地震时供水管网的可靠性和功能分析(上)
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摘要
本文以管线的可靠度分析为基础,对震后供水管网的可靠性及其功能进行分析。将直埋管线看作地基梁,考虑它和地震波引起土层位移的相互作用,建立极限状态函数。假设其随机矢量正态分布和线性无关或非正态分布和非线性无关。对于这两种情形,可采用电子表格的规划求解方法,或采用可靠度指数的Hasofer-Lind公式,都可得到管线的可靠度指数。用电子表格法对于用户无需求偏导数等复杂的数学运算,而采用H-L公式则要涉及偏导数和R-F变换等的运算,通常这是很困难的。本文借助MATLAB的符号运算程序可给出偏导数和其他相关函数,使得可靠度指数计算变得容易。在给出所有管线的失效概率后,就可对震后管网的可靠性及供水功能进行分析。管网的连通性估计是由Monte-Carlo法进行模拟计算得到的,可以给出任意两节点间的可靠概率估计。供水管网在地震时由于受损可能出现渗透漏,它的供水功能可能降低,可以通过管网的水力分析进行评价。本文采用点式渗漏模型模拟震后管线的渗漏,提出用管线损坏概率的反正弦函数来表示渗漏面积,实现对震后供水管网的水力计算。基于地理信息系统的供水管网抗震能力分析方法已经建立。依据来自GIS的管线失效概率、管网的可靠性和供水功能的分析信息可以对供水管网的抗震能力做出全面的评价。
In this paper,the reliability and function analysis of water supply networks post-earthquake are calculated based on the reliability analysis of pipelines.In order to establish the limit state function,a buried pipeline is considered as a foundation beam to account the interaction between the pipeline and subsoil deformation due to seismic wave.The main variables of the limit state function are assumed to be normally distributed and uncorrelated or nonnormally distributed and correlated.For these two cases,the reliability index of pipelines can be calculated by the optimization tool of a spreadsheet software or Hasofer and Lind' reliability index definition.The arithmetic of partial derivatives is not necessary on the user' part if using a spreadsheet software,while H-L' formula is used,the arithmetic of partial derivatives and R-F transformation will be involved on the user' part,and it usually is very difficult to do it.But to compute the reliability index of a pipeline could become much simpler if the MATLAB program library(Symbolic Math Toolbox) is used to find partial derivatives and other functions.After the reliability index and losing probability of each pipeline in the water system have been given,the reliability and function analysis of the water supply network could be conducted. The reliability(connectivity) of the network is obtained from the Monte Carlo simulating calculation,and the reliability probability between any both nodes in the network can be given. Leakage in water systems can be occured due to the damage during an earthquake.The function of water systems may be reduced.In order to evaluate the function of water systems,it is necessary that the hydraulic analysis accounting the leakage of water supply network is made.In this paper,the point leakage modal is adopted to simulate the leakage,and the leakage area is expressed by the anti-sin function of losing probability of a pipeline.Based on the methodology for water systems implemented by a geographic information system,the seismic capability of water supply networks is roundly evaluated according to these analytic results from the GIS.
In this paper,the reliability and function analysis of water supply networks post-earthquake are calculated based on the reliability analysis of pipelines.In order to establish the limit state function,a buried pipeline is considered as a foundation beam to account the interaction between the pipeline and subsoil deformation due to seismic wave.The main variables of the limit state function are assumed to be normally distributed and uncorrelated or nonnormally distributed and correlated.For these two cases,the reliability index of pipelines can be calculated by the optimization tool of a spreadsheet software or Hasofer and Lind' reliability index definition.The arithmetic of partial derivatives is not necessary on the user' part if using a spreadsheet software,while H-L' formula is used,the arithmetic of partial derivatives and R-F transformation will be involved on the user' part,and it usually is very difficult to do it.But to compute the reliability index of a pipeline could become much simpler if the MATLAB program library(Symbolic Math Toolbox) is used to find partial derivatives and other functions.After the reliability index and losing probability of each pipeline in the water system have been given,the reliability and function analysis of the water supply network could be conducted. The reliability(connectivity) of the network is obtained from the Monte Carlo simulating calculation,and the reliability probability between any both nodes in the network can be given. Leakage in water systems can be occured due to the damage during an earthquake.The function of water systems may be reduced.In order to evaluate the function of water systems,it is necessary that the hydraulic analysis accounting the leakage of water supply network is made.In this paper,the point leakage modal is adopted to simulate the leakage,and the leakage area is expressed by the anti-sin function of losing probability of a pipeline.Based on the methodology for water systems implemented by a geographic information system,the seismic capability of water supply networks is roundly evaluated according to these analytic results from the GIS.
引文
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