岩体结构非平衡演化稳定与控制理论基础研究

发布时间：2018-06-12 20:46

本文选题：裂隙岩体 + 非平衡演化　；参考：《清华大学》2013年博士论文

【摘要】：天然岩石受不同尺度节理、裂隙切割，构成裂隙岩体复合介质。各种裂隙岩体进一步构成大规模岩体工程结构。我国岩石工程规模与复杂度迅速增长，岩体工程结构稳定性问题突出。本文采用动态演化观点研究岩体结构稳定与控制问题，提出相对完整的岩体结构非平衡演化研究体系，重点研究该体系数学与力学相关理论基础。主要工作与创新性成果如下： (1)非平衡态热力学基础研究：证明齐次Onsager流必然全等次，从而证明基于齐次Onsager流的Rice正则结构等价于Ziegler最大耗散率原理；该结论表明岩土类材料本构关系热力学基础需要建立在有旋热力学流范围。 (2)方向分布函数与组构张量：提出最一般形式的方向分布函数——张量型方向分布函数，建立其相对完备的组构张量代数，，包括非对称与全对称组构张量解析解、收敛性与拟合精度、不同阶组构张量关系等。 (3) Kachanov-Rabotnov (K-R)损伤有效应力：基于矢量型方向分布函数建立K-R损伤有效应力三维各向异性微平面模型，实现严格宏—细观几何等效原理；该模型澄清连续体损伤力学若干基本问题，包括常用各向异性与各向同性有效应力模型适用条件、损伤效应张量正定性与Voigt对称性等。 (4)广义Hamilton原理：建立内变量热力学耗散材料体系广义Hamilton原理，相比经典弹性体Hamilton原理，只需将结构弹性应变能替换为特定内能与非弹性内耗散功之和，适用于非保守外力与内力以及有限变形情况；广义Hamilton原理是以下Lyapunov稳定与控制理论的连续介质力学基础。 (5) Rice非弹性体Lyapunov稳定与控制理论：基于Lyapunov第二类稳定性方法，证明理想Rice非弹性体在恒定外部作用条件与拟静力条件下的最小流动势原理，结合材料损伤效应阐明结构非平衡演化的一般规律；在此基础上提出结构稳定评价与失稳控制的有效方法，同时阐明新奥法原理、潘家铮最大最小原理等岩土工程实用稳定性原理的理论依据。 (6)变形加固理论：基于Rice非弹性体Lyapunov稳定与控制理论证明变形加固理论，并依托变形加固理论这一特例将前者应用于工程结构稳定评价与加固设计。结合有限元算例初步研究结构整体稳定性、加固措施效果与效率、结构长期稳定性监测与预测等岩土工程重要问题。
[Abstract]:Natural rock is cut by joints and fissures of different scales, forming composite medium of fractured rock mass. All kinds of fractured rock mass further constitute large-scale rock mass engineering structure. The scale and complexity of rock engineering in China are increasing rapidly, and the stability of rock mass engineering structure is prominent. In this paper, the problem of stability and control of rock mass structure is studied from the viewpoint of dynamic evolution, and a relatively complete research system of non-equilibrium evolution of rock mass structure is proposed, with emphasis on the theoretical basis of mathematics and mechanics of the system. The main work and innovative results are as follows: 1) the fundamental study of nonequilibrium thermodynamics: it is proved that the homogeneous Onsager flow must be all equal, and that the Rice canonical structure based on the homogeneous Onsager flow is equivalent to the Ziegler principle of maximum dissipation rate; The conclusion shows that the thermodynamic basis of constitutive relations of geotechnical materials needs to be based on the direction distribution function and fabric Zhang Liang distribution function in the range of rotational thermodynamic flow. The most general form of directional distribution function-Zhang Liang directional distribution function is proposed. Its relatively complete fabric Zhang Liang algebras are established, including asymmetric and fully symmetric Zhang Liang analytic solutions, convergence and fitting accuracy. (3) Kachanov-Rabotnov) damage effective stress: based on vector direction distribution function, a three-dimensional anisotropic micro-plane model of K-R damage effective stress is established to realize the strict macro-meso-geometric equivalent principle; The model clarifies some basic problems of continuum damage mechanics, including the applicable conditions of anisotropic and isotropic effective stress models. Damage effect Zhang Liang positive definite and Voigt Symmetry etc. Generalized Hamiltonian principle: the generalized Hamiltonian principle of internal variable thermodynamic dissipative material system is established, compared with the classical elastic body Hamiltonian principle. It is only necessary to replace the elastic strain energy of the structure with the sum of specific internal energy and inelastic internal dissipative work, which is suitable for non-conservative external force and internal force and finite deformation. The generalized Hamilton principle is the continuous medium mechanics foundation of the following Lyapunov stability and control theory. 5) Rice nonelastic Lyapunov stability and control theory: based on Lyapunov second stability method, The principle of minimum flow potential of ideal Rice non-elastic body under constant external and quasi-static conditions is proved, and the general law of non-equilibrium evolution of structure is explained by combining material damage effect. On this basis, an effective method for structural stability evaluation and instability control is proposed, and the principle of the new Austrian method is expounded. The theoretical basis of the practical stability principle of geotechnical engineering, such as the Pan Jiazheng maximum and minimum principle, and the deformation reinforcement theory: based on the Lyapunov stability and control theory of Rice non-elastic body, the deformation strengthening theory is proved. Based on the theory of deformation reinforcement, the former is applied to the stability evaluation and reinforcement design of engineering structures. Combined with finite element examples, the main problems of geotechnical engineering, such as overall stability of structure, effect and efficiency of reinforcement measures, monitoring and prediction of long-term stability of structures, are studied.
【学位授予单位】：清华大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU45

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