Influence of Seismic Scale Factor - Continued

DOE-STD-1020-2002

Over any ten-fold difference in exceedance probabilities, seismic hazard curves may be

approximated by:

H ( a ) = Ka - k H

(C-3)

where H(a) is the annual probability of exceedance of ground motion level "a," K is a constant,

and kH is a slope parameter. Slope coefficient, AR is the ratio of the increase in ground motion

corresponding to a ten-fold reduction in exceedance probability. AR is related to kH by:

kH =

log( AR )

(C-4)

The Basis for Seismic Provisions of DOE-STD-1020 (Ref. C-20) presents estimates

of seismic hazard curve slope ratios AR for typical U.S. sites over the annual probability range of

10-3 to 10-5. For eastern U.S. sites, AR typically falls within the range of 2 to 4 although AR

values as large as 6 have been estimated. For California and other high seismic sites near

tectonic plate boundaries with seismicity dominated by close active faults with high recurrence

rates, AR typically ranges from 1.5 to 2.25. For other western sites with seismicity not

dominated by close active faults with high recurrence rates such as INEL, LANL, and Hanford,

AR typically ranges from 1.75 to 3.0. Therefore, seismic design/evaluation criteria should be

applicable over the range of AR from 1.5 to 6 with emphasis on the range from 2 to 4.

DOE seismic design and evaluation criteria presented in Chapter 2 is independent of AR

and, thus, does not reflect its effect on meeting target goals. The performance of structures,

systems, and components in terms of annual probability of exceeding acceptable behavior limits

can be evaluated by convolution of seismic hazard and seismic fragility curves. Seismic fragility

curves describe the probability of unacceptable performance versus ground motion level. The

fragility curve is defined as being lognormally distributed and is expressed in terms of two

parameters: a median capacity level, C50, and a logarithmic standard deviation, β. β expresses

the uncertainty in the capacity level and generally lies within the range of 0.3 to 0.6. For DBE

ground motion specified at annual probability, PH, it is shown in Ref. C-20 that the risk reduction

C-9