青藏铁路冻土路基温度场随机有限元分析与变形可靠性研究
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摘要
青藏铁路是我国西部开发中的重大工程,具有重大的政治、国防和经济意义。路基是铁路的基础,长期的实践表明青藏铁路的成败在于冻土路基问题,因此加强冻土路基变形可靠性的研究对减少路基病害、保证青藏铁路安全高效运行有重要意义。论文从冻土工程研究现状和冻土路基工程建设需要出发,在冻土路基热状况数值模拟的基础上,对路基变形预测和可靠性评价进行了比较系统的研究,取得了如下成果和创新:
1、在分析冻土路基工程特点和回顾冻土工程研究成果的基础上,首次建立了冻土路基随机温度场模拟和变形可靠性评价系统,该系统可以综合考虑各种随机因素的影响,对冻土路基的可靠性进行概率评估,为客观和准确的评价青藏铁路冻土路基温度场和变形,指导和改进工程设计、施工和建设提供科学依据。
2、引入随机场概念,利用数值方法对冻土路基热状况动态特征进行模拟研究,利用摄动随机有限元法,推导出了冻土路基温度场计算的随机有限元方程,并对青藏铁路北麓河试验段冻土路基随机温度场进行了计算。结果表明,外界环境的随机性是影响冻土路基地温波动的主导因素,随着深度的增加,环境温度的主导作用逐渐减弱,路基温度的标准差也逐渐减小,在一定的深度达到平均化。随着铁路运营时间的增长,路基下冻土的热敏感性增加,对热参数波动的反应变得强烈,冻土路基温度标准差明显增大,标准差在冻土路基下的分布范围也进一步扩大,将会严重影响路基可靠性。
3、针对目前冻土路基变形计算上存在的困难,用BP-人工神经网络建立起了路基变形与地温、路基高度和上限之间的非线性映射,测试结果比较令人满意。对第30年的路基过程进行了预测,结果显示,神经网络可以相对精确的预测较长时间的路基变形量,预测结果能清晰的反映出路基的变形状况,即随着温度的降低路基的冻胀量加大,随着温度的升高路基的融沉量加大。
4、首次采用可靠度指标和失效概率代替传统的安全系数来评价冻土路基变形的可靠性,根据可靠度指标的几何含义,建立了冻土路基可靠度指标求解的优化模型。可靠度指标的求解是一个约束优化问题,传统的计算方法十分复杂且效率较低,为此本文采用惩罚算子将约束问题转化为无约束问题,并利用遗传算法完成该优化问题的求解,使可靠度指标的求解更加精确和容易。
5、对于冻土路基变形的功能函数无法明确表达的问题,论文中利用了响应面可靠度分析法,结合BP神经网络,建立了响应面函数以近似代替原来的功能函数,响应面函数在验算点附近可以较好的模拟真实的功能函数,不会降低可靠度分析的精度,从而很好的完成了冻土路基变形可靠度的计算。
6、利用随机温度场的求解结果,对青藏北麓河段冻土路基运营后第30的变形可靠度进行了预测。结果表明,热参数的变异性越大,温度的标准差越大,路基的破坏概率增大,可靠性显著降低。因此为了提高冻土路基的可靠性,应降低环境随机性对路基温度场的影响,减少对多年冻土的热扰动,从而降低地温的标准差,提高冻土路基的稳定性。
7、在冻土变形实测资料基础上,提出了冻土路基变形预测和评价模型,弥补了当前冻土路基工程以经验为主的设计原则带来的不足,使冻土路基的改良和加固工作更加定量化和科学化。
Qinghai-Tibet Railway is a great project of the Western Development in China. Researches on frozen soil problems become more and more important because of its fatal effect to the railway. Based on the analysis of thermal regime of the railway roadbed, the deformation and reliability of the roadbed were studied systemically in the thesis according to current situation and demand of frozen soil engineering. The main contents of the thesis are summarized as follows:
1. Based on the analysis of the characteristics of permafrost engineering and the detailed review of the past research achievements, an evaluation system for thermal regime calculating and deformation evaluating of permafrost roadbed was made for the first time. It can be used as a basis for evaluating the effect of the structure, guiding and ameliorating the design of construction.
