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• Dynamic responses of eccentrically loaded rigid strip foundation are solved analytically. • Extended precise integration method is employed to solve layered poroelastic media. • Contact interface stresses on rigid strip are modelled by bessel series expansions. • Linear equations can be developed and solved for obtaining explicit contact stresses. • Effects of stratification, transverse isotropy and permeability of media are investigated. This paper presents an analytical method for analyzing vertical and rocking motions of a rigid strip foundation on layered transversely isotropic poroelastic media. The extended precise integration method is employed to obtain the plain strain dynamic responses of layered poroelastic media due to the reaction force from the rigid strip. Then, the contact stresses for dynamic soil-structure interactions (SSI) are modelled by the Bessel series expansions, and a set of linear equations can be developed from the dual integral equations of mixed boundary value problems. The explicit expressions for the contact stresses are further obtained by solving these linear equations. Finally, the presented method is verified, and numerical examples are provided to demonstrate the effects of stratifications, transverse isotropy and permeability of media on the dynamic responses of eccentrically loaded rigid strip foundation. [ABSTRACT FROM AUTHOR]

• The coupling effects between solid and fluid portions is considered in the analytical solution. • The surrounding soil can consider the variations of vertical displacements in both horizontal and vertical directions. • The research on floating piles is no longer limited to the assumption of semi-infinite space. • The proposed model can be degenerated to the condition of end-bearing pile. Decades of high-speed railways operation around the world have revealed an increasing number of maintenance issues of pile-supported embankments subjected to long-term dynamic train loads in typical unsaturated soft soil areas. As the physical explanation of vibration characteristics of unsaturated soil piles is a theoretical basis for pile foundation design and pile integrity detection, a developed analytical solution of the vertical dynamic response of a floating pile in homogeneous unsaturated soils is proposed in this work. Based on the fictitious unsaturated soil pile (FUSP) model, the influence of saturation degree on soil shear modulus is considered in governing equations, uncoupled by using potential function and operator decomposition methods. The vertical dynamic response of a floating pile in a frequency domain is derived by employing the pile–soil compatibility conditions and the impedance function transfer method. Time-domain results are obtained by utilizing inverse Fourier transform and the convolution theorem. The correctness of the proposed model is verified by degradation to compare with the two existing solutions. Finally, a parameter study is undertaken to find the most sensitive parameters to the dynamic response of the floating pile in unsaturated soils. [ABSTRACT FROM AUTHOR]

We present and analyze a robust and mass conservative virtual element method for the three-field formulation of Biot’s consolidation problem in poroelasticity. The displacement and fluid flux are respectively approximated by enriched H (div) virtual elements and H (div) virtual elements, while the pressure is discretized by piecewise polynomial functions. Optimal a priori error estimates are obtained, including the semi-discrete scheme and the fully-discrete scheme with the implicit Euler approximation in time. Moreover, our method achieves robustness with respect to the constants hidden in the error estimates, even for the Lamé coefficient tending to infinity and the arbitrarily small constrained specific storage coefficient, and therefore it is free of both volumetric (Poisson) locking and nonphysical pressure oscillations. Meanwhile, it also conserves pointwise mass conservation for Biot’s consolidation problem on the discrete level. [ABSTRACT FROM AUTHOR]

In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the immune-driven dynamics between leukocytes and pathogens. The governing partial differential equations are formulated in terms of skeleton displacement, fluid pressure, Lagrangian porosity, and the concentrations of pathogens and leukocytes. A five-field finite element scheme is proposed for the numerical approximation of the problem, and we provide the stability analysis for a simplified system emanating from linearisation. We also discuss the construction of an adequate, Schur complement based, nested preconditioner. The produced computational tests exemplify the properties of the new model and of the finite element schemes. [ABSTRACT FROM AUTHOR]

Many moderate to large historical and instrumental events have been documented in the Mitidja basin, affecting in particular the southern edge of the active Quaternary Mitidja basin, which is composed of nearly NE–SW-trending fault system. The earthquake catalogue reports that the Hammam Melouane region has experienced several moderate seismic events such as those of 8 February 1937 (I0 = V), 20 July 1975 (I0 = V–VI), 29 September 1981 (I0 = V) and 17 December 1986 (I0 = V). Recently, between 2013 and 2016, this area experienced three moderate earthquakes with a series of aftershocks. In this paper, we present an analysis of the seismic sequences that occurred in the Hammam Melouane Geothermal Spring area on 17 July 2013 (ML 4.9), 23 December 2014 (ML 5.3) and 10 February 2016 (Mw 4.8), about 3–7 km apart, at hypocentral depths of 11.5 km, 19.0 km and 18.0 km, respectively, with centroid depth of 5 km for the first main shock. Ninety-seven events with local magnitude ranging between ML 0.9 and ML 5.3 were recorded and analyzed. The series of aftershocks display two clusters, trending N–S for the 2013 event and NE–SW for the 2014 event, located at shallow depths of 1.5–14 km and 18–28 km, respectively. The event distribution shows variability in faulting, combining strike-slip and thrust focal mechanisms of the main events, leading us to hypothesize a simultaneous interaction between two geological active structures represented by the ~ N–S- to NE–SW-trending faults belonging to the southern Mitidja fault system. On one hand, the computed ΔCFF indeed supports and strengthens the fault interaction model between the three events. On the other hand, the analysis of the post-seismic stress distribution caused by fluid circulation reveals that the 2013 and 2014 events seem to have caused a poroelastic stress relaxation and thus influenced the occurrence of the 2016 main shock. [ABSTRACT FROM AUTHOR]

We used the 250‐day postseismic displacements derived from Global Positioning System data to explore various postseismic deformation processes of the 14 April 2010 Mw 6.9 Yushu earthquake, including the afterslip of the fault, viscoelastic relaxation in the lower crust and upper mantle, and the poroelastic rebound. The preferred model shows that the afterslip of the fault decays rapidly with time. Viscoelastic relaxation in the lower crust and upper mantle decays slower with time but affects a broader area. Our results show that the range of the steady‐state viscosity in the lower crust is 0.3–2 × $\times $ 1019 Pa s. The optimal steady‐state viscosity in the lower crust is ∼5 × $\times $ 1018 Pa s. We simulate the deformation due to the poroelastic rebound in the top 10 km upper crust. Model results indicate that the poroelastic rebound only produces a few millimeters surface deformation and may be a secondary‐order postseismic process. Plain Language Summary: In 2010, the Mw 6.9 Yushu earthquake occurred on the Yushu fault in the eastern Tibetan Plateau. Global Positioning System (GPS) measurements in the first 250 days after the 2010 event show that short‐term postseismic displacements featured mainly a left‐lateral motion across the fault. Model results show that the afterslip of the fault controls mainly the deformation in the near‐field area. The rheological structure in the lower crust in this region has no obvious heterogeneity. Our model provides further constraints on the rheological structures in the lower crust and upper mantle beneath the eastern Tibetan Plateau. Key Points: Afterslip of the fault and viscoelastic relaxation in the lower crust together control the short‐term postseismic deformationAfterslip takes place mostly within 10 years after the earthquake and decays rapidly with timeThe steady‐state viscosity in the lower crust is 0.3–2 × 1019 Pa s with an optimal value ∼5 × 1018 Pa s [ABSTRACT FROM AUTHOR]

