本文關(guān)鍵詞： 可靠度 蒙特卡羅法 子集模擬法 數(shù)論方法 重要抽樣法 隧道工程　出處：《北京交通大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：在我國經(jīng)濟(jì)高速的發(fā)展下,特長隧道、高度超過200m的高壩、城市地鐵工程、具有復(fù)雜結(jié)構(gòu)的建筑物等一系列重大工程都在興建之中,對待此類工程的安全要得到充分的重視,傳統(tǒng)的安全系數(shù)法雖然在一定程度上能夠反映工程的安全性,但是未考慮變量的不確定性與隨機(jī)性,無法更加全面而又準(zhǔn)確地評價工程的安全性,所以可靠度理論的發(fā)展對于評價工程的安全性具有重要意義。 本文主要對蒙特卡羅法、一次二階矩法、響應(yīng)面法等常用可靠度分析方法的基本原理進(jìn)行了介紹,分析了各個方法在實(shí)際應(yīng)用中的優(yōu)缺點(diǎn);針對常用方法的優(yōu)缺點(diǎn),文中從子集模擬法的基本思想、中間失效事件的選擇、實(shí)現(xiàn)步驟及其在實(shí)現(xiàn)過程中所涉及到馬爾科夫鏈蒙特卡洛模擬的原理等方面進(jìn)行了詳細(xì)介紹,分析了子集模擬法本身具有的優(yōu)缺點(diǎn),考慮了在增加馬爾科夫鏈數(shù)量和馬爾科夫鏈長度兩種情況下對于子集模擬計算精度的影響,根據(jù)子集模擬法的特點(diǎn)提出了基于改進(jìn)子集模擬法兩個方向即改進(jìn)替換蒙特卡羅法(MC)抽樣或者馬爾科夫鏈蒙特卡羅模擬(MCMC)抽樣。 文中針對子集模擬法、數(shù)論方法、重要抽樣法三種可靠度分析方法的特點(diǎn),采用子集模擬法的分層抽樣原理,利用數(shù)論中的低偏差點(diǎn)集抽樣和重要抽樣法構(gòu)造重要抽樣密度函數(shù),提出了一種基于三者結(jié)合的可靠度分析方法。用實(shí)際數(shù)值算例驗證了其準(zhǔn)確性及其應(yīng)用的可能性,新提出的方法有較好的計算精度,并且在樣本點(diǎn)數(shù)量和失效概率的變異系數(shù)上相對于傳統(tǒng)的子集模擬法有較好的改進(jìn)。 以蘭渝鐵路大斷面黃土隧道為工程背景,采用“荷載—結(jié)構(gòu)”力學(xué)模型,利用ANSYS中的PDS技術(shù),采用APDL語言建立大斷面黃土隧道二次襯砌的可靠性分析文件,采用蒙特卡羅—隨機(jī)有限元法對隧道二次襯砌的荷載效應(yīng)進(jìn)行統(tǒng)計分析,得到襯砌內(nèi)力以及偏心率等變量的統(tǒng)計特征,并分析了隨機(jī)變量對于軸力、彎矩、偏心率影響系數(shù)的靈敏度。 最后利用子集模擬法和改進(jìn)的結(jié)合方法對計算了各截面失效概率和可靠度指標(biāo),通過計算表明,兩種方法在計算隧道襯砌可靠度問題上具有較好的優(yōu)勢,可以作為計算分析隧道襯砌可靠度的方法；從可靠度指標(biāo)可以看出,本工程隧道襯砌截面在拱頂靠下位置以及拱肩位置可能會出現(xiàn)拉裂情況；襯砌不會出現(xiàn)壓壞情況,但是需要注意監(jiān)測拱肩、拱腳等目標(biāo)可靠度在臨界值的部分襯砌截面。
[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.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：U455.91

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