2. The conception of random fields was introduced and stochastic finite element formulas were formed by use of perturbation stochastic finite element method. At the same time, random temperature field of frozen soil roadbed in Bailu River of Qinghai-Tibet Railway is calculated as an example. The result shows that the randomicity of environmental temperature is the main factor affecting the random temperature field of the roadbed. The temperature-standard deviation is remarkable at the top of the roadbed and diminishes with the depth, and it increases sharply with the time and the rising of coefficient of variation of thermal parameters.
3. Aiming at current methods have their disadvantage on deformation calculation of permafrost engineering, the BP neural network was introduced and the non-linear function of deformation and its influence factors were established by BP neural network. The deformation of permafrost roadbed in Bailu River of Qinghai-Tibet Railway was predicted as an example. The result shows the process of the freezing heaving and thawing of the frozen soil roadbed and indicates the accuracy and practicability of BP neural network.
4. Reliability index was used instead of safety factor to evaluate the stability of permafrost roadbed. An optimal model was built up for the calculation of reliability index according to its geometry meaning. Penalty function and genetic algorithm were given to deal with the problems of complexity and slow convergence in the solution of the model.
5. Response Surface method was used for the engineering problem that their ultimate condition equation couldn’t be exactly expressed. Adoption of BP-ANN method, the Response Surface Reliability Analysis method was used to form the Response Surface function and get the reliability index.
6. The evaluation model was used to analysis the reliability of frozen soil roadbed in Bailu River of Qinghai-Tibet and reliability index and failure probability were obtained. The result shows that the reliability of the roadbed is determined mainly by the temperature deviation. With the rising of temperature deviation, the reliability index decreases quickly and the failure probability increases sharply.
7. Against the deficiency of the traditional design principles based on experience, a prediction and evaluation method for the deformation of permafrost roadbed was established based on the measurement data. Quantitative and scientific design can be achieved by using of this method for the improvement and reinforcement of the roadbed.
1、在分析冻土路基工程特点和回顾冻土工程研究成果的基础上,首次建立了冻土路基随机温度场模拟和变形可靠性评价系统,该系统可以综合考虑各种随机因素的影响,对冻土路基的可靠性进行概率评估,为客观和准确的评价青藏铁路冻土路基温度场和变形,指导和改进工程设计、施工和建设提供科学依据。
2、引入随机场概念,利用数值方法对冻土路基热状况动态特征进行模拟研究,利用摄动随机有限元法,推导出了冻土路基温度场计算的随机有限元方程,并对青藏铁路北麓河试验段冻土路基随机温度场进行了计算。结果表明,外界环境的随机性是影响冻土路基地温波动的主导因素,随着深度的增加,环境温度的主导作用逐渐减弱,路基温度的标准差也逐渐减小,在一定的深度达到平均化。随着铁路运营时间的增长,路基下冻土的热敏感性增加,对热参数波动的反应变得强烈,冻土路基温度标准差明显增大,标准差在冻土路基下的分布范围也进一步扩大,将会严重影响路基可靠性。
3、针对目前冻土路基变形计算上存在的困难,用BP-人工神经网络建立起了路基变形与地温、路基高度和上限之间的非线性映射,测试结果比较令人满意。对第30年的路基过程进行了预测,结果显示,神经网络可以相对精确的预测较长时间的路基变形量,预测结果能清晰的反映出路基的变形状况,即随着温度的降低路基的冻胀量加大,随着温度的升高路基的融沉量加大。
4、首次采用可靠度指标和失效概率代替传统的安全系数来评价冻土路基变形的可靠性,根据可靠度指标的几何含义,建立了冻土路基可靠度指标求解的优化模型。可靠度指标的求解是一个约束优化问题,传统的计算方法十分复杂且效率较低,为此本文采用惩罚算子将约束问题转化为无约束问题,并利用遗传算法完成该优化问题的求解,使可靠度指标的求解更加精确和容易。
5、对于冻土路基变形的功能函数无法明确表达的问题,论文中利用了响应面可靠度分析法,结合BP神经网络,建立了响应面函数以近似代替原来的功能函数,响应面函数在验算点附近可以较好的模拟真实的功能函数,不会降低可靠度分析的精度,从而很好的完成了冻土路基变形可靠度的计算。
6、利用随机温度场的求解结果,对青藏北麓河段冻土路基运营后第30的变形可靠度进行了预测。结果表明,热参数的变异性越大,温度的标准差越大,路基的破坏概率增大,可靠性显著降低。因此为了提高冻土路基的可靠性,应降低环境随机性对路基温度场的影响,减少对多年冻土的热扰动,从而降低地温的标准差,提高冻土路基的稳定性。
