长距离输水工程的关键结构体系可靠度研究
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摘要
实际工程中存在大量的不确定性，定量描述和把握不确定性对工程的影响，对保障工程的安全性具有重要的意义。长距离输水工程规模大、线路长，面对众多复杂的不确定环境因素影响，其安全性倍受关注。从宏观上看，长距离输水工程是一个主要由渠道和建筑物组成的串联体系，而串联体系中关键结构的安全性对整个体系的安全性具有重大影响。本文以南水北调中线工程为背景，研究长距离输水工程的关键结构体系可靠度问题。渡槽在南水北调中线工程建筑物中，规模相对较大、结构相对复杂；南水北调中线工程绝大部分渠段均采用明渠输水，线路总长中渠道所占比重大。因此，大型渡槽和渠道边坡的体系可靠性在一定程度上就反映了整个供水系统的可靠性，其体系可靠性评价是长距离输水系统安全分析需要解决的一个关键问题。由此，论文在可靠度计算的基本理论、渡槽的体系可靠度计算方法、渠道边坡稳定的体系可靠度计算方法等方面开展了深入的研究，取得以下主要研究成果：
(1)将抽样点投影到失效面上，利用被分离变量的分布函数的解析解，结合剩余变量的重要抽样，提出了失效面上的重要抽样方法，给出了原始空间(X)和旋转后的标准正态空间(V)的实现方法。直接将抽样点取在失效面上，提高了抽样有效性和对非线性极限状态方程的适应能力；解析解的引入降低了抽样维数，提高了计算精度。理论推导和数值计算证明了该方法的适用性。
(2)响应面方法是解决具有隐式极限状态方程的大型复杂结构可靠度分析问题的理想途径，极限状态函数重构方法的选择是其关键问题。文中引入人工智能新技术支持向量机(SVM)方法，结合可靠度分析的几何方法，建立了基于SVM的可靠度分析响应面方法，在此基础上进一步提出了改进的SVM可靠度分析响应面方法和SVM重要抽样方法。改进方法每加入一个新的验算点就可拟合出一个新的极限状态方程，所需的有限元计算工作量少，具有较快的收敛速度和较强的非线性拟合能力。
(3)渡槽建筑物的上部槽身一旦开裂，容易因漏水影响建筑物的耐久性和安全性。有些情况下，正常使用极限状态可能成为渡槽结构设计的控制工况条件。文中建立了大型预应力渡槽槽身三维有限元模型，选择主要的受力构件作为分析对象，采用SVM方法重构极限状态方程，计算了主要受力构件的抗裂可靠度指标，分析了可靠度指标对变量的敏感性。采用体系可靠度界限方法，对构件失效相关性和体系可靠度进行分析，得到了渡槽抗裂体系可靠度的宽限和窄限解。同时，采用SVM方法拟合渡槽的静力位移反应，分析了渡槽的挠度可靠度。
(4)基于随机场局部平均理论，提出了边坡二维滑弧和三维滑动面上土性参数局部平均的离散化计算方法。该方法与边坡稳定条分法的特点相适应，对滑动面的具体形状没有特别的限制，计算简便，可以有效考虑土性参数相关函数的具体形式对局部平均的影响。并且，基于该方法分析了土性参数空间相关结构对边坡稳定可靠度的影响。
(5)考虑土性参数空间相关性，边坡三维可靠度指标随着滑坡宽度的加长，先减后增，存在一个最小值。论文结合算例对出现这一规律的原因进行了解释，为采用优化方法计算边坡三维可靠度指标提供了基础。文中给出了基于遗传算法的边坡三维可靠度分析方法，可以用于边坡三维稳定分析和三维空间滑坡形态预测。
(6)基于Poisson随机过程理论，采用最小三维可靠指标对应的三维滑坡体宽度来划分定长边坡，推导和建立了一个新的定长边坡体系可靠度计算方法，运用该方法对南水北调中线工程渠道边坡实例进行了分析。
(7)编制了SVM方法可靠度计算程序和遗传算法边坡稳定三维可靠度计算程序。
Many uncertainties are inherent in engineering practices. It is significant to quantify the influence of those uncertainties on safety of engineering projects. The long-distance water transfer project is of a large scale and a long route, and is affected by more complex uncertainties, so more attention is paid to its safety. In a point of macroview, the long-distance water transfer project is a series system which mainly consists of trenches and constructions, therefore safety of key structures of the series system has important influence on the safety of the whole system. System reliability of key structures of long-distance water transfer project is analysised based on the middle route of South-North Water Transfer Project (SNWTP). Aqueduct has a larger size and a more complex structure among the constructions of the middle route of SNWTP, and the water is transferred mainly by trenches, so the system safety of the large aqueducts and the slope stability of trenches reflect the safety level of the whole long-distance water transfer project at a certain extent. As a key problem of the system safety of long-distance water transfer projects, the system reliability analysis of the large aqueducts and the slope stability should be solved. In this paper, three aspects were studied: the fundamental theory of reliability analysis, the system reliability assessment method of aqueduct structures, the system reliability assessment method of slope stability of trenches. The major contents are summarized as follows:
(1) A partly analytical complex Monte-Carlo method in structural failure hypersurface is proposed. Samples are mapped to the structural failure hypersurface by separating a random variable or an expression of the limit state function and evaluating the cumulative distribution function of it analytically, then the structural failure probability is estimated in combination with importance sampling method. Approaches for the original X-space and the rotated orthogonal normal V-space are presented respectively. Samples are mapped to the hyperplane of structural failure, so the availability of sampling is guaranteed and the proposed method is more suitable for highly nonlinear limit state functions. The dimension of sampling may be reduced and a more accurate and stable result is achieved in virtue of adopting analytical
