深埋公路隧洞围岩应力和位移分布的复变函数解

Abstract

In order to optimize the design of highway tunnels and ensure the safety of construction, mechanical behavior of rock shall be made clear during highway tunnel excavation. With the complex variable method, firstly, the exterior domain of the tunnel was transformed into a unit-circle domain through the conformal mapping function; then 2 stress functions were derived with the Cauchy integral formula and the residue theorem; thereby, closed-form plane strain solutions of the surrounding rock were obtained for stresses and displacements. The curved-wall horseshoe-shaped cross section was adopted, and the distributions of stresses and excavation displacements along the tunnel boundary and the coordinate axes were calculated respectively with mathematical software MATLAB. To verify the accuracy of the stress and displacement distributions derived with analytical solutions, a 2D plane strain model was established with finite element software ANSYS. Comparison between the numerical results and the approximate analytical results shows good agreement. The results show that, the maximum hoop stress occurs at the arch foot, the maximum horizontal displacement occurs at the hance, the largest settlement and uplift are at the centers of the vault and the invert, respectively. Normal stresses along coordinate axes change obviously near the tunnel, and the maximum stress doesn’t always occur at the tunnel boundary. The maximum stress approaches the applied load at a distance less than 10 m from the tunnel boundary. The largest displacement occurs at the tunnel boundary, and gradually reaches zero with an increasing distance from the tunnel boundary.