Toppling of a Rectangular Prismatic Block Resting on Two Orthogonal Planes

Abstract Toppling is an important rock slope failure mechanism, particularly in jointed rock masses. This study investigates a novel toppling mechanism of a rectangular prismatic block resting on two planes, for the case in which the block is formed by three orthogonal discontinuities. Two of these discontinuities would typically be cross-joints, forming a dihedral structure, with the third most persistent discontinuity being foliation or bedding planes dipping toward the slope. Block rotation around one edge, with lateral friction mobilized along the side discontinuity, characterizes the failure mechanism. To study this often-overlooked mechanism, the authors present a conceptual model consisting of a rectangular prismatic block resting on two orthogonal basal planes. The base of the lower rigid block, that is, the intersection of the two orthogonal basal planes, is inclined to the horizontal, and the lateral side of the block tends to generate lateral friction. A simplified analytical model based on the limit equilibrium method (LEM) was first introduced to assess stability of such a block considering lateral friction. This approach can be used to estimate critical toppling inclination angles and to identify the toppling rotation axis. Building on this model, a multi-scope approach was applied combining analytical, physical, and numerical investigations. Physical tilt tests and numerical simulations were then designed to investigate both the toppling behavior and critical toppling inclination angle allowing verification of the proposed theory. A preliminary field application illustrates the practical interest of the study to assess prismatic block toppling risk of failure. An effort is made to understand all the factors influencing the occurrence of this toppling failure mechanism which to date has often been unidentified and the subject of limited research.