resolution. This method has been proved to be more efficient by theoretical analysis and numerical examples.
(2) Response Surface Method (RSM) can deal with the issue with implicit performance functions well for its famous accuracy and good efficiency. The key problem of RSM is the reconstruction of the response surface. The amount of sample set used to reconstruct the response surface usually is small. According to the excellent learning and generalization ability of support vector machine (SVM) even with small samples, the response surface of the structure is reconstructed by SVM, and then a new RSM based on SVM for structural reliability analysis is proposed. Furthermore, an improved RSM based on SVM is developed. A new response surface and a new design point are achieved by adding the old design point to sample set in iterative process of the improved method, so no any result of FEM calculation is abnegated and the amount of FEM calculations is reduced dramatically. It is proved by examples that the calculation efficiencies and accuracy can been increased by proposed methods.
(3) Cracks of aqueduct structures could decrease the durability and safety of the aqueduct. Sometimes, the serviceability limit state may be as the control condition in design. A three-dimensional finite element model of a large prestressed aqueduct is constructed to calculate the maximal tensile stresses of selected mainly components, and reliabilities of crack resistance of the selected main components are calculated by SVM response surface method and the corresponding sensitivity analyses are performed. Then the correlation coefficients between failure modes are evaluated and system reliability of crack resistance is computed by wide bounds method and Ditlevsen bounds method. At last, the deflection reliability of aqueduct is calculated by SVM response surface method.
(4) Based on local average method of random field, Discrete spatial average variance functions of soil parameter over two-dimensional slip arc and three-dimensional slip surface are developed. The proposed methods are simple and suitable to characteristics of slices method of slope stability analysis, and can take the effect of spatial correlation of soil parameters on reliability of slope stability into consideration efficiently. Influence of spatial relative distance of soil parameters on the reliability of slope stability is investigated.
(5) Actually there should be a critical three-dimensional slip surfaces which give the highest failure probability if spatial variabilities of soil parameters are taken into consideration. The existent reasons of the minimal three-dimensional reliability index and the corresponding critical slip surface are investigated and illustrated by examples. This makes it possible to get three-dimensional reliability index of soil slope by means of optimization techniques. Therefore, a model of spatial variability of soil parameters is adopted and Genetic Algorithm (GA) method is used to search for the reliability index directly, then three-dimensional reliability analysis method for slope stability, based on GA method, is proposed. The minimal three-dimensional reliability index and the corresponding three-dimensional slip surface are achieved by the proposed method.
