A thermodynamical gradient theory for deformation and strain localization of porous media

A fully coupled dynamic model is presented in this paper by considering the effect of matric suction, varying parameters in connection with saturation, stratification and transverse isotropy. This model can describe separate flows of two immiscible fluids in layered transversely isotropic unsaturated poroelastic media subjected to harmonically dynamic loads. The ordinary differential matrix equations of this model are derived based on Hankel integral transform and a series of algebraic manipulations. Then the final solution is obtained by conducting the extended precise integration method, and further verified against the existing solution. Numerical examples are carried out to demonstrate the effects of saturation, transversely isotropic parameters, angular frequency and soil thickness on dynamic behavior of unsaturated porous media.

Extended precise integration solution to layered transversely isotropic unsaturated poroelastic media under harmonically dynamic loads

A study on dynamic response of transversely isotropic saturated poroelastic media under a circular non-axisymmetrical harmonic source has been presented by Huang Yi et al. using the technique of Fourier expansion and Hankel transform. However, the method may not always be valid. The work is extended to the general case being in the rectangular coordinate. The purpose is to study the 3-d dynamic response of transversely isotropic saturated soils under a general source distributing in arbitrary rectangular zoon on the medium surface. Based on Biot’s theory for fluid-saturated porous media, the 3-d wave motion equations in rectangular coordinate for transversely isotropic saturated poroelastic media were transformed into the two uncoupling governing differential equations of 6-order and 2-order respectively by means of the displacement functions. Then, using the technique of double Fourier transform, the governing differential equations were easily solved. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media were obtained. Furthermore, a systematic study on half-space problem in saturated soils was performed. Integral solutions for surface displacements under the general harmonic source distributing on arbitrary surface zone, considering both case of drained surface and undrained surface,were presented.

3-d dynamic response of transversely isotropic saturated soils

The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel transform. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multilayered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation

Dynamic response of a stratified transversely isotropic half-space with a poroelastic interlayer due to a buried moving source

The Biot's wave equations of transversely isotropic saturated poroelastic media excited by non-axisymmetrical harmonic source were solved by means of Fourier expansion and Hankel transform. Then the components of total stress in porous media are expressed with the solutions of Biot's wave equations. The method of research on non-axisymmetrical dynamic response of saturated porous media is discussed, and a numerical result is presented.

The Non-Axisymmetrical Dynamic Response of Transversely Isotropic Saturated Poroelastic Media

The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.

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Huang Yi

Papers

The Non-Axisymmetrical Dynamic Response of Transversely Isotropic Saturated Poroelastic Media

Constitutive Relation of Unsaturated Soil by Use of the Mixture Theory (I)-Nonlinear Constitutive Equations and Field Equations