accurate determination. This study aims to address this issue by developing a numerical model. The primary objective is to estimate the vulnerability of different fault types to reservoir impoundment. This model integrates essential parameters such as fault dip and the relative orientation between the reservoir and potential earthquakes, and it is structured within a risk framework using polar coordinates. Through comprehensive computations, we evaluate the alterations in elastic stress and fluid pore pressure resulting from water impoundment. This is achieved by employing a fully coupled two-dimensional poroelastic approach. Furthermore, our model incorporates relevant seismic data to enhance its accuracy. The findings of our study underscore that the critical factor lies in the fault's precise positioning with respect to the reservoir. The risk associated with a fault is contingent upon both its location and its orientation, emphasizing the importance of these factors in determining hazardous zones. [ABSTRACT FROM AUTHOR]

In this paper, we consider the poroelasticity problem in three-dimensional heterogeneous media. The mathematical model contains a coupled system of equations for fluid pressures and displacements. The poroelasticity problem in heterogeneous media is an important topic in the field of geomechanics, involving the modeling of the interaction between fluid flow and deformation in porous media. This topic is of great relevance in many engineering applications, such as oil and gas reservoirs, groundwater systems, and geothermal energy production. In recent years, the development of Online Generalized Multiscale Finite Element Methods (GMsFEM) has offered a promising solution to efficiently tackle this challenging problem. GMsFEM involves the use of a coarse-scale model that captures the macroscopic behavior of the system, combined with a fine-scale model that captures the local heterogeneities. This approach enables accurate and efficient simulations of the poroelasticity problem in heterogeneous media, with reduced computational costs compared to traditional methods. We utilize online basis functions to enhance the offline multiscale space and quickly reduce errors using residual data. Fast convergence of online methods can only be ensured with suitable offline coarse-grid spaces. This paper highlights the potential of online GMsFEM in advancing the modeling and simulation of poroelasticity problems in three-dimensional heterogeneous media. We investigate how the number of online and offline basis functions affects the relative errors between the multiscale solution and the reference (fine-scale) solution. [ABSTRACT FROM AUTHOR]

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Indiscriminate extraction of underground water sources causes a drop in the water level and an increase in the stress on the soil particles, which leads to the subsidence of the earth's surface. Shahryar's critical plain has been affected by the phenomenon of subsidence for the past few years. The existence of vital arteries, economic, pilgrimage and military areas has turned it into a strategic area, which doubles the cost of the harmful consequences of subsidence. In this research, a new method is used to predict and analyze subsidence, under the title of Poroelasticity module of COMSOL software, which uses the simultaneous solution of equations related to fluid movement in porous media and mechanical deformation. The output of the numerical model was validated and compared between 2003 and 2019 at 24 points with the alignment observations, the Sentinel 1 radar interferometric images. The correlation coefficient of 0.97 indicates an acceptable correlation between the data values, the good matching of the interferometric images with the maps of the subsidence zones obtained from the software data and the approach of the squared values of the mean squared error and the efficiency coefficient towards zero and one was obtained. The general result of the finite element numerical modeling showed that the average rate of subsidence during the year 2031 due to the successive compression of the upper layers of the aquifer, with a lower rate, about 13.19 cm and in the places where the thickness of the fine-grained layers increased, He finds that it will reach 18.38 cm. Also, the range of changes in the underground water level in the period of time, the type of land and the number of geological units are among the factors affecting the subsidence pattern and rate.

Flow of gas through porous media can be coupled with sorption against the pore walls and deformation of the solid phase. This paper presents a thermodynamic description of the described three-way coupling in porous elastic media with two distinct networks or scales of porosity. The developed framework is next applied to the problem of natural gas sorption and flow toward a producing boundary in fractured rocks. The considered problem involves a set of strong and entangled nonlinearities arising from the coupled processes of sorption and solid strain, resulting changes in rock permeability, as well as pressure dependence of gas compressibility. An analytical solution to this problem is developed using the homotopy-perturbation method. The obtained solution compares well against a numerical solution to the same problem. The solution rigorously accounts for local dependence of the involved parameters on the pore fluid pressure. Results from a case study indicate that compaction of the pore space and the consequential permeability loss would cause substantial reduction in gas production rate. However, the same process triggers desorption of excess gas molecules from the pore walls serving to negate the compromised flow rate due to rock compaction. The arisen entanglement between gas desorption and bulk deformation in rocks is further studied by identifying the pertinent dimensionless variable groups. Gas flow rate for a given pressure disturbance at the producing boundary is shown to exhibit nontrivial variations with changes in the values of two dimensionless groups describing the porous frame compressibility and sorption strength at the pore walls. Article Highlights: A constitutive model for sorption and poromechanics in dual-porosity media is developed. An analytical solution for nonlinear gas flow and sorption in poroelastic media is developed. The dimensionless groups that control the coupled flow and sorption of gas in deformable rocks are identified. [ABSTRACT FROM AUTHOR]

