隧洞工程弹性参数反演的可辨识性及量测优化布置探讨

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。

Discussion of identifiability and optimal measured arrangement for elastic back-analysis of parameters in underground tunnel engineering

Based on complete measurement information, it has important practical value for guiding back analysis practice in geotechnical engineering to study the identifiability and optimal measured arrangement of elastic back analysis of parameters. Via planar elastic function of complex variable technique and general elastic theory, the analytic formulas of displacement and stress are derived; and based on the displacement and disturbed stress solutions for the plane elasticity problems, this paper studies the identifiability and optimal measured arrangement of back analysis of elastic parameters by use of differentiability condition of parameters and most sensitive principle of optimal measured arrangement, and uses a simple example to validate the conclusion. The study shows, based on the complete measured information to carry out elastic back-analysis, the five parameters P, Q, M, E and ? can be identified uniquely under condition that the measured arrangement is appropriate and the parameters satisfy the restrictive conditions. The identifiability of inversion parameters is influenced by the shape complexity of tunnel; and with the shape complexity of tunnel increasing, the restrictive conditions of the parameters are decreased; the requirement for the measured arrangement is also reduced. To avoid the substantial fluctuation of inversion results arisen from a small error of measurement data in engineering practice, the combination of measured points (lines) which has the largest sensitivity coefficient value of each inversion parameter should be chosen as the optimal measured arrangement based on the most sensitive principle.