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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]

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]

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]

This paper introduces the von Neumann method to investigate the temporal stability of the displacement-pressure $$(u{-}p)$$ reproducing kernel formulation for saturated porous media. Both dynamic and quasi-static formulations are considered and the critical time steps are derived. The effect of lumped and consistent matrices on temporal stability is analyzed under explicit temporal discretization. It is shown that lumped matrices have better temporal stability than consistent matrices. The study also shows that nodal support size greatly affects the critical time step size of the formulations. For consistent matrices, larger support size results in smaller critical time step size; however, opposite relation occurs if lumped scheme is used. The numerical study shows that stabilization parameter of the stabilized nodal integration methods reduces the critical time step size. Transient analyses are performed to verify the results from von Neumann analysis. [ABSTRACT FROM AUTHOR]

In this study, both the effects of suspension ionic strength and flow velocity on deposition and the clogging phenomena are investigated. Experimental tests are performed in the case of the silt microparticle transport through a saturated sand column with the presence of repulsive interactions. The specific size of these particles is chosen to ensure the presence of both physicochemical and mechanical retention mechanisms. The injection of particle suspension is conducted for long durations at different ionic strength and flow velocities. The deposition rate and the porous media clogging mainly depend on the ionic strength. An increase in the ionic strength causes an increase in the deposition rate and a reduction of the hydraulic conductivity which leads to the progress of the clogging phenomenon through the porous medium. Experimental analyses show the presence of a clogging front whose spatial distribution and temporal progress depend on the suspension ionic strength. Its velocity advancement is proportional to the ionic strength. Within the validity range of Darcy's law, the dynamics of deposition and clogging also depend on the flow rate. In particular, the retention of silt microparticles is more important for low flow velocities. The influence of the physicochemical effects on the deposition rate and therefore sand texture clogging is more significant at low flow rates. [ABSTRACT FROM AUTHOR]

A study on the effects of Navier slip, in conjunction with other flow parameters, on unsteady flow of reactive variable viscosity third-grade fluid through a porous saturated medium with asymmetric convective boundary conditions is presented. The channel walls are assumed to be subjected to asymmetric convective heat exchange with the ambient, and exothermic chemical reactions take place within the flow system. The heat exchange with the ambient obeys Newton's law of cooling. The coupled equations, arising from the law of conservation of momentum and the first law of thermodynamics, then the derived system are non-dimensionalised and solved using a semi-implicit finite difference scheme. The lower wall slip parameter is observed to increase the fluid velocity profiles, whereas the upper wall slip parameter retards them because of backflow at the upper channel wall. Heat production in the fluid is seen to increase with the slip parameters. The wall shear stress increases with the slip parameters while the wall heat transfer rate is largely unaltered by the lower wall slip parameter but marginally increased by the upper wall slip parameter. [ABSTRACT FROM AUTHOR]

The flow past an impermeable sphere embedded in a fluid-saturated porous medium was investigated numerically. The flow is considered viscous, laminar, axisymmetric, steady and incompressible. The generalized model for fluid flow through an isotropic, rigid and homogeneous porous medium was used. The stream function-vorticity equations were solved numerically in spherical coordinates system by a defect correction multigrid method. The computations were focused on the influence of the Darcy number ( Da) and Forchheimer constant on the flow field for two boundary conditions on the surface of the sphere: slip and no-slip. The conditions when the macroscopic inertial terms of the generalized model can be neglected are presented. For high-porosity porous media, the macroscopic inertial terms of the generalized model can be neglected if Da $$Re< 1$$ ( Re is the sphere Reynolds number). [ABSTRACT FROM AUTHOR]

In this paper, the thermo-poroelasticity theory is used to investigate the quasi-static response of temperatures, pore pressure, stress, displacement, and fluid flux around a cylindrical borehole subjected to impact thermal and mechanical loadings in an infinite saturated poroelastic medium. It has been reported in literatures that coupled flow known as thermo-osmosis by which flux is driven by temperature gradient, can significantly change the fluid flux in clay, argillaceous and many other porous materials whose permeability coefficients are very small. This study presents a mathematical model to investigate the coupled effect of thermo-osmosis in saturated porous medium. The energy balance equations presented here fulfill local thermal non-equilibrium condition (LTNE) which is different from the local thermal equilibrium transfer theory, accounting for that temperatures of solid and fluid phases are not the same and governed by different heat transfer equations. Analytical solutions of temperatures, pore pressure, stress, displacement, and fluid flux are obtained in Laplace transform space. Numerical results for a typical clay are used to investigate the effect of thermo-osmosis. The effects of LTNE on temperatures, pore pressure, and stress are also studied in this paper. [ABSTRACT FROM AUTHOR]