This article presented the possible mechanism of arthritis damaged changes in cartilage's interstitial fluid flowing behavior. Firstly, the analytical solutions for the pore fluid pressure and velocity in the idealized cartilage defect model were obtained, which are employed to validate the finite element (FE) method. Then according to the MRI data, an articular cartilage FE model was developed to study the effects of defect characteristics on its poroelastic behaviors. The results showed the interstitial fluid pressure and velocity in defected articular cartilage is diminished, moreover, this trend is even more severe as the defect radius or thickness increased. As the development of osteoarthritis goes, the fluid velocity is decreased and cause the even serious nutrients loss. [ABSTRACT FROM AUTHOR]

In this paper, we consider Mandel's problem in the context of nonlinear single-phase poroelasticity, where it is assumed that the fluid is sightly compressible and porosity and permeability are given functions of the volume strain. In the first part of the paper we prove well-posedness of the time-discrete incremental problem by recasting the equations in an abstract form involving a pseudo-monotone operator. Further, we show existence of a Lyapunov functional yielding a global time discrete solution. In the second part, we investigate numerically the behavior of the poroelastic structure. In particular, we verify the assumptions leading to Mandel's solution. We also demonstrate some consequences of the proposed nonlinearities. [ABSTRACT FROM AUTHOR]

We consider a model for the flow of two immiscible and incompressible fluid phases in a porous medium. A surfactant is dissolved in one of the fluid phases, and its concentration at the interface separating the two fluids can change the surface tension. At the scale of pores, we assume that the flow is governed by the Navier-Stokes equations, while for the phase separation, a Cahn-Hilliard phase-field model is adopted. Using formal homogenization, we derive a two-scale model describing the averaged behaviour of the system at the larger Darcy scale, where effective quantities are found through local (cell) problems at the smaller pore scale. For this two-scale model, we formulate a numerical scheme and present numerical results highlighting the influence of the solute-dependent surface tension. [ABSTRACT FROM AUTHOR]

This paper considers a coupled flow and mechanics problem in a fractured poro-elastic medium. The fracture geometry is explicitly treated as a possibly non-planar interface. The model equations are of mixed dimensional type where the flow equation on a d − 1 dimensional fracture surface is coupled to a d dimensional porous matrix. An extension of the widely used undrained split iterative coupling scheme to the fractured poro-elastic media is performed. The particularity is in the time-discretization where both the single rate scheme in which flow and mechanics share the exact same time step, and the multirate scheme in which flow takes multiple fine time steps within one coarse mechanics time step. In the coupled model considered here, the fracture flow model is a lubrication-type system (Girault et al. Math. Models Methods Appl. Sci. 25(4):587–645 2015) whereas in the porous matrix the linear quasi-static Biot equations are considered. Convergence analysis of the undrained split iterative scheme and Banach fixed-point contraction type results are obtained that establish the geometric convergence of the scheme and the uniqueness of the obtained solution. [ABSTRACT FROM AUTHOR]

Detecting fracture intersections is crucial for understanding rock hydraulic properties. For this purpose, we study the dynamic SV‐wave signatures of fluid‐saturated porous rocks containing intersecting fractures. A theoretical model is derived using the dynamic Biot's poroelasticity equations. Using this model, we analyze the features of SV‐waves and compare to those of previously studied P‐waves. The results show that the dispersion and attenuation of SV‐waves caused by elastic scattering and FF‐WIFF (Fracture‐Fracture Wave‐induced Fluid Flow) have a similar dependence on properties of intersecting fractures and fluid as those of P‐waves. However, the FB‐WIFF (Fracture‐Background Wave‐induced Fluid Flow) causes much smaller dispersion and attenuation for SV‐waves than for P‐waves. In particular, such dispersion and attenuation of SV‐waves are negligibly small for the orthogonally intersecting fractures regardless of wave incidence angles. In addition to the dispersion and attenuation, the WIFF and elastic scattering also greatly affect the anisotropy properties, which gives rise to frequency‐dependent velocity and attenuation anisotropies for both SV‐ and P‐ waves. Such anisotropy properties are sensitive to fracture intersection angles and are quite different between SV‐ and P‐ waves. These complementary features of SV‐ and P‐ waves provide the basis for fracture intersection detection using the combined features of these two waves. By comparing our model to the known results for the limiting cases, we validate our model. Plain Language Summary: Detecting intersecting open fractures can help us understand rock hydraulic properties. Because rock elastic properties are sensitive to fractures, the seismic exploration and sonic logging are widely used for the detection of fractures. To detect the fracture intersection, its effects on rock elastic properties need to be studied. However, previous studies show that fracture intersections have little effects on rock static elastic properties. Hence, studying the effects of fracture intersections on rock dynamic elastic properties is of great importance. For this purpose, we study the dynamic SV‐wave signatures of intersecting fractures in fluid‐saturated porous rocks and compare the results to those of previously studied P‐waves. We find that the dispersion and attenuation caused by elastic scattering and FF‐WIFF (Fracture‐Fracture Wave‐induced Fluid Flow) have similar characteristics between SV‐ and P‐ waves. However, those caused by FB‐WIFF (Fracture‐Background Wave‐induced Fluid Flow) are quite different. In addition, the WIFF and elastic scattering also cause distinctly different frequency‐dependent anisotropy between SV‐ and P‐waves. These complementary features of SV‐ and P‐ waves indicate that the fracture intersections can be detected by combining the seismic or sonic logging data of these two waves. Key Points: Dynamic SV‐wave signatures of fluid‐saturated porous rocks containing intersecting fractures are studied and compared to P‐wavesFracture‐Background Wave‐induced Fluid Flow causes much smaller dispersion and attenuation for SV‐waves than for P‐wavesSV‐wave anisotropy is greatly affected by Wave‐induced Fluid Flow and elastic scattering, which has distinctly different features compared to P‐waves [ABSTRACT FROM AUTHOR]

Abstract—Volumetric (non-shear) deformations of fault zones measured from leveling data are analyzed. It is shown that volumetric deformations within fault zones lead to symmetric local surface subsidence. Examples of anomalous subsidence identified in the Ashgabat fault zone (North Kopet Dag) and in the fault zones of the underground gas storage facility are presented. A mechanism describing the formation of these anomalous deformations based on the models of poroelastic inclusion and poroelastic inhomogeneity is proposed. The problem about surface displacements of elastic halfspace with a poroelastic region in the form of vertical extended rectangular prism simulating active fragment of a fault zone is solved. Analytical formulas for surface-displacement estimation are derived for two variants of poroelastic models: a model of inclusion and a model of heterogeneity. The comparison of the two models based on the case study of the Ashgabat fault has shown that the mechanism of anomalous deformations with poroelastic heterogeneity model much better describes the observed displacements than poroelastic inclusion model. The analysis of anomalous surface displacements at an underground gas storage facility indicates that local subsidence occurs during both gas withdrawal and injection. It is established that the formation of anomalous subsidence in the first case follows the poroelastic inclusion model, and in the second case it corresponds to the poroelastic heterogeneity model. This means that local subsidence in a fault zone during gas withdrawal is linearly related to the change in reservoir pressure. Anomalous subsidence during gas injection is nonlinearly linked to the change in reservoir pressure. This is a striking example of induced deformations in the fault zones when temporal variations of poroelastic parameters within a fault zone in the setting of external quasistatic loading induce local perturbation in the stress-strain state of rocks in the vicinity of fault. [ABSTRACT FROM AUTHOR]

