Search

• The aggregation and mobility of chloropyromorphite (CPY) were studied firstly. • HA enhanced CPY colloids transport by electrostatic and steric repulsions. • Ca2+ consistently inhibited the transport of CPY more than Na+ with/without HA. • The CPY adhesion to porous sandy medium was reversible. Conversion of labile Pb species into chloropyromorphite (CPY) using phosphorus-bearing amendments was considered to be an ideal strategy in soil passivation remediation. However, the fate and transport of CPY in the soil are poorly understood. This study aims to fill the knowledge gap by evaluating the fate and transport of CPY under environmentally relevant conditions of humic acid (HA), pH, electrolyte concentration, and species through the saturated sandy medium. Results showed that bare CPY colloids are basically immobile in sandy porous media while the co-existence of HA made the transport of CPY improved by 30%–93.5%. Facilitated transport of CPY was attributed to the increased stability of CPY and the repulsive interaction between CPY particles and sands due to HA adsorption. The mobility of CPY was also increased with increasing pH from 5.0 to 9.0. When the pH was 9 with a 10 mmol/L NaCl background solution, the stronger energy barrier between CPY and sand led to enhanced transport behavior. The divalent Ca2+ had a more dramatic effect than monovalent Na+ on the aggregation and sedimentation of CPY colloids due to its effectivescreening of the surface charge of CPY and bridging interaction with CPY particles. Derjaguin-Landau-Verwey-Overbeek theory and attachment efficiency calculation indicated that high energy barriers were responsible for the high mobility of CPY colloids, while the retention of CPY in sands was mainly caused by secondary energy minimum and physically straining. The findings of this work can help to evaluate the fate of soil passivation remediation products in natural water and soil. [Display omitted] [ABSTRACT FROM AUTHOR]

Summary: A multiscale model for saturated porous media is proposed, based on the concept of representative volume element (RVE). The physics between macro and micro‐scales is linked in terms of virtual power measures given by the general theory of poromechanics. Then, applying the so‐called Principle of Multiscale Virtual Power, together with suitable admissible constraints on micro‐scale displacement and pore pressure fields, a well‐established variational framework is obtained. This setting allows deriving the weak form of micro‐scale balance equations as well as the homogenization rules for the macro‐scale stress‐like variables and body forces. Whenever the micro‐scale mechanical constitutive functionals admit, as input arguments, the full‐order expansion of the micro‐scale pore pressure field, a size effect is inherited on the macro‐scale material response. The current literature attributes this issue to the so‐called "dynamical" or "second‐order" term of the homogenized flux velocity. It has been commonly suggested that the influence of this term is negligible by assuming infinitely small micro‐scale dimensions. However, such an idea compromises the fundamental notion of the existence of RVE for highly heterogeneous media. In this work, we show that the micro‐scale size dependence can be consistently eliminated by a simple constitutive‐like assumption. Accordingly, slight and selective redefinitions in the input arguments of micro‐scale material laws are proposed, leading to a constitutive formulation that allows the combination of micro‐scale variables with different orders of expansion. Just at this specific (constitutive) level, a reduced‐order expansion is selectively adopted for the micro‐scale pore pressure field. Thus, the RVE notion is restored while still retaining the major effects of the "dynamical" component of the homogenized flux velocity. The proposed formulation is implemented within a finite element squared (FE2$$ {}^2 $$) environment. Some numerical experiments are presented showing the viability of the methodology, including comparisons against analytical, mono‐scale and DNS solutions. [ABSTRACT FROM AUTHOR]

