Method Of The Complex Variables For Tunnel Problem In A Half Space

Using the conformal mapping ,the region of a half plane exclusion of a hole is tansfered into a cirque. Then the analytic functions can be expanded as Laurent series in this region . The stresses and displacements under rotational uniformal surface forces can be solved by the complex method founded by Muskhelishvili. The influence of the stresses and displacements due to different angle , deepth is discussed . The results is usefull in the directional drilling and the controllable construction of NO-DIG GUIDED BORING .Using the conformal mapping ,the region of a half plane exclusion of a hole is tansfered into a cirque. Then the analytic functions can be expanded as Laurent seriers in this region . The stresses and displacements under certain displacement can be solved by the complex method founded by Muskhelishvili. The influence of the displacements due to different deepth , different Poisson's ratio is discussed ,and the influence of the stresses due to different deepth is discussed also. The results is obvious that the exact solutions of the third and the forth boundary condition suggested by the author is important in the designing of shield tunnling after the comparision of the solutions under the four different boundary conditions with the data observed in five different tunnels.utilizing the complete stress solution of the gravity tunnel in a half plane solved by Mindlin ,we analyse the stress distribution around the periphery of the tunnel and detecte the maximum compressive stress using numeric method .Combining with the Mohr-Coulomb yield criterion,we analyse the relation between the the diameter, the cohesion, the angle of internal friction and the relative deepth which is very convenient for engineering design.