A simple analytical approach to simulate the arch umbrella supporting system in deep tunnels based on convergence confinement method

Sensitive analyses are performed, and on the basis of the proposed analytical method, some graphs are prepared to give the ratio of total displacement of supported tunnel to that of unsupported for the various arch umbrella systems installed in the tunnels with different potential of squeezing. Some examples are solved, and the results are compared with those obtained by FLAC3D software.