Abstract
Abstract After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential stress potential complex function and analyses the relationship between stress component, strain component and stress potential function, and applies the complex variable function. The expression of the relevant stress component is derived, and the displacement boundary conditions of the surrounding rock of shallow circular tunnel are obtained. Furthermore, the paper applies the basic theory of complex variable function to solve the boundary condition complex variable function for common tunnel sections, and obtains the analytical expression of the surrounding rock stress of shallow circular tunnel. The simulation is carried out by finite element method. The establishment of complex variable function has a good application value in solving the stress of surrounding rock of shallow tunnel.
Highlights
Shallow-buried tunnel refers to the fact that the tunnel is too shallow, the stress distribution of the surrounding rock is relatively complicated and the stress distribution around the surrounding rock is not uniform, so the solution process is more troublesome [1]
After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential stress potential complex function and analyses the relationship between stress component, strain component and stress potential function, and applies the complex variable function
The paper applies the basic theory of complex variable function to solve the boundary condition complex variable function for common tunnel sections, and obtains the analytical expression of the surrounding rock stress of shallow circular tunnel
Summary
Shallow-buried tunnel refers to the fact that the tunnel is too shallow, the stress distribution of the surrounding rock is relatively complicated and the stress distribution around the surrounding rock is not uniform, so the solution process is more troublesome [1]. In order to analyse the variation law of stress and displacement, this paper uses the complex variable function method to solve the shallow-buried circular tunnel retaining structure under radial deformation, and gives the analytical solution. Based on the above problems, this paper applies the complex variable function method to give the exact solution of the shallow-buried tunnel, and applies the equivalent radius method to give the analytical solution of the circular shallow tunnel section. The analytic solution and the equivalent radius of the circular shallow tunnel section given by the complex variable function method are given. The theoretical basis of the strength of the supporting structure required for deformation is provided In practical engineering, this solution can be applied to provide a reference for theoretical analysis
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