| Transversely isotropic rock mass exists widely in nature, and all kinds of geotechnical engineering constructions will encounter many stability problems of transversely isotropic rock mass. There are difficulties to determine the rock mass parameters accurately. Displacement back analysis is an effective method for geotechnical engineering to ascertain the rock mass parameters. Currently, the studies on the displacement back analysis of transversely isotropic rock mass did not take into account the influence of shear stress. Therefore, the shear stress is increased to the study of the displacement back analysis of the transversely isotropic rock mass in this paper, to provide ideas and methods for determining the elastic parameters of transversely isotropic rock mass.Based on the stress analytical solution of a circular hole in elasticity, the stress analytical solution considering shear stress for a circular tunnel is obtained. On this basis, According to the geometric equation and the theory of stress increment, the displacement analytical solution considering shear stress for a circular tunnel in transversely isotropic rock mass is derived. Based on the complex function expressions of stress and displacement components in plane strain, the displacement analytical solution considering shear stress for a tunnel with arbitrary cross section in transversely isotropic rock mass is derived by conformal mapping method. And the displacement analytical solution of an elliptical tunnel is also given.By means of identifiability conditions, the uniqueness of displacement back analysis in transversely isotropic rock mass is analyzed. The results for the uniqueness of inverse analysis and the parameter identifiability are given. The results shows that only when there are at least 3 parameters are known, the displacement back analysis can be carried out. Compared with the results of the uniqueness of inverse analysis which did not consider the shear stress, the results of this analysis show that the parameters can be identified by the same order, and the identifiability is enhanced.Based on the displacement analytical solution and the uniqueness of the back analysis, the engineering application research of the displacement back analysis in the transversely isotropic rock mass is studied, which provides a concrete theoretical and practical guidance for the application of the displacement back analysis. |
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