(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
A new simple mathematical method has been proposed to predict rock stress around a noncircular tunnel and the method is calibrated and validated with a numerical model. It can be found that the tunnel shapes and polar angles affect the applicable zone of the theoretical model significantly and the applicable zone of a rectangular tunnel was obtained using this method. The method can be used to predict the values of the concentrated stress, and to analyze the change rate of rock stress and back to calculate the mechanical boundary condition in the applicable zone. The results of the stress change rate indicate that the horizontal stress is negatively related to the vertical boundary load and positively related to the horizontal boundary load. The vertical stress is negatively related to the horizontal boundary load and positively related to the vertical boundary load. These findings can be used to explain the evolution of the vertical increment in stress obtained with field-based borehole stress monitoring.