This study considers to solve the complex dispersion equation for propagation of Rayleigh waves in a dissipative porous composite. This porous medium is a viscoelastic porous solid frame saturated with a viscous fluid. Seepage of fluid at the boundary is controlled through pore-fluid pressure and its normal gradient. A complex irrational equation governs the propagation, attenuation and dispersion of the Rayleigh waves. A complex analysis technique is used to solve this equation into an explicit expression for complex phase velocity. Effects of porosity and seepage from surface pores are analyzed numerically on the velocity of Rayleigh wave in a saturated poroelastic material. [ABSTRACT FROM AUTHOR]

The problem of scattering of a plane compressional acoustic wave in a fluid from a spherical poroelastic inclusion is considered. The elastic wave propagation in the inclusion is described by the equations of the Biot theory. The wave field in the inclusion consists of fast and slow compressional and shear waves. Outside the inclusion, a scattered spherical compressional wave is formed. The solution for an isolated inclusion is obtained in terms of series of spherical Bessel functions and Legendre polynomials. This solution is used for the calculation of effective wave number of compressional wave propagating in the fluid containing a set of poroelastic inclusions (suspension). For deriving the effective wave number, the theory of multiple scattering is used. It is shown that the effective wave number depends strongly on hydrodynamic permeability of inclusions and fluid properties in the inclusion pore space. [ABSTRACT FROM AUTHOR]

InSAR displacement time-series are emerging as a valuable product to study a number of Earth processes. One challenge to current time-series processing methods, however, is that when large earthquakes occur, they can leave sharp coseismic steps in the time-series. These discontinuities can cause current atmospheric correction and noise smoothing algorithms to break down, as these algorithms commonly assume that deformation is steady through time. Here, we aim to remedy this by exploring two methods for correcting earthquake offsets in InSAR time-series: a simple difference offset estimate (SDOE) process and a multiparameter offset estimate (MPOE) parametric time-series inversion technique. We apply these methods to a 2-yr time-series of Sentinel-1 interferograms spanning the 2019 Ridgecrest, CA earthquake sequence. Descending track results indicate that the SDOE method precisely corrects for only 20 per cent of the coseismic offsets at 62 study locations included in our scene and only partially corrects or sometimes overcorrects for the rest of our study sites. On the other hand, the MPOE estimate method successfully corrects the coseismic offset for the majority of sites in our analysis. This MPOE method allows us to produce InSAR time-series and data-derived estimates of deformation during each phase of the earthquake cycle. In order to better isolate and estimate the signal of post-seismic lithospheric deformation in the InSAR time-series, we apply a GNSS-based correction to our interferograms. This correction ties the interferograms to median-filtered weekly GNSS displacements and removes additional atmospheric artefacts. We present InSAR-based estimates of post-seismic deformation for the area around the Ridgecrest rupture, as well as a 2-yr coseismic-corrected, GNSS-corrected InSAR time-series data set. This GNSS-corrected InSAR time-series will enable future modelling of post-seismic processes such as afterslip in the near field of the rupture, poroelastic deformation at intermediate distances and viscoelastic deformation at longer timescales in the far field. [ABSTRACT FROM AUTHOR]

Large earthquakes can alter regional groundwater pressure, resulting in fluid flow, and the process of restoring hydrostatic equilibrium would in turn lead to observable surface deformation, termed poroelastic rebound, which is one of the most important post-seismic mechanisms for stress transfer and triggering. To constrain the poroelastic contributions to the early post-seismic deformation, we model the hydrologic response within 1.5 months following the 2015 M w 8.3 Illapel earthquake and remove its effects from the observed geodetic signals. Results demonstrate the post-seismic fluid-flow patterns from the co-seismic high-slip region to the north and south sides, and the northern poroelastic effects are remarkably stronger than those on the south side, verified by northern liquefaction phenomena. Therefore, previous pure afterslip models overestimate the asperities on both flanks of the co-seismic rupture zone and underestimate the middle region, with local errors of more than 50 per cent. It highlights the importance of considering the poroelastic effects, when modelling the transient post-seismic deformation. [ABSTRACT FROM AUTHOR]

This article presents an algorithm for the numerical solution of an initial-boundary value problem for a symmetric t-hyperbolic system of partial differential equations. This problem is based on continual filtration model, which describes the propagation of seismic waves in a poroelastic medium saturated with a fluid characterized by such physical parameters as the propagation velocities of longitudinal P- (fast and slow) and transverse S-waves, the density of the medium materials, and porosity. The system of linearized equations of saturated porous media is formulated in terms of physical variables of the velocity–stress tensor of the porous matrix and the velocity–pressure of the saturating fluid in the absence of energy dissipation. The solution is implemented numerically using an explicit finite difference upwind scheme built on a staggered grid to avoid the appearance of oscillations in the solution functions. The program code implementing parallel computing is developed in the high-performance Julia programming language. The possibility of using the approach is demonstrated by the example of solving the problem of propagation of seismic waves from a source located in the formation. Computational experiments based on real data from oil reservoirs have been implemented, and dynamic visualization of solutions consistent with the first waves arrival times has been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider the poroelasticity problem in heterogeneous media. The mathematical model is described by a coupled system of equations for displacement and pressure in the coupled dual continuum porous media. We propose a new method based on hybrid explicit–implicit (HEI) learning to solve the poroelasticity problem in dual continuum heterogeneous media. We use a finite element method with standard linear basis functions for spatial approximation. We apply the explicit–implicit time scheme, where the explicit scheme is used for the low-conductive continuum and the implicit scheme for the high-conductive. The fixed-strain splitting scheme is used to accelerate the computation and decouple the flow and mechanics problems. The main idea of the proposed method is partial learning of particular degrees of freedom of the high-conductive continuum's pressure (implicit part of the flow). First, we train a deep neural network (DNN) to obtain values of the implicit part of the flow at some spatial points at some time moments. Then, we apply the Discrete Empirical Interpolation Method (DEIM) combined with Proper Orthogonal Decomposition (POD) to restore the complete implicit parts and perform linear interpolation over time. Consequently, we treat the high-conductive continuum's pressure as a known function and use it to find the other continuum's pressure and displacements. Numerical results for the two-dimensional model problem are presented. The results demonstrate that the proposed method provides fast and accurate predictions. [ABSTRACT FROM AUTHOR]

Studies of seismicity induced by water level changes in reservoirs and lakes focus typically on well-documented contemporary records. Can such interactions be explored on a historical timescale when the two data types suffer from severe uncertainties stemming from the different nature of the data, methods and resolution? In this study, we show a way to considerably improve the correlation between interpolated records of historical Dead Sea level reconstructions and discrete seismicity patterns in the area, over the period of the past 2 millennia. Inspired by the results of our previous study, we carefully revise the historical earthquake catalog in the Dead Sea to exclude remote earthquakes and include small local events. For addressing the uncertainties in lake levels, we generate an ensemble of random interpolations of water level curves and rank them by correlation with the historical records of seismic stress release. We compute a synthetic catalog of earthquakes, applying a Mohr–Coulomb failure criterion. The critical state of stress at hypocentral depths is achieved by static poroelastic deformations incorporating the change in effective normal stress (due to the best-fit water level curve) superimposed on the regional strike-slip tectonic deformations. The earthquakes of this synthetic catalog show an impressive agreement with historical earthquakes documented to have damaged Jerusalem. We refine the seismic catalog by searching for small local events that toppled houses in Jerusalem; including all local events improves the correlation with lake levels. We demonstrate for the first time a high correlation between water level changes and the recorded recurrence intervals of historical earthquakes. [ABSTRACT FROM AUTHOR]

