Report - PEER - University of California, Berkeley

5.2 Method B: MDOF Residual Displacement MethodThis method introduces residual displacement U res as an intermediate responseparameter to improve the PSDM relating bridge-level engineering responseparameters and earthquake intensity (IM). Analytical simulations were then used torelate residual displacement of the bridge and its vertical and horizontal load carryingcapacity degradation due to a combination of material and geometric nonlinearities.The resulting DV fragility formulation is shown in Equation 6.[ ] [ | ] [ | ] [ | ] [ |resres ]P DV IM = ∫∫∫ P DV DM dP DM EDP dP EDP U dP U IM (6)Once again, it is assumed that the EDP can be conditioned solely on U res , withoutany additional IM information. While there is lower uncertainty in the EDP|U rescorrelation, this method also suffers from large model error due to the largeuncertainty in the residual displacement demand model. However, it does provide amore realistic prediction of the onset of bridge-level damage. Comparison between allfour methods for a DV limit state of 25% traffic volume loss is shown in Figure 6.5.3 Method C: SDOF Residual Displacement MethodThis method is equivalent to Method B, except the residual displacements areobtained from residual displacement spectra (Kawashima et al., 1998) rather thananalysis of actual bridge models. This method was affected to reduce the uncertaintyin the residual displacement demand model. The single-degree-of-freedom (SDOF)oscillator properties were selected based on the initial elastic period of the bridge andan R-factor obtained from demand model simulations. While the method does resultin slightly reduced uncertainty, the median prediction is largely dependent on theselection of SDOF oscillator properties.5.4 Method D: EDP Conditioning MethodIn an attempt to further reduce the interim uncertainty (model error), maximumdisplacement U max is introduced and correlated with residual displacement U res . Thisis achieved by integrating over maximum displacement and residual displacement inthe third term of Equation 5. The expanded third term is shown in Equation 7.Application of Equation 7 requires the EDP to be conditioned on U res only (no U maxinformation), and U res to be conditioned on U max only (no IM information). This wasverified by showing that dependence of the residuals on U max and IM, respectively, issmall.[ ] [ | ] [ |max ] [ |resresmax ]P EDP IM = ∫∫ P EDP U dP U U dP U IM(7)61