• A transmission and reflection matrix method for moving loads on a stratified TI saturated half-space is proposed. • An analytical model is proposed to simulate the responses of railway tracks on a stratified TI saturated half-space. • The effect of the material anisotropy and soil layering on the critical speed is investigated. The responses of railway tracks are significantly amplified when the high-speed train travels around the speed of waves propagating in underlying soils. The dynamic amplification phenomenon corresponding to the issue of the critical speed may compromise the stability and safety of operation and increase track damage. This paper proposes an analytical model to analyze the effect of the transverse isotropy of ground on the critical speed of railway tracks on stratified saturated soils. By using the Biot's theory, the general solutions of the transversely isotropic saturated porous medium are derived by employing the potential decomposition and Fourier transform. The transmission and reflection matrix method is extended to derive the three-dimensional fundamental solution for moving point loads acting on a multi-layered transversely isotropic saturated half-space. The models for railway tracks and wheel-axle loads are subsequently coupled to the ground. The proposed model is validated through a comparison with two existing models. Numerical studies demonstrate that the material anisotropy changes the critical speed and the corresponding dynamic amplification coefficient by up to 20%. The anisotropy in the shear modulus has the most significant influence on the critical speed, followed by Young's modulus and the permeability coefficient. The material anisotropy and soil layering cannot be ignored for the assessment of the critical speed of a track-ground system. [ABSTRACT FROM AUTHOR]

• Dynamic response of a layered saturated porous half-space due to seismic dislocation sources is addressed by using a revised stiffness matrix method. • The seismic dislocation source action is equal to the external forces imposed on the total saturated porous half-space. • The stiffness matrix is revised to capture the multi-scale and the near-surface fine structure characteristics of real half-space. The study investigating the dynamic response of seismic dislocation source in a layered saturated porous half-space, particularly the multi-scale characteristic of half-space, from crustal to geotechnical scale, is still lacking in the literature. particularly in will lead to the computation bottlenecks for multi-scale seismic wave propagation. Based on Biot's theory of wave propagation in a fluid-saturated porous solid, a dynamic stiffness matrix method is proposed to investigate the dynamic response of a multi-scale layered saturated porous half-space due to the seismic dislocation source. Assembling each layer stiffness matrix in the frequency-wavenumber domain, the global dynamic stiffness matrix is constructed to avoid errors accumulative compared to the reflection and transmission matrix method. The divergent index terms of the stiffness matrix with respect to thickness and wavenumber are extracted to revise the dynamic stiffness matrix adapted for multi-scale half-space. The seismic dislocation source action is equal to the external forces imposed on the total saturated porous half-space, which can obtain the dynamic response by using revised dynamic stiffness matrix method. The accuracy of the proposed method is verified via the comparison between the calculated results and of three published literatures. The multi-scale model with realistic near-surface fine structure is selected to investigate the effects of superficial fine structures on the dynamic responses. The numerical simulations results show that the presence of low-velocity saturated porous layers has a prominent impact on ground motion. The dynamic response seems to be sensitive to the porosity conditions, especially for high frequency, which cause the difference in variation of peak displacement value. [ABSTRACT FROM AUTHOR]

Two conventional experimental procedures for determination of the water permeability of saturated porous medium are the constant and the falling head permeability tests. The first one is more applicable on more permeable materials where the outflow from the sample is measured at variety of constant water heads, while the second one is more convenient for low permeable materials, utilizing the continuous measurements of the water head falling due to filtration through the saturated sample. However, neither of the two is useful for materials of high permeability and large cross‐sectional area. The constant head permeability test faces technical issues since a significant and continuous water discharge is required, while the falling head permeability test has limitations due to neglection of the Forchheimer's high‐velocity flow through the sample, but also the influence of inertia on the fluid mass. Here we proposed an approach for determination of the water permeability of saturated porous medium based on the agreement between the measured water level change in two connected reservoirs containing a porous sample and the new semi‐analytical expression describing that change by accounting for the mentioned theoretical deficiencies. This efficient approach has been tested on four pervious paver samples, and results showed satisfactory agreement with the constant head permeability data. It has been also confirmed the proposed semi‐analytical solution is more accurate than the falling head permeability approach in case of highly pervious materials, while for low permeable materials it reduces to the conventional approach. Key Points: The constant and the falling head permeability tests are not useful for highly pervious porous samples of large sizesA new semi‐analytical model considering Forchheimer's high‐velocity flow through the sample and inertia of the fluid mass is proposed hereThis formula is applied on a new permeability test where water flows through a highly pervious sample located between two reservoirs [ABSTRACT FROM AUTHOR]

