【作者】 黄林冲；

【导师】 徐志胜； Jose E.Andrade； 彭立敏；

【作者基本信息】 中南大学 ， 防灾减灾工程及防护工程， 2009， 博士

【摘要】 土体本构模型的建立直接影响数值计算结果,在前人研究的基础上,本论文针对多孔介质,建立了固-液-气三相耦合状态下的本构方程,设计了弹塑性变形的积分求解算法,编制了大型有限元数值计算程序;以多孔泥质页岩隧道为研究对象,探讨了渗水作用下,多孔土体质的软弱围岩隧道发生变形的内涵以及变形特征,其主要成果有:(1)基于非线性连续力学以及混沌理论,建立了多孔介质中,三相形变和应变集中的数学和力学本构模型。从质量守恒、动量守恒和能量守恒三大物理定律出发,建立了固-液-气三相耦合本构模型;并从有效应力σ~*与固相矩阵形变ε、饱和度S_r与吸力s、三相状态中固有质量密度与固有压力p_α以及相关联的流动法则与固有压力之间的发展方程这四个方面,详细阐述了本构关系模型;基于达西定律,进行了本构模型孔隙水压力的修正,通过Piola转换,得到了相关流体向量的拉格朗日完全形式。(2)对非线性准则下的弹塑性本构关系进行积分求解,得到了其增量表达形式,设计了迭代求解算法。通过引入牛顿迭代-预条件共轭梯度法的复合算法来进行有限元计算中大型刚度矩阵的迭代求解,编制了算法程序,并进行了与传统Newton迭代法相比较的效率分析;给出了土体产生局部化变形时的数值表达,即计算高斯点的第一切线算子为零,为判断土体变形发生的数值计算提供了理论依据,从而能够模拟出岩土体发生局部化变形的发展过程。(3)编写了基于有限元理论大型有限元计算软件SN-2D,实现了本构模型的有限元程序化。开发了FORTRAN语言平台的大型有限元数值计算程序以及Q9P4数值模拟单元,并实现了与Matlab的程序对接,实现了计算程序的图形输出功能。(4)通过开发的SN-2D有限元分析软件,进行了多孔渗水砂土和泥质页岩隧道的数值模拟分析,揭示了多孔渗水介质变形的内涵。模拟了非饱和砂土在不排水平面应变压缩下局部变形带的形成和发展过程,讨论了所编写程序的网格尺寸效应;分析了多孔泥质页岩隧道围岩变形的规律和应力特征。(5)对多孔渗水泥质页岩隧道围岩的变形进行了数值分析与实测的对比分析。分别对围岩内部位移量测、围岩与初期支护之间接触压力量测、型钢支撑与格栅支撑内力量测、喷射混凝土层应力量测以及模筑混凝土二次衬砌内力量测数据进行了分析讨论;研究了多孔渗水泥质页岩隧道的变形破坏成因、变形破坏特点、失稳破坏机理和破坏形式,得出了多孔介质隧道围岩的破坏机理,即多孔结构在渗水环境下的损伤扩容、剪胀引起隧道的收敛变形。(6)在程序实现、数值模拟和现场实测的基础上,研究了隧道围岩的变形预测。将隧道围岩变形预测分为超前预测和过程预测两个部分的基础上,引入了基于粘、弹、塑性理论的切向应变超前预测方法,采用等维灰数递补数据处理技术建立等维灰数递补GM(1,1)模型来对灰色GM(1,1)模型进行修正,预测结果能较为真实地反映现场实测数据。更多还原

【Abstract】 The constitutive model of the soil mass determines the computation results greatly in the numerical Geomechanics. Based on the former researches, this dissertation presents a constitutive relations coupling with the solid-fluid-air for the porous medium, and designs a new integration arithmetic for elasto-plastic deformation, and then a finite element program is coded by FORTRAN. Utilizing a porous argillaceous shale tunnel as the research project, the deformation mechanism of the surrounding wall mass in porous tunnel is studied systematically. The main contents are as follows:(1) The governing three-phase mathematic and mechanics model about the deformation and strain localization is derived in porous medium from nonlinear continuum mechanics and mixture theory. According from mass balance equations, momentum balance equations and energy balance equations, the solid-fluid-air model is set up. These constitutive laws relate: the evolution of the constitutive effective stressσ~* with imposed solid matrix deformations; the degree of saturation s_r with suction stress s; the intrinsic mass densities with intrinsic pressure on all three phase; and the relative flow vector with intrinsic pressure p_αfor the water and air phase. Also, the fully Lagrangian form of the Darcy law is resolved by Piola algorithm and then the flow law is gained, leading to the implementing of a modified pore water pressure in the constitutive model.(2) An improved stress integration algorithm is proposed based on the nonlinear elasto-plastic constitutive laws, and then a new iterative algorithm is designed here. The dissertation introduces the Newton-PCG (Preconditioned Conjugate Gradient) composite algorithm to solve the iterative algorithm in large-scale problems with huge stiffness matrixes, which is coded by FORTRAN program, together with an efficiency analysis compared with standard Newton’s iterative method. Next the necessary condition for localization is obtained by introducing the first tangent operator, which presents a theoretical basis in deformation simulation.(3) A large-scale finite element numerical software is written based on the FEM theory, leading the code implementing of the above constitutive relation frame. This dissertation presents a systemic numerical computational program with the FORTRAN language, as well as the Q9P4 numerical simulation element. Next this program is interfaced with Matlab, which leads to the implementing of figure output.(4) The deformation behavior of the porous sand and argillaceous shale tunnel are simulated with the self-written FEM program. Numerical simulation on saturated sand under the undrained condition is performed to study the onset and development of the shear band, and the mesh sensitivity is studied. Next the deformation and the stress of the soft argillaceous shale under construction are simulated to study the deformation behavior of porous medium.(5) The dissertation presents comparative analysis between the numerical simulation and in-situ testing in a porous argillaceous shale tunnel. The inner displacement of the surrounding rock mass, the contact pressure between the surrounding rock and the primary support, the force between the steel support and the grating support, the force of the primary support and the force of the secondary support, are all studied here according to the in-situ testing data. Then we systematically discuss the deformation failure condition, deformation failure character, instability failure mechanism and failure mode, leading to the study of tunnel deformation mechanism.(6) Based on the coding, numerical simulation and in-situ testing, this dissertation develops the prediction researches on tunnel deformation. Systematic advanced prediction and process prediction researches into tunnel deformation are carried out, based on the solid mechanics theory and the grey systems theory; especially in process prediction, we adopt the data processing of filling vacancies in the proper order and establish the A GM (1,1) model to modify the grey GM (1,1) model. The prediction well matches the in-situ testing data when this method is applied in the Guankouya tunnel.更多还原