供水管网系统抗震可靠性分析及加固优化研究
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摘要
供水管网系统是城市生命线工程的重要组成部分,在强烈地震作用下,供水系统的破坏及其功能失效会产生次生灾害并引起巨大的生命、财产损失。而我国现有的供水管网系统,大多数没有经过正规的抗震设计,且不少城市又有着可能遭受中、强地震影响的背景。因此,对供水管网系统进行震害预测和地震可靠性分析,评估系统震后运行状态、掌握其抗震薄弱环节,进一步增强其抗震能力,对开展城市防震减灾工作具有重要的现实意义。本文在综合分析国内外相关研究的基础上,对供水管网系统的地震功能分析和抗震加固优化问题作了较为全面系统的研究,主要内容如下:
(1)以地震波作用下埋地管道的接头损坏作为主要破坏模式,主要考虑管道的轴向变形性能,采用波动理论对供水管线进行地震反应分析,比较了两种管土间轴向变形传递系数的计算差异,建议采用《室外给水排水和燃气热力工程抗震设计规范》(GB50032-2003)中给出的变形传递系数进行管道抗震验算,并讨论了地震波入射角、剪切波速、管径等参数对管道变形的影响。考虑地震作用效应和管道抗力的随机特性,建立了埋地管道单元的概率预测模型,评估其在地震时的震害状态,比较了管道随机变量采用不同的概率分布模型对管道抗震可靠性的影响差异,建议管道的允许变形和实际变形分别采用正态分布和极值Ⅰ型分布进行计算。
(2)根据管线抗震可靠性分析结果,通过Monte Carlo随机模拟过程,近似再现管网中各管段的破坏状态。把供水管网系统简化为边权有向网络图,分别结合图论理论方法和模糊关系矩阵法,对管网进行连通可靠性分析,定性评价管网系统的运行状态,为进一步分析其抗震功能可靠性提供参考。由于Monte Carlo模拟方法是以管网各节点与水源点处于连通状态的近似频率计算代替精确概率分析,所得数值解具有一定的误差,为获得稳定的计算结果,对文中所用算例进行了5000次模拟。算例分析表明,基于图论方法和模糊关系矩阵法得到的管网连通可靠性结果基本相等。
(3)首先建立管网微观水力模型,进行震前无破坏状态下的流分析。然后根据震后管线的破坏情况,对严重破坏的管线关闭其两端阀门;对轻微或中等破坏的管线在其中间位置增设虚拟漏水节点,建立带渗漏管网的水力分析模型,进行管网震后服务功能分析。该模型在传统的管网水力计算基础上,考虑了节点流量随水压的动态变化,避免了负的压力计算值的产生。同时震后的及时关阀措施,有效地提高了管网系统的供水能力。在进行供水管网的抗震功能可靠度分析时,借鉴结构可靠度的分析方法,以节点水压为评价指标,采用均值一次二阶矩方法计算管网各节点的功能可靠度,该方法通过一次水力分析即可给出震后低压供水和渗漏状态下管网各节点的可靠性指标,较之前发展的随机模拟方法大为简化且概念清晰。
(4)以节点水压和流量为指标,建立了管网系统的服务性能准则。基于震后管网功能分析结果,绘制了节点水压和节点流量的服务性能曲线,采用转换函数的方法对其进行服务性能等级划分。引入模糊数学的理论与方法,构造节点水压和节点流量两个单因素指标的梯形隶属函数,建立震后管网系统服务性能的二级模糊综合评判模型,通过加权平均型评判模型和最大隶属度原则对管网系统进行综合评定,实现了地震对供水管网系统服务性能影响的量化评价。同时兼顾管网系统的连通特性和水力特性,采用分层的分析方法,对其进行地震易损性风险评估,以便找出系统薄弱环节进而确定减少风险的合理方法。
(5)通过优化管道接头形式,来减少震时管道接头处的变形和渗漏、提高其抗震性能,进而增强管网的抗震功能可靠性,实现系统的抗震加固优化。从系统全局出发,以管网系统震后水压总降幅和系统加固总投入最小为目标函数,以管线抗震可靠度和震后管网各节点的自由水压为约束,建立多目标优化数学模型,将优化变量转化为较少的离散变量,对管网系统进行抗震加固优化。基于不刻意追求最优解,而寻求满意解的优化思想,利用正交枚举法进行简化计算,从而避免了大规模非线性规划求解的困难,为已建供水管网系统的抗震加固及拟建管网系统的抗震优化设计提供了理论依据。
Water supply network system is an important constituent of urban lifeline engineering, its damage and disabler under the destructive earthquake will cause great loss on life and property or even severe secondary disaster. Most of the water supply systems in our country were not designed with seismic standards, while many cities may have the seismic risk background. Therefore, earthquake disaster predictions and seismic reliability analysis of water supply network are of great importance to evaluate cities' ability of reducing earthquake disasters, which constitute the basis for finding out the vulnerable spot and enhancing seismic reliability of the system. Based on related research at home and abroad, this paper focuses on the further study of seismic reliability and optimum retrofit of water supply network system. The main contents are included as follows:
(1) Taking the breakage of the conduit joints caused by seismic wave propagation as main failure mode, seismic performance analysis of the pipeline was performed with wave theory method by considering pipe's axial deformation. Two different methods for calculating axial deformation transfer coefficient were presented to check pipeline's seismic deformation, and influencing factors such as seismic wave's incident angle, shear wave velocity, pipeline's diameter and wall thickness were deeply discussed. Considering the randomness of seismic response and resistance of the pipe, probabilistic forecasting model was built to evaluate pipe's earthquake disaster. Comparisons of pipe's seismic reliability analysis with different probability distribution models of the random variable shows that it is conservative to evaluate pipe's seismic reliability by considering that seismic response and resistance of the pipe are all submitting normal distribution.