This paper concerns the analytical investigation of the axisymmetric and steady flow of incompressible couple stress fluid through a rigid sphere embedded in a porous medium. In the porous region, the flow field is governed by Brinkman's equation. Here we consider uniform flow at a distance from the sphere. The boundary conditions applied on the surface of the sphere are the slip condition and zero couple stress. Analytical solution of the problem in the terms of stream function is presented by modified Bessel functions. The drag experienced by an incompressible couple stress fluid on the sphere within the porous medium is calculated. The effects of the slip parameter, the couple stress parameter, and permeability on the drag are represented graphically. Special cases of viscous flow through a sphere are obtained and the results are compared with earlier published results.

The current article focuses on mass and thermal transfer analysis of a two‐dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature‐dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters. [ABSTRACT FROM AUTHOR]

This paper concerns the analytical investigation of the axisymmetric and steady flow of incompressible couple stress fluid through a rigid sphere embedded in a porous medium. In the porous region, the flow field is governed by Brinkman's equation. Here we consider uniform flow at a distance from the sphere. The boundary conditions applied on the surface of the sphere are the slip condition and zero couple stress. Analytical solution of the problem in the terms of stream function is presented by modified Bessel functions. The drag experienced by an incompressible couple stress fluid on the sphere within the porous medium is calculated. The effects of the slip parameter, the couple stress parameter, and permeability on the drag are represented graphically. Special cases of viscous flow through a sphere are obtained and the results are compared with earlier published results. [ABSTRACT FROM AUTHOR]

The hazards of man-made chiral compounds are of great public concern, with reports of worrying stereoselective compounds and an urgent need to assess their transport. This study evaluated the transport of 2-arylpropionic acid derivatives enantiomers (2-APA) in porous media under a variety of solution chemistry conditions via column packing assays. The results revealed the introduction of Malic acid (MA) enantiomers enhanced the mobility of 2-APA enantiomers, but the enhancement effect was different for different 2-APA enantiomers. Batch sorption experiments confirmed that the MA enantiomers occupied the sorption site of the quartz sand, thus reducing the deposition of the 2-APA enantiomer. Homo- or heterochirality between 2-APA and MA dominates the transport of 2-APA enantiomers, with homochirality between them triggering stronger retention and vice versa. Further evaluating the effect of solution chemistry conditions on the transport of 2-APA enantiomers, increased ionic strength attenuated the mobility of 2-APA enantiomers, whereas introduced coexisting cations enhanced the retention of 2-APA enantiomers in the column. The redundancy analyses corroborated these solution chemistry conditions were negatively correlated with the transport of 2-APA enantiomers. The coupling of pH and these conditions reveals electrostatic forces dominate the transport behavior and stereoselective interactions of 2-APA enantiomers. Distinguishing the transport of enantiomeric pair helps to understand the difference in stereoselectivity of enantiomers and promises to remove the more hazardous one. [Display omitted] • Stereoselectivity force of 2-APA and MA depend on homo- or heterochirality among them. • Increased ISs and introduction of coexisting cations weaken chiral interactions. • Enhanced electrostatic forces weaken chiral interactions and guide transport of 2-APA. • Divalent ions increase the retention of 2-APA in the column via bridging effects. [ABSTRACT FROM AUTHOR]

This paper investigates the propagation of thermoelastic waves in a homogeneous, linear, and isotropic porous solid. For physical and mathematical simplicity, one-dimensional wave propagation in a porous solid rod is considered to explain the concept of heat transfer caused by motion. The solutions of governing equations show that the transfer of heat in a porous rod is not only due to the conduction but also produced by the local particle displacement phenomenon. It is observed that the time-averaged transfer of heat depends on the circular frequency, porosity, thermal conductivity, thermal relaxation, specific heat, and other material coefficients. [ABSTRACT FROM AUTHOR]

