基于复变函数解法和突变理论的隧洞围岩稳定性研究

发布时间：2019-05-03 18:08

【摘要】：随着岩土工程的发展,围岩的失稳得到了各界的关注。围岩的失稳破坏问题是非常复杂的,具有非线性、突变性、离散性以及不确定性。目前针对围岩失稳破坏的研究大都停留在概念上或者精度较低的判据和理论上,因此需要寻找量化的、精度较高的判据来解决此问题。随着复变函数解法和突变理论在岩土工程中的研究逐步深入,发现突变理论可提供一个量化的围岩失稳判据来判定,同时考虑到复变函数解法提供的围岩弹性应力应变解析解可用于建立较高精度突变理论判据所需的势能方程。因此,本文考虑结合突变理论分析和复变函数解法,编辑相关计算程序探索性的研究隧道围岩稳定性问题,主要从以下几个方面开展研究： (1)利用复变函数解法求解隧洞围岩的应力应变,并给出隧洞内任意点应力应变解析解的计算程序； (2)建立突变理论能量势能标准化方程和面积势能标准化方程,并给出计算标准势能方程的计算程序； (3)利用突变理论依据能量判据和面积判据研究隧洞围岩的整体和局部稳定性,并给出稳定性判据的计算程序,然后通过计算和分析相关围岩参数对隧洞围岩稳定性的影响规律。本研究创新点如下： (1)在岩土工程稳定性分析时,采用了突变理论,给该领域研究提供了一大研究思路,具有很强的科研价值。对尖点突变模型进行的较为深入的研究,初步获得尖点突变模型的适用性,并进一步阐述了拟合方法的操作； (2)在复变函数解法研究模型应力应变的基础上,利用突变理论进行稳定性分析,使得研究结果更加精确、稳定。根据复变函数解法,借助Fortran语言编辑程序成功的获得围岩的弹性应力应变解析解,使得结果更加准确合理,给予后续的研究结果给予强大的精度支持。给现代化施工与设计提供了更加精确合理理论依据,摆脱以往对安全系数的依赖,具有相当的经济价值； (3)通过研究,将突变理论和复变函数解法结合,对以往研究思路的重大突破,提高了这两个理论的工程应用价值和科研价值。借鉴复变函数解法得到准确弹性解析解的优势,将其引入以塑性区面积势和弹性应变能作为突变势的突变理论模型中,结合突变理论来研究使得结果更加准确合理。
[Abstract]:With the development of geotechnical engineering, the instability of surrounding rock has been paid more and more attention. The problem of instability and failure of surrounding rock is very complex, which is nonlinear, abrupt, discrete and uncertain. At present, the research on instability failure of surrounding rock mostly stays on the concept or the criterion and theory of low precision, so it is necessary to find a quantitative and high precision criterion to solve this problem. With the further study of complex function method and catastrophe theory in geotechnical engineering, it is found that the catastrophe theory can provide a quantitative criterion to judge the instability of surrounding rock. At the same time, the analytical solution of elastic stress and strain of surrounding rock provided by the method of complex variable function can be used to establish the potential energy equation required for the criterion of catastrophe theory with higher accuracy. Therefore, considering the combination of catastrophe theory analysis and complex variable function solution, this paper compiles the relevant calculation program to explore the stability of tunnel surrounding rock. The research is mainly carried out from the following aspects: (1) the complex variable function method is used to solve the stress and strain of the surrounding rock of the tunnel, and the calculation program of the analytical solution of stress and strain at any point in the tunnel is given; (2) the energy potential standardization equation and area potential energy standardization equation of catastrophe theory are established, and the calculation program of the standard potential energy equation is given. (3) on the basis of energy criterion and area criterion, the global and local stability of surrounding rock of tunnel is studied by catastrophe theory, and the calculation program of stability criterion is given. Then, the influence of the surrounding rock parameters on the stability of tunnel surrounding rock is calculated and analyzed. The innovations of this study are as follows: (1) in the stability analysis of geotechnical engineering, the catastrophe theory is adopted, which provides a great idea for the research in this field and has a strong scientific research value. Based on the in-depth study of the cusp mutation model, the applicability of the cusp mutation model is preliminarily obtained, and the operation of the fitting method is further expounded. (2) based on the study of the stress and strain of the model by the method of complex variable function, the stability analysis of the model is carried out by using the catastrophe theory, which makes the research results more accurate and stable. According to the method of complex variable function, the analytical solution of elastic stress and strain of surrounding rock is obtained successfully by means of Fortran language editing program, which makes the result more accurate and reasonable, and gives strong precision support to the follow-up research results. It provides a more accurate and reasonable theoretical basis for modern construction and design, and it has considerable economic value to get rid of the dependence on safety factor in the past. (3) through the research, the combination of catastrophe theory and complex function method can improve the engineering application value and scientific research value of the two theories. The advantage of accurate elastic analytical solution is obtained by using complex variable function method for reference. It is introduced into the catastrophe theoretical model in which the plastic area product potential and elastic strain energy are used as abrupt potentials. The results are more accurate and reasonable with the study of catastrophe theory.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU457

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