Thermal vibrational convection in a saturated porous medium is theoretically studied on the basis of a thermal nonequilibrium model, in accordance with which the temperatures of the porous medium and the saturating liquid can be different. In the high-frequency vibration approximation the averaged equations of convection are derived. The dependence of the vibration force direction on the interphase heat transfer coefficient and the vibration frequency is established. Vibrational convection in a cylindrical layer is studied. It is shown that, depending on the interphase heat transfer coefficient, the flows of two types differing in the liquid circulation direction can exist. [ABSTRACT FROM AUTHOR]

In this paper, the influence of ionic strength on the dynamic transport of silt microparticles through saturated sand texture is studied in the presence of repulsive interactions. The deposition and release phenomenon is investigated through experimental column trials. Different ionic strengths are applied by adjustment of suspension salinity. Two trial configurations are performed: Monotonic experiments highlight particle deposition mechanisms, and non-monotonic tests focus on release phenomena under ionic strength and flow rate perturbations. Through this experimental study, the ionic strength influence on the deposition and release phenomenon is shown. The presence of both mechanical and physico-chemical mechanisms is proved experimentally. This study proves that ionic strength variation is a primal parameter which predicts the attachment and detachment of particles at constant flow. These experiments are simulated and reproduced through a numerical model based on original deposit and release kinetics which are proposed in this study. This model is the coupling of two multiphasic problems describing conservative salt and microparticle transport. The proposed kinetics formulations are founded on performed experimental test constitutions in this study. They take into account the flow rate and the suspension ionic strength. The suggested model reproduces well the experimental description of the suspended particles transport under the influence of ionic strength and flow velocity variations. It permits to predict the deposition and release phenomenon. [ABSTRACT FROM AUTHOR]

This study focuses analytically on the local thermal non-equilibrium (LTNE) effects in the developed region of forced convection in a saturated porous medium bounded by isothermal parallel-plates. The flow in the channel is described by the Brinkman-Forchheimer-extended Darcy equation and the LTNE effects are accounted by utilizing the two-equation model. Profiles describing the velocity field obtained by perturbation techniques are used to find the temperature distributions by the successive approximation method. A fundamental relation for the temperature difference between the fluid and solid phases (the LTNE intensity) is established based on a perturbation analysis. It is found that the LTNE intensity ( $$\Delta \textit{NE}$$ ) is proportional to the product of the normalized velocity and the dimensionless temperature at LTE condition. Also, it depends on the conductivity ratio, Da number, and the porosity of the medium. The intensity of LTNE condition ( $$\Delta \textit{NE}$$ ) is maximum at the middle of the channel and decreases smoothly to zero by moving to the wall. Finally, the established relation for the intensity of LTNE condition is simple and fundamental for estimating the importance of LTNE condition and validation of numerical simulation results. [ABSTRACT FROM AUTHOR]

Under analysis is the model of two-phase flow in porous medium and deformation of the pore space. The model includes the equations of fluid transfer and porous matrix deformation, derived from the conservation laws. It is shown that the system of the constitutive equations contains a few small parameters, and the corresponding expansion allows obtaining a hierarchical sequence of models of certain deformation conditions. The zero approximation and first approximation models are written in explicit form. It is found that if fluids are incompressible, the first approximation equations go to the Buckley-Leverett model-like system with account for the change of the porous space. The zero approximation equations describe the porous medium behavior under condition of the unchanged volume. In this case, the equation of the pore pressure is separated from the equation of the elastic matrix. The analytical solutions obtained for the zero approximation model in cylindrical coordinates feature shear stresses capable to cause failure. [ABSTRACT FROM AUTHOR]