The results of a study of seismoacoustic emission appearing in a saturated porous geological environment with forced acoustic impact on cores and in wells are presented. It is shown that the wave action effectively influences the increase in permeability relative to the initial value and the acoustic emission of a saturated porous medium caused by the wave action serves as a reliable source of information on its reservoir roperties. The hydrostatic pressure gradient contributes to the acoustic emission mechanism, which creates fluid filtration. In this case, the greater the core permeability, the wider the emission frequency band, the smaller the permeability, the narrower the band of the spectrum, which approaches the form of a discrete set of frequencies. Similar data were obtained in oil reservoirs, where a continuous spectrum is characteristic of porous sandstones of terrigenous reservoirs, and single narrow-band spectra, for fractured carbonate reservoirs. The principle of excitation of high-intensity waves of elastic energy and registration of waves of emission origin in the reservoir provides reliable information on reservoir productivity in both perforated well and non-perforated well, and can give recommendations on the selection of the perforation interval and also stimulate the inflow of oil from the reservoir.

This paper presents an analytical method to analyze the effect of the variation in the groundwater table on train-induced vibrations from subway tunnels. The soil above the groundwater table is considered as a dry single-phase medium, while the soil under the groundwater table is simulated as a saturated porous medium. The solution for wave propagation in a multilayered half-space is derived by using the transfer matrix method. By using the wave transformation, the multilayered soil is subsequently coupled with the tunnel via boundary conditions at their interface. The train-induced vibrations are computed by coupling the proposed tunnel–soil model with the vehicle–track model. The numerical results demonstrate that the displacement field tends to that of a saturated half-space when the groundwater table is above the tunnel, while it tends to that of a dry single-phase half-space as the groundwater table is under the tunnel. The vibration levels increase as the groundwater table drops. Furthermore, the effect of the variation in the groundwater table becomes more significant as the soil permeability decreases. [ABSTRACT FROM AUTHOR]

In this study, a directional interpolation infinite element suited to a saturated porous medium is presented to account for dynamic problems with semi-infinite or infinite domain. By employing the Galerkin method, the element property matrixes for a two-dimensional space are given. Using the governing differential equations for wave propagation in the saturated porous media, the analytical solutions for one-dimensional wave propagation are derived in detail. Then the shape functions for the infinite element based on the analytical solutions are formulated and the dynamic stiffness matrix is presented in analytical form is presented. As a result, a fully coupled 2D infinite element for the analysis of dynamic problems in unbounded saturated porous media is presented. The effectiveness and accuracy of the proposed element is well demonstrated by a comparison of the numerical results with known analytical solutions for 1D and 2D wave propagation problems. The results highlight that the proposed directional interpolation infinite element is useful and effective for addressing the dynamic problems with semi-infinite or infinite domain, with consideration of both compression and shear waves. [ABSTRACT FROM AUTHOR]

• Two-stage porothermoelastic solutions include axisymmetric strains and stresses. • Volumetric strain integrates displacements with the pore pressure and temperature. • Thermal expansion and contraction induce pore pressures during heat propagation. Porothermoelastic responses of saturated porous media find wide applications in geotechnical engineering. However, the coupled partial differential equations describing the conservation of momentum, mass, and energy in the porous medium posed mathematical difficulties in obtaining analytical solutions. In this paper, we provided a two-stage porothermoelastic model for comprehensive solutions under axisymmetric loadings. At the first stage, the governing equations were decoupled by the Laplace–Hankel transform, which yielded the explicit expressions of the temperature, pore pressure, displacements, and the vertical and shear stresses. At the second stage, the radial and tangential strains were obtained after the numerical inversion of the volumetric strain and displacements. We also found that the volumetric strain played an important role in this model: (1) coupled displacements with the pore pressure and temperature at the first stage; (2) combined the vertical, radial, and tangential strains at the second stage. Results of a finite layer under a disk thermal loading showed that this model could capture the thermal expansion and contraction in terms of displacements, strains and stresses, and such mechanical interactions could give rise to the buildup and dissipation of pore pressures during the thermal conduction. [ABSTRACT FROM AUTHOR]

