Special Workshop on Risk Acceptance and Risk Communication March 26-27, 2007, Stanford University Probabilistic comparison of seismic design response spectra Sei’ichiro Fukushima Senior researcher, Tokyo Electric Power Services, Co., Ltd. 3-3-3, Higashi-Ueno, Taito, Tokyo 110-0015, Japan and Tsuyoshi Takada Professor, University of Tokyo 7-3-1, Hongo, Bunkyo, Tokyo 113-8656, Japan Abstract

Since the performance of building against earthquakes is described by limit states and their exceedance probability, seismic load for building shall also be examined not only from the viewpoint of intensity but also from that of occurrence probability. This paper compares two seismic response spectra; one is for building and the other is for highway bridge with soil type 1. For the comparison of occurrence probability, we newly introduced the concept of return period spectrum that shows the relationship between the natural period and the return period. The return period spectrum is evaluated from the design response spectrum and uniform hazard spectrum, which is calculated from probabilistic seismic hazard analysis. 1. Introduction

It is necessary to examine the return period of the design seismic load as well as its intensity, since seismic performance of the structure is described by limit states and its probability of exceedance. Of course, the probability of exceedance is also affected by the probability distribution of response and/or capacity. It is, however, important to know the return period or occurrence probability of the existing design seismic load. This paper investigates the relationship between intensity and return period of design response spectra and examines the difference between design spectra and that among sites. 2. Probabilistic comparison

In this paper, the response spectrum for building and that for highway bridge are selected. The former is defined at engineering bedrock, and on the other hand the latter at surface. Type 1 soil corresponding to hard soil is selected so that the response spectrum at surface can be regarded as that in the ground. As mentioned above, It is important to compare the response spectra from viewpoint of intensity and of return period. For the purpose, the concept of the return period spectrum (hereinafter called RPS) is newly introduced. The evaluation method of RPS is illustrated in Fig.1. In evaluating RPS the uniform hazard spectrum (hereinafter called UHS) is used.

Figure 1: Evaluation of return period spectrum 3. Outline of existing design spectra

In this paper, the response spectrum for building and that for highway bridge are selected. The former is defined at engineering bedrock, and on the other hand the latter at surface. Type 1 soil corresponding to hard soil is selected so that the responses

3.1. Design spectra for building In the Building law of Japan, 5% damped response spectrum at engineering bedrock where shear wave velocity is 400m/s or greater, is employed. Table 1 shows the formula and Fig. 2 shows the corresponding zone factor.

Table 1: Formula of response spectra for building Spectral acceleration (m/s/s) Period (s) Rare earthquake Very rare earthquake

T<0.16 (0.64+6T)Z 0.16<=T<0.64 1.6Z

0.64<=T (1.024/T)Z

Five times of spectral acceleration for rare earthquake

T: Natural period (s) Z: Zone factor

3.2. Design spectra for highway bridge In the design recommendation for highway bridge, design response spectra for three types of soils are proposed, among which type 1 soil is selected for the examination since the response spectrum at the surface of the soil type can be regarded as that at engineering bedrock. Table 2 shows the formula and Fig.3 shows the corresponding zone factor. It is noted that two types of response spectra corresponding to ultimate state are used: one for inter plate earthquake and the other for in-crust earthquake. The latter was introduced after Kobe earthquake (1995).

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

: Design Spectrum : UHS

10-3

10-4

10-2

Natural Period (s)

Ret

urn

Per

iod

(yr.)