(6) A new system reliability method of a given length slope is proposed based on Poisson stochastic process theory and by measuring the whole length of the slope with the width of three-dimensional failing soil mass. The system reliability of an example trench slope of middle route of SWTP is assessed.
(7) Computer program for SVM reliability analysis method and program for three-dimensional reliability analysis of slope are developed in this paper.
This research work is sponsored by Technical Innovation Fund of the Ministry of Water Resources of PRC.
(1)将抽样点投影到失效面上，利用被分离变量的分布函数的解析解，结合剩余变量的重要抽样，提出了失效面上的重要抽样方法，给出了原始空间(X)和旋转后的标准正态空间(V)的实现方法。直接将抽样点取在失效面上，提高了抽样有效性和对非线性极限状态方程的适应能力；解析解的引入降低了抽样维数，提高了计算精度。理论推导和数值计算证明了该方法的适用性。
(2)响应面方法是解决具有隐式极限状态方程的大型复杂结构可靠度分析问题的理想途径，极限状态函数重构方法的选择是其关键问题。文中引入人工智能新技术支持向量机(SVM)方法，结合可靠度分析的几何方法，建立了基于SVM的可靠度分析响应面方法，在此基础上进一步提出了改进的SVM可靠度分析响应面方法和SVM重要抽样方法。改进方法每加入一个新的验算点就可拟合出一个新的极限状态方程，所需的有限元计算工作量少，具有较快的收敛速度和较强的非线性拟合能力。
(3)渡槽建筑物的上部槽身一旦开裂，容易因漏水影响建筑物的耐久性和安全性。有些情况下，正常使用极限状态可能成为渡槽结构设计的控制工况条件。文中建立了大型预应力渡槽槽身三维有限元模型，选择主要的受力构件作为分析对象，采用SVM方法重构极限状态方程，计算了主要受力构件的抗裂可靠度指标，分析了可靠度指标对变量的敏感性。采用体系可靠度界限方法，对构件失效相关性和体系可靠度进行分析，得到了渡槽抗裂体系可靠度的宽限和窄限解。同时，采用SVM方法拟合渡槽的静力位移反应，分析了渡槽的挠度可靠度。
(4)基于随机场局部平均理论，提出了边坡二维滑弧和三维滑动面上土性参数局部平均的离散化计算方法。该方法与边坡稳定条分法的特点相适应，对滑动面的具体形状没有特别的限制，计算简便，可以有效考虑土性参数相关函数的具体形式对局部平均的影响。并且，基于该方法分析了土性参数空间相关结构对边坡稳定可靠度的影响。
(5)考虑土性参数空间相关性，边坡三维可靠度指标随着滑坡宽度的加长，先减后增，存在一个最小值。论文结合算例对出现这一规律的原因进行了解释，为采用优化方法计算边坡三维可靠度指标提供了基础。文中给出了基于遗传算法的边坡三维可靠度分析方法，可以用于边坡三维稳定分析和三维空间滑坡形态预测。
(6)基于Poisson随机过程理论，采用最小三维可靠指标对应的三维滑坡体宽度来划分定长边坡，推导和建立了一个新的定长边坡体系可靠度计算方法，运用该方法对南水北调中线工程渠道边坡实例进行了分析。
(7)编制了SVM方法可靠度计算程序和遗传算法边坡稳定三维可靠度计算程序。
Many uncertainties are inherent in engineering practices. It is significant to quantify the influence of those uncertainties on safety of engineering projects. The long-distance water transfer project is of a large scale and a long route, and is affected by more complex uncertainties, so more attention is paid to its safety. In a point of macroview, the long-distance water transfer project is a series system which mainly consists of trenches and constructions, therefore safety of key structures of the series system has important influence on the safety of the whole system. System reliability of key structures of long-distance water transfer project is analysised based on the middle route of South-North Water Transfer Project (SNWTP). Aqueduct has a larger size and a more complex structure among the constructions of the middle route of SNWTP, and the water is transferred mainly by trenches, so the system safety of the large aqueducts and the slope stability of trenches reflect the safety level of the whole long-distance water transfer project at a certain extent. As a key problem of the system safety of long-distance water transfer projects, the system reliability analysis of the large aqueducts and the slope stability should be solved. In this paper, three aspects were studied: the fundamental theory of reliability analysis, the system reliability assessment method of aqueduct structures, the system reliability assessment method of slope stability of trenches. The major contents are summarized as follows:
(1) A partly analytical complex Monte-Carlo method in structural failure hypersurface is proposed. Samples are mapped to the structural failure hypersurface by separating a random variable or an expression of the limit state function and evaluating the cumulative distribution function of it analytically, then the structural failure probability is estimated in combination with importance sampling method. Approaches for the original X-space and the rotated orthogonal normal V-space are presented respectively. Samples are mapped to the hyperplane of structural failure, so the availability of sampling is guaranteed and the proposed method is more suitable for highly nonlinear limit state functions. The dimension of sampling may be reduced and a more accurate and stable result is achieved in virtue of adopting analytical
