Coupled Chemo-thermo-hydro-mechanical Analysis And Mixed Finite Element Method In Porous Media

In the recent years, the coupled chemo-thermo-hydro-mechanical (CTHM) behavior of unsaturated porous media has attracted comprehensive attentions in engineering practice. Many efforts have been devoted to quantitative study of coupled transient THM behavior in porous media.The emphases of this thesis focus on the three aspects of the subject. First a mathematic model to quantitatively describe the coupled CTHM behavior in porous media is proposed. Second a mixed finite element method for the numerical solution of the initial and boundary value problem of the mathematical model is formulated. Finally a coupled CTHM constitutive model for the porous media is developed.The mathematical model consists of a set of coupled partial differential equations governing the mass balance of the gas, the mass balance of the water species, the mass balance of the chemical pollutants miscible with the liquid phase, the enthalpy (energy) balance and momentum balance of the whole medium mixture. It is remarked that to model miscible contaminant transport through unsaturated porous media, six phenomena governing the pollutant transport, i.e. convection, dispersion, molecular diffusion, adsorption, degradation, and immobile water effect, are integrated into the present model.The finite element method is used to numerically solve the initial and boundary value problem of the mathematical model. Considering the convection-diffusion nature in physics and the non-self-adjoint and hyperbolic nature in mathematics of the transport equation, which governs the mass balance of the chemical pollutants, a staggered finite element procedure is designed. The mass balance equation of the chemical pollutants and the rest of the governing equations are discretized and solved separately.The mass balance equation governing the chemical pollutants is discretized and solved by using the implicit characteristic Galerkin method for time-dependent convection-diffusion equations, in which the pollutant concentration is taken as the primary variable. The basic idea of the method is to discrete the particle (Lagrangian) derivative of the concentration, instead of the spatial (Eulerian) derivative of the concentration, with respect to time.Finite element simulation of the coupled thermo-hydro-mechanical (THM) behavior in unsaturated porous media generally requires to solve the mixed formulations with theu-p_w -p_a -T form, in which u,p_w,p_a,T are, as the primitive unknowns of the mixedformulations, the displacements, water pressure, gas pressure and temperature.The displacement field, the water and the gas pressure fields and the temperature field belong to different functional spaces, hence different types of finite element interpolation approximations should be used for each of them in order to discretize weak form of coupled governing equations with corresponding natural boundary conditions in the spatial domain.The studies on the mixed finite element formulations with the u - p form for the solid and the fluid mechanics indicated that the u-p interpolation function spaces have to be chosento fulfill the Babuska-Brezzi condition or the much simpler Zienkiewicz-Taylor patch test. These requirements exclude the use of convenient elements with equal low order shape function for displacements (or velocities) and pressures, in incompressible limit condition, for which spurious oscillations in spatial domain may occur in the pressure field.Moreover, compared with the u - p mixed formulations, the u - pw - pa - T mixedformulations of unsaturated porous media are much more complex, and much more computing time is required to solve the global semi-discretized equations with nodal variablesof u - pw - pa - T, to fulfil the coupled non-linear constitutive equations and to computeconsistent tangent modulus matrices at each of local Gauss-Legendre quadrature points. It is rather advantageous to develop the new low order elements with high accuracy for coarse discretizations in order to avoid the spurious oscillations in spatial domain as well as to save the computational cost while the accuracy of the numerical solutions is still ensured.Guided by the success of the one-point quadrature mixed strain elements in solids a stabilized one-point quadrature mixed finite element for the coupled THM process in saturated/unsaturated porous media is derived. The present Galerkin weak form is based on the extension of the Hu-Washizu three-field variational principle in solids to the mixture composed of three coupled phases, i.e. the solid and the two immiscible pore fluids, interacted with the thermal field.The element formulations are derived on the basis of the Galerkin weak form of the partial differential equation system governing the coupled thermo-hydro-mechanical behavior in theu,pw,pa,T fields within the framework of porous continua theory. In the derivation ofelement formulations, the material and the geometrical non-linearity of the solid skeleton are taken into the account.It has been recognized that certain chemical concentration in the pore fluid may have a negative effect on the hydraulic-mechanical quantities of clayey soil. The existence of chemical pollutants may change the electro-chemical properties of pore liquid and the microstructure of clay, and then lead to the change of volume, porosity and the permeability of porous media. Understanding of the chemical effects is essential for the design and the stability assessment of the earth structures such as clay barriers, boreholes and tunnels.A coupled chemo-thermo-hydro-mechanical (CTHM) constitutive model of porous media is developed on the basis of the related experimental results, existing chemo-mechanical (CM) constitutive models and thermo-hydro-mechanical (THM) constitutive models. Particularly, the present constitutive model is developed on the basis of the CAP model for unsaturated porous media with integration of the thermal and chemical effects on the hydro-mechanical behavior into the model. The chemo-softening function is introduced into the constitutive model to simulate the effects of contaminants in pore water on the mechanical properties of the porous media. The present CTHM constitutive model to describe the chemo-thermo -hydro-mechanical behavior of unsaturated porous media is composed of fivefold non-smooth yield surfaces in the four-dimensional stress-suction-temperature space.