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探讨依据完备的量测信息开展弹性参数反演的可辨识性及量测的优化布置,对于指导岩土工程反演实践具有重要的实用价值。利用平面弹性复变函数方法和一般弹性理论,推导出任意形状隧洞的位移、应力解析表达式,基于隧洞围岩位移、应力的解析解,依据参数可辨识条件和量测优化布置的最灵敏原则,探讨了地下隧洞工程弹性反演参数的可辨识性及测点优化布置,并通过算例进行了验证。研究表明,依据完备的量测信息开展弹性反分析,只要测点布置方式适当、反演参数满足相应的限定条件,可同时惟一辨识出5个参数P、Q、M、E、μ。参数反演的可辨识性受隧洞形状复杂性的影响,随着隧洞复杂性的提高,参数可同时惟一辨识需满足的限制条件大为减少,对测点布置方式的要求也会降低。工程实践中,为避免量测数据的少量误差导致反演计算结果的大幅度波动,测点(线)应根据最灵敏原则优化选择各反演参数的灵敏系数最大的测点(线)组合进行量测布置。
It is of great practical value to explore the identifiability of elastic parameter inversion and the optimal layout of measurement based on complete measurement information for guiding the geotechnical inversion. Based on the plane elastic complex function method and the general elastic theory, the displacement and stress analytical expressions of tunnel with arbitrary shape are deduced. Based on the analysis of displacement and stress of tunnel surrounding rock, the most sensitive principle , Discussed the identifiability of elastic inversion parameters of underground tunnel project and the optimal arrangement of measuring points, and verified by examples. The research shows that the elastic back analysis based on the complete measurement information can identify five parameters P, Q, M, E, μ at the same time as long as the measuring points are arranged properly and the inversion parameters satisfy the corresponding constraints. The identifiability of the parameter inversion is affected by the complexity of the tunnel shape. With the increase of the tunnel complexity, the constraints that the parameter can meet simultaneously and uniquely identify are greatly reduced, and the requirements for the arrangement of measuring points are also reduced. In practice, in order to avoid the small amount of error in the measurement data lead to large fluctuations in the calculation results, the measurement points (lines) should be optimized according to the most sensitive principle to select the best combination of measurement points (lines) Measurement layout.