Probabilistic comparison of seismic design response spectra

Transcription

1 Special Workshop on Risk Acceptance and Risk Communication March 26-27, 27, Stanford University Probabilistic comparison of seismic design response spectra Sei ichiro Fukushima Senior researcher, Electric Power Services, Co., Ltd , Higashi-Ueno, Taito, 11-15, Japan and Tsuyoshi Takada Professor, University of 7-3-1, Hongo, Bunkyo, , 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.

2 A B C : Design Spectrum : UHS D 1-2 A B C RPS D Outline of existing design spectra Figure 1: Evaluation of return period spectrum 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 4m/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) earthquake earthquake T<.16 (.64+6T)Z Five times of spectral acceleration.16<=t< Z for rare earthquake.64<=t (1.24/T)Z 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).

3 Table 2(1): Formula of response spectra for highway bridge (service limit) Period (s) Spectral acceleration (cm/s/s) T<.1 431T 1/3, and greater then or equal to 16.1<=T<= <T 22/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<= <T 98/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< T 2/3.3<=T<=.7 2.7<T 114/T 5/3 T: Natural period (s) Figure 2: Zone factor for building Figure 3: Zone factor for highway bridge

4 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 P ref. Seismic hazard curve for each period Exceedance Prob p ref Period; T A Period; T B Period; T C Period; T D Period; T E S A (T C ) S A (T B ) S A (T D ) S A (T A ) S A (T E ) UHS corresponding to P ref S A (T A ) S A (T B ) S A (T C ) S A (T D ) S A (T E ) Spectral Acceleration (cm/s/s) T A T B T C T D T E 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. 45N 45N 4N 4N 14E 14E 145E (km) 15 2 (km) N 13E 135E 14E 145E 15E (km) 13E 135E (km) 2 1 Figure 5(1): Source zone for large EQs (km)

5 45N 45N 4N 45N 4N 4N 4N 3N 3N 3N 25N 3N 13E 135E 14E 145E 15E (km) 13E 135E 14E 145E 15E (km) 125E 13E 135E 14E (km) 13E 135E 14E 145E 15E (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; log S ( T ) = C ( T ) M + C ( T ) h C ( T )log[ R +.334exp(.653M )] C ( ), (1) A m h c d + where, T is a natural period, M is a magnitude in JMA scale, hc is a center depth of the rupture plane, and R is the closest distance. Coefficients, C m (T ), C h (T ), C d (T ), C ( ) are given as shown in Fig.6. T T Cm Ch Cd C Figure 6: Coefficients for attenuation relation UHS for seven sites in Japan Seven sites;,,,,, and, are selected for illustration. UHS for the sites are shown in Fig. 7. Except for, spectral peaks appear in the natural period of.2s to.3s. On the contrary, spectral peaks at 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 2 year. It must also be noted that there exist very thick sedimentary layer in Kanto district which includes. This layer is the on of factors that gives the ground motion with dominant component in the longer natural period.

6 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr 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 Comparison of RPS Figs. 1 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.

7 yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. Rere yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. Figure 8: Comparison of design spectra (service limit) yr. 2 yr. 5 yr. 1 yr. 2 yr. 5. yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr yr. 2 yr. 5 yr. 1 yr. 2 yr. 5 yr. Figure 9: Comparison of design spectra (ultimate limit)

8 1.E+4 1.E+4 1.E+4 1.E+3 1.E+3 1.E+3 1.E+2 1.E+2 1.E+2 1.E+1 1.E+1 1.E+1 1.E+ 1.E+ 1.E+ 1.E+4 1.E+4 1.E+4 1.E+3 1.E+3 1.E+3 1.E+2 1.E+2 1.E+2 1.E+1 1.E+1 1.E+1 1.E+ 1.E+4 1.E+ 1.E+ 1.E+3 1.E+2 1.E+1 1.E+ 1.E+6 1.E+6 Figure 1: Comparison of RPS (service limit) 1.E+6 1.E+5 1.E+5 1.E+5 1.E+4 1.E+4 1.E+4 1.E+3 1.E+3 1.E+3 1.E+2 1.E+2 1.E+2 1.E+6 1.E+5 1.E+6 1.E+5 1.E+6 1.E+5 1.E+4 1.E+4 1.E+4 1.E+3 1.E+3 1.E+3 1.E+2 1.E+2 1.E+2 1.E+6 1.E+5 1.E+4 1.E+3 " 1.E+2 Figure 11: Comparison of RPS (ultimate limit)

9 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 (24) 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 , 1998.