Methods of designing circular tunnel linings located near the Earth's surface upon the action of the rock own weight, ground water external pressure, weight of buildings and structures on the surface, internal water head (in the tunnels of downpour severs) are proposed. Methods are based on the analytical solutions of elasticity theory corresponding plane contact problems and allow also the influence of the linear hereditary rock creep to be taken into account using the method of variable moduli.


On examine les methodes des calculs des blindages des tunnels de faible profondeurs charges par Ies forces de propre pesanteur du massif, par la pression exterieur de l'eau souterrain, par les forces de propre pesanteur des batiments situes sur la surface du sol, par la pression interieur de l'eau (pour les tunnels d'evacuation des eaux). Les methodes ses reposent sur les solutions analytique des problèmes de la theorie de l'elastisite (Ies problèmes des contacts plans). Les methodes cites permettent de prendre en considèration I'influence de la fluage hereditaire lineaire à l'aide de la methode des modules variables.


Es wird eine Methode der Berechnung der Verkleidung von kreisförmige Tonnel, den sich in der Naherung der Tagesoberflache finden, in der Beruecksichtigung des Gesteinsgewichts außeres Wasserdruck, des Gewicht der Übertagebauten, inneres Wasserdruck (im Kanalisations- tonnel) vorgeshlagen. Die Methoden werden auf analytische Lösungen der zweidimensional kontakt Aufgaber der Elastizitat - lehre gegrundet und muessen auch die Wirkung des linear Kriechen mit der Hilfe des Methodes des variabel Modul beruecksichtigen.


Analytical methods for designing shallow circular tunnel linings based on the investigation of interacting the tunnel lining and the surrounding rock mass as elements of a common deformable system undergoing the action of the rock's own weight, ground water external pressure, the weight of buildings and structures on the surface and internal water head have been developed at Tula State University. The general design scheme is given in Figure 1, where the elastic Sı ring having the Rı external radius and R2 internal one, the Eı deformation modulus and the Vı Poisson ratio supporting a circular opening in the S0 semi-plane having the E0 and v0 deformation characteristics simulates the tunnel lining. The rock mass is simulated by a linearly deformable homogeneous isotropic semi- infinite medium S0 or a visco-elastic one being subject to the linear hereditary creep. For determining the lining stressed state the analytical solutions of corresponding elasticity theory plane contact problems are applied. It is assumed that the Sı ring and the S0 medium undergo deformation together i.e. conditions of displacements and complete stresses vectors continuity are satisfied on the Lı contact line. The internal L2 outline is free from loads or loaded by the normal pressure distributed. The L0 straight boundary is free from loads or is loaded on its part a0 ≤ × ≤ b0 by uniform P pressure simulating the action of the building or structure weight on the Earth's surface. There are two cases under consideration - when the structure on the surface is being built after the tunnel construction or vice-versa when the tunnel is being constructed under existing structure. In the second case displacements in the rock mass are considered only as additional caused by presence of surface loads are excluded from consideration. The action of the rock own weight is simulated.

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