7、在冻土变形实测资料基础上,提出了冻土路基变形预测和评价模型,弥补了当前冻土路基工程以经验为主的设计原则带来的不足,使冻土路基的改良和加固工作更加定量化和科学化。
Qinghai-Tibet Railway is a great project of the Western Development in China. Researches on frozen soil problems become more and more important because of its fatal effect to the railway. Based on the analysis of thermal regime of the railway roadbed, the deformation and reliability of the roadbed were studied systemically in the thesis according to current situation and demand of frozen soil engineering. The main contents of the thesis are summarized as follows:
1. Based on the analysis of the characteristics of permafrost engineering and the detailed review of the past research achievements, an evaluation system for thermal regime calculating and deformation evaluating of permafrost roadbed was made for the first time. It can be used as a basis for evaluating the effect of the structure, guiding and ameliorating the design of construction.
2. The conception of random fields was introduced and stochastic finite element formulas were formed by use of perturbation stochastic finite element method. At the same time, random temperature field of frozen soil roadbed in Bailu River of Qinghai-Tibet Railway is calculated as an example. The result shows that the randomicity of environmental temperature is the main factor affecting the random temperature field of the roadbed. The temperature-standard deviation is remarkable at the top of the roadbed and diminishes with the depth, and it increases sharply with the time and the rising of coefficient of variation of thermal parameters.
3. Aiming at current methods have their disadvantage on deformation calculation of permafrost engineering, the BP neural network was introduced and the non-linear function of deformation and its influence factors were established by BP neural network. The deformation of permafrost roadbed in Bailu River of Qinghai-Tibet Railway was predicted as an example. The result shows the process of the freezing heaving and thawing of the frozen soil roadbed and indicates the accuracy and practicability of BP neural network.
4. Reliability index was used instead of safety factor to evaluate the stability of permafrost roadbed. An optimal model was built up for the calculation of reliability index according to its geometry meaning. Penalty function and genetic algorithm were given to deal with the problems of complexity and slow convergence in the solution of the model.
5. Response Surface method was used for the engineering problem that their ultimate condition equation couldn’t be exactly expressed. Adoption of BP-ANN method, the Response Surface Reliability Analysis method was used to form the Response Surface function and get the reliability index.
6. The evaluation model was used to analysis the reliability of frozen soil roadbed in Bailu River of Qinghai-Tibet and reliability index and failure probability were obtained. The result shows that the reliability of the roadbed is determined mainly by the temperature deviation. With the rising of temperature deviation, the reliability index decreases quickly and the failure probability increases sharply.
7. Against the deficiency of the traditional design principles based on experience, a prediction and evaluation method for the deformation of permafrost roadbed was established based on the measurement data. Quantitative and scientific design can be achieved by using of this method for the improvement and reinforcement of the roadbed.
引文
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