Assessment of the hazard from rock fall on a highway: Discussion

Abstract

The purpose of this discussion is to indicate an error in the application of probability theory in the Authors’ paper. The Authors’ error does not significantly affect the numerical results of their study, but leads to counter-intuitive results in limiting cases. We provide alternative expressions that yield the correct result. Intuition suggests that as the number of rock fall events in a rock fall zone grows, the chance of a vehicle being hit will increase, everything else being equal. In the limit, if rocks are falling at an infinitely high rate in a rock fall zone, then a vehicle will almost surely be hit when it enters the zone for a length of time. The expression the Authors give for P(A), the annual probability of a rock hitting a vehicle that is a part of a row of vehicles stopped in a rock fall zone for one half hour, does not approach the correct value of 1 in the limit of an infinitely high number of rock falls, but rather 1 in 17 520 (page 352 of the article). To explain this error, we first describe the Authors’ approach, provide a simple example which more clearly shows the error, then provide the correct result. The Authors calculate P(A) from an expression given on the bottom of page 351 (continued on page 352):