Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity (UPC) of anchor cables in most previous research. This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass. The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method. The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory, which more accurately reflects the failure state of the anchor cable, as opposed to that being assumed in advance. The results reveal that relying solely on a single failure mode for UPC calculations has limitations, as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.