• 3D dynamic response of a multi-layered transversely isotropic saturated half-space subjected to forces and pore pressure. • The Fourier expansion and Hankel transform are used to solve the wave equation for transversely isotropic saturated medium. • The stiffness matrix method is applied to obtain the fundamental solution of the multi-layered half-space. • The free surface is considered either completely permeable or impermeable boundary. Dynamic Green's function plays an important role in the study of various wave radiation, scattering and soil-structure interaction problems. However, little research has been done on the response of transversely isotropic saturated layered media. In this paper, the 3D dynamic responses of a multi-layered transversely isotropic saturated half-space subjected to concentrated forces and pore pressure are investigated. First, utilizing Fourier expansion in circumferential direction accompanied by Hankel integral transform in radial direction, the wave equations for transversely isotropic saturated medium in cylindrical coordinate system are solved. Next, with the aid of the exact dynamic stiffness matrix for in-plane and out-of-plane motions, the solutions for multi-layered transversely isotropic saturated half-space under concentrated forces and pore pressure are obtained by direct stiffness method. A FORTRAN computer code is developed to achieve numerical evaluation of the proposed method, and its accuracy is validated through comparison with existing solutions that are special cases of the more general problems addressed. In addition, selected numerical results for a homogeneous and a layered material model are performed to illustrate the effects of material anisotropy, load frequency, drainage condition and layering on the dynamic responses. The presented solutions form a complete set of Green's functions for concentrated forces (including horizontal load in x (y)-direction, vertical load in z -direction) as well as pore pressure, which lays the foundation for further exploring wave propagation of complex local site in a layered transversely isotropic saturated half-space by using the BEMs. [ABSTRACT FROM AUTHOR]

River valley terrain can lead to local amplification effects of site seismic responses and significant spatial variation of strong ground motions. This paper presented a semi-analytical solution for the scattering of incident plane P-waves by a saturated river valley with arbitrary shapes containing water, using the moment method and the wave function expansion method. The influence of factors such as valley geometry shapes, soil porosity, wave incident angle and frequency on the seismic response of valley topography is further investigated. Parameter analysis shows that these factors have a significant impact on the site seismic response. Soil porosity has a greater impact on the horizontal response of the site than on the vertical response. Moreover, the soil porosity is directly related to the amplitude of the pore pressure, while the incidence angle and frequency of the incident wave determine the distribution position of the pore pressure amplitude. This semi-analytical solution can be seen as an attempt to solve the scattering problem of incident P wave by saturated river valleys of arbitrary shapes containing water. The purpose of this paper is to provide a reference and a possible way for subsequent scholars to study the analytical solution to this problem. The conclusions drawn from the parameter analysis in this paper can also serve as a theoretical basis for seismic fortification in saturated valley areas. • Semi-analytical model for plane P waves scattering by saturated river valley with arbitrary shapes containing water. • Moment method is applied to obtain the semi-analytical solution to system response. • Influence of the water, medium porosity, and incident wave on ground surface displacement is investigated. [ABSTRACT FROM AUTHOR]

