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

Abstract

We are grateful to Hungr and Beckie for the opportunity ofdiscussing in a more comprehensive way the hazard to trafficstopped for half an hour inarock cut on a highway. We believetheir discussion correctly calculates hazards in an alternatescenario, which did not, in our judgement, optimally representthe circumstances of the Just case, the focus of our article.Nevertheless, it may be useful for other circumstances.We considered in our paper the hazard to traffic halted fora single, 30 minute period each year. Our estimate was par-ticularly applicable to a regularly scheduled maintenance ac-tivity. In this situation, there was only one Bernoulli trial byrock fall each year. We then calculated the probability that allthe rocks from the annual average of 2.2 rock falls will missthe traffic halted for the half hour period. This conservativeapproach to the calculation is only appropriate when there arefew rock falls reaching the highway; this is the usual situationin practice. We drew attention to this limitation by the phrasefi...within the range we examine...fl in our discussion of theresults (p. 353).Our discussion, then, of the stationary traffic specified boththe length, 30 min, and the frequency, once, of the delays totraffic each year. Hungr and Beckie™s analysis has assumedonly the average total delay time. Conceptually a car or carsmight be at hazard on two or more separate occasions in theHungr and Beckie analysis. The hazard they have estimated isthat to traffic which may be halted for 30 minutes during eachof an average of 2.2 rock falls per annum. Thus the total timehalted traffic is exposed to rock fall is up to 30 ×2.2 minutesper year, 66 minutes per year. The hazard from this exposurefor 66 min is, of course, considerably greater than the hazardfrom being exposed for 30 minutes (under slightly differentassumptions about the rock falls). Hence the greater estimatedhazard in the Hungr and Beckie scenario. The sequence ofevents they analyze might be particularly applicable to therandom delays caused, for instance, by traffic accidents on thehighway.Unfortunately, no statistics of the length or frequency oftraffic delays on B.C. Highway 99 were available to us whenthe paper was written. The hazard we estimated was our bestjudgement of the circumstances of the Just case. While Hungrand Beckie have usefully explored other possible scenarios,we might draw attentiontoourconclusionthathazardstomov-ing traffic from rock fall are generally much greater than haz-ards to stationary traffic at the present time on Highway 99.We emphasize that neither the Hungr and Beckie hazard forstationary vehicles nor our own makes a significant contribu-tion to the hazard to vehicles from rock fall on a highway. Thisis dominated by the likelihood of rock impact on a movingvehicle or of a moving vehicle on a stationary rock. Indeed,another recent study of hazards from rock fall ignores station-ary vehicle scenarios (Geotechnical Engineering Bureau 1996;Cruden 1997).