Summary: A general technique to develop arbitrary‐sided polygonal elements based on the scaled boundary finite element method is presented. Shape functions are derived from the solution of the Poisson's equation in contrast to the well‐known Laplace shape functions that are only linearly complete. The application of the Poisson shape functions can be complete up to any specific order. The shape functions retain the advantage of the scaled boundary finite element method allowing direct formulation on polygons with arbitrary number of sides and quadtree meshes. The resulting formulation is similar to the finite element method where each field variable is interpolated by the same set of shape functions in parametric space and differs only in the integration of the stiffness and mass matrices. Well‐established finite element procedures can be applied with the developed shape functions, to solve a variety of engineering problems including, for example, coupled field problems, phase field fracture, and addressing volumetric locking in the near‐incompressibility limit by adopting a mixed formulation. Application of the formulation is demonstrated in several engineering problems. Optimal convergence rates are observed. [ABSTRACT FROM AUTHOR]

Cryogelation is a powerful technique for producing macroporous hydrogels called cryogels. Although cryogelation reactions and cryogels were discovered more than 70 years ago, they attracted significant interest only in the last 20 years mainly due to their extraordinary properties compared to the classical hydrogels such as a high toughness, almost complete squeezability, a mechanically stable porous structure with honeycomb arrangement, poroelasticity, and fast responsivity against external stimuli. In this mini review, general properties of cryogelation systems including the cryoconcentration phenomenon responsible for the unique properties of the cryogels are discussed. The squeezability and poroelasticity of cryogels comparable to those seen with articular cartilage are also discussed. Cryogelation reactions conducted within the pores of preformed cryogels and some novel cryogels with attractive properties are then discussed in the last section. [ABSTRACT FROM AUTHOR]

In this paper we consider a three-field formulation of the Biot model which has the displacement, the total pressure, and the pore pressure as unknowns. For parameter-robust stability analysis, we first show a priori estimates of the continuous problem with parameter-dependent norms. Then we study finite element discretizations which provide parameter-robust error estimates and preconditioners. For finite element discretizations we consider standard mixed finite element as well as stabilized methods for the Stokes equations, and the complete error analysis of semidiscrete solutions is given. Abstract forms of parameter-robust preconditioners are investigated by the operator preconditioning approach. The theoretical results are illustrated with numerical experiments. [ABSTRACT FROM AUTHOR]

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples. To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability. We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods. [ABSTRACT FROM AUTHOR]

Plenty of studies have suggested that pore fluid may play an important role in earthquake rupture processes. Establishing numerical models can provide great insight into how pore fluid may affect earthquake rupture processes. However, numerical simulation of 3-D spontaneous ruptures in poroelastic mediums is still a challenging task. In this paper, it is found that a closed-form time-domain Green's function of Biot's poroelastodynamic model can be constructed when the source frequency and source-field distance are within a certain range. The time-domain Green's function is validated by being transformed into the frequency domain and comparing with the frequency-domain Green's functions obtained by former papers. Poroelastic wave propagation phase diagrams for various two-phase poroelastic mediums are then plotted to show the applicable range of frequency and source-field distance for the new time-domain Green's function. It is shown that the applicable range not only include the frequency and spatial range of concern in seismology but also overlap that in acoustics. Based on the time-domain Green's function, the boundary integral equations (BIEs) for modelling dynamic ruptures in elastic mediums are extended to fluid-saturated mediums. In the meantime, a functional relationship between the effective stress tensor and the total stress tensor in fluid-saturated mediums is also obtained, which allows us to directly obtain the effective stress by BIEs. The spontaneous rupture processes controlled by the slip-weakening friction law on faults in elastic mediums and in fluid-saturated mediums are compared. It is found that under the same conditions, fluid-saturated rocks are more prone to supershear rupture than dry rocks. This result suggests that pore fluid may promote the excitation of supershear rupture. The poroelastic wave propagation phase diagrams also suggest that simulating a coseismic phase in the real scale requires a certain sample length in laboratories. They also suggest that an undrained governing equation is suitable for seismic wave propagation simulation in poroelastic media. [ABSTRACT FROM AUTHOR]

