GURTIN VARIATIONAL PRINCIPLE AND FINITE ELEMENT SIMULATION FOR DYNAMICAL PROBLEMS OF FLUID-SATURATED POROUS MEDIA

Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constituents of the solid and fluid phase. The finite element formulation based on this variational principle is also derived. As the functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in the time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations and, as a numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide further understanding of the wave propagation in porous media.

Response of saturated porous media subjected to local thermal loading on the surface of semi-infinite space

Heat source function method is adopted in the present paper to derive elementary solutions of coupled thermo-hydro-mechanical consolidation for saturated porous media under conjunct actions of instantaneous point heat source, instantaneous point fluid source and constant volume force. By using the so-called fictitious heat source method and images method, the solutions of a semi-infinite saturated porous medium subjected to a local heat source with time-varied intensity on its free surface are developed from elementary solutions. The numerical integral methods for calculating the unsteady temperature, pore pressure and displacement fields are given. The thermomechanical response are analyzed for the case of a circular planar heat source. Besides, the thermal consolidation characteristics of a saturated porous medium subjected to a harmonic thermal loading are also given, and the fluctuation processes of the field variables located below the center of heat source are analyzed.

Dynamic response of bilayered saturated porous media based on fractional thermoelastic theory

Considering the thermal contact resistance and elastic wave impedance at the interface,in this paper we theoretically investigate the thermo-hydro-mechanical(THM)coupling dynamic response of bilayered saturated porous media.Fractional thermoelastic theory is applied to porous media with imperfect thermal and mechanical contact.The analytical solutions of the dynamic response of the bilayered saturated porous media are obtained in frequency domain.Furthermore,the effects of fractional derivative parameters and thermal contact resistance on the dynamic response of such media are systematically discussed.Results show that the effects of fractional derivative parameters on the dynamic response of bilayered saturated porous media are related to the thermal contact resistance at the interface.With increasing thermal contact resistance,the displacement,pore water pressure,and stress decrease gradually.

AN ELLIPTIC-PARABOLIC SYSTEM ARISING FROM THE FLUID-SOLITE-HEAT FLOW THROUGH SATURATED POROUS MEDIA

In this paper an elliptic-parabolic coupled system arising from the fluid-solute-heat flowthrough a saturated porous medium is considerd.The uniqueness and the existence of classicalsolutions are proved.The asymptotic behavior of solutions for large time is shown,too.

Dynamic and quasi-static bending of saturated poroelastic Timoshenko cantilever beam

Based on the three-dimensional Gurtin-type variational principle of the incompressible saturated porous media, a one-dimensional mathematical model for dynamics of the saturated poroelastic Timoshenko cantilever beam is established with two assumptions, i.e., the deformation satisfies the classical single phase Timoshenko beam and the movement of the pore fluid is only in the axial direction of the saturated poroelastic beam. Under some special cases, this mathematical model can be degenerated into the Euler-Bernoulli model, the Rayleigh model, and the shear model of the saturated poroelastic beam, respectively. The dynamic and quasi-static behaviors of a saturated poroelastic Timoshenko cantilever beam with an impermeable fixed end and a permeable free end subjected to a step load at its free end are analyzed by the Laplace transform. The variations of the deflections at the beam free end against time are shown in figures. The influences of the interaction coefficient between the pore fluid and the solid skeleton as well as the slenderness ratio of the beam on the dynamic/quasi-static performances of the beam are examined. It is shown that the quasi-static deflections of the saturated poroelastic beam possess a creep behavior similar to that of viscoelastic beams. In dynamic responses, with the increase of the slenderness ratio, the vibration periods and amplitudes of the deflections at the free end increase, and the time needed for deflections approaching to their stationary values also increases. Moreover, with the increase of the interaction coefficient, the vibrations of the beam deflections decay more strongly, and, eventually, the deflections of the saturated poroelastic beam converge to the static deflections of the classic single phase Timoshenko beam.

Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation

Abstract An analytical solution to the three-dimen-sional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expan-sion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot＇s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn： （1） there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; （2） the nor-malized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; （3） with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

Multi-transmitting formula for attenuating waves

The MTF is extended to case of attenuating incident wave by introducing an attenuation coefficient. The reflection coefficients of this modified MTF and MTF are evaluated and compared when an attenuating wave impinges on the boundary, and the results demonstrate that MTF can be used to absorb slightly attenuating waves and the modified MTF is more capable of absorbing heavily attenuating waves than MTF. The accuracy of modified MTF is also tested by numerical examples of fluid saturated porous media.

Response of a spherical cavity in a fully-coupled thermo-poro-elastodynamic medium by cell-adaptive second-order central high resolution schemes

In this study,fully coupled thermo-poroelastic saturated media are simulated by a grid/cell adaptive central high resolution scheme.The central method corresponds to the second order Kurganov-Tadmor(KT)scheme working on adapted cells with the total variation diminishing(TVD)stability condition.The coupled equations include motion,fluid flow,heat flow,continuity condition,and a constitutive equation.The grid/cell adaptation is performed by the interpolating wavelet transform in the multiresolution framework to capture fine scale responses and to obtain a computationally effective solver.With respect to the use of central schemes,the coupled equations should be re-expressed as a system of coupled first-order hyperbolic-parabolic partial differential equations(PDEs)with possible source(load)terms.The system is initially derived in the Cartesian coordinate system,and it is subsequently modified to consider a spherical cavity in isotropic,symmetric,and saturated media in the spherical coordinate system.It is assumed that the cavity boundary is subjected to sudden time-dependent thermal/mechanical sources.Discontinuous propagating fronts develop in the media due to the aforementioned loading.It is challenging to handle these solutions with numerical methods,and special attention is required to prevent/control numerical dispersion and dissipation.Hence,as previously mentioned,adaptive central high resolution schemes are employed in the present study.