Based on elasticity and the theory of saturated porous media, and regarding the pile and the soil as a single phase elastic and a saturated viscoelastic media, respectively, the dynamical behavior of vertical vibration of an end-bearing pile in a saturated viscoelastic soil layer is investigated in the frequency domain using the Helmholtz decomposition and variable separation method. The axisymmetrical analytical solutions for vertical vibrations of the pile in a saturated viscoelastic soil layer are obtained, and the analytical expression of the dynamical complex stiffness of the pile top is presented. Responses of dynamic stiffness factor and equivalent damping of pile top with respect to the frequency are shown in figures using a numerical method. Effects of the saturated soil parameters, modulus ratio of the pile to soil, slenderness ratio of pile and pile’s Poisson ratio, etc. on the stiffness factor and damping are examined. It is shown that, due to the effect of the transversal deformation of the pile and the radial force of the saturated viscoelastic soil acting on the pile, the dynamic stiffness factor and the damping derived from the axisymmetrical solution are greatly different from those derived from the classical Euler-Bernoulli rod model, especially at some specific excitation frequencies. Therefore, there are limitations on applicability of the Euler-Bernoulli rod model in analyzing vertical vibration of the pile. More accurate analysis should be based on a three-dimensional model. [ABSTRACT FROM AUTHOR]

The structures of the convective motions and the nature of the heat transfer in a horizontal cylindrical layer are studied numerically for the Forchheimer model of a porous medium in the Boussinesq approximation. New asymmetric solutions of the equations of convection flow through a porous medium are found. Their development, domains of existence, and stability are investigated. One consists of a multivortex structure with asymmetric vortices in the near-polar region. Another asymmetric solution is realized at large Grashof numbers in the form of a convective plume deflected from the vertical. The threshold Grashof number of formation of the asymmetric motions depends on the Prandtl number and the cylindrical layer thickness. [ABSTRACT FROM AUTHOR]

Based on the Darcy fluid model, by considering the effects of viscous dissipation due to the interaction between solid skeleton and pore fluid flow and thermal conduction in the direction of the fluid flow, the thermally developing forced convection of the local thermal equilibrium and the corresponding thermal stresses in a semi-infinite saturated porous plate channel are investigated in this paper. The expressions of temperature, local Nusselt number and corresponding thermal stresses are obtained by means of the Fourier series, and the distributions of the same are also shown. Furthermore, influences of the Péclet number ( Pe) and Brinkman number ( Br) on temperature, Nusselt number ( Nu) and thermal stress are revealed numerically. [ABSTRACT FROM AUTHOR]

A physically based conceptual model for the influence of barometric pressure on groundwater wells was developed and tested in this study. It was proposed that water level fluctuations in response to barometric pressure are due in large part to the different manner in which the pressure is propagated through the water column in the well and the porous media outside the well. The loss in pressure head through the porous media causes a lateral hydraulic head gradient to be developed around the well-screen region, as well as a vertical one through the porous medium. The well-water flux across the screen and the consequent change in well-casing storage were appropriately linked with groundwater flow and estimated through an iteration technique. Results suggest that the physically based model in this study is effective in estimating the water level fluctuations in a well due to changes in barometric pressure. The magnitude and behavior of well response varies with the hydraulic properties (hydraulic conductivity and specific storage) and well geometry (casing radius, screened length, and depth of well). Therefore, the model relating the barograph and responding water levels can potentially serve as a tool for estimation of hydraulic parameters of the tested formation in the equivalent manner of slug tests. In conclusion, the influence of barometric pressure on groundwater wells is solved by relevant integration of three parts: i) the solution of the differential equation governing groundwater flow, ii) the estimation of well-water flux across the screen and changes in well-casing storage, and iii) use of the well screen as a boundary condition for coupling between i) and ii). [ABSTRACT FROM AUTHOR]

