Examining the effects of ground motion and rock strength on the size of boulders falling from an overhanging cliff

The presence of boulders, a result of rockfall events, at the foot of cliffs testifies for a mass wasting process which is widely observed and is often considered to be triggered by earthquakes. Here we investigate boulders under an overhanging cliff with an emphasis on the principal factors that control boulder size. We used a conceptual cantilever beam model to predict the expected maximum length of the overhanging cliff. We then compared these calculated lengths to those of the field observed boulders and the length of the overhanging cliff ledge. Our observations show that the actual lengths of the boulders and overhanging cliff are much shorter than expected from the model. As the study area is located in a tectonically active region, we first suggested solving this discrepancy by adding the possible effect of ground motion on the size of a boulder. Detailed pseudo-static and dynamic analysis of the effect of earthquakes on the failure of rock beams shows that boulder length may not significantly be shortened by induced ground motions. We therefore conclude that strong earthquakes, although triggering rockfalls, are not expected to control the resultant size of the boulders found at the base of overhanging cliffs. We alternatively suggest that the maximum length of a boulder is strongly controlled by the rock strength. We conclude that the maximum boulder size that may fall during an earthquake event can be predicted by calculating the cantilever critical length including the effect of the rock size on its tensile strength. This, together with the measured rock discontinuities in an overhanging cliff suggests an upper-bound for the volume of the falling boulders, a crucial factor in assessing rockfall hazards.