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where the San Andreas and Hayward faults govern the seismic hazard. The seismic hazard ischaracterized two ways: (1) through an explicit probabilistic seismic hazard analysis of the siteand (2) using spectral acceleration hazard maps from building code provisions.Annual Hazard CurvesProbabilistic Seismic Hazard Analysis (PSHA): Using the Abrahamson and Silva attenuationrelationship presented in Eqs. 7 and 8, annual hazard curves for spectral acceleration, S aT ) ,and the proposed intensity measure,SaR Sa0.5( 1, can be developed through a standard probabilisticseismic hazard analysis for the Yerba-Buena Site site. Details of the hazard analysis are beyondthe scope of this paper, but basically, this analysis provides a probabilistic assessment ofearthquake magnitude and distance (M-R) pairs for the site, given its proximity to nearby faults.Code Based Technique: An alternative (simplified) technique to obtain the hazard curve is toinfer it from mapped spectral and site coefficients such as those provided by the seismic designprovisions of the International Building Code (ICC 2000). The first step is to calculate thespectral acceleration for the site using the following equation:F SSv 1a= (18)T1where F v is a tabulated site coefficient, given as a function of the site (soil) class and the spectralcoefficients, and S 1 is the spectral hazard coefficient obtained from seismic hazard maps with aan average probability of occurrence of 2% in 50-years. Implied by Eq. 18 is a 1/T spectralcurve in the long period range. Using Eq. 18, one can directly obtain the 2% in 50 year (P o =0.0004) spectral acceleration at the first mode period T 1 , i.e., S a (T 1 ). One can also approximatethe two-parameter index0.5SaR Sa, by assuming that RS a2 = Sa( T1 ) / Sa(2T1) = 2T1/ T1= . Twoapproximations inherent in this assumption are that there is full correlation between the hazardvalues of S a (T 1 ) and S a (2T 1 ) and the 1/T design spectrum accurately represents the hazardspectrum. Once the 2% in 50 year spectral values are known, the full hazard curve is constructedassuming k = 4, and then back-calculating the k o parameter.Hazard Curve Comparison: Hazard curves for T 1 = 1.5 seconds (the natural period for the sixstoryRCS perimeter frame) are shown in Fig. 8, and the corresponding hazard curve parameters16
1e-1IBC CodeY-B PSHA1e-1IBC CodeY-B PSHAMean Annual Prob. [S a >x]1e-21e-31e-41e-52% in 50 yr(a)Mean Annual Prob. [S a R 0.5 >x]1e-21e-31e-41e-52% in 50 yr(b)1e-60.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Sa T=1.5sec1e-60.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Sa T=1.5sec R 0.5Figure 8 – Site Hazard Curves (a) S a and (b) S a R 0.5 (T 1 = 1.5 seconds)are summarized in Table 2. Also summarized in Table 2 are capacity statisticsµˆλ fandλ fδ forthe frame. Referring to Fig. 8a, the 2% in 50 year value of S a (T 1 ) PSHA = 0.57g from theprobabilistic seismic hazard analysis is about 20% less than the code-value of S a (T 1 ) Code = 0.72g,and there are corresponding differences over the entire hazard curve. Presumably the PSHAresults are more accurate, but further studies would need to be done to confirm this. Referring toFig. 8b, the difference between the PSHA and code approach at the 2% in 50 year level for theS a R sa index is also about 20%,IMSaT ) 0.51R Sa PSHA( = 0.40 versus S ( aT ) 0.51R = 0.51g.Sa CodeTable 2 – Hazard curve coefficients and mean and dispersion of capacityYerba Buena Site Code Based Techniqueµˆλ fk o k k o kS a (T 1 ) 2.3x10 -5 5.0 1.1x10 -4 4 1.45 0.31S a R Sa0.51.6x10 -6 6.0 2.6x10 -5 4 0.76 0.15δλ fProbability of FailureSummarized in Table 2 are all the necessary data to compute the mean annual failureprobabilities for the six-story RCS perimeter frame using the two alternative hazard intensitymeasures, S aT ) and S( 1( ) 0.5aT1 RSa, and two alternative hazard curves (PSHA and building codeapproach). Substituting these data into Eqs. 13 and 14, the resulting collapse probabilities, P f ,are calculated and summarized in Table 3.For the code hazard spectra and the S aT ) index, the mean annual probability of exceeding the( 1stability (collapse) performance is about 0.00005 or roughly a 0.3% chance of exceedance in 5017
Page 1 and 2: DEVELOPMENT OF A TWO-PARAMETER SEIS
Page 3 and 4: development of seismic hazard maps
Page 5 and 6: S a( T f) . Inoue (1990) provides t
Page 7 and 8: 6 @ 4m = 24mW530x92W610x101W610x101
Page 9 and 10: While the two-parameter index reduc
Page 11 and 12: significantly degrade. This point,
Page 13 and 14: already low when scaled by spectral
Page 15: whereIM is the hazard intensity mea
Page 19 and 20: elated to the reduced dispersion ac

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