To overcome the shortcoming of existing plane failure mechanism, Yang and Huang constructed a 3D rotational failure mechanism aiming at the relatively accurate description of actual roof failure and the improvement of existing findings.
Thereafter, considering the non-ignorable influence of ground water imposed on the impending collapse, Huang and Yang incorporated the pore pressure into upper bound theorem, being regarded as external forces, and some discussions were made to estimate the region of failure in tunnel roofs.
Evaluated the effect of seepage forces in the process of analyzing roof stability with 2D and 3D collapse mechanisms respectively and the findings obtained are in sound agreement with the existing results.