| 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.
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