In a reversible hydrodynamic approximation, a closed system of second order dynamic equation with respect to the displacement vector of an elastic porous body and pore pressure has been obtained. The Cauchy problem for the obtained system of poroelasticity equations in the stationary case is considered. The Carleman formula for the Cauchy problem under consideration has been constructed. [ABSTRACT FROM AUTHOR]

Hydrocarbon reservoirs with low porosity and permeability are usually vulnerable to be contaminated owing to the drilling and completion fluids-induced formation damage, which significantly impedes the efficient production of hydrocarbon. However, most current productivity prediction models introduce the concept of skin factor to capture the near-wellbore contamination, which only considers the change of permeability before and after contamination, whereas neglecting the change of threshold pressure gradient (TPG) affected by the permeability reduction. Also, few works have been done to focus on the influences of contamination, TPG, sensitivity of rock porosity to internal stress, and fluid compressibility simultaneously in the actual production process of the low-permeability reservoir. Therefore, to bridge the knowledge gap, this study presents a new comprehensive productivity model encompassing those multiple influencing factors. Firstly, the seepage area is divided into contaminated zone and uncontaminated zone. Thereafter, the proposed model is established based on non-Darcy seepage theory and continuity principle, comprehensively taking account of the effects of different permeability and TPG between contaminated zone and uncontaminated zone, stress sensitivity based on primary stress in porous media, and the fluid compressibility. Subsequently, the newly proposed model is proved to be reliable through the consistency between the simplified model and the existing models in the literatures. Finally, the sensitivity analysis is employed to investigate the effects of key parameters. Main results show that a) the decreased permeability affected by contamination would result in increased TPG, further lowering the well productivity. b) Contamination, TPG and stress sensitivity will cause additional pressure drop and production loss, which will overestimate the production rate by neglecting them. While the fluid compressibility could boost the well productivity, which will underestimate the production rate by ignoring it. c) The order of productivity influencing factors is contamination > TPG > the fluid compressibility > stress sensitivity. d) Contamination and the TPG are significant influencing factors at stage of high bottomhole pressure. Moreover, the influence degree of contamination, the fluid compressibility and stress sensitivity gradually increase, while the influence degree of the TPG greatly decreases with lower pressure. • Established a new productivity prediction model considering the contamination impact for the low-permeability reservoirs. • The contamination, threshold pressure gradient, stress sensitivity, and fluid compressibility were all considered. • The newly proposed model was validated by compared with the one presented by other scholars. • Main-dominated productivity factors were significantly investigated. [ABSTRACT FROM AUTHOR]

Myocarditis is a general set of mechanisms that manifest themselves into the inflammation of the heart muscle. In 2017, more than 3 million people were affected by this disease worldwide, causing about 47,000 deaths. Many aspects of the origin of this disease are well known, but several important questions regarding the disease remain open. One of them is why some patients develop a significantly localised inflammation while others develop a much more diffuse inflammation, reaching across large portions of the heart. Furthermore, the specific role of the pathogenic agent that causes inflammation as well as the interaction with the immune system in the progression of the disease are still under discussion. Providing answers to these crucial questions can have an important impact on patient treatment. In this scenario, computational methods can aid specialists to understand better the relationships between pathogens and the immune system and elucidate why some patients develop diffuse myocarditis. This paper alters a recently developed model to study the myocardial oedema formation in acute infectious myocarditis. The model describes the finite deformation regime using partial differential equations to represent tissue displacement, fluid pressure, fluid phase, and the concentrations of pathogens and leukocytes. A sensitivity analysis was performed to understand better the influence of the most relevant model parameters on the disease dynamics. The results showed that the poroelastic model could reproduce local and diffuse myocarditis dynamics in simplified and complex geometrical domains. [ABSTRACT FROM AUTHOR]

This paper concerns the Time-Domain Full Waveform Inversion (FWI) for dispersive and dissipative poroelastic materials. The forward problem is an initial boundary value problem (IBVP) of the poroelastic equations with a memory term; the FWI is formulated as a minimization problem of a least-square misfit function with the (IBVP) as the constraint. In this paper, we derive the adjoint problem of this minimization problem, whose solution can be applied to computed the direction of steepest descent in the iterative process for minimization. The adjoint problem has a similar numerical structure as the forward problem and hence can be solved by the same numerical solver. Because the tracking of the energy evolution plays an important role in the FWI for dissipative and dispersive equations, the energy analysis of the forward system is also carried out in this paper. [ABSTRACT FROM AUTHOR]

Squirt flow is a wave-induced fluid flow mechanism to account for the velocity dispersion and attenuation of fluid-saturated porous media. Theoretical models of squirt flow cannot deal with complex microcrack-pore networks and thus cannot give accurate dispersion and attenuation curves with respect to frequency. We adopt a numerical oscillatory compressibility test method, based on the quasi-static poroelastic equation of Biot, to model the squirt flow and calculate corresponding P-wave modulus dispersion and attenuation. We also designed nine porous medium models containing different crack-pore configurations and investigated the effects of microcrack porosity, orientation and connectivity on the elastic responses. Modelling results show that not only microcrack porosity but also their orientation has control on the magnitude of the P-wave modulus dispersion and attenuation. Preferentially aligned microcracks may cause frequency-dependent anisotropy in the P-wave modulus and attenuation. Microcrack connectivity has a negligible influence on the dispersion and attenuation magnitude but a large influence on the characteristic frequency of the squirt flow, which is not predicted by theoretical models based on simple representative element volume of crack-pore structure. Therefore, detailed geometry of crack-pore network, of which microcrack porosity, orientation, aspect ratio and connectivity are vital factors, dictates the unique variations in the elastic modulus and associated attenuation with frequency caused by the squirt flow. Pore structure obtained by CT scanning representative of that of the whole rock is needed to obtain more accurate poroelastic responses of the rock with the numerical oscillatory compressibility test method. In this regard, we provide a powerful tool for evaluating dispersion and attenuation of fluid-saturated rock media with complex crack-pore structure, which have potential applications in seismic exploration of hydrocarbon in the subsurface. [ABSTRACT FROM AUTHOR]

Crustal magmatic systems likely consist of magmatic reservoirs dominated by crystal mush. Recent studies suggest that the physical processes occurring in crystal mush could alter the response of magmatic reservoirs during volcanic unrest. Here, we present a magma chamber deformation model that incorporates two new aspects in crystal mush: heat and exsolved gas. The model is based on earlier studies by Liao et al. (2021, https://doi.org/10.1029/2020JB019395) with additional processes including thermal‐mechanical coupling, dependence of material properties on gas content, and temperature evolution following an injection of hotter magma. The post‐injection time‐dependent evolution of the system can be grouped into three periods, which are dominated by poroelastic diffusion (short term), viscoelastic relaxation (mid term), and thermal equilibration (long term). All three time‐regimes are strongly affected by gas distribution, which alters the relative compressibility of the crystal‐rich and crystal‐poor regions in the chamber. The contribution of thermal evolution emerges during the mid‐term evolution. The time‐dependent evolution of the system highlights the intrinsic ability of a gas‐bearing mushy magma chamber to generate non‐monotonic time series of stresses, deformation, and magma transport. Plain Language Summary: The processes that occur in magmatic reservoirs and their surrounding crustal rocks can modulate the triggering, duration, and style of volcanic eruptions. Although magmatic reservoirs are typically modeled as cavities filled with fluid magma, geophysical and petrological observations have long suggested that they likely contain crystal mush, an ensemble of solid crystals and fluid (gas/melt) that reside in interstitial pore spaces. Some recent studies show that a mushy magma chamber could behave differently than a fluid‐filled chamber, leading to different interpretation of observations such as ground deformation. Here, we extend these studies to incorporate two new aspects that are typical for crustal magmatic systems: gas phase (in the form of disconnected gas bubbles) and nonuniform temperature. The incorporation of these two new aspects allows for more processes that can be examined quantitatively, and a more realistic depiction of crustal magmatic reservoirs. We find that when gas and heat distribute unevenly, a simple magma injection event could result in complex time‐dependent changes in pressure, stress, and magma flows in the chamber. Key Points: A physics‐based model explores the influence of gas and heat in the a magma chamber containing crystal mush upon magma injectionThe non‐uniform distributions of gas and heat cause non‐monotonic time evolution of deformation, crustal stresses, and magma transportPoroelastic diffusion, viscous relaxation, and thermal equilibration lead to three time regimes in the post‐injection evolution [ABSTRACT FROM AUTHOR]