(2) According to seismic reliability analysis, each pipeline's damage state was simulated by Monte Carlo random process. Simplifying the water supply network system as an edge-weighted directed network figure, connectivity reliability of the network was performed by graph theory and fuzzy relation matrix method separately, which referenced for qualitative analysis of system's running status and seismic functional reliability evaluation of network. Since precision probability analysis was substituted by approximate frequency of the connectivity between each node of the network and water source for Monte Carlo method, the arithmetic solution were with errors, therefore, 5000 simulations were proceeded to obtain steady numerical solution. Results indicate that there is almost no difference between graph theory and fuzzy relation matrix method to analysis the network's connectivity reliability.
(3) Normal flow analysis of the water supply network before earthquake was performed by establishing microscopic hydraulic model. According to damage states of the pipelines after earthquake, heavy damaged pipelines were isolated by cutting off valves setting on its two terminals, dummy leaky nodes were extended on center position of the pipes with medium damage state, and hydraulic model of the network with leakage was built to evaluate seismic functional reliability of the system. Since nodal flows were considered to vary with nodal pressures in this model, negative pressures were avoided during the hydraulic calculation. And the measure of cutting-off valves increased system's water-supply ability effectively. Considering nodal pressure as the evaluating indicator, functional reliability indexes of the nodes were calculated by the mean-first-order-second-moment method which was originally developed for structural reliability analysis. And the indexes can be obtained by once hydraulic analysis in this method, which is greatly simplified compared with stochastic simulation method.
(4) Based on hydraulic analysis and serviceability criterions of the water supply network after an earthquake, a two level fuzzy comprehensive evaluation model considering nodal pressure and flow as evaluating indicators was built to assess the influence of earthquake on the network's serviceability by introducing fuzzy mathematical theory. According to the serviceability scales of the nodal pressure and flow divided by transfer function method, the trapezoidal membership function of each index was constituted, and comprehensive assessment of the network was performed through weighted average model and maximum membership grade principle, which is a realization of quantitative evaluation of the network's seismic serviceability. Considering system's topological and hydraulic characteristics simultaneously, earthquake vulnerability risk assessment of the water supply network was performed by stratified analytical method, which is convenient to find out system's vulnerable spot and make decisions of reducing risks.
(5) Flexible joint model of the pipe was selected as the optimization manner to reduce joint deformation and leakage, which could strengthen the pipe's or even system's seismic reliability. With the global view of the water supply network, taking element seismic reliability and nodal pressure of the post-earthquake system as bounded variables, the multi-objective optimum mathematical model was discussed to make the system's total pressure shortfalls and strengthening expense be minimum. According to functional requirements of the system and earthquake disaster characteristics, the optimum variables were conversed to fewer discrete varieties. For the purpose of seeking satisfactory solution instead of optimum solution, orthogonal enumeration method was adopted to solve optimum retrofit problems for water supply network system, which avoided the difficulty of solving large nonlinear scheme, and referenced for the seismic optimum retrofit of existing network and optimum design of quasi-built system.