Impermeable barriers are abundant in rock formations and their delineation via seismic reflections are of prime importance. However, such barriers have received little attention in the poroelasticity literature. For this reason, we revisit the reflection–transmission problem for two porous half-spaces which are in welded contact and across which no fluid exchange is possible. We carry out this analysis in the poroelastic theory initiated by de la Cruz and Spanos (1985), which describes four waves: the fast P , fast S -, slow P and slow S waves. The fast P and S waves account for the in-phase motion in compression and shear nature, whereas the slow P and S waves are the out-of-phase motion. We find that the often times suggested notion of effective elastic scattering is not quite correct because of the generation of slow waves at the impermeable contact. The energy flux the slow waves carry is negligibly small at low frequencies when the fluid is viscously coupled to the solid frame. In contrast, slow waves carry substantial energy flux at high frequencies when the fluid is viscously decoupled. Moreover, the reflection–transmission behaviour at an impermeable contact is distinctively different when compared to that of a permeable contact, which means that, in principle, amplitudes of scattered waves can be used to identify the kind of contact. A seemingly unnoted but important result is the strong conversion scattering from a fast S wave into the slow P wave at high frequencies, which may be an alternative way to observe slow P waves in the laboratory as well as a means to characterize impermeable contacts. [ABSTRACT FROM AUTHOR]

In this paper, the Biot's consolidation model is considered, and Darcy‐Forchheimer equation is used to describe the relationship between the fluid velocity and pressure. The model is nonlinear and the unknown variables are the solid displacement, the fluid velocity and pressure. The Bernardi‐Raugel element is used for displacement and the RT mixed element is used for the fluid velocity and pressure. The parameter‐robust BR‐RT0‐P0 method presented here is uniformly stable not only with respect to the Lamé constant λ$$ \lambda $$, but also with respect to the constrained specific storage coefficient c0$$ {c}_0 $$. We demonstrate the well‐posedness of the BR‐RT0‐P0 finite element solutions, and give the error estimates of the finite element approximations using the monotonicity of the nonlinear Forchheimer term. The error estimates are divided into two cases, that is, c0$$ {c}_0 $$ is positive and c0$$ {c}_0 $$ is nonnegative. Numerical experiments are presented to verify theoretical analysis. Moreover we focus on the variation of pressure by several poroelasticity problems. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing is an efficient technology to extract hydrocarbon within natural caves. However, these caves can markedly affect the fracture propagation behavior. This paper proposes a novel hydraulic fracturing model to simulate the fracture propagation in poroelastic media containing the natural cave, utilizing the strengths of the phase-field method. By coupling the Reynolds flow with cubic law in fracture domain, free flow in cave domain, and low-permeability Darcy flow in reservoir domain, the fracture-cave-reservoir flow governing equations are established. The Biot poroelasticity theory and fracture width are the links of hydro-mechanical coupling. The smooth phase-field is introduced to diffuse not only the sharp fracture but also the sharp cave edge. The fully coupling model is solved by a staggered scheme, which independently solves the pressure field and displacement field in inner cycle, and then independently solves the phase field in outer cycle. The proposed model is verified by comparing with the Khristianovic–Geertsma–de Klerk (KGD) model and Cheng's hydraulic fracturing model. Then, the interaction between hydraulic fracture and natural cave is investigated through several two-dimensional and three-dimensional cases. The result shows that the cave effect can make the hydraulic fracture deflect and raise its propagation velocity. Increasing the fracture-cave distance, injection rate, and in situ stress difference can all decline the cave effect. The displayed cases also substantiate the capability and efficiency of the proposed model. [ABSTRACT FROM AUTHOR]

