Non-iterative stress-displacement solution for surrounding rock mass with multiple non-circular deep tunnels

A non-iterative stress-displacement solution is proposed in this paper to investigate surrounding rock mass with multiple non-circular deep tunnels. Compared with the Schwarz alternating method, the proposed method only spends one-time matrix operation, showing considerable efficiency and accuracy of the matrix solution. First, a matrix solution is formulated to obtain the conformal mapping function for the non-circular tunnel. Then, in consideration of multiple boundary conditions, the generalized complex variable theory and fast Fourier transform (FFT) algorithm are used to formulate a matrix solution of potential functions. The stress and displacement fields around multiple non-circular tunnels can be further determined from the matrix solution. A series of numerical examples are conducted to verify the proposed method, perform the convergency study, and discuss the effects of tunnel geometries, distances, and arrangements. The convergency study shows that the more accurate conformal mapping function requires more sampling points in the FFT. In addition, the high stress zone would be amplified if the arrangement of multiple tunnels makes the high stress zone adjacent or overlapped.