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中文摘要：
利用齐次马尔可夫过程模拟埋地管线腐蚀的发生，并利用线性腐蚀模型模拟埋地管线腐蚀的发展，将线性腐蚀模型中腐蚀速率考虑为确定性参数，推导给出了管线面积腐蚀率随服役时间变化的概率密度函数，并获得了管线截面面积随服役时间变化的均值和方差。在此基础上，根据弹性地基梁模型，将管线周围土体位移正交展开为余弦级数的形式，获得了地震作用下腐蚀管线位移反应和应力反应的解析表达式。对腐蚀管线地震反应进行线性展开，采用随机摄动理论推导给出了腐蚀管线在地震激励下位移和应力反应的均值和标准差。利用上述分析模型对一根200m长的埋地管线进行了实例分析，结果表明建议模型可以反映管线面积随服役时间的变化规律，并能反映腐蚀管线在地震作用下位移反应和应力反应的基本概率特征。
英文摘要：
In order to evaluate the corrosions of buried pipelines as the service time increases, Markov process is employed to simulate the occurrence of corrosion of the pipelines. Combining with a linear corrosion development model with deterministic corrosion rate parameters, the evolution of probability density function of the corrosion percentage of buried pipeline section area as service time increases is derived, and the mean and the covariance of pipeline section area are also obtained. Based on such a pipeline corrosion model, an elastic foundation beam model is employed to express the seismic displacement and stress of pipeline as orthogonal cosine series. Using the random perturbation approach, the random seismic response of pipelines is simplified as a linear function of the section areas of pipe segments, and then the mean and the covariance of seismic response are derived. In order to validate the proposed approach, a 200-meter long pipeline is investigated in detail, and the results indicate that the proposed approach can efficiently simulate the evolution of buried pipeline section area as service time increases.
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