Abstract: 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.

Key words: shear stress, transverse isotropy, displacement analytical solution, sensitivity coefficient, uniqueness of back analysis