Analytical method of designing multi-layer circular tunnel linings in the transversely isotropic medium simulating naturally anisotropic solid rock or the rock weakened by a double periodic chink set is proposed.
On examine une methode analytique de calcule des blindages circulaires des tunnels situes dans Ie massif transversal isotrope, que modèle Ie massif vierge anisotrope ou bien dans Ie massif affaibli par un système des fissures biperiodique.
Es wird eine analitische Methode del' Berechnung der Verkleidung von kreisförmige Tunnel im transversal-isotrop Medium, das natural anisotrop Gestein oder das Gestein mit doppel periodische System del' Kluft modelliert, vorgeschlagen.
The method proposed is based on mathematical modeling the interaction of the underground structure and the surrounding rock mass as elements of a united deformable system undergoing the actions of the rock's own weight, internal water head and external ground water pres- sure. For the analysis of the lining stressed state the elasticity theory corresponding plane contact problems are considered. The general de- sign scheme is given in Figure 1. The lining is simulated by the multi-layer ring consisting of n layers having the R;(i = 1, …, n) internal radii, isotropic materials of which possess the E i (i = 1,, n) deformation moduli and the Vi (i = 1,.., n) Poisson ratios, and supporting the opening of the R° radius in a transversely isotropic S° medium with an arbitrary directed plane of isotropy (in which the Ox axis inclined by the ß angle to the Ox' horizontal one is located), simulating the naturally anisotropic solid rock or the rock weakened by a double - periodic chink set. In the latter case the deformation characteristics of the equivalent transversely isotropic medium namely: the Eo,¹, Eo,2 deformation moduli correspondingly in the plane of isotropy and in the direction of normal to that plane. The corresponding contact problems of the elasticity theory are solved with the application of the complex variables analytic functions theory. Then expressions (26) and (27) are substituted in the (16)-(19) boundary conditions. The coefficients at the same degrees of the s variable in the left and right parts of the equations obtained are equated to each other. It allows the recurrent correlations combining coefficients. Substituting expression obtained into the (20) boundary condition we come to an infinite system of linear algebraic equations relative to the unknown cv(j)(0) (j= 1,2) coefficients. On the above system being solved the stress state of the lining layers is determined. The computer program has been developed.
The example of designing tunnel lining upon the action of the rock's own weight is given below. The double-layer lining including the external concrete layer with R0 = 3.42 m, R1 = 3.02 m outer and inner radii correspondingly and the internal steel layer having R2 = 3.00 m inner radius supports the circular tunnel located in the transversely isotropic rock with the plane of isotropy inclined under the ß = 45° angle to the horizontal plane.
