Upper bound limit analysis of unsymmetrical progressive collapse of shallow tunnels in inclined rock stratum

In order to provide more reasonable support design for shallow tunnels in inclined stratum, it is necessary to investigate the collapse of shallow tunnels in inclined stratum. A new collapse mechanism of shallow rectangular and circular tunnels in inclined rock stratum is constructed, which includes four curves. On the basis of the upper bound theorem of limit analysis and the nonlinear Hoek-Brown yield criterion, obtaining the precise expressions of four curves by means of the variational principle, and deriving the equations of the range and total gravity of the potential collapsing block of rectangular and circular tunnels can be solved respectively. The results are consistent with those published and numerical simulation, which confirms the rationality of this research. The parametric sensitivity analysis of the collapse of rectangular and circular tunnels is carried out, which shows that rock mechanics parameters and geometric parameters have a significant impact on the range and total gravity of the potential collapsing block is obvious. Especially, the dip angle of rock stratum plays a key role in the symmetry of tunnel collapse and the progressive collapsing block is unsymmetrical unless the rock strata are horizontal.