Elastic Stress and Plastic Zone Distributions around a Deeply Buried Tunnel under the Nonhydrostatic Pressure

Abstract

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.