| Stress concentration will inevitably occur on the boundary of the deep-buried non-circular double-hole tunnel under the external loads,which affects the normal use of the tunnel and brings great threat to the security and stability of the tunnel.Therefore,it is of great significance to calculate the stress distribution on the boundary of tunnel accurately for engineering practice.Previous researches on stress distribution of tunnel mainly focus on the circular tunnel and there are few methods can accurately solve the problem of non-circular double-hole tunnel.For this purpose,this paper uses the complex variable method to study the stress solution of deep-buried non-circular double-hole tunnels.The key step is transforming the deep-buried tunnel problem into an infinite domain problem and getting the mapping function of the specific tunnel cross-section by using the method of conformal mapping.Finally,according to the calculation example,it analyses the influence of some parameters on the tunnel stress and gives some suggestions for the design of tunnel cross-section with engineering examples.The main research contents are as follows:(1)Determine the general expression and coefficient properties of the mapping function.Aiming at the problem of two adjacent tunnels in the infinite domain,,based on the Riemann mapping theorem,putting forward a method that can map any tunnel area on the physical plane to the annular domain on the image plane by deducing the mapping function of the special single-hole tunnel.The general expression of the mapping function only requires the two tunnels to be symmetrical.(2)Solve the coefficient of mapping function.By using symmetry,it is proved that some coefficients of the mapping function have conjugate relation,and according to the correspondence relation of boundary points,the mapping function of specific tunnel cross-section is obtained through optimization method.An example of the curved wall horseshoe tunnel mapping is given.(3)Obtain the stress analytical solution of the specific problem.Based on the stress boundary conditions,the linear equations are established to obtain the analytical stress solution of the the deep double-hole tunnel under general load.Use Fourier series to expand the limited mapping function to avoid the generation of fractions.(4)Verify the correctness of the analytical solution.Establish the ANSYS finite element model and compare the analytical solution with ANSYS numerical solution,Hoang analytical solution and Ukadgaonker analytical solution.The result shows that the analytical solution obtained by the method in this paper has high accuracy.(5)Parameter analysis.Taking horseshoe tunnel,circular tunnel and rectangular tunnel as examples,the effects of tunnel spacing,lateral pressure coefficient,pressure in hole,shear stress in the distance and direction of principal stress on tunnel boundary tangential stress are studied by analytical solutions.The results show that the boundary of the horseshoe tunnel and the rectangular tunnel will produce large stress concentration under most loads.Use the analytical solutions to analyse an improved rectangular tunnel.The results show that the tunnel saves about 40% of the underground space compared with the circular tunnel with the same effective space.And there is no great stress concentration phenomenon.It shows that the analytical method proposed in this paper can effectively obtain the stress distribution around the tunnel,which has definite engineering significance for tunnel cross-section optimization. |
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