Combining long- and short-term probabilistic volcanic hazard assessment with cost-benefit analysis to support decision making in a volcanic crisis from the Auckland Volcanic Field,New Zealand

By using BET_VH, we propose a quantitative probabilistic hazard assessment for base surge impact in Auckland, New Zealand. Base surges resulting from phreatomagmatic eruptions are among the most dangerous phenomena likely to be associated with the initial phase of a future eruption in the Auckland Volcanic Field. The assessment is done both in the long-term and in a specific short-term case study, i.e. the simulated pre-eruptive unrest episode during Exercise Ruaumoko, a national civil defence exercise. The most important factors to account for are the uncertainties in the vent location (expected for a volcanic field) and in the run-out distance of base surges. Here, we propose a statistical model of base surge run-out distance based on deposits from past eruptions in Auckland and in analogous volcanoes. We then combine our hazard assessment with an analysis of the costs and benefits of evacuating people (on a 1 × 1-km cell grid). In addition to stressing the practical importance of a cost-benefit analysis in creating a bridge between volcanologists and decision makers, our study highlights some important points. First, in the Exercise Ruaumoko application, the evacuation call seems to be required as soon as the unrest phase is clear; additionally, the evacuation area is much larger than what is recommended in the current contingency plan. Secondly, the evacuation area changes in size with time, due to a reduction in the uncertainty in the vent location and increase in the probability of eruption. It is the tradeoff between these two factors that dictates which cells must be evacuated, and when, thus determining the ultimate size and shape of the area to be evacuated.     

Kirsch problem and the lower natural frequencies of a clamped square-plate

A clamped square-plate is subjected to a uniform state of stress in the x-direction. The present study deals with the basic question of determining the variation of the lower natural frequencies of transverse vibration of a plate as a small diameter, central hole is made in it, introducing a stress concentration field.     

Plane state of stress and transverse oscillations of a simply supported rectangular plate

This paper deals with a general discussion of the subject matter. Recent literature is analyzed including some incorrect treatments of particular cases. Finally, a variational solution is obtained for the case where a linear distribution of stresses is applied to the plate boundaries. The lower natural frequencies are then tabulated as a function of the governing geometric and mechanical parameters.     

Transverse vibrations of a rectangular cantilever plate with thickness varying in a discontinuous fashion

A numerical solution is obtained for the title problem by means of the popular finite element method. An experimental investigation of the problem is also presented for plates of square planform. The agreement between theoretical and experimental values is very good in the case of the fundamental frequency, and reasonably good when the second and third normal modes of transverse vibration are considered. It is concluded that beneficial effects are obtained in the sense that one generates a lighter structural element with higher fundamental frequency of transverse vibration. Hence, dynamic stiffening is achieved.     

Correction to: Cultural heritage and earthquakes: bridging the gap between geophysics,archaeoseismology and engineering

Journal of Seismology -