We observed temperature variations over 10 months within a Kuroko ore (hydrothermal sulfide) cultivation apparatus installed atop a 50‐m‐deep borehole drilled in the Noho hydrothermal system in the mid‐Okinawa Trough, southwestern Japan, for monitoring of hydrothermal fluids and in situ mineral precipitation experiments. Temperature and pressure in the apparatus fluctuated with the tidal period immediately after its installation. Initially, the average temperature was 75–76°C and the amplitude of the semidiurnal tidal temperature modulation was ∼0.3°C. Four months later, the amplitude of tidal temperature modulation had gradually increased to 4°C in synchrony with an average temperature decrease to ∼40°C. Numerical modeling showed that both the increase in tidal amplitude and the decrease in average temperature were attributable to a gradual decrease in inflow to the apparatus, which promoted conductive cooling through the pipe wall. The reduced inflow was probably caused by clogging inside the apparatus, but we cannot rule out a natural cause, because the drilling would have significantly decreased the volume of hot fluid in the reservoir. The temperature fluctuation phase lagged the pressure fluctuation phase by ∼150°. Assuming that the fluctuations originated from inflow from the reservoir, we conducted 2D numerical hydrothermal modeling for a poroelastic medium. To generate the 150° phase lag, the permeability in the reservoir needed to exceed that in the ambient formation by ∼three orders of magnitude. The tidal variation phase can be a useful tool for assessing the hydrological state and response of a hydrothermal system. Plain Language Summary: Subseafloor magmatic activity causes vigorous fluid flow, called hydrothermal circulation, between magma and seawater. Hot hydrothermal fluid vented at the seafloor often contains many valuable metals and minerals, which precipitate instantly when the fluid is released into the cold seawater. The Kuroko ore‐cultivation project envisions collecting these metals and minerals by drilling into a hydrothermal reservoir and deploying an artificial cultivation apparatus atop the borehole. In this study, we aimed to characterize the behavior of the captured fluid by continuously monitoring temperature and pressure in the cultivation apparatus. We successfully obtained a 10‐month‐long data series from atop a 50‐m‐deep borehole drilled in the Noho hydrothermal system in the mid‐Okinawa Trough, southwestern Japan. Initially, the hot fluid (∼76°C) flowed freely through the cultivation apparatus, but after about 4 months, the inflow dropped significantly, probably because of clogging inside the apparatus. The reduction in flow causes conductive cooling of the fluid to ∼40°C, and the amplitude of the tidally modulated temperature variation also increased. The phase difference between the pressure and temperature variations allowed us to infer the permeability of the reservoir. We propose that the Noho hydrothermal system has higher permeability than the surrounding materials. Key Points: Temperature and pressure atop a borehole in the mid‐Okinawa Trough hydrothermal system fluctuated with the tidal period during 10 monthsThe temperature tidal fluctuation phase lagged pressure by ∼150° likely because of the poroelastic response of higher permeability sedimentA gradual temperature decrease and tidal amplitude increase were caused by reduced inflows that promoted conductive cooling [ABSTRACT FROM AUTHOR]

We develop the a posteriori error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretizations use H1-conforming finite elements of degree k+1 for displacement and fluid pressure, and discontinuous piecewise polynomials of degree k for rotation vector, total pressure, and elastic pressure. Residual-based estimators are constructed, and upper and lower bounds (up to data oscillations) for all global estimators are rigorously derived. The methods are all robust with respect to the model parameters (in particular, the Lamé constants); they are valid in 2D and 3D, and also for arbitrary polynomial degree k≥0. The error behavior predicted by the theoretical analysis is then demonstrated numerically on a set of computational examples including different geometries on which we perform adaptive mesh refinement guided by the a posteriori error estimators. [ABSTRACT FROM AUTHOR]

Although different fluid pressure diffusion mechanisms caused by fractures have been extensively studied using analytical and numerical methods, there is little to no experimental work completed on them in laboratory conditions. In this paper, hydrostatic-stress oscillations (frequency − 0.04 to 1 Hz) are used on an intact and saw cut sample, in dry and water saturated conditions, in a triaxial cell at different effective pressures in undrained conditions. The objective is to study the fracture's effect on the elastic properties of the sample and validate some computational fracture models, that have been explored in the literature. Experimental results highlight dispersion and attenuation in saturated conditions due to the fracture, which diminishes in amplitude as the effective pressure is increased, i.e. as the fracture is closed. From local strain gauge measurements, it is found that there is a local negative phase shift between stress and strain in water saturated conditions for the fractured sample, due to the location of the strain measurements. No attenuation observed in dry conditions. A simple 1D model using mass balance and mechanical equilibrium equations for a linear isotropic poroelastic homogeneous medium give prediction in very good agreement with the experimental results. A 3D model was also developed to allow a comparison between analytic, numerical and experimental results. Highlights: Using innovative microvalves in an experimental setup on a fractured rock sample, to reach undrained conditions, in seismic frequency range. Local strain measurements, for the first time experimentally, show local negative phase shift between stress and strain in water saturated conditions. A 1D analytical and 3D numerical model were created which are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

Complex coupled thermo-hydromechanical (THM) loading paths are expected to occur in clay rocks which serve as host formations for geological radioactive waste repositories. Exothermic waste packages heat the rock, causing thermal strains and temperature induced pore pressure build-up. The drifts are designed in such a way as to limit these effects. One has to anticipate failure and fracturing of the material, should pore pressures exceed the tensile resistance of the rock. To characterise the behaviour of the Callovo-Oxfordian claystone (COx) under effective tension and to quantify the tensile failure criterion, a laboratory program is carried out in this work. THM loading paths which correspond to the expected in situ conditions are recreated in the laboratory. To this end, a special triaxial system was developed, which allows the independent control of radial and axial stresses, as well as of pore pressure and temperature of rock specimens. More importantly, the device allows one to maintain axial effective tension on a specimen. Saturated cylindrical claystone specimens were tested in undrained conditions under constrained lateral deformation and under nearly constant axial stress. The specimens were heated until the induced pore pressures created effective tensile stresses and ultimately fractured the material. The failure happened at average axial effective tensile stresses around 3.0 MPa. Fracturing under different lateral total stresses allows one to describe the failure with a Hoek–Brown or Fairhurst's generalized Griffith criterion. Measured axial extension strains are analysed based on a transversely isotropic thermo-poroelastic constitutive model, which is able to satisfactorily reproduce the observed behaviour. Highlights: Thermal pressurization of clay rock in deep radioactive waste repositories can reduce the effective stresses, which can lead to damage or failure. Our novel laboratory triaxial device is able mimic in situ conditions: Constant vertical total stress, zero lateral deformation and thermal pressurization. Pore pressure increase, vertical extension strains and thermal pressurization failure were recorded in a series of tests on Callovo-Oxfordian claystone specimens. The effective tensile strength was reached at values around 3 MPa in tension and temperatures between 53 and 64 °C, creating sub-horizontal fractures. The experimental responses can be well reproduced using a thermo-poroelasticity model. Hoek–Brown and Fairhurst generalized Griffith criteria appear suitable to account for the rock's tensile resistance. [ABSTRACT FROM AUTHOR]

