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水、气二相渗流与双重介质变形的流固耦合数学模型
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摘要
本文基于岩体水力学和多相渗流力学理论,将工程地质体简化为双重介质,系统研究了水、气二相流体渗流与双重介质变形耦合作用,包括二相渗流理论分析、孔隙—裂隙复杂多孔介质力学特性分析和耦合效应分析三部分。主要开展了以下几方面的工作:
     (1)针对岩土体的孔隙—裂隙二重性,发展了新的双重介质本构关系即“经典弹塑性—损伤复合本构模型”:孔隙介质用经典本构模型表述,裂隙介质用损伤本构模型表达,而双重介质的形变由孔隙形变和裂隙形变叠加组成。在此基础上,提出了一种孔隙、裂隙功能分配的权重方案。
     (2)从系统科学的观点出发,将相互联系的地质固体系统和地质流体系统作为一个整体,分析了水、气二相渗流与双重介质变形耦合作用机理,并应用连续介质力学理论,推证了二相渗流与孔隙—裂隙双重岩土体介质变形耦合作用的理论方程,联合初始和边界条件,组成了能够反映二相流体渗流与岩体变形耦合作用过程的数学模型。
     (3)基于二相流固耦合理论模型形式复杂性的考虑,建立解耦形式的二相流压力、饱和度方程和岩土体变形方程,并给出相应的Galerkin有限元数值求解公式。
     (4)针对地质岩体数据有限、“参数给不准”以及尺度效应等瓶颈难题,采用了人工神经网络的非线性参数识别方法对岩土体力学与水力学参数进行反演;提出了一种近似确定神经网络隐含层结点个数的方法-区间率定法,并用于算例分析中。
     (5)采用“模块化”的软件设计方法,利用VC++、VB和Visual Fortran混合编程进行面向对象有限元计算程序的编制,完成了二相渗流与孔隙—裂隙岩土体介质变形流固耦合有限元数值模拟软件的初步开发。
     (6)结合算例,采用理论分析与数值分析相结合,定性分析与定量分析相结合,静态模拟与动态模拟相结合的方式,针对具体问题,采用不同的处理方法,使研究更具有科学性和实用性。
Based on rock hydraulics and multiphase seepage mechanics, the engineering geologic body is simplified as double porosity media, and the coupled effects of water-air two-phase flow penetrating and double porosity media deforming are studied systematically. The main researches include water-air two-phase flow penetrating theories, mechanical behavior of complicated porous media with pore-fissure structure and the analysis of coupled effects. The followings are some of the major works in detail in this dissertation:
    (1) To the duality of pore-fissure structure in rock and soil, one kind of new constitutive relation, classical elastic-plastic-damage combination model, is developed for double porosity media. In this model, the mechanical behavior of the part which contains pores is described with the classical elastic-plastic constitutive model; while to the part which contains fissures, the damage model is referred. And to the double porosity media, as a combination of pores and fissures, the elastic-plastic-damage combination model is presented to model its constitutive relation. In addition, a method of weight coefficients distribution is provided, which is able to illustrate the allocated effects or functions of pores and fissures.
    (2) From the viewpoint of system science, the interconnecting and interactional geologic solid body and liquids within are considered one system, and the coupled effects mechanics of water-air two-phase flow infiltrating and double porosity media deforming are analyzed. Furthermore, continuum mechanics is applied to derive the theoretical formulations of two-phase flow seeping and pore-fissure dual rock medium deforming. The mathematical formulations, combined with the boundary and initial condition equations, form the mathematical model, which reflects the coupling process of two-phase flow seeping and rock deforming.
    (3) The resultant governing equations of the mathematical model are very complex in both expression and mathematical properties. In order to derive an efficient numerical solution scheme, an uncoupled equation system is proposed. With the system, the uncoupled equations describing water-air two-phase flow pressure, saturation, and rock or soil deformation are established. Moreover, the numerical solution formulas with Galerkin finite element method are provided.
    
    
    
    (4) Lack of data, inaccurate parameters given and scale effect problems are bottleneck difficulties in research of geologic rock. In order to avoid these problems, the artificial neural network (ANN) nonlinear method for parameter recognition is adopted to inverse the mechanical and hydraulic parameters, and a method. Interval Rating method, determining approximately the nodes number of neural network is developed. Moreover, an example is analyzed to illustrate and verify the ANN method.
    (5) With the computer program design method of modularization, computer languages VC++, VB and Visual Fortran mixed programming technique and object-oriented finite element method (FEM) are adopted to develop a FEM-based computer program, which is utilized to compute and simulate the liquid-solid coupling phenomena of water-air two-phase flow and pore-fissure double porosity rock and soil medium.
    (6) Theoretical analysis and numerical analysis, qualitative analysis and quantitative analysis, and static simulation and dynamic simulation are combined to illustrate the example. To the specific problem, different methods are adopted, which makes the study of more scientificalness and practicality.
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