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

In this study, a simple analytical method is presented to investigate the behavior of arch umbrella supporting system (the forepolling system) in deep tunnels. For this purpose, a qualitative distribution of the load on the arch umbrella elements (the beams) is proposed by using longitudinal deformation profile of unsupported tunnel. The flexural stiffness of an element is then obtained and finally, the deformation of supported tunnel are calculated by convergence-confinement method. That is, further advancement of tunnel leads the more length of umbrella elements to be activated; and therefore, the corresponding stiffness is reduced. Hence, the non-linear support characteristic curve is drown to intersect the ground response curve. 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.