Formulation of thermo-hydro-mechanical coupling behavior of unsaturated soils based on hybrid mixture theory

Thermo-Hydro-Mechanical （THM） coupling pro- cesses in unsaturated soils are very important in both theoretical researches and engineering applications. A coupled formulation based on hybrid mixture theory is derived to model the THM coupling behavior of unsaturated soils. The free-energy and dissipative functions for different phases are derived from Taylor＇s series expansions. Constitutive relations for THM coupled behaviors of unsaturated soils, which include deformation, entropy change, fluid flow, heat conduction, and dynamic compatibility conditions on the interfaces, are then established. The number of field equations is shown to be equal to the number of unknown variables; thus, a closure of this coupling problem is established. In addition to modifications of the physical conservation equations with coupling effect terms, the constitutive equations, which consider the coupling between elastoplastic deformation of the soil skeleton, fluid flow, and heat transfer, are also derived.

A micropolar mixture theory of multi-component porous media

A mixture theory is developed for multi-component micropolar porous media with a combination of the hybrid mixture theory and the micropolar continuum theory. The system is modeled as multi-component micropolar elastic solids saturated with multi- component micropolar viscous fluids. Balance equations are given through the mixture theory. Constitutive equations are developed based on the second law of thermodynamics and constitutive assumptions. Taking account of compressibility of solid phases, the volume fraction of fluid as an independent state variable is introduced in the free energy function, and the dynamic compatibility condition is obtained to restrict the change of pressure difference on the solid-fluid interface. The constructed constitutive equations are used to close the field equations. The linear field equations are obtained using a linearization procedure, and the micropolar thermo-hydro-mechanical component transport model is established. This model can be applied to practical problems, such as contaminant, drug, and pesticide transport. When the proposed model is supposed to be porous media, and both fluid and solid are single-component, it will almost agree with Eringen＇s model.

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)—LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY(Ⅰ)—NONLINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

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.

CONSOLIDATION HEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Unsaturated soil is a three-phase media and is composed of soil grain,water and gas.In this paper,the consolidation problem of unsaturated soil is investigated based on the theory of mixture.A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived.The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil.A mathematical model of consolidation of unsaturated soil is proposed,which consists of 25 partial differenfial equations with 25 unknowns.With the help of increament linearizing method,the model is reduced to 5 governing equations with 5 unknowns,i.e.,the three displacement components of solid phase,the pore water pressure and the pore gas pressure.7 material parameters are involved in the model and all of them can he measured using soil tests.It is convenient to use the model to engineering practice.The well known Biot's theory is a special case of the model.

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.

A lubrication model for bubbly oil lubrication with interfacial effect and thermal effect using the theory of multiphase mixtures

Bubbly oil lubrication is a type of lubrication method.However,the lubrication model of the bubbly oil has not been thoroughly considered.This paper aims to investigate the modelling for bubbly oil lubrication considering the interfacial effect and thermal effect,and a theoretical model is established based on the theory of multiphase mixtures.The interfacial and thermal effects on the static characteristics of a thrust bearing are analyzed.A test rig for the thrust bearing is developed to measure the static characteristics of the bearing under bubbly oil lubrication.The results show that the bearing static characteristics,i.e.bearing temperature rise,film thickness,friction torque,and volume flow,increase with consideration of three interfacial effects;the bearing temperature rise increases but the film thickness,friction torque,and volume flow rate decrease with consideration of the three thermal effects;the thermal effect on the bearing static characteristics is greater than the interfacial effect.

Bi-phasic Simulation of Metal Injection Moulding:Constitutive Determinations

To predict the segregation effect in metal injection moulding (MIM) injection, a bi-phasic model based on mixture theory is adopted in simulation. An explicit algorithm is developed and realized by the authors, which conducts the simulation to be a cost-effective tool in MIM technology. In case of the bi-phasic simulation, the viscosity behaviours are necessary to be determined for the flows of each phase while only the viscosity of mixture is measurable by tests. It is a crucial problem for application of the bi-phasic simulation of MIM injection. A reasonable method is hence analysed and proposed to determine the viscosity behaviours of each phase. Even though this method may be furthermore modified in the future, it results in the practical simulation of segregation effects with reasonable parameters. The simulation results are compared with the measurements on injected specimens.

