Report - PEER - University of California, Berkeley

The variability is associated with such factors as the random character of the primarystructural and associated nonstructural response to individual ground motion recordsand the inability of simple engineering demand parameters to distinguish between thisresponse variation and the damage it causes. For example, two different groundmotions may each produce peak interstory drift demands of 4 inches in a structure,however, one of these ground motions may cycle the structure to this drift level onetime then restore the structure to small oscillations about its original position whilethe second ground motion may cycle the structure to this drift level several times andleave the structure displaced nearly to this level. Clearly the latter motion will bemore damaging of the structure than the first motion, though the value of theengineering demand parameter is the same. Such effects are not predictable unlessthe precise ground motion and structural response is known. Uncertainty isintroduced through such factors as lack of precise definition of material strength andconstruction quality.In order to form fragility functions it is first necessary to establish measures ofdamage. A variety of such measures are possible. Damage states that may bemeaningful for nonstructural components and systems could include “no damage,”“leakage,” “loss of function,” “loss of structural integrity” and “toppling”. In general,each category of nonstructural component or system will have different fragilityfunctions perhaps tied to several different EDP-Ns.While initially the fragility functions for the broad categories will be establishedby expert opinion, over time they can be determined more rigorously determinedthrough collection of earthquake performance data on damage sustained by actualinstallations, through laboratory testing programs and in some cases, throughstructural analysis, just as would be done for the building structure itself. For criticalequipment which must function, the fragility data may come from seismicqualification testing.In some cases the fragility level may be associated with some mean design level.For example, under systems which have high repair cost, we may have a subcategoryof components that are sensitive to peak floor accelerations. A component that isdesigned for twice the force might have a fragility that is twice as high.Also as part of this task loss functions would be developed corresponding to eachof the fragility functions. Loss functions indicate the probability of incurring variouslevels of loss, given that a structure or nonstructural component or system is damagedto a given level, expressed in such parameters as repair cost (dollars), lives lost(deaths) and hours of lost service or occupancy (downtime). These curves show theprobability, that loss will be less than or equal to an indicated amount, given that thebuilding is damaged to a given level. Loss functions can be constructed for a givenbuilding or class of buildings, by postulating damage to the structure (or nonstructuralcomponent/system) that is representative of a damage level for which there is anavailable fragility function, and estimating the losses associated with this damage. Byvarying the assumptions, or exploring the level of uncertainty associated with these133