Report - PEER - University of California, Berkeley

quantification tools could be used to assess whether the seismic resilience is enhancedor not, i.e., whether a set of interventions reduce the loss in patient-day capacity, or ifa local overflow can be absorbed globally, and how long will take to restore capacity.4. RESILIENCE OF STRUCTURAL AND NON-STRUCTURALCOMPONENTSA first step toward the aboveobjectives is the definitionand quantification ofengineering resilience. Thisis illustrated here byfocusing on the resilience ofstructural and non-structuralcomponents.In light of theconsiderable uncertaintiesinherent to the field ofearthquake engineering(both in the demandsStructural System ConsiderationsIntegrity132t oCollapse1Serviceability – “clean aesthetic”2Threshold of collapse3Damage statesFragility functionsfor initial limitstate,condition attime t i , and time torecovery alsorandom variablesFigure 4. Probabilistic aspect of seismicresilience, (structural integrity example).estimated throughengineering seismology, andin the capacities that ensue from the non-linear inelastic seismic performance of thestructure), the quantification of seismic resilience proceeds through a probabilisticframe-work, as illustrated in Figure 4. A serviceability level is defined as a small lossin structural integrity. A collapse level is defined as the maximum loss of integrityprior to collapse; other resilience curves are shown to represent various structuralintegrity conditions between the serviceability and collapse levels, and the fact that aproportional coupling often (but not always) exists between the time to recovery andthe initial loss of structural integrity. It is also illustrated that over time, structuralintegrity could return to the initial pre-earthquake condition, to less than thiscondition (e.g., cracking in some structural element may never be repaired), or abovethis condition if the structure is repaired to a superior seismic performance level. Thebell-curves show that these integrity levels are random variable.One way to achieve quantification of engineering seismic resilience is throughthe concept of Multidimensional Bell-curve of Response. Therefore, for the purposeof this discussion, the probability distribution surface schematically shown in Figure 5is used. Viewed from above, the surface can be expressed by isoprobability contours.Spherical contours are used here for expediency. Floor pseudo-accelerations (PSAfloor) and interstory drifts (S d floor) express the Limit Space (LS), with specificstructural and non-structural limit states shown by dotted lines; for the former, aserviceability limit state (cracking of concrete structural elements) and a collapselimit state are indicated. Deterministic limit states are used here, but need not be.t165