Suppose that a city is susceptible to carthquakes, and the Modified Mercalli Int

Question

Suppose that a city is susceptible to carthquakes, and the Modified Mercalli Intensity of the next earthquake is classified (for simplicity) as VI (or less) VII, VIII, and IX with relative likelihoods 50:30-15:3, Building construction is classified as Good or Poor, 20% of buildings in the city are poorly constructed. Seismic fragility analysis has indicated that poorly constructed buildings are damaged with probabilities 0.05, 0.25, 0.50 and 0.75, respectively, when subjected to intensities of VI (or less). VII, VII1 and IX, respectively. Well-constructed buildings suffer no damage under a VI (or less) event; however, the probability that such a building will be damaged under a VIL, VIII or IX event is 0.05. 0.10 and 0.20, respectively (a) What is the probablity that a well-constructed building will be damaged during the next earthquake? propanio (e) If a building is damaged, what is the probability that the building was poorly constructed? uch a calculation is sometimes (d) What intensity of earthquake is the source of most losses? (S referred to as a risk dis-aggregation. In seismic hazard analysis, it is used to determine the contributors to a design event; dis-aggregation plots by zipcode can be found on the USGs website)

Explanation / Answer

probability of low intensity earthquake=15/20=3/4

probability of mid intensity earthquake=4/20=1/5

probability of high intensity earthquake=1/20

proportion of poorly constructed building=20/100=1/5

proportion of well constructed building=1-1/5=4/5

proportion of building damaged= building damaged by low intensity earthquake+ building damaged by mid intensity earthquake+ building damaged by high intensity earthquake

building damaged by low intensity earthquake= prob of low intensity eathquake*(poorly constructed building damaged+well constructed building damaged)

=3/4*(1/5*1/10+4/5*0)=3/4*1/50=3/200

building damaged by mid intensity earthquake= prob of mid intensity eathquake*(poorly constructed building damaged+well constructed building damaged)

=1/5*(1/5*1/2+4/5*1/20)=1/5*(1/10+4/100)=14/500

building damaged by high intensity earthquake= prob of high intensity eathquake*(poorly constructed building damaged+well constructed building damaged)

=1/20*(1/5*9/10+4/5*1/5)=1/20*(9/50+4/25)=17/1000

Therefore,

proportion of building damaged= building damaged by low intensity earthquake+ building damaged by mid intensity earthquake+ building damaged by high intensity earthquake

=3/200+14/500+17/1000

=60/1000

0.06

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