The elastic stress and the plastic zone are the important mechanical parameters to determine the tunnel support design. Based on Muskhelishvili’s complex variable function, the analytical solution for the elastic stress around a deeply buried noncircular tunnel under the nonhydrostatic pressure is firstly derived. The shape and size of the plastic zone of the surrounding rock mass are then determined by substituting the elastic stresses into the Drucker-Prager yield criterion. Finally, taking a horseshoe-shaped tunnel as an example, the analytical solutions of elastic stress distribution and plastic zone shape around the tunnel under different lateral pressure coefficients are in good agreement with ANSYS numerical solutions. The calculation results show that if the vertical in situ stress exceeds the critical value, with increasing lateral pressure coefficient, the hoop stress at the roof and floor of the tunnel increases significantly and the shape and size of the plastic zone change obviously.
Stress and displacement of the composite lining are important factors to be considered during tunnel design. By the complex variable method, analytical solutions for stress and displacement of surrounding rock, primary support and secondary lining satisfying the interface continuity and boundary conditions under far-field stresses are derived. Taking the railway composite lining tunnel as an example, the analytical distributions of stress and displacement along boundaries are given, which was in good agreement with the numerical solution calculated by finite element software. The results show that the maximum normal stress ratio (load sharing ratio) of the outer boundary between the secondary lining and the primary support is 0.74. The radial displacement of the inner boundary of surrounding rock, primary support, and secondary lining change consistently. The maximum settlement and uplift occur at the vault and bottom, respectively. The tangential stress of secondary lining is compressive stress, while the tangential stress of primary support is tensile stress and compressive stress. The maximum tangential stress of primary support and secondary lining is smaller than the allowable stress of concrete.
For the generalized plane strain problem of a deep-buried tunnel excavated in orthotropic rock mass under far-field biaxial compression, the stress and displacement are the most important basis for determining tunnel support design. First, by using the complex variable method, the conformal mapping and affine transformation functions are represented by the same variable. Two stress functions are obtained by the integral method, and thus, the analytical solutions for stress and displacement in orthotropic rock mass are obtained. Second, taking a horseshoe-shaped tunnel as an example, the stress and displacement distributions around the tunnel are given by using the analytical and the finite element method software ANSYS, respectively. The analytical and numerical results are in good agreement, especially at the tunnel edge. Finally, compared with isotropic rock mass, the results show that material constants of the rock mass have little effect on the stress and significant effect on the displacement.
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