A new failure mode chart for toppling and sliding with consideration of earthquake inertia force

The toppling vs. sliding failure mode chart for a slender block resting on an inclined plane and subjected to gravitational loading with the analytical solutions for limiting equilibrium have been published long ago and are currently used routinely in rock slope stability investigations. The failure mode of a block on an incline is a function of three angles: the block angle δ, defining the geometry of the block, the slope inclination angle α, and the interface friction angle φ. We generalize here the mode chart to three dimensions. We present a new failure mode chart that incorporates a pseudo-static horizontal force F, simulating the seismic forces that act upon a block during an earthquake. In the new chart, the failure mode of a block is a function of three angles as well, with δ and φ remaining the same, but a new angle is introduced, ψ = α + β, with β being the angle between the resultant of the block's weight W and F, and the vertical direction, and replaces α. We present 2D and 3D numerical simulations that confirm the analytical basis for the proposed stability and mode chart.