Limit-Equilibrium Analysis of Stability of Footwall Slope with Respect to Biplanar Failure

Biplanar failure is the most common instability type of footwall slopes, with a steeply dipping joint (typically the bedding plane) and a gently dipping joint (i.e., the daylighting toe joint) forming the basic failure surface. Limit equilibrium, due to its high efficiency and accuracy, is a widespread method in the analysis of such a failure. In this paper, a new block model of biplanar failure is first proposed on the basis of the interaction mechanisms between the active and passive blocks. Then, considering the orientation of the interblock boundary, a biplanar failure analysis method (BFAM) is presented that satisfies both the force and moment equilibrium conditions. Subsequently, a simplified biplanar failure analysis method (SBFAM) is also proposed for ease of use. Finally, parametric analysis was carried out to investigate the influence of the sliding mass depth, slope height, dip angles, and shear strength of the joints on slope stability. It was found that the safety factors of the footwall slope obtained using the BFAM approach are generally consistent with those found using the Morgenstern-Price and Spencer methods. Additionally, the safety factors using the SBFAM approach are well consistent with the physical modeling and BFAM results.