基于子集模拟法及其改进方法的隧道衬砌可靠度研究

发布时间：2018-02-07 11:25

本文关键词： 可靠度蒙特卡罗法子集模拟法数论方法重要抽样法隧道工程　出处：《北京交通大学》2015年硕士论文　论文类型：学位论文

【摘要】：在我国经济高速的发展下,特长隧道、高度超过200m的高坝、城市地铁工程、具有复杂结构的建筑物等一系列重大工程都在兴建之中,对待此类工程的安全要得到充分的重视,传统的安全系数法虽然在一定程度上能够反映工程的安全性,但是未考虑变量的不确定性与随机性,无法更加全面而又准确地评价工程的安全性,所以可靠度理论的发展对于评价工程的安全性具有重要意义。本文主要对蒙特卡罗法、一次二阶矩法、响应面法等常用可靠度分析方法的基本原理进行了介绍,分析了各个方法在实际应用中的优缺点;针对常用方法的优缺点,文中从子集模拟法的基本思想、中间失效事件的选择、实现步骤及其在实现过程中所涉及到马尔科夫链蒙特卡洛模拟的原理等方面进行了详细介绍,分析了子集模拟法本身具有的优缺点,考虑了在增加马尔科夫链数量和马尔科夫链长度两种情况下对于子集模拟计算精度的影响,根据子集模拟法的特点提出了基于改进子集模拟法两个方向即改进替换蒙特卡罗法(MC)抽样或者马尔科夫链蒙特卡罗模拟(MCMC)抽样。文中针对子集模拟法、数论方法、重要抽样法三种可靠度分析方法的特点,采用子集模拟法的分层抽样原理,利用数论中的低偏差点集抽样和重要抽样法构造重要抽样密度函数,提出了一种基于三者结合的可靠度分析方法。用实际数值算例验证了其准确性及其应用的可能性,新提出的方法有较好的计算精度,并且在样本点数量和失效概率的变异系数上相对于传统的子集模拟法有较好的改进。以兰渝铁路大断面黄土隧道为工程背景,采用“荷载—结构”力学模型,利用ANSYS中的PDS技术,采用APDL语言建立大断面黄土隧道二次衬砌的可靠性分析文件,采用蒙特卡罗—随机有限元法对隧道二次衬砌的荷载效应进行统计分析,得到衬砌内力以及偏心率等变量的统计特征,并分析了随机变量对于轴力、弯矩、偏心率影响系数的灵敏度。最后利用子集模拟法和改进的结合方法对计算了各截面失效概率和可靠度指标,通过计算表明,两种方法在计算隧道衬砌可靠度问题上具有较好的优势,可以作为计算分析隧道衬砌可靠度的方法；从可靠度指标可以看出,本工程隧道衬砌截面在拱顶靠下位置以及拱肩位置可能会出现拉裂情况；衬砌不会出现压坏情况,但是需要注意监测拱肩、拱脚等目标可靠度在临界值的部分衬砌截面。
[Abstract]:With the rapid economic development of our country, a series of major projects, such as super long tunnels, high dams over 200m, urban subway projects and buildings with complex structures, are under construction, and the safety of such projects should be given full attention. Although the traditional safety factor method can reflect the safety of the project to a certain extent, it does not take into account the uncertainty and randomness of the variables, so it is impossible to evaluate the safety of the project more comprehensively and accurately. Therefore, the development of reliability theory is of great significance to evaluate the safety of engineering. This paper mainly introduces the basic principles of common reliability analysis methods, such as Monte Carlo method, first order second moment method, response surface method and so on, and analyzes the advantages and disadvantages of each method in practical application, aiming at the advantages and disadvantages of common methods. In this paper, the basic idea of subset simulation method, the selection of intermediate failure events, the realization steps and the principle of Markov chain Monte Carlo simulation are introduced in detail. The advantages and disadvantages of subset simulation are analyzed, and the effect of increasing the number of Markov chains and the length of Markov chains on the accuracy of subset simulation is considered. According to the characteristics of subset simulation method, two directions of modified subset simulation method are proposed, that is, modified substitution Monte Carlo method (MCMC) sampling or Markov chain Monte Carlo simulation (MCMC) sampling. Aiming at the characteristics of three reliability analysis methods, subset simulation method, number theory method and important sampling method, this paper adopts the stratified sampling principle of subset simulation method. The density function of important sampling is constructed by using the low deviation point set sampling and the important sampling method in the number theory. A reliability analysis method based on the combination of the three methods is proposed. The accuracy and the possibility of its application are verified by an actual numerical example. The new method has good calculation accuracy, and the variation coefficient of sample number and failure probability is better than the traditional subset simulation method. Taking the large section loess tunnel of Lanyu railway as the engineering background, adopting the "load-structure" mechanics model, using the PDS technology in ANSYS, using APDL language to establish the reliability analysis document of the secondary lining of the large-section loess tunnel. Monte Carlo stochastic finite element method is used to analyze the load effect of tunnel secondary lining. The statistical characteristics of lining internal force and eccentricity are obtained, and the axial force and bending moment of random variables are analyzed. The sensitivity of the influence coefficient of eccentricity. Finally, the failure probability and reliability index of each section are calculated by using the subset simulation method and the improved combination method. The results show that the two methods have good advantages in calculating the reliability of tunnel lining. It can be used as a method to calculate and analyze the reliability of tunnel lining. From the reliability index, it can be seen that the tunnel lining section of this project may be cracked at the bottom of the arch top and the arch shoulder, and the lining will not be crushed. However, attention should be paid to monitoring the reliability of the arch shoulder and arch foot in the critical part of the lining section.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U455.91

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