�RPS

103

104

102 A A

B

B

C

C

D

D

Table 2(1): Formula of response spectra for highway bridge (service limit) Period (s) Spectral acceleration (cm/s/s)

T<0.1 431T1/3, and greater then or equal to 160 0.1<=T<=1.1 200

1.1<T 220/T T: Natural period (s)

Table 2(2): Formula of response spectra for highway bridge (ultimate limit, inter plate EQ ) Period (s) Spectral acceleration (cm/s/s) T<=1.4 700 1.4<T 980/T

T: Natural period (s)

Table 2(1): Formula of response spectra for highway bridge (service limit) Period (s) Spectral acceleration (cm/s/s)

T<0.3 4463T2/3 0.3<=T<=0.7 2000

0.7<T 1104/T5/3 T: Natural period (s)

Figure 2: Zone factor for building Figure 3: Zone factor for highway bridge

4. Evaluation of uniform hazard spectra

Procedure to obtain UHS is illustrated in Fig. 4. UHS is a spectrum that shows the relationship between a natural period and a spectral acceleration for given reference probability refP .

Figure 4: Evaluation of uniform hazard spectrum

4.1. Seismic hazard analysis using spectral acceleration as ground motion intensity measure

Seismic hazard analysis used in this paper is based on the probabilistic models. Seismic source zone models are summarized in Fig.5. For seismic zones corresponding to the active faults and area source where large earthquakes occur periodically, the characteristics earthquake model is employed. On the contrary, Gutenberg-Richter model is used for seismic zones where medium or small earthquake occur.

Figure 5(1): Source zone for large EQs

Spectral Acceleration (cm/s/s)

Exc

eeda

nce

Pro

b

pref

SA(TA) SA(TB) SA(TC) SA(TD) SA(TE)

Period; TA Period; TB Period; TC Period; TD Period; TE

Seismic hazard curve for each period

TA

Spe

ctra

l Acc

. (cm

/s/s

)

SA(TA)

SA(TB)SA(TC)

SA(TD)

SA(TE)

Natural Period (s) TB TC TD TE

UHS corresponding to

Pref

130E 135E 140E 145E 150E

30N

35N

40N

45N

0

100

200

500

1000(km)

140E 145E

40N

45N

0

10

20

50

100

200(km)

140E

35N

0

10

20

50

100

200(km)

135E

35N

0

10

20

50

100(km)

130E

35N

0

10

20

50

100

200(km)

Figure 5(2): Source zone for medium or small EQs For propagation model of ground motion, empirical model proposed by Annaka et al. is employed. The empirical formula is shown below;

)()]653.0exp(334.0log[)()()()(log 0 TCMRTChTCMTCTS dchmA ++−+= , (1)

where, T is a natural period, M is a magnitude in JMA scale, ch is a center depth of the rupture plane, and R is the closest distance. Coefficients, )(TCm , )(TCh , )(TCd , )(0 TC are given as shown in Fig.6.

Figure 6: Coefficients for attenuation relation

4.2. UHS for seven sites in Japan Seven sites; Sapporo, Sendai, Niigata, Tokyo, Nagoya, Osaka and Fukuoka, are selected for illustration. UHS for the sites are shown in Fig. 7. Except for Tokyo, spectral peaks appear in the natural period of 0.2s to 0.3s. On the contrary, spectral peaks at Tokyo appear in longer natural period, especially in case of longer return period. This tendency is given by the large Kanto earthquake whose magnitude is 7.9 and return period is 200 year. It must also be noted that there exist very thick sedimentary layer in Kanto district which includes Tokyo. This layer is the on of factors that gives the ground motion with dominant component in the longer natural period.

130E 135E 140E 145E 150E

30N

35N

40N

45N

0

100

200

500

1000(km)

130E 135E 140E 145E 150E

30N

35N

40N

45N

0

100

200

500

1000(km)

125E 130E 135E 140E

25N

30N

35N

40N

0

100

200

500

1000(km)

130E 135E 140E 145E 150E

30N

35N

40N

45N

0

100

200

500

1000(km)

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0.01 0.10 1.00 10.00

Natural Period (s)

Cm

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.01 0.10 1.00 10.00

Natural Period (s)

Ch

1.400

1.600

1.800

2.000

2.200

2.400

0.01 0.10 1.00 10.00

Natural Period (s)

Cd

-3.000

-2.000

-1.000

0.000

1.000

2.000

3.000

0.01 0.10 1.00 10.00

Natural Period (s)

C0

Figure 7: UHS for seven sites in Japan 5. Comparison of spectra

5.1. Comparison of design spectra Design spectrum of “rare earthquake” for building is compared with that of “service limit” for highway bridge. Also compared are the design spectrum “very rare earthquake” for building and that of “ultimate limit” for highway bridge. These comparisons are shown in Figs. 8 and 9. In these figures, UHSs are also drawn.