This contribution is devoted to the implementation of a homogenization method for deriving the strength or failure properties of a fluid-saturated porous medium, from those exhibited by its individual constituents at the microscopic level. Within this context, a specific attention is paid to the possibility of adopting an effective stress formulation. While the case of a purely cohesive solid matrix provides the first illustrative example where the ‘effective stress principle’ as originally stated by Terzaghi is fully applicable, the analysis is then particularly focused on porous sandstones, modelled as periodic packings of cemented rigid grains. A closed-form analytical expression is thus obtained for the strength criterion of such rock materials, which proves to be a function of a generalized effective stress formed as a linear combination of the total stress and the pore pressure, as in the case of poroelasticity. It is shown in particular that the key microstructural parameter involved in this formulation is the ratio between the intergranular contact area and the grain cross-section area. A possible extension of the homogenization procedure in order to account for a still more realistic description of the sandstone microstructure is finally outlined. [ABSTRACT FROM AUTHOR]

The analysis of the trajectory's scaling properties of tracer particles and preliminary valuations on their relation to experimentally determined dispersion coefficient tensor components in a saturated porous medium are presented. The matching index technique is used to assure optical access inside a three-dimensional laboratory model of a porous medium. In this way it is possible to determine the trajectories of the tracer particles. Using the methods suggested by PIV (Particle Image Velocimetry), the test section is illuminated with a light sheet and images are acquired and digitalized by means of an acquisition apparatus. A Lagrangian description of the motion is carried out and the statistical analysis performed on the experimental field allows for the estimation of velocity probability density functions, velocity components correlation functions and components of the mechanic dispersion coefficient tensor. The statistical analysis results are briefly recalled. The reconstructed tracer trajectories are analysed to verify the self-similarity or the self-affinity properties. The results show self-affine characteristics of the trajectories confirming the anisotropy of the pollutant plume. A relation between the two components of the dispersion coefficient determined by the scaling analysis of the tracer particles is derived. [ABSTRACT FROM AUTHOR]

The features of propagation of one-dimensional monochromatic waves and dynamics of weak perturbations with axial and central symmetries in liquid-saturated porous medium are investigated. Non-stationary interaction forces and viscoelastic skeleton characteristics are taken into account. The research is carried out within the two-velocity, two-stress tensor model by applying methods of multiphase media mechanics. The system of equations is solved numerically by applying Fast Fourier Transform (FFT) algorithm. The influence of geometry of the process on wave propagation behavior is studied. It is shown that the initial pressure perturbation splits into two waves: fast (deformational) wave and slow (filtrational) one. Each of them is followed by the balance wave: that is, rarefaction wave after compression wave and compression wave after rarefaction wave; at that slow wave and balance one following fast wave may interfere. [ABSTRACT FROM AUTHOR]

A modification to the Forchheimer-Brinkman equation, for the modelling of high speed flow of a compressible fluid in a dense saturated porous medium, is proposed. The modified equation is applied to a flow in which choking can occur. [ABSTRACT FROM AUTHOR]

The behaviour of the soil under a dynamically loaded pile toe is studied. The soil is modelled as a fluid saturated porous continuum. The constitutive behaviour of the solid skeleton is described by the elasto-plastic model of Drücker-Prager. The wave propagation is simulated with a dynamical finite-element program. A two-phase model of soil gives useful information about effective stress and pore pressure in the soil. In saturated soil the main wave under the pile toe propagates more downards than in dry soil, due to the higher compressional stiffness in saturated soil. The plastic zone under the pile toe propagates with the velocity of the fast compressional wave. The pore fluid influences the plasticity strongly and can be expected to affect pile driving too. The distribution of effective stress and pore pressure under the pile toe depends on the permeability of the soil and cannot be calculated uniquely from a single-phase calculation. Therefore, a nonlinear soil cannot be modelled correctly as a conventional single-phase material. [ABSTRACT FROM AUTHOR]

An analytic study of the response of saturated layered half-space under surface point loading is presented, with particular attention paid to the effect of hydraulic interface condition. A simplified formulation is adopted to describe the motion of the saturated porous medium, and a simple and direct approach is presented which does not involve the conventional Helmholtz decomposition in poroelasticity. Integral solutions for surface displacements are derived for different hydraulic interface conditions, and verified by reducing to well-known results of the Lamb's problem for a conventional one-phase medium. Numerical results for surface displacements in the near field are given, and the influence of the interface hydraulic condition on the displacements is shown. The present formulation possesses potential applications in practical engineering in solving various related source problems associated with uniform or layered saturated soil deposits. [ABSTRACT FROM AUTHOR]