We present a new approach and an algorithm for solving two-scale material optimization problems to optimize the behaviour of a fluid-saturated porous medium in a given domain. While the state problem is governed by the Biot model describing the fluid–structure interaction in homogenized poroelastic structures, the approach is widely applicable to multiphysics problems involving several macroscopic fields in which homogenization provides the relationship between the microconfigurations and the macroscopic mathematical model. The optimization variables describe the local microstructure design by virtue of the pore shape which determines the effective medium properties, namely the material coefficients, computed by the homogenization method. The numerical optimization strategy involves (a) precomputing a database of the material coefficients associated with the geometric parameters and (b) applying the sequential global programming (SGP) method for solving the problem of macroscopically optimized distribution of material coefficients. Although there are similarities to the free material optimization (FMO) approach, only effective material coefficients are considered admissible, for which a well-defined set of corresponding configurable microstructures exists. Due to the flexibility of the SGP approach, different types of microstructures with fully independent parametrizations can easily be handled. The efficiency of the concept is demonstrated by a series of numerical experiments that show that the SGP method can simultaneously handle multiple types of microstructures with nontrivial parametrizations using a considerably low and stable number of state problems to be solved. [ABSTRACT FROM AUTHOR]

This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart--Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method is based on the formulation of linearized elasticity as a weighted vector Laplace problem. By introducing the solid rotation and fluid flux as auxiliary variables, we form a four-field formulation of the Biot system, which is discretized using conforming mixed finite element spaces. The auxiliary variables are subsequently removed from the system in a local hybridization technique to obtain a multipoint rotation-flux mixed finite element method. Stability and convergence of the four-field and multipoint mixed finite element methods are shown in terms of weighted norms, which additionally leads to parameter-robust preconditioners. Numerical experiments confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The role of poroelasticity on the functional performance of articular cartilage has been established in the scientific literature since the 1960s. Despite the extensive knowledge on this topic there remain few attempts to design for poroelasticity and to our knowledge no demonstration of an engineered poroelastic material that approaches the physiological performance. In this paper, we report on the development of an engineered material that begins to approach physiological poroelasticity. We quantify poroelasticity using the fluid load fraction, apply mixture theory to model the material system, and determine cytocompatibility using primary human mesenchymal stem cells. The design approach is based on a fiber reinforced hydrated network and uses routine fabrication methods (electrohydrodynamic deposition) and materials (poly[ɛ-caprolactone] and gelatin) to develop the engineered poroelastic material. This composite material achieved a mean peak fluid load fraction of 68%, displayed consistency with mixture theory, and demonstrated cytocompatibility. This work creates a foundation for designing poroelastic cartilage implants and developing scaffold systems to study chondrocyte mechanobiology and tissue engineering. Poroelasticity drives the functional mechanics of articular cartilage (load bearing and lubrication). In this work we develop the design rationale and approach to produce a poroelastic material, known as a fiber reinforced hydrated network (FiHy™), that begins to approach the native performance of articular cartilage. This is the first engineered material system capable of exceeding isotropic linear poroelastic theory. The framework developed here enables fundamental studies of poroelasticity and the development of translational materials for cartilage repair. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper we propose and analyze a staggered discontinuous Galerkin method for a five-field formulation of the Biot system of poroelasticity on general polygonal meshes. Elasticity is equipped with a stress–displacement–rotation formulation with weak stress symmetry for arbitrary polynomial orders, which extends the piecewise constant approximation developed in Zhao and Park (2020, A staggered cell-centered DG method for linear elasticity on polygonal meshes, SIAM J. Sci. Comput. 42 , A2158–A2181). The proposed method is locking-free and can handle highly distorted grids, possibly including hanging nodes, which is desirable for practical applications. We prove the convergence estimates for the semidiscrete scheme and fully discrete scheme for all the variables in their natural norms. In particular, the stability and convergence analyses do not need a uniformly positive storativity coefficient. Moreover, to reduce the size of the global system, we propose a five-field-formulation-based fixed stress splitting scheme, where the linear convergence of the scheme is proved. Several numerical experiments are carried out to confirm the optimal convergence rates and the locking-free property of the proposed method. [ABSTRACT FROM AUTHOR]

We present and analyze a hybridizable discontinuous Galerkin (HDG) finite element method for the coupled Stokes–Biot problem. Of particular interest is that the discrete velocities and displacement are H (div) -conforming and satisfy the compressibility equations pointwise on the elements. Furthermore, in the incompressible limit, the discretization is strongly conservative. We prove well-posedness of the discretization and, after combining the HDG method with backward Euler time stepping, present a priori error estimates that demonstrate that the method is free of volumetric locking. Numerical examples further demonstrate optimal rates of convergence in the L 2 -norm for all unknowns and that the discretization is locking-free. [ABSTRACT FROM AUTHOR]

