考虑剪应力作用时横观各向同性岩体中圆形巷道位移反分析的惟一性

推导了考虑剪应力作用时横观各向同性岩体中圆形巷道的位移解析解，利用参数可辨识条件对考虑剪应力作用时横观各向同性岩体中圆形巷道位移反分析的惟一性进行了探讨。结果表明，无论布置多少个测点也不能惟一地反分析出所有7个参数，必须至少已知3个参数，才有可能惟一地反分析出其他参数；水平与竖直地应力分量是否为 0 对反分析惟一性有一定影响；3个地应力分量的可辨识性最好，各向同性面上的弹性模量和泊松比次之，垂直于各向同性面方向的弹性模量和泊松比最差。与不考虑剪应力时位移反分析惟一性结果相比，考虑剪应力时参数的可辨识性顺序不变，但是条件惟一的比例降低，不惟一和绝对惟一的比例增加，说明考虑剪应力能够提高位移反分析的惟一性。工程实例计算表明，推导的位移解析解和反分析惟一性探讨结果能够很好地指导岩体参数反演计算。

Uniqueness of displacement back analysis of circular tunnel in transversely isotropic rock mass when considering shear stress

The displacement analytic solution of a circular tunnel in transversely isotropic rock mass considering shear stress is deduced firstly; and then the uniqueness of displacement back analysis of a circular tunnel in transversely isotropic rock mass considering shear stress is investigated by means of parameters identifiability conditions. The results show that no matter how many measuring points are set, all the 7 parameters can not be determined simultaneously. It is possible to determine other parameters only when there are at least 3 parameters are known in advance; whether the horizontal and vertical components of ground stress are 0 has certain effect on the uniqueness of back analysis. The ground stress components show the best identifiability, the elastic modulus and Poisson’s ratio in the isotropic plane are the second; and the elastic modulus and Poisson’s ratio in the direction vertical to the isotropic plane are the worst. Compared with the uniqueness results of displacement back analysis without considering the shear stress, the order of identifiability for the parameters is unchanged. But the proportion of the conditional uniqueness decreases; while the proportion of the non-uniqueness and absolutely uniqueness increase, which show that taking shear stress into account may raise the proportion of the uniqueness of displacement back analysis. The case studies show that the inversion calculation of rock mass parameters can be conducted well by the displacement analytic solution and the uniqueness results of the displacement back analysis.