Report - PEER - University of California, Berkeley

parameter k (the slope of the hazard curve when plotted in a log-log form) which is inessence a Jacobian insuring that the two net dispersions are reflecting uncertainty incommon (i.e., frequency) terms. As shown in Figure 3 the value of capacity randomor aleatory dispersion, β RC , in that example is about 0.37. Representative values forβ UC and β UH might be 0.5 and 0.35 in coastal California, while k there (for S a in themoderate period, here 1.5 seconds, and order 10 -3 hazard range) might be 2.3. For acase in which the best (median) estimate of the median, Cˆ , is 0.45g (as in Figure 3)and the mean estimate of the hazard at this level is 0.0025, the mean estimate of thecollapse limit state frequency is 0.0068 or (1.44)(1.9) = 2.7 times the (mean estimateof the) likelihood that ground motion exceeds the estimated median capacity. Theincrease reflects the indicated product of the effects of aleatory and epistemicuncertainty (respectively) in the capacity (Eq. 5). In this case the mean estimate ofthe hazard curve at 0.45g is only 6% larger than the median estimate due to the lowestimate of the β UH value; this 6% ground motion hazard uncertainty effect on themean limit state estimate will be larger in many locations and at lower hazard levelsof usual safety interest. On the other hand at non-coastal California or analogous highseismicity areas the slope k will typically be lower reducing the impact of the capacityuncertainties. The total epistemic uncertainty in the limit state frequency,2 2 2β λ = βUH+ k β , is about 1.45 and is dominated in this case by the secondLimit StateUCterm, reflecting the factors just cited and the high epistemic uncertainty we now faceas professionals trying to estimate the highly nonlinear, near-collapse regime, whichis governed by factors such as P-delta and post-peak force decay in the hystereticmodels of nonlinear elements.ACKNOWLEDGEMENTSResearch by my students and co-researchers such as P. Bazzurro, N. Shome, J.Carballo, N. Luco, D. Vamavatsikos, F. Jalayer, G.-L. Yeo, J. Baker, P. Tothong,Prof. G. Beroza, Prof. Yasuhiro Mori, and Dr. Iunio Iervolino have contributedimportantly to the results and conclusions reported here. Stanford Blume Centercolleagues and their students have been a constant source of stimulation, insights andresults. Their contributions and those of many researchers every where are notadequately reflected in the references below. These efforts have been supportedgenerously by the US National Science Foundation, through the U.S.-Japan Programand through PEER.REFERENCESDeierlein, G. (2004). Overview of a comprehensive framework for earthquake performanceassessment. Proceedings Inter. Workshop on Performance Based Design, Bled, Slovenia,June.51