An urban road collapse has become one of the significant geohazards frequently occurring in metropolitan cities worldwide. In most cases, these devastating superficial collapses are known to be induced by small underground cavities. They are created by the failure of subsurface structures and pipelines (e.g., water supply/sewer lines, subway tunnels). However, the cavity generation and expansion process, interacted by intense precipitation, groundwater movement, and subsurface geologic environment, is not yet fully understood. This study aims to understand the mechanism of cavity initiation and expansion using a numerical model coupling groundwater flow, poroelastic deformation, and internal soil erosion. The model is then applied to road collapse cases by a damaged sewer line failure and internal erosion. Effects of the precipitation rate and period on internal erosion are also investigated to predict potential risks for road collapse. Numerical simulation results show that the underground cavities are closely related to the focused groundwater flow by the leakage through an opening in the damaged pipeline. Internal erosion accelerates the removal of fine soil particles and creates collapsing-susceptible vacant areas. The results also show that intense precipitation in a short interval exerts the most damaging effects on the subsurface stability comparing other scenarios with less severe and continuous rainfalls. [ABSTRACT FROM AUTHOR]

Due to the unique specifications of porous materials, such as lightweight, researchers are encouraged to study more about them and use them in different engineering structures. Also, they can be integrated with other stiffer materials to overwhelm their main limitation, i.e., their low stiffness. So, this work considers the frequency response of a functionally graded (FG) porous material annular plate, which is coated with two piezo-electro-magnetic layers. The FG porous core is assumed to be saturated by fluid, and the pores' compressibility effect is examined. Besides, the pores' placement patterns are regarded as three different thickness-dependent functions that affect the core's mechanical properties. Since the coating layers have electromagnetic properties, therefore electromagnetic potentials are externally applied to them. The whole structure is also rested on Pasternak elastic foundation, and the thermal environment influence is evaluated on its behavior. The trigonometric type of higher-order shear deformation theory is employed, and the governing motion equations are derived to obtain more accurate results. Then, they are solved utilizing the generalized differential quadrature method for various boundary conditions. After ensuring the validity of the results by comparing them with known data in the available literature, the effect of the most vital parameters on the frequencies of the plate is discussed. For instance, it is seen that the impact of the porosity coefficient on the natural frequencies is utterly dependent on the pores' distribution patterns. [ABSTRACT FROM AUTHOR]

Highlights: Laboratory experiments were designed to measure Skempton coefficient B for Dunnville sandstone using small and large specimens. The pore volume Vp of the small specimen was on the same order as the system volume Vl, while Vp of the large specimen was 100 times Vl. The large specimen provided a direct measurement of B. For Dunnville sandstone, Skempton coefficient B calculated with the appropriate poroelastic model and material parameters agrees with the measured B. [ABSTRACT FROM AUTHOR]

Analytic solutions are derived for the problem of scattering of obliquely incident plane waves from a rectangular crack in a fluid-saturated porous solid. The propagation direction and polarization direction of the incident waves can be arbitrary. The solutions are based on expanding the crack opening displacements in terms of Chebyshev functions. Explicit expressions for the frequency-dependent stress intensity factors and scattering far fields are obtained. The poroelastic effects play a key role in determining the crack opening mode by changing the effective normal stress applied on the crack surfaces. Consequently, the dynamic responses of the crack can be quite different from those of conventional dry crack in an elastic solid. The effects of scattered slow-P waves as well as wave-induced crack fluid pressure on the dynamic stress intensity factors are clarified, and a corner effect is observed in the scattering patterns for moderately high frequencies. The comparisons of synthetic seismograms with the elastic model show the slow-P waves can cause significant energy loss and waveform change. This study can be used for fracture analysis of porous media and nondestructive testing for individual hydraulic fractures in reservoirs. [ABSTRACT FROM AUTHOR]

