bray 24 may 2002 arias intensity attenuation

8/3/2019 Bray 24 May 2002 Arias Intensity Attenuation

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Definition of Arias Intensity

Arias Intensity is defined by Arias (1970) as:

=0

2)(

2dtta

gI

a

Equation 1

where aI is the Arias Intensity in units of length per time, )(ta is the acceleration-time history in

units of g, and g is the acceleration of gravity.

Empirical Equation

The median Arias Intensity can be predicted by Equation 2. Figure 1, shows dependence of thepredicted median Arias Intensity on distance for a strike-slip fault 3 different site categories and 3

different magnitude earthquakes

=)ln( aI

RN

DC

FfFf

SMssSMss

hRcMcMcc

+

++++

+++++

21

22211211

22

4321

))6(())6((

)ln()6/ln()6( Equation 2

where:

aI : Arias Intensity in m/s (average of the

two horizontal components)

M: moment magnitude

R: closest distance to the rupture plane in

km

SC, SD: both 0 for site B, 1 and 0 for site

C, and 0 and 1 for site D

FN, FR: both 0 for strike slip, 1 and 0 fornormal, and 0 and 1 for reverse

or reverse oblique faults

c1, c2, c3, c4, h, s11, s12, s21, s22, f1, and f2:

coefficients determined by the regression

shown in Table 1.

The error term in Equation 2 is normallydistributed with zero mean and standard

Figure 1 Median value of Arias Intensity

against distance for three different site

categories and three different magnitude

earthquakes for a strike-slip fault


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deviation tot . It is dependent on magnitude (M), median Arias Intensity ( aI ), (coefficients are

listed in Table 2) and site category (Table 3).

22 ),()(),,( siteIMsiteIM aatot += Equation 3

0.611 for M 4.7() = 0.611 - 0.0466 (M - 4.7) for 4.7 < M < 7.6 Equation 4

0.476 for M 7.6

1 for aI 0.0132 m/s

(Ia, site) = 1 0.1064 ( ))0132.0ln()ln( aI for 0.0132 < aI < 0.1245 m/s Equation 5

2 for aI 0.1245 m/s

Table 1 Coefficients of Empirical Equation for Median Arias Intensity

c1 c2 c3 c4 h s11 s12 s21 s22 f1 f2

2.799 -1.981 20.724 -1.703 8.775 0.454 0.101 0.479 0.334 -0.166 0.512

Table 2 Parameters for Computation of the Site Dependent Error Term ()

B C D

1 1.181 1.166 0.965

2 0.942 0.972 0.726

Table 3 - Bray and Rodriguez-Marek 1997 Site Classification Scheme

Site Category Description

B Rock, most unweathered California rock cases (Vs 760 m/s or < 6m of soil)

C Weathered soft rock and shallow stiff soil ( < 60 m of soil)

D Deep stiff Holocene or Pleistocene soil ( > 60 m of soil and no soft soils)

Example Calculation

The median and plus one and minus one standard deviation are computed for a typical

earthquake scenario in the Bay Area of a magnitude M=7 strike-slip earthquake at R=10km fromthe fault rupture on a D site .


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Median Arias Intensity

418.0)ln( =aI median 5.1=aI sm/

Error Term

504.0)7.40.7(0466.0611.0)( == M

726.0),( = siteIa , because 1245.0/5.1 >= smIa and Site = D

867.0726.0504.0 22 =+=tot

16% and 84% levels of Arias Intensity

16% 64.0)867.0418.0exp( ==aI sm/

84% 6.3)867.0418.0exp( =+=aI sm/

For further information

See Travasarou et al. (2002) referenced below, or contact Thaleia Travasarou or Jonathan Bray

by e-mail at [email protected] and [email protected].

Acknowledgment

This work was supported in part by the Pacific Earthquake Engineering Research Center throughthe Earthquake Engineering Research Centers Program of the National Science Foundation under

Award Number EEC-9701568.

References

Arias, A. (1970). "A Measure of Earthquake Intensity," R.J. Hansen, ed. Seismic Design for

Nuclear Power Plants, MIT Press, Cambridge, Massachusetts, pp. 438-483.

Bray, J. D. and Rodriguez-Marek, A. (1997). Geotechnical Site Categories, Proceedings, First

PEER-PG&E Workshop on Seismic Reliability of Utility Lifelines, San Francisco, CA, August.

UBC (1997) Uniform Building Code

Travasarou, T., Bray, J.D., and Abrahamson, N.A. (2002). "Empirical Attenuation Relationship

for Arias Intensity," submitted toEarthquake Engineering and Structural Dynamics, April, 2002.

Keywords

attenuation relationship, Arias Intensity, engineering demand parameter, ground motion, intensitymeasure, performance

bray 24 may 2002 arias intensity attenuation

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