Analytical Method to Interpret Displacement in Elastic Anisotropic Soil due to a Tunnel Cavity with an Arbitrary Cross Section

Based on complex variable theory and conformal mapping method, the paper presents full plane elastic solutions around an unlined tunnel with arbitrary cross section in anisotropic soil. The solutions describe soil elastic solutions for assuming that the displacement vectors along the tunnel boundary are directed towards the center of the tunnel. Tunnels with different cross sections are used to illustrate the method and its correctness. An elliptical unlined tunnel case is discussed in detail in the paper. Using the image method, an approximate solution for predicting surface displacement and subsurface horizontal displacement around an unlined tunnel in anisotropic soil can be obtained. The results show anisotropic stiffness properties n(n = E_h/E_v) and m(m = G_vh/E_v) have a great effect on the displacement distribution patterns around an elliptical tunnel with certain shape.

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