基于极限分析有限元法的隧道稳定性研究

发布时间：2018-03-30 20:04

本文选题：隧道稳定性　切入点：极限分析有限元法　出处：《湖南大学》2015年硕士论文

【摘要】：稳定性问题的研究对于隧道设计、施工以及理论研究均有重要的指导意义。目前,采用传统的滑移线法、极限平衡法和极限分析法研究该课题时存在诸多困难,如难以有效考虑复杂的几何边界、荷载以及非均质材料等问题。而常用的有限元数值方法在研究隧道稳定性问题时,需要进行大量的迭代计算,极为耗时且不易收敛。相比而言,极限分析有限元法是解决上述问题的有效途径。其实质是采用数值分析方法求解极限问题,可考虑不同的力学参数与复杂工况,并避开了复杂的应力-应变增量迭代过程,直接针对最终的极限状态进行处理,无需假定破坏模式即可进行稳定性计算,利用计算机自动搜索出连续体破坏时的极限荷载及速度场或应力场,具有计算稳定、高效、易收敛等特点。为此,本文采用极限分析有限元法,对不同参数条件下隧道稳定性问题进行深入探讨,具体研究工作如下:(1)从介绍塑性极限理论的基本原理开始,对极限分析有限元法数值方法的基本内容进行系统的阐述,涉及单元离散化、数学规划模型的建立及其优化求解、计算机实现过程等内容。(2)基于某些合理的计算假定,建立一个可考虑多种因素影响的计算模型;针对不同参数条件下的隧道稳定性问题,利用极限分析有限元法进行计算分析,得到稳定系数的相关计算图表和经验计算公式,并探讨方形隧道的稳定性影响因素和破坏模式的形态特征及其演变规律,为实际工程提供参考。(3)参照Terzaghi地基承载力计算公式,对关于黏聚力、超载和重力的支护反力分项系数N'c、N's、N'γ分别进行数值计算,整理形成相应的计算图表,并对圆形隧道破坏的形态特征和演变规律进行总结。(4)结合云阳山隧道开挖过程中围岩与支护结构的大变形和冒顶坍塌的工程实例,采用极限分析有限元法分析隧道围岩发生失稳破坏时的形态特征和破坏范围,获取隧道周边围岩需要进行重点加强的区域,验证本文方法的实用性和有效性。
[Abstract]:The study of stability is of great significance for tunnel design, construction and theoretical research. At present, there are many difficulties in using the traditional slip line method, limit equilibrium method and limit analysis method to study the problem. For example, it is difficult to effectively consider the complex geometric boundary, load and heterogeneous materials, while the commonly used finite element numerical method needs a large number of iterative calculations to study the stability problem of the tunnel. In contrast, the finite element method of limit analysis is an effective way to solve the above problems. The essence of the finite element method is to use numerical analysis method to solve the limit problem, which can take into account different mechanical parameters and complex working conditions. The complex stress-strain increment iteration process is avoided, and the ultimate limit state is processed directly, and the stability can be calculated without assuming the failure mode. In this paper, the finite element method of limit analysis is used to automatically search the limit load, velocity field or stress field of continuum failure, which has the characteristics of stable calculation, high efficiency and easy convergence. The problem of tunnel stability under different parameters is discussed in depth. The specific research work is as follows: (1) starting with the introduction of the basic principle of plastic limit theory, the basic contents of finite element method for limit analysis are systematically expounded. It involves the discretization of units, the establishment of mathematical programming model and its optimization solution, the process of computer realization, etc.) based on some reasonable calculation assumptions, a calculation model which can take into account the influence of many factors is established. Aiming at the tunnel stability problem under different parameters, the finite element method of limit analysis is used to calculate and analyze the stability coefficient. The paper also discusses the influencing factors of stability of square tunnel, the morphological characteristics of failure mode and its evolution law, which provides a reference for practical engineering. (3) with reference to the calculation formula of bearing capacity of Terzaghi foundation, the cohesion force is discussed. The partial coefficients of support reaction of overload and gravity are calculated numerically respectively, and the corresponding calculation charts are formed. Combined with the engineering examples of large deformation and roof collapse of surrounding rock and supporting structure during the excavation of Yunyang Mountain Tunnel, the paper summarizes the morphological characteristics and evolution law of circular tunnel failure. The finite element method of limit analysis is used to analyze the morphological characteristics and failure range of the surrounding rock in the tunnel, and the area where the surrounding rock around the tunnel needs to be strengthened is obtained, which verifies the practicability and validity of the method in this paper.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U451

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