SUMMARY: Based on the propagation theory of elastic waves in three-phase frozen poroelastic media and single-phase elastic media, the energy transmission problem of a plane harmonic P-wave incident at the planar interface between elastic medium and frozen poroelastic medium is studied. According to the boundary conditions at the planar interface, the analytical expressions of the transmission and reflection coefficients and energy ratios of the transmitted and reflected waves are derived. The relationship between the energy of plane harmonic P-wave incident on the planar interface between elastic medium and frozen poroelastic medium and the incident angle, frequency of incident wave, cementation parameters, porosity, saturation and contact parameters are investigated. The results show that the incident angle significantly affects the reflection and transmission energy ratios; the incidence frequency only has a large effect on the transmission energy ratios of the transmitted P2, P3 and S2 waves; the contact parameters have a relatively large effect on the reflected S wave and the transmitted P2, P3, S1 and S2 waves, but have a smaller effect on the reflected P wave and the transmitted P1 wave; cementing parameters, porosity, saturation has a great influence on the energy ratios. [ABSTRACT FROM AUTHOR]

In this paper, we develop a weak Galerkin (WG) finite element method for a linear poroelasticity model where weak divergence and weak gradient operators defined over discontinuous functions are introduced. We establish both the continuous and discrete time WG schemes, and obtain their optimal convergence order estimates in a discrete H 1 norm for the displacement and in H 1 and L 2 norms for the pressure. Finally, we present some numerical experiments on different kinds of meshes to illustrate the theoretical error estimates, and furthermore verify the locking-free property of our proposed method. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem for a one-dimensional homogeneous system of poroelasticity equations described by three elastic parameters in a reversible hydrodynamic approximation. We find a solution to the Cauchy problem in the form of the d'Alembert formula and show the influence of porosity on the acoustic wave propagation. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyse pressure-correction schemes based on marker and cell (MAC) method for the linear Stokes–Biot system with a fixed interface. The implicit backward Euler scheme for the time discretization is used, whereas the coupling terms are treated explicitly. These schemes are computationally efficient in that we only solve two decoupled problems. And for Stokes equations, we solve one vector-valued elliptic equation and one scalar-value Poisson equation per time step. These methods have optimal order without the incompressibility constraint of the Stokes system. We prove rigorously that they are unconditionally stable and present the numerical experiments to show their performance. [ABSTRACT FROM AUTHOR]

Better understanding of skin tissue's permeability and poroelasticity could help advance biomedical technologies concerning skin such as intradermal injection and grafting. We applied a pressure driven fluid flow across skin tissue's epidermal and dermal layers in a simple one-dimensional configuration, while measuring the resulting flow rate and capturing cross sectional optical coherence tomography (OCT) images of the tissue's deformation. Digital image correlation was used to analyze the OCT images and via a novel method, image analysis corrected for the change in the tissue's refractive index, which occurred due to flow-induced deformation, thus providing accurate one-dimensional depth-wise deformation profiles. Skin tissue was found to exhibit a nonlinear relationship between pressure and the resulting fluid flow rate, where the increase in flow rate with pressure decreased as pressure increased. The skin tissue was observed to experience compressive strain closest to the supported base, with magnitudes increasing with increasing driving pressure, and the tissue near the free surface experienced relatively little strain. Permeability was found to follow an exponential permeability-volumetric strain relationship with material constants: k 0 (initial uniform permeability) of 9.6 × 10−15 m2 and m (extent of nonlinearity for the permeability–strain relationship) of 2.94. Darcy's law and the permeability–strain relationship were used to analyze results with good similarity between observed and calculated flowrates. This work presents a novel and direct method of characterizing soft tissue permeability and provides a fundamental understanding to skin behavior under pressurized driving fluid, which can be generalized to study or model other geometries of induced flow through skin tissue. [ABSTRACT FROM AUTHOR]

Two-dimensional single-phase flow of a weakly compressible fluid through a deformable fractured-porous medium is considered. A poroelastic model is used for coupled simulation of the fluid flow and the related changes in the stress state of the medium. Fracture network is simulated using the discrete fracture model. The fractures in the region under consideration have random location and orientations, and the fracture length distribution follows a power law. The dependence of the hydraulic properties of fractured porous media on its stress-strain state and the structure of the fracture network is studied. Numerical study was performed for various realizations of fracture network obtained using multiple random generation. It is found that the permeability of the fractured porous medium is determined mainly by the structure of the fracture system characterized by the percolation parameter. According to the simulations results, hydraulic properties are significantly affected by the stress-strain state only for connected fracture systems. An approximation is proposed to define the dependence of the equivalent permeability of a fractured-porous medium on the following parameters: the connectivity of the fracture system, the stress-strain state of the medium, and fracture properties such as stiffness and aperture. [ABSTRACT FROM AUTHOR]