(1)以地震波作用下埋地管道的接头损坏作为主要破坏模式,主要考虑管道的轴向变形性能,采用波动理论对供水管线进行地震反应分析,比较了两种管土间轴向变形传递系数的计算差异,建议采用《室外给水排水和燃气热力工程抗震设计规范》(GB50032-2003)中给出的变形传递系数进行管道抗震验算,并讨论了地震波入射角、剪切波速、管径等参数对管道变形的影响。考虑地震作用效应和管道抗力的随机特性,建立了埋地管道单元的概率预测模型,评估其在地震时的震害状态,比较了管道随机变量采用不同的概率分布模型对管道抗震可靠性的影响差异,建议管道的允许变形和实际变形分别采用正态分布和极值Ⅰ型分布进行计算。
(2)根据管线抗震可靠性分析结果,通过Monte Carlo随机模拟过程,近似再现管网中各管段的破坏状态。把供水管网系统简化为边权有向网络图,分别结合图论理论方法和模糊关系矩阵法,对管网进行连通可靠性分析,定性评价管网系统的运行状态,为进一步分析其抗震功能可靠性提供参考。由于Monte Carlo模拟方法是以管网各节点与水源点处于连通状态的近似频率计算代替精确概率分析,所得数值解具有一定的误差,为获得稳定的计算结果,对文中所用算例进行了5000次模拟。算例分析表明,基于图论方法和模糊关系矩阵法得到的管网连通可靠性结果基本相等。
(3)首先建立管网微观水力模型,进行震前无破坏状态下的流分析。然后根据震后管线的破坏情况,对严重破坏的管线关闭其两端阀门;对轻微或中等破坏的管线在其中间位置增设虚拟漏水节点,建立带渗漏管网的水力分析模型,进行管网震后服务功能分析。该模型在传统的管网水力计算基础上,考虑了节点流量随水压的动态变化,避免了负的压力计算值的产生。同时震后的及时关阀措施,有效地提高了管网系统的供水能力。在进行供水管网的抗震功能可靠度分析时,借鉴结构可靠度的分析方法,以节点水压为评价指标,采用均值一次二阶矩方法计算管网各节点的功能可靠度,该方法通过一次水力分析即可给出震后低压供水和渗漏状态下管网各节点的可靠性指标,较之前发展的随机模拟方法大为简化且概念清晰。
(4)以节点水压和流量为指标,建立了管网系统的服务性能准则。基于震后管网功能分析结果,绘制了节点水压和节点流量的服务性能曲线,采用转换函数的方法对其进行服务性能等级划分。引入模糊数学的理论与方法,构造节点水压和节点流量两个单因素指标的梯形隶属函数,建立震后管网系统服务性能的二级模糊综合评判模型,通过加权平均型评判模型和最大隶属度原则对管网系统进行综合评定,实现了地震对供水管网系统服务性能影响的量化评价。同时兼顾管网系统的连通特性和水力特性,采用分层的分析方法,对其进行地震易损性风险评估,以便找出系统薄弱环节进而确定减少风险的合理方法。
(5)通过优化管道接头形式,来减少震时管道接头处的变形和渗漏、提高其抗震性能,进而增强管网的抗震功能可靠性,实现系统的抗震加固优化。从系统全局出发,以管网系统震后水压总降幅和系统加固总投入最小为目标函数,以管线抗震可靠度和震后管网各节点的自由水压为约束,建立多目标优化数学模型,将优化变量转化为较少的离散变量,对管网系统进行抗震加固优化。基于不刻意追求最优解,而寻求满意解的优化思想,利用正交枚举法进行简化计算,从而避免了大规模非线性规划求解的困难,为已建供水管网系统的抗震加固及拟建管网系统的抗震优化设计提供了理论依据。
Water supply network system is an important constituent of urban lifeline engineering, its damage and disabler under the destructive earthquake will cause great loss on life and property or even severe secondary disaster. Most of the water supply systems in our country were not designed with seismic standards, while many cities may have the seismic risk background. Therefore, earthquake disaster predictions and seismic reliability analysis of water supply network are of great importance to evaluate cities' ability of reducing earthquake disasters, which constitute the basis for finding out the vulnerable spot and enhancing seismic reliability of the system. Based on related research at home and abroad, this paper focuses on the further study of seismic reliability and optimum retrofit of water supply network system. The main contents are included as follows:
(1) Taking the breakage of the conduit joints caused by seismic wave propagation as main failure mode, seismic performance analysis of the pipeline was performed with wave theory method by considering pipe's axial deformation. Two different methods for calculating axial deformation transfer coefficient were presented to check pipeline's seismic deformation, and influencing factors such as seismic wave's incident angle, shear wave velocity, pipeline's diameter and wall thickness were deeply discussed. Considering the randomness of seismic response and resistance of the pipe, probabilistic forecasting model was built to evaluate pipe's earthquake disaster. Comparisons of pipe's seismic reliability analysis with different probability distribution models of the random variable shows that it is conservative to evaluate pipe's seismic reliability by considering that seismic response and resistance of the pipe are all submitting normal distribution.