5.2. Comparison of RPS Figs. 10 and 11 show the comparison of RPS. As in Figs. 8 and 9, “rare earthquake” for building is compared with “service limit” for highway bridge, and “ vary rare earthquake” for building is compared with “ultimate limit” for highway bridge.

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.

Sendai Sapporo Niigata

Nagoya Tokyo

Fukuoka

Osaka

Figure 8: Comparison of design spectra (service limit)

Figure 9: Comparison of design spectra (ultimate limit)

0

100

200

300

400

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.RareS.L.

0

100

200

300

400

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.RareS.L.

0

100

200

300

400

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.RareS.L.

0

100

200

300

400

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.RareS.L.

0

100

200

300

400

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.RareS.L.

0

100

200

300

400

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.RereS.L.

0

100

200

300

400

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

10 yr.20 yr.50 yr.100 yr.200 yr.500 yr.RareS.L.

Sendai Sapporo Niigata

Nagoya Tokyo

Fukuoka

Osaka

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.Very rareU.L.-1U.L.-2

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

100 yr.200 yr.500 yr.1000 yr.2000 yr.5000. yrVery rareU.L.-1U.L.-2

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.Very rareU.L.-1U.L.-2

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.Very rareU.L.-1U.L.-2

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.Very rareU.L.-1U.L.-2

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.Very rareU.L.-1U.L.-2

0

500

1000

1500

2000

0.01 0.1 1 10

Natural Period (s)

Spe

ctra

l Acc

. (cm

/s/s

)

100 yr.200 yr.500 yr.1000 yr.2000 yr.5000 yr.Very rareU.L.-1U.L.-2

Sendai Sapporo Niigata

Nagoya Tokyo

Fukuoka

Osaka

Figure 10: Comparison of RPS (service limit)

Figure 11: Comparison of RPS (ultimate limit)

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

RareS.L.

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

RareS.L.

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

RareS.L.

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

RareS.L.

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

RareS.L.

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

RareS.L.

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

RareS.L.

Sendai Sapporo Niigata

Nagoya Tokyo

Fukuoka

Osaka

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

Very rareU.L.-1U.L.-2

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

Very rareU.L.-1U.L.-2

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

Very rareU.L.-1U.L.-2

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

Very rareU.L.-1U.L.-2

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

Very rareU.L.-1U.L.-2

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

Very rareU.L.-1U.L.-2

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

0.01 0.1 1 10

Natural Period (s)

Ret

urn

Per

iod

(yr.)

Very rare"U.L.-1U.L.-2

Sendai Sapporo Niigata

Nagoya Tokyo

Fukuoka

Osaka

Conclusions

As practical design spectra for building and for civil structures, spectrum given by Japanese building law and that by design recommendation for highway bridge were selected. For these spectra, return period was compared as well as intensity, using the newly introduced return period spectrum. By comparing the spectra, the followings were obtained, • seismic actions given by the design spectra above are close to each other except for the one

corresponding to the ultimate design with in-crust earthquake, and, • deference among the sites are much greater than that between design spectra. Acknowledgements

Special thanks are given to Dr. Inoue, Dr. Ishida, Dr. Ishii, Prof. Emeritus Ishiyama, Prof. Matsumura, Dr. Nakamura, Prof. Soda, Dr. Tamura and Dr. Todo for their comments and suggestions on this paper. References

Architectural Institute of Japan (2004) Recommendations for Loads on Buildings. Annaka, T. and Yashiro, H.: A seismic source model with temporal dependency of large earthquake occurrence

for probabilistic seismic hazard analysis in Japan, Risk Analysis, WIT PRESS, pp.233-242, 1998.