resolution. This method has been proved to be more efficient by theoretical analysis and numerical examples.
(2) Response Surface Method (RSM) can deal with the issue with implicit performance functions well for its famous accuracy and good efficiency. The key problem of RSM is the reconstruction of the response surface. The amount of sample set used to reconstruct the response surface usually is small. According to the excellent learning and generalization ability of support vector machine (SVM) even with small samples, the response surface of the structure is reconstructed by SVM, and then a new RSM based on SVM for structural reliability analysis is proposed. Furthermore, an improved RSM based on SVM is developed. A new response surface and a new design point are achieved by adding the old design point to sample set in iterative process of the improved method, so no any result of FEM calculation is abnegated and the amount of FEM calculations is reduced dramatically. It is proved by examples that the calculation efficiencies and accuracy can been increased by proposed methods.
(3) Cracks of aqueduct structures could decrease the durability and safety of the aqueduct. Sometimes, the serviceability limit state may be as the control condition in design. A three-dimensional finite element model of a large prestressed aqueduct is constructed to calculate the maximal tensile stresses of selected mainly components, and reliabilities of crack resistance of the selected main components are calculated by SVM response surface method and the corresponding sensitivity analyses are performed. Then the correlation coefficients between failure modes are evaluated and system reliability of crack resistance is computed by wide bounds method and Ditlevsen bounds method. At last, the deflection reliability of aqueduct is calculated by SVM response surface method.
(4) Based on local average method of random field, Discrete spatial average variance functions of soil parameter over two-dimensional slip arc and three-dimensional slip surface are developed. The proposed methods are simple and suitable to characteristics of slices method of slope stability analysis, and can take the effect of spatial correlation of soil parameters on reliability of slope stability into consideration efficiently. Influence of spatial relative distance of soil parameters on the reliability of slope stability is investigated.
(5) Actually there should be a critical three-dimensional slip surfaces which give the highest failure probability if spatial variabilities of soil parameters are taken into consideration. The existent reasons of the minimal three-dimensional reliability index and the corresponding critical slip surface are investigated and illustrated by examples. This makes it possible to get three-dimensional reliability index of soil slope by means of optimization techniques. Therefore, a model of spatial variability of soil parameters is adopted and Genetic Algorithm (GA) method is used to search for the reliability index directly, then three-dimensional reliability analysis method for slope stability, based on GA method, is proposed. The minimal three-dimensional reliability index and the corresponding three-dimensional slip surface are achieved by the proposed method.
(6) A new system reliability method of a given length slope is proposed based on Poisson stochastic process theory and by measuring the whole length of the slope with the width of three-dimensional failing soil mass. The system reliability of an example trench slope of middle route of SWTP is assessed.
(7) Computer program for SVM reliability analysis method and program for three-dimensional reliability analysis of slope are developed in this paper.
This research work is sponsored by Technical Innovation Fund of the Ministry of Water Resources of PRC.
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