MATHEMATICAL MODELING OF THE INTERACTION OF THE SOIL MASS AND THE LINING OF CIRCULAR TUNNELS CROSS-SECTIONAL STRUCTURES CONSTRUCTED USING A PROTECTIVE SHIELD MADE OF PIPES

The main theoretical principles used in the mathematical modeling of the interaction of the soil mass and the lining of a tunnel of circular cross-section, constructed under the protection of a shield made of pipes in a closed way in close proximity to the earth's surface. A formulation has been made and an analytical solution has been obtained for a plane elasticity theory problem on the equilibrium of a geomechanical system, including a weighty semi-infinite region containing arbitrarily located solid washers and a circular hole supported by a ring, simulating a soil mass, cross-sections of protective shield pipes and the lining of a tunnel. The boundary conditions of the problem reflect the action of gravitational forces in the mass and the presence of full contact at the boundaries of regions with different deformation characteristics. To solve the problem, the theory of functions of a complex variable, the mathematical apparatus of complex Kolosov-Muskhelishvili potentials and Laurent series were used. This solution, which makes it possible to determine the components of the stress tensor at any point in each of the considered areas, is the basis for the method of lining a tunnel constructed using a protective shield made of pipes.