Fe3O4 magnetic nanoparticles (MNPs) can control and remove heavy metal pollution from wastewater. This approach has gained broad attention due to its excellent surface properties. However, there have been limited studies for Cu2+ retention and transfer regulation in saturated porous media in the presence of MNPs. The objectives of this study were to analyze the migration and deposition mechanism of Cu2+ under different conditions through static adsorption and numerical models. The results indicated that the MNPs-quartz sand had better adsorption capacity for Cu2+ (59.1 mg/kg) than quartz sand only (26.84 mg/kg), and thus it inhibited the migration of Cu2+; the effect improved with increasing MNP content. Furthermore, high ion strength (IS) and flow velocity were beneficial to the migration of Cu2+, and a high pH inhibited the migration of Cu2+. The numerical simulation results showed that the two-site model (TSM) nicely fitted the migration of Cu2+ in quartz sand and MNPs-sand. The migration of Cu2+ in both media was affected by chemical nonequilibrium. We also found that the presence of MNPs had little impact on the dispersion of porous media by observing the fitting parameters D (dispersion coefficient) 0.202 for both media. Our results can evaluate the risk of heavy metal migration and retention in saturated porous media in the presence of nanoparticles; this can prevent aquifer pollution. [ABSTRACT FROM AUTHOR]

The dynamic responses of a lined tunnel subjected to dynamic loading is one of the key issues that needs to be addressed prior to the design and construction of tunnels. While the tunnel lining and surrounding soil are commonly designed in ideal explosion-proof engineering as ideal elastic media to simplify the problem, in reality; soils are porous geo-materials. Therefore, the concern is whether this practice is more conservative or close to the reality, in contrast to the scenario where the surrounding soil is assumed as a saturated porous medium. This study investigates the differences and relationships between the dynamic responses of the lining structures in two immensely disparate media: ideal elastic medium and porous saturated medium. Firstly, to avoid the complexity of 3D numerical studies, 3D analytical solutions for the responses of the lined tunnel in both the ideal elastic medium and porous medium due to internal dynamic loading are derived using Fourier and Laplace transforms. Also, the differences between the dynamic responses (e.g., the radial displacement, radial effective stress, and hoop effective stress) of the lining structures in two media are determined to assess the rationality of assuming that the soil around the lined tunnel is an infinite elastic compressible medium. Finally, the influence of the porosity on the dynamic response of a cylindrical lined tunnel subjected to dynamic loads is examined. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South China University of Technology (Natural Science Edition) is the property of South China University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper analytically investigates the dynamic interaction of two neighboring tunnels in the saturated soil. The twin tunnels are simulated using the Flügge shell theory, and the surrounding soil is modelled by the Biot's theory. The solution for cylindrical waves in saturated porous media is derived by applying the potential decomposition. The addition theorem is subsequently introduced to translate cylindrical waves, thereby satisfying the boundary conditions at the interfaces between the twin tunnels and saturated soil. Numerical examples are presented to analyze soil vibrations under different loading conditions calculated by different tunnel models. The neighboring tunnels have strong dynamic interaction, resulting in the insertion gain up to ± 20 dB. It is recommended to account for the interaction between neighboring tunnels when calculating the vibrations from underground railways. [ABSTRACT FROM AUTHOR]

The influences of thermal gradient on the fluid flux (thermo-osmosis effect) and pore-pressure gradient on the heat flux (mechano-caloric effect) are usually ignored in the thermo-hydro-mechanical (THM) analysis of porous media. However, this assumption could have significant impacts on the analyses of geomaterials of relatively low permeability. In this paper, a point heat source was deeply buried in a saturated porous medium where the thermo-osmosis and mechano-caloric effects were considered. Laplace-Hankel transforms were applied to the linear equations governed by porothermoelasticity and to obtain the analytical solutions, the volumetric strain connected the displacements with the pore pressure and the temperature change. By applying the Laplace-Hankel inversion, the solutions in the real domain were obtained and verified by the existing results. The numerical results showed: (1) in geomaterials of low permeability, the mechano-caloric effect on the temperature change, heat flux and thermal gradient was negligible but the thermo-osmosis effect caused negative pore pressures which increased the effective stress of porous medium; (2) the thermo-osmosis effect pronouncedly drove the outflow of pore fluid away from the heat source which would be balanced by an inflow of pore fluid toward the heat source caused by the negative pore pressure. [ABSTRACT FROM AUTHOR]

