Analytical Method For Stress Analysis Of Underground Tunnel Under Temperature Influence

Underground tunnels are often affected by both temperature load and original ground stress.With the development of geotechnical and underground engineering,the geological conditions of surrounding rock of underground tunnels are becoming more complex,and the depth of burial is increasing,so the stability of tunnel surrounding rock is becoming more and more serious,and the temperature stress analysis of tunnel surrounding rock is very important.At present,when the hole shape of the tunnel is relatively simple,the analytical method can be used for stress analysis,when the hole shape is relatively complicated,using the analytical method is very complicated,and the stress analysis is usually performed by the numerical method.However,the analytical method is clearer in physical concept than the numerical method,and the conclusion is concise and clear,which brings great convenience to subsequent operations and has strong guiding significance in practical engineering.This paper uses analytical methods to analyze the stress of underground tunnels under the combined action of temperature load and original ground stress.This paper uses the complex variable function method to map the plane double connected domain in the physical plane into the axisymmetric circular domain in the image plane.The radius of the inner and outer boundaries of the ring are 1 and h respectively.In the temperature stress analysis,the temperature of the inner and outer boundaries of the surrounding rock is known and constant,and the temperature dose not change with time.The analytical solution of the steady temperature field of the plane double connected domain in the physical plane is obtained by using the mapping function and conformal transformation.Firstly,considering only the effect of temperature load on surrounding rock of tunnel,since the original ground stress is not considered,the boundary stress in the tunnel is 0.When the outer radius h of the ring is large,it is considered that the surrounding rock is not subject to the change of temperature at infinity,so the displacement is 0,and then using the boundary conditions can establish linear equations.By solving linear equations,two analytical functions can be obtained that are represented by complex variable functions,and analytical solutions of stress components can be obtained.When considering only the effect of the original ground stress on surrounding rock of tunnel,the problem can be simplified to solve the problem of the analytical solution of the stress of any hole tunnel in the infinite domain.The analytical solution of the stress is easily obtained by the complex variable function method.Then by principle superposition,adding the stress of the two models together can obtain the stress solution of the underground tunnel under the combined action of temperature load and original ground stress.Because the calculation process is more complicated,this paper uses the Fortran and MATLAB language to calculate the program,and compares analytical solutions with the numerical solution obtained by ANSYS finite element software,and it proves the correctness of the proposed method.