非线性破坏准则下浅埋隧道围岩压力的上限分析
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摘要
隧道结构设计的关键在于确定隧道围岩压力。现有关于浅埋隧道围岩压力的计算方法包括：极限平衡法、太沙基法及我国公路和铁路隧道规范推荐的方法。近些年来,在岩土工程中应用比较广泛的极限分析方法也被逐步应用到了隧道围岩压力计算中。上述计算方法绝大多数都是在岩土体线性破坏准则下进行的,而大量实验表明,岩土体服从非线性破坏准则。因此,研究非线性破坏准则下浅埋隧道围岩压力是一个新的课题。
本文在极限分析法的基础上,引入了非线性破坏准则,对浅埋隧道围岩压力问题进行了以下工作：
1.介绍了非线性破坏准则以及其在岩土工程中的应用。
2.介绍了极限分析原理,并重点介绍了极限分析上限定理及其应用条件,指出极限分析上限法计算浅埋隧道围岩压力的具体方法和步骤。
3.首次提出两种新的破坏模式,并在非线性破坏准则下,分别推导出相应破坏模式下围岩压力的计算公式。
4.介绍了最优化问题的一些基本理论,包括：拟牛顿法、遗传算法、序列二次规划算法,并重点介绍了序列二次规划算法在Matlab中的实现。通过Matlab及其优化工具箱,本文得出不同破坏模式下围岩压力的最优上限解,通过将所得结果与现有研究成果和实际工程进行了对比发现,本文所提出的破坏模式是合理的。
5.讨论了非线性系数及各围岩参数对隧道围岩压力上限解和隧道破裂面形状的影响,得出一些有益结论。另外,还探讨了Hoek-Brown准则下围岩压力上限解与Hoek-Brown参数的关系,并分析了各参数对围岩破裂面形状的影响。
How to determine surrounding rock pressure is always the key of tunnel structure design.The current calculation methods of shallow buried tunnel contain limit equilibrium method, Terzaghi theory, and method which the highway and railway codes have recommended.In the past few years, the limit analysis method which has been widely applied in geotechnical engineering is also gradually used in some aspects of tunnel engineering. However, it is well known that almost all these methods above are carried out in the precondition that soil and rock masses satisfy the linear criterion.But a large number of experiments have proved the fact that soil and rock masses obey nonlinear criterion. So it is necessary to do some work about the surrounding rock pressure of shallow buried tunnel in the nonlinear criterion.
On the basis of limit analysis theory, by introducing the nonlinear criterion, the thesis has done the following work about surrounding rock pressure of shallow buried tunnel:
Firstly, nonlinear criterions and their applications in geotechnical engineering were presented.
Secondly, the limit analysis theory was described. Specially, specify of the upper bound theory of limit analysis and its application conditions were given out.Then the thesis list out concrete method and steps of how to use the upper bound theory to calculate surrounding rock pressure of shallow buried tunnel.
Thirdly, two new failure mechanisms were given and the corresponding calculation formulas about surrounding rock pressure were deduced in the frame of nonlinear criterions.
Fourthly, some basic optimization theories such as quasi-newton method, genetic algorithm, sequential quadratic programming method were elaborated. Especially, the process of how to practice SQP method by Matlab was mainly explained.By using Matlab and its optimization toolbox, the optimal upper bound solutions corresponding to different failure patterns were got.Besides,through comparisons with existing analytical results and an illustration of practical engineering,it is found that the two patterns are reasonable for limit analysis of surrounding rock pressure.
Finally, influences of nonlinear coefficient and other rock parameters on surrounding rock pressure were discussed.It was found that these parameters have significant effects on the shape of fracture plane of tunnel.Besides,another nonlinear failure criterion named Hoek-Brown criterion was applied in the calculation of pressure.A list of value of upper bound solutions and corresponding angles were got.Then the relationships between the Hoek-Brown parameters and upper bound solution, and the shape of failure plane were analysised.
本文在极限分析法的基础上,引入了非线性破坏准则,对浅埋隧道围岩压力问题进行了以下工作：
1.介绍了非线性破坏准则以及其在岩土工程中的应用。
2.介绍了极限分析原理,并重点介绍了极限分析上限定理及其应用条件,指出极限分析上限法计算浅埋隧道围岩压力的具体方法和步骤。
3.首次提出两种新的破坏模式,并在非线性破坏准则下,分别推导出相应破坏模式下围岩压力的计算公式。
4.介绍了最优化问题的一些基本理论,包括：拟牛顿法、遗传算法、序列二次规划算法,并重点介绍了序列二次规划算法在Matlab中的实现。通过Matlab及其优化工具箱,本文得出不同破坏模式下围岩压力的最优上限解,通过将所得结果与现有研究成果和实际工程进行了对比发现,本文所提出的破坏模式是合理的。
5.讨论了非线性系数及各围岩参数对隧道围岩压力上限解和隧道破裂面形状的影响,得出一些有益结论。另外,还探讨了Hoek-Brown准则下围岩压力上限解与Hoek-Brown参数的关系,并分析了各参数对围岩破裂面形状的影响。
How to determine surrounding rock pressure is always the key of tunnel structure design.The current calculation methods of shallow buried tunnel contain limit equilibrium method, Terzaghi theory, and method which the highway and railway codes have recommended.In the past few years, the limit analysis method which has been widely applied in geotechnical engineering is also gradually used in some aspects of tunnel engineering. However, it is well known that almost all these methods above are carried out in the precondition that soil and rock masses satisfy the linear criterion.But a large number of experiments have proved the fact that soil and rock masses obey nonlinear criterion. So it is necessary to do some work about the surrounding rock pressure of shallow buried tunnel in the nonlinear criterion.
On the basis of limit analysis theory, by introducing the nonlinear criterion, the thesis has done the following work about surrounding rock pressure of shallow buried tunnel:
Firstly, nonlinear criterions and their applications in geotechnical engineering were presented.
Secondly, the limit analysis theory was described. Specially, specify of the upper bound theory of limit analysis and its application conditions were given out.Then the thesis list out concrete method and steps of how to use the upper bound theory to calculate surrounding rock pressure of shallow buried tunnel.
Thirdly, two new failure mechanisms were given and the corresponding calculation formulas about surrounding rock pressure were deduced in the frame of nonlinear criterions.
Fourthly, some basic optimization theories such as quasi-newton method, genetic algorithm, sequential quadratic programming method were elaborated. Especially, the process of how to practice SQP method by Matlab was mainly explained.By using Matlab and its optimization toolbox, the optimal upper bound solutions corresponding to different failure patterns were got.Besides,through comparisons with existing analytical results and an illustration of practical engineering,it is found that the two patterns are reasonable for limit analysis of surrounding rock pressure.
Finally, influences of nonlinear coefficient and other rock parameters on surrounding rock pressure were discussed.It was found that these parameters have significant effects on the shape of fracture plane of tunnel.Besides,another nonlinear failure criterion named Hoek-Brown criterion was applied in the calculation of pressure.A list of value of upper bound solutions and corresponding angles were got.Then the relationships between the Hoek-Brown parameters and upper bound solution, and the shape of failure plane were analysised.
引文
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