Influence of Seismic Scale Factor - Continued

DOE-STD-1020-2002

ratio, RR, between the annual probability of exceeding the DBE and the annual probability of

unacceptable performance is given by:

2

-

k β

RR = (C50 / DBE )





2



(C-5)

where C50 and β define the seismic fragility curve and DBE and kH define the seismic hazard

curve.

Using the basic criterion of DOE-STD-1020 that target performance goals are achieved

when the minimum required 10% probability of failure capacity, C10 is equal to 1.5 times the

seismic scale factor, SF, times the DBE ground motion, Equation (C-5) may be rewritten as:

( ) 



2

1.282 k Hβ - 2 k Hβ

RR = (1.5SF ) e



(C-6)

Equation (C-6) demonstrates the risk reduction ratio achieved by DOE seismic criteria as a

function of hazard curve slope, uncertainty, and seismic scale factor, SF. Note from Table C-3

that for PC-4 (not near tectonic plate boundaries), the hazard probability is 1x10-4 and the

performance goal is 1x10-5 such that the target risk reduction ratio, RR is 10 and for PC-3, the

hazard probability is 4x10-4 and the performance goal is 1x10-4 such that the target risk reduction

ratio, RR is 4. The actual risk reduction ratios from Equation (C-6) versus slope coefficient AR

are plotted in Reference C-20 for Performance Categories 3 and 4, respectively. In these figures,

SF of 0.9 is used for PC 3 and SF of 1.25 is used for PC 4 and the range of from 0.3 to 0.6 has

been considered. For the hazard curves considered by DOE-STD-1023-92 (Ref. C-13), AR

values average about 3.2 in the probability range associated with PC 3 and about 2.4 in the

probability range associated with PC 4. More recent seismic hazard studies (Ref. C-6) gives AR

values which average about 3.8 in the probability range associated with PC 3 and about 3.0 in

the probability range associated with PC 4.

Figures in Reference C-20 demonstrate that for SF= 0.9 risk reduction ratios between

about 3 and 10 are achieved over the AR range from 2 to 6. These risk reduction ratios support

achieving performance goals between about 2x10-4 to 5x10-5. In the primary region of interest of

AR between 2.5 and 4, risk reduction ratios from 4 to 6 are achieved as compared to the target

level of 4 for PC 3 and sites not near tectonic plate boundaries. Figures in Reference C-20

demonstrate that for SF = 1.25, risk reduction ratios between about 3 and 20 are achieved over

C-10