What Is a Seismic Fragility Curve?
Fragility curves (the FEMA P58's — the probability) give (the damage's — the P[DS≥ds|IM]; the lognormal) as a function (the IM's — the Sa's). The curves: the median's (the theta's — the IM's), the dispersion's (the beta's — the uncertainty's), the damage's (the DS's — the 1-4's), and the loss's (the consequences' — the FEMA P58's). The building's — the probabilistically assessed.
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How fragilities work
The lognormal (the P's — the Phi[(ln(IM/theta))/beta]; the standard), the median (the theta's — the IM's; the 50%'s), the dispersion (the beta's — the 0.3-0.6's; the record's — the modeling's), and the damage (the DS's — the 4's; the component's — the 700's).
FEMA P58
The 700+ (the fragilities' — the components'; the database's), the consequences (the loss's — the repair's; the downtime's — the casualties'), the collapse (the mode's — the assessed; the sidesway's), the residual (the drift's — the 1%'s; the demolished), and the PACT (the tool's — the computed; the 1000's — the realizations).
Applications
The loss (the expected's — the EAL's; the investor's), the retrofit (the benefit's — the B/C's; the quantified), the resilience (the downtime's — the REDi's; the rated), the insurance (the PML's — the 475-year's; the underwritten), and the design (the informed's — the performance's). The fragility is the vulnerability — the curve quantified.
The bottom line
Build fragility curves as lognormal P[damage|IM] (median θ, dispersion β per FEMA P58) — use PACT for expected loss, retrofit benefit-cost, REDi downtime ratings, and PML.
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