Plastic Zone Analysis of Deep-Buried, Noncircular Tunnel and Application on the High-Speed Railway in the Karst Area

With the conformal mapping function provided by Verruijt, the outland of a noncircular tunnel can be mapped to a circular unit in the complex plane and then spread the analytic function into a Laurent series. The stress unified solution of oval and horseshoe cross section can be determined using Muskhelishvili’s complex variables function method. Subsequently, the solution can be taken into the Griffith strength failure criterion and determine the scale and shape of plastic zone in the tunnel surrounding rock. Aiming at the critical safety thickness between a concealed cave and tunnel in the karst area and determining whether the plastic zone of tunnel surrounding rock is connected with the plastic zone of cave as a judgment standard, the model of critical safety thickness among the concealed caves and tunnels is established. The numerical model is established in comparison with the computing method of rock plate critical safety thickness in actual engineering based on the Doumo tunnel engineering of Shanghai-Kunming (Guizhou segment) high-speed railway. The following conclusions can be drawn: the analytical approximation method has less indexes, and the output of this method is approximately close to actual engineering and numerical analysis, in which it is reliable and rational.