(2) According to seismic reliability analysis, each pipeline's damage state was simulated by Monte Carlo random process. Simplifying the water supply network system as an edge-weighted directed network figure, connectivity reliability of the network was performed by graph theory and fuzzy relation matrix method separately, which referenced for qualitative analysis of system's running status and seismic functional reliability evaluation of network. Since precision probability analysis was substituted by approximate frequency of the connectivity between each node of the network and water source for Monte Carlo method, the arithmetic solution were with errors, therefore, 5000 simulations were proceeded to obtain steady numerical solution. Results indicate that there is almost no difference between graph theory and fuzzy relation matrix method to analysis the network's connectivity reliability.
(3) Normal flow analysis of the water supply network before earthquake was performed by establishing microscopic hydraulic model. According to damage states of the pipelines after earthquake, heavy damaged pipelines were isolated by cutting off valves setting on its two terminals, dummy leaky nodes were extended on center position of the pipes with medium damage state, and hydraulic model of the network with leakage was built to evaluate seismic functional reliability of the system. Since nodal flows were considered to vary with nodal pressures in this model, negative pressures were avoided during the hydraulic calculation. And the measure of cutting-off valves increased system's water-supply ability effectively. Considering nodal pressure as the evaluating indicator, functional reliability indexes of the nodes were calculated by the mean-first-order-second-moment method which was originally developed for structural reliability analysis. And the indexes can be obtained by once hydraulic analysis in this method, which is greatly simplified compared with stochastic simulation method.
(4) Based on hydraulic analysis and serviceability criterions of the water supply network after an earthquake, a two level fuzzy comprehensive evaluation model considering nodal pressure and flow as evaluating indicators was built to assess the influence of earthquake on the network's serviceability by introducing fuzzy mathematical theory. According to the serviceability scales of the nodal pressure and flow divided by transfer function method, the trapezoidal membership function of each index was constituted, and comprehensive assessment of the network was performed through weighted average model and maximum membership grade principle, which is a realization of quantitative evaluation of the network's seismic serviceability. Considering system's topological and hydraulic characteristics simultaneously, earthquake vulnerability risk assessment of the water supply network was performed by stratified analytical method, which is convenient to find out system's vulnerable spot and make decisions of reducing risks.
(5) Flexible joint model of the pipe was selected as the optimization manner to reduce joint deformation and leakage, which could strengthen the pipe's or even system's seismic reliability. With the global view of the water supply network, taking element seismic reliability and nodal pressure of the post-earthquake system as bounded variables, the multi-objective optimum mathematical model was discussed to make the system's total pressure shortfalls and strengthening expense be minimum. According to functional requirements of the system and earthquake disaster characteristics, the optimum variables were conversed to fewer discrete varieties. For the purpose of seeking satisfactory solution instead of optimum solution, orthogonal enumeration method was adopted to solve optimum retrofit problems for water supply network system, which avoided the difficulty of solving large nonlinear scheme, and referenced for the seismic optimum retrofit of existing network and optimum design of quasi-built system.
引文
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