【作者】 刘泽佳；

【导师】 李锡夔；

【作者基本信息】 大连理工大学 ， 固体力学， 2005， 博士

【摘要】 近年来,非饱和多孔介质的热—水力—力学耦合行为的研究引起了工程界的广泛的注意。人们已经投入了很大的精力来进行多孔介质瞬态THM耦合行为的定量研究。 本论文致力于这个课题的三方面的工作:1)建立了求解多孔介质中化学—热—水力—力学耦合行为的数学模型;2)发展了这个数学模型初值、边值问题的混合元方法的数值解法;3)建立多孔介质中的化学—热—水力—力学(CTHM)耦合本构模型。 这个数学模型由一组偏微分方程组成:包括孔隙水、孔隙气的质量守恒方程;混溶于孔隙流体中的化学污染物的质量守恒方程;热量守恒方程和多孔介质混合物的总体动量守恒方程。为了模拟混溶污染物在非饱和多孔介质中的传输,模型中包含了污染物传输的六种控制机制:对流、分子弥散、机械逸散、吸附、降解、不动水效应。 采用有限元法求解数学模型的初值、边值问题。考虑到化学污染物质量守恒方程在物理上的对流—扩散的特性和数学上的非自伴随和双曲线的特性,采用交错算法进行求解,即:对化学污染物的质量守恒方程和其余的控制方程分别进行离散和求解。 化学污染物的质量守恒方程采用依赖于时间的对流—扩散方程的隐式特征线Galerkin方法进行离散和求解,其中污染物的浓度作为基本未知量。该方法的基本思想是对浓度在时域中进行针对物质粒子(Lagrangain)而不是空间点(Eulerain)的离散。 非饱和多孔介质中热—水力—力学(THM)耦合行为的有限元模拟通常要求解u-p_w-p_a-T混合形式的方程。混合方程的基本未知数u,p_w,p_a,T分别为固相位移、孔隙水压力、孔隙气压力和温度。位移场、水压力和气压力场及温度场分属于不同的函数空间,因此应该对他们采用不同的有限元插值近似,以进行满足自然边界条件的耦合控制方程弱形式的空间离散。 流体和固体力学u-p混合形式的有限元公式研究表明,u-p有限元插值的函数空间必须满足Babuska-Brezzi条件或更简明的Zienkiewicz-Taylor分片试验。这些限制条件判定了应用方便的位移(或速度)和压力采用等阶插值的低阶形函数的单元在不可压缩条件下压力场会产生虚假的数值振荡。 与u-p形式的混合公式相比,非饱和多孔介质的u-p_w-p_a-T公式更加复杂,求解以u,p_w,p_a,T为基本未知数的整体半离散方程、高斯积分点上耦合的非线性本构方程迭代及计算一致性切线模量矩阵所需要的时间要长很多。因此就更加迫切需要发展低阶高精度粗网格的有限元方法避免虚假的数值振荡,同时在满足数值计算精度基础上又能降低计算费用。 本论文基于一点积分混合应变元在固体中的成功应用,提出了饱和、非饱和多孔介质中THM耦合问题的稳定的一点积分混合应变元。本文提出的偏微分方程组的Galerkin弱形式基于固体力学中的胡海昌-Washizu三变量广义变分原理,将之推广到由固体骨架和不混溶的两种孔隙流体组成的三相非饱和多孔介质与温度场的相互作用的耦合场分析中。更多还原

【Abstract】 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.更多还原