| 基于蒙特卡罗随机有限元法的三维随机渗流场研究 |
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| 引用本文： | 王 林,徐 青.基于蒙特卡罗随机有限元法的三维随机渗流场研究[J].岩土力学,2014,35(1):287-292. |
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| 作者姓名： | 王 林 徐 青 |
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| 作者单位： | 武汉大学 水资源与水电工程科学国家重点实验室，武汉 430072 |
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| 摘 要： | 通过建立改进Latin超立方抽样和对偶抽样相结合的复合抽样法,以提高Monte Carlo方法的计算效率,并将其引入Monte Carlo随机有限元(MSFEM)。基于三维有限元模型,采用MCSFEM对山坪土石坝进行随机渗流场分析,研究渗透系数和水头边界条件的随机特性对渗流场的干扰,进行变异系数和抽样次数的敏感性分析。最后,对渗流场的求解量进行概型分析。研究表明:总水头势、流速及渗透体积力的变异性随着渗透系数随机性的增强而变大;复合抽样法既能有效加快Monte Carlo的收敛速度,又能降低样本间的统计相关性,说明了该方法的实用性与有效性;当渗透系数服从正态分布时,渗流场中所取结点的水头和坡降也服从正态分布。
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| 关 键 词： | 渗流场 Monte Carlo随机有限元 复合抽样法 |
| 收稿时间： | 2012-09-28 |
Analysis of three dimensional random seepage field based on Monte Carlo stochastic finite element method |
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| WANG Lin,XU Qing.Analysis of three dimensional random seepage field based on Monte Carlo stochastic finite element method[J].Rock and Soil Mechanics,2014,35(1):287-292. |
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| Authors: | WANG Lin XU Qing |
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| Institution: | State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China |
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| Abstract: | In order to improve the calculation efficiency of Monte Carlo method, composite sampling has been put forward which is a combination of updated Latin hypercube sampling and antithetic sampling, then introduce it into Monte Carlo stochastic finite element method (MCSFEM). Based on the three dimensional finite element model, studying the random disturbance of seepage field due to the variability of permeability coefficient and head boundary condition by using MCSFEM to analyze the random seepage field of Shanping embankment dam. Besides, an analysis on the sensitivity of the variation coefficient and sampling number are carried out. Finally, probability analysis of the result of the seepage field is taken. The results show that: with the randomness of the permeability coefficient increases, the variability of total head potential, velocity and permeation volume force is also getting higher. In addition, composite sampling method not only can effectively accelerate the convergence rate of the MC, but also can reduce the statistical correlation between the samples, verifies the practicality and reliability of the new sampling method. Furthermore, when the permeability coefficient obeys the normal distribution, the head and hydraulic gradient of the selected nodes also obey the normal distribution. |
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| Keywords: | seepage field Monte Carlo stochastic finite element method composite sampling |
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