基于Kelvin-Voigt模型的黏弹性岩体位移反分析唯一性研究

Research on the uniqueness of displacements back analysis for viscoelastic rock masses based on the Kelvin-Voigt model

在岩土工程中,准确的岩体力学参数对于工程项目的建设和维护极为重要,相较于现场原位试验、实验室试验、数值模拟等获取参数的方法,岩体位移反分析方法具有方便操作、条件获取难度小、数据准确等特点,而反分析结果的唯一性是位移反分析能否成功的重要影响因素。为了研究位移反分析结果的唯一性问题,使用Laplace变换和蠕变柔量的方法,推导了在圆形巷道中符合Kelvin-Voigt模型的黏弹性岩体的位移解析解,并运用参数可辨识准则研究了已知参数对黏弹性岩体反分析唯一性的影响。研究结果表明,无论在任何条件下,都无法唯一地反演出所有6个参数,在至少有2个参数是已知的情况下,才可能唯一地反演出其他参数;地应力分量被唯一反演的概率最大,弹性模量、泊松比和黏滞系数根据控制条件的不同,其可辨识性存在差异,并随着已知参数数量的增加,参数可辨识性也随之增强;地应力是否为0对反演结果的唯一性有着显著的影响。工程算例表明,研究结果对于岩体参数的反分析计算具有重要的指导意义。

In geotechnical engineering,accurate mechanical parameters of rock mass are very important for the construction and maintenance of engineering projects.Compared with the methods of obtaining parameters such as in-situ test,laboratory test and numerical simulation,the displacements back analysis method of rock mass has the characteristics of convenient operation,less difficulty in obtaining conditions and accurate data.The uniqueness of the back analysis results is an important factor affecting the success of the displacements back analysis.In order to study the uniqueness of displacements back analysis results,the displacement analytical solution of viscoelastic rock mass conforming to Kelvin-Voigt model in circular roadway is derived by using Laplace transform and creep compliance method,and the influence of known parameters on the uniqueness of viscoelastic rock mass back analysis is studied by using parameter variability criterion.The results show that under any conditions,it is impossible to uniquely invert all six parameters,and it is possible to uniquely invert other parameters when at least two parameters are known.The probability that the in-situ stress component is uniquely inverted is the largest.The identifiability of elastic modulus,Poisson’s ratio and viscosity coefficient varies according to different control conditions,and the identifiability of parameters increases with the increase of the number of known parameters.Whether the ground stress is 0 has a significant impact on the uniqueness of the inversion results.The calculation of engineering examples shows that the research results have important guiding significance for the back analysis and calculation of rock mass parameters.