地下隧洞工程弹性反演唯一性的探讨

Study on the Inversion Uniqueness of Elastic Back-analysis in Tunnel Engineering

对于地下隧洞工程,依据完备的量测信息开展弹性反分析,可望唯一反演确定岩土力学参数。文章利用平面弹性复变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、应力解析解,依据参数可辨识条件探讨了地下隧洞工程弹性反演参数的唯一性,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,五个参数(σv、σh、τ、E、μ)和同时反演具有唯一性。参数反演唯一性对参数的限制条件及对测点布置方式的要求受隧洞形状复杂性的影响,随着隧洞复杂性的提高对参数的限制条件大为减少,对测点布置方式的要求也会降低。算例结果表明,结论是正确的。

Utilizing the complete measured information to perform elastic back-analysis,all mechanical parameters may be determined uniquely in tunnel engineering.Via planar elastic complex variable technique and general elastic theory,the analytic formulas of displacements and stresses were derived.Based on the displacement and disturbed stress solutions for plane elasticity problems,this paper studies the inversion uniqueness of parameters according to the differentiability condition of parameters,and uses a simple example to validate the conclusion.The study shows,based on the complete measured information,the elastic inversion of the five parameters is unique on condition that the arrangement of measuring points is appropriate and the parameters satisfy the restrictive conditions.The restrictive conditions and the required arrangement are influenced by the shape complexity of tunnel,and with the shape complexity of tunnel increasing,the restrictive conditions of the parameters are decreased,and the requirement for the arrangement of the measuring points is reduced.Results of an example indicated the validity of the conclusions.