Report - PEER - University of California, Berkeley

as undamaged. Surveyors may make their own subjective decisions that abuilding that has tilted is damaged beyond repair, but the applicationdescribed above is the only one that can be interpreted without uncertainty.• The study by Bird et al. (2004) discussed in Section 2.2 attempted toreproduce observed damage by superimposing ground shaking and groundfailure damage, but without much success.Therefore, the superposition of two separate damage distributions cannot entirelyexplain the Type II damage distributions.Another possible cause relates to structural ductility. In stiff and brittlestructures, there may be little damage up to the point of effective yield. However,even small demands beyond this point may lead to a rapid increase in deflections anddamage, due to loss of stiffness and strength. Such structures might therefore beexpected to show either low damage or very high damage, with little in-between (e.g.Crowley et al. 2004). The non-ductile concrete frames with rigid, brittle and weakmasonry infill found in the Kocaeli region might have had these characteristics,particularly since in many cases open ground floors were present. A model that gavea damage distribution dependent on ductility as well as yield strength and stiffnessmight therefore be of value.Unfortunately, the HAZUS methodology is of no direct help here. Damagedistributions for a given seismic input are based on the expected deflection (thecrossing point of demand and capacity spectra), and no account is taken of how far ornear that point is from brittle collapse. The distribution of deflections around thatexpected point is assumed to be log-normally distributed, based on the central limittheorem and the assumption that both demand (ground motion intensity) and capacity(structural characteristics) are also normally or log-normally distributed. This latterassumption may be reasonable, but in a highly non-linear brittle system, with a ‘cliffedge’in response around fracture, the assumption that response is also lognormallydistributed is unlikely to apply. To investigate this further, this study developed themodel described in the next section.4. MONTE-CARLO BASED SIMULATIONS FOR THIS STUDYIn order to investigate further the possibility that the ‘Type II’ damage distributionsdiscussed above were due to a brittle structural response, the HAZUS approach wasmodified as follows. The capacity spectrum method was still used for determiningexpected deflection, but the damage distribution was generated from a series of‘Monte Carlo’ type simulations, assuming that both the demand (ground) and capacityspectra were lognormally distributed. Figure 6 shows the idealized capacityspectrum, and Figure 7 shows the ground spectrum, which was a smoothed andsimplified version of the SKR stiff soil recording from Kocaeli; Figure 7 also showsspectra recorded at the recording sites shown in Figure 3.403