Crustal rocks undergo repeated cycles of stress over time. In complex tectonic environments where stresses may evolve both spatially and temporally, such as volcanoes or active fault zones, these rocks may experience not only cyclic loading and unloading, but also rotation and/or reorientation of stresses. In such situations, any resulting crack distributions form sequentially and may therefore be highly anisotropic. Thus, the tectonic history of the crust as recorded in deformed rocks may include evidence for complex stress paths, encompassing different magnitudes and orientations. Despite this, the ways in which variations in principal stresses influence the evolution of anisotropic crack distributions remain poorly constrained. In this work, we build on the previous non-linear anisotropic damage rheology model by presenting a newly developed poroelastic rheological model which accounts for both coupled anisotropic damage and porosity evolution. The new model shares the main features of previously developed anisotropic damage and scalar poroelastic damage models, including the ability to simulate the entire yield curve through a single formulation. In the new model, the yield condition is defined in terms of invariants of the strain tensor, and so the new formulation operates with directional yield conditions (different values for each principal direction) depending on the damage tensor and triaxial loading conditions. This allows us to discern evolving yield conditions for each principal stress direction and fit the measured amounts of accumulated damage from previous loading cycles. Coupling between anisotropic damage and anisotropic compaction along with the damage-dependent yield condition produces a reasonable fit to the experimentally obtained stress–strain curves. Furthermore, the simulated time-dependent cumulative damage is well correlated with experimentally observed acoustic emissions during cyclic loading in different directions. As such, we are able to recreate many of the features of the experimentally observed directional 3-D Kaiser 'damage memory' effect. [ABSTRACT FROM AUTHOR]

This article describes a novel technique to estimate static Young’s modulus of stress-sensitive rocks using dynamic linear and nonlinear constants estimated from borehole sonic data. Two linear and three nonlinear constants are estimated from the transit time of compressional headwaves and inversion of borehole-guided Stoneley and crossdipole dispersions in tectonically stressed formations. A major advantage of this technique is that the rock static Young’s modulus is determined from the dynamic elastic constants measured at a chosen reference state that is rather close to the in situ conditions. These dynamic elastic constants are used in the nonlinear constitutive relations for poroelastic rocks subject to finite deformations. These relations express the second Piola–Kirchhoff axial stresses in terms of elastic constants together with up to quadratic terms in Lagrangian axial strains. Strain derivatives of the second Piola–Kirchhoff stress yield the static Young’s modulus as a function of incremental axial strains from a chosen reference state. Consequently, static Young’s modulus can also be determined at other depths with different overburden stresses and associated incremental axial strains from a chosen reference state. In contrast, strain derivative of the second Piola–Kirchhoff axial stress expressed in terms of linear elastic constants and only linear terms in axial strain provides the dynamic Young’s modulus. Two useful outputs from this workflow are the static stress–strain deformation curves for a core plug and static Young’s modulus under in situ conditions as a function of logging depth. The proposed technique has been validated with the available experimental stress–strain data from Castlegate and Berea sandstones core plugs. Results have been obtained for the static Young’s modulus and finite deformation stress–strain curves for two different stress-sensitive poroelastic formations using borehole sonic data. [ABSTRACT FROM AUTHOR]

Belarusian Potash salt deposits are bedded under aquifers and unstable soil layers. Therefore, to develop the deposits a vertical mine shaft sinking is performed using the artificial ground freezing technology. Nowadays, real-time observations of ground temperature and groundwater level is applied to control the ground freezing process. Numerical simulation can be used for a comprehensive analysis of measurements results. In this paper, a thermo-hydro-mechanical model of freezing for water-saturated soil is proposed. The governing equations of the model are based on balance laws for mass, energy and momentum for a fully saturated porous media. Clausius-Clayperon equation and poroelastic constitutive relations are adopted to describe coupled processes in water and ice pore pressure, porosity and a stress-strain state of freezing soil. The proposed model was used to predict equivalent water content measured in Mizoguchi's test and frost heave in a one-sided freezing test. Numerical simulation of ground freezing in the Petrikov mining complex located in Belarus has shown that the model is able to describe field measurements of pore pressure inside a forming frozen wall. Furthermore, the mismatch between hydro- and thermo-monitoring data obtained during the artificial freezing is analyzed. [ABSTRACT FROM AUTHOR]

The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multicompartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential. To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with precomputed cardiac displacements, obtained form other models or medical imaging data. We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon, which is particularly challenging to capture as it arises from the interaction of several parts of the model. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the dynamic behaviour of layered transversely isotropic (TI) poroelastic media subjected to rectangular harmonic loads. First, governing equations of a medium layer derived from Biot's dynamic theory of porous media and constitutive equations of TI materials are converted into the ordinary differential domain by means of integral transform techniques. Next, by introducing boundary and load conditions, the extended precise integration method (PIM) is applied to obtain the solution for a multi‐layered system. Then, after an inverse integral treatment, the numerical results in the physical domain are verified with published work, and some examples are designed to unravel the effect of transverse isotropy, load frequencies and stratification on the dynamic behaviour of media. [ABSTRACT FROM AUTHOR]

We revisit the general theory of finite-strain deformations in fluid-saturated porous media via the thermodynamics of nonequilibrium processes. Our aim is the thermodynamically consistent derivation of governing equations that satisfy the principle of material frame indifference, starting with the minimal number of assumptions. In the first part, we treat the relative fluid velocity as a constitutive variable, and hence fully determined by the macroscopic thermodynamic state of the continuum. However, this hypothesis is not rich enough to account for the tortuosity effect in poroacoustics, second-gradient effects, or Brinkman's correction to Darcy's law, thus motivating its relaxation in the second part, where we consider the relative fluid velocity as an independent kinematic variable. This approach yields an additional balance equation reflecting, in an average sense, the micromechanics of the fluid flow, which is derived from the principle of virtual power. Finally, we show that the resulting general model is consistent with Biot's linear theory of acousto-poro-elasticity. [ABSTRACT FROM AUTHOR]

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We present a multi-scale mathematical model and a novel numerical solver to study blood plasma flow and oxygen concentration in a prototype model of an implantable Bioartificial Pancreas (iBAP) that operates under arteriovenous pressure differential without the need for immunosuppressive therapy. The iBAP design consists of a poroelastic cell scaffold containing the healthy transplanted cells, encapsulated between two semi-permeable nano-pore size membranes to prevent the patient's own immune cells from attacking the transplant. The device is connected to the patient's vascular system via an anastomosis graft bringing oxygen and nutrients to the transplanted cells of which oxygen is the limiting factor for long-term viability. Mathematically, we propose a (nolinear) fluid–poroelastic structure interaction model to describe the flow of blood plasma through the scaffold containing the cells, and a set of (nonlinear) advection–reaction–diffusion equations defined on moving domains to study oxygen supply to the cells. These macro-scale models are solved using finite element method based solvers. One of the novelties of this work is the design of a novel second-order accurate fluid–poroelastic structure interaction solver, for which we prove that it is unconditionally stable. At the micro/nano-scale, Smoothed Particle Hydrodynamics (SPH) simulations are used to capture the micro/nano-structure (architecture) of cell scaffolds and obtain macro-scale parameters, such as hydraulic conductivity/permeability, from the micro-scale scaffold-specific architecture. To avoid expensive micro-scale simulations based on SPH simulations for every new scaffold architecture, we use Encoder–Decoder Convolution Neural Networks. Based on our numerical simulations, we propose improvements in the current prototype design. For example, we show that highly elastic scaffolds have a higher capacity for oxygen transfer, which is an important finding considering that scaffold elasticity can be controlled during their fabrication, and that elastic scaffolds improve cell viability. The mathematical and computational approaches developed in this work provide a benchmark tool for computational analysis of not only iBAP, but also, more generally, of cell encapsulation strategies used in the design of devices for cell therapy and bio-artificial organs. [ABSTRACT FROM AUTHOR]