An extended finite element incremental iterative solution scheme for the hydraulic fracturing problem with saturated porous media was derived. Based on the analysis of analytical solutions of crack tip displacement field of infinite plate with central crack, a new cohesive crack tip strengthening function was constructed according to the deformation characteristics of modelⅠand modelⅡ, which reduced the degree of freedom of the nodes affected by the crack tip strengthening from 8 to 2 in the traditional extended finite element method (for plane problem). The issue has greatly reduced the computation scale. Taking a porous medium plate with a central oblique crack as an example, the correctness of the cohesive crack tip strengthening model was verified. The condition numbers of Jacobian matrices of two kinds of crack tip strengthening modes were calculated. The results show that the accuracy of the extended finite element method under the cohesive crack tip strengthening mode is the same as that of the traditional extended finite element method. When the grid is denser, the accuracy of this method is higher than that of the traditional one. Finally, the improved cohesive crack tip strengthening model is applied to the hydraulic fracturing simulation of concrete gravity dam and good results are obtained. [ABSTRACT FROM AUTHOR]

Highlights • An analytical approach for stress distribution in a saturated medium with collinear cracks is developed. • Biot's theory is utilized in conjunction with the Fourier and Laplace transforms. • The influence of pore fluid on the mode-I dynamic stress-intensity factor is investigated. • The effect of crack size with respect to the distance between cracks is discussed. Abstract The transient stress distribution is obtained for a saturated porous medium containing an array of equally distributed collinear cracks when each crack is opened by suddenly applied internal pressure. The integral and Laplace transforms are employed to reduce the mixed boundary-value problem to solving the Fredholm integral equation. The influence of pore fluid and the size of the crack with respect to the distance between the neighbouring cracks on the dynamic stress intensity factor are investigated. Numerical results are presented and compared with the corresponding values of the dry medium. [ABSTRACT FROM AUTHOR]

This article represents numerical simulation technique for determining effective spectral electromagnetic properties (effective electrical conductivity and relative dielectric permittivity) of saturated porous media. Information about these properties is vastly applied during the interpretation of petrophysical exploration data of boreholes and studying of rock core samples. The main feature of the present paper consists in the fact, that it involves three-dimensional saturated digital rock models, which were constructed based on the combined data considering microscopic structure of the porous media and the information about capillary equilibrium of oil-water mixture in pores. Data considering microscopic structure of the model are obtained by means of X-ray microscopic tomography. Information about distributions of saturating fluids is based on hydrodynamic simulations with density functional technique. In order to determine electromagnetic properties of the numerical model time-domain Fourier transform of Maxwell equations is considered. In low frequency approximation the problem can be reduced to solving elliptic equation for the distribution of complex electric potential. Finite difference approximation is based on discretization of the model with homogeneous isotropic orthogonal grid. This discretization implies that each computational cell contains exclusively one medium: water, oil or rock. In order to obtain suitable numerical model the distributions of saturating components is segmented. Such kind of modification enables avoiding usage of heterogeneous grids and disregards influence on the results of simulations of the additional techniques, required in order to determine properties of cells, filled with mixture of media. Corresponding system of differential equations is solved by means of biconjugate gradient stabilized method with multigrid preconditioner. Based on the results of complex electric potential computations average values of electrical conductivity and relative dielectric permittivity is calculated. For the sake of simplicity, this paper considers exclusively simulations with no spectral dependence of conductivities and permittivities of model components. The results of numerical simulations of spectral dependence of effective characteristics of heterogeneously saturated porous media (electrical conductivity and relative dielectric permittivity) in broad range of frequencies and multiple water saturations are represented in figures and table. Efficiency of the presented approach for determining spectral electrical properties of saturated rocks is discussed in conclusion.