The method of designing tunnel linings of an arbitrary cross-section shape located in the rock mass subjected to the action of tectonic forces typical for mountain territories is described in the paper presented. According to that method both features of initial stresses in the rock mass, the principal axes of which may be inclined with respect to the vertical and the horizontal, and the influence of the rock technological heterogeneity i.e. changing the rock deformation modulus with an increase of the distance from the opening surface caused for example by weakening the rocks due to drilling-and-blasting operations may be taken into account.
One of the main factors influencing on the stress state of tunnel linings constructed in mountain territories is a presence of tectonic initial stresses in the rock mass the principal axes of which may be inclined to the vertical and the horizontal. The so called technological heterogeneity of rocks i.e. changing their deformation and strength characteristics with increasing the distance from the opening surface caused for example by weakening of the rock mass due to drilling-and-blasting operations may also render a substantial influence on the lining stress state. The existing analytical design methods allow the circular tunnel linings stress state to be determined taking the rock technological heterogeneity into account. The method of designing tunnel linings of non-circular cross-section shape in technologically heterogeneous rock mass under the action of gravitational forces has been developed at Tula State University (Sammal 1995) as well as the method of designing tunnel linings in homogeneous rock mass subjected to the action of tectonic forces (Fotieva 1980). A method of designing tunnel linings of an arbitrary cross-section shape located in the rock mass subjected to the action of tectonic forces and possessing the technological heterogeneity developed on the basis of generalizing the methods mentioned above is described in the paper presented.
The method is based on an analytical solution of the elasticity theory plane contact problem for a multi-layer ring of an arbitrary form with one axis of symmetry simulating the lining and the heterogeneous part of the rock mass and supporting the opening in a linearly deformable homogeneous isotropic medium simulating the rock mass in a natural condition at the presence of initial stresses with principal axes inclined to the vertical and the horizontal. Substituting the (13), (14) expressions into the (10), (11) boundary conditions and equating the coefficients at the same degrees of the σ variable to each other in the left and right parts of the equations obtained after some algebraic transformations we obtain the correlations combining the coefficients of the complex potentials regular in the two contacting areas. It allows to express the coefficients of complex potentials regular in the internal layer SN of the ring through the coefficients of potentials characterizing the stress-strain state of the medium So and to come to a system of the linear algebraic equations having the order not depending on a number of layers considered.