Benchmark problems commonly used to test numerical methods for fluid-poroelastic structure interaction often rely on simple examples constructed using the method of manufactured solutions. In this work, we show that such examples are not adequate to demonstrate the performance of the method, especially in cases when the poroelastic system is written in the primal or primal-mixed formulation, and when the dynamics of the poroelastic structure are driven only by dynamic loading from the fluid, which often occurs in biomedical applications. In those cases, the only forcing on the structure comes from the interaction with the fluid at the fluid-structure interface, where the coupling conditions are imposed. One of those conditions is a kinematic condition which enforces the conservation of mass. If this condition is not accurately satisfied, the resulting dynamics might lead to highly inaccurate results in the entire domain. We present three benchmark problems: Example 1 is based on the method of manufactured solutions; Example 2 is based on parameters used in geomechanics; and Example 3 is a benchmark problem with parameters from hemodynamics. Using these examples, we test the performance of the primal, primal-mixed and dual-mixed formulations. While all methods perform well in the first two examples, the primal and primal-mixed formulations exhibit large errors in Example 3, where the densities of the fluid and solid are comparable, and the structure dynamics is purely driven by the fluid loading. To recover the accuracy, we propose to use the primal and primal-mixed methods with a penalty term, which helps to enforce the conservation of mass. • Simple benchmark problems may not be sufficient for validating numerical solvers for fluid-poroelastic structure interaction. • The mass conservation is not accurately satisfied in the primal and primal mixed formulations. • To address these issues, we propose modifications to the primal and primal mixed methods by adding a penalization term. [ABSTRACT FROM AUTHOR]

A poroelastic medium is defined as a continuous system in which the mechanical response arises from the interaction between a deformable elastic solid skeleton and a pressurised fluid, fully saturating the interconnected porous network. The coupled theory of Poromechanics is effectively employed to solve a broad class of problems spanning various fields, ranging from its original application in Geomechanics to addressing contemporary challenges in tissue Biomechanics. Besides the seminal theory introduced by Biot, several variational multi-field principles have been proposed, leading to various finite element formulations. Finite Element approaches are mostly based on a two-field discretisation involving the coupled solid displacement and interstitial fluid pressure as primary variables. However, this choice of the two-primary variables leads to a saddle-point problem, posing a challenge in achieving accurate solutions and thus making the use of stabilisation methods rather mandatory. This study proposes a novel variationally consistent Hybrid Equilibrium Element formulation, based on the complementary strain energy function. A two-field minimisation principle is formulated, with total Cauchy stress and interstitial fluid pressure serving as primary variables. The proposed variational principle provides a variationally consistent framework for designing inherently self-equilibrated Hybrid Equilibrium Elements, where the solid displacement field emerges as a Lagrangian variable to enforce a co-diffusivity constraint at element sides. The fulfilment of the inf-sup condition, typically challenging in developing stable and computationally efficient finite element formulations, is no longer required, a minimisation principle having been adopted, rather than the classical saddle-point principle. The proposed Hybrid Equilibrium Element approach offers a statically admissible solution even in the proximity of singularities or high space gradient stress distribution, providing a more comprehensive assessment of stress distributions and concentrations. The convexity of the new variational principle has been established, ensuring solution uniqueness. The formulation is based on a 2-D triangular Hybrid Equilibrium Element employed to solve plane strain problems. The element has been implemented in the Open source Finite Element Analysis Program (FEAP) and its performance evaluated against classical benchmark problems for poroelasticity, with the emphasis on stress accuracy. The numerical results obtained for the quasi-static analysis of poroelastic systems show the advantages of the proposed approach, in which accurate stress distributions are displayed, even adopting quite coarse meshes. Remarkably, in the proposed approach no stabilisation technique is required. [ABSTRACT FROM AUTHOR]

Conventional technical means are no longer sufficient to fully explain the intrinsic linkage between exogenous fillers and structural changes of meat gels. In this study, poroviscoelasticity (PVE) as a new perspective was introduced. Firstly, the effects of regenerated cellulose microspheres (RCM) and spherical nanocellulose (SNC) in varying amounts (0, 2.5, 5.0, 7.5, 10.0 wt%) on the meat gels were investigated. The incorporation of both RCM and SNC resulted in a denser and more uniform microstructure of meat gels. Compared to pure meat gels, the cooking loss was reduced by 23.8 % and 33.6 %, respectively. The better effect of SNC on meat gels was correlated with its smaller size. Secondly, the mechanical responses of meat gels at different indentation depths were characterized by the spherical indentation method. The results showed that the force relaxation during the indentation process of meat gels was primarily due to the combined effects of poroelasticity (PE) and viscoelasticity (VE). Specifically, a quick VE relaxation was observed with a relaxation time of 10.0 s and 14.5 s for RCM-meat gels and SNC-meat gels, respectively. When RCM and SNC were added at 5.0 wt% and 7.5 wt%, the permeability of gels was significantly lower than that of pure meat gels (p < 0.05), especially when the indentation depth was 2 mm and 3 mm. On the whole, the PVE parameters aligned well with the results of hydration properties and microstructure, so the meat gels could be regarded as a type of porous viscoelastic material, and this study can provide a theoretical basis for the in-depth analysis of the structural properties of meat products using the PVE model. [Display omitted] • Cellulose improves the microstructure and hydration properties of meat gels. • SNC provides a superior filling effect. • Indentation technique applied to obtain material parameters of meat gels. • Hydration capacity of meat gels can explain poroviscoelasticity characteristics. [ABSTRACT FROM AUTHOR]

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including phase-field dependent material properties, with the Cahn–Hilliard equation to model the evolution of the solid, and is further augmented by a visco-elastic regularization of Kelvin–Voigt type. To obtain this result, we approximate the problem in two steps, where first a semi-Galerkin ansatz is employed to show existence of weak solutions to regularized systems, for which later on compactness arguments allow limit passage. Notably, we also establish a maximal regularity theory for linear visco-elastic problems. [ABSTRACT FROM AUTHOR]

