Report - PEER - University of California, Berkeley

7. SEISMIC PERFORMANCE RISKBecause the deterministic performance index expresses only performance relative tothe standard earthquake, the level should ideally be expressed in probabilistic form,namely, using the absolute values of probability of exceeding the limit states.However, it is difficult by our present state of knowledge to predict accurately theprobabilistic density of seismic activity and the deviations in site-specific groundcharacteristics. Also still large deviations and errors exist in evaluation of capacityand response. Therefore, in the Guidelines, the probability formula is introducedadditionally with concept of the site earthquake for evaluation. The site earthquakesshall be evaluated based on site-specific parameters including seismic activity, groundamplification, source characteristics, propagation path and so on, also reflecting thefuture research development in engineering seismology.A new method of evaluating the probability of exceeding the limit states isexplained in the level 2 documents, where inelastic displacement responses areformulated by the modified CSM and poly-linear spectrum of the site earthquakes.The seismic hazard model is based on a recent research paper. The hazard maps arebeing developed in national research institutes, although preconditions in thedevelopment should be revised further from future research. The probabilities ofexceedance calculated for an evaluation example are shown in the next section.8. EVALUATION EXAMPLEIn the third level document, Evaluation example, a calculation procedure ofevaluation is shown for an example building. The building is 12-story reinforcedconcrete structure, which is a design example in the past AIJ guidelines[2]. The limitstate deformations, the seismic capacity index, the probability of exceeding the limitstates are calculated for the building numerically in detail. The structure is a regularshaped,open-frame in X-direction and wall-frame in Y-direction. In accordance withthe past guidelines, the building has been designed more carefully than by BSL withdesign factors, so that the ductile overall mechanism is ensured. Deformability ofmembers are ensured up to the deformation angles of 1/50, 1/67 and 1/100 for beam,column and wall, respectively, although the lateral ultimate lateral load-carryingcapacities are made almost equal to the required strength in the BSL, that aredetermined from the structural characteristics coefficients, Ds=0.3 for open frame inX-dir, and Ds=0.4 for wall-frame in Y-dir.The calculated overall and story limit deformations are shown in Table 1. Theseismic capacity indices, the ratios of the capacity earthquakes to the standardearthquake are also shown in the right column of the table. These estimates by thepushover analysis and CSM are almost equal to the responses calculated fromadditional time-history analysis. The seismic performance indices, namely theamplification factors of the earthquakes are around 1.0 for the reparable limit I, 1.5for the reparable limit II, and higher than 2.0 for the safety limit.36