The Kinematics and Field Equations for Porous Media

With a porous medium regarded as an immiscible mixture of multiphase and each phase as a miscible mixture of multi constituent, a systematical research on the kinematics and field equations for porous media is carried out from the point of view of mixture theory. It is shown that the motion of each phase is the mathematical average of the motions of all constituents in the phase, and that the motion of porous media may be described as the motion of the skeleton and the relative motion of each phase with respect to the skeleton. The influence of mass exchange between different constituents in each phase and the influence of mass exchange of same constituent between different phases in porous media are considered in field equations which are self consistent in theory. All the field equations in the references are special cases of the equations proposed in this paper.

A MIXED METHOD FOR THE CREEP OF A SKIN LAYER

The creep of a skin layer under a distributed surface pressure was solved by ananalysical method using Hankel transform and Laplace transform.The surface stressboundary conditions lead io a Volterra integral equation of the first kind, which was then solved by a numerical method.The IMSL subroutines DINLAP and DGORUL were employed to numerically obtain the Hankel-Laplace inversion. The calculateddisplacements at two distinctive moments were compared respectively with those obtained by an elastic solution for either incompressible or compressible solid. Thetransient creep responses of the skin layer were also presented.

A nonlinear multi-field coupled model for soils

A nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory. The balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multi-constituent elastic-plastic solid skeleton (which is different from the linearization method) and viscous liquid and ideal gas. With reasonable constitutive assumptions in such restrictive conditions as the principles of determinism, equipresence, material frame-indifference and the compatible principle in continuum mechanics, a theoretical framework of constitutive relations modeling three-phase soil in both non-equilibrium and equilibrium states is established, thus the closed field equations are formed. In the theoretical framework, the concept of effective generalized thermodynamic forces is introduced, and the nonlinear coupling constitutive relations between generalized dissipation forces and generalized flows within the system at nonequilibrium state are also presented. On such a basis, four special coupling relations, i.e., solid thermal elastic-plastic constitutive relation, liquid visco-elastic-plastic constitutive relation, the generalized Fourier’s law, and the generalized Darcy’s law are put forward. The generalized or nonlinear results mentioned above can degenerate into the linear coupling results given by Bennethum and Singh. Based on a specific dissipation function, the concrete form of generalized Darcy’s law is deduced, which may degenerate into the traditional form of Darcy’s law by neglecting the influence of skeleton deformation and temperature. Without considering temperature and other coupling effects, the nonlinear coupled model in this paper can degenerate into a soil elastic-plastic constitutive model.

ELECTROHYDRODYNAMIC DISPERSION OF DEFORMABLE AEROSOLS IN THE PRESENCE OF AN ELECTRIC FIELD AND CHEMICAL REACTION USING TAYLOR DISPERSION MODEL

Under the effects of electric field and chemical reaction, the problem of dispersion of aerosols in a poorly conducting fluid in a channel is solved analytically using the mixture theory together with a regular perturbation technique. It is shown that the aerosols are dispersed relative to a plane moving with the mean speed of atmospheric fluid as well as the mean speed of agglomeration of aerosol with a relative diffusion coefficient, called the Taylor dispersion coefficient. This coefficient is numerically computed and the results reveal that it increases with an increase in the electric number, but decreases with increasing porous parameter. The physical explanations for the phenomena are given in this article.

A theoretical study on the elastic deformation of cellular phase and creation of necrosis due to the convection reaction process inside a spherical tumor

Several biological processes, such as convective nutrient transport and convective drug delivery in biological tissues involves the transvascular and interstitial movement of biofluids. This work addresses transvascular and interstitial transport of nutrient inside a spherical tumor. Most of the biological tissues behave like deformable porous materiM and show mechanical behavior towards the fluid motion, due to the fact, that the forces like the drag, which is associated with fluid flow may compress the tissue material. On the macroscopic level, transport of solutes like nutrients, drug molecules, etc. within the tumor interstitial space is modeled. The hydrodynamic problem is treated with biphasic mixture theory under steady state and spherically symmetry situation. The transvascular transport of nutrient is modeled with the modified Sterling＇s equation. The present model describes the overall nutrient distribution and predicts various criteria for the necrosis formation inside the tumor. Present study justifies that the parameters, which controls the nutrient supply to the tumor interstitial space through the blood vessel network inside the tumor, competes with reversible nutrient consumption kinetics of the tumor cells. This study also finds the role of some of those parameters on the deformation of cellular phase of the tumor as a consequence of interstitial fluid flow.