The present study aims to analyze the propagation behavior of Love-type wave in a composite transversely isotropic porous structure. The structure comprises an inhomogeneous sandy porous layer lying between a non-homogeneous magneto-poroelastic layer and a heterogeneous fractured porous half-space. Analytic solutions of the field equations of the respective media involve the application of the variable separable method and Wentzel-Kramers-Brillouin (WKB) asymptotic approach for the conversion of partial differential equations into ordinary differential equations. Through careful imposition of boundary conditions and subsequent elimination of arbitrary constants, we derive a complex dispersion relation governing the propagation of Love-type waves. This dispersion equation yields both the phase velocity curve, corresponding to the real expression, and the damping velocity curve, derived from the imaginary expression. To represent our findings, we conduct extensive calculations and graphical simulations illustrating the influence of various material parameters such as heterogeneity, porosity, volume fraction of fractures, sandiness, magnet-oelastic coupling, angle at which wave crosses the magnetic field, and layer thickness on the dispersive nature of Love-type waves using MATHEMATICA software. Furthermore, we conduct case-specific analyses, revealing instances where the dispersion equation simplifies to the standard Love wave equation, thereby validating our mathematical framework. Our findings underscore the significant influence of the aforementioned material parameters on the phase and damping velocities of Love-type wave. This interdisciplinary investigation into different porous media opens new avenues for future research and has significant implications in various disciplines, ranging from engineering and geophysics to environmental science and beyond.   • Study of Love-type wave in a composite structure of anisotropic porous materials. • Variable separable and WKB approach for Love wave dispersion equation. • Comparison with classical Love wave equations for validation. • Impact of Quadratic, linear, and exponential heterogeneity on Love wave propagation. • Phase and damping velocity profiles of Love waves with different material parameters. [ABSTRACT FROM AUTHOR]

We introduce a second-order computational homogenization procedure designed to address heterogeneous poromechanical media. Our approach relies on the method of multiscale virtual power, a variational multiscale method that extends the Hill–Mandel principle of macro-homogeneity. Constraints on displacement and pore pressure fields are managed using periodic and second-order minimally constrained fluctuating spaces. Numerical comparisons reveal that first-order models fail to accurately represent nonzero net fluid flow and volume changes at the micro-scale. In contrast, our second-order approach effectively captures nonuniform fluid flow across representative volume element boundaries, in agreement with results from direct numerical simulations. Our findings indicate that the classical first-order expansion of the pressure field is inadequate for poromechanical homogenization in cases involving micro-scale volume changes, such as swelling or contraction. The proposed second-order approach not only overcomes these limitations but also proves effective in cases where the principle of separation of scales is not strictly upheld. • Numerical scheme for second-order homogenization of heterogeneous poromechanical media. • Second-order model is able to represent nonzero net fluid flow at the micro-scale unlike first-order models. • Results of numerical examples show very good agreement with direct numerical simulation (DNS). [ABSTRACT FROM AUTHOR]

The role of poroelasticity in influencing the frequency of ruptures jumping through strike-slip stepovers remains unclear. To understand how poroelastic effects govern long-term rupture behavior in strike-slip fault systems with stepovers, we conduct earthquake sequence simulations incorporating undrained pore pressure responses across the full spectrum of Skempton's coefficient. Our findings reveal that Skempton's coefficient significantly affects the effective normal stress, which can either cause fault clamping or unclamping, and ultimately influences rupture propagation across fault stepovers. The likelihood of rupture jumping is predominantly determined by Skempton's coefficient and the width of the stepover, with Skempton's coefficient showing an approximately linear relationship to the critical jumpable step size. Specifically, a higher Skempton's coefficient facilitates rupture jumping across fault segments, even over larger stepover distances. Analytical solutions involving dislocation and Skempton's coefficient provide practical methods for evaluating pore pressure changes and associated seismic hazards near fault stepovers. Our statistical analysis identifies a critical jumpable width of 4.4–5.1 km due to static stress transfer, assuming a typical range of Skempton's coefficient for compressional stepovers, beyond which ruptures are unlikely to propagate. This study underscores the potential of using physics-based earthquake sequence models to reflect statistical fault rupture behaviors. Given that multi-segment earthquake ruptures present challenges in assessing maximum rupture lengths, our findings offer crucial insights into the role of poroelastic effects and the conditions that facilitate or limit rupture propagation across fault stepovers. • Poroelastic effects influence rupture behavior in strike-slip fault systems. • Skempton's coefficient impacts rupture propagation across stepovers. • Higher Skempton's coefficient facilitates rupture jumping across larger stepovers. • Critical jumpable width for ruptures identified as 4.4–5.1 km. • Analytical solutions offer practical methods for assessing seismic hazards. [ABSTRACT FROM AUTHOR]

Many hydraulic fracturing experiments suggest that low-viscosity fluid tends to generate a complex fracture network, which may be beneficial for geo-energy production. However, the precise impacts of low-viscosity fluid on the fracture nucleation and propagation are unknown. This study focuses on the stress jump at weak interfaces (e.g., grain boundaries or natural fractures) caused by the contrast in Biot's coefficient, which is prevalent in hard rocks, and how failure may develop. We found that fracture nucleation at weak interfaces becomes favorable under certain Biot's coefficient contrast and fluid viscosity. Our numerical simulations of fluid injection through a borehole demonstrate that low-viscosity fluid injection can nucleate isolated fractures at remote interfaces without connecting to the main propagating fracture. These findings imply the necessity to consider Biot's coefficient variations within a rock mass in applications such as hydraulic fracturing or induced seismicity, especially when a diffused pressure gradient persists due to the low-viscosity fluid. • Tensile stress can develop at an interface whose Biot coefficient is lower. • A contrast in Biot coefficient and low fluid viscosity can promote remote fracturing. • Remote fracturing may be engineered to stimulate stiff and tight rock formations. [ABSTRACT FROM AUTHOR]

To provide theoretical guidance for intelligent compaction, this study proposes an efficient analytical model that considers the coupled dynamic interaction between a vibratory roller and a layered subgrade. The vibratory roller is simulated using a lumped parameter model, while the subgrade is characterized as a layered unsaturated poroelastic medium. The governing equations are solved using the double Fourier transform to derive the steady-state solution of this fully coupled model. The correctness of the proposed model is verified by comparing it with published analytical results and field test results. Results indicate that the vertical acceleration response of the roller drum is sensitive to variations in subgrade modulus. However, when evaluating the modulus of the current filling layer, it is crucial to consider the effects of the underlying layer on the acceleration response of the roller drum, especially when the existing subgrade thickness is less than 2 m. The influence of excitation frequency on the sensitivity of vertical acceleration response is found to be significant. For subgrade quality assessment with existing subgrade thickness less than 2 m, a low-frequency excitation load is recommended to maximize sensitivity, while both low and high excitation frequencies can be employed for thicker existing subgrades. [ABSTRACT FROM AUTHOR]

Induced seismicity due to natural gas production is observed at different sites worldwide. Common understanding states that the pressure drop caused by gas production leads to compaction, which affects the stress field in the reservoir and the surrounding rock formations and hence reactivates preexisting faults and induces earthquakes. In this study, we show that the multiphase fluid flow involved in natural gas extraction activities should be included. We use a fully coupled fluid flow and geomechanics simulator, which accounts for stress-dependent permeability and linear poroelasticity, to better determine the conditions leading to fault reactivation. In our model setup, gas is produced from a porous reservoir, divided into two compartments that are offset by a normal fault. Results show that fluid flow plays a major role in pore pressure and stress evolution within the fault. Fault strength is significantly reduced due to fluid flow into the fault zone from the neighboring reservoir compartment and other formations. We also analyze scenarios for minimizing seismicity after a period of production, such as (i) well shut-in and (ii) gas reinjection. In the case of well shut-in, a highly stressed fault zone can still be reactivated several decades after production has ceased, although on average the shut-in results in a reduction in seismicity. In the case of gas reinjection, fault reactivation can be avoided if gas is injected directly into the compartment under depletion. However, gas reinjection